diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-128')
111 files changed, 6013 insertions, 4972 deletions
diff --git a/sysdeps/ieee754/ldbl-128/Makeconfig b/sysdeps/ieee754/ldbl-128/Makeconfig new file mode 100644 index 0000000000..ca17c1b12a --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/Makeconfig @@ -0,0 +1,4 @@ +# Include this earlier so it can be used earlier in Makefiles, +# and sysdep/ makefiles. +float128-alias-fcts = yes +float64x-alias-fcts = yes diff --git a/sysdeps/ieee754/ldbl-128/bits/floatn.h b/sysdeps/ieee754/ldbl-128/bits/floatn.h new file mode 100644 index 0000000000..1d21ccee24 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/bits/floatn.h @@ -0,0 +1,97 @@ +/* Macros to control TS 18661-3 glibc features on ldbl-128 platforms. + Copyright (C) 2017-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _BITS_FLOATN_H +#define _BITS_FLOATN_H + +#include <features.h> +#include <bits/long-double.h> + +/* Defined to 1 if the current compiler invocation provides a + floating-point type with the IEEE 754 binary128 format, and this + glibc includes corresponding *f128 interfaces for it. */ +#ifndef __NO_LONG_DOUBLE_MATH +# define __HAVE_FLOAT128 1 +#else +/* glibc does not support _Float128 for platforms where long double is + normally binary128 when building with long double as binary64. + GCC's default for supported scalar modes does not support it either + in that case. */ +# define __HAVE_FLOAT128 0 +#endif + +/* Defined to 1 if __HAVE_FLOAT128 is 1 and the type is ABI-distinct + from the default float, double and long double types in this glibc. */ +#define __HAVE_DISTINCT_FLOAT128 0 + +/* Defined to 1 if the current compiler invocation provides a + floating-point type with the right format for _Float64x, and this + glibc includes corresponding *f64x interfaces for it. */ +#define __HAVE_FLOAT64X __HAVE_FLOAT128 + +/* Defined to 1 if __HAVE_FLOAT64X is 1 and _Float64x has the format + of long double. Otherwise, if __HAVE_FLOAT64X is 1, _Float64x has + the format of _Float128, which must be different from that of long + double. */ +#define __HAVE_FLOAT64X_LONG_DOUBLE __HAVE_FLOAT128 + +#ifndef __ASSEMBLER__ + +/* Defined to concatenate the literal suffix to be used with _Float128 + types, if __HAVE_FLOAT128 is 1. */ +# if __HAVE_FLOAT128 +# if !__GNUC_PREREQ (7, 0) || defined __cplusplus +/* The literal suffix f128 exists only since GCC 7.0. */ +# define __f128(x) x##l +# else +# define __f128(x) x##f128 +# endif +# endif + +/* Defined to a complex binary128 type if __HAVE_FLOAT128 is 1. */ +# if __HAVE_FLOAT128 +# if !__GNUC_PREREQ (7, 0) || defined __cplusplus +# define __CFLOAT128 _Complex long double +# else +# define __CFLOAT128 _Complex _Float128 +# endif +# endif + +/* The remaining of this file provides support for older compilers. */ +# if __HAVE_FLOAT128 + +/* The type _Float128 exists only since GCC 7.0. */ +# if !__GNUC_PREREQ (7, 0) || defined __cplusplus +typedef long double _Float128; +# endif + +/* Various built-in functions do not exist before GCC 7.0. */ +# if !__GNUC_PREREQ (7, 0) +# define __builtin_huge_valf128() (__builtin_huge_vall ()) +# define __builtin_inff128() (__builtin_infl ()) +# define __builtin_nanf128(x) (__builtin_nanl (x)) +# define __builtin_nansf128(x) (__builtin_nansl (x)) +# endif + +# endif + +#endif /* !__ASSEMBLER__. */ + +#include <bits/floatn-common.h> + +#endif /* _BITS_FLOATN_H */ diff --git a/sysdeps/ieee754/ldbl-128/bits/long-double.h b/sysdeps/ieee754/ldbl-128/bits/long-double.h new file mode 100644 index 0000000000..3d6e1139f8 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/bits/long-double.h @@ -0,0 +1,20 @@ +/* Properties of long double type. ldbl-128 version. + Copyright (C) 2016-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* long double is distinct from double, so there is nothing to + define here. */ diff --git a/sysdeps/ieee754/ldbl-128/e_acoshl.c b/sysdeps/ieee754/ldbl-128/e_acoshl.c index 6234289e1e..c292759ac6 100644 --- a/sysdeps/ieee754/ldbl-128/e_acoshl.c +++ b/sysdeps/ieee754/ldbl-128/e_acoshl.c @@ -30,15 +30,15 @@ #include <math.h> #include <math_private.h> -static const long double +static const _Float128 one = 1.0, -ln2 = 0.6931471805599453094172321214581766L; +ln2 = L(0.6931471805599453094172321214581766); -long double -__ieee754_acoshl(long double x) +_Float128 +__ieee754_acoshl(_Float128 x) { - long double t; - u_int64_t lx; + _Float128 t; + uint64_t lx; int64_t hx; GET_LDOUBLE_WORDS64(hx,lx,x); if(hx<0x3fff000000000000LL) { /* x < 1 */ @@ -49,13 +49,13 @@ __ieee754_acoshl(long double x) } else return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */ } else if(((hx-0x3fff000000000000LL)|lx)==0) { - return 0.0L; /* acosh(1) = 0 */ + return 0; /* acosh(1) = 0 */ } else if (hx > 0x4000000000000000LL) { /* 2**28 > x > 2 */ t=x*x; - return __ieee754_logl(2.0L*x-one/(x+__ieee754_sqrtl(t-one))); + return __ieee754_logl(2*x-one/(x+sqrtl(t-one))); } else { /* 1<x<2 */ t = x-one; - return __log1pl(t+__sqrtl(2.0L*t+t*t)); + return __log1pl(t+sqrtl(2*t+t*t)); } } strong_alias (__ieee754_acoshl, __acoshl_finite) diff --git a/sysdeps/ieee754/ldbl-128/e_acosl.c b/sysdeps/ieee754/ldbl-128/e_acosl.c index 8c8ec93339..0dc23dee2b 100644 --- a/sysdeps/ieee754/ldbl-128/e_acosl.c +++ b/sysdeps/ieee754/ldbl-128/e_acosl.c @@ -51,107 +51,107 @@ * if x is NaN, return x itself; * if |x|>1, return NaN with invalid signal. * - * Functions needed: __ieee754_sqrtl. + * Functions needed: sqrtl. */ #include <math.h> #include <math_private.h> -static const long double - one = 1.0L, - pio2_hi = 1.5707963267948966192313216916397514420986L, - pio2_lo = 4.3359050650618905123985220130216759843812E-35L, +static const _Float128 + one = 1, + pio2_hi = L(1.5707963267948966192313216916397514420986), + pio2_lo = L(4.3359050650618905123985220130216759843812E-35), /* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) -0.0625 <= x <= 0.0625 peak relative error 3.3e-35 */ - rS0 = 5.619049346208901520945464704848780243887E0L, - rS1 = -4.460504162777731472539175700169871920352E1L, - rS2 = 1.317669505315409261479577040530751477488E2L, - rS3 = -1.626532582423661989632442410808596009227E2L, - rS4 = 3.144806644195158614904369445440583873264E1L, - rS5 = 9.806674443470740708765165604769099559553E1L, - rS6 = -5.708468492052010816555762842394927806920E1L, - rS7 = -1.396540499232262112248553357962639431922E1L, - rS8 = 1.126243289311910363001762058295832610344E1L, - rS9 = 4.956179821329901954211277873774472383512E-1L, - rS10 = -3.313227657082367169241333738391762525780E-1L, + rS0 = L(5.619049346208901520945464704848780243887E0), + rS1 = L(-4.460504162777731472539175700169871920352E1), + rS2 = L(1.317669505315409261479577040530751477488E2), + rS3 = L(-1.626532582423661989632442410808596009227E2), + rS4 = L(3.144806644195158614904369445440583873264E1), + rS5 = L(9.806674443470740708765165604769099559553E1), + rS6 = L(-5.708468492052010816555762842394927806920E1), + rS7 = L(-1.396540499232262112248553357962639431922E1), + rS8 = L(1.126243289311910363001762058295832610344E1), + rS9 = L(4.956179821329901954211277873774472383512E-1), + rS10 = L(-3.313227657082367169241333738391762525780E-1), - sS0 = -4.645814742084009935700221277307007679325E0L, - sS1 = 3.879074822457694323970438316317961918430E1L, - sS2 = -1.221986588013474694623973554726201001066E2L, - sS3 = 1.658821150347718105012079876756201905822E2L, - sS4 = -4.804379630977558197953176474426239748977E1L, - sS5 = -1.004296417397316948114344573811562952793E2L, - sS6 = 7.530281592861320234941101403870010111138E1L, - sS7 = 1.270735595411673647119592092304357226607E1L, - sS8 = -1.815144839646376500705105967064792930282E1L, - sS9 = -7.821597334910963922204235247786840828217E-2L, + sS0 = L(-4.645814742084009935700221277307007679325E0), + sS1 = L(3.879074822457694323970438316317961918430E1), + sS2 = L(-1.221986588013474694623973554726201001066E2), + sS3 = L(1.658821150347718105012079876756201905822E2), + sS4 = L(-4.804379630977558197953176474426239748977E1), + sS5 = L(-1.004296417397316948114344573811562952793E2), + sS6 = L(7.530281592861320234941101403870010111138E1), + sS7 = L(1.270735595411673647119592092304357226607E1), + sS8 = L(-1.815144839646376500705105967064792930282E1), + sS9 = L(-7.821597334910963922204235247786840828217E-2), /* 1.000000000000000000000000000000000000000E0 */ - acosr5625 = 9.7338991014954640492751132535550279812151E-1L, - pimacosr5625 = 2.1682027434402468335351320579240000860757E0L, + acosr5625 = L(9.7338991014954640492751132535550279812151E-1), + pimacosr5625 = L(2.1682027434402468335351320579240000860757E0), /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x) -0.0625 <= x <= 0.0625 peak relative error 2.1e-35 */ - P0 = 2.177690192235413635229046633751390484892E0L, - P1 = -2.848698225706605746657192566166142909573E1L, - P2 = 1.040076477655245590871244795403659880304E2L, - P3 = -1.400087608918906358323551402881238180553E2L, - P4 = 2.221047917671449176051896400503615543757E1L, - P5 = 9.643714856395587663736110523917499638702E1L, - P6 = -5.158406639829833829027457284942389079196E1L, - P7 = -1.578651828337585944715290382181219741813E1L, - P8 = 1.093632715903802870546857764647931045906E1L, - P9 = 5.448925479898460003048760932274085300103E-1L, - P10 = -3.315886001095605268470690485170092986337E-1L, - Q0 = -1.958219113487162405143608843774587557016E0L, - Q1 = 2.614577866876185080678907676023269360520E1L, - Q2 = -9.990858606464150981009763389881793660938E1L, - Q3 = 1.443958741356995763628660823395334281596E2L, - Q4 = -3.206441012484232867657763518369723873129E1L, - Q5 = -1.048560885341833443564920145642588991492E2L, - Q6 = 6.745883931909770880159915641984874746358E1L, - Q7 = 1.806809656342804436118449982647641392951E1L, - Q8 = -1.770150690652438294290020775359580915464E1L, - Q9 = -5.659156469628629327045433069052560211164E-1L, + P0 = L(2.177690192235413635229046633751390484892E0), + P1 = L(-2.848698225706605746657192566166142909573E1), + P2 = L(1.040076477655245590871244795403659880304E2), + P3 = L(-1.400087608918906358323551402881238180553E2), + P4 = L(2.221047917671449176051896400503615543757E1), + P5 = L(9.643714856395587663736110523917499638702E1), + P6 = L(-5.158406639829833829027457284942389079196E1), + P7 = L(-1.578651828337585944715290382181219741813E1), + P8 = L(1.093632715903802870546857764647931045906E1), + P9 = L(5.448925479898460003048760932274085300103E-1), + P10 = L(-3.315886001095605268470690485170092986337E-1), + Q0 = L(-1.958219113487162405143608843774587557016E0), + Q1 = L(2.614577866876185080678907676023269360520E1), + Q2 = L(-9.990858606464150981009763389881793660938E1), + Q3 = L(1.443958741356995763628660823395334281596E2), + Q4 = L(-3.206441012484232867657763518369723873129E1), + Q5 = L(-1.048560885341833443564920145642588991492E2), + Q6 = L(6.745883931909770880159915641984874746358E1), + Q7 = L(1.806809656342804436118449982647641392951E1), + Q8 = L(-1.770150690652438294290020775359580915464E1), + Q9 = L(-5.659156469628629327045433069052560211164E-1), /* 1.000000000000000000000000000000000000000E0 */ - acosr4375 = 1.1179797320499710475919903296900511518755E0L, - pimacosr4375 = 2.0236129215398221908706530535894517323217E0L, + acosr4375 = L(1.1179797320499710475919903296900511518755E0), + pimacosr4375 = L(2.0236129215398221908706530535894517323217E0), /* asin(x) = x + x^3 pS(x^2) / qS(x^2) 0 <= x <= 0.5 peak relative error 1.9e-35 */ - pS0 = -8.358099012470680544198472400254596543711E2L, - pS1 = 3.674973957689619490312782828051860366493E3L, - pS2 = -6.730729094812979665807581609853656623219E3L, - pS3 = 6.643843795209060298375552684423454077633E3L, - pS4 = -3.817341990928606692235481812252049415993E3L, - pS5 = 1.284635388402653715636722822195716476156E3L, - pS6 = -2.410736125231549204856567737329112037867E2L, - pS7 = 2.219191969382402856557594215833622156220E1L, - pS8 = -7.249056260830627156600112195061001036533E-1L, - pS9 = 1.055923570937755300061509030361395604448E-3L, + pS0 = L(-8.358099012470680544198472400254596543711E2), + pS1 = L(3.674973957689619490312782828051860366493E3), + pS2 = L(-6.730729094812979665807581609853656623219E3), + pS3 = L(6.643843795209060298375552684423454077633E3), + pS4 = L(-3.817341990928606692235481812252049415993E3), + pS5 = L(1.284635388402653715636722822195716476156E3), + pS6 = L(-2.410736125231549204856567737329112037867E2), + pS7 = L(2.219191969382402856557594215833622156220E1), + pS8 = L(-7.249056260830627156600112195061001036533E-1), + pS9 = L(1.055923570937755300061509030361395604448E-3), - qS0 = -5.014859407482408326519083440151745519205E3L, - qS1 = 2.430653047950480068881028451580393430537E4L, - qS2 = -4.997904737193653607449250593976069726962E4L, - qS3 = 5.675712336110456923807959930107347511086E4L, - qS4 = -3.881523118339661268482937768522572588022E4L, - qS5 = 1.634202194895541569749717032234510811216E4L, - qS6 = -4.151452662440709301601820849901296953752E3L, - qS7 = 5.956050864057192019085175976175695342168E2L, - qS8 = -4.175375777334867025769346564600396877176E1L; + qS0 = L(-5.014859407482408326519083440151745519205E3), + qS1 = L(2.430653047950480068881028451580393430537E4), + qS2 = L(-4.997904737193653607449250593976069726962E4), + qS3 = L(5.675712336110456923807959930107347511086E4), + qS4 = L(-3.881523118339661268482937768522572588022E4), + qS5 = L(1.634202194895541569749717032234510811216E4), + qS6 = L(-4.151452662440709301601820849901296953752E3), + qS7 = L(5.956050864057192019085175976175695342168E2), + qS8 = L(-4.175375777334867025769346564600396877176E1); /* 1.000000000000000000000000000000000000000E0 */ -long double -__ieee754_acosl (long double x) +_Float128 +__ieee754_acosl (_Float128 x) { - long double z, r, w, p, q, s, t, f2; + _Float128 z, r, w, p, q, s, t, f2; int32_t ix, sign; ieee854_long_double_shape_type u; @@ -204,7 +204,7 @@ __ieee754_acosl (long double x) return z; } /* .4375 <= |x| < .5 */ - t = u.value - 0.4375L; + t = u.value - L(0.4375); p = ((((((((((P10 * t + P9) * t + P8) * t @@ -237,7 +237,7 @@ __ieee754_acosl (long double x) } else if (ix < 0x3ffe4000) /* |x| < 0.625 */ { - t = u.value - 0.5625L; + t = u.value - L(0.5625); p = ((((((((((rS10 * t + rS9) * t + rS8) * t @@ -270,7 +270,7 @@ __ieee754_acosl (long double x) else { /* |x| >= .625 */ z = (one - u.value) * 0.5; - s = __ieee754_sqrtl (z); + s = sqrtl (z); /* Compute an extended precision square root from the Newton iteration s -> 0.5 * (s + z / s). The change w from s to the improved value is diff --git a/sysdeps/ieee754/ldbl-128/e_asinl.c b/sysdeps/ieee754/ldbl-128/e_asinl.c index 5a0e473ef0..4835962db4 100644 --- a/sysdeps/ieee754/ldbl-128/e_asinl.c +++ b/sysdeps/ieee754/ldbl-128/e_asinl.c @@ -61,78 +61,79 @@ #include <float.h> #include <math.h> +#include <math-barriers.h> #include <math_private.h> -long double sqrtl (long double); +#include <math-underflow.h> -static const long double - one = 1.0L, - huge = 1.0e+4932L, - pio2_hi = 1.5707963267948966192313216916397514420986L, - pio2_lo = 4.3359050650618905123985220130216759843812E-35L, - pio4_hi = 7.8539816339744830961566084581987569936977E-1L, +static const _Float128 + one = 1, + huge = L(1.0e+4932), + pio2_hi = L(1.5707963267948966192313216916397514420986), + pio2_lo = L(4.3359050650618905123985220130216759843812E-35), + pio4_hi = L(7.8539816339744830961566084581987569936977E-1), /* coefficient for R(x^2) */ /* asin(x) = x + x^3 pS(x^2) / qS(x^2) 0 <= x <= 0.5 peak relative error 1.9e-35 */ - pS0 = -8.358099012470680544198472400254596543711E2L, - pS1 = 3.674973957689619490312782828051860366493E3L, - pS2 = -6.730729094812979665807581609853656623219E3L, - pS3 = 6.643843795209060298375552684423454077633E3L, - pS4 = -3.817341990928606692235481812252049415993E3L, - pS5 = 1.284635388402653715636722822195716476156E3L, - pS6 = -2.410736125231549204856567737329112037867E2L, - pS7 = 2.219191969382402856557594215833622156220E1L, - pS8 = -7.249056260830627156600112195061001036533E-1L, - pS9 = 1.055923570937755300061509030361395604448E-3L, + pS0 = L(-8.358099012470680544198472400254596543711E2), + pS1 = L(3.674973957689619490312782828051860366493E3), + pS2 = L(-6.730729094812979665807581609853656623219E3), + pS3 = L(6.643843795209060298375552684423454077633E3), + pS4 = L(-3.817341990928606692235481812252049415993E3), + pS5 = L(1.284635388402653715636722822195716476156E3), + pS6 = L(-2.410736125231549204856567737329112037867E2), + pS7 = L(2.219191969382402856557594215833622156220E1), + pS8 = L(-7.249056260830627156600112195061001036533E-1), + pS9 = L(1.055923570937755300061509030361395604448E-3), - qS0 = -5.014859407482408326519083440151745519205E3L, - qS1 = 2.430653047950480068881028451580393430537E4L, - qS2 = -4.997904737193653607449250593976069726962E4L, - qS3 = 5.675712336110456923807959930107347511086E4L, - qS4 = -3.881523118339661268482937768522572588022E4L, - qS5 = 1.634202194895541569749717032234510811216E4L, - qS6 = -4.151452662440709301601820849901296953752E3L, - qS7 = 5.956050864057192019085175976175695342168E2L, - qS8 = -4.175375777334867025769346564600396877176E1L, + qS0 = L(-5.014859407482408326519083440151745519205E3), + qS1 = L(2.430653047950480068881028451580393430537E4), + qS2 = L(-4.997904737193653607449250593976069726962E4), + qS3 = L(5.675712336110456923807959930107347511086E4), + qS4 = L(-3.881523118339661268482937768522572588022E4), + qS5 = L(1.634202194895541569749717032234510811216E4), + qS6 = L(-4.151452662440709301601820849901296953752E3), + qS7 = L(5.956050864057192019085175976175695342168E2), + qS8 = L(-4.175375777334867025769346564600396877176E1), /* 1.000000000000000000000000000000000000000E0 */ /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x) -0.0625 <= x <= 0.0625 peak relative error 3.3e-35 */ - rS0 = -5.619049346208901520945464704848780243887E0L, - rS1 = 4.460504162777731472539175700169871920352E1L, - rS2 = -1.317669505315409261479577040530751477488E2L, - rS3 = 1.626532582423661989632442410808596009227E2L, - rS4 = -3.144806644195158614904369445440583873264E1L, - rS5 = -9.806674443470740708765165604769099559553E1L, - rS6 = 5.708468492052010816555762842394927806920E1L, - rS7 = 1.396540499232262112248553357962639431922E1L, - rS8 = -1.126243289311910363001762058295832610344E1L, - rS9 = -4.956179821329901954211277873774472383512E-1L, - rS10 = 3.313227657082367169241333738391762525780E-1L, + rS0 = L(-5.619049346208901520945464704848780243887E0), + rS1 = L(4.460504162777731472539175700169871920352E1), + rS2 = L(-1.317669505315409261479577040530751477488E2), + rS3 = L(1.626532582423661989632442410808596009227E2), + rS4 = L(-3.144806644195158614904369445440583873264E1), + rS5 = L(-9.806674443470740708765165604769099559553E1), + rS6 = L(5.708468492052010816555762842394927806920E1), + rS7 = L(1.396540499232262112248553357962639431922E1), + rS8 = L(-1.126243289311910363001762058295832610344E1), + rS9 = L(-4.956179821329901954211277873774472383512E-1), + rS10 = L(3.313227657082367169241333738391762525780E-1), - sS0 = -4.645814742084009935700221277307007679325E0L, - sS1 = 3.879074822457694323970438316317961918430E1L, - sS2 = -1.221986588013474694623973554726201001066E2L, - sS3 = 1.658821150347718105012079876756201905822E2L, - sS4 = -4.804379630977558197953176474426239748977E1L, - sS5 = -1.004296417397316948114344573811562952793E2L, - sS6 = 7.530281592861320234941101403870010111138E1L, - sS7 = 1.270735595411673647119592092304357226607E1L, - sS8 = -1.815144839646376500705105967064792930282E1L, - sS9 = -7.821597334910963922204235247786840828217E-2L, + sS0 = L(-4.645814742084009935700221277307007679325E0), + sS1 = L(3.879074822457694323970438316317961918430E1), + sS2 = L(-1.221986588013474694623973554726201001066E2), + sS3 = L(1.658821150347718105012079876756201905822E2), + sS4 = L(-4.804379630977558197953176474426239748977E1), + sS5 = L(-1.004296417397316948114344573811562952793E2), + sS6 = L(7.530281592861320234941101403870010111138E1), + sS7 = L(1.270735595411673647119592092304357226607E1), + sS8 = L(-1.815144839646376500705105967064792930282E1), + sS9 = L(-7.821597334910963922204235247786840828217E-2), /* 1.000000000000000000000000000000000000000E0 */ - asinr5625 = 5.9740641664535021430381036628424864397707E-1L; + asinr5625 = L(5.9740641664535021430381036628424864397707E-1); -long double -__ieee754_asinl (long double x) +_Float128 +__ieee754_asinl (_Float128 x) { - long double t, w, p, q, c, r, s; + _Float128 t, w, p, q, c, r, s; int32_t ix, sign, flag; ieee854_long_double_shape_type u; @@ -154,7 +155,7 @@ __ieee754_asinl (long double x) if (ix < 0x3fc60000) /* |x| < 2**-57 */ { math_check_force_underflow (x); - long double force_inexact = huge + x; + _Float128 force_inexact = huge + x; math_force_eval (force_inexact); return x; /* return x with inexact if x!=0 */ } @@ -232,7 +233,7 @@ __ieee754_asinl (long double x) return x + x * w; } - s = __ieee754_sqrtl (t); + s = sqrtl (t); if (ix >= 0x3ffef333) /* |x| > 0.975 */ { w = p / q; diff --git a/sysdeps/ieee754/ldbl-128/e_atan2l.c b/sysdeps/ieee754/ldbl-128/e_atan2l.c index d31ee70dbd..8b4afa4bd5 100644 --- a/sysdeps/ieee754/ldbl-128/e_atan2l.c +++ b/sysdeps/ieee754/ldbl-128/e_atan2l.c @@ -43,20 +43,20 @@ #include <math.h> #include <math_private.h> -static const long double -tiny = 1.0e-4900L, +static const _Float128 +tiny = L(1.0e-4900), zero = 0.0, -pi_o_4 = 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */ -pi_o_2 = 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */ -pi = 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */ -pi_lo = 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */ +pi_o_4 = L(7.85398163397448309615660845819875699e-01), /* 3ffe921fb54442d18469898cc51701b8 */ +pi_o_2 = L(1.57079632679489661923132169163975140e+00), /* 3fff921fb54442d18469898cc51701b8 */ +pi = L(3.14159265358979323846264338327950280e+00), /* 4000921fb54442d18469898cc51701b8 */ +pi_lo = L(8.67181013012378102479704402604335225e-35); /* 3f8dcd129024e088a67cc74020bbea64 */ -long double -__ieee754_atan2l(long double y, long double x) +_Float128 +__ieee754_atan2l(_Float128 y, _Float128 x) { - long double z; + _Float128 z; int64_t k,m,hx,hy,ix,iy; - u_int64_t lx,ly; + uint64_t lx,ly; GET_LDOUBLE_WORDS64(hx,lx,x); ix = hx&0x7fffffffffffffffLL; @@ -86,8 +86,8 @@ __ieee754_atan2l(long double y, long double x) switch(m) { case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ - case 2: return 3.0L*pi_o_4+tiny;/*atan(+INF,-INF)*/ - case 3: return -3.0L*pi_o_4-tiny;/*atan(-INF,-INF)*/ + case 2: return 3*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3*pi_o_4-tiny;/*atan(-INF,-INF)*/ } } else { switch(m) { @@ -103,13 +103,13 @@ __ieee754_atan2l(long double y, long double x) /* compute y/x */ k = (iy-ix)>>48; - if(k > 120) z=pi_o_2+0.5L*pi_lo; /* |y/x| > 2**120 */ - else if(hx<0&&k<-120) z=0.0L; /* |y|/x < -2**120 */ + if(k > 120) z=pi_o_2+L(0.5)*pi_lo; /* |y/x| > 2**120 */ + else if(hx<0&&k<-120) z=0; /* |y|/x < -2**120 */ else z=__atanl(fabsl(y/x)); /* safe to do y/x */ switch (m) { case 0: return z ; /* atan(+,+) */ case 1: { - u_int64_t zh; + uint64_t zh; GET_LDOUBLE_MSW64(zh,z); SET_LDOUBLE_MSW64(z,zh ^ 0x8000000000000000ULL); } diff --git a/sysdeps/ieee754/ldbl-128/e_atanhl.c b/sysdeps/ieee754/ldbl-128/e_atanhl.c index 7fa53ef436..13b7683e17 100644 --- a/sysdeps/ieee754/ldbl-128/e_atanhl.c +++ b/sysdeps/ieee754/ldbl-128/e_atanhl.c @@ -35,16 +35,17 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> -static const long double one = 1.0L, huge = 1e4900L; +static const _Float128 one = 1, huge = L(1e4900); -static const long double zero = 0.0L; +static const _Float128 zero = 0; -long double -__ieee754_atanhl(long double x) +_Float128 +__ieee754_atanhl(_Float128 x) { - long double t; - u_int32_t jx, ix; + _Float128 t; + uint32_t jx, ix; ieee854_long_double_shape_type u; u.value = x; diff --git a/sysdeps/ieee754/ldbl-128/e_coshl.c b/sysdeps/ieee754/ldbl-128/e_coshl.c index 488c318d27..70a2fe3e84 100644 --- a/sysdeps/ieee754/ldbl-128/e_coshl.c +++ b/sysdeps/ieee754/ldbl-128/e_coshl.c @@ -54,13 +54,13 @@ #include <math.h> #include <math_private.h> -static const long double one = 1.0, half = 0.5, huge = 1.0e4900L, -ovf_thresh = 1.1357216553474703894801348310092223067821E4L; +static const _Float128 one = 1.0, half = 0.5, huge = L(1.0e4900), +ovf_thresh = L(1.1357216553474703894801348310092223067821E4); -long double -__ieee754_coshl (long double x) +_Float128 +__ieee754_coshl (_Float128 x) { - long double t, w; + _Float128 t, w; int32_t ex; ieee854_long_double_shape_type u; diff --git a/sysdeps/ieee754/ldbl-128/e_exp10l.c b/sysdeps/ieee754/ldbl-128/e_exp10l.c index 987002567a..9b1ff9d821 100644 --- a/sysdeps/ieee754/ldbl-128/e_exp10l.c +++ b/sysdeps/ieee754/ldbl-128/e_exp10l.c @@ -1,4 +1,4 @@ -/* Copyright (C) 2012-2016 Free Software Foundation, Inc. +/* Copyright (C) 2012-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -19,15 +19,15 @@ #include <math_private.h> #include <float.h> -static const long double log10_high = 0x2.4d763776aaa2bp0L; -static const long double log10_low = 0x5.ba95b58ae0b4c28a38a3fb3e7698p-60L; +static const _Float128 log10_high = L(0x2.4d763776aaa2bp0); +static const _Float128 log10_low = L(0x5.ba95b58ae0b4c28a38a3fb3e7698p-60); -long double -__ieee754_exp10l (long double arg) +_Float128 +__ieee754_exp10l (_Float128 arg) { ieee854_long_double_shape_type u; - long double arg_high, arg_low; - long double exp_high, exp_low; + _Float128 arg_high, arg_low; + _Float128 exp_high, exp_low; if (!isfinite (arg)) return __ieee754_expl (arg); @@ -35,8 +35,8 @@ __ieee754_exp10l (long double arg) return LDBL_MIN * LDBL_MIN; else if (arg > LDBL_MAX_10_EXP + 1) return LDBL_MAX * LDBL_MAX; - else if (fabsl (arg) < 0x1p-116L) - return 1.0L; + else if (fabsl (arg) < L(0x1p-116)) + return 1; u.value = arg; u.parts64.lsw &= 0xfe00000000000000LL; diff --git a/sysdeps/ieee754/ldbl-128/e_expl.c b/sysdeps/ieee754/ldbl-128/e_expl.c index 7b71e644be..b4b21c4957 100644 --- a/sysdeps/ieee754/ldbl-128/e_expl.c +++ b/sysdeps/ieee754/ldbl-128/e_expl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point e^x. - Copyright (C) 1999-2016 Free Software Foundation, Inc. + Copyright (C) 1999-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jj@ultra.linux.cz> Partly based on double-precision code @@ -64,58 +64,60 @@ #include <math.h> #include <fenv.h> #include <inttypes.h> +#include <math-barriers.h> #include <math_private.h> +#include <math-underflow.h> #include <stdlib.h> #include "t_expl.h" -static const long double C[] = { +static const _Float128 C[] = { /* Smallest integer x for which e^x overflows. */ #define himark C[0] - 11356.523406294143949491931077970765L, + L(11356.523406294143949491931077970765), /* Largest integer x for which e^x underflows. */ #define lomark C[1] --11433.4627433362978788372438434526231L, +L(-11433.4627433362978788372438434526231), /* 3x2^96 */ #define THREEp96 C[2] - 59421121885698253195157962752.0L, + L(59421121885698253195157962752.0), /* 3x2^103 */ #define THREEp103 C[3] - 30423614405477505635920876929024.0L, + L(30423614405477505635920876929024.0), /* 3x2^111 */ #define THREEp111 C[4] - 7788445287802241442795744493830144.0L, + L(7788445287802241442795744493830144.0), /* 1/ln(2) */ #define M_1_LN2 C[5] - 1.44269504088896340735992468100189204L, + L(1.44269504088896340735992468100189204), /* first 93 bits of ln(2) */ #define M_LN2_0 C[6] - 0.693147180559945309417232121457981864L, + L(0.693147180559945309417232121457981864), /* ln2_0 - ln(2) */ #define M_LN2_1 C[7] --1.94704509238074995158795957333327386E-31L, +L(-1.94704509238074995158795957333327386E-31), /* very small number */ #define TINY C[8] - 1.0e-4900L, + L(1.0e-4900), /* 2^16383 */ #define TWO16383 C[9] - 5.94865747678615882542879663314003565E+4931L, + L(5.94865747678615882542879663314003565E+4931), /* 256 */ #define TWO8 C[10] - 256.0L, + 256, /* 32768 */ #define TWO15 C[11] - 32768.0L, + 32768, /* Chebyshev polynom coefficients for (exp(x)-1)/x */ #define P1 C[12] @@ -124,22 +126,22 @@ static const long double C[] = { #define P4 C[15] #define P5 C[16] #define P6 C[17] - 0.5L, - 1.66666666666666666666666666666666683E-01L, - 4.16666666666666666666654902320001674E-02L, - 8.33333333333333333333314659767198461E-03L, - 1.38888888889899438565058018857254025E-03L, - 1.98412698413981650382436541785404286E-04L, + L(0.5), + L(1.66666666666666666666666666666666683E-01), + L(4.16666666666666666666654902320001674E-02), + L(8.33333333333333333333314659767198461E-03), + L(1.38888888889899438565058018857254025E-03), + L(1.98412698413981650382436541785404286E-04), }; -long double -__ieee754_expl (long double x) +_Float128 +__ieee754_expl (_Float128 x) { /* Check for usual case. */ if (isless (x, himark) && isgreater (x, lomark)) { int tval1, tval2, unsafe, n_i; - long double x22, n, t, result, xl; + _Float128 x22, n, t, result, xl; union ieee854_long_double ex2_u, scale_u; fenv_t oldenv; @@ -185,13 +187,14 @@ __ieee754_expl (long double x) ex2_u.ieee.exponent += n_i >> unsafe; /* Compute scale = 2^n_1. */ - scale_u.d = 1.0L; + scale_u.d = 1; scale_u.ieee.exponent += n_i - (n_i >> unsafe); /* Approximate e^x2 - 1, using a seventh-degree polynomial, with maximum error in [-2^-16-2^-53,2^-16+2^-53] less than 4.8e-39. */ x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6))))); + math_force_eval (x22); /* Return result. */ fesetenv (&oldenv); diff --git a/sysdeps/ieee754/ldbl-128/e_fmodl.c b/sysdeps/ieee754/ldbl-128/e_fmodl.c index 33280030f1..73465126b4 100644 --- a/sysdeps/ieee754/ldbl-128/e_fmodl.c +++ b/sysdeps/ieee754/ldbl-128/e_fmodl.c @@ -21,13 +21,13 @@ #include <math.h> #include <math_private.h> -static const long double one = 1.0, Zero[] = {0.0, -0.0,}; +static const _Float128 one = 1.0, Zero[] = {0.0, -0.0,}; -long double -__ieee754_fmodl (long double x, long double y) +_Float128 +__ieee754_fmodl (_Float128 x, _Float128 y) { int64_t n,hx,hy,hz,ix,iy,sx,i; - u_int64_t lx,ly,lz; + uint64_t lx,ly,lz; GET_LDOUBLE_WORDS64(hx,lx,x); GET_LDOUBLE_WORDS64(hy,ly,y); @@ -42,7 +42,7 @@ __ieee754_fmodl (long double x, long double y) if(hx<=hy) { if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ if(lx==ly) - return Zero[(u_int64_t)sx>>63]; /* |x|=|y| return x*0*/ + return Zero[(uint64_t)sx>>63]; /* |x|=|y| return x*0*/ } /* determine ix = ilogb(x) */ @@ -96,7 +96,7 @@ __ieee754_fmodl (long double x, long double y) if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;} else { if((hz|lz)==0) /* return sign(x)*0 */ - return Zero[(u_int64_t)sx>>63]; + return Zero[(uint64_t)sx>>63]; hx = hz+hz+(lz>>63); lx = lz+lz; } } @@ -105,7 +105,7 @@ __ieee754_fmodl (long double x, long double y) /* convert back to floating value and restore the sign */ if((hx|lx)==0) /* return sign(x)*0 */ - return Zero[(u_int64_t)sx>>63]; + return Zero[(uint64_t)sx>>63]; while(hx<0x0001000000000000LL) { /* normalize x */ hx = hx+hx+(lx>>63); lx = lx+lx; iy -= 1; @@ -116,7 +116,7 @@ __ieee754_fmodl (long double x, long double y) } else { /* subnormal output */ n = -16382 - iy; if(n<=48) { - lx = (lx>>n)|((u_int64_t)hx<<(64-n)); + lx = (lx>>n)|((uint64_t)hx<<(64-n)); hx >>= n; } else if (n<=63) { lx = (hx<<(64-n))|(lx>>n); hx = sx; diff --git a/sysdeps/ieee754/ldbl-128/e_gammal_r.c b/sysdeps/ieee754/ldbl-128/e_gammal_r.c index d0286e31eb..e2730b8fc2 100644 --- a/sysdeps/ieee754/ldbl-128/e_gammal_r.c +++ b/sysdeps/ieee754/ldbl-128/e_gammal_r.c @@ -1,5 +1,5 @@ /* Implementation of gamma function according to ISO C. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz, 1999. @@ -20,27 +20,28 @@ #include <math.h> #include <math_private.h> +#include <math-underflow.h> #include <float.h> /* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's approximation to gamma function. */ -static const long double gamma_coeff[] = +static const _Float128 gamma_coeff[] = { - 0x1.5555555555555555555555555555p-4L, - -0xb.60b60b60b60b60b60b60b60b60b8p-12L, - 0x3.4034034034034034034034034034p-12L, - -0x2.7027027027027027027027027028p-12L, - 0x3.72a3c5631fe46ae1d4e700dca8f2p-12L, - -0x7.daac36664f1f207daac36664f1f4p-12L, - 0x1.a41a41a41a41a41a41a41a41a41ap-8L, - -0x7.90a1b2c3d4e5f708192a3b4c5d7p-8L, - 0x2.dfd2c703c0cfff430edfd2c703cp-4L, - -0x1.6476701181f39edbdb9ce625987dp+0L, - 0xd.672219167002d3a7a9c886459cp+0L, - -0x9.cd9292e6660d55b3f712eb9e07c8p+4L, - 0x8.911a740da740da740da740da741p+8L, - -0x8.d0cc570e255bf59ff6eec24b49p+12L, + L(0x1.5555555555555555555555555555p-4), + L(-0xb.60b60b60b60b60b60b60b60b60b8p-12), + L(0x3.4034034034034034034034034034p-12), + L(-0x2.7027027027027027027027027028p-12), + L(0x3.72a3c5631fe46ae1d4e700dca8f2p-12), + L(-0x7.daac36664f1f207daac36664f1f4p-12), + L(0x1.a41a41a41a41a41a41a41a41a41ap-8), + L(-0x7.90a1b2c3d4e5f708192a3b4c5d7p-8), + L(0x2.dfd2c703c0cfff430edfd2c703cp-4), + L(-0x1.6476701181f39edbdb9ce625987dp+0), + L(0xd.672219167002d3a7a9c886459cp+0), + L(-0x9.cd9292e6660d55b3f712eb9e07c8p+4), + L(0x8.911a740da740da740da740da741p+8), + L(-0x8.d0cc570e255bf59ff6eec24b49p+12), }; #define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) @@ -49,42 +50,42 @@ static const long double gamma_coeff[] = 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to avoid overflow or underflow in intermediate calculations. */ -static long double -gammal_positive (long double x, int *exp2_adj) +static _Float128 +gammal_positive (_Float128 x, int *exp2_adj) { int local_signgam; - if (x < 0.5L) + if (x < L(0.5)) { *exp2_adj = 0; return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x; } - else if (x <= 1.5L) + else if (x <= L(1.5)) { *exp2_adj = 0; return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam)); } - else if (x < 12.5L) + else if (x < L(12.5)) { /* Adjust into the range for using exp (lgamma). */ *exp2_adj = 0; - long double n = __ceill (x - 1.5L); - long double x_adj = x - n; - long double eps; - long double prod = __gamma_productl (x_adj, 0, n, &eps); + _Float128 n = __ceill (x - L(1.5)); + _Float128 x_adj = x - n; + _Float128 eps; + _Float128 prod = __gamma_productl (x_adj, 0, n, &eps); return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam)) - * prod * (1.0L + eps)); + * prod * (1 + eps)); } else { - long double eps = 0; - long double x_eps = 0; - long double x_adj = x; - long double prod = 1; - if (x < 24.0L) + _Float128 eps = 0; + _Float128 x_eps = 0; + _Float128 x_adj = x; + _Float128 prod = 1; + if (x < 24) { /* Adjust into the range for applying Stirling's approximation. */ - long double n = __ceill (24.0L - x); + _Float128 n = __ceill (24 - x); x_adj = x + n; x_eps = (x - (x_adj - n)); prod = __gamma_productl (x_adj - n, x_eps, n, &eps); @@ -93,25 +94,25 @@ gammal_positive (long double x, int *exp2_adj) Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, starting by computing pow (X_ADJ, X_ADJ) with a power of 2 factored out. */ - long double exp_adj = -eps; - long double x_adj_int = __roundl (x_adj); - long double x_adj_frac = x_adj - x_adj_int; + _Float128 exp_adj = -eps; + _Float128 x_adj_int = __roundl (x_adj); + _Float128 x_adj_frac = x_adj - x_adj_int; int x_adj_log2; - long double x_adj_mant = __frexpl (x_adj, &x_adj_log2); + _Float128 x_adj_mant = __frexpl (x_adj, &x_adj_log2); if (x_adj_mant < M_SQRT1_2l) { x_adj_log2--; - x_adj_mant *= 2.0L; + x_adj_mant *= 2; } *exp2_adj = x_adj_log2 * (int) x_adj_int; - long double ret = (__ieee754_powl (x_adj_mant, x_adj) - * __ieee754_exp2l (x_adj_log2 * x_adj_frac) - * __ieee754_expl (-x_adj) - * __ieee754_sqrtl (2 * M_PIl / x_adj) - / prod); + _Float128 ret = (__ieee754_powl (x_adj_mant, x_adj) + * __ieee754_exp2l (x_adj_log2 * x_adj_frac) + * __ieee754_expl (-x_adj) + * sqrtl (2 * M_PIl / x_adj) + / prod); exp_adj += x_eps * __ieee754_logl (x_adj); - long double bsum = gamma_coeff[NCOEFF - 1]; - long double x_adj2 = x_adj * x_adj; + _Float128 bsum = gamma_coeff[NCOEFF - 1]; + _Float128 x_adj2 = x_adj * x_adj; for (size_t i = 1; i <= NCOEFF - 1; i++) bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; exp_adj += bsum / x_adj; @@ -119,12 +120,12 @@ gammal_positive (long double x, int *exp2_adj) } } -long double -__ieee754_gammal_r (long double x, int *signgamp) +_Float128 +__ieee754_gammal_r (_Float128 x, int *signgamp) { int64_t hx; - u_int64_t lx; - long double ret; + uint64_t lx; + _Float128 ret; GET_LDOUBLE_WORDS64 (hx, lx, x); @@ -134,7 +135,7 @@ __ieee754_gammal_r (long double x, int *signgamp) *signgamp = 0; return 1.0 / x; } - if (hx < 0 && (u_int64_t) hx < 0xffff000000000000ULL && __rintl (x) == x) + if (hx < 0 && (uint64_t) hx < 0xffff000000000000ULL && __rintl (x) == x) { /* Return value for integer x < 0 is NaN with invalid exception. */ *signgamp = 0; @@ -154,7 +155,7 @@ __ieee754_gammal_r (long double x, int *signgamp) return x + x; } - if (x >= 1756.0L) + if (x >= 1756) { /* Overflow. */ *signgamp = 0; @@ -163,33 +164,33 @@ __ieee754_gammal_r (long double x, int *signgamp) else { SET_RESTORE_ROUNDL (FE_TONEAREST); - if (x > 0.0L) + if (x > 0) { *signgamp = 0; int exp2_adj; ret = gammal_positive (x, &exp2_adj); ret = __scalbnl (ret, exp2_adj); } - else if (x >= -LDBL_EPSILON / 4.0L) + else if (x >= -LDBL_EPSILON / 4) { *signgamp = 0; - ret = 1.0L / x; + ret = 1 / x; } else { - long double tx = __truncl (x); - *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1; - if (x <= -1775.0L) + _Float128 tx = __truncl (x); + *signgamp = (tx == 2 * __truncl (tx / 2)) ? -1 : 1; + if (x <= -1775) /* Underflow. */ ret = LDBL_MIN * LDBL_MIN; else { - long double frac = tx - x; - if (frac > 0.5L) - frac = 1.0L - frac; - long double sinpix = (frac <= 0.25L - ? __sinl (M_PIl * frac) - : __cosl (M_PIl * (0.5L - frac))); + _Float128 frac = tx - x; + if (frac > L(0.5)) + frac = 1 - frac; + _Float128 sinpix = (frac <= L(0.25) + ? __sinl (M_PIl * frac) + : __cosl (M_PIl * (L(0.5) - frac))); int exp2_adj; ret = M_PIl / (-x * sinpix * gammal_positive (-x, &exp2_adj)); diff --git a/sysdeps/ieee754/ldbl-128/e_hypotl.c b/sysdeps/ieee754/ldbl-128/e_hypotl.c index 80e5e38c72..7bafd4ae29 100644 --- a/sysdeps/ieee754/ldbl-128/e_hypotl.c +++ b/sysdeps/ieee754/ldbl-128/e_hypotl.c @@ -47,11 +47,12 @@ #include <math.h> #include <math_private.h> +#include <math-underflow.h> -long double -__ieee754_hypotl(long double x, long double y) +_Float128 +__ieee754_hypotl(_Float128 x, _Float128 y) { - long double a,b,t1,t2,y1,y2,w; + _Float128 a,b,t1,t2,y1,y2,w; int64_t j,k,ha,hb; GET_LDOUBLE_MSW64(ha,x); @@ -65,8 +66,10 @@ __ieee754_hypotl(long double x, long double y) k=0; if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */ if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */ - u_int64_t low; + uint64_t low; w = a+b; /* for sNaN */ + if (issignaling (a) || issignaling (b)) + return w; GET_LDOUBLE_LSW64(low,a); if(((ha&0xffffffffffffLL)|low)==0) w = a; GET_LDOUBLE_LSW64(low,b); @@ -81,7 +84,7 @@ __ieee754_hypotl(long double x, long double y) } if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */ if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */ - u_int64_t low; + uint64_t low; GET_LDOUBLE_LSW64(low,b); if((hb|low)==0) return a; t1=0; @@ -114,7 +117,7 @@ __ieee754_hypotl(long double x, long double y) t1 = 0; SET_LDOUBLE_MSW64(t1,ha); t2 = a-t1; - w = __ieee754_sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); + w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1))); } else { a = a+a; y1 = 0; @@ -123,11 +126,11 @@ __ieee754_hypotl(long double x, long double y) t1 = 0; SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL); t2 = a - t1; - w = __ieee754_sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); + w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b))); } if(k!=0) { - u_int64_t high; - t1 = 1.0L; + uint64_t high; + t1 = 1; GET_LDOUBLE_MSW64(high,t1); SET_LDOUBLE_MSW64(t1,high+(k<<48)); w *= t1; diff --git a/sysdeps/ieee754/ldbl-128/e_ilogbl.c b/sysdeps/ieee754/ldbl-128/e_ilogbl.c index 0a476492d6..9effe6386a 100644 --- a/sysdeps/ieee754/ldbl-128/e_ilogbl.c +++ b/sysdeps/ieee754/ldbl-128/e_ilogbl.c @@ -28,7 +28,7 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> -int __ieee754_ilogbl (long double x) +int __ieee754_ilogbl (_Float128 x) { int64_t hx,lx; int ix; diff --git a/sysdeps/ieee754/ldbl-128/e_j0l.c b/sysdeps/ieee754/ldbl-128/e_j0l.c index c208916a79..5c699956b6 100644 --- a/sysdeps/ieee754/ldbl-128/e_j0l.c +++ b/sysdeps/ieee754/ldbl-128/e_j0l.c @@ -96,33 +96,33 @@ #include <float.h> /* 1 / sqrt(pi) */ -static const long double ONEOSQPI = 5.6418958354775628694807945156077258584405E-1L; +static const _Float128 ONEOSQPI = L(5.6418958354775628694807945156077258584405E-1); /* 2 / pi */ -static const long double TWOOPI = 6.3661977236758134307553505349005744813784E-1L; -static const long double zero = 0.0L; +static const _Float128 TWOOPI = L(6.3661977236758134307553505349005744813784E-1); +static const _Float128 zero = 0; /* J0(x) = 1 - x^2/4 + x^2 x^2 R(x^2) Peak relative error 3.4e-37 0 <= x <= 2 */ #define NJ0_2N 6 -static const long double J0_2N[NJ0_2N + 1] = { - 3.133239376997663645548490085151484674892E16L, - -5.479944965767990821079467311839107722107E14L, - 6.290828903904724265980249871997551894090E12L, - -3.633750176832769659849028554429106299915E10L, - 1.207743757532429576399485415069244807022E8L, - -2.107485999925074577174305650549367415465E5L, - 1.562826808020631846245296572935547005859E2L, +static const _Float128 J0_2N[NJ0_2N + 1] = { + L(3.133239376997663645548490085151484674892E16), + L(-5.479944965767990821079467311839107722107E14), + L(6.290828903904724265980249871997551894090E12), + L(-3.633750176832769659849028554429106299915E10), + L(1.207743757532429576399485415069244807022E8), + L(-2.107485999925074577174305650549367415465E5), + L(1.562826808020631846245296572935547005859E2), }; #define NJ0_2D 6 -static const long double J0_2D[NJ0_2D + 1] = { - 2.005273201278504733151033654496928968261E18L, - 2.063038558793221244373123294054149790864E16L, - 1.053350447931127971406896594022010524994E14L, - 3.496556557558702583143527876385508882310E11L, - 8.249114511878616075860654484367133976306E8L, - 1.402965782449571800199759247964242790589E6L, - 1.619910762853439600957801751815074787351E3L, +static const _Float128 J0_2D[NJ0_2D + 1] = { + L(2.005273201278504733151033654496928968261E18), + L(2.063038558793221244373123294054149790864E16), + L(1.053350447931127971406896594022010524994E14), + L(3.496556557558702583143527876385508882310E11), + L(8.249114511878616075860654484367133976306E8), + L(1.402965782449571800199759247964242790589E6), + L(1.619910762853439600957801751815074787351E3), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -130,30 +130,30 @@ static const long double J0_2D[NJ0_2D + 1] = { 0 <= 1/x <= .0625 Peak relative error 3.3e-36 */ #define NP16_IN 9 -static const long double P16_IN[NP16_IN + 1] = { - -1.901689868258117463979611259731176301065E-16L, - -1.798743043824071514483008340803573980931E-13L, - -6.481746687115262291873324132944647438959E-11L, - -1.150651553745409037257197798528294248012E-8L, - -1.088408467297401082271185599507222695995E-6L, - -5.551996725183495852661022587879817546508E-5L, - -1.477286941214245433866838787454880214736E-3L, - -1.882877976157714592017345347609200402472E-2L, - -9.620983176855405325086530374317855880515E-2L, - -1.271468546258855781530458854476627766233E-1L, +static const _Float128 P16_IN[NP16_IN + 1] = { + L(-1.901689868258117463979611259731176301065E-16), + L(-1.798743043824071514483008340803573980931E-13), + L(-6.481746687115262291873324132944647438959E-11), + L(-1.150651553745409037257197798528294248012E-8), + L(-1.088408467297401082271185599507222695995E-6), + L(-5.551996725183495852661022587879817546508E-5), + L(-1.477286941214245433866838787454880214736E-3), + L(-1.882877976157714592017345347609200402472E-2), + L(-9.620983176855405325086530374317855880515E-2), + L(-1.271468546258855781530458854476627766233E-1), }; #define NP16_ID 9 -static const long double P16_ID[NP16_ID + 1] = { - 2.704625590411544837659891569420764475007E-15L, - 2.562526347676857624104306349421985403573E-12L, - 9.259137589952741054108665570122085036246E-10L, - 1.651044705794378365237454962653430805272E-7L, - 1.573561544138733044977714063100859136660E-5L, - 8.134482112334882274688298469629884804056E-4L, - 2.219259239404080863919375103673593571689E-2L, - 2.976990606226596289580242451096393862792E-1L, - 1.713895630454693931742734911930937246254E0L, - 3.231552290717904041465898249160757368855E0L, +static const _Float128 P16_ID[NP16_ID + 1] = { + L(2.704625590411544837659891569420764475007E-15), + L(2.562526347676857624104306349421985403573E-12), + L(9.259137589952741054108665570122085036246E-10), + L(1.651044705794378365237454962653430805272E-7), + L(1.573561544138733044977714063100859136660E-5), + L(8.134482112334882274688298469629884804056E-4), + L(2.219259239404080863919375103673593571689E-2), + L(2.976990606226596289580242451096393862792E-1), + L(1.713895630454693931742734911930937246254E0), + L(3.231552290717904041465898249160757368855E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -161,32 +161,32 @@ static const long double P16_ID[NP16_ID + 1] = { 0.0625 <= 1/x <= 0.125 Peak relative error 2.4e-35 */ #define NP8_16N 10 -static const long double P8_16N[NP8_16N + 1] = { - -2.335166846111159458466553806683579003632E-15L, - -1.382763674252402720401020004169367089975E-12L, - -3.192160804534716696058987967592784857907E-10L, - -3.744199606283752333686144670572632116899E-8L, - -2.439161236879511162078619292571922772224E-6L, - -9.068436986859420951664151060267045346549E-5L, - -1.905407090637058116299757292660002697359E-3L, - -2.164456143936718388053842376884252978872E-2L, - -1.212178415116411222341491717748696499966E-1L, - -2.782433626588541494473277445959593334494E-1L, - -1.670703190068873186016102289227646035035E-1L, +static const _Float128 P8_16N[NP8_16N + 1] = { + L(-2.335166846111159458466553806683579003632E-15), + L(-1.382763674252402720401020004169367089975E-12), + L(-3.192160804534716696058987967592784857907E-10), + L(-3.744199606283752333686144670572632116899E-8), + L(-2.439161236879511162078619292571922772224E-6), + L(-9.068436986859420951664151060267045346549E-5), + L(-1.905407090637058116299757292660002697359E-3), + L(-2.164456143936718388053842376884252978872E-2), + L(-1.212178415116411222341491717748696499966E-1), + L(-2.782433626588541494473277445959593334494E-1), + L(-1.670703190068873186016102289227646035035E-1), }; #define NP8_16D 10 -static const long double P8_16D[NP8_16D + 1] = { - 3.321126181135871232648331450082662856743E-14L, - 1.971894594837650840586859228510007703641E-11L, - 4.571144364787008285981633719513897281690E-9L, - 5.396419143536287457142904742849052402103E-7L, - 3.551548222385845912370226756036899901549E-5L, - 1.342353874566932014705609788054598013516E-3L, - 2.899133293006771317589357444614157734385E-2L, - 3.455374978185770197704507681491574261545E-1L, - 2.116616964297512311314454834712634820514E0L, - 5.850768316827915470087758636881584174432E0L, - 5.655273858938766830855753983631132928968E0L, +static const _Float128 P8_16D[NP8_16D + 1] = { + L(3.321126181135871232648331450082662856743E-14), + L(1.971894594837650840586859228510007703641E-11), + L(4.571144364787008285981633719513897281690E-9), + L(5.396419143536287457142904742849052402103E-7), + L(3.551548222385845912370226756036899901549E-5), + L(1.342353874566932014705609788054598013516E-3), + L(2.899133293006771317589357444614157734385E-2), + L(3.455374978185770197704507681491574261545E-1), + L(2.116616964297512311314454834712634820514E0), + L(5.850768316827915470087758636881584174432E0), + L(5.655273858938766830855753983631132928968E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -194,31 +194,31 @@ static const long double P8_16D[NP8_16D + 1] = { 0.125 <= 1/x <= 0.1875 Peak relative error 2.7e-35 */ #define NP5_8N 10 -static const long double P5_8N[NP5_8N + 1] = { - -1.270478335089770355749591358934012019596E-12L, - -4.007588712145412921057254992155810347245E-10L, - -4.815187822989597568124520080486652009281E-8L, - -2.867070063972764880024598300408284868021E-6L, - -9.218742195161302204046454768106063638006E-5L, - -1.635746821447052827526320629828043529997E-3L, - -1.570376886640308408247709616497261011707E-2L, - -7.656484795303305596941813361786219477807E-2L, - -1.659371030767513274944805479908858628053E-1L, - -1.185340550030955660015841796219919804915E-1L, - -8.920026499909994671248893388013790366712E-3L, +static const _Float128 P5_8N[NP5_8N + 1] = { + L(-1.270478335089770355749591358934012019596E-12), + L(-4.007588712145412921057254992155810347245E-10), + L(-4.815187822989597568124520080486652009281E-8), + L(-2.867070063972764880024598300408284868021E-6), + L(-9.218742195161302204046454768106063638006E-5), + L(-1.635746821447052827526320629828043529997E-3), + L(-1.570376886640308408247709616497261011707E-2), + L(-7.656484795303305596941813361786219477807E-2), + L(-1.659371030767513274944805479908858628053E-1), + L(-1.185340550030955660015841796219919804915E-1), + L(-8.920026499909994671248893388013790366712E-3), }; #define NP5_8D 9 -static const long double P5_8D[NP5_8D + 1] = { - 1.806902521016705225778045904631543990314E-11L, - 5.728502760243502431663549179135868966031E-9L, - 6.938168504826004255287618819550667978450E-7L, - 4.183769964807453250763325026573037785902E-5L, - 1.372660678476925468014882230851637878587E-3L, - 2.516452105242920335873286419212708961771E-2L, - 2.550502712902647803796267951846557316182E-1L, - 1.365861559418983216913629123778747617072E0L, - 3.523825618308783966723472468855042541407E0L, - 3.656365803506136165615111349150536282434E0L, +static const _Float128 P5_8D[NP5_8D + 1] = { + L(1.806902521016705225778045904631543990314E-11), + L(5.728502760243502431663549179135868966031E-9), + L(6.938168504826004255287618819550667978450E-7), + L(4.183769964807453250763325026573037785902E-5), + L(1.372660678476925468014882230851637878587E-3), + L(2.516452105242920335873286419212708961771E-2), + L(2.550502712902647803796267951846557316182E-1), + L(1.365861559418983216913629123778747617072E0), + L(3.523825618308783966723472468855042541407E0), + L(3.656365803506136165615111349150536282434E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -226,30 +226,30 @@ static const long double P5_8D[NP5_8D + 1] = { Peak relative error 3.5e-35 0.1875 <= 1/x <= 0.25 */ #define NP4_5N 9 -static const long double P4_5N[NP4_5N + 1] = { - -9.791405771694098960254468859195175708252E-10L, - -1.917193059944531970421626610188102836352E-7L, - -1.393597539508855262243816152893982002084E-5L, - -4.881863490846771259880606911667479860077E-4L, - -8.946571245022470127331892085881699269853E-3L, - -8.707474232568097513415336886103899434251E-2L, - -4.362042697474650737898551272505525973766E-1L, - -1.032712171267523975431451359962375617386E0L, - -9.630502683169895107062182070514713702346E-1L, - -2.251804386252969656586810309252357233320E-1L, +static const _Float128 P4_5N[NP4_5N + 1] = { + L(-9.791405771694098960254468859195175708252E-10), + L(-1.917193059944531970421626610188102836352E-7), + L(-1.393597539508855262243816152893982002084E-5), + L(-4.881863490846771259880606911667479860077E-4), + L(-8.946571245022470127331892085881699269853E-3), + L(-8.707474232568097513415336886103899434251E-2), + L(-4.362042697474650737898551272505525973766E-1), + L(-1.032712171267523975431451359962375617386E0), + L(-9.630502683169895107062182070514713702346E-1), + L(-2.251804386252969656586810309252357233320E-1), }; #define NP4_5D 9 -static const long double P4_5D[NP4_5D + 1] = { - 1.392555487577717669739688337895791213139E-8L, - 2.748886559120659027172816051276451376854E-6L, - 2.024717710644378047477189849678576659290E-4L, - 7.244868609350416002930624752604670292469E-3L, - 1.373631762292244371102989739300382152416E-1L, - 1.412298581400224267910294815260613240668E0L, - 7.742495637843445079276397723849017617210E0L, - 2.138429269198406512028307045259503811861E1L, - 2.651547684548423476506826951831712762610E1L, - 1.167499382465291931571685222882909166935E1L, +static const _Float128 P4_5D[NP4_5D + 1] = { + L(1.392555487577717669739688337895791213139E-8), + L(2.748886559120659027172816051276451376854E-6), + L(2.024717710644378047477189849678576659290E-4), + L(7.244868609350416002930624752604670292469E-3), + L(1.373631762292244371102989739300382152416E-1), + L(1.412298581400224267910294815260613240668E0), + L(7.742495637843445079276397723849017617210E0), + L(2.138429269198406512028307045259503811861E1), + L(2.651547684548423476506826951831712762610E1), + L(1.167499382465291931571685222882909166935E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -257,30 +257,30 @@ static const long double P4_5D[NP4_5D + 1] = { Peak relative error 2.3e-36 0.25 <= 1/x <= 0.3125 */ #define NP3r2_4N 9 -static const long double P3r2_4N[NP3r2_4N + 1] = { - -2.589155123706348361249809342508270121788E-8L, - -3.746254369796115441118148490849195516593E-6L, - -1.985595497390808544622893738135529701062E-4L, - -5.008253705202932091290132760394976551426E-3L, - -6.529469780539591572179155511840853077232E-2L, - -4.468736064761814602927408833818990271514E-1L, - -1.556391252586395038089729428444444823380E0L, - -2.533135309840530224072920725976994981638E0L, - -1.605509621731068453869408718565392869560E0L, - -2.518966692256192789269859830255724429375E-1L, +static const _Float128 P3r2_4N[NP3r2_4N + 1] = { + L(-2.589155123706348361249809342508270121788E-8), + L(-3.746254369796115441118148490849195516593E-6), + L(-1.985595497390808544622893738135529701062E-4), + L(-5.008253705202932091290132760394976551426E-3), + L(-6.529469780539591572179155511840853077232E-2), + L(-4.468736064761814602927408833818990271514E-1), + L(-1.556391252586395038089729428444444823380E0), + L(-2.533135309840530224072920725976994981638E0), + L(-1.605509621731068453869408718565392869560E0), + L(-2.518966692256192789269859830255724429375E-1), }; #define NP3r2_4D 9 -static const long double P3r2_4D[NP3r2_4D + 1] = { - 3.682353957237979993646169732962573930237E-7L, - 5.386741661883067824698973455566332102029E-5L, - 2.906881154171822780345134853794241037053E-3L, - 7.545832595801289519475806339863492074126E-2L, - 1.029405357245594877344360389469584526654E0L, - 7.565706120589873131187989560509757626725E0L, - 2.951172890699569545357692207898667665796E1L, - 5.785723537170311456298467310529815457536E1L, - 5.095621464598267889126015412522773474467E1L, - 1.602958484169953109437547474953308401442E1L, +static const _Float128 P3r2_4D[NP3r2_4D + 1] = { + L(3.682353957237979993646169732962573930237E-7), + L(5.386741661883067824698973455566332102029E-5), + L(2.906881154171822780345134853794241037053E-3), + L(7.545832595801289519475806339863492074126E-2), + L(1.029405357245594877344360389469584526654E0), + L(7.565706120589873131187989560509757626725E0), + L(2.951172890699569545357692207898667665796E1), + L(5.785723537170311456298467310529815457536E1), + L(5.095621464598267889126015412522773474467E1), + L(1.602958484169953109437547474953308401442E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -288,29 +288,29 @@ static const long double P3r2_4D[NP3r2_4D + 1] = { Peak relative error 1.0e-35 0.3125 <= 1/x <= 0.375 */ #define NP2r7_3r2N 9 -static const long double P2r7_3r2N[NP2r7_3r2N + 1] = { - -1.917322340814391131073820537027234322550E-7L, - -1.966595744473227183846019639723259011906E-5L, - -7.177081163619679403212623526632690465290E-4L, - -1.206467373860974695661544653741899755695E-2L, - -1.008656452188539812154551482286328107316E-1L, - -4.216016116408810856620947307438823892707E-1L, - -8.378631013025721741744285026537009814161E-1L, - -6.973895635309960850033762745957946272579E-1L, - -1.797864718878320770670740413285763554812E-1L, - -4.098025357743657347681137871388402849581E-3L, +static const _Float128 P2r7_3r2N[NP2r7_3r2N + 1] = { + L(-1.917322340814391131073820537027234322550E-7), + L(-1.966595744473227183846019639723259011906E-5), + L(-7.177081163619679403212623526632690465290E-4), + L(-1.206467373860974695661544653741899755695E-2), + L(-1.008656452188539812154551482286328107316E-1), + L(-4.216016116408810856620947307438823892707E-1), + L(-8.378631013025721741744285026537009814161E-1), + L(-6.973895635309960850033762745957946272579E-1), + L(-1.797864718878320770670740413285763554812E-1), + L(-4.098025357743657347681137871388402849581E-3), }; #define NP2r7_3r2D 8 -static const long double P2r7_3r2D[NP2r7_3r2D + 1] = { - 2.726858489303036441686496086962545034018E-6L, - 2.840430827557109238386808968234848081424E-4L, - 1.063826772041781947891481054529454088832E-2L, - 1.864775537138364773178044431045514405468E-1L, - 1.665660052857205170440952607701728254211E0L, - 7.723745889544331153080842168958348568395E0L, - 1.810726427571829798856428548102077799835E1L, - 1.986460672157794440666187503833545388527E1L, - 8.645503204552282306364296517220055815488E0L, +static const _Float128 P2r7_3r2D[NP2r7_3r2D + 1] = { + L(2.726858489303036441686496086962545034018E-6), + L(2.840430827557109238386808968234848081424E-4), + L(1.063826772041781947891481054529454088832E-2), + L(1.864775537138364773178044431045514405468E-1), + L(1.665660052857205170440952607701728254211E0), + L(7.723745889544331153080842168958348568395E0), + L(1.810726427571829798856428548102077799835E1), + L(1.986460672157794440666187503833545388527E1), + L(8.645503204552282306364296517220055815488E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -318,29 +318,29 @@ static const long double P2r7_3r2D[NP2r7_3r2D + 1] = { Peak relative error 1.3e-36 0.3125 <= 1/x <= 0.4375 */ #define NP2r3_2r7N 9 -static const long double P2r3_2r7N[NP2r3_2r7N + 1] = { - -1.594642785584856746358609622003310312622E-6L, - -1.323238196302221554194031733595194539794E-4L, - -3.856087818696874802689922536987100372345E-3L, - -5.113241710697777193011470733601522047399E-2L, - -3.334229537209911914449990372942022350558E-1L, - -1.075703518198127096179198549659283422832E0L, - -1.634174803414062725476343124267110981807E0L, - -1.030133247434119595616826842367268304880E0L, - -1.989811539080358501229347481000707289391E-1L, - -3.246859189246653459359775001466924610236E-3L, +static const _Float128 P2r3_2r7N[NP2r3_2r7N + 1] = { + L(-1.594642785584856746358609622003310312622E-6), + L(-1.323238196302221554194031733595194539794E-4), + L(-3.856087818696874802689922536987100372345E-3), + L(-5.113241710697777193011470733601522047399E-2), + L(-3.334229537209911914449990372942022350558E-1), + L(-1.075703518198127096179198549659283422832E0), + L(-1.634174803414062725476343124267110981807E0), + L(-1.030133247434119595616826842367268304880E0), + L(-1.989811539080358501229347481000707289391E-1), + L(-3.246859189246653459359775001466924610236E-3), }; #define NP2r3_2r7D 8 -static const long double P2r3_2r7D[NP2r3_2r7D + 1] = { - 2.267936634217251403663034189684284173018E-5L, - 1.918112982168673386858072491437971732237E-3L, - 5.771704085468423159125856786653868219522E-2L, - 8.056124451167969333717642810661498890507E-1L, - 5.687897967531010276788680634413789328776E0L, - 2.072596760717695491085444438270778394421E1L, - 3.801722099819929988585197088613160496684E1L, - 3.254620235902912339534998592085115836829E1L, - 1.104847772130720331801884344645060675036E1L, +static const _Float128 P2r3_2r7D[NP2r3_2r7D + 1] = { + L(2.267936634217251403663034189684284173018E-5), + L(1.918112982168673386858072491437971732237E-3), + L(5.771704085468423159125856786653868219522E-2), + L(8.056124451167969333717642810661498890507E-1), + L(5.687897967531010276788680634413789328776E0), + L(2.072596760717695491085444438270778394421E1), + L(3.801722099819929988585197088613160496684E1), + L(3.254620235902912339534998592085115836829E1), + L(1.104847772130720331801884344645060675036E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -348,28 +348,28 @@ static const long double P2r3_2r7D[NP2r3_2r7D + 1] = { Peak relative error 1.2e-35 0.4375 <= 1/x <= 0.5 */ #define NP2_2r3N 8 -static const long double P2_2r3N[NP2_2r3N + 1] = { - -1.001042324337684297465071506097365389123E-4L, - -6.289034524673365824853547252689991418981E-3L, - -1.346527918018624234373664526930736205806E-1L, - -1.268808313614288355444506172560463315102E0L, - -5.654126123607146048354132115649177406163E0L, - -1.186649511267312652171775803270911971693E1L, - -1.094032424931998612551588246779200724257E1L, - -3.728792136814520055025256353193674625267E0L, - -3.000348318524471807839934764596331810608E-1L, +static const _Float128 P2_2r3N[NP2_2r3N + 1] = { + L(-1.001042324337684297465071506097365389123E-4), + L(-6.289034524673365824853547252689991418981E-3), + L(-1.346527918018624234373664526930736205806E-1), + L(-1.268808313614288355444506172560463315102E0), + L(-5.654126123607146048354132115649177406163E0), + L(-1.186649511267312652171775803270911971693E1), + L(-1.094032424931998612551588246779200724257E1), + L(-3.728792136814520055025256353193674625267E0), + L(-3.000348318524471807839934764596331810608E-1), }; #define NP2_2r3D 8 -static const long double P2_2r3D[NP2_2r3D + 1] = { - 1.423705538269770974803901422532055612980E-3L, - 9.171476630091439978533535167485230575894E-2L, - 2.049776318166637248868444600215942828537E0L, - 2.068970329743769804547326701946144899583E1L, - 1.025103500560831035592731539565060347709E2L, - 2.528088049697570728252145557167066708284E2L, - 2.992160327587558573740271294804830114205E2L, - 1.540193761146551025832707739468679973036E2L, - 2.779516701986912132637672140709452502650E1L, +static const _Float128 P2_2r3D[NP2_2r3D + 1] = { + L(1.423705538269770974803901422532055612980E-3), + L(9.171476630091439978533535167485230575894E-2), + L(2.049776318166637248868444600215942828537E0), + L(2.068970329743769804547326701946144899583E1), + L(1.025103500560831035592731539565060347709E2), + L(2.528088049697570728252145557167066708284E2), + L(2.992160327587558573740271294804830114205E2), + L(1.540193761146551025832707739468679973036E2), + L(2.779516701986912132637672140709452502650E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -378,31 +378,31 @@ static const long double P2_2r3D[NP2_2r3D + 1] = { Peak relative error 2.2e-35 0 <= 1/x <= .0625 */ #define NQ16_IN 10 -static const long double Q16_IN[NQ16_IN + 1] = { - 2.343640834407975740545326632205999437469E-18L, - 2.667978112927811452221176781536278257448E-15L, - 1.178415018484555397390098879501969116536E-12L, - 2.622049767502719728905924701288614016597E-10L, - 3.196908059607618864801313380896308968673E-8L, - 2.179466154171673958770030655199434798494E-6L, - 8.139959091628545225221976413795645177291E-5L, - 1.563900725721039825236927137885747138654E-3L, - 1.355172364265825167113562519307194840307E-2L, - 3.928058355906967977269780046844768588532E-2L, - 1.107891967702173292405380993183694932208E-2L, +static const _Float128 Q16_IN[NQ16_IN + 1] = { + L(2.343640834407975740545326632205999437469E-18), + L(2.667978112927811452221176781536278257448E-15), + L(1.178415018484555397390098879501969116536E-12), + L(2.622049767502719728905924701288614016597E-10), + L(3.196908059607618864801313380896308968673E-8), + L(2.179466154171673958770030655199434798494E-6), + L(8.139959091628545225221976413795645177291E-5), + L(1.563900725721039825236927137885747138654E-3), + L(1.355172364265825167113562519307194840307E-2), + L(3.928058355906967977269780046844768588532E-2), + L(1.107891967702173292405380993183694932208E-2), }; #define NQ16_ID 9 -static const long double Q16_ID[NQ16_ID + 1] = { - 3.199850952578356211091219295199301766718E-17L, - 3.652601488020654842194486058637953363918E-14L, - 1.620179741394865258354608590461839031281E-11L, - 3.629359209474609630056463248923684371426E-9L, - 4.473680923894354600193264347733477363305E-7L, - 3.106368086644715743265603656011050476736E-5L, - 1.198239259946770604954664925153424252622E-3L, - 2.446041004004283102372887804475767568272E-2L, - 2.403235525011860603014707768815113698768E-1L, - 9.491006790682158612266270665136910927149E-1L, +static const _Float128 Q16_ID[NQ16_ID + 1] = { + L(3.199850952578356211091219295199301766718E-17), + L(3.652601488020654842194486058637953363918E-14), + L(1.620179741394865258354608590461839031281E-11), + L(3.629359209474609630056463248923684371426E-9), + L(4.473680923894354600193264347733477363305E-7), + L(3.106368086644715743265603656011050476736E-5), + L(1.198239259946770604954664925153424252622E-3), + L(2.446041004004283102372887804475767568272E-2), + L(2.403235525011860603014707768815113698768E-1), + L(9.491006790682158612266270665136910927149E-1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -411,34 +411,34 @@ static const long double Q16_ID[NQ16_ID + 1] = { Peak relative error 5.1e-36 0.0625 <= 1/x <= 0.125 */ #define NQ8_16N 11 -static const long double Q8_16N[NQ8_16N + 1] = { - 1.001954266485599464105669390693597125904E-17L, - 7.545499865295034556206475956620160007849E-15L, - 2.267838684785673931024792538193202559922E-12L, - 3.561909705814420373609574999542459912419E-10L, - 3.216201422768092505214730633842924944671E-8L, - 1.731194793857907454569364622452058554314E-6L, - 5.576944613034537050396518509871004586039E-5L, - 1.051787760316848982655967052985391418146E-3L, - 1.102852974036687441600678598019883746959E-2L, - 5.834647019292460494254225988766702933571E-2L, - 1.290281921604364618912425380717127576529E-1L, - 7.598886310387075708640370806458926458301E-2L, +static const _Float128 Q8_16N[NQ8_16N + 1] = { + L(1.001954266485599464105669390693597125904E-17), + L(7.545499865295034556206475956620160007849E-15), + L(2.267838684785673931024792538193202559922E-12), + L(3.561909705814420373609574999542459912419E-10), + L(3.216201422768092505214730633842924944671E-8), + L(1.731194793857907454569364622452058554314E-6), + L(5.576944613034537050396518509871004586039E-5), + L(1.051787760316848982655967052985391418146E-3), + L(1.102852974036687441600678598019883746959E-2), + L(5.834647019292460494254225988766702933571E-2), + L(1.290281921604364618912425380717127576529E-1), + L(7.598886310387075708640370806458926458301E-2), }; #define NQ8_16D 11 -static const long double Q8_16D[NQ8_16D + 1] = { - 1.368001558508338469503329967729951830843E-16L, - 1.034454121857542147020549303317348297289E-13L, - 3.128109209247090744354764050629381674436E-11L, - 4.957795214328501986562102573522064468671E-9L, - 4.537872468606711261992676606899273588899E-7L, - 2.493639207101727713192687060517509774182E-5L, - 8.294957278145328349785532236663051405805E-4L, - 1.646471258966713577374948205279380115839E-2L, - 1.878910092770966718491814497982191447073E-1L, - 1.152641605706170353727903052525652504075E0L, - 3.383550240669773485412333679367792932235E0L, - 3.823875252882035706910024716609908473970E0L, +static const _Float128 Q8_16D[NQ8_16D + 1] = { + L(1.368001558508338469503329967729951830843E-16), + L(1.034454121857542147020549303317348297289E-13), + L(3.128109209247090744354764050629381674436E-11), + L(4.957795214328501986562102573522064468671E-9), + L(4.537872468606711261992676606899273588899E-7), + L(2.493639207101727713192687060517509774182E-5), + L(8.294957278145328349785532236663051405805E-4), + L(1.646471258966713577374948205279380115839E-2), + L(1.878910092770966718491814497982191447073E-1), + L(1.152641605706170353727903052525652504075E0), + L(3.383550240669773485412333679367792932235E0), + L(3.823875252882035706910024716609908473970E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -447,32 +447,32 @@ static const long double Q8_16D[NQ8_16D + 1] = { Peak relative error 3.9e-35 0.125 <= 1/x <= 0.1875 */ #define NQ5_8N 10 -static const long double Q5_8N[NQ5_8N + 1] = { - 1.750399094021293722243426623211733898747E-13L, - 6.483426211748008735242909236490115050294E-11L, - 9.279430665656575457141747875716899958373E-9L, - 6.696634968526907231258534757736576340266E-7L, - 2.666560823798895649685231292142838188061E-5L, - 6.025087697259436271271562769707550594540E-4L, - 7.652807734168613251901945778921336353485E-3L, - 5.226269002589406461622551452343519078905E-2L, - 1.748390159751117658969324896330142895079E-1L, - 2.378188719097006494782174902213083589660E-1L, - 8.383984859679804095463699702165659216831E-2L, +static const _Float128 Q5_8N[NQ5_8N + 1] = { + L(1.750399094021293722243426623211733898747E-13), + L(6.483426211748008735242909236490115050294E-11), + L(9.279430665656575457141747875716899958373E-9), + L(6.696634968526907231258534757736576340266E-7), + L(2.666560823798895649685231292142838188061E-5), + L(6.025087697259436271271562769707550594540E-4), + L(7.652807734168613251901945778921336353485E-3), + L(5.226269002589406461622551452343519078905E-2), + L(1.748390159751117658969324896330142895079E-1), + L(2.378188719097006494782174902213083589660E-1), + L(8.383984859679804095463699702165659216831E-2), }; #define NQ5_8D 10 -static const long double Q5_8D[NQ5_8D + 1] = { - 2.389878229704327939008104855942987615715E-12L, - 8.926142817142546018703814194987786425099E-10L, - 1.294065862406745901206588525833274399038E-7L, - 9.524139899457666250828752185212769682191E-6L, - 3.908332488377770886091936221573123353489E-4L, - 9.250427033957236609624199884089916836748E-3L, - 1.263420066165922645975830877751588421451E-1L, - 9.692527053860420229711317379861733180654E-1L, - 3.937813834630430172221329298841520707954E0L, - 7.603126427436356534498908111445191312181E0L, - 5.670677653334105479259958485084550934305E0L, +static const _Float128 Q5_8D[NQ5_8D + 1] = { + L(2.389878229704327939008104855942987615715E-12), + L(8.926142817142546018703814194987786425099E-10), + L(1.294065862406745901206588525833274399038E-7), + L(9.524139899457666250828752185212769682191E-6), + L(3.908332488377770886091936221573123353489E-4), + L(9.250427033957236609624199884089916836748E-3), + L(1.263420066165922645975830877751588421451E-1), + L(9.692527053860420229711317379861733180654E-1), + L(3.937813834630430172221329298841520707954E0), + L(7.603126427436356534498908111445191312181E0), + L(5.670677653334105479259958485084550934305E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -481,31 +481,31 @@ static const long double Q5_8D[NQ5_8D + 1] = { Peak relative error 3.2e-35 0.1875 <= 1/x <= 0.25 */ #define NQ4_5N 10 -static const long double Q4_5N[NQ4_5N + 1] = { - 2.233870042925895644234072357400122854086E-11L, - 5.146223225761993222808463878999151699792E-9L, - 4.459114531468296461688753521109797474523E-7L, - 1.891397692931537975547242165291668056276E-5L, - 4.279519145911541776938964806470674565504E-4L, - 5.275239415656560634702073291768904783989E-3L, - 3.468698403240744801278238473898432608887E-2L, - 1.138773146337708415188856882915457888274E-1L, - 1.622717518946443013587108598334636458955E-1L, - 7.249040006390586123760992346453034628227E-2L, - 1.941595365256460232175236758506411486667E-3L, +static const _Float128 Q4_5N[NQ4_5N + 1] = { + L(2.233870042925895644234072357400122854086E-11), + L(5.146223225761993222808463878999151699792E-9), + L(4.459114531468296461688753521109797474523E-7), + L(1.891397692931537975547242165291668056276E-5), + L(4.279519145911541776938964806470674565504E-4), + L(5.275239415656560634702073291768904783989E-3), + L(3.468698403240744801278238473898432608887E-2), + L(1.138773146337708415188856882915457888274E-1), + L(1.622717518946443013587108598334636458955E-1), + L(7.249040006390586123760992346453034628227E-2), + L(1.941595365256460232175236758506411486667E-3), }; #define NQ4_5D 9 -static const long double Q4_5D[NQ4_5D + 1] = { - 3.049977232266999249626430127217988047453E-10L, - 7.120883230531035857746096928889676144099E-8L, - 6.301786064753734446784637919554359588859E-6L, - 2.762010530095069598480766869426308077192E-4L, - 6.572163250572867859316828886203406361251E-3L, - 8.752566114841221958200215255461843397776E-2L, - 6.487654992874805093499285311075289932664E-1L, - 2.576550017826654579451615283022812801435E0L, - 5.056392229924022835364779562707348096036E0L, - 4.179770081068251464907531367859072157773E0L, +static const _Float128 Q4_5D[NQ4_5D + 1] = { + L(3.049977232266999249626430127217988047453E-10), + L(7.120883230531035857746096928889676144099E-8), + L(6.301786064753734446784637919554359588859E-6), + L(2.762010530095069598480766869426308077192E-4), + L(6.572163250572867859316828886203406361251E-3), + L(8.752566114841221958200215255461843397776E-2), + L(6.487654992874805093499285311075289932664E-1), + L(2.576550017826654579451615283022812801435E0), + L(5.056392229924022835364779562707348096036E0), + L(4.179770081068251464907531367859072157773E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -514,31 +514,31 @@ static const long double Q4_5D[NQ4_5D + 1] = { Peak relative error 1.4e-36 0.25 <= 1/x <= 0.3125 */ #define NQ3r2_4N 10 -static const long double Q3r2_4N[NQ3r2_4N + 1] = { - 6.126167301024815034423262653066023684411E-10L, - 1.043969327113173261820028225053598975128E-7L, - 6.592927270288697027757438170153763220190E-6L, - 2.009103660938497963095652951912071336730E-4L, - 3.220543385492643525985862356352195896964E-3L, - 2.774405975730545157543417650436941650990E-2L, - 1.258114008023826384487378016636555041129E-1L, - 2.811724258266902502344701449984698323860E-1L, - 2.691837665193548059322831687432415014067E-1L, - 7.949087384900985370683770525312735605034E-2L, - 1.229509543620976530030153018986910810747E-3L, +static const _Float128 Q3r2_4N[NQ3r2_4N + 1] = { + L(6.126167301024815034423262653066023684411E-10), + L(1.043969327113173261820028225053598975128E-7), + L(6.592927270288697027757438170153763220190E-6), + L(2.009103660938497963095652951912071336730E-4), + L(3.220543385492643525985862356352195896964E-3), + L(2.774405975730545157543417650436941650990E-2), + L(1.258114008023826384487378016636555041129E-1), + L(2.811724258266902502344701449984698323860E-1), + L(2.691837665193548059322831687432415014067E-1), + L(7.949087384900985370683770525312735605034E-2), + L(1.229509543620976530030153018986910810747E-3), }; #define NQ3r2_4D 9 -static const long double Q3r2_4D[NQ3r2_4D + 1] = { - 8.364260446128475461539941389210166156568E-9L, - 1.451301850638956578622154585560759862764E-6L, - 9.431830010924603664244578867057141839463E-5L, - 3.004105101667433434196388593004526182741E-3L, - 5.148157397848271739710011717102773780221E-2L, - 4.901089301726939576055285374953887874895E-1L, - 2.581760991981709901216967665934142240346E0L, - 7.257105880775059281391729708630912791847E0L, - 1.006014717326362868007913423810737369312E1L, - 5.879416600465399514404064187445293212470E0L, +static const _Float128 Q3r2_4D[NQ3r2_4D + 1] = { + L(8.364260446128475461539941389210166156568E-9), + L(1.451301850638956578622154585560759862764E-6), + L(9.431830010924603664244578867057141839463E-5), + L(3.004105101667433434196388593004526182741E-3), + L(5.148157397848271739710011717102773780221E-2), + L(4.901089301726939576055285374953887874895E-1), + L(2.581760991981709901216967665934142240346E0), + L(7.257105880775059281391729708630912791847E0), + L(1.006014717326362868007913423810737369312E1), + L(5.879416600465399514404064187445293212470E0), /* 1.000000000000000000000000000000000000000E0*/ }; @@ -547,30 +547,30 @@ static const long double Q3r2_4D[NQ3r2_4D + 1] = { Peak relative error 3.8e-36 0.3125 <= 1/x <= 0.375 */ #define NQ2r7_3r2N 9 -static const long double Q2r7_3r2N[NQ2r7_3r2N + 1] = { - 7.584861620402450302063691901886141875454E-8L, - 9.300939338814216296064659459966041794591E-6L, - 4.112108906197521696032158235392604947895E-4L, - 8.515168851578898791897038357239630654431E-3L, - 8.971286321017307400142720556749573229058E-2L, - 4.885856732902956303343015636331874194498E-1L, - 1.334506268733103291656253500506406045846E0L, - 1.681207956863028164179042145803851824654E0L, - 8.165042692571721959157677701625853772271E-1L, - 9.805848115375053300608712721986235900715E-2L, +static const _Float128 Q2r7_3r2N[NQ2r7_3r2N + 1] = { + L(7.584861620402450302063691901886141875454E-8), + L(9.300939338814216296064659459966041794591E-6), + L(4.112108906197521696032158235392604947895E-4), + L(8.515168851578898791897038357239630654431E-3), + L(8.971286321017307400142720556749573229058E-2), + L(4.885856732902956303343015636331874194498E-1), + L(1.334506268733103291656253500506406045846E0), + L(1.681207956863028164179042145803851824654E0), + L(8.165042692571721959157677701625853772271E-1), + L(9.805848115375053300608712721986235900715E-2), }; #define NQ2r7_3r2D 9 -static const long double Q2r7_3r2D[NQ2r7_3r2D + 1] = { - 1.035586492113036586458163971239438078160E-6L, - 1.301999337731768381683593636500979713689E-4L, - 5.993695702564527062553071126719088859654E-3L, - 1.321184892887881883489141186815457808785E-1L, - 1.528766555485015021144963194165165083312E0L, - 9.561463309176490874525827051566494939295E0L, - 3.203719484883967351729513662089163356911E1L, - 5.497294687660930446641539152123568668447E1L, - 4.391158169390578768508675452986948391118E1L, - 1.347836630730048077907818943625789418378E1L, +static const _Float128 Q2r7_3r2D[NQ2r7_3r2D + 1] = { + L(1.035586492113036586458163971239438078160E-6), + L(1.301999337731768381683593636500979713689E-4), + L(5.993695702564527062553071126719088859654E-3), + L(1.321184892887881883489141186815457808785E-1), + L(1.528766555485015021144963194165165083312E0), + L(9.561463309176490874525827051566494939295E0), + L(3.203719484883967351729513662089163356911E1), + L(5.497294687660930446641539152123568668447E1), + L(4.391158169390578768508675452986948391118E1), + L(1.347836630730048077907818943625789418378E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -579,29 +579,29 @@ static const long double Q2r7_3r2D[NQ2r7_3r2D + 1] = { Peak relative error 2.2e-35 0.375 <= 1/x <= 0.4375 */ #define NQ2r3_2r7N 9 -static const long double Q2r3_2r7N[NQ2r3_2r7N + 1] = { - 4.455027774980750211349941766420190722088E-7L, - 4.031998274578520170631601850866780366466E-5L, - 1.273987274325947007856695677491340636339E-3L, - 1.818754543377448509897226554179659122873E-2L, - 1.266748858326568264126353051352269875352E-1L, - 4.327578594728723821137731555139472880414E-1L, - 6.892532471436503074928194969154192615359E-1L, - 4.490775818438716873422163588640262036506E-1L, - 8.649615949297322440032000346117031581572E-2L, - 7.261345286655345047417257611469066147561E-4L, +static const _Float128 Q2r3_2r7N[NQ2r3_2r7N + 1] = { + L(4.455027774980750211349941766420190722088E-7), + L(4.031998274578520170631601850866780366466E-5), + L(1.273987274325947007856695677491340636339E-3), + L(1.818754543377448509897226554179659122873E-2), + L(1.266748858326568264126353051352269875352E-1), + L(4.327578594728723821137731555139472880414E-1), + L(6.892532471436503074928194969154192615359E-1), + L(4.490775818438716873422163588640262036506E-1), + L(8.649615949297322440032000346117031581572E-2), + L(7.261345286655345047417257611469066147561E-4), }; #define NQ2r3_2r7D 8 -static const long double Q2r3_2r7D[NQ2r3_2r7D + 1] = { - 6.082600739680555266312417978064954793142E-6L, - 5.693622538165494742945717226571441747567E-4L, - 1.901625907009092204458328768129666975975E-2L, - 2.958689532697857335456896889409923371570E-1L, - 2.343124711045660081603809437993368799568E0L, - 9.665894032187458293568704885528192804376E0L, - 2.035273104990617136065743426322454881353E1L, - 2.044102010478792896815088858740075165531E1L, - 8.445937177863155827844146643468706599304E0L, +static const _Float128 Q2r3_2r7D[NQ2r3_2r7D + 1] = { + L(6.082600739680555266312417978064954793142E-6), + L(5.693622538165494742945717226571441747567E-4), + L(1.901625907009092204458328768129666975975E-2), + L(2.958689532697857335456896889409923371570E-1), + L(2.343124711045660081603809437993368799568E0), + L(9.665894032187458293568704885528192804376E0), + L(2.035273104990617136065743426322454881353E1), + L(2.044102010478792896815088858740075165531E1), + L(8.445937177863155827844146643468706599304E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -610,39 +610,39 @@ static const long double Q2r3_2r7D[NQ2r3_2r7D + 1] = { Peak relative error 3.1e-36 0.4375 <= 1/x <= 0.5 */ #define NQ2_2r3N 9 -static const long double Q2_2r3N[NQ2_2r3N + 1] = { - 2.817566786579768804844367382809101929314E-6L, - 2.122772176396691634147024348373539744935E-4L, - 5.501378031780457828919593905395747517585E-3L, - 6.355374424341762686099147452020466524659E-2L, - 3.539652320122661637429658698954748337223E-1L, - 9.571721066119617436343740541777014319695E-1L, - 1.196258777828426399432550698612171955305E0L, - 6.069388659458926158392384709893753793967E-1L, - 9.026746127269713176512359976978248763621E-2L, - 5.317668723070450235320878117210807236375E-4L, +static const _Float128 Q2_2r3N[NQ2_2r3N + 1] = { + L(2.817566786579768804844367382809101929314E-6), + L(2.122772176396691634147024348373539744935E-4), + L(5.501378031780457828919593905395747517585E-3), + L(6.355374424341762686099147452020466524659E-2), + L(3.539652320122661637429658698954748337223E-1), + L(9.571721066119617436343740541777014319695E-1), + L(1.196258777828426399432550698612171955305E0), + L(6.069388659458926158392384709893753793967E-1), + L(9.026746127269713176512359976978248763621E-2), + L(5.317668723070450235320878117210807236375E-4), }; #define NQ2_2r3D 8 -static const long double Q2_2r3D[NQ2_2r3D + 1] = { - 3.846924354014260866793741072933159380158E-5L, - 3.017562820057704325510067178327449946763E-3L, - 8.356305620686867949798885808540444210935E-2L, - 1.068314930499906838814019619594424586273E0L, - 6.900279623894821067017966573640732685233E0L, - 2.307667390886377924509090271780839563141E1L, - 3.921043465412723970791036825401273528513E1L, - 3.167569478939719383241775717095729233436E1L, - 1.051023841699200920276198346301543665909E1L, +static const _Float128 Q2_2r3D[NQ2_2r3D + 1] = { + L(3.846924354014260866793741072933159380158E-5), + L(3.017562820057704325510067178327449946763E-3), + L(8.356305620686867949798885808540444210935E-2), + L(1.068314930499906838814019619594424586273E0), + L(6.900279623894821067017966573640732685233E0), + L(2.307667390886377924509090271780839563141E1), + L(3.921043465412723970791036825401273528513E1), + L(3.167569478939719383241775717095729233436E1), + L(1.051023841699200920276198346301543665909E1), /* 1.000000000000000000000000000000000000000E0*/ }; /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ -static long double -neval (long double x, const long double *p, int n) +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = *p--; @@ -657,10 +657,10 @@ neval (long double x, const long double *p, int n) /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ -static long double -deval (long double x, const long double *p, int n) +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = x + *p--; @@ -675,31 +675,31 @@ deval (long double x, const long double *p, int n) /* Bessel function of the first kind, order zero. */ -long double -__ieee754_j0l (long double x) +_Float128 +__ieee754_j0l (_Float128 x) { - long double xx, xinv, z, p, q, c, s, cc, ss; + _Float128 xx, xinv, z, p, q, c, s, cc, ss; if (! isfinite (x)) { if (x != x) - return x; + return x + x; else - return 0.0L; + return 0; } - if (x == 0.0L) - return 1.0L; + if (x == 0) + return 1; xx = fabsl (x); - if (xx <= 2.0L) + if (xx <= 2) { - if (xx < 0x1p-57L) - return 1.0L; + if (xx < L(0x1p-57)) + return 1; /* 0 <= x <= 2 */ z = xx * xx; p = z * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D); - p -= 0.25L * z; - p += 1.0L; + p -= L(0.25) * z; + p += 1; return p; } @@ -713,7 +713,7 @@ __ieee754_j0l (long double x) __sincosl (xx, &s, &c); ss = s - c; cc = s + c; - if (xx <= LDBL_MAX / 2.0L) + if (xx <= LDBL_MAX / 2) { z = -__cosl (xx + xx); if ((s * c) < 0) @@ -722,10 +722,10 @@ __ieee754_j0l (long double x) ss = z / cc; } - if (xx > 0x1p256L) - return ONEOSQPI * cc / __ieee754_sqrtl (xx); + if (xx > L(0x1p256)) + return ONEOSQPI * cc / sqrtl (xx); - xinv = 1.0L / xx; + xinv = 1 / xx; z = xinv * xinv; if (xinv <= 0.25) { @@ -783,10 +783,10 @@ __ieee754_j0l (long double x) q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); } } - p = 1.0L + z * p; + p = 1 + z * p; q = z * xinv * q; - q = q - 0.125L * xinv; - z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx); + q = q - L(0.125) * xinv; + z = ONEOSQPI * (p * cc - q * ss) / sqrtl (xx); return z; } strong_alias (__ieee754_j0l, __j0l_finite) @@ -796,55 +796,50 @@ strong_alias (__ieee754_j0l, __j0l_finite) Peak absolute error 1.7e-36 (relative where Y0 > 1) 0 <= x <= 2 */ #define NY0_2N 7 -static long double Y0_2N[NY0_2N + 1] = { - -1.062023609591350692692296993537002558155E19L, - 2.542000883190248639104127452714966858866E19L, - -1.984190771278515324281415820316054696545E18L, - 4.982586044371592942465373274440222033891E16L, - -5.529326354780295177243773419090123407550E14L, - 3.013431465522152289279088265336861140391E12L, - -7.959436160727126750732203098982718347785E9L, - 8.230845651379566339707130644134372793322E6L, +static const _Float128 Y0_2N[NY0_2N + 1] = { + L(-1.062023609591350692692296993537002558155E19), + L(2.542000883190248639104127452714966858866E19), + L(-1.984190771278515324281415820316054696545E18), + L(4.982586044371592942465373274440222033891E16), + L(-5.529326354780295177243773419090123407550E14), + L(3.013431465522152289279088265336861140391E12), + L(-7.959436160727126750732203098982718347785E9), + L(8.230845651379566339707130644134372793322E6), }; #define NY0_2D 7 -static long double Y0_2D[NY0_2D + 1] = { - 1.438972634353286978700329883122253752192E20L, - 1.856409101981569254247700169486907405500E18L, - 1.219693352678218589553725579802986255614E16L, - 5.389428943282838648918475915779958097958E13L, - 1.774125762108874864433872173544743051653E11L, - 4.522104832545149534808218252434693007036E8L, - 8.872187401232943927082914504125234454930E5L, - 1.251945613186787532055610876304669413955E3L, +static const _Float128 Y0_2D[NY0_2D + 1] = { + L(1.438972634353286978700329883122253752192E20), + L(1.856409101981569254247700169486907405500E18), + L(1.219693352678218589553725579802986255614E16), + L(5.389428943282838648918475915779958097958E13), + L(1.774125762108874864433872173544743051653E11), + L(4.522104832545149534808218252434693007036E8), + L(8.872187401232943927082914504125234454930E5), + L(1.251945613186787532055610876304669413955E3), /* 1.000000000000000000000000000000000000000E0 */ }; -static const long double U0 = -7.3804295108687225274343927948483016310862e-02L; +static const _Float128 U0 = L(-7.3804295108687225274343927948483016310862e-02); /* Bessel function of the second kind, order zero. */ -long double - __ieee754_y0l(long double x) +_Float128 + __ieee754_y0l(_Float128 x) { - long double xx, xinv, z, p, q, c, s, cc, ss; + _Float128 xx, xinv, z, p, q, c, s, cc, ss; if (! isfinite (x)) + return 1 / (x + x * x); + if (x <= 0) { - if (x != x) - return x; - else - return 0.0L; - } - if (x <= 0.0L) - { - if (x < 0.0L) + if (x < 0) return (zero / (zero * x)); - return -HUGE_VALL + x; + return -1 / zero; /* -inf and divide by zero exception. */ } xx = fabsl (x); if (xx <= 0x1p-57) return U0 + TWOOPI * __ieee754_logl (x); - if (xx <= 2.0L) + if (xx <= 2) { /* 0 <= x <= 2 */ z = xx * xx; @@ -863,7 +858,7 @@ long double __sincosl (x, &s, &c); ss = s - c; cc = s + c; - if (xx <= LDBL_MAX / 2.0L) + if (xx <= LDBL_MAX / 2) { z = -__cosl (x + x); if ((s * c) < 0) @@ -872,10 +867,10 @@ long double ss = z / cc; } - if (xx > 0x1p256L) - return ONEOSQPI * ss / __ieee754_sqrtl (x); + if (xx > L(0x1p256)) + return ONEOSQPI * ss / sqrtl (x); - xinv = 1.0L / xx; + xinv = 1 / xx; z = xinv * xinv; if (xinv <= 0.25) { @@ -933,10 +928,10 @@ long double q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); } } - p = 1.0L + z * p; + p = 1 + z * p; q = z * xinv * q; - q = q - 0.125L * xinv; - z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x); + q = q - L(0.125) * xinv; + z = ONEOSQPI * (p * ss + q * cc) / sqrtl (x); return z; } strong_alias (__ieee754_y0l, __y0l_finite) diff --git a/sysdeps/ieee754/ldbl-128/e_j1l.c b/sysdeps/ieee754/ldbl-128/e_j1l.c index f5b04c073d..e6f46f52e9 100644 --- a/sysdeps/ieee754/ldbl-128/e_j1l.c +++ b/sysdeps/ieee754/ldbl-128/e_j1l.c @@ -98,36 +98,37 @@ #include <errno.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> #include <float.h> /* 1 / sqrt(pi) */ -static const long double ONEOSQPI = 5.6418958354775628694807945156077258584405E-1L; +static const _Float128 ONEOSQPI = L(5.6418958354775628694807945156077258584405E-1); /* 2 / pi */ -static const long double TWOOPI = 6.3661977236758134307553505349005744813784E-1L; -static const long double zero = 0.0L; +static const _Float128 TWOOPI = L(6.3661977236758134307553505349005744813784E-1); +static const _Float128 zero = 0; /* J1(x) = .5x + x x^2 R(x^2) Peak relative error 1.9e-35 0 <= x <= 2 */ #define NJ0_2N 6 -static const long double J0_2N[NJ0_2N + 1] = { - -5.943799577386942855938508697619735179660E16L, - 1.812087021305009192259946997014044074711E15L, - -2.761698314264509665075127515729146460895E13L, - 2.091089497823600978949389109350658815972E11L, - -8.546413231387036372945453565654130054307E8L, - 1.797229225249742247475464052741320612261E6L, - -1.559552840946694171346552770008812083969E3L +static const _Float128 J0_2N[NJ0_2N + 1] = { + L(-5.943799577386942855938508697619735179660E16), + L(1.812087021305009192259946997014044074711E15), + L(-2.761698314264509665075127515729146460895E13), + L(2.091089497823600978949389109350658815972E11), + L(-8.546413231387036372945453565654130054307E8), + L(1.797229225249742247475464052741320612261E6), + L(-1.559552840946694171346552770008812083969E3) }; #define NJ0_2D 6 -static const long double J0_2D[NJ0_2D + 1] = { - 9.510079323819108569501613916191477479397E17L, - 1.063193817503280529676423936545854693915E16L, - 5.934143516050192600795972192791775226920E13L, - 2.168000911950620999091479265214368352883E11L, - 5.673775894803172808323058205986256928794E8L, - 1.080329960080981204840966206372671147224E6L, - 1.411951256636576283942477881535283304912E3L, +static const _Float128 J0_2D[NJ0_2D + 1] = { + L(9.510079323819108569501613916191477479397E17), + L(1.063193817503280529676423936545854693915E16), + L(5.934143516050192600795972192791775226920E13), + L(2.168000911950620999091479265214368352883E11), + L(5.673775894803172808323058205986256928794E8), + L(1.080329960080981204840966206372671147224E6), + L(1.411951256636576283942477881535283304912E3), /* 1.000000000000000000000000000000000000000E0L */ }; @@ -135,30 +136,30 @@ static const long double J0_2D[NJ0_2D + 1] = { 0 <= 1/x <= .0625 Peak relative error 3.6e-36 */ #define NP16_IN 9 -static const long double P16_IN[NP16_IN + 1] = { - 5.143674369359646114999545149085139822905E-16L, - 4.836645664124562546056389268546233577376E-13L, - 1.730945562285804805325011561498453013673E-10L, - 3.047976856147077889834905908605310585810E-8L, - 2.855227609107969710407464739188141162386E-6L, - 1.439362407936705484122143713643023998457E-4L, - 3.774489768532936551500999699815873422073E-3L, - 4.723962172984642566142399678920790598426E-2L, - 2.359289678988743939925017240478818248735E-1L, - 3.032580002220628812728954785118117124520E-1L, +static const _Float128 P16_IN[NP16_IN + 1] = { + L(5.143674369359646114999545149085139822905E-16), + L(4.836645664124562546056389268546233577376E-13), + L(1.730945562285804805325011561498453013673E-10), + L(3.047976856147077889834905908605310585810E-8), + L(2.855227609107969710407464739188141162386E-6), + L(1.439362407936705484122143713643023998457E-4), + L(3.774489768532936551500999699815873422073E-3), + L(4.723962172984642566142399678920790598426E-2), + L(2.359289678988743939925017240478818248735E-1), + L(3.032580002220628812728954785118117124520E-1), }; #define NP16_ID 9 -static const long double P16_ID[NP16_ID + 1] = { - 4.389268795186898018132945193912677177553E-15L, - 4.132671824807454334388868363256830961655E-12L, - 1.482133328179508835835963635130894413136E-9L, - 2.618941412861122118906353737117067376236E-7L, - 2.467854246740858470815714426201888034270E-5L, - 1.257192927368839847825938545925340230490E-3L, - 3.362739031941574274949719324644120720341E-2L, - 4.384458231338934105875343439265370178858E-1L, - 2.412830809841095249170909628197264854651E0L, - 4.176078204111348059102962617368214856874E0L, +static const _Float128 P16_ID[NP16_ID + 1] = { + L(4.389268795186898018132945193912677177553E-15), + L(4.132671824807454334388868363256830961655E-12), + L(1.482133328179508835835963635130894413136E-9), + L(2.618941412861122118906353737117067376236E-7), + L(2.467854246740858470815714426201888034270E-5), + L(1.257192927368839847825938545925340230490E-3), + L(3.362739031941574274949719324644120720341E-2), + L(4.384458231338934105875343439265370178858E-1), + L(2.412830809841095249170909628197264854651E0), + L(4.176078204111348059102962617368214856874E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -166,33 +167,33 @@ static const long double P16_ID[NP16_ID + 1] = { 0.0625 <= 1/x <= 0.125 Peak relative error 1.9e-36 */ #define NP8_16N 11 -static const long double P8_16N[NP8_16N + 1] = { - 2.984612480763362345647303274082071598135E-16L, - 1.923651877544126103941232173085475682334E-13L, - 4.881258879388869396043760693256024307743E-11L, - 6.368866572475045408480898921866869811889E-9L, - 4.684818344104910450523906967821090796737E-7L, - 2.005177298271593587095982211091300382796E-5L, - 4.979808067163957634120681477207147536182E-4L, - 6.946005761642579085284689047091173581127E-3L, - 5.074601112955765012750207555985299026204E-2L, - 1.698599455896180893191766195194231825379E-1L, - 1.957536905259237627737222775573623779638E-1L, - 2.991314703282528370270179989044994319374E-2L, +static const _Float128 P8_16N[NP8_16N + 1] = { + L(2.984612480763362345647303274082071598135E-16), + L(1.923651877544126103941232173085475682334E-13), + L(4.881258879388869396043760693256024307743E-11), + L(6.368866572475045408480898921866869811889E-9), + L(4.684818344104910450523906967821090796737E-7), + L(2.005177298271593587095982211091300382796E-5), + L(4.979808067163957634120681477207147536182E-4), + L(6.946005761642579085284689047091173581127E-3), + L(5.074601112955765012750207555985299026204E-2), + L(1.698599455896180893191766195194231825379E-1), + L(1.957536905259237627737222775573623779638E-1), + L(2.991314703282528370270179989044994319374E-2), }; #define NP8_16D 10 -static const long double P8_16D[NP8_16D + 1] = { - 2.546869316918069202079580939942463010937E-15L, - 1.644650111942455804019788382157745229955E-12L, - 4.185430770291694079925607420808011147173E-10L, - 5.485331966975218025368698195861074143153E-8L, - 4.062884421686912042335466327098932678905E-6L, - 1.758139661060905948870523641319556816772E-4L, - 4.445143889306356207566032244985607493096E-3L, - 6.391901016293512632765621532571159071158E-2L, - 4.933040207519900471177016015718145795434E-1L, - 1.839144086168947712971630337250761842976E0L, - 2.715120873995490920415616716916149586579E0L, +static const _Float128 P8_16D[NP8_16D + 1] = { + L(2.546869316918069202079580939942463010937E-15), + L(1.644650111942455804019788382157745229955E-12), + L(4.185430770291694079925607420808011147173E-10), + L(5.485331966975218025368698195861074143153E-8), + L(4.062884421686912042335466327098932678905E-6), + L(1.758139661060905948870523641319556816772E-4), + L(4.445143889306356207566032244985607493096E-3), + L(6.391901016293512632765621532571159071158E-2), + L(4.933040207519900471177016015718145795434E-1), + L(1.839144086168947712971630337250761842976E0), + L(2.715120873995490920415616716916149586579E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -200,32 +201,32 @@ static const long double P8_16D[NP8_16D + 1] = { 0.125 <= 1/x <= 0.1875 Peak relative error 1.3e-36 */ #define NP5_8N 10 -static const long double P5_8N[NP5_8N + 1] = { - 2.837678373978003452653763806968237227234E-12L, - 9.726641165590364928442128579282742354806E-10L, - 1.284408003604131382028112171490633956539E-7L, - 8.524624695868291291250573339272194285008E-6L, - 3.111516908953172249853673787748841282846E-4L, - 6.423175156126364104172801983096596409176E-3L, - 7.430220589989104581004416356260692450652E-2L, - 4.608315409833682489016656279567605536619E-1L, - 1.396870223510964882676225042258855977512E0L, - 1.718500293904122365894630460672081526236E0L, - 5.465927698800862172307352821870223855365E-1L +static const _Float128 P5_8N[NP5_8N + 1] = { + L(2.837678373978003452653763806968237227234E-12), + L(9.726641165590364928442128579282742354806E-10), + L(1.284408003604131382028112171490633956539E-7), + L(8.524624695868291291250573339272194285008E-6), + L(3.111516908953172249853673787748841282846E-4), + L(6.423175156126364104172801983096596409176E-3), + L(7.430220589989104581004416356260692450652E-2), + L(4.608315409833682489016656279567605536619E-1), + L(1.396870223510964882676225042258855977512E0), + L(1.718500293904122365894630460672081526236E0), + L(5.465927698800862172307352821870223855365E-1) }; #define NP5_8D 10 -static const long double P5_8D[NP5_8D + 1] = { - 2.421485545794616609951168511612060482715E-11L, - 8.329862750896452929030058039752327232310E-9L, - 1.106137992233383429630592081375289010720E-6L, - 7.405786153760681090127497796448503306939E-5L, - 2.740364785433195322492093333127633465227E-3L, - 5.781246470403095224872243564165254652198E-2L, - 6.927711353039742469918754111511109983546E-1L, - 4.558679283460430281188304515922826156690E0L, - 1.534468499844879487013168065728837900009E1L, - 2.313927430889218597919624843161569422745E1L, - 1.194506341319498844336768473218382828637E1L, +static const _Float128 P5_8D[NP5_8D + 1] = { + L(2.421485545794616609951168511612060482715E-11), + L(8.329862750896452929030058039752327232310E-9), + L(1.106137992233383429630592081375289010720E-6), + L(7.405786153760681090127497796448503306939E-5), + L(2.740364785433195322492093333127633465227E-3), + L(5.781246470403095224872243564165254652198E-2), + L(6.927711353039742469918754111511109983546E-1), + L(4.558679283460430281188304515922826156690E0), + L(1.534468499844879487013168065728837900009E1), + L(2.313927430889218597919624843161569422745E1), + L(1.194506341319498844336768473218382828637E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -233,31 +234,31 @@ static const long double P5_8D[NP5_8D + 1] = { Peak relative error 1.4e-36 0.1875 <= 1/x <= 0.25 */ #define NP4_5N 10 -static const long double P4_5N[NP4_5N + 1] = { - 1.846029078268368685834261260420933914621E-10L, - 3.916295939611376119377869680335444207768E-8L, - 3.122158792018920627984597530935323997312E-6L, - 1.218073444893078303994045653603392272450E-4L, - 2.536420827983485448140477159977981844883E-3L, - 2.883011322006690823959367922241169171315E-2L, - 1.755255190734902907438042414495469810830E-1L, - 5.379317079922628599870898285488723736599E-1L, - 7.284904050194300773890303361501726561938E-1L, - 3.270110346613085348094396323925000362813E-1L, - 1.804473805689725610052078464951722064757E-2L, +static const _Float128 P4_5N[NP4_5N + 1] = { + L(1.846029078268368685834261260420933914621E-10), + L(3.916295939611376119377869680335444207768E-8), + L(3.122158792018920627984597530935323997312E-6), + L(1.218073444893078303994045653603392272450E-4), + L(2.536420827983485448140477159977981844883E-3), + L(2.883011322006690823959367922241169171315E-2), + L(1.755255190734902907438042414495469810830E-1), + L(5.379317079922628599870898285488723736599E-1), + L(7.284904050194300773890303361501726561938E-1), + L(3.270110346613085348094396323925000362813E-1), + L(1.804473805689725610052078464951722064757E-2), }; #define NP4_5D 9 -static const long double P4_5D[NP4_5D + 1] = { - 1.575278146806816970152174364308980863569E-9L, - 3.361289173657099516191331123405675054321E-7L, - 2.704692281550877810424745289838790693708E-5L, - 1.070854930483999749316546199273521063543E-3L, - 2.282373093495295842598097265627962125411E-2L, - 2.692025460665354148328762368240343249830E-1L, - 1.739892942593664447220951225734811133759E0L, - 5.890727576752230385342377570386657229324E0L, - 9.517442287057841500750256954117735128153E0L, - 6.100616353935338240775363403030137736013E0L, +static const _Float128 P4_5D[NP4_5D + 1] = { + L(1.575278146806816970152174364308980863569E-9), + L(3.361289173657099516191331123405675054321E-7), + L(2.704692281550877810424745289838790693708E-5), + L(1.070854930483999749316546199273521063543E-3), + L(2.282373093495295842598097265627962125411E-2), + L(2.692025460665354148328762368240343249830E-1), + L(1.739892942593664447220951225734811133759E0), + L(5.890727576752230385342377570386657229324E0), + L(9.517442287057841500750256954117735128153E0), + L(6.100616353935338240775363403030137736013E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -265,30 +266,30 @@ static const long double P4_5D[NP4_5D + 1] = { Peak relative error 3.0e-36 0.25 <= 1/x <= 0.3125 */ #define NP3r2_4N 9 -static const long double P3r2_4N[NP3r2_4N + 1] = { - 8.240803130988044478595580300846665863782E-8L, - 1.179418958381961224222969866406483744580E-5L, - 6.179787320956386624336959112503824397755E-4L, - 1.540270833608687596420595830747166658383E-2L, - 1.983904219491512618376375619598837355076E-1L, - 1.341465722692038870390470651608301155565E0L, - 4.617865326696612898792238245990854646057E0L, - 7.435574801812346424460233180412308000587E0L, - 4.671327027414635292514599201278557680420E0L, - 7.299530852495776936690976966995187714739E-1L, +static const _Float128 P3r2_4N[NP3r2_4N + 1] = { + L(8.240803130988044478595580300846665863782E-8), + L(1.179418958381961224222969866406483744580E-5), + L(6.179787320956386624336959112503824397755E-4), + L(1.540270833608687596420595830747166658383E-2), + L(1.983904219491512618376375619598837355076E-1), + L(1.341465722692038870390470651608301155565E0), + L(4.617865326696612898792238245990854646057E0), + L(7.435574801812346424460233180412308000587E0), + L(4.671327027414635292514599201278557680420E0), + L(7.299530852495776936690976966995187714739E-1), }; #define NP3r2_4D 9 -static const long double P3r2_4D[NP3r2_4D + 1] = { - 7.032152009675729604487575753279187576521E-7L, - 1.015090352324577615777511269928856742848E-4L, - 5.394262184808448484302067955186308730620E-3L, - 1.375291438480256110455809354836988584325E-1L, - 1.836247144461106304788160919310404376670E0L, - 1.314378564254376655001094503090935880349E1L, - 4.957184590465712006934452500894672343488E1L, - 9.287394244300647738855415178790263465398E1L, - 7.652563275535900609085229286020552768399E1L, - 2.147042473003074533150718117770093209096E1L, +static const _Float128 P3r2_4D[NP3r2_4D + 1] = { + L(7.032152009675729604487575753279187576521E-7), + L(1.015090352324577615777511269928856742848E-4), + L(5.394262184808448484302067955186308730620E-3), + L(1.375291438480256110455809354836988584325E-1), + L(1.836247144461106304788160919310404376670E0), + L(1.314378564254376655001094503090935880349E1), + L(4.957184590465712006934452500894672343488E1), + L(9.287394244300647738855415178790263465398E1), + L(7.652563275535900609085229286020552768399E1), + L(2.147042473003074533150718117770093209096E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -296,29 +297,29 @@ static const long double P3r2_4D[NP3r2_4D + 1] = { Peak relative error 1.0e-35 0.3125 <= 1/x <= 0.375 */ #define NP2r7_3r2N 9 -static const long double P2r7_3r2N[NP2r7_3r2N + 1] = { - 4.599033469240421554219816935160627085991E-7L, - 4.665724440345003914596647144630893997284E-5L, - 1.684348845667764271596142716944374892756E-3L, - 2.802446446884455707845985913454440176223E-2L, - 2.321937586453963310008279956042545173930E-1L, - 9.640277413988055668692438709376437553804E-1L, - 1.911021064710270904508663334033003246028E0L, - 1.600811610164341450262992138893970224971E0L, - 4.266299218652587901171386591543457861138E-1L, - 1.316470424456061252962568223251247207325E-2L, +static const _Float128 P2r7_3r2N[NP2r7_3r2N + 1] = { + L(4.599033469240421554219816935160627085991E-7), + L(4.665724440345003914596647144630893997284E-5), + L(1.684348845667764271596142716944374892756E-3), + L(2.802446446884455707845985913454440176223E-2), + L(2.321937586453963310008279956042545173930E-1), + L(9.640277413988055668692438709376437553804E-1), + L(1.911021064710270904508663334033003246028E0), + L(1.600811610164341450262992138893970224971E0), + L(4.266299218652587901171386591543457861138E-1), + L(1.316470424456061252962568223251247207325E-2), }; #define NP2r7_3r2D 8 -static const long double P2r7_3r2D[NP2r7_3r2D + 1] = { - 3.924508608545520758883457108453520099610E-6L, - 4.029707889408829273226495756222078039823E-4L, - 1.484629715787703260797886463307469600219E-2L, - 2.553136379967180865331706538897231588685E-1L, - 2.229457223891676394409880026887106228740E0L, - 1.005708903856384091956550845198392117318E1L, - 2.277082659664386953166629360352385889558E1L, - 2.384726835193630788249826630376533988245E1L, - 9.700989749041320895890113781610939632410E0L, +static const _Float128 P2r7_3r2D[NP2r7_3r2D + 1] = { + L(3.924508608545520758883457108453520099610E-6), + L(4.029707889408829273226495756222078039823E-4), + L(1.484629715787703260797886463307469600219E-2), + L(2.553136379967180865331706538897231588685E-1), + L(2.229457223891676394409880026887106228740E0), + L(1.005708903856384091956550845198392117318E1), + L(2.277082659664386953166629360352385889558E1), + L(2.384726835193630788249826630376533988245E1), + L(9.700989749041320895890113781610939632410E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -326,29 +327,29 @@ static const long double P2r7_3r2D[NP2r7_3r2D + 1] = { Peak relative error 1.7e-36 0.3125 <= 1/x <= 0.4375 */ #define NP2r3_2r7N 9 -static const long double P2r3_2r7N[NP2r3_2r7N + 1] = { - 3.916766777108274628543759603786857387402E-6L, - 3.212176636756546217390661984304645137013E-4L, - 9.255768488524816445220126081207248947118E-3L, - 1.214853146369078277453080641911700735354E-1L, - 7.855163309847214136198449861311404633665E-1L, - 2.520058073282978403655488662066019816540E0L, - 3.825136484837545257209234285382183711466E0L, - 2.432569427554248006229715163865569506873E0L, - 4.877934835018231178495030117729800489743E-1L, - 1.109902737860249670981355149101343427885E-2L, +static const _Float128 P2r3_2r7N[NP2r3_2r7N + 1] = { + L(3.916766777108274628543759603786857387402E-6), + L(3.212176636756546217390661984304645137013E-4), + L(9.255768488524816445220126081207248947118E-3), + L(1.214853146369078277453080641911700735354E-1), + L(7.855163309847214136198449861311404633665E-1), + L(2.520058073282978403655488662066019816540E0), + L(3.825136484837545257209234285382183711466E0), + L(2.432569427554248006229715163865569506873E0), + L(4.877934835018231178495030117729800489743E-1), + L(1.109902737860249670981355149101343427885E-2), }; #define NP2r3_2r7D 8 -static const long double P2r3_2r7D[NP2r3_2r7D + 1] = { - 3.342307880794065640312646341190547184461E-5L, - 2.782182891138893201544978009012096558265E-3L, - 8.221304931614200702142049236141249929207E-2L, - 1.123728246291165812392918571987858010949E0L, - 7.740482453652715577233858317133423434590E0L, - 2.737624677567945952953322566311201919139E1L, - 4.837181477096062403118304137851260715475E1L, - 3.941098643468580791437772701093795299274E1L, - 1.245821247166544627558323920382547533630E1L, +static const _Float128 P2r3_2r7D[NP2r3_2r7D + 1] = { + L(3.342307880794065640312646341190547184461E-5), + L(2.782182891138893201544978009012096558265E-3), + L(8.221304931614200702142049236141249929207E-2), + L(1.123728246291165812392918571987858010949E0), + L(7.740482453652715577233858317133423434590E0), + L(2.737624677567945952953322566311201919139E1), + L(4.837181477096062403118304137851260715475E1), + L(3.941098643468580791437772701093795299274E1), + L(1.245821247166544627558323920382547533630E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -356,28 +357,28 @@ static const long double P2r3_2r7D[NP2r3_2r7D + 1] = { Peak relative error 1.7e-35 0.4375 <= 1/x <= 0.5 */ #define NP2_2r3N 8 -static const long double P2_2r3N[NP2_2r3N + 1] = { - 3.397930802851248553545191160608731940751E-4L, - 2.104020902735482418784312825637833698217E-2L, - 4.442291771608095963935342749477836181939E-1L, - 4.131797328716583282869183304291833754967E0L, - 1.819920169779026500146134832455189917589E1L, - 3.781779616522937565300309684282401791291E1L, - 3.459605449728864218972931220783543410347E1L, - 1.173594248397603882049066603238568316561E1L, - 9.455702270242780642835086549285560316461E-1L, +static const _Float128 P2_2r3N[NP2_2r3N + 1] = { + L(3.397930802851248553545191160608731940751E-4), + L(2.104020902735482418784312825637833698217E-2), + L(4.442291771608095963935342749477836181939E-1), + L(4.131797328716583282869183304291833754967E0), + L(1.819920169779026500146134832455189917589E1), + L(3.781779616522937565300309684282401791291E1), + L(3.459605449728864218972931220783543410347E1), + L(1.173594248397603882049066603238568316561E1), + L(9.455702270242780642835086549285560316461E-1), }; #define NP2_2r3D 8 -static const long double P2_2r3D[NP2_2r3D + 1] = { - 2.899568897241432883079888249845707400614E-3L, - 1.831107138190848460767699919531132426356E-1L, - 3.999350044057883839080258832758908825165E0L, - 3.929041535867957938340569419874195303712E1L, - 1.884245613422523323068802689915538908291E2L, - 4.461469948819229734353852978424629815929E2L, - 5.004998753999796821224085972610636347903E2L, - 2.386342520092608513170837883757163414100E2L, - 3.791322528149347975999851588922424189957E1L, +static const _Float128 P2_2r3D[NP2_2r3D + 1] = { + L(2.899568897241432883079888249845707400614E-3), + L(1.831107138190848460767699919531132426356E-1), + L(3.999350044057883839080258832758908825165E0), + L(3.929041535867957938340569419874195303712E1), + L(1.884245613422523323068802689915538908291E2), + L(4.461469948819229734353852978424629815929E2), + L(5.004998753999796821224085972610636347903E2), + L(2.386342520092608513170837883757163414100E2), + L(3.791322528149347975999851588922424189957E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -386,31 +387,31 @@ static const long double P2_2r3D[NP2_2r3D + 1] = { Peak relative error 8.0e-36 0 <= 1/x <= .0625 */ #define NQ16_IN 10 -static const long double Q16_IN[NQ16_IN + 1] = { - -3.917420835712508001321875734030357393421E-18L, - -4.440311387483014485304387406538069930457E-15L, - -1.951635424076926487780929645954007139616E-12L, - -4.318256438421012555040546775651612810513E-10L, - -5.231244131926180765270446557146989238020E-8L, - -3.540072702902043752460711989234732357653E-6L, - -1.311017536555269966928228052917534882984E-4L, - -2.495184669674631806622008769674827575088E-3L, - -2.141868222987209028118086708697998506716E-2L, - -6.184031415202148901863605871197272650090E-2L, - -1.922298704033332356899546792898156493887E-2L, +static const _Float128 Q16_IN[NQ16_IN + 1] = { + L(-3.917420835712508001321875734030357393421E-18), + L(-4.440311387483014485304387406538069930457E-15), + L(-1.951635424076926487780929645954007139616E-12), + L(-4.318256438421012555040546775651612810513E-10), + L(-5.231244131926180765270446557146989238020E-8), + L(-3.540072702902043752460711989234732357653E-6), + L(-1.311017536555269966928228052917534882984E-4), + L(-2.495184669674631806622008769674827575088E-3), + L(-2.141868222987209028118086708697998506716E-2), + L(-6.184031415202148901863605871197272650090E-2), + L(-1.922298704033332356899546792898156493887E-2), }; #define NQ16_ID 9 -static const long double Q16_ID[NQ16_ID + 1] = { - 3.820418034066293517479619763498400162314E-17L, - 4.340702810799239909648911373329149354911E-14L, - 1.914985356383416140706179933075303538524E-11L, - 4.262333682610888819476498617261895474330E-9L, - 5.213481314722233980346462747902942182792E-7L, - 3.585741697694069399299005316809954590558E-5L, - 1.366513429642842006385029778105539457546E-3L, - 2.745282599850704662726337474371355160594E-2L, - 2.637644521611867647651200098449903330074E-1L, - 1.006953426110765984590782655598680488746E0L, +static const _Float128 Q16_ID[NQ16_ID + 1] = { + L(3.820418034066293517479619763498400162314E-17), + L(4.340702810799239909648911373329149354911E-14), + L(1.914985356383416140706179933075303538524E-11), + L(4.262333682610888819476498617261895474330E-9), + L(5.213481314722233980346462747902942182792E-7), + L(3.585741697694069399299005316809954590558E-5), + L(1.366513429642842006385029778105539457546E-3), + L(2.745282599850704662726337474371355160594E-2), + L(2.637644521611867647651200098449903330074E-1), + L(1.006953426110765984590782655598680488746E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -419,34 +420,34 @@ static const long double Q16_ID[NQ16_ID + 1] = { Peak relative error 1.9e-36 0.0625 <= 1/x <= 0.125 */ #define NQ8_16N 11 -static const long double Q8_16N[NQ8_16N + 1] = { - -2.028630366670228670781362543615221542291E-17L, - -1.519634620380959966438130374006858864624E-14L, - -4.540596528116104986388796594639405114524E-12L, - -7.085151756671466559280490913558388648274E-10L, - -6.351062671323970823761883833531546885452E-8L, - -3.390817171111032905297982523519503522491E-6L, - -1.082340897018886970282138836861233213972E-4L, - -2.020120801187226444822977006648252379508E-3L, - -2.093169910981725694937457070649605557555E-2L, - -1.092176538874275712359269481414448063393E-1L, - -2.374790947854765809203590474789108718733E-1L, - -1.365364204556573800719985118029601401323E-1L, +static const _Float128 Q8_16N[NQ8_16N + 1] = { + L(-2.028630366670228670781362543615221542291E-17), + L(-1.519634620380959966438130374006858864624E-14), + L(-4.540596528116104986388796594639405114524E-12), + L(-7.085151756671466559280490913558388648274E-10), + L(-6.351062671323970823761883833531546885452E-8), + L(-3.390817171111032905297982523519503522491E-6), + L(-1.082340897018886970282138836861233213972E-4), + L(-2.020120801187226444822977006648252379508E-3), + L(-2.093169910981725694937457070649605557555E-2), + L(-1.092176538874275712359269481414448063393E-1), + L(-2.374790947854765809203590474789108718733E-1), + L(-1.365364204556573800719985118029601401323E-1), }; #define NQ8_16D 11 -static const long double Q8_16D[NQ8_16D + 1] = { - 1.978397614733632533581207058069628242280E-16L, - 1.487361156806202736877009608336766720560E-13L, - 4.468041406888412086042576067133365913456E-11L, - 7.027822074821007443672290507210594648877E-9L, - 6.375740580686101224127290062867976007374E-7L, - 3.466887658320002225888644977076410421940E-5L, - 1.138625640905289601186353909213719596986E-3L, - 2.224470799470414663443449818235008486439E-2L, - 2.487052928527244907490589787691478482358E-1L, - 1.483927406564349124649083853892380899217E0L, - 4.182773513276056975777258788903489507705E0L, - 4.419665392573449746043880892524360870944E0L, +static const _Float128 Q8_16D[NQ8_16D + 1] = { + L(1.978397614733632533581207058069628242280E-16), + L(1.487361156806202736877009608336766720560E-13), + L(4.468041406888412086042576067133365913456E-11), + L(7.027822074821007443672290507210594648877E-9), + L(6.375740580686101224127290062867976007374E-7), + L(3.466887658320002225888644977076410421940E-5), + L(1.138625640905289601186353909213719596986E-3), + L(2.224470799470414663443449818235008486439E-2), + L(2.487052928527244907490589787691478482358E-1), + L(1.483927406564349124649083853892380899217E0), + L(4.182773513276056975777258788903489507705E0), + L(4.419665392573449746043880892524360870944E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -455,32 +456,32 @@ static const long double Q8_16D[NQ8_16D + 1] = { Peak relative error 1.5e-35 0.125 <= 1/x <= 0.1875 */ #define NQ5_8N 10 -static const long double Q5_8N[NQ5_8N + 1] = { - -3.656082407740970534915918390488336879763E-13L, - -1.344660308497244804752334556734121771023E-10L, - -1.909765035234071738548629788698150760791E-8L, - -1.366668038160120210269389551283666716453E-6L, - -5.392327355984269366895210704976314135683E-5L, - -1.206268245713024564674432357634540343884E-3L, - -1.515456784370354374066417703736088291287E-2L, - -1.022454301137286306933217746545237098518E-1L, - -3.373438906472495080504907858424251082240E-1L, - -4.510782522110845697262323973549178453405E-1L, - -1.549000892545288676809660828213589804884E-1L, +static const _Float128 Q5_8N[NQ5_8N + 1] = { + L(-3.656082407740970534915918390488336879763E-13), + L(-1.344660308497244804752334556734121771023E-10), + L(-1.909765035234071738548629788698150760791E-8), + L(-1.366668038160120210269389551283666716453E-6), + L(-5.392327355984269366895210704976314135683E-5), + L(-1.206268245713024564674432357634540343884E-3), + L(-1.515456784370354374066417703736088291287E-2), + L(-1.022454301137286306933217746545237098518E-1), + L(-3.373438906472495080504907858424251082240E-1), + L(-4.510782522110845697262323973549178453405E-1), + L(-1.549000892545288676809660828213589804884E-1), }; #define NQ5_8D 10 -static const long double Q5_8D[NQ5_8D + 1] = { - 3.565550843359501079050699598913828460036E-12L, - 1.321016015556560621591847454285330528045E-9L, - 1.897542728662346479999969679234270605975E-7L, - 1.381720283068706710298734234287456219474E-5L, - 5.599248147286524662305325795203422873725E-4L, - 1.305442352653121436697064782499122164843E-2L, - 1.750234079626943298160445750078631894985E-1L, - 1.311420542073436520965439883806946678491E0L, - 5.162757689856842406744504211089724926650E0L, - 9.527760296384704425618556332087850581308E0L, - 6.604648207463236667912921642545100248584E0L, +static const _Float128 Q5_8D[NQ5_8D + 1] = { + L(3.565550843359501079050699598913828460036E-12), + L(1.321016015556560621591847454285330528045E-9), + L(1.897542728662346479999969679234270605975E-7), + L(1.381720283068706710298734234287456219474E-5), + L(5.599248147286524662305325795203422873725E-4), + L(1.305442352653121436697064782499122164843E-2), + L(1.750234079626943298160445750078631894985E-1), + L(1.311420542073436520965439883806946678491E0), + L(5.162757689856842406744504211089724926650E0), + L(9.527760296384704425618556332087850581308E0), + L(6.604648207463236667912921642545100248584E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -489,31 +490,31 @@ static const long double Q5_8D[NQ5_8D + 1] = { Peak relative error 1.3e-35 0.1875 <= 1/x <= 0.25 */ #define NQ4_5N 10 -static const long double Q4_5N[NQ4_5N + 1] = { - -4.079513568708891749424783046520200903755E-11L, - -9.326548104106791766891812583019664893311E-9L, - -8.016795121318423066292906123815687003356E-7L, - -3.372350544043594415609295225664186750995E-5L, - -7.566238665947967882207277686375417983917E-4L, - -9.248861580055565402130441618521591282617E-3L, - -6.033106131055851432267702948850231270338E-2L, - -1.966908754799996793730369265431584303447E-1L, - -2.791062741179964150755788226623462207560E-1L, - -1.255478605849190549914610121863534191666E-1L, - -4.320429862021265463213168186061696944062E-3L, +static const _Float128 Q4_5N[NQ4_5N + 1] = { + L(-4.079513568708891749424783046520200903755E-11), + L(-9.326548104106791766891812583019664893311E-9), + L(-8.016795121318423066292906123815687003356E-7), + L(-3.372350544043594415609295225664186750995E-5), + L(-7.566238665947967882207277686375417983917E-4), + L(-9.248861580055565402130441618521591282617E-3), + L(-6.033106131055851432267702948850231270338E-2), + L(-1.966908754799996793730369265431584303447E-1), + L(-2.791062741179964150755788226623462207560E-1), + L(-1.255478605849190549914610121863534191666E-1), + L(-4.320429862021265463213168186061696944062E-3), }; #define NQ4_5D 9 -static const long double Q4_5D[NQ4_5D + 1] = { - 3.978497042580921479003851216297330701056E-10L, - 9.203304163828145809278568906420772246666E-8L, - 8.059685467088175644915010485174545743798E-6L, - 3.490187375993956409171098277561669167446E-4L, - 8.189109654456872150100501732073810028829E-3L, - 1.072572867311023640958725265762483033769E-1L, - 7.790606862409960053675717185714576937994E-1L, - 3.016049768232011196434185423512777656328E0L, - 5.722963851442769787733717162314477949360E0L, - 4.510527838428473279647251350931380867663E0L, +static const _Float128 Q4_5D[NQ4_5D + 1] = { + L(3.978497042580921479003851216297330701056E-10), + L(9.203304163828145809278568906420772246666E-8), + L(8.059685467088175644915010485174545743798E-6), + L(3.490187375993956409171098277561669167446E-4), + L(8.189109654456872150100501732073810028829E-3), + L(1.072572867311023640958725265762483033769E-1), + L(7.790606862409960053675717185714576937994E-1), + L(3.016049768232011196434185423512777656328E0), + L(5.722963851442769787733717162314477949360E0), + L(4.510527838428473279647251350931380867663E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -522,30 +523,30 @@ static const long double Q4_5D[NQ4_5D + 1] = { Peak relative error 2.1e-35 0.25 <= 1/x <= 0.3125 */ #define NQ3r2_4N 9 -static const long double Q3r2_4N[NQ3r2_4N + 1] = { - -1.087480809271383885936921889040388133627E-8L, - -1.690067828697463740906962973479310170932E-6L, - -9.608064416995105532790745641974762550982E-5L, - -2.594198839156517191858208513873961837410E-3L, - -3.610954144421543968160459863048062977822E-2L, - -2.629866798251843212210482269563961685666E-1L, - -9.709186825881775885917984975685752956660E-1L, - -1.667521829918185121727268867619982417317E0L, - -1.109255082925540057138766105229900943501E0L, - -1.812932453006641348145049323713469043328E-1L, +static const _Float128 Q3r2_4N[NQ3r2_4N + 1] = { + L(-1.087480809271383885936921889040388133627E-8), + L(-1.690067828697463740906962973479310170932E-6), + L(-9.608064416995105532790745641974762550982E-5), + L(-2.594198839156517191858208513873961837410E-3), + L(-3.610954144421543968160459863048062977822E-2), + L(-2.629866798251843212210482269563961685666E-1), + L(-9.709186825881775885917984975685752956660E-1), + L(-1.667521829918185121727268867619982417317E0), + L(-1.109255082925540057138766105229900943501E0), + L(-1.812932453006641348145049323713469043328E-1), }; #define NQ3r2_4D 9 -static const long double Q3r2_4D[NQ3r2_4D + 1] = { - 1.060552717496912381388763753841473407026E-7L, - 1.676928002024920520786883649102388708024E-5L, - 9.803481712245420839301400601140812255737E-4L, - 2.765559874262309494758505158089249012930E-2L, - 4.117921827792571791298862613287549140706E-1L, - 3.323769515244751267093378361930279161413E0L, - 1.436602494405814164724810151689705353670E1L, - 3.163087869617098638064881410646782408297E1L, - 3.198181264977021649489103980298349589419E1L, - 1.203649258862068431199471076202897823272E1L, +static const _Float128 Q3r2_4D[NQ3r2_4D + 1] = { + L(1.060552717496912381388763753841473407026E-7), + L(1.676928002024920520786883649102388708024E-5), + L(9.803481712245420839301400601140812255737E-4), + L(2.765559874262309494758505158089249012930E-2), + L(4.117921827792571791298862613287549140706E-1), + L(3.323769515244751267093378361930279161413E0), + L(1.436602494405814164724810151689705353670E1), + L(3.163087869617098638064881410646782408297E1), + L(3.198181264977021649489103980298349589419E1), + L(1.203649258862068431199471076202897823272E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -554,30 +555,30 @@ static const long double Q3r2_4D[NQ3r2_4D + 1] = { Peak relative error 1.6e-36 0.3125 <= 1/x <= 0.375 */ #define NQ2r7_3r2N 9 -static const long double Q2r7_3r2N[NQ2r7_3r2N + 1] = { - -1.723405393982209853244278760171643219530E-7L, - -2.090508758514655456365709712333460087442E-5L, - -9.140104013370974823232873472192719263019E-4L, - -1.871349499990714843332742160292474780128E-2L, - -1.948930738119938669637865956162512983416E-1L, - -1.048764684978978127908439526343174139788E0L, - -2.827714929925679500237476105843643064698E0L, - -3.508761569156476114276988181329773987314E0L, - -1.669332202790211090973255098624488308989E0L, - -1.930796319299022954013840684651016077770E-1L, +static const _Float128 Q2r7_3r2N[NQ2r7_3r2N + 1] = { + L(-1.723405393982209853244278760171643219530E-7), + L(-2.090508758514655456365709712333460087442E-5), + L(-9.140104013370974823232873472192719263019E-4), + L(-1.871349499990714843332742160292474780128E-2), + L(-1.948930738119938669637865956162512983416E-1), + L(-1.048764684978978127908439526343174139788E0), + L(-2.827714929925679500237476105843643064698E0), + L(-3.508761569156476114276988181329773987314E0), + L(-1.669332202790211090973255098624488308989E0), + L(-1.930796319299022954013840684651016077770E-1), }; #define NQ2r7_3r2D 9 -static const long double Q2r7_3r2D[NQ2r7_3r2D + 1] = { - 1.680730662300831976234547482334347983474E-6L, - 2.084241442440551016475972218719621841120E-4L, - 9.445316642108367479043541702688736295579E-3L, - 2.044637889456631896650179477133252184672E-1L, - 2.316091982244297350829522534435350078205E0L, - 1.412031891783015085196708811890448488865E1L, - 4.583830154673223384837091077279595496149E1L, - 7.549520609270909439885998474045974122261E1L, - 5.697605832808113367197494052388203310638E1L, - 1.601496240876192444526383314589371686234E1L, +static const _Float128 Q2r7_3r2D[NQ2r7_3r2D + 1] = { + L(1.680730662300831976234547482334347983474E-6), + L(2.084241442440551016475972218719621841120E-4), + L(9.445316642108367479043541702688736295579E-3), + L(2.044637889456631896650179477133252184672E-1), + L(2.316091982244297350829522534435350078205E0), + L(1.412031891783015085196708811890448488865E1), + L(4.583830154673223384837091077279595496149E1), + L(7.549520609270909439885998474045974122261E1), + L(5.697605832808113367197494052388203310638E1), + L(1.601496240876192444526383314589371686234E1), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -586,29 +587,29 @@ static const long double Q2r7_3r2D[NQ2r7_3r2D + 1] = { Peak relative error 9.5e-36 0.375 <= 1/x <= 0.4375 */ #define NQ2r3_2r7N 9 -static const long double Q2r3_2r7N[NQ2r3_2r7N + 1] = { - -8.603042076329122085722385914954878953775E-7L, - -7.701746260451647874214968882605186675720E-5L, - -2.407932004380727587382493696877569654271E-3L, - -3.403434217607634279028110636919987224188E-2L, - -2.348707332185238159192422084985713102877E-1L, - -7.957498841538254916147095255700637463207E-1L, - -1.258469078442635106431098063707934348577E0L, - -8.162415474676345812459353639449971369890E-1L, - -1.581783890269379690141513949609572806898E-1L, - -1.890595651683552228232308756569450822905E-3L, +static const _Float128 Q2r3_2r7N[NQ2r3_2r7N + 1] = { + L(-8.603042076329122085722385914954878953775E-7), + L(-7.701746260451647874214968882605186675720E-5), + L(-2.407932004380727587382493696877569654271E-3), + L(-3.403434217607634279028110636919987224188E-2), + L(-2.348707332185238159192422084985713102877E-1), + L(-7.957498841538254916147095255700637463207E-1), + L(-1.258469078442635106431098063707934348577E0), + L(-8.162415474676345812459353639449971369890E-1), + L(-1.581783890269379690141513949609572806898E-1), + L(-1.890595651683552228232308756569450822905E-3), }; #define NQ2r3_2r7D 8 -static const long double Q2r3_2r7D[NQ2r3_2r7D + 1] = { - 8.390017524798316921170710533381568175665E-6L, - 7.738148683730826286477254659973968763659E-4L, - 2.541480810958665794368759558791634341779E-2L, - 3.878879789711276799058486068562386244873E-1L, - 3.003783779325811292142957336802456109333E0L, - 1.206480374773322029883039064575464497400E1L, - 2.458414064785315978408974662900438351782E1L, - 2.367237826273668567199042088835448715228E1L, - 9.231451197519171090875569102116321676763E0L, +static const _Float128 Q2r3_2r7D[NQ2r3_2r7D + 1] = { + L(8.390017524798316921170710533381568175665E-6), + L(7.738148683730826286477254659973968763659E-4), + L(2.541480810958665794368759558791634341779E-2), + L(3.878879789711276799058486068562386244873E-1), + L(3.003783779325811292142957336802456109333E0), + L(1.206480374773322029883039064575464497400E1), + L(2.458414064785315978408974662900438351782E1), + L(2.367237826273668567199042088835448715228E1), + L(9.231451197519171090875569102116321676763E0), /* 1.000000000000000000000000000000000000000E0 */ }; @@ -617,39 +618,39 @@ static const long double Q2r3_2r7D[NQ2r3_2r7D + 1] = { Peak relative error 1.4e-36 0.4375 <= 1/x <= 0.5 */ #define NQ2_2r3N 9 -static const long double Q2_2r3N[NQ2_2r3N + 1] = { - -5.552507516089087822166822364590806076174E-6L, - -4.135067659799500521040944087433752970297E-4L, - -1.059928728869218962607068840646564457980E-2L, - -1.212070036005832342565792241385459023801E-1L, - -6.688350110633603958684302153362735625156E-1L, - -1.793587878197360221340277951304429821582E0L, - -2.225407682237197485644647380483725045326E0L, - -1.123402135458940189438898496348239744403E0L, - -1.679187241566347077204805190763597299805E-1L, - -1.458550613639093752909985189067233504148E-3L, +static const _Float128 Q2_2r3N[NQ2_2r3N + 1] = { + L(-5.552507516089087822166822364590806076174E-6), + L(-4.135067659799500521040944087433752970297E-4), + L(-1.059928728869218962607068840646564457980E-2), + L(-1.212070036005832342565792241385459023801E-1), + L(-6.688350110633603958684302153362735625156E-1), + L(-1.793587878197360221340277951304429821582E0), + L(-2.225407682237197485644647380483725045326E0), + L(-1.123402135458940189438898496348239744403E0), + L(-1.679187241566347077204805190763597299805E-1), + L(-1.458550613639093752909985189067233504148E-3), }; #define NQ2_2r3D 8 -static const long double Q2_2r3D[NQ2_2r3D + 1] = { - 5.415024336507980465169023996403597916115E-5L, - 4.179246497380453022046357404266022870788E-3L, - 1.136306384261959483095442402929502368598E-1L, - 1.422640343719842213484515445393284072830E0L, - 8.968786703393158374728850922289204805764E0L, - 2.914542473339246127533384118781216495934E1L, - 4.781605421020380669870197378210457054685E1L, - 3.693865837171883152382820584714795072937E1L, - 1.153220502744204904763115556224395893076E1L, +static const _Float128 Q2_2r3D[NQ2_2r3D + 1] = { + L(5.415024336507980465169023996403597916115E-5), + L(4.179246497380453022046357404266022870788E-3), + L(1.136306384261959483095442402929502368598E-1), + L(1.422640343719842213484515445393284072830E0), + L(8.968786703393158374728850922289204805764E0), + L(2.914542473339246127533384118781216495934E1), + L(4.781605421020380669870197378210457054685E1), + L(3.693865837171883152382820584714795072937E1), + L(1.153220502744204904763115556224395893076E1), /* 1.000000000000000000000000000000000000000E0 */ }; /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ -static long double -neval (long double x, const long double *p, int n) +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = *p--; @@ -664,10 +665,10 @@ neval (long double x, const long double *p, int n) /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ -static long double -deval (long double x, const long double *p, int n) +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = x + *p--; @@ -682,35 +683,35 @@ deval (long double x, const long double *p, int n) /* Bessel function of the first kind, order one. */ -long double -__ieee754_j1l (long double x) +_Float128 +__ieee754_j1l (_Float128 x) { - long double xx, xinv, z, p, q, c, s, cc, ss; + _Float128 xx, xinv, z, p, q, c, s, cc, ss; if (! isfinite (x)) { if (x != x) - return x; + return x + x; else - return 0.0L; + return 0; } - if (x == 0.0L) + if (x == 0) return x; xx = fabsl (x); - if (xx <= 0x1p-58L) + if (xx <= L(0x1p-58)) { - long double ret = x * 0.5L; + _Float128 ret = x * L(0.5); math_check_force_underflow (ret); if (ret == 0) __set_errno (ERANGE); return ret; } - if (xx <= 2.0L) + if (xx <= 2) { /* 0 <= x <= 2 */ z = xx * xx; p = xx * z * neval (z, J0_2N, NJ0_2N) / deval (z, J0_2D, NJ0_2D); - p += 0.5L * xx; + p += L(0.5) * xx; if (x < 0) p = -p; return p; @@ -725,7 +726,7 @@ __ieee754_j1l (long double x) __sincosl (xx, &s, &c); ss = -s - c; cc = s - c; - if (xx <= LDBL_MAX / 2.0L) + if (xx <= LDBL_MAX / 2) { z = __cosl (xx + xx); if ((s * c) > 0) @@ -734,15 +735,15 @@ __ieee754_j1l (long double x) ss = z / cc; } - if (xx > 0x1p256L) + if (xx > L(0x1p256)) { - z = ONEOSQPI * cc / __ieee754_sqrtl (xx); + z = ONEOSQPI * cc / sqrtl (xx); if (x < 0) z = -z; return z; } - xinv = 1.0L / xx; + xinv = 1 / xx; z = xinv * xinv; if (xinv <= 0.25) { @@ -800,10 +801,10 @@ __ieee754_j1l (long double x) q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); } } - p = 1.0L + z * p; + p = 1 + z * p; q = z * q; - q = q * xinv + 0.375L * xinv; - z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx); + q = q * xinv + L(0.375) * xinv; + z = ONEOSQPI * (p * cc - q * ss) / sqrtl (xx); if (x < 0) z = -z; return z; @@ -815,49 +816,44 @@ strong_alias (__ieee754_j1l, __j1l_finite) Peak relative error 6.2e-38 0 <= x <= 2 */ #define NY0_2N 7 -static long double Y0_2N[NY0_2N + 1] = { - -6.804415404830253804408698161694720833249E19L, - 1.805450517967019908027153056150465849237E19L, - -8.065747497063694098810419456383006737312E17L, - 1.401336667383028259295830955439028236299E16L, - -1.171654432898137585000399489686629680230E14L, - 5.061267920943853732895341125243428129150E11L, - -1.096677850566094204586208610960870217970E9L, - 9.541172044989995856117187515882879304461E5L, +static const _Float128 Y0_2N[NY0_2N + 1] = { + L(-6.804415404830253804408698161694720833249E19), + L(1.805450517967019908027153056150465849237E19), + L(-8.065747497063694098810419456383006737312E17), + L(1.401336667383028259295830955439028236299E16), + L(-1.171654432898137585000399489686629680230E14), + L(5.061267920943853732895341125243428129150E11), + L(-1.096677850566094204586208610960870217970E9), + L(9.541172044989995856117187515882879304461E5), }; #define NY0_2D 7 -static long double Y0_2D[NY0_2D + 1] = { - 3.470629591820267059538637461549677594549E20L, - 4.120796439009916326855848107545425217219E18L, - 2.477653371652018249749350657387030814542E16L, - 9.954678543353888958177169349272167762797E13L, - 2.957927997613630118216218290262851197754E11L, - 6.748421382188864486018861197614025972118E8L, - 1.173453425218010888004562071020305709319E6L, - 1.450335662961034949894009554536003377187E3L, +static const _Float128 Y0_2D[NY0_2D + 1] = { + L(3.470629591820267059538637461549677594549E20), + L(4.120796439009916326855848107545425217219E18), + L(2.477653371652018249749350657387030814542E16), + L(9.954678543353888958177169349272167762797E13), + L(2.957927997613630118216218290262851197754E11), + L(6.748421382188864486018861197614025972118E8), + L(1.173453425218010888004562071020305709319E6), + L(1.450335662961034949894009554536003377187E3), /* 1.000000000000000000000000000000000000000E0 */ }; /* Bessel function of the second kind, order one. */ -long double -__ieee754_y1l (long double x) +_Float128 +__ieee754_y1l (_Float128 x) { - long double xx, xinv, z, p, q, c, s, cc, ss; + _Float128 xx, xinv, z, p, q, c, s, cc, ss; if (! isfinite (x)) + return 1 / (x + x * x); + if (x <= 0) { - if (x != x) - return x; - else - return 0.0L; - } - if (x <= 0.0L) - { - if (x < 0.0L) + if (x < 0) return (zero / (zero * x)); - return -HUGE_VALL + x; + return -1 / zero; /* -inf and divide by zero exception. */ } xx = fabsl (x); if (xx <= 0x1p-114) @@ -867,7 +863,7 @@ __ieee754_y1l (long double x) __set_errno (ERANGE); return z; } - if (xx <= 2.0L) + if (xx <= 2) { /* 0 <= x <= 2 */ SET_RESTORE_ROUNDL (FE_TONEAREST); @@ -887,7 +883,7 @@ __ieee754_y1l (long double x) __sincosl (xx, &s, &c); ss = -s - c; cc = s - c; - if (xx <= LDBL_MAX / 2.0L) + if (xx <= LDBL_MAX / 2) { z = __cosl (xx + xx); if ((s * c) > 0) @@ -896,10 +892,10 @@ __ieee754_y1l (long double x) ss = z / cc; } - if (xx > 0x1p256L) - return ONEOSQPI * ss / __ieee754_sqrtl (xx); + if (xx > L(0x1p256)) + return ONEOSQPI * ss / sqrtl (xx); - xinv = 1.0L / xx; + xinv = 1 / xx; z = xinv * xinv; if (xinv <= 0.25) { @@ -957,10 +953,10 @@ __ieee754_y1l (long double x) q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); } } - p = 1.0L + z * p; + p = 1 + z * p; q = z * q; - q = q * xinv + 0.375L * xinv; - z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx); + q = q * xinv + L(0.375) * xinv; + z = ONEOSQPI * (p * ss + q * cc) / sqrtl (xx); return z; } strong_alias (__ieee754_y1l, __y1l_finite) diff --git a/sysdeps/ieee754/ldbl-128/e_jnl.c b/sysdeps/ieee754/ldbl-128/e_jnl.c index 98669e6e3e..7739eec291 100644 --- a/sysdeps/ieee754/ldbl-128/e_jnl.c +++ b/sysdeps/ieee754/ldbl-128/e_jnl.c @@ -60,21 +60,22 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> -static const long double - invsqrtpi = 5.6418958354775628694807945156077258584405E-1L, - two = 2.0e0L, - one = 1.0e0L, - zero = 0.0L; +static const _Float128 + invsqrtpi = L(5.6418958354775628694807945156077258584405E-1), + two = 2, + one = 1, + zero = 0; -long double -__ieee754_jnl (int n, long double x) +_Float128 +__ieee754_jnl (int n, _Float128 x) { - u_int32_t se; + uint32_t se; int32_t i, ix, sgn; - long double a, b, temp, di, ret; - long double z, w; + _Float128 a, b, temp, di, ret; + _Float128 z, w; ieee854_long_double_shape_type u; @@ -108,9 +109,9 @@ __ieee754_jnl (int n, long double x) { SET_RESTORE_ROUNDL (FE_TONEAREST); - if (x == 0.0L || ix >= 0x7fff0000) /* if x is 0 or inf */ + if (x == 0 || ix >= 0x7fff0000) /* if x is 0 or inf */ return sgn == 1 ? -zero : zero; - else if ((long double) n <= x) + else if ((_Float128) n <= x) { /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ if (ix >= 0x412D0000) @@ -131,8 +132,8 @@ __ieee754_jnl (int n, long double x) * 2 -s+c -c-s * 3 s+c c-s */ - long double s; - long double c; + _Float128 s; + _Float128 c; __sincosl (x, &s, &c); switch (n & 3) { @@ -149,7 +150,7 @@ __ieee754_jnl (int n, long double x) temp = c - s; break; } - b = invsqrtpi * temp / __ieee754_sqrtl (x); + b = invsqrtpi * temp / sqrtl (x); } else { @@ -158,7 +159,7 @@ __ieee754_jnl (int n, long double x) for (i = 1; i < n; i++) { temp = b; - b = b * ((long double) (i + i) / x) - a; /* avoid underflow */ + b = b * ((_Float128) (i + i) / x) - a; /* avoid underflow */ a = temp; } } @@ -178,7 +179,7 @@ __ieee754_jnl (int n, long double x) b = temp; for (a = one, i = 2; i <= n; i++) { - a *= (long double) i; /* a = n! */ + a *= (_Float128) i; /* a = n! */ b *= temp; /* b = (x/2)^n */ } b = b / a; @@ -215,16 +216,16 @@ __ieee754_jnl (int n, long double x) * When Q(k) > 1e17 good for quadruple */ /* determine k */ - long double t, v; - long double q0, q1, h, tmp; + _Float128 t, v; + _Float128 q0, q1, h, tmp; int32_t k, m; - w = (n + n) / (long double) x; - h = 2.0L / (long double) x; + w = (n + n) / (_Float128) x; + h = 2 / (_Float128) x; q0 = w; z = w + h; - q1 = w * z - 1.0L; + q1 = w * z - 1; k = 1; - while (q1 < 1.0e17L) + while (q1 < L(1.0e17)) { k += 1; z += h; @@ -249,9 +250,9 @@ __ieee754_jnl (int n, long double x) v = two / x; tmp = tmp * __ieee754_logl (fabsl (v * tmp)); - if (tmp < 1.1356523406294143949491931077970765006170e+04L) + if (tmp < L(1.1356523406294143949491931077970765006170e+04)) { - for (i = n - 1, di = (long double) (i + i); i > 0; i--) + for (i = n - 1, di = (_Float128) (i + i); i > 0; i--) { temp = b; b *= di; @@ -262,7 +263,7 @@ __ieee754_jnl (int n, long double x) } else { - for (i = n - 1, di = (long double) (i + i); i > 0; i--) + for (i = n - 1, di = (_Float128) (i + i); i > 0; i--) { temp = b; b *= di; @@ -270,7 +271,7 @@ __ieee754_jnl (int n, long double x) a = temp; di -= two; /* scale b to avoid spurious overflow */ - if (b > 1e100L) + if (b > L(1e100)) { a /= b; t /= b; @@ -306,13 +307,13 @@ __ieee754_jnl (int n, long double x) } strong_alias (__ieee754_jnl, __jnl_finite) -long double -__ieee754_ynl (int n, long double x) +_Float128 +__ieee754_ynl (int n, _Float128 x) { - u_int32_t se; + uint32_t se; int32_t i, ix; int32_t sign; - long double a, b, temp, ret; + _Float128 a, b, temp, ret; ieee854_long_double_shape_type u; u.value = x; @@ -325,10 +326,10 @@ __ieee754_ynl (int n, long double x) if ((u.parts32.w0 & 0xffff) | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) return x + x; } - if (x <= 0.0L) + if (x <= 0) { - if (x == 0.0L) - return ((n < 0 && (n & 1) != 0) ? 1.0L : -1.0L) / 0.0L; + if (x == 0) + return ((n < 0 && (n & 1) != 0) ? 1 : -1) / L(0.0); if (se & 0x80000000) return zero / (zero * x); } @@ -367,8 +368,8 @@ __ieee754_ynl (int n, long double x) * 2 -s+c -c-s * 3 s+c c-s */ - long double s; - long double c; + _Float128 s; + _Float128 c; __sincosl (x, &s, &c); switch (n & 3) { @@ -385,7 +386,7 @@ __ieee754_ynl (int n, long double x) temp = s + c; break; } - b = invsqrtpi * temp / __ieee754_sqrtl (x); + b = invsqrtpi * temp / sqrtl (x); } else { @@ -397,7 +398,7 @@ __ieee754_ynl (int n, long double x) for (i = 1; i < n && se != 0xffff0000; i++) { temp = b; - b = ((long double) (i + i) / x) * b - a; + b = ((_Float128) (i + i) / x) * b - a; u.value = b; se = u.parts32.w0 & 0xffff0000; a = temp; diff --git a/sysdeps/ieee754/ldbl-128/e_lgammal_r.c b/sysdeps/ieee754/ldbl-128/e_lgammal_r.c index 5b513ea1df..5c50e4616a 100644 --- a/sysdeps/ieee754/ldbl-128/e_lgammal_r.c +++ b/sysdeps/ieee754/ldbl-128/e_lgammal_r.c @@ -72,35 +72,31 @@ #include <math_private.h> #include <float.h> -static const long double PIL = 3.1415926535897932384626433832795028841972E0L; -#if LDBL_MANT_DIG == 106 -static const long double MAXLGM = 0x5.d53649e2d469dbc1f01e99fd66p+1012L; -#else -static const long double MAXLGM = 1.0485738685148938358098967157129705071571E4928L; -#endif -static const long double one = 1.0L; -static const long double huge = LDBL_MAX; +static const _Float128 PIL = L(3.1415926535897932384626433832795028841972E0); +static const _Float128 MAXLGM = L(1.0485738685148938358098967157129705071571E4928); +static const _Float128 one = 1; +static const _Float128 huge = LDBL_MAX; /* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x P(1/x^2) 1/x <= 0.0741 (x >= 13.495...) Peak relative error 1.5e-36 */ -static const long double ls2pi = 9.1893853320467274178032973640561763986140E-1L; +static const _Float128 ls2pi = L(9.1893853320467274178032973640561763986140E-1); #define NRASY 12 -static const long double RASY[NRASY + 1] = +static const _Float128 RASY[NRASY + 1] = { - 8.333333333333333333333333333310437112111E-2L, - -2.777777777777777777777774789556228296902E-3L, - 7.936507936507936507795933938448586499183E-4L, - -5.952380952380952041799269756378148574045E-4L, - 8.417508417507928904209891117498524452523E-4L, - -1.917526917481263997778542329739806086290E-3L, - 6.410256381217852504446848671499409919280E-3L, - -2.955064066900961649768101034477363301626E-2L, - 1.796402955865634243663453415388336954675E-1L, - -1.391522089007758553455753477688592767741E0L, - 1.326130089598399157988112385013829305510E1L, - -1.420412699593782497803472576479997819149E2L, - 1.218058922427762808938869872528846787020E3L + L(8.333333333333333333333333333310437112111E-2), + L(-2.777777777777777777777774789556228296902E-3), + L(7.936507936507936507795933938448586499183E-4), + L(-5.952380952380952041799269756378148574045E-4), + L(8.417508417507928904209891117498524452523E-4), + L(-1.917526917481263997778542329739806086290E-3), + L(6.410256381217852504446848671499409919280E-3), + L(-2.955064066900961649768101034477363301626E-2), + L(1.796402955865634243663453415388336954675E-1), + L(-1.391522089007758553455753477688592767741E0), + L(1.326130089598399157988112385013829305510E1), + L(-1.420412699593782497803472576479997819149E2), + L(1.218058922427762808938869872528846787020E3) }; @@ -108,30 +104,30 @@ static const long double RASY[NRASY + 1] = -0.5 <= x <= 0.5 12.5 <= x+13 <= 13.5 Peak relative error 1.1e-36 */ -static const long double lgam13a = 1.9987213134765625E1L; -static const long double lgam13b = 1.3608962611495173623870550785125024484248E-6L; +static const _Float128 lgam13a = L(1.9987213134765625E1); +static const _Float128 lgam13b = L(1.3608962611495173623870550785125024484248E-6); #define NRN13 7 -static const long double RN13[NRN13 + 1] = +static const _Float128 RN13[NRN13 + 1] = { - 8.591478354823578150238226576156275285700E11L, - 2.347931159756482741018258864137297157668E11L, - 2.555408396679352028680662433943000804616E10L, - 1.408581709264464345480765758902967123937E9L, - 4.126759849752613822953004114044451046321E7L, - 6.133298899622688505854211579222889943778E5L, - 3.929248056293651597987893340755876578072E3L, - 6.850783280018706668924952057996075215223E0L + L(8.591478354823578150238226576156275285700E11), + L(2.347931159756482741018258864137297157668E11), + L(2.555408396679352028680662433943000804616E10), + L(1.408581709264464345480765758902967123937E9), + L(4.126759849752613822953004114044451046321E7), + L(6.133298899622688505854211579222889943778E5), + L(3.929248056293651597987893340755876578072E3), + L(6.850783280018706668924952057996075215223E0) }; #define NRD13 6 -static const long double RD13[NRD13 + 1] = +static const _Float128 RD13[NRD13 + 1] = { - 3.401225382297342302296607039352935541669E11L, - 8.756765276918037910363513243563234551784E10L, - 8.873913342866613213078554180987647243903E9L, - 4.483797255342763263361893016049310017973E8L, - 1.178186288833066430952276702931512870676E7L, - 1.519928623743264797939103740132278337476E5L, - 7.989298844938119228411117593338850892311E2L + L(3.401225382297342302296607039352935541669E11), + L(8.756765276918037910363513243563234551784E10), + L(8.873913342866613213078554180987647243903E9), + L(4.483797255342763263361893016049310017973E8), + L(1.178186288833066430952276702931512870676E7), + L(1.519928623743264797939103740132278337476E5), + L(7.989298844938119228411117593338850892311E2) /* 1.0E0L */ }; @@ -140,30 +136,30 @@ static const long double RD13[NRD13 + 1] = -0.5 <= x <= 0.5 11.5 <= x+12 <= 12.5 Peak relative error 4.1e-36 */ -static const long double lgam12a = 1.75023040771484375E1L; -static const long double lgam12b = 3.7687254483392876529072161996717039575982E-6L; +static const _Float128 lgam12a = L(1.75023040771484375E1); +static const _Float128 lgam12b = L(3.7687254483392876529072161996717039575982E-6); #define NRN12 7 -static const long double RN12[NRN12 + 1] = +static const _Float128 RN12[NRN12 + 1] = { - 4.709859662695606986110997348630997559137E11L, - 1.398713878079497115037857470168777995230E11L, - 1.654654931821564315970930093932954900867E10L, - 9.916279414876676861193649489207282144036E8L, - 3.159604070526036074112008954113411389879E7L, - 5.109099197547205212294747623977502492861E5L, - 3.563054878276102790183396740969279826988E3L, - 6.769610657004672719224614163196946862747E0L + L(4.709859662695606986110997348630997559137E11), + L(1.398713878079497115037857470168777995230E11), + L(1.654654931821564315970930093932954900867E10), + L(9.916279414876676861193649489207282144036E8), + L(3.159604070526036074112008954113411389879E7), + L(5.109099197547205212294747623977502492861E5), + L(3.563054878276102790183396740969279826988E3), + L(6.769610657004672719224614163196946862747E0) }; #define NRD12 6 -static const long double RD12[NRD12 + 1] = +static const _Float128 RD12[NRD12 + 1] = { - 1.928167007860968063912467318985802726613E11L, - 5.383198282277806237247492369072266389233E10L, - 5.915693215338294477444809323037871058363E9L, - 3.241438287570196713148310560147925781342E8L, - 9.236680081763754597872713592701048455890E6L, - 1.292246897881650919242713651166596478850E5L, - 7.366532445427159272584194816076600211171E2L + L(1.928167007860968063912467318985802726613E11), + L(5.383198282277806237247492369072266389233E10), + L(5.915693215338294477444809323037871058363E9), + L(3.241438287570196713148310560147925781342E8), + L(9.236680081763754597872713592701048455890E6), + L(1.292246897881650919242713651166596478850E5), + L(7.366532445427159272584194816076600211171E2) /* 1.0E0L */ }; @@ -172,30 +168,30 @@ static const long double RD12[NRD12 + 1] = -0.5 <= x <= 0.5 10.5 <= x+11 <= 11.5 Peak relative error 1.8e-35 */ -static const long double lgam11a = 1.5104400634765625E1L; -static const long double lgam11b = 1.1938309890295225709329251070371882250744E-5L; +static const _Float128 lgam11a = L(1.5104400634765625E1); +static const _Float128 lgam11b = L(1.1938309890295225709329251070371882250744E-5); #define NRN11 7 -static const long double RN11[NRN11 + 1] = +static const _Float128 RN11[NRN11 + 1] = { - 2.446960438029415837384622675816736622795E11L, - 7.955444974446413315803799763901729640350E10L, - 1.030555327949159293591618473447420338444E10L, - 6.765022131195302709153994345470493334946E8L, - 2.361892792609204855279723576041468347494E7L, - 4.186623629779479136428005806072176490125E5L, - 3.202506022088912768601325534149383594049E3L, - 6.681356101133728289358838690666225691363E0L + L(2.446960438029415837384622675816736622795E11), + L(7.955444974446413315803799763901729640350E10), + L(1.030555327949159293591618473447420338444E10), + L(6.765022131195302709153994345470493334946E8), + L(2.361892792609204855279723576041468347494E7), + L(4.186623629779479136428005806072176490125E5), + L(3.202506022088912768601325534149383594049E3), + L(6.681356101133728289358838690666225691363E0) }; #define NRD11 6 -static const long double RD11[NRD11 + 1] = +static const _Float128 RD11[NRD11 + 1] = { - 1.040483786179428590683912396379079477432E11L, - 3.172251138489229497223696648369823779729E10L, - 3.806961885984850433709295832245848084614E9L, - 2.278070344022934913730015420611609620171E8L, - 7.089478198662651683977290023829391596481E6L, - 1.083246385105903533237139380509590158658E5L, - 6.744420991491385145885727942219463243597E2L + L(1.040483786179428590683912396379079477432E11), + L(3.172251138489229497223696648369823779729E10), + L(3.806961885984850433709295832245848084614E9), + L(2.278070344022934913730015420611609620171E8), + L(7.089478198662651683977290023829391596481E6), + L(1.083246385105903533237139380509590158658E5), + L(6.744420991491385145885727942219463243597E2) /* 1.0E0L */ }; @@ -204,31 +200,31 @@ static const long double RD11[NRD11 + 1] = -0.5 <= x <= 0.5 9.5 <= x+10 <= 10.5 Peak relative error 5.4e-37 */ -static const long double lgam10a = 1.280181884765625E1L; -static const long double lgam10b = 8.6324252196112077178745667061642811492557E-6L; +static const _Float128 lgam10a = L(1.280181884765625E1); +static const _Float128 lgam10b = L(8.6324252196112077178745667061642811492557E-6); #define NRN10 7 -static const long double RN10[NRN10 + 1] = +static const _Float128 RN10[NRN10 + 1] = { - -1.239059737177249934158597996648808363783E14L, - -4.725899566371458992365624673357356908719E13L, - -7.283906268647083312042059082837754850808E12L, - -5.802855515464011422171165179767478794637E11L, - -2.532349691157548788382820303182745897298E10L, - -5.884260178023777312587193693477072061820E8L, - -6.437774864512125749845840472131829114906E6L, - -2.350975266781548931856017239843273049384E4L + L(-1.239059737177249934158597996648808363783E14), + L(-4.725899566371458992365624673357356908719E13), + L(-7.283906268647083312042059082837754850808E12), + L(-5.802855515464011422171165179767478794637E11), + L(-2.532349691157548788382820303182745897298E10), + L(-5.884260178023777312587193693477072061820E8), + L(-6.437774864512125749845840472131829114906E6), + L(-2.350975266781548931856017239843273049384E4) }; #define NRD10 7 -static const long double RD10[NRD10 + 1] = +static const _Float128 RD10[NRD10 + 1] = { - -5.502645997581822567468347817182347679552E13L, - -1.970266640239849804162284805400136473801E13L, - -2.819677689615038489384974042561531409392E12L, - -2.056105863694742752589691183194061265094E11L, - -8.053670086493258693186307810815819662078E9L, - -1.632090155573373286153427982504851867131E8L, - -1.483575879240631280658077826889223634921E6L, - -4.002806669713232271615885826373550502510E3L + L(-5.502645997581822567468347817182347679552E13), + L(-1.970266640239849804162284805400136473801E13), + L(-2.819677689615038489384974042561531409392E12), + L(-2.056105863694742752589691183194061265094E11), + L(-8.053670086493258693186307810815819662078E9), + L(-1.632090155573373286153427982504851867131E8), + L(-1.483575879240631280658077826889223634921E6), + L(-4.002806669713232271615885826373550502510E3) /* 1.0E0L */ }; @@ -237,31 +233,31 @@ static const long double RD10[NRD10 + 1] = -0.5 <= x <= 0.5 8.5 <= x+9 <= 9.5 Peak relative error 3.6e-36 */ -static const long double lgam9a = 1.06045989990234375E1L; -static const long double lgam9b = 3.9037218127284172274007216547549861681400E-6L; +static const _Float128 lgam9a = L(1.06045989990234375E1); +static const _Float128 lgam9b = L(3.9037218127284172274007216547549861681400E-6); #define NRN9 7 -static const long double RN9[NRN9 + 1] = +static const _Float128 RN9[NRN9 + 1] = { - -4.936332264202687973364500998984608306189E13L, - -2.101372682623700967335206138517766274855E13L, - -3.615893404644823888655732817505129444195E12L, - -3.217104993800878891194322691860075472926E11L, - -1.568465330337375725685439173603032921399E10L, - -4.073317518162025744377629219101510217761E8L, - -4.983232096406156139324846656819246974500E6L, - -2.036280038903695980912289722995505277253E4L + L(-4.936332264202687973364500998984608306189E13), + L(-2.101372682623700967335206138517766274855E13), + L(-3.615893404644823888655732817505129444195E12), + L(-3.217104993800878891194322691860075472926E11), + L(-1.568465330337375725685439173603032921399E10), + L(-4.073317518162025744377629219101510217761E8), + L(-4.983232096406156139324846656819246974500E6), + L(-2.036280038903695980912289722995505277253E4) }; #define NRD9 7 -static const long double RD9[NRD9 + 1] = +static const _Float128 RD9[NRD9 + 1] = { - -2.306006080437656357167128541231915480393E13L, - -9.183606842453274924895648863832233799950E12L, - -1.461857965935942962087907301194381010380E12L, - -1.185728254682789754150068652663124298303E11L, - -5.166285094703468567389566085480783070037E9L, - -1.164573656694603024184768200787835094317E8L, - -1.177343939483908678474886454113163527909E6L, - -3.529391059783109732159524500029157638736E3L + L(-2.306006080437656357167128541231915480393E13), + L(-9.183606842453274924895648863832233799950E12), + L(-1.461857965935942962087907301194381010380E12), + L(-1.185728254682789754150068652663124298303E11), + L(-5.166285094703468567389566085480783070037E9), + L(-1.164573656694603024184768200787835094317E8), + L(-1.177343939483908678474886454113163527909E6), + L(-3.529391059783109732159524500029157638736E3) /* 1.0E0L */ }; @@ -270,32 +266,32 @@ static const long double RD9[NRD9 + 1] = -0.5 <= x <= 0.5 7.5 <= x+8 <= 8.5 Peak relative error 2.4e-37 */ -static const long double lgam8a = 8.525146484375E0L; -static const long double lgam8b = 1.4876690414300165531036347125050759667737E-5L; +static const _Float128 lgam8a = L(8.525146484375E0); +static const _Float128 lgam8b = L(1.4876690414300165531036347125050759667737E-5); #define NRN8 8 -static const long double RN8[NRN8 + 1] = +static const _Float128 RN8[NRN8 + 1] = { - 6.600775438203423546565361176829139703289E11L, - 3.406361267593790705240802723914281025800E11L, - 7.222460928505293914746983300555538432830E10L, - 8.102984106025088123058747466840656458342E9L, - 5.157620015986282905232150979772409345927E8L, - 1.851445288272645829028129389609068641517E7L, - 3.489261702223124354745894067468953756656E5L, - 2.892095396706665774434217489775617756014E3L, - 6.596977510622195827183948478627058738034E0L + L(6.600775438203423546565361176829139703289E11), + L(3.406361267593790705240802723914281025800E11), + L(7.222460928505293914746983300555538432830E10), + L(8.102984106025088123058747466840656458342E9), + L(5.157620015986282905232150979772409345927E8), + L(1.851445288272645829028129389609068641517E7), + L(3.489261702223124354745894067468953756656E5), + L(2.892095396706665774434217489775617756014E3), + L(6.596977510622195827183948478627058738034E0) }; #define NRD8 7 -static const long double RD8[NRD8 + 1] = +static const _Float128 RD8[NRD8 + 1] = { - 3.274776546520735414638114828622673016920E11L, - 1.581811207929065544043963828487733970107E11L, - 3.108725655667825188135393076860104546416E10L, - 3.193055010502912617128480163681842165730E9L, - 1.830871482669835106357529710116211541839E8L, - 5.790862854275238129848491555068073485086E6L, - 9.305213264307921522842678835618803553589E4L, - 6.216974105861848386918949336819572333622E2L + L(3.274776546520735414638114828622673016920E11), + L(1.581811207929065544043963828487733970107E11), + L(3.108725655667825188135393076860104546416E10), + L(3.193055010502912617128480163681842165730E9), + L(1.830871482669835106357529710116211541839E8), + L(5.790862854275238129848491555068073485086E6), + L(9.305213264307921522842678835618803553589E4), + L(6.216974105861848386918949336819572333622E2) /* 1.0E0L */ }; @@ -304,32 +300,32 @@ static const long double RD8[NRD8 + 1] = -0.5 <= x <= 0.5 6.5 <= x+7 <= 7.5 Peak relative error 3.2e-36 */ -static const long double lgam7a = 6.5792388916015625E0L; -static const long double lgam7b = 1.2320408538495060178292903945321122583007E-5L; +static const _Float128 lgam7a = L(6.5792388916015625E0); +static const _Float128 lgam7b = L(1.2320408538495060178292903945321122583007E-5); #define NRN7 8 -static const long double RN7[NRN7 + 1] = +static const _Float128 RN7[NRN7 + 1] = { - 2.065019306969459407636744543358209942213E11L, - 1.226919919023736909889724951708796532847E11L, - 2.996157990374348596472241776917953749106E10L, - 3.873001919306801037344727168434909521030E9L, - 2.841575255593761593270885753992732145094E8L, - 1.176342515359431913664715324652399565551E7L, - 2.558097039684188723597519300356028511547E5L, - 2.448525238332609439023786244782810774702E3L, - 6.460280377802030953041566617300902020435E0L + L(2.065019306969459407636744543358209942213E11), + L(1.226919919023736909889724951708796532847E11), + L(2.996157990374348596472241776917953749106E10), + L(3.873001919306801037344727168434909521030E9), + L(2.841575255593761593270885753992732145094E8), + L(1.176342515359431913664715324652399565551E7), + L(2.558097039684188723597519300356028511547E5), + L(2.448525238332609439023786244782810774702E3), + L(6.460280377802030953041566617300902020435E0) }; #define NRD7 7 -static const long double RD7[NRD7 + 1] = +static const _Float128 RD7[NRD7 + 1] = { - 1.102646614598516998880874785339049304483E11L, - 6.099297512712715445879759589407189290040E10L, - 1.372898136289611312713283201112060238351E10L, - 1.615306270420293159907951633566635172343E9L, - 1.061114435798489135996614242842561967459E8L, - 3.845638971184305248268608902030718674691E6L, - 7.081730675423444975703917836972720495507E4L, - 5.423122582741398226693137276201344096370E2L + L(1.102646614598516998880874785339049304483E11), + L(6.099297512712715445879759589407189290040E10), + L(1.372898136289611312713283201112060238351E10), + L(1.615306270420293159907951633566635172343E9), + L(1.061114435798489135996614242842561967459E8), + L(3.845638971184305248268608902030718674691E6), + L(7.081730675423444975703917836972720495507E4), + L(5.423122582741398226693137276201344096370E2) /* 1.0E0L */ }; @@ -338,33 +334,33 @@ static const long double RD7[NRD7 + 1] = -0.5 <= x <= 0.5 5.5 <= x+6 <= 6.5 Peak relative error 6.2e-37 */ -static const long double lgam6a = 4.7874908447265625E0L; -static const long double lgam6b = 8.9805548349424770093452324304839959231517E-7L; +static const _Float128 lgam6a = L(4.7874908447265625E0); +static const _Float128 lgam6b = L(8.9805548349424770093452324304839959231517E-7); #define NRN6 8 -static const long double RN6[NRN6 + 1] = +static const _Float128 RN6[NRN6 + 1] = { - -3.538412754670746879119162116819571823643E13L, - -2.613432593406849155765698121483394257148E13L, - -8.020670732770461579558867891923784753062E12L, - -1.322227822931250045347591780332435433420E12L, - -1.262809382777272476572558806855377129513E11L, - -7.015006277027660872284922325741197022467E9L, - -2.149320689089020841076532186783055727299E8L, - -3.167210585700002703820077565539658995316E6L, - -1.576834867378554185210279285358586385266E4L + L(-3.538412754670746879119162116819571823643E13), + L(-2.613432593406849155765698121483394257148E13), + L(-8.020670732770461579558867891923784753062E12), + L(-1.322227822931250045347591780332435433420E12), + L(-1.262809382777272476572558806855377129513E11), + L(-7.015006277027660872284922325741197022467E9), + L(-2.149320689089020841076532186783055727299E8), + L(-3.167210585700002703820077565539658995316E6), + L(-1.576834867378554185210279285358586385266E4) }; #define NRD6 8 -static const long double RD6[NRD6 + 1] = +static const _Float128 RD6[NRD6 + 1] = { - -2.073955870771283609792355579558899389085E13L, - -1.421592856111673959642750863283919318175E13L, - -4.012134994918353924219048850264207074949E12L, - -6.013361045800992316498238470888523722431E11L, - -5.145382510136622274784240527039643430628E10L, - -2.510575820013409711678540476918249524123E9L, - -6.564058379709759600836745035871373240904E7L, - -7.861511116647120540275354855221373571536E5L, - -2.821943442729620524365661338459579270561E3L + L(-2.073955870771283609792355579558899389085E13), + L(-1.421592856111673959642750863283919318175E13), + L(-4.012134994918353924219048850264207074949E12), + L(-6.013361045800992316498238470888523722431E11), + L(-5.145382510136622274784240527039643430628E10), + L(-2.510575820013409711678540476918249524123E9), + L(-6.564058379709759600836745035871373240904E7), + L(-7.861511116647120540275354855221373571536E5), + L(-2.821943442729620524365661338459579270561E3) /* 1.0E0L */ }; @@ -373,34 +369,34 @@ static const long double RD6[NRD6 + 1] = -0.5 <= x <= 0.5 4.5 <= x+5 <= 5.5 Peak relative error 3.4e-37 */ -static const long double lgam5a = 3.17803955078125E0L; -static const long double lgam5b = 1.4279566695619646941601297055408873990961E-5L; +static const _Float128 lgam5a = L(3.17803955078125E0); +static const _Float128 lgam5b = L(1.4279566695619646941601297055408873990961E-5); #define NRN5 9 -static const long double RN5[NRN5 + 1] = +static const _Float128 RN5[NRN5 + 1] = { - 2.010952885441805899580403215533972172098E11L, - 1.916132681242540921354921906708215338584E11L, - 7.679102403710581712903937970163206882492E10L, - 1.680514903671382470108010973615268125169E10L, - 2.181011222911537259440775283277711588410E9L, - 1.705361119398837808244780667539728356096E8L, - 7.792391565652481864976147945997033946360E6L, - 1.910741381027985291688667214472560023819E5L, - 2.088138241893612679762260077783794329559E3L, - 6.330318119566998299106803922739066556550E0L + L(2.010952885441805899580403215533972172098E11), + L(1.916132681242540921354921906708215338584E11), + L(7.679102403710581712903937970163206882492E10), + L(1.680514903671382470108010973615268125169E10), + L(2.181011222911537259440775283277711588410E9), + L(1.705361119398837808244780667539728356096E8), + L(7.792391565652481864976147945997033946360E6), + L(1.910741381027985291688667214472560023819E5), + L(2.088138241893612679762260077783794329559E3), + L(6.330318119566998299106803922739066556550E0) }; #define NRD5 8 -static const long double RD5[NRD5 + 1] = +static const _Float128 RD5[NRD5 + 1] = { - 1.335189758138651840605141370223112376176E11L, - 1.174130445739492885895466097516530211283E11L, - 4.308006619274572338118732154886328519910E10L, - 8.547402888692578655814445003283720677468E9L, - 9.934628078575618309542580800421370730906E8L, - 6.847107420092173812998096295422311820672E7L, - 2.698552646016599923609773122139463150403E6L, - 5.526516251532464176412113632726150253215E4L, - 4.772343321713697385780533022595450486932E2L + L(1.335189758138651840605141370223112376176E11), + L(1.174130445739492885895466097516530211283E11), + L(4.308006619274572338118732154886328519910E10), + L(8.547402888692578655814445003283720677468E9), + L(9.934628078575618309542580800421370730906E8), + L(6.847107420092173812998096295422311820672E7), + L(2.698552646016599923609773122139463150403E6), + L(5.526516251532464176412113632726150253215E4), + L(4.772343321713697385780533022595450486932E2) /* 1.0E0L */ }; @@ -409,35 +405,35 @@ static const long double RD5[NRD5 + 1] = -0.5 <= x <= 0.5 3.5 <= x+4 <= 4.5 Peak relative error 6.7e-37 */ -static const long double lgam4a = 1.791748046875E0L; -static const long double lgam4b = 1.1422353055000812477358380702272722990692E-5L; +static const _Float128 lgam4a = L(1.791748046875E0); +static const _Float128 lgam4b = L(1.1422353055000812477358380702272722990692E-5); #define NRN4 9 -static const long double RN4[NRN4 + 1] = +static const _Float128 RN4[NRN4 + 1] = { - -1.026583408246155508572442242188887829208E13L, - -1.306476685384622809290193031208776258809E13L, - -7.051088602207062164232806511992978915508E12L, - -2.100849457735620004967624442027793656108E12L, - -3.767473790774546963588549871673843260569E11L, - -4.156387497364909963498394522336575984206E10L, - -2.764021460668011732047778992419118757746E9L, - -1.036617204107109779944986471142938641399E8L, - -1.895730886640349026257780896972598305443E6L, - -1.180509051468390914200720003907727988201E4L + L(-1.026583408246155508572442242188887829208E13), + L(-1.306476685384622809290193031208776258809E13), + L(-7.051088602207062164232806511992978915508E12), + L(-2.100849457735620004967624442027793656108E12), + L(-3.767473790774546963588549871673843260569E11), + L(-4.156387497364909963498394522336575984206E10), + L(-2.764021460668011732047778992419118757746E9), + L(-1.036617204107109779944986471142938641399E8), + L(-1.895730886640349026257780896972598305443E6), + L(-1.180509051468390914200720003907727988201E4) }; #define NRD4 9 -static const long double RD4[NRD4 + 1] = +static const _Float128 RD4[NRD4 + 1] = { - -8.172669122056002077809119378047536240889E12L, - -9.477592426087986751343695251801814226960E12L, - -4.629448850139318158743900253637212801682E12L, - -1.237965465892012573255370078308035272942E12L, - -1.971624313506929845158062177061297598956E11L, - -1.905434843346570533229942397763361493610E10L, - -1.089409357680461419743730978512856675984E9L, - -3.416703082301143192939774401370222822430E7L, - -4.981791914177103793218433195857635265295E5L, - -2.192507743896742751483055798411231453733E3L + L(-8.172669122056002077809119378047536240889E12), + L(-9.477592426087986751343695251801814226960E12), + L(-4.629448850139318158743900253637212801682E12), + L(-1.237965465892012573255370078308035272942E12), + L(-1.971624313506929845158062177061297598956E11), + L(-1.905434843346570533229942397763361493610E10), + L(-1.089409357680461419743730978512856675984E9), + L(-3.416703082301143192939774401370222822430E7), + L(-4.981791914177103793218433195857635265295E5), + L(-2.192507743896742751483055798411231453733E3) /* 1.0E0L */ }; @@ -446,36 +442,36 @@ static const long double RD4[NRD4 + 1] = -0.25 <= x <= 0.5 2.75 <= x+3 <= 3.5 Peak relative error 6.0e-37 */ -static const long double lgam3a = 6.93145751953125E-1L; -static const long double lgam3b = 1.4286068203094172321214581765680755001344E-6L; +static const _Float128 lgam3a = L(6.93145751953125E-1); +static const _Float128 lgam3b = L(1.4286068203094172321214581765680755001344E-6); #define NRN3 9 -static const long double RN3[NRN3 + 1] = +static const _Float128 RN3[NRN3 + 1] = { - -4.813901815114776281494823863935820876670E11L, - -8.425592975288250400493910291066881992620E11L, - -6.228685507402467503655405482985516909157E11L, - -2.531972054436786351403749276956707260499E11L, - -6.170200796658926701311867484296426831687E10L, - -9.211477458528156048231908798456365081135E9L, - -8.251806236175037114064561038908691305583E8L, - -4.147886355917831049939930101151160447495E7L, - -1.010851868928346082547075956946476932162E6L, - -8.333374463411801009783402800801201603736E3L + L(-4.813901815114776281494823863935820876670E11), + L(-8.425592975288250400493910291066881992620E11), + L(-6.228685507402467503655405482985516909157E11), + L(-2.531972054436786351403749276956707260499E11), + L(-6.170200796658926701311867484296426831687E10), + L(-9.211477458528156048231908798456365081135E9), + L(-8.251806236175037114064561038908691305583E8), + L(-4.147886355917831049939930101151160447495E7), + L(-1.010851868928346082547075956946476932162E6), + L(-8.333374463411801009783402800801201603736E3) }; #define NRD3 9 -static const long double RD3[NRD3 + 1] = +static const _Float128 RD3[NRD3 + 1] = { - -5.216713843111675050627304523368029262450E11L, - -8.014292925418308759369583419234079164391E11L, - -5.180106858220030014546267824392678611990E11L, - -1.830406975497439003897734969120997840011E11L, - -3.845274631904879621945745960119924118925E10L, - -4.891033385370523863288908070309417710903E9L, - -3.670172254411328640353855768698287474282E8L, - -1.505316381525727713026364396635522516989E7L, - -2.856327162923716881454613540575964890347E5L, - -1.622140448015769906847567212766206894547E3L + L(-5.216713843111675050627304523368029262450E11), + L(-8.014292925418308759369583419234079164391E11), + L(-5.180106858220030014546267824392678611990E11), + L(-1.830406975497439003897734969120997840011E11), + L(-3.845274631904879621945745960119924118925E10), + L(-4.891033385370523863288908070309417710903E9), + L(-3.670172254411328640353855768698287474282E8), + L(-1.505316381525727713026364396635522516989E7), + L(-2.856327162923716881454613540575964890347E5), + L(-1.622140448015769906847567212766206894547E3) /* 1.0E0L */ }; @@ -483,33 +479,33 @@ static const long double RD3[NRD3 + 1] = /* log gamma(x+2.5) = log gamma(2.5) + x P(x)/Q(x) -0.125 <= x <= 0.25 2.375 <= x+2.5 <= 2.75 */ -static const long double lgam2r5a = 2.8466796875E-1L; -static const long double lgam2r5b = 1.4901722919159632494669682701924320137696E-5L; +static const _Float128 lgam2r5a = L(2.8466796875E-1); +static const _Float128 lgam2r5b = L(1.4901722919159632494669682701924320137696E-5); #define NRN2r5 8 -static const long double RN2r5[NRN2r5 + 1] = +static const _Float128 RN2r5[NRN2r5 + 1] = { - -4.676454313888335499356699817678862233205E9L, - -9.361888347911187924389905984624216340639E9L, - -7.695353600835685037920815799526540237703E9L, - -3.364370100981509060441853085968900734521E9L, - -8.449902011848163568670361316804900559863E8L, - -1.225249050950801905108001246436783022179E8L, - -9.732972931077110161639900388121650470926E6L, - -3.695711763932153505623248207576425983573E5L, - -4.717341584067827676530426007495274711306E3L + L(-4.676454313888335499356699817678862233205E9), + L(-9.361888347911187924389905984624216340639E9), + L(-7.695353600835685037920815799526540237703E9), + L(-3.364370100981509060441853085968900734521E9), + L(-8.449902011848163568670361316804900559863E8), + L(-1.225249050950801905108001246436783022179E8), + L(-9.732972931077110161639900388121650470926E6), + L(-3.695711763932153505623248207576425983573E5), + L(-4.717341584067827676530426007495274711306E3) }; #define NRD2r5 8 -static const long double RD2r5[NRD2r5 + 1] = +static const _Float128 RD2r5[NRD2r5 + 1] = { - -6.650657966618993679456019224416926875619E9L, - -1.099511409330635807899718829033488771623E10L, - -7.482546968307837168164311101447116903148E9L, - -2.702967190056506495988922973755870557217E9L, - -5.570008176482922704972943389590409280950E8L, - -6.536934032192792470926310043166993233231E7L, - -4.101991193844953082400035444146067511725E6L, - -1.174082735875715802334430481065526664020E5L, - -9.932840389994157592102947657277692978511E2L + L(-6.650657966618993679456019224416926875619E9), + L(-1.099511409330635807899718829033488771623E10), + L(-7.482546968307837168164311101447116903148E9), + L(-2.702967190056506495988922973755870557217E9), + L(-5.570008176482922704972943389590409280950E8), + L(-6.536934032192792470926310043166993233231E7), + L(-4.101991193844953082400035444146067511725E6), + L(-1.174082735875715802334430481065526664020E5), + L(-9.932840389994157592102947657277692978511E2) /* 1.0E0L */ }; @@ -519,32 +515,32 @@ static const long double RD2r5[NRD2r5 + 1] = 1.875 <= x+2 <= 2.375 Peak relative error 4.6e-36 */ #define NRN2 9 -static const long double RN2[NRN2 + 1] = +static const _Float128 RN2[NRN2 + 1] = { - -3.716661929737318153526921358113793421524E9L, - -1.138816715030710406922819131397532331321E10L, - -1.421017419363526524544402598734013569950E10L, - -9.510432842542519665483662502132010331451E9L, - -3.747528562099410197957514973274474767329E9L, - -8.923565763363912474488712255317033616626E8L, - -1.261396653700237624185350402781338231697E8L, - -9.918402520255661797735331317081425749014E6L, - -3.753996255897143855113273724233104768831E5L, - -4.778761333044147141559311805999540765612E3L + L(-3.716661929737318153526921358113793421524E9), + L(-1.138816715030710406922819131397532331321E10), + L(-1.421017419363526524544402598734013569950E10), + L(-9.510432842542519665483662502132010331451E9), + L(-3.747528562099410197957514973274474767329E9), + L(-8.923565763363912474488712255317033616626E8), + L(-1.261396653700237624185350402781338231697E8), + L(-9.918402520255661797735331317081425749014E6), + L(-3.753996255897143855113273724233104768831E5), + L(-4.778761333044147141559311805999540765612E3) }; #define NRD2 9 -static const long double RD2[NRD2 + 1] = +static const _Float128 RD2[NRD2 + 1] = { - -8.790916836764308497770359421351673950111E9L, - -2.023108608053212516399197678553737477486E10L, - -1.958067901852022239294231785363504458367E10L, - -1.035515043621003101254252481625188704529E10L, - -3.253884432621336737640841276619272224476E9L, - -6.186383531162456814954947669274235815544E8L, - -6.932557847749518463038934953605969951466E7L, - -4.240731768287359608773351626528479703758E6L, - -1.197343995089189188078944689846348116630E5L, - -1.004622911670588064824904487064114090920E3L + L(-8.790916836764308497770359421351673950111E9), + L(-2.023108608053212516399197678553737477486E10), + L(-1.958067901852022239294231785363504458367E10), + L(-1.035515043621003101254252481625188704529E10), + L(-3.253884432621336737640841276619272224476E9), + L(-6.186383531162456814954947669274235815544E8), + L(-6.932557847749518463038934953605969951466E7), + L(-4.240731768287359608773351626528479703758E6), + L(-1.197343995089189188078944689846348116630E5), + L(-1.004622911670588064824904487064114090920E3) /* 1.0E0 */ }; @@ -553,33 +549,33 @@ static const long double RD2[NRD2 + 1] = -0.125 <= x <= +0.125 1.625 <= x+1.75 <= 1.875 Peak relative error 9.2e-37 */ -static const long double lgam1r75a = -8.441162109375E-2L; -static const long double lgam1r75b = 1.0500073264444042213965868602268256157604E-5L; +static const _Float128 lgam1r75a = L(-8.441162109375E-2); +static const _Float128 lgam1r75b = L(1.0500073264444042213965868602268256157604E-5); #define NRN1r75 8 -static const long double RN1r75[NRN1r75 + 1] = +static const _Float128 RN1r75[NRN1r75 + 1] = { - -5.221061693929833937710891646275798251513E7L, - -2.052466337474314812817883030472496436993E8L, - -2.952718275974940270675670705084125640069E8L, - -2.132294039648116684922965964126389017840E8L, - -8.554103077186505960591321962207519908489E7L, - -1.940250901348870867323943119132071960050E7L, - -2.379394147112756860769336400290402208435E6L, - -1.384060879999526222029386539622255797389E5L, - -2.698453601378319296159355612094598695530E3L + L(-5.221061693929833937710891646275798251513E7), + L(-2.052466337474314812817883030472496436993E8), + L(-2.952718275974940270675670705084125640069E8), + L(-2.132294039648116684922965964126389017840E8), + L(-8.554103077186505960591321962207519908489E7), + L(-1.940250901348870867323943119132071960050E7), + L(-2.379394147112756860769336400290402208435E6), + L(-1.384060879999526222029386539622255797389E5), + L(-2.698453601378319296159355612094598695530E3) }; #define NRD1r75 8 -static const long double RD1r75[NRD1r75 + 1] = +static const _Float128 RD1r75[NRD1r75 + 1] = { - -2.109754689501705828789976311354395393605E8L, - -5.036651829232895725959911504899241062286E8L, - -4.954234699418689764943486770327295098084E8L, - -2.589558042412676610775157783898195339410E8L, - -7.731476117252958268044969614034776883031E7L, - -1.316721702252481296030801191240867486965E7L, - -1.201296501404876774861190604303728810836E6L, - -5.007966406976106636109459072523610273928E4L, - -6.155817990560743422008969155276229018209E2L + L(-2.109754689501705828789976311354395393605E8), + L(-5.036651829232895725959911504899241062286E8), + L(-4.954234699418689764943486770327295098084E8), + L(-2.589558042412676610775157783898195339410E8), + L(-7.731476117252958268044969614034776883031E7), + L(-1.316721702252481296030801191240867486965E7), + L(-1.201296501404876774861190604303728810836E6), + L(-5.007966406976106636109459072523610273928E4), + L(-6.155817990560743422008969155276229018209E2) /* 1.0E0L */ }; @@ -588,35 +584,35 @@ static const long double RD1r75[NRD1r75 + 1] = -0.0867 <= x <= +0.1634 1.374932... <= x+x0 <= 1.625032... Peak relative error 4.0e-36 */ -static const long double x0a = 1.4616241455078125L; -static const long double x0b = 7.9994605498412626595423257213002588621246E-6L; -static const long double y0a = -1.21490478515625E-1L; -static const long double y0b = 4.1879797753919044854428223084178486438269E-6L; +static const _Float128 x0a = L(1.4616241455078125); +static const _Float128 x0b = L(7.9994605498412626595423257213002588621246E-6); +static const _Float128 y0a = L(-1.21490478515625E-1); +static const _Float128 y0b = L(4.1879797753919044854428223084178486438269E-6); #define NRN1r5 8 -static const long double RN1r5[NRN1r5 + 1] = +static const _Float128 RN1r5[NRN1r5 + 1] = { - 6.827103657233705798067415468881313128066E5L, - 1.910041815932269464714909706705242148108E6L, - 2.194344176925978377083808566251427771951E6L, - 1.332921400100891472195055269688876427962E6L, - 4.589080973377307211815655093824787123508E5L, - 8.900334161263456942727083580232613796141E4L, - 9.053840838306019753209127312097612455236E3L, - 4.053367147553353374151852319743594873771E2L, - 5.040631576303952022968949605613514584950E0L + L(6.827103657233705798067415468881313128066E5), + L(1.910041815932269464714909706705242148108E6), + L(2.194344176925978377083808566251427771951E6), + L(1.332921400100891472195055269688876427962E6), + L(4.589080973377307211815655093824787123508E5), + L(8.900334161263456942727083580232613796141E4), + L(9.053840838306019753209127312097612455236E3), + L(4.053367147553353374151852319743594873771E2), + L(5.040631576303952022968949605613514584950E0) }; #define NRD1r5 8 -static const long double RD1r5[NRD1r5 + 1] = +static const _Float128 RD1r5[NRD1r5 + 1] = { - 1.411036368843183477558773688484699813355E6L, - 4.378121767236251950226362443134306184849E6L, - 5.682322855631723455425929877581697918168E6L, - 3.999065731556977782435009349967042222375E6L, - 1.653651390456781293163585493620758410333E6L, - 4.067774359067489605179546964969435858311E5L, - 5.741463295366557346748361781768833633256E4L, - 4.226404539738182992856094681115746692030E3L, - 1.316980975410327975566999780608618774469E2L, + L(1.411036368843183477558773688484699813355E6), + L(4.378121767236251950226362443134306184849E6), + L(5.682322855631723455425929877581697918168E6), + L(3.999065731556977782435009349967042222375E6), + L(1.653651390456781293163585493620758410333E6), + L(4.067774359067489605179546964969435858311E5), + L(5.741463295366557346748361781768833633256E4), + L(4.226404539738182992856094681115746692030E3), + L(1.316980975410327975566999780608618774469E2), /* 1.0E0L */ }; @@ -625,34 +621,34 @@ static const long double RD1r5[NRD1r5 + 1] = -.125 <= x <= +.125 1.125 <= x+1.25 <= 1.375 Peak relative error = 4.9e-36 */ -static const long double lgam1r25a = -9.82818603515625E-2L; -static const long double lgam1r25b = 1.0023929749338536146197303364159774377296E-5L; +static const _Float128 lgam1r25a = L(-9.82818603515625E-2); +static const _Float128 lgam1r25b = L(1.0023929749338536146197303364159774377296E-5); #define NRN1r25 9 -static const long double RN1r25[NRN1r25 + 1] = +static const _Float128 RN1r25[NRN1r25 + 1] = { - -9.054787275312026472896002240379580536760E4L, - -8.685076892989927640126560802094680794471E4L, - 2.797898965448019916967849727279076547109E5L, - 6.175520827134342734546868356396008898299E5L, - 5.179626599589134831538516906517372619641E5L, - 2.253076616239043944538380039205558242161E5L, - 5.312653119599957228630544772499197307195E4L, - 6.434329437514083776052669599834938898255E3L, - 3.385414416983114598582554037612347549220E2L, - 4.907821957946273805080625052510832015792E0L + L(-9.054787275312026472896002240379580536760E4), + L(-8.685076892989927640126560802094680794471E4), + L(2.797898965448019916967849727279076547109E5), + L(6.175520827134342734546868356396008898299E5), + L(5.179626599589134831538516906517372619641E5), + L(2.253076616239043944538380039205558242161E5), + L(5.312653119599957228630544772499197307195E4), + L(6.434329437514083776052669599834938898255E3), + L(3.385414416983114598582554037612347549220E2), + L(4.907821957946273805080625052510832015792E0) }; #define NRD1r25 8 -static const long double RD1r25[NRD1r25 + 1] = +static const _Float128 RD1r25[NRD1r25 + 1] = { - 3.980939377333448005389084785896660309000E5L, - 1.429634893085231519692365775184490465542E6L, - 2.145438946455476062850151428438668234336E6L, - 1.743786661358280837020848127465970357893E6L, - 8.316364251289743923178092656080441655273E5L, - 2.355732939106812496699621491135458324294E5L, - 3.822267399625696880571810137601310855419E4L, - 3.228463206479133236028576845538387620856E3L, - 1.152133170470059555646301189220117965514E2L + L(3.980939377333448005389084785896660309000E5), + L(1.429634893085231519692365775184490465542E6), + L(2.145438946455476062850151428438668234336E6), + L(1.743786661358280837020848127465970357893E6), + L(8.316364251289743923178092656080441655273E5), + L(2.355732939106812496699621491135458324294E5), + L(3.822267399625696880571810137601310855419E4), + L(3.228463206479133236028576845538387620856E3), + L(1.152133170470059555646301189220117965514E2) /* 1.0E0L */ }; @@ -662,29 +658,29 @@ static const long double RD1r25[NRD1r25 + 1] = 1.0 <= x+1 <= 1.125 Peak relative error 1.1e-35 */ #define NRN1 8 -static const long double RN1[NRN1 + 1] = +static const _Float128 RN1[NRN1 + 1] = { - -9.987560186094800756471055681088744738818E3L, - -2.506039379419574361949680225279376329742E4L, - -1.386770737662176516403363873617457652991E4L, - 1.439445846078103202928677244188837130744E4L, - 2.159612048879650471489449668295139990693E4L, - 1.047439813638144485276023138173676047079E4L, - 2.250316398054332592560412486630769139961E3L, - 1.958510425467720733041971651126443864041E2L, - 4.516830313569454663374271993200291219855E0L + L(-9.987560186094800756471055681088744738818E3), + L(-2.506039379419574361949680225279376329742E4), + L(-1.386770737662176516403363873617457652991E4), + L(1.439445846078103202928677244188837130744E4), + L(2.159612048879650471489449668295139990693E4), + L(1.047439813638144485276023138173676047079E4), + L(2.250316398054332592560412486630769139961E3), + L(1.958510425467720733041971651126443864041E2), + L(4.516830313569454663374271993200291219855E0) }; #define NRD1 7 -static const long double RD1[NRD1 + 1] = +static const _Float128 RD1[NRD1 + 1] = { - 1.730299573175751778863269333703788214547E4L, - 6.807080914851328611903744668028014678148E4L, - 1.090071629101496938655806063184092302439E5L, - 9.124354356415154289343303999616003884080E4L, - 4.262071638655772404431164427024003253954E4L, - 1.096981664067373953673982635805821283581E4L, - 1.431229503796575892151252708527595787588E3L, - 7.734110684303689320830401788262295992921E1L + L(1.730299573175751778863269333703788214547E4), + L(6.807080914851328611903744668028014678148E4), + L(1.090071629101496938655806063184092302439E5), + L(9.124354356415154289343303999616003884080E4), + L(4.262071638655772404431164427024003253954E4), + L(1.096981664067373953673982635805821283581E4), + L(1.431229503796575892151252708527595787588E3), + L(7.734110684303689320830401788262295992921E1) /* 1.0E0 */ }; @@ -694,40 +690,40 @@ static const long double RD1[NRD1 + 1] = 0.875 <= x+1 <= 1.0 Peak relative error 7.0e-37 */ #define NRNr9 8 -static const long double RNr9[NRNr9 + 1] = +static const _Float128 RNr9[NRNr9 + 1] = { - 4.441379198241760069548832023257571176884E5L, - 1.273072988367176540909122090089580368732E6L, - 9.732422305818501557502584486510048387724E5L, - -5.040539994443998275271644292272870348684E5L, - -1.208719055525609446357448132109723786736E6L, - -7.434275365370936547146540554419058907156E5L, - -2.075642969983377738209203358199008185741E5L, - -2.565534860781128618589288075109372218042E4L, - -1.032901669542994124131223797515913955938E3L, + L(4.441379198241760069548832023257571176884E5), + L(1.273072988367176540909122090089580368732E6), + L(9.732422305818501557502584486510048387724E5), + L(-5.040539994443998275271644292272870348684E5), + L(-1.208719055525609446357448132109723786736E6), + L(-7.434275365370936547146540554419058907156E5), + L(-2.075642969983377738209203358199008185741E5), + L(-2.565534860781128618589288075109372218042E4), + L(-1.032901669542994124131223797515913955938E3), }; #define NRDr9 8 -static const long double RDr9[NRDr9 + 1] = +static const _Float128 RDr9[NRDr9 + 1] = { - -7.694488331323118759486182246005193998007E5L, - -3.301918855321234414232308938454112213751E6L, - -5.856830900232338906742924836032279404702E6L, - -5.540672519616151584486240871424021377540E6L, - -3.006530901041386626148342989181721176919E6L, - -9.350378280513062139466966374330795935163E5L, - -1.566179100031063346901755685375732739511E5L, - -1.205016539620260779274902967231510804992E4L, - -2.724583156305709733221564484006088794284E2L + L(-7.694488331323118759486182246005193998007E5), + L(-3.301918855321234414232308938454112213751E6), + L(-5.856830900232338906742924836032279404702E6), + L(-5.540672519616151584486240871424021377540E6), + L(-3.006530901041386626148342989181721176919E6), + L(-9.350378280513062139466966374330795935163E5), + L(-1.566179100031063346901755685375732739511E5), + L(-1.205016539620260779274902967231510804992E4), + L(-2.724583156305709733221564484006088794284E2) /* 1.0E0 */ }; /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ -static long double -neval (long double x, const long double *p, int n) +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = *p--; @@ -742,10 +738,10 @@ neval (long double x, const long double *p, int n) /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ -static long double -deval (long double x, const long double *p, int n) +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = x + *p--; @@ -758,10 +754,10 @@ deval (long double x, const long double *p, int n) } -long double -__ieee754_lgammal_r (long double x, int *signgamp) +_Float128 +__ieee754_lgammal_r (_Float128 x, int *signgamp) { - long double p, q, w, z, nx; + _Float128 p, q, w, z, nx; int i, nn; *signgamp = 1; @@ -769,31 +765,31 @@ __ieee754_lgammal_r (long double x, int *signgamp) if (! isfinite (x)) return x * x; - if (x == 0.0L) + if (x == 0) { if (signbit (x)) *signgamp = -1; } - if (x < 0.0L) + if (x < 0) { - if (x < -2.0L && x > (LDBL_MANT_DIG == 106 ? -48.0L : -50.0L)) + if (x < -2 && x > -50) return __lgamma_negl (x, signgamp); q = -x; p = __floorl (q); if (p == q) - return (one / (p - p)); - long double halfp = p * 0.5L; + return (one / fabsl (p - p)); + _Float128 halfp = p * L(0.5); if (halfp == __floorl (halfp)) *signgamp = -1; else *signgamp = 1; - if (q < 0x1p-120L) + if (q < L(0x1p-120)) return -__logl (q); z = q - p; - if (z > 0.5L) + if (z > L(0.5)) { - p += 1.0L; + p += 1; z = p - q; } z = q * __sinl (PIL * z); @@ -802,16 +798,16 @@ __ieee754_lgammal_r (long double x, int *signgamp) return (z); } - if (x < 13.5L) + if (x < L(13.5)) { - p = 0.0L; - nx = __floorl (x + 0.5L); + p = 0; + nx = __floorl (x + L(0.5)); nn = nx; switch (nn) { case 0: /* log gamma (x + 1) = log(x) + log gamma(x) */ - if (x < 0x1p-120L) + if (x < L(0x1p-120)) return -__logl (x); else if (x <= 0.125) { @@ -819,14 +815,14 @@ __ieee754_lgammal_r (long double x, int *signgamp) } else if (x <= 0.375) { - z = x - 0.25L; + z = x - L(0.25); p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); p += lgam1r25b; p += lgam1r25a; } else if (x <= 0.625) { - z = x + (1.0L - x0a); + z = x + (1 - x0a); z = z - x0b; p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); p = p * z * z; @@ -835,25 +831,25 @@ __ieee754_lgammal_r (long double x, int *signgamp) } else if (x <= 0.875) { - z = x - 0.75L; + z = x - L(0.75); p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); p += lgam1r75b; p += lgam1r75a; } else { - z = x - 1.0L; + z = x - 1; p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); } p = p - __logl (x); break; case 1: - if (x < 0.875L) + if (x < L(0.875)) { if (x <= 0.625) { - z = x + (1.0L - x0a); + z = x + (1 - x0a); z = z - x0b; p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); p = p * z * z; @@ -862,7 +858,7 @@ __ieee754_lgammal_r (long double x, int *signgamp) } else if (x <= 0.875) { - z = x - 0.75L; + z = x - L(0.75); p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); p += lgam1r75b; @@ -870,26 +866,26 @@ __ieee754_lgammal_r (long double x, int *signgamp) } else { - z = x - 1.0L; + z = x - 1; p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); } p = p - __logl (x); } - else if (x < 1.0L) + else if (x < 1) { - z = x - 1.0L; + z = x - 1; p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9); } - else if (x == 1.0L) - p = 0.0L; - else if (x <= 1.125L) + else if (x == 1) + p = 0; + else if (x <= L(1.125)) { - z = x - 1.0L; + z = x - 1; p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1); } else if (x <= 1.375) { - z = x - 1.25L; + z = x - L(1.25); p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); p += lgam1r25b; p += lgam1r25a; @@ -907,7 +903,7 @@ __ieee754_lgammal_r (long double x, int *signgamp) break; case 2: - if (x < 1.625L) + if (x < L(1.625)) { z = x - x0a; z = z - x0b; @@ -916,23 +912,23 @@ __ieee754_lgammal_r (long double x, int *signgamp) p = p + y0b; p = p + y0a; } - else if (x < 1.875L) + else if (x < L(1.875)) { - z = x - 1.75L; + z = x - L(1.75); p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); p += lgam1r75b; p += lgam1r75a; } - else if (x == 2.0L) - p = 0.0L; - else if (x < 2.375L) + else if (x == 2) + p = 0; + else if (x < L(2.375)) { - z = x - 2.0L; + z = x - 2; p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); } else { - z = x - 2.5L; + z = x - L(2.5); p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); p += lgam2r5b; p += lgam2r5a; @@ -942,14 +938,14 @@ __ieee754_lgammal_r (long double x, int *signgamp) case 3: if (x < 2.75) { - z = x - 2.5L; + z = x - L(2.5); p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); p += lgam2r5b; p += lgam2r5a; } else { - z = x - 3.0L; + z = x - 3; p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3); p += lgam3b; p += lgam3a; @@ -957,70 +953,70 @@ __ieee754_lgammal_r (long double x, int *signgamp) break; case 4: - z = x - 4.0L; + z = x - 4; p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4); p += lgam4b; p += lgam4a; break; case 5: - z = x - 5.0L; + z = x - 5; p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5); p += lgam5b; p += lgam5a; break; case 6: - z = x - 6.0L; + z = x - 6; p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6); p += lgam6b; p += lgam6a; break; case 7: - z = x - 7.0L; + z = x - 7; p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7); p += lgam7b; p += lgam7a; break; case 8: - z = x - 8.0L; + z = x - 8; p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8); p += lgam8b; p += lgam8a; break; case 9: - z = x - 9.0L; + z = x - 9; p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9); p += lgam9b; p += lgam9a; break; case 10: - z = x - 10.0L; + z = x - 10; p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10); p += lgam10b; p += lgam10a; break; case 11: - z = x - 11.0L; + z = x - 11; p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11); p += lgam11b; p += lgam11a; break; case 12: - z = x - 12.0L; + z = x - 12; p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12); p += lgam12b; p += lgam12a; break; case 13: - z = x - 13.0L; + z = x - 13; p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13); p += lgam13b; p += lgam13a; @@ -1032,14 +1028,14 @@ __ieee754_lgammal_r (long double x, int *signgamp) if (x > MAXLGM) return (*signgamp * huge * huge); - if (x > 0x1p120L) - return x * (__logl (x) - 1.0L); + if (x > L(0x1p120)) + return x * (__logl (x) - 1); q = ls2pi - x; - q = (x - 0.5L) * __logl (x) + q; - if (x > 1.0e18L) + q = (x - L(0.5)) * __logl (x) + q; + if (x > L(1.0e18)) return (q); - p = 1.0L / (x * x); + p = 1 / (x * x); q += neval (p, RASY, NRASY) / x; return (q); } diff --git a/sysdeps/ieee754/ldbl-128/e_log10l.c b/sysdeps/ieee754/ldbl-128/e_log10l.c index 618255f2fa..e8f33984f2 100644 --- a/sysdeps/ieee754/ldbl-128/e_log10l.c +++ b/sysdeps/ieee754/ldbl-128/e_log10l.c @@ -68,36 +68,36 @@ * Theoretical peak relative error = 5.3e-37, * relative peak error spread = 2.3e-14 */ -static const long double P[13] = +static const _Float128 P[13] = { - 1.313572404063446165910279910527789794488E4L, - 7.771154681358524243729929227226708890930E4L, - 2.014652742082537582487669938141683759923E5L, - 3.007007295140399532324943111654767187848E5L, - 2.854829159639697837788887080758954924001E5L, - 1.797628303815655343403735250238293741397E5L, - 7.594356839258970405033155585486712125861E4L, - 2.128857716871515081352991964243375186031E4L, - 3.824952356185897735160588078446136783779E3L, - 4.114517881637811823002128927449878962058E2L, - 2.321125933898420063925789532045674660756E1L, - 4.998469661968096229986658302195402690910E-1L, - 1.538612243596254322971797716843006400388E-6L + L(1.313572404063446165910279910527789794488E4), + L(7.771154681358524243729929227226708890930E4), + L(2.014652742082537582487669938141683759923E5), + L(3.007007295140399532324943111654767187848E5), + L(2.854829159639697837788887080758954924001E5), + L(1.797628303815655343403735250238293741397E5), + L(7.594356839258970405033155585486712125861E4), + L(2.128857716871515081352991964243375186031E4), + L(3.824952356185897735160588078446136783779E3), + L(4.114517881637811823002128927449878962058E2), + L(2.321125933898420063925789532045674660756E1), + L(4.998469661968096229986658302195402690910E-1), + L(1.538612243596254322971797716843006400388E-6) }; -static const long double Q[12] = +static const _Float128 Q[12] = { - 3.940717212190338497730839731583397586124E4L, - 2.626900195321832660448791748036714883242E5L, - 7.777690340007566932935753241556479363645E5L, - 1.347518538384329112529391120390701166528E6L, - 1.514882452993549494932585972882995548426E6L, - 1.158019977462989115839826904108208787040E6L, - 6.132189329546557743179177159925690841200E5L, - 2.248234257620569139969141618556349415120E5L, - 5.605842085972455027590989944010492125825E4L, - 9.147150349299596453976674231612674085381E3L, - 9.104928120962988414618126155557301584078E2L, - 4.839208193348159620282142911143429644326E1L + L(3.940717212190338497730839731583397586124E4), + L(2.626900195321832660448791748036714883242E5), + L(7.777690340007566932935753241556479363645E5), + L(1.347518538384329112529391120390701166528E6), + L(1.514882452993549494932585972882995548426E6), + L(1.158019977462989115839826904108208787040E6), + L(6.132189329546557743179177159925690841200E5), + L(2.248234257620569139969141618556349415120E5), + L(5.605842085972455027590989944010492125825E4), + L(9.147150349299596453976674231612674085381E3), + L(9.104928120962988414618126155557301584078E2), + L(4.839208193348159620282142911143429644326E1) /* 1.000000000000000000000000000000000000000E0L, */ }; @@ -107,44 +107,44 @@ static const long double Q[12] = * Theoretical peak relative error = 1.1e-35, * relative peak error spread 1.1e-9 */ -static const long double R[6] = +static const _Float128 R[6] = { - 1.418134209872192732479751274970992665513E5L, - -8.977257995689735303686582344659576526998E4L, - 2.048819892795278657810231591630928516206E4L, - -2.024301798136027039250415126250455056397E3L, - 8.057002716646055371965756206836056074715E1L, - -8.828896441624934385266096344596648080902E-1L + L(1.418134209872192732479751274970992665513E5), + L(-8.977257995689735303686582344659576526998E4), + L(2.048819892795278657810231591630928516206E4), + L(-2.024301798136027039250415126250455056397E3), + L(8.057002716646055371965756206836056074715E1), + L(-8.828896441624934385266096344596648080902E-1) }; -static const long double S[6] = +static const _Float128 S[6] = { - 1.701761051846631278975701529965589676574E6L, - -1.332535117259762928288745111081235577029E6L, - 4.001557694070773974936904547424676279307E5L, - -5.748542087379434595104154610899551484314E4L, - 3.998526750980007367835804959888064681098E3L, - -1.186359407982897997337150403816839480438E2L + L(1.701761051846631278975701529965589676574E6), + L(-1.332535117259762928288745111081235577029E6), + L(4.001557694070773974936904547424676279307E5), + L(-5.748542087379434595104154610899551484314E4), + L(3.998526750980007367835804959888064681098E3), + L(-1.186359407982897997337150403816839480438E2) /* 1.000000000000000000000000000000000000000E0L, */ }; -static const long double +static const _Float128 /* log10(2) */ -L102A = 0.3125L, -L102B = -1.14700043360188047862611052755069732318101185E-2L, +L102A = L(0.3125), +L102B = L(-1.14700043360188047862611052755069732318101185E-2), /* log10(e) */ -L10EA = 0.5L, -L10EB = -6.570551809674817234887108108339491770560299E-2L, +L10EA = L(0.5), +L10EB = L(-6.570551809674817234887108108339491770560299E-2), /* sqrt(2)/2 */ -SQRTH = 7.071067811865475244008443621048490392848359E-1L; +SQRTH = L(7.071067811865475244008443621048490392848359E-1); /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ -static long double -neval (long double x, const long double *p, int n) +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = *p--; @@ -159,10 +159,10 @@ neval (long double x, const long double *p, int n) /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ -static long double -deval (long double x, const long double *p, int n) +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = x + *p--; @@ -176,25 +176,25 @@ deval (long double x, const long double *p, int n) -long double -__ieee754_log10l (long double x) +_Float128 +__ieee754_log10l (_Float128 x) { - long double z; - long double y; + _Float128 z; + _Float128 y; int e; int64_t hx, lx; /* Test for domain */ GET_LDOUBLE_WORDS64 (hx, lx, x); if (((hx & 0x7fffffffffffffffLL) | lx) == 0) - return (-1.0L / (x - x)); + return (-1 / fabsl (x)); /* log10l(+-0)=-inf */ if (hx < 0) return (x - x) / (x - x); if (hx >= 0x7fff000000000000LL) return (x + x); - if (x == 1.0L) - return 0.0L; + if (x == 1) + return 0; /* separate mantissa from exponent */ @@ -212,14 +212,14 @@ __ieee754_log10l (long double x) if (x < SQRTH) { /* 2( 2x-1 )/( 2x+1 ) */ e -= 1; - z = x - 0.5L; - y = 0.5L * z + 0.5L; + z = x - L(0.5); + y = L(0.5) * z + L(0.5); } else { /* 2 (x-1)/(x+1) */ - z = x - 0.5L; - z -= 0.5L; - y = 0.5L * x + 0.5L; + z = x - L(0.5); + z -= L(0.5); + y = L(0.5) * x + L(0.5); } x = z / y; z = x * x; @@ -233,11 +233,11 @@ __ieee754_log10l (long double x) if (x < SQRTH) { e -= 1; - x = 2.0 * x - 1.0L; /* 2x - 1 */ + x = 2.0 * x - 1; /* 2x - 1 */ } else { - x = x - 1.0L; + x = x - 1; } z = x * x; y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); diff --git a/sysdeps/ieee754/ldbl-128/e_log2l.c b/sysdeps/ieee754/ldbl-128/e_log2l.c index 6b1faa0523..06bf04f5e3 100644 --- a/sysdeps/ieee754/ldbl-128/e_log2l.c +++ b/sysdeps/ieee754/ldbl-128/e_log2l.c @@ -67,36 +67,36 @@ * Theoretical peak relative error = 5.3e-37, * relative peak error spread = 2.3e-14 */ -static const long double P[13] = +static const _Float128 P[13] = { - 1.313572404063446165910279910527789794488E4L, - 7.771154681358524243729929227226708890930E4L, - 2.014652742082537582487669938141683759923E5L, - 3.007007295140399532324943111654767187848E5L, - 2.854829159639697837788887080758954924001E5L, - 1.797628303815655343403735250238293741397E5L, - 7.594356839258970405033155585486712125861E4L, - 2.128857716871515081352991964243375186031E4L, - 3.824952356185897735160588078446136783779E3L, - 4.114517881637811823002128927449878962058E2L, - 2.321125933898420063925789532045674660756E1L, - 4.998469661968096229986658302195402690910E-1L, - 1.538612243596254322971797716843006400388E-6L + L(1.313572404063446165910279910527789794488E4), + L(7.771154681358524243729929227226708890930E4), + L(2.014652742082537582487669938141683759923E5), + L(3.007007295140399532324943111654767187848E5), + L(2.854829159639697837788887080758954924001E5), + L(1.797628303815655343403735250238293741397E5), + L(7.594356839258970405033155585486712125861E4), + L(2.128857716871515081352991964243375186031E4), + L(3.824952356185897735160588078446136783779E3), + L(4.114517881637811823002128927449878962058E2), + L(2.321125933898420063925789532045674660756E1), + L(4.998469661968096229986658302195402690910E-1), + L(1.538612243596254322971797716843006400388E-6) }; -static const long double Q[12] = +static const _Float128 Q[12] = { - 3.940717212190338497730839731583397586124E4L, - 2.626900195321832660448791748036714883242E5L, - 7.777690340007566932935753241556479363645E5L, - 1.347518538384329112529391120390701166528E6L, - 1.514882452993549494932585972882995548426E6L, - 1.158019977462989115839826904108208787040E6L, - 6.132189329546557743179177159925690841200E5L, - 2.248234257620569139969141618556349415120E5L, - 5.605842085972455027590989944010492125825E4L, - 9.147150349299596453976674231612674085381E3L, - 9.104928120962988414618126155557301584078E2L, - 4.839208193348159620282142911143429644326E1L + L(3.940717212190338497730839731583397586124E4), + L(2.626900195321832660448791748036714883242E5), + L(7.777690340007566932935753241556479363645E5), + L(1.347518538384329112529391120390701166528E6), + L(1.514882452993549494932585972882995548426E6), + L(1.158019977462989115839826904108208787040E6), + L(6.132189329546557743179177159925690841200E5), + L(2.248234257620569139969141618556349415120E5), + L(5.605842085972455027590989944010492125825E4), + L(9.147150349299596453976674231612674085381E3), + L(9.104928120962988414618126155557301584078E2), + L(4.839208193348159620282142911143429644326E1) /* 1.000000000000000000000000000000000000000E0L, */ }; @@ -106,39 +106,39 @@ static const long double Q[12] = * Theoretical peak relative error = 1.1e-35, * relative peak error spread 1.1e-9 */ -static const long double R[6] = +static const _Float128 R[6] = { - 1.418134209872192732479751274970992665513E5L, - -8.977257995689735303686582344659576526998E4L, - 2.048819892795278657810231591630928516206E4L, - -2.024301798136027039250415126250455056397E3L, - 8.057002716646055371965756206836056074715E1L, - -8.828896441624934385266096344596648080902E-1L + L(1.418134209872192732479751274970992665513E5), + L(-8.977257995689735303686582344659576526998E4), + L(2.048819892795278657810231591630928516206E4), + L(-2.024301798136027039250415126250455056397E3), + L(8.057002716646055371965756206836056074715E1), + L(-8.828896441624934385266096344596648080902E-1) }; -static const long double S[6] = +static const _Float128 S[6] = { - 1.701761051846631278975701529965589676574E6L, - -1.332535117259762928288745111081235577029E6L, - 4.001557694070773974936904547424676279307E5L, - -5.748542087379434595104154610899551484314E4L, - 3.998526750980007367835804959888064681098E3L, - -1.186359407982897997337150403816839480438E2L + L(1.701761051846631278975701529965589676574E6), + L(-1.332535117259762928288745111081235577029E6), + L(4.001557694070773974936904547424676279307E5), + L(-5.748542087379434595104154610899551484314E4), + L(3.998526750980007367835804959888064681098E3), + L(-1.186359407982897997337150403816839480438E2) /* 1.000000000000000000000000000000000000000E0L, */ }; -static const long double +static const _Float128 /* log2(e) - 1 */ -LOG2EA = 4.4269504088896340735992468100189213742664595E-1L, +LOG2EA = L(4.4269504088896340735992468100189213742664595E-1), /* sqrt(2)/2 */ -SQRTH = 7.071067811865475244008443621048490392848359E-1L; +SQRTH = L(7.071067811865475244008443621048490392848359E-1); /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ -static long double -neval (long double x, const long double *p, int n) +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = *p--; @@ -153,10 +153,10 @@ neval (long double x, const long double *p, int n) /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ -static long double -deval (long double x, const long double *p, int n) +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = x + *p--; @@ -170,25 +170,25 @@ deval (long double x, const long double *p, int n) -long double -__ieee754_log2l (long double x) +_Float128 +__ieee754_log2l (_Float128 x) { - long double z; - long double y; + _Float128 z; + _Float128 y; int e; int64_t hx, lx; /* Test for domain */ GET_LDOUBLE_WORDS64 (hx, lx, x); if (((hx & 0x7fffffffffffffffLL) | lx) == 0) - return (-1.0L / (x - x)); + return (-1 / fabsl (x)); /* log2l(+-0)=-inf */ if (hx < 0) return (x - x) / (x - x); if (hx >= 0x7fff000000000000LL) return (x + x); - if (x == 1.0L) - return 0.0L; + if (x == 1) + return 0; /* separate mantissa from exponent */ @@ -206,14 +206,14 @@ __ieee754_log2l (long double x) if (x < SQRTH) { /* 2( 2x-1 )/( 2x+1 ) */ e -= 1; - z = x - 0.5L; - y = 0.5L * z + 0.5L; + z = x - L(0.5); + y = L(0.5) * z + L(0.5); } else { /* 2 (x-1)/(x+1) */ - z = x - 0.5L; - z -= 0.5L; - y = 0.5L * x + 0.5L; + z = x - L(0.5); + z -= L(0.5); + y = L(0.5) * x + L(0.5); } x = z / y; z = x * x; @@ -227,11 +227,11 @@ __ieee754_log2l (long double x) if (x < SQRTH) { e -= 1; - x = 2.0 * x - 1.0L; /* 2x - 1 */ + x = 2.0 * x - 1; /* 2x - 1 */ } else { - x = x - 1.0L; + x = x - 1; } z = x * x; y = x * (z * neval (x, P, 12) / deval (x, Q, 11)); diff --git a/sysdeps/ieee754/ldbl-128/e_logl.c b/sysdeps/ieee754/ldbl-128/e_logl.c index cb43816793..8672047e43 100644 --- a/sysdeps/ieee754/ldbl-128/e_logl.c +++ b/sysdeps/ieee754/ldbl-128/e_logl.c @@ -58,134 +58,135 @@ License along with this library; if not, see <http://www.gnu.org/licenses/>. */ +#include <math.h> #include <math_private.h> /* log(1+x) = x - .5 x^2 + x^3 l(x) -.0078125 <= x <= +.0078125 peak relative error 1.2e-37 */ -static const long double -l3 = 3.333333333333333333333333333333336096926E-1L, -l4 = -2.499999999999999999999999999486853077002E-1L, -l5 = 1.999999999999999999999999998515277861905E-1L, -l6 = -1.666666666666666666666798448356171665678E-1L, -l7 = 1.428571428571428571428808945895490721564E-1L, -l8 = -1.249999999999999987884655626377588149000E-1L, -l9 = 1.111111111111111093947834982832456459186E-1L, -l10 = -1.000000000000532974938900317952530453248E-1L, -l11 = 9.090909090915566247008015301349979892689E-2L, -l12 = -8.333333211818065121250921925397567745734E-2L, -l13 = 7.692307559897661630807048686258659316091E-2L, -l14 = -7.144242754190814657241902218399056829264E-2L, -l15 = 6.668057591071739754844678883223432347481E-2L; +static const _Float128 +l3 = L(3.333333333333333333333333333333336096926E-1), +l4 = L(-2.499999999999999999999999999486853077002E-1), +l5 = L(1.999999999999999999999999998515277861905E-1), +l6 = L(-1.666666666666666666666798448356171665678E-1), +l7 = L(1.428571428571428571428808945895490721564E-1), +l8 = L(-1.249999999999999987884655626377588149000E-1), +l9 = L(1.111111111111111093947834982832456459186E-1), +l10 = L(-1.000000000000532974938900317952530453248E-1), +l11 = L(9.090909090915566247008015301349979892689E-2), +l12 = L(-8.333333211818065121250921925397567745734E-2), +l13 = L(7.692307559897661630807048686258659316091E-2), +l14 = L(-7.144242754190814657241902218399056829264E-2), +l15 = L(6.668057591071739754844678883223432347481E-2); /* Lookup table of ln(t) - (t-1) t = 0.5 + (k+26)/128) k = 0, ..., 91 */ -static const long double logtbl[92] = { --5.5345593589352099112142921677820359632418E-2L, --5.2108257402767124761784665198737642086148E-2L, --4.8991686870576856279407775480686721935120E-2L, --4.5993270766361228596215288742353061431071E-2L, --4.3110481649613269682442058976885699556950E-2L, --4.0340872319076331310838085093194799765520E-2L, --3.7682072451780927439219005993827431503510E-2L, --3.5131785416234343803903228503274262719586E-2L, --3.2687785249045246292687241862699949178831E-2L, --3.0347913785027239068190798397055267411813E-2L, --2.8110077931525797884641940838507561326298E-2L, --2.5972247078357715036426583294246819637618E-2L, --2.3932450635346084858612873953407168217307E-2L, --2.1988775689981395152022535153795155900240E-2L, --2.0139364778244501615441044267387667496733E-2L, --1.8382413762093794819267536615342902718324E-2L, --1.6716169807550022358923589720001638093023E-2L, --1.5138929457710992616226033183958974965355E-2L, --1.3649036795397472900424896523305726435029E-2L, --1.2244881690473465543308397998034325468152E-2L, --1.0924898127200937840689817557742469105693E-2L, --9.6875626072830301572839422532631079809328E-3L, --8.5313926245226231463436209313499745894157E-3L, --7.4549452072765973384933565912143044991706E-3L, --6.4568155251217050991200599386801665681310E-3L, --5.5356355563671005131126851708522185605193E-3L, --4.6900728132525199028885749289712348829878E-3L, --3.9188291218610470766469347968659624282519E-3L, --3.2206394539524058873423550293617843896540E-3L, --2.5942708080877805657374888909297113032132E-3L, --2.0385211375711716729239156839929281289086E-3L, --1.5522183228760777967376942769773768850872E-3L, --1.1342191863606077520036253234446621373191E-3L, --7.8340854719967065861624024730268350459991E-4L, --4.9869831458030115699628274852562992756174E-4L, --2.7902661731604211834685052867305795169688E-4L, --1.2335696813916860754951146082826952093496E-4L, --3.0677461025892873184042490943581654591817E-5L, +static const _Float128 logtbl[92] = { +L(-5.5345593589352099112142921677820359632418E-2), +L(-5.2108257402767124761784665198737642086148E-2), +L(-4.8991686870576856279407775480686721935120E-2), +L(-4.5993270766361228596215288742353061431071E-2), +L(-4.3110481649613269682442058976885699556950E-2), +L(-4.0340872319076331310838085093194799765520E-2), +L(-3.7682072451780927439219005993827431503510E-2), +L(-3.5131785416234343803903228503274262719586E-2), +L(-3.2687785249045246292687241862699949178831E-2), +L(-3.0347913785027239068190798397055267411813E-2), +L(-2.8110077931525797884641940838507561326298E-2), +L(-2.5972247078357715036426583294246819637618E-2), +L(-2.3932450635346084858612873953407168217307E-2), +L(-2.1988775689981395152022535153795155900240E-2), +L(-2.0139364778244501615441044267387667496733E-2), +L(-1.8382413762093794819267536615342902718324E-2), +L(-1.6716169807550022358923589720001638093023E-2), +L(-1.5138929457710992616226033183958974965355E-2), +L(-1.3649036795397472900424896523305726435029E-2), +L(-1.2244881690473465543308397998034325468152E-2), +L(-1.0924898127200937840689817557742469105693E-2), +L(-9.6875626072830301572839422532631079809328E-3), +L(-8.5313926245226231463436209313499745894157E-3), +L(-7.4549452072765973384933565912143044991706E-3), +L(-6.4568155251217050991200599386801665681310E-3), +L(-5.5356355563671005131126851708522185605193E-3), +L(-4.6900728132525199028885749289712348829878E-3), +L(-3.9188291218610470766469347968659624282519E-3), +L(-3.2206394539524058873423550293617843896540E-3), +L(-2.5942708080877805657374888909297113032132E-3), +L(-2.0385211375711716729239156839929281289086E-3), +L(-1.5522183228760777967376942769773768850872E-3), +L(-1.1342191863606077520036253234446621373191E-3), +L(-7.8340854719967065861624024730268350459991E-4), +L(-4.9869831458030115699628274852562992756174E-4), +L(-2.7902661731604211834685052867305795169688E-4), +L(-1.2335696813916860754951146082826952093496E-4), +L(-3.0677461025892873184042490943581654591817E-5), #define ZERO logtbl[38] - 0.0000000000000000000000000000000000000000E0L, --3.0359557945051052537099938863236321874198E-5L, --1.2081346403474584914595395755316412213151E-4L, --2.7044071846562177120083903771008342059094E-4L, --4.7834133324631162897179240322783590830326E-4L, --7.4363569786340080624467487620270965403695E-4L, --1.0654639687057968333207323853366578860679E-3L, --1.4429854811877171341298062134712230604279E-3L, --1.8753781835651574193938679595797367137975E-3L, --2.3618380914922506054347222273705859653658E-3L, --2.9015787624124743013946600163375853631299E-3L, --3.4938307889254087318399313316921940859043E-3L, --4.1378413103128673800485306215154712148146E-3L, --4.8328735414488877044289435125365629849599E-3L, --5.5782063183564351739381962360253116934243E-3L, --6.3731336597098858051938306767880719015261E-3L, --7.2169643436165454612058905294782949315193E-3L, --8.1090214990427641365934846191367315083867E-3L, --9.0486422112807274112838713105168375482480E-3L, --1.0035177140880864314674126398350812606841E-2L, --1.1067990155502102718064936259435676477423E-2L, --1.2146457974158024928196575103115488672416E-2L, --1.3269969823361415906628825374158424754308E-2L, --1.4437927104692837124388550722759686270765E-2L, --1.5649743073340777659901053944852735064621E-2L, --1.6904842527181702880599758489058031645317E-2L, --1.8202661505988007336096407340750378994209E-2L, --1.9542647000370545390701192438691126552961E-2L, --2.0924256670080119637427928803038530924742E-2L, --2.2346958571309108496179613803760727786257E-2L, --2.3810230892650362330447187267648486279460E-2L, --2.5313561699385640380910474255652501521033E-2L, --2.6856448685790244233704909690165496625399E-2L, --2.8438398935154170008519274953860128449036E-2L, --3.0058928687233090922411781058956589863039E-2L, --3.1717563112854831855692484086486099896614E-2L, --3.3413836095418743219397234253475252001090E-2L, --3.5147290019036555862676702093393332533702E-2L, --3.6917475563073933027920505457688955423688E-2L, --3.8723951502862058660874073462456610731178E-2L, --4.0566284516358241168330505467000838017425E-2L, --4.2444048996543693813649967076598766917965E-2L, --4.4356826869355401653098777649745233339196E-2L, --4.6304207416957323121106944474331029996141E-2L, --4.8285787106164123613318093945035804818364E-2L, --5.0301169421838218987124461766244507342648E-2L, --5.2349964705088137924875459464622098310997E-2L, --5.4431789996103111613753440311680967840214E-2L, --5.6546268881465384189752786409400404404794E-2L, --5.8693031345788023909329239565012647817664E-2L, --6.0871713627532018185577188079210189048340E-2L, --6.3081958078862169742820420185833800925568E-2L, --6.5323413029406789694910800219643791556918E-2L, --6.7595732653791419081537811574227049288168E-2L + L(0.0000000000000000000000000000000000000000E0), +L(-3.0359557945051052537099938863236321874198E-5), +L(-1.2081346403474584914595395755316412213151E-4), +L(-2.7044071846562177120083903771008342059094E-4), +L(-4.7834133324631162897179240322783590830326E-4), +L(-7.4363569786340080624467487620270965403695E-4), +L(-1.0654639687057968333207323853366578860679E-3), +L(-1.4429854811877171341298062134712230604279E-3), +L(-1.8753781835651574193938679595797367137975E-3), +L(-2.3618380914922506054347222273705859653658E-3), +L(-2.9015787624124743013946600163375853631299E-3), +L(-3.4938307889254087318399313316921940859043E-3), +L(-4.1378413103128673800485306215154712148146E-3), +L(-4.8328735414488877044289435125365629849599E-3), +L(-5.5782063183564351739381962360253116934243E-3), +L(-6.3731336597098858051938306767880719015261E-3), +L(-7.2169643436165454612058905294782949315193E-3), +L(-8.1090214990427641365934846191367315083867E-3), +L(-9.0486422112807274112838713105168375482480E-3), +L(-1.0035177140880864314674126398350812606841E-2), +L(-1.1067990155502102718064936259435676477423E-2), +L(-1.2146457974158024928196575103115488672416E-2), +L(-1.3269969823361415906628825374158424754308E-2), +L(-1.4437927104692837124388550722759686270765E-2), +L(-1.5649743073340777659901053944852735064621E-2), +L(-1.6904842527181702880599758489058031645317E-2), +L(-1.8202661505988007336096407340750378994209E-2), +L(-1.9542647000370545390701192438691126552961E-2), +L(-2.0924256670080119637427928803038530924742E-2), +L(-2.2346958571309108496179613803760727786257E-2), +L(-2.3810230892650362330447187267648486279460E-2), +L(-2.5313561699385640380910474255652501521033E-2), +L(-2.6856448685790244233704909690165496625399E-2), +L(-2.8438398935154170008519274953860128449036E-2), +L(-3.0058928687233090922411781058956589863039E-2), +L(-3.1717563112854831855692484086486099896614E-2), +L(-3.3413836095418743219397234253475252001090E-2), +L(-3.5147290019036555862676702093393332533702E-2), +L(-3.6917475563073933027920505457688955423688E-2), +L(-3.8723951502862058660874073462456610731178E-2), +L(-4.0566284516358241168330505467000838017425E-2), +L(-4.2444048996543693813649967076598766917965E-2), +L(-4.4356826869355401653098777649745233339196E-2), +L(-4.6304207416957323121106944474331029996141E-2), +L(-4.8285787106164123613318093945035804818364E-2), +L(-5.0301169421838218987124461766244507342648E-2), +L(-5.2349964705088137924875459464622098310997E-2), +L(-5.4431789996103111613753440311680967840214E-2), +L(-5.6546268881465384189752786409400404404794E-2), +L(-5.8693031345788023909329239565012647817664E-2), +L(-6.0871713627532018185577188079210189048340E-2), +L(-6.3081958078862169742820420185833800925568E-2), +L(-6.5323413029406789694910800219643791556918E-2), +L(-6.7595732653791419081537811574227049288168E-2) }; /* ln(2) = ln2a + ln2b with extended precision. */ -static const long double - ln2a = 6.93145751953125e-1L, - ln2b = 1.4286068203094172321214581765680755001344E-6L; +static const _Float128 + ln2a = L(6.93145751953125e-1), + ln2b = L(1.4286068203094172321214581765680755001344E-6); -long double -__ieee754_logl(long double x) +_Float128 +__ieee754_logl(_Float128 x) { - long double z, y, w; + _Float128 z, y, w; ieee854_long_double_shape_type u, t; unsigned int m; int k, e; @@ -198,7 +199,7 @@ __ieee754_logl(long double x) /* log(0) = -infinity. */ if ((k | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) { - return -0.5L / ZERO; + return L(-0.5) / ZERO; } /* log ( x < 0 ) = NaN */ if (m & 0x80000000) @@ -238,13 +239,13 @@ __ieee754_logl(long double x) t.parts32.w3 = 0; } /* On this interval the table is not used due to cancellation error. */ - if ((x <= 1.0078125L) && (x >= 0.9921875L)) + if ((x <= L(1.0078125)) && (x >= L(0.9921875))) { - if (x == 1.0L) - return 0.0L; - z = x - 1.0L; + if (x == 1) + return 0; + z = x - 1; k = 64; - t.value = 1.0L; + t.value = 1; e = 0; } else @@ -274,7 +275,7 @@ __ieee754_logl(long double x) y += e * ln2b; /* Base 2 exponent offset times ln(2). */ y += z; y += logtbl[k-26]; /* log(t) - (t-1) */ - y += (t.value - 1.0L); + y += (t.value - 1); y += e * ln2a; return y; } diff --git a/sysdeps/ieee754/ldbl-128/e_powl.c b/sysdeps/ieee754/ldbl-128/e_powl.c index 7f3037fb51..dc748c3a0b 100644 --- a/sysdeps/ieee754/ldbl-128/e_powl.c +++ b/sysdeps/ieee754/ldbl-128/e_powl.c @@ -65,93 +65,94 @@ */ #include <math.h> +#include <math-barriers.h> #include <math_private.h> -static const long double bp[] = { - 1.0L, - 1.5L, +static const _Float128 bp[] = { + 1, + L(1.5), }; /* log_2(1.5) */ -static const long double dp_h[] = { +static const _Float128 dp_h[] = { 0.0, - 5.8496250072115607565592654282227158546448E-1L + L(5.8496250072115607565592654282227158546448E-1) }; /* Low part of log_2(1.5) */ -static const long double dp_l[] = { +static const _Float128 dp_l[] = { 0.0, - 1.0579781240112554492329533686862998106046E-16L + L(1.0579781240112554492329533686862998106046E-16) }; -static const long double zero = 0.0L, - one = 1.0L, - two = 2.0L, - two113 = 1.0384593717069655257060992658440192E34L, - huge = 1.0e3000L, - tiny = 1.0e-3000L; +static const _Float128 zero = 0, + one = 1, + two = 2, + two113 = L(1.0384593717069655257060992658440192E34), + huge = L(1.0e3000), + tiny = L(1.0e-3000); /* 3/2 log x = 3 z + z^3 + z^3 (z^2 R(z^2)) z = (x-1)/(x+1) 1 <= x <= 1.25 Peak relative error 2.3e-37 */ -static const long double LN[] = +static const _Float128 LN[] = { - -3.0779177200290054398792536829702930623200E1L, - 6.5135778082209159921251824580292116201640E1L, - -4.6312921812152436921591152809994014413540E1L, - 1.2510208195629420304615674658258363295208E1L, - -9.9266909031921425609179910128531667336670E-1L + L(-3.0779177200290054398792536829702930623200E1), + L(6.5135778082209159921251824580292116201640E1), + L(-4.6312921812152436921591152809994014413540E1), + L(1.2510208195629420304615674658258363295208E1), + L(-9.9266909031921425609179910128531667336670E-1) }; -static const long double LD[] = +static const _Float128 LD[] = { - -5.129862866715009066465422805058933131960E1L, - 1.452015077564081884387441590064272782044E2L, - -1.524043275549860505277434040464085593165E2L, - 7.236063513651544224319663428634139768808E1L, - -1.494198912340228235853027849917095580053E1L + L(-5.129862866715009066465422805058933131960E1), + L(1.452015077564081884387441590064272782044E2), + L(-1.524043275549860505277434040464085593165E2), + L(7.236063513651544224319663428634139768808E1), + L(-1.494198912340228235853027849917095580053E1) /* 1.0E0 */ }; /* exp(x) = 1 + x - x / (1 - 2 / (x - x^2 R(x^2))) 0 <= x <= 0.5 Peak relative error 5.7e-38 */ -static const long double PN[] = +static const _Float128 PN[] = { - 5.081801691915377692446852383385968225675E8L, - 9.360895299872484512023336636427675327355E6L, - 4.213701282274196030811629773097579432957E4L, - 5.201006511142748908655720086041570288182E1L, - 9.088368420359444263703202925095675982530E-3L, + L(5.081801691915377692446852383385968225675E8), + L(9.360895299872484512023336636427675327355E6), + L(4.213701282274196030811629773097579432957E4), + L(5.201006511142748908655720086041570288182E1), + L(9.088368420359444263703202925095675982530E-3), }; -static const long double PD[] = +static const _Float128 PD[] = { - 3.049081015149226615468111430031590411682E9L, - 1.069833887183886839966085436512368982758E8L, - 8.259257717868875207333991924545445705394E5L, - 1.872583833284143212651746812884298360922E3L, + L(3.049081015149226615468111430031590411682E9), + L(1.069833887183886839966085436512368982758E8), + L(8.259257717868875207333991924545445705394E5), + L(1.872583833284143212651746812884298360922E3), /* 1.0E0 */ }; -static const long double +static const _Float128 /* ln 2 */ - lg2 = 6.9314718055994530941723212145817656807550E-1L, - lg2_h = 6.9314718055994528622676398299518041312695E-1L, - lg2_l = 2.3190468138462996154948554638754786504121E-17L, - ovt = 8.0085662595372944372e-0017L, + lg2 = L(6.9314718055994530941723212145817656807550E-1), + lg2_h = L(6.9314718055994528622676398299518041312695E-1), + lg2_l = L(2.3190468138462996154948554638754786504121E-17), + ovt = L(8.0085662595372944372e-0017), /* 2/(3*log(2)) */ - cp = 9.6179669392597560490661645400126142495110E-1L, - cp_h = 9.6179669392597555432899980587535537779331E-1L, - cp_l = 5.0577616648125906047157785230014751039424E-17L; + cp = L(9.6179669392597560490661645400126142495110E-1), + cp_h = L(9.6179669392597555432899980587535537779331E-1), + cp_l = L(5.0577616648125906047157785230014751039424E-17); -long double -__ieee754_powl (long double x, long double y) +_Float128 +__ieee754_powl (_Float128 x, _Float128 y) { - long double z, ax, z_h, z_l, p_h, p_l; - long double y1, t1, t2, r, s, sgn, t, u, v, w; - long double s2, s_h, s_l, t_h, t_l, ay; + _Float128 z, ax, z_h, z_l, p_h, p_l; + _Float128 y1, t1, t2, r, s, sgn, t, u, v, w; + _Float128 s2, s_h, s_l, t_h, t_l, ay; int32_t i, j, k, yisint, n; - u_int32_t ix, iy; + uint32_t ix, iy; int32_t hx, hy; ieee854_long_double_shape_type o, p, q; @@ -165,13 +166,14 @@ __ieee754_powl (long double x, long double y) /* y==zero: x**0 = 1 */ - if ((iy | q.parts32.w1 | q.parts32.w2 | q.parts32.w3) == 0) + if ((iy | q.parts32.w1 | q.parts32.w2 | q.parts32.w3) == 0 + && !issignaling (x)) return one; /* 1.0**y = 1; -1.0**+-Inf = 1 */ - if (x == one) + if (x == one && !issignaling (y)) return one; - if (x == -1.0L && iy == 0x7fff0000 + if (x == -1 && iy == 0x7fff0000 && (q.parts32.w1 | q.parts32.w2 | q.parts32.w3) == 0) return one; @@ -232,7 +234,7 @@ __ieee754_powl (long double x, long double y) if (hy == 0x3ffe0000) { /* y is 0.5 */ if (hx >= 0) /* x >= +0 */ - return __ieee754_sqrtl (x); + return sqrtl (x); } } @@ -259,12 +261,12 @@ __ieee754_powl (long double x, long double y) } /* (x<0)**(non-int) is NaN */ - if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0) + if (((((uint32_t) hx >> 31) - 1) | yisint) == 0) return (x - x) / (x - x); /* sgn (sign of result -ve**odd) = -1 else = 1 */ sgn = one; - if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) + if (((((uint32_t) hx >> 31) - 1) | (yisint - 1)) == 0) sgn = -one; /* (-ve)**(odd int) */ /* |y| is huge. @@ -363,7 +365,7 @@ __ieee754_powl (long double x, long double y) z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ z_l = cp_l * p_h + p_l * cp + dp_l[k]; /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ - t = (long double) n; + t = (_Float128) n; t1 = (((z_h + z_l) + dp_h[k]) + t); o.value = t1; o.parts32.w3 = 0; @@ -411,7 +413,7 @@ __ieee754_powl (long double x, long double y) n = 0; if (i > 0x3ffe0000) { /* if |z| > 0.5, set n = [z+0.5] */ - n = __floorl (z + 0.5L); + n = __floorl (z + L(0.5)); t = n; p_h -= t; } @@ -437,7 +439,7 @@ __ieee754_powl (long double x, long double y) if ((j >> 16) <= 0) { z = __scalbnl (z, n); /* subnormal output */ - long double force_underflow = z * z; + _Float128 force_underflow = z * z; math_force_eval (force_underflow); } else diff --git a/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c b/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c index 101a4c9015..d226d4218d 100644 --- a/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c +++ b/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c @@ -1,5 +1,5 @@ /* Quad-precision floating point argument reduction. - Copyright (C) 1999-2016 Free Software Foundation, Inc. + Copyright (C) 1999-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jj@ultra.linux.cz> @@ -183,22 +183,22 @@ static const int32_t two_over_pi[] = { 0x7b7b89, 0x483d38, }; -static const long double c[] = { +static const _Float128 c[] = { /* 113 bits of pi/2 */ #define PI_2_1 c[0] - 0x1.921fb54442d18469898cc51701b8p+0L, + L(0x1.921fb54442d18469898cc51701b8p+0), /* pi/2 - PI_2_1 */ #define PI_2_1t c[1] - 0x3.9a252049c1114cf98e804177d4c8p-116L, + L(0x3.9a252049c1114cf98e804177d4c8p-116), }; -int32_t __ieee754_rem_pio2l(long double x, long double *y) +int32_t __ieee754_rem_pio2l(_Float128 x, _Float128 *y) { - long double z, w, t; + _Float128 z, w, t; double tx[8]; int64_t exp, n, ix, hx; - u_int64_t lx; + uint64_t lx; GET_LDOUBLE_WORDS64 (hx, lx, x); ix = hx & 0x7fffffffffffffffLL; @@ -255,8 +255,8 @@ int32_t __ieee754_rem_pio2l(long double x, long double *y) /* The result is now stored in 3 double values, we need to convert it into two long double values. */ - t = (long double) tx [6] + (long double) tx [7]; - w = (long double) tx [5]; + t = (_Float128) tx [6] + (_Float128) tx [7]; + w = (_Float128) tx [5]; if (hx >= 0) { diff --git a/sysdeps/ieee754/ldbl-128/e_remainderl.c b/sysdeps/ieee754/ldbl-128/e_remainderl.c index 88df6f54c2..09b8640b78 100644 --- a/sysdeps/ieee754/ldbl-128/e_remainderl.c +++ b/sysdeps/ieee754/ldbl-128/e_remainderl.c @@ -24,15 +24,15 @@ #include <math.h> #include <math_private.h> -static const long double zero = 0.0L; +static const _Float128 zero = 0; -long double -__ieee754_remainderl(long double x, long double p) +_Float128 +__ieee754_remainderl(_Float128 x, _Float128 p) { int64_t hx,hp; - u_int64_t sx,lx,lp; - long double p_half; + uint64_t sx,lx,lp; + _Float128 p_half; GET_LDOUBLE_WORDS64(hx,lx,x); GET_LDOUBLE_WORDS64(hp,lp,p); @@ -58,7 +58,7 @@ __ieee754_remainderl(long double x, long double p) if(x+x>=p) x -= p; } } else { - p_half = 0.5L*p; + p_half = L(0.5)*p; if(x>p_half) { x-=p; if(x>=p_half) x -= p; diff --git a/sysdeps/ieee754/ldbl-128/e_sinhl.c b/sysdeps/ieee754/ldbl-128/e_sinhl.c index 11974a39af..39e7cf3084 100644 --- a/sysdeps/ieee754/ldbl-128/e_sinhl.c +++ b/sysdeps/ieee754/ldbl-128/e_sinhl.c @@ -56,15 +56,16 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> -static const long double one = 1.0, shuge = 1.0e4931L, -ovf_thresh = 1.1357216553474703894801348310092223067821E4L; +static const _Float128 one = 1.0, shuge = L(1.0e4931), +ovf_thresh = L(1.1357216553474703894801348310092223067821E4); -long double -__ieee754_sinhl (long double x) +_Float128 +__ieee754_sinhl (_Float128 x) { - long double t, w, h; - u_int32_t jx, ix; + _Float128 t, w, h; + uint32_t jx, ix; ieee854_long_double_shape_type u; /* Words of |x|. */ diff --git a/sysdeps/ieee754/ldbl-128/float128-abi.h b/sysdeps/ieee754/ldbl-128/float128-abi.h new file mode 100644 index 0000000000..3077ffc7fe --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/float128-abi.h @@ -0,0 +1,2 @@ +/* ABI version for _Float128 ABI introduction. */ +#define FLOAT128_VERSION GLIBC_2.27 diff --git a/sysdeps/ieee754/ldbl-128/gamma_productl.c b/sysdeps/ieee754/ldbl-128/gamma_productl.c index 849b57d95d..2c1a03a915 100644 --- a/sysdeps/ieee754/ldbl-128/gamma_productl.c +++ b/sysdeps/ieee754/ldbl-128/gamma_productl.c @@ -1,5 +1,5 @@ /* Compute a product of X, X+1, ..., with an error estimate. - Copyright (C) 2013-2016 Free Software Foundation, Inc. + Copyright (C) 2013-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -18,37 +18,7 @@ #include <math.h> #include <math_private.h> -#include <float.h> - -/* Calculate X * Y exactly and store the result in *HI + *LO. It is - given that the values are small enough that no overflow occurs and - large enough (or zero) that no underflow occurs. */ - -static inline void -mul_split (long double *hi, long double *lo, long double x, long double y) -{ -#ifdef __FP_FAST_FMAL - /* Fast built-in fused multiply-add. */ - *hi = x * y; - *lo = __builtin_fmal (x, y, -*hi); -#elif defined FP_FAST_FMAL - /* Fast library fused multiply-add, compiler before GCC 4.6. */ - *hi = x * y; - *lo = __fmal (x, y, -*hi); -#else - /* Apply Dekker's algorithm. */ - *hi = x * y; -# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) - long double x1 = x * C; - long double y1 = y * C; -# undef C - x1 = (x - x1) + x1; - y1 = (y - y1) + y1; - long double x2 = x - x1; - long double y2 = y - y1; - *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; -#endif -} +#include <mul_splitl.h> /* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N - 1, in the form R * (1 + *EPS) where the return value R is an @@ -58,17 +28,17 @@ mul_split (long double *hi, long double *lo, long double x, long double y) X is small enough that factors quadratic in it can be neglected. */ -long double -__gamma_productl (long double x, long double x_eps, int n, long double *eps) +_Float128 +__gamma_productl (_Float128 x, _Float128 x_eps, int n, _Float128 *eps) { SET_RESTORE_ROUNDL (FE_TONEAREST); - long double ret = x; + _Float128 ret = x; *eps = x_eps / x; for (int i = 1; i < n; i++) { *eps += x_eps / (x + i); - long double lo; - mul_split (&ret, &lo, ret, x + i); + _Float128 lo; + mul_splitl (&ret, &lo, ret, x + i); *eps += lo / ret; } return ret; diff --git a/sysdeps/ieee754/ldbl-128/ieee754.h b/sysdeps/ieee754/ldbl-128/ieee754.h index fb42140933..d7173b6a8b 100644 --- a/sysdeps/ieee754/ldbl-128/ieee754.h +++ b/sysdeps/ieee754/ldbl-128/ieee754.h @@ -1,4 +1,4 @@ -/* Copyright (C) 1992-2016 Free Software Foundation, Inc. +/* Copyright (C) 1992-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or diff --git a/sysdeps/ieee754/ldbl-128/k_cosl.c b/sysdeps/ieee754/ldbl-128/k_cosl.c index 3985b1225b..866af57921 100644 --- a/sysdeps/ieee754/ldbl-128/k_cosl.c +++ b/sysdeps/ieee754/ldbl-128/k_cosl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point cosine on <-pi/4,pi/4>. - Copyright (C) 1999-2016 Free Software Foundation, Inc. + Copyright (C) 1999-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jj@ultra.linux.cz> @@ -20,9 +20,9 @@ #include <math.h> #include <math_private.h> -static const long double c[] = { +static const _Float128 c[] = { #define ONE c[0] - 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) x in <0,1/256> */ @@ -31,11 +31,11 @@ static const long double c[] = { #define SCOS3 c[3] #define SCOS4 c[4] #define SCOS5 c[5] --5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ - 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ --1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ - 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ --2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ +L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */ + L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */ +L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */ + L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */ /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) x in <0,0.1484375> */ @@ -47,14 +47,14 @@ static const long double c[] = { #define COS6 c[11] #define COS7 c[12] #define COS8 c[13] --4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */ - 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */ --1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */ - 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ --2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */ - 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */ --1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */ - 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ +L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */ + L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */ +L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */ + L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ +L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */ + L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */ +L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */ + L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) x in <0,1/256> */ @@ -63,27 +63,27 @@ static const long double c[] = { #define SSIN3 c[16] #define SSIN4 c[17] #define SSIN5 c[18] --1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ - 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ --1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ - 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ --2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ +L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */ + L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */ +L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */ + L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */ +L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */ }; #define SINCOSL_COS_HI 0 #define SINCOSL_COS_LO 1 #define SINCOSL_SIN_HI 2 #define SINCOSL_SIN_LO 3 -extern const long double __sincosl_table[]; +extern const _Float128 __sincosl_table[]; -long double -__kernel_cosl(long double x, long double y) +_Float128 +__kernel_cosl(_Float128 x, _Float128 y) { - long double h, l, z, sin_l, cos_l_m1; + _Float128 h, l, z, sin_l, cos_l_m1; int64_t ix; - u_int32_t tix, hix, index; + uint32_t tix, hix, index; GET_LDOUBLE_MSW64 (ix, x); - tix = ((u_int64_t)ix) >> 32; + tix = ((uint64_t)ix) >> 32; tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ { @@ -118,7 +118,7 @@ __kernel_cosl(long double x, long double y) case 2: index = (hix - 0x3ffc3000) >> 10; break; } - SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0); + SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0); l = y - (h - x); z = l * l; sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5))))); diff --git a/sysdeps/ieee754/ldbl-128/k_sincosl.c b/sysdeps/ieee754/ldbl-128/k_sincosl.c index 404df352d3..6eb33ae375 100644 --- a/sysdeps/ieee754/ldbl-128/k_sincosl.c +++ b/sysdeps/ieee754/ldbl-128/k_sincosl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. - Copyright (C) 1999-2016 Free Software Foundation, Inc. + Copyright (C) 1999-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jj@ultra.linux.cz> @@ -20,10 +20,11 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> -static const long double c[] = { +static const _Float128 c[] = { #define ONE c[0] - 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) x in <0,1/256> */ @@ -32,11 +33,11 @@ static const long double c[] = { #define SCOS3 c[3] #define SCOS4 c[4] #define SCOS5 c[5] --5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ - 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ --1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ - 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ --2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ +L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */ + L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */ +L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */ + L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */ /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 ) x in <0,0.1484375> */ @@ -48,14 +49,14 @@ static const long double c[] = { #define COS6 c[11] #define COS7 c[12] #define COS8 c[13] --4.99999999999999999999999999999999759E-01L, /* bffdfffffffffffffffffffffffffffb */ - 4.16666666666666666666666666651287795E-02L, /* 3ffa5555555555555555555555516f30 */ --1.38888888888888888888888742314300284E-03L, /* bff56c16c16c16c16c16c16a463dfd0d */ - 2.48015873015873015867694002851118210E-05L, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ --2.75573192239858811636614709689300351E-07L, /* bfe927e4fb7789f5aa8142a22044b51f */ - 2.08767569877762248667431926878073669E-09L, /* 3fe21eed8eff881d1e9262d7adff4373 */ --1.14707451049343817400420280514614892E-11L, /* bfda9397496922a9601ed3d4ca48944b */ - 4.77810092804389587579843296923533297E-14L, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ +L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */ + L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */ +L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */ + L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */ +L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */ + L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */ +L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */ + L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */ /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) x in <0,1/256> */ @@ -64,11 +65,11 @@ static const long double c[] = { #define SSIN3 c[16] #define SSIN4 c[17] #define SSIN5 c[18] --1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ - 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ --1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ - 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ --2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ +L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */ + L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */ +L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */ + L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */ +L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */ /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) x in <0,0.1484375> */ @@ -80,30 +81,30 @@ static const long double c[] = { #define SIN6 c[24] #define SIN7 c[25] #define SIN8 c[26] --1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */ - 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */ --1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */ - 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */ --2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */ - 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */ --7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ - 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */ +L(-1.66666666666666666666666666666666538e-01), /* bffc5555555555555555555555555550 */ + L(8.33333333333333333333333333307532934e-03), /* 3ff811111111111111111111110e7340 */ +L(-1.98412698412698412698412534478712057e-04), /* bff2a01a01a01a01a01a019e7a626296 */ + L(2.75573192239858906520896496653095890e-06), /* 3fec71de3a556c7338fa38527474b8f5 */ +L(-2.50521083854417116999224301266655662e-08), /* bfe5ae64567f544e16c7de65c2ea551f */ + L(1.60590438367608957516841576404938118e-10), /* 3fde6124613a811480538a9a41957115 */ +L(-7.64716343504264506714019494041582610e-13), /* bfd6ae7f3d5aef30c7bc660b060ef365 */ + L(2.81068754939739570236322404393398135e-15), /* 3fce9510115aabf87aceb2022a9a9180 */ }; #define SINCOSL_COS_HI 0 #define SINCOSL_COS_LO 1 #define SINCOSL_SIN_HI 2 #define SINCOSL_SIN_LO 3 -extern const long double __sincosl_table[]; +extern const _Float128 __sincosl_table[]; void -__kernel_sincosl(long double x, long double y, long double *sinx, long double *cosx, int iy) +__kernel_sincosl(_Float128 x, _Float128 y, _Float128 *sinx, _Float128 *cosx, int iy) { - long double h, l, z, sin_l, cos_l_m1; + _Float128 h, l, z, sin_l, cos_l_m1; int64_t ix; - u_int32_t tix, hix, index; + uint32_t tix, hix, index; GET_LDOUBLE_MSW64 (ix, x); - tix = ((u_int64_t)ix) >> 32; + tix = ((uint64_t)ix) >> 32; tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ { @@ -149,7 +150,7 @@ __kernel_sincosl(long double x, long double y, long double *sinx, long double *c case 2: index = (hix - 0x3ffc3000) >> 10; break; } - SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0); + SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0); if (iy) l = y - (h - x); else diff --git a/sysdeps/ieee754/ldbl-128/k_sinl.c b/sysdeps/ieee754/ldbl-128/k_sinl.c index 6290b173b4..9c19fb1bf2 100644 --- a/sysdeps/ieee754/ldbl-128/k_sinl.c +++ b/sysdeps/ieee754/ldbl-128/k_sinl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point sine on <-pi/4,pi/4>. - Copyright (C) 1999-2016 Free Software Foundation, Inc. + Copyright (C) 1999-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jj@ultra.linux.cz> @@ -20,10 +20,11 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> -static const long double c[] = { +static const _Float128 c[] = { #define ONE c[0] - 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 ) x in <0,1/256> */ @@ -32,11 +33,11 @@ static const long double c[] = { #define SCOS3 c[3] #define SCOS4 c[4] #define SCOS5 c[5] --5.00000000000000000000000000000000000E-01L, /* bffe0000000000000000000000000000 */ - 4.16666666666666666666666666556146073E-02L, /* 3ffa5555555555555555555555395023 */ --1.38888888888888888888309442601939728E-03L, /* bff56c16c16c16c16c16a566e42c0375 */ - 2.48015873015862382987049502531095061E-05L, /* 3fefa01a01a019ee02dcf7da2d6d5444 */ --2.75573112601362126593516899592158083E-07L, /* bfe927e4f5dce637cb0b54908754bde0 */ +L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */ + L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */ +L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */ + L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */ +L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */ /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 ) x in <0,0.1484375> */ @@ -48,14 +49,14 @@ static const long double c[] = { #define SIN6 c[11] #define SIN7 c[12] #define SIN8 c[13] --1.66666666666666666666666666666666538e-01L, /* bffc5555555555555555555555555550 */ - 8.33333333333333333333333333307532934e-03L, /* 3ff811111111111111111111110e7340 */ --1.98412698412698412698412534478712057e-04L, /* bff2a01a01a01a01a01a019e7a626296 */ - 2.75573192239858906520896496653095890e-06L, /* 3fec71de3a556c7338fa38527474b8f5 */ --2.50521083854417116999224301266655662e-08L, /* bfe5ae64567f544e16c7de65c2ea551f */ - 1.60590438367608957516841576404938118e-10L, /* 3fde6124613a811480538a9a41957115 */ --7.64716343504264506714019494041582610e-13L, /* bfd6ae7f3d5aef30c7bc660b060ef365 */ - 2.81068754939739570236322404393398135e-15L, /* 3fce9510115aabf87aceb2022a9a9180 */ +L(-1.66666666666666666666666666666666538e-01), /* bffc5555555555555555555555555550 */ + L(8.33333333333333333333333333307532934e-03), /* 3ff811111111111111111111110e7340 */ +L(-1.98412698412698412698412534478712057e-04), /* bff2a01a01a01a01a01a019e7a626296 */ + L(2.75573192239858906520896496653095890e-06), /* 3fec71de3a556c7338fa38527474b8f5 */ +L(-2.50521083854417116999224301266655662e-08), /* bfe5ae64567f544e16c7de65c2ea551f */ + L(1.60590438367608957516841576404938118e-10), /* 3fde6124613a811480538a9a41957115 */ +L(-7.64716343504264506714019494041582610e-13), /* bfd6ae7f3d5aef30c7bc660b060ef365 */ + L(2.81068754939739570236322404393398135e-15), /* 3fce9510115aabf87aceb2022a9a9180 */ /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 ) x in <0,1/256> */ @@ -64,27 +65,27 @@ static const long double c[] = { #define SSIN3 c[16] #define SSIN4 c[17] #define SSIN5 c[18] --1.66666666666666666666666666666666659E-01L, /* bffc5555555555555555555555555555 */ - 8.33333333333333333333333333146298442E-03L, /* 3ff81111111111111111111110fe195d */ --1.98412698412698412697726277416810661E-04L, /* bff2a01a01a01a01a019e7121e080d88 */ - 2.75573192239848624174178393552189149E-06L, /* 3fec71de3a556c640c6aaa51aa02ab41 */ --2.50521016467996193495359189395805639E-08L, /* bfe5ae644ee90c47dc71839de75b2787 */ +L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */ + L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */ +L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */ + L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */ +L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */ }; #define SINCOSL_COS_HI 0 #define SINCOSL_COS_LO 1 #define SINCOSL_SIN_HI 2 #define SINCOSL_SIN_LO 3 -extern const long double __sincosl_table[]; +extern const _Float128 __sincosl_table[]; -long double -__kernel_sinl(long double x, long double y, int iy) +_Float128 +__kernel_sinl(_Float128 x, _Float128 y, int iy) { - long double h, l, z, sin_l, cos_l_m1; + _Float128 h, l, z, sin_l, cos_l_m1; int64_t ix; - u_int32_t tix, hix, index; + uint32_t tix, hix, index; GET_LDOUBLE_MSW64 (ix, x); - tix = ((u_int64_t)ix) >> 32; + tix = ((uint64_t)ix) >> 32; tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ if (tix < 0x3ffc3000) /* |x| < 0.1484375 */ { @@ -118,7 +119,7 @@ __kernel_sinl(long double x, long double y, int iy) case 2: index = (hix - 0x3ffc3000) >> 10; break; } - SET_LDOUBLE_WORDS64(h, ((u_int64_t)hix) << 32, 0); + SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0); if (iy) l = (ix < 0 ? -y : y) - (h - x); else diff --git a/sysdeps/ieee754/ldbl-128/k_tanl.c b/sysdeps/ieee754/ldbl-128/k_tanl.c index 6bb221e4a6..8da794d80c 100644 --- a/sysdeps/ieee754/ldbl-128/k_tanl.c +++ b/sysdeps/ieee754/ldbl-128/k_tanl.c @@ -57,36 +57,38 @@ */ #include <float.h> -#include <libc-internal.h> #include <math.h> #include <math_private.h> -static const long double - one = 1.0L, - pio4hi = 7.8539816339744830961566084581987569936977E-1L, - pio4lo = 2.1679525325309452561992610065108379921906E-35L, +#include <math-underflow.h> +#include <libc-diag.h> + +static const _Float128 + one = 1, + pio4hi = L(7.8539816339744830961566084581987569936977E-1), + pio4lo = L(2.1679525325309452561992610065108379921906E-35), /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2) 0 <= x <= 0.6743316650390625 Peak relative error 8.0e-36 */ - TH = 3.333333333333333333333333333333333333333E-1L, - T0 = -1.813014711743583437742363284336855889393E7L, - T1 = 1.320767960008972224312740075083259247618E6L, - T2 = -2.626775478255838182468651821863299023956E4L, - T3 = 1.764573356488504935415411383687150199315E2L, - T4 = -3.333267763822178690794678978979803526092E-1L, + TH = L(3.333333333333333333333333333333333333333E-1), + T0 = L(-1.813014711743583437742363284336855889393E7), + T1 = L(1.320767960008972224312740075083259247618E6), + T2 = L(-2.626775478255838182468651821863299023956E4), + T3 = L(1.764573356488504935415411383687150199315E2), + T4 = L(-3.333267763822178690794678978979803526092E-1), - U0 = -1.359761033807687578306772463253710042010E8L, - U1 = 6.494370630656893175666729313065113194784E7L, - U2 = -4.180787672237927475505536849168729386782E6L, - U3 = 8.031643765106170040139966622980914621521E4L, - U4 = -5.323131271912475695157127875560667378597E2L; + U0 = L(-1.359761033807687578306772463253710042010E8), + U1 = L(6.494370630656893175666729313065113194784E7), + U2 = L(-4.180787672237927475505536849168729386782E6), + U3 = L(8.031643765106170040139966622980914621521E4), + U4 = L(-5.323131271912475695157127875560667378597E2); /* 1.000000000000000000000000000000000000000E0 */ -long double -__kernel_tanl (long double x, long double y, int iy) +_Float128 +__kernel_tanl (_Float128 x, _Float128 y, int iy) { - long double z, r, v, w, s; + _Float128 z, r, v, w, s; int32_t ix, sign; ieee854_long_double_shape_type u, u1; @@ -98,7 +100,7 @@ __kernel_tanl (long double x, long double y, int iy) { /* generate inexact */ if ((ix | u.parts32.w1 | u.parts32.w2 | u.parts32.w3 | (iy + 1)) == 0) - return one / fabs (x); + return one / fabsl (x); else if (iy == 1) { math_check_force_underflow (x); @@ -134,7 +136,7 @@ __kernel_tanl (long double x, long double y, int iy) w = x + r; if (ix >= 0x3ffe5942) { - v = (long double) iy; + v = (_Float128) iy; w = (v - 2.0 * (x - (w * w / (w + v) - r))); /* SIGN is set for arguments that reach this code, but not otherwise, resulting in warnings that it may be used diff --git a/sysdeps/ieee754/ldbl-128/ldbl2mpn.c b/sysdeps/ieee754/ldbl-128/ldbl2mpn.c index e3f97623ed..0c0d43155d 100644 --- a/sysdeps/ieee754/ldbl-128/ldbl2mpn.c +++ b/sysdeps/ieee754/ldbl-128/ldbl2mpn.c @@ -1,4 +1,4 @@ -/* Copyright (C) 1995-2016 Free Software Foundation, Inc. +/* Copyright (C) 1995-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -21,6 +21,7 @@ #include <ieee754.h> #include <float.h> #include <math.h> +#include <math_private.h> #include <stdlib.h> /* Convert a `long double' in IEEE854 quad-precision format to a @@ -31,7 +32,7 @@ mp_size_t __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, int *expt, int *is_neg, - long double value) + _Float128 value) { union ieee854_long_double u; u.d = value; diff --git a/sysdeps/ieee754/ldbl-128/lgamma_negl.c b/sysdeps/ieee754/ldbl-128/lgamma_negl.c index df46199b82..f5043719ad 100644 --- a/sysdeps/ieee754/ldbl-128/lgamma_negl.c +++ b/sysdeps/ieee754/ldbl-128/lgamma_negl.c @@ -1,5 +1,5 @@ /* lgammal expanding around zeros. - Copyright (C) 2015-2016 Free Software Foundation, Inc. + Copyright (C) 2015-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -20,142 +20,142 @@ #include <math.h> #include <math_private.h> -static const long double lgamma_zeros[][2] = +static const _Float128 lgamma_zeros[][2] = { - { -0x2.74ff92c01f0d82abec9f315f1a08p+0L, 0xe.d3ccb7fb2658634a2b9f6b2ba81p-116L }, - { -0x2.bf6821437b20197995a4b4641eaep+0L, -0xb.f4b00b4829f961e428533e6ad048p-116L }, - { -0x3.24c1b793cb35efb8be699ad3d9bap+0L, -0x6.5454cb7fac60e3f16d9d7840c2ep-116L }, - { -0x3.f48e2a8f85fca170d4561291236cp+0L, -0xc.320a4887d1cb4c711828a75d5758p-116L }, - { -0x4.0a139e16656030c39f0b0de18114p+0L, 0x1.53e84029416e1242006b2b3d1cfp-112L }, - { -0x4.fdd5de9bbabf3510d0aa40769884p+0L, -0x1.01d7d78125286f78d1e501f14966p-112L }, - { -0x5.021a95fc2db6432a4c56e595394cp+0L, -0x1.ecc6af0430d4fe5746fa7233356fp-112L }, - { -0x5.ffa4bd647d0357dd4ed62cbd31ecp+0L, -0x1.f8e3f8e5deba2d67dbd70dd96ce1p-112L }, - { -0x6.005ac9625f233b607c2d96d16384p+0L, -0x1.cb86ac569340cf1e5f24df7aab7bp-112L }, - { -0x6.fff2fddae1bbff3d626b65c23fd4p+0L, 0x1.e0bfcff5c457ebcf4d3ad9674167p-112L }, - { -0x7.000cff7b7f87adf4482dcdb98784p+0L, 0x1.54d99e35a74d6407b80292df199fp-112L }, - { -0x7.fffe5fe05673c3ca9e82b522b0ccp+0L, 0x1.62d177c832e0eb42c2faffd1b145p-112L }, - { -0x8.0001a01459fc9f60cb3cec1cec88p+0L, 0x2.8998835ac7277f7bcef67c47f188p-112L }, - { -0x8.ffffd1c425e80ffc864e95749258p+0L, -0x1.e7e20210e7f81cf781b44e9d2b02p-112L }, - { -0x9.00002e3bb47d86d6d843fedc352p+0L, 0x2.14852f613a16291751d2ab751f7ep-112L }, - { -0x9.fffffb606bdfdcd062ae77a50548p+0L, 0x3.962d1490cc2e8f031c7007eaa1ap-116L }, - { -0xa.0000049f93bb9927b45d95e1544p+0L, -0x1.e03086db9146a9287bd4f2172d5ap-112L }, - { -0xa.ffffff9466e9f1b36dacd2adbd18p+0L, -0xd.05a4e458062f3f95345a4d9c9b6p-116L }, - { -0xb.0000006b9915315d965a6ffea41p+0L, 0x1.b415c6fff233e7b7fdc3a094246fp-112L }, - { -0xb.fffffff7089387387de41acc3d4p+0L, 0x3.687427c6373bd74a10306e10a28ep-112L }, - { -0xc.00000008f76c7731567c0f0250fp+0L, -0x3.87920df5675833859190eb128ef6p-112L }, - { -0xc.ffffffff4f6dcf617f97a5ffc758p+0L, 0x2.ab72d76f32eaee2d1a42ed515d3ap-116L }, - { -0xd.00000000b092309c06683dd1b9p+0L, -0x3.e3700857a15c19ac5a611de9688ap-112L }, - { -0xd.fffffffff36345ab9e184a3e09dp+0L, -0x1.176dc48e47f62d917973dd44e553p-112L }, - { -0xe.000000000c9cba545e94e75ec57p+0L, -0x1.8f753e2501e757a17cf2ecbeeb89p-112L }, - { -0xe.ffffffffff28c060c6604ef3037p+0L, -0x1.f89d37357c9e3dc17c6c6e63becap-112L }, - { -0xf.0000000000d73f9f399bd0e420f8p+0L, -0x5.e9ee31b0b890744fc0e3fbc01048p-116L }, - { -0xf.fffffffffff28c060c6621f512e8p+0L, 0xd.1b2eec9d960bd9adc5be5f5fa5p-116L }, - { -0x1.000000000000d73f9f399da1424cp+4L, 0x6.c46e0e88305d2800f0e414c506a8p-116L }, - { -0x1.0ffffffffffff3569c47e7a93e1cp+4L, -0x4.6a08a2e008a998ebabb8087efa2cp-112L }, - { -0x1.1000000000000ca963b818568887p+4L, -0x6.ca5a3a64ec15db0a95caf2c9ffb4p-112L }, - { -0x1.1fffffffffffff4bec3ce234132dp+4L, -0x8.b2b726187c841cb92cd5221e444p-116L }, - { -0x1.20000000000000b413c31dcbeca5p+4L, 0x3.c4d005344b6cd0e7231120294abcp-112L }, - { -0x1.2ffffffffffffff685b25cbf5f54p+4L, -0x5.ced932e38485f7dd296b8fa41448p-112L }, - { -0x1.30000000000000097a4da340a0acp+4L, 0x7.e484e0e0ffe38d406ebebe112f88p-112L }, - { -0x1.3fffffffffffffff86af516ff7f7p+4L, -0x6.bd67e720d57854502b7db75e1718p-112L }, - { -0x1.40000000000000007950ae900809p+4L, 0x6.bec33375cac025d9c073168c5d9p-112L }, - { -0x1.4ffffffffffffffffa391c4248c3p+4L, 0x5.c63022b62b5484ba346524db607p-112L }, - { -0x1.500000000000000005c6e3bdb73dp+4L, -0x5.c62f55ed5322b2685c5e9a51e6a8p-112L }, - { -0x1.5fffffffffffffffffbcc71a492p+4L, -0x1.eb5aeb96c74d7ad25e060528fb5p-112L }, - { -0x1.6000000000000000004338e5b6ep+4L, 0x1.eb5aec04b2f2eb663e4e3d8a018cp-112L }, - { -0x1.6ffffffffffffffffffd13c97d9dp+4L, -0x3.8fcc4d08d6fe5aa56ab04307ce7ep-112L }, - { -0x1.70000000000000000002ec368263p+4L, 0x3.8fcc4d090cee2f5d0b69a99c353cp-112L }, - { -0x1.7fffffffffffffffffffe0d30fe7p+4L, 0x7.2f577cca4b4c8cb1dc14001ac5ecp-112L }, - { -0x1.800000000000000000001f2cf019p+4L, -0x7.2f577cca4b3442e35f0040b3b9e8p-112L }, - { -0x1.8ffffffffffffffffffffec0c332p+4L, -0x2.e9a0572b1bb5b95f346a92d67a6p-112L }, - { -0x1.90000000000000000000013f3ccep+4L, 0x2.e9a0572b1bb5c371ddb3561705ap-112L }, - { -0x1.9ffffffffffffffffffffff3b8bdp+4L, -0x1.cad8d32e386fd783e97296d63dcbp-116L }, - { -0x1.a0000000000000000000000c4743p+4L, 0x1.cad8d32e386fd7c1ab8c1fe34c0ep-116L }, - { -0x1.afffffffffffffffffffffff8b95p+4L, -0x3.8f48cc5737d5979c39db806c5406p-112L }, - { -0x1.b00000000000000000000000746bp+4L, 0x3.8f48cc5737d5979c3b3a6bda06f6p-112L }, - { -0x1.bffffffffffffffffffffffffbd8p+4L, 0x6.2898d42174dcf171470d8c8c6028p-112L }, - { -0x1.c000000000000000000000000428p+4L, -0x6.2898d42174dcf171470d18ba412cp-112L }, - { -0x1.cfffffffffffffffffffffffffdbp+4L, -0x4.c0ce9794ea50a839e311320bde94p-112L }, - { -0x1.d000000000000000000000000025p+4L, 0x4.c0ce9794ea50a839e311322f7cf8p-112L }, - { -0x1.dfffffffffffffffffffffffffffp+4L, 0x3.932c5047d60e60caded4c298a174p-112L }, - { -0x1.e000000000000000000000000001p+4L, -0x3.932c5047d60e60caded4c298973ap-112L }, - { -0x1.fp+4L, 0xa.1a6973c1fade2170f7237d35fe3p-116L }, - { -0x1.fp+4L, -0xa.1a6973c1fade2170f7237d35fe08p-116L }, - { -0x2p+4L, 0x5.0d34b9e0fd6f10b87b91be9aff1p-120L }, - { -0x2p+4L, -0x5.0d34b9e0fd6f10b87b91be9aff0cp-120L }, - { -0x2.1p+4L, 0x2.73024a9ba1aa36a7059bff52e844p-124L }, - { -0x2.1p+4L, -0x2.73024a9ba1aa36a7059bff52e844p-124L }, - { -0x2.2p+4L, 0x1.2710231c0fd7a13f8a2b4af9d6b7p-128L }, - { -0x2.2p+4L, -0x1.2710231c0fd7a13f8a2b4af9d6b7p-128L }, - { -0x2.3p+4L, 0x8.6e2ce38b6c8f9419e3fad3f0312p-136L }, - { -0x2.3p+4L, -0x8.6e2ce38b6c8f9419e3fad3f0312p-136L }, - { -0x2.4p+4L, 0x3.bf30652185952560d71a254e4eb8p-140L }, - { -0x2.4p+4L, -0x3.bf30652185952560d71a254e4eb8p-140L }, - { -0x2.5p+4L, 0x1.9ec8d1c94e85af4c78b15c3d89d3p-144L }, - { -0x2.5p+4L, -0x1.9ec8d1c94e85af4c78b15c3d89d3p-144L }, - { -0x2.6p+4L, 0xa.ea565ce061d57489e9b85276274p-152L }, - { -0x2.6p+4L, -0xa.ea565ce061d57489e9b85276274p-152L }, - { -0x2.7p+4L, 0x4.7a6512692eb37804111dabad30ecp-156L }, - { -0x2.7p+4L, -0x4.7a6512692eb37804111dabad30ecp-156L }, - { -0x2.8p+4L, 0x1.ca8ed42a12ae3001a07244abad2bp-160L }, - { -0x2.8p+4L, -0x1.ca8ed42a12ae3001a07244abad2bp-160L }, - { -0x2.9p+4L, 0xb.2f30e1ce812063f12e7e8d8d96e8p-168L }, - { -0x2.9p+4L, -0xb.2f30e1ce812063f12e7e8d8d96e8p-168L }, - { -0x2.ap+4L, 0x4.42bd49d4c37a0db136489772e428p-172L }, - { -0x2.ap+4L, -0x4.42bd49d4c37a0db136489772e428p-172L }, - { -0x2.bp+4L, 0x1.95db45257e5122dcbae56def372p-176L }, - { -0x2.bp+4L, -0x1.95db45257e5122dcbae56def372p-176L }, - { -0x2.cp+4L, 0x9.3958d81ff63527ecf993f3fb6f48p-184L }, - { -0x2.cp+4L, -0x9.3958d81ff63527ecf993f3fb6f48p-184L }, - { -0x2.dp+4L, 0x3.47970e4440c8f1c058bd238c9958p-188L }, - { -0x2.dp+4L, -0x3.47970e4440c8f1c058bd238c9958p-188L }, - { -0x2.ep+4L, 0x1.240804f65951062ca46e4f25c608p-192L }, - { -0x2.ep+4L, -0x1.240804f65951062ca46e4f25c608p-192L }, - { -0x2.fp+4L, 0x6.36a382849fae6de2d15362d8a394p-200L }, - { -0x2.fp+4L, -0x6.36a382849fae6de2d15362d8a394p-200L }, - { -0x3p+4L, 0x2.123680d6dfe4cf4b9b1bcb9d8bdcp-204L }, - { -0x3p+4L, -0x2.123680d6dfe4cf4b9b1bcb9d8bdcp-204L }, - { -0x3.1p+4L, 0xa.d21786ff5842eca51fea0870919p-212L }, - { -0x3.1p+4L, -0xa.d21786ff5842eca51fea0870919p-212L }, - { -0x3.2p+4L, 0x3.766dedc259af040be140a68a6c04p-216L }, + { L(-0x2.74ff92c01f0d82abec9f315f1a08p+0), L(0xe.d3ccb7fb2658634a2b9f6b2ba81p-116) }, + { L(-0x2.bf6821437b20197995a4b4641eaep+0), L(-0xb.f4b00b4829f961e428533e6ad048p-116) }, + { L(-0x3.24c1b793cb35efb8be699ad3d9bap+0), L(-0x6.5454cb7fac60e3f16d9d7840c2ep-116) }, + { L(-0x3.f48e2a8f85fca170d4561291236cp+0), L(-0xc.320a4887d1cb4c711828a75d5758p-116) }, + { L(-0x4.0a139e16656030c39f0b0de18114p+0), L(0x1.53e84029416e1242006b2b3d1cfp-112) }, + { L(-0x4.fdd5de9bbabf3510d0aa40769884p+0), L(-0x1.01d7d78125286f78d1e501f14966p-112) }, + { L(-0x5.021a95fc2db6432a4c56e595394cp+0), L(-0x1.ecc6af0430d4fe5746fa7233356fp-112) }, + { L(-0x5.ffa4bd647d0357dd4ed62cbd31ecp+0), L(-0x1.f8e3f8e5deba2d67dbd70dd96ce1p-112) }, + { L(-0x6.005ac9625f233b607c2d96d16384p+0), L(-0x1.cb86ac569340cf1e5f24df7aab7bp-112) }, + { L(-0x6.fff2fddae1bbff3d626b65c23fd4p+0), L(0x1.e0bfcff5c457ebcf4d3ad9674167p-112) }, + { L(-0x7.000cff7b7f87adf4482dcdb98784p+0), L(0x1.54d99e35a74d6407b80292df199fp-112) }, + { L(-0x7.fffe5fe05673c3ca9e82b522b0ccp+0), L(0x1.62d177c832e0eb42c2faffd1b145p-112) }, + { L(-0x8.0001a01459fc9f60cb3cec1cec88p+0), L(0x2.8998835ac7277f7bcef67c47f188p-112) }, + { L(-0x8.ffffd1c425e80ffc864e95749258p+0), L(-0x1.e7e20210e7f81cf781b44e9d2b02p-112) }, + { L(-0x9.00002e3bb47d86d6d843fedc352p+0), L(0x2.14852f613a16291751d2ab751f7ep-112) }, + { L(-0x9.fffffb606bdfdcd062ae77a50548p+0), L(0x3.962d1490cc2e8f031c7007eaa1ap-116) }, + { L(-0xa.0000049f93bb9927b45d95e1544p+0), L(-0x1.e03086db9146a9287bd4f2172d5ap-112) }, + { L(-0xa.ffffff9466e9f1b36dacd2adbd18p+0), L(-0xd.05a4e458062f3f95345a4d9c9b6p-116) }, + { L(-0xb.0000006b9915315d965a6ffea41p+0), L(0x1.b415c6fff233e7b7fdc3a094246fp-112) }, + { L(-0xb.fffffff7089387387de41acc3d4p+0), L(0x3.687427c6373bd74a10306e10a28ep-112) }, + { L(-0xc.00000008f76c7731567c0f0250fp+0), L(-0x3.87920df5675833859190eb128ef6p-112) }, + { L(-0xc.ffffffff4f6dcf617f97a5ffc758p+0), L(0x2.ab72d76f32eaee2d1a42ed515d3ap-116) }, + { L(-0xd.00000000b092309c06683dd1b9p+0), L(-0x3.e3700857a15c19ac5a611de9688ap-112) }, + { L(-0xd.fffffffff36345ab9e184a3e09dp+0), L(-0x1.176dc48e47f62d917973dd44e553p-112) }, + { L(-0xe.000000000c9cba545e94e75ec57p+0), L(-0x1.8f753e2501e757a17cf2ecbeeb89p-112) }, + { L(-0xe.ffffffffff28c060c6604ef3037p+0), L(-0x1.f89d37357c9e3dc17c6c6e63becap-112) }, + { L(-0xf.0000000000d73f9f399bd0e420f8p+0), L(-0x5.e9ee31b0b890744fc0e3fbc01048p-116) }, + { L(-0xf.fffffffffff28c060c6621f512e8p+0), L(0xd.1b2eec9d960bd9adc5be5f5fa5p-116) }, + { L(-0x1.000000000000d73f9f399da1424cp+4), L(0x6.c46e0e88305d2800f0e414c506a8p-116) }, + { L(-0x1.0ffffffffffff3569c47e7a93e1cp+4), L(-0x4.6a08a2e008a998ebabb8087efa2cp-112) }, + { L(-0x1.1000000000000ca963b818568887p+4), L(-0x6.ca5a3a64ec15db0a95caf2c9ffb4p-112) }, + { L(-0x1.1fffffffffffff4bec3ce234132dp+4), L(-0x8.b2b726187c841cb92cd5221e444p-116) }, + { L(-0x1.20000000000000b413c31dcbeca5p+4), L(0x3.c4d005344b6cd0e7231120294abcp-112) }, + { L(-0x1.2ffffffffffffff685b25cbf5f54p+4), L(-0x5.ced932e38485f7dd296b8fa41448p-112) }, + { L(-0x1.30000000000000097a4da340a0acp+4), L(0x7.e484e0e0ffe38d406ebebe112f88p-112) }, + { L(-0x1.3fffffffffffffff86af516ff7f7p+4), L(-0x6.bd67e720d57854502b7db75e1718p-112) }, + { L(-0x1.40000000000000007950ae900809p+4), L(0x6.bec33375cac025d9c073168c5d9p-112) }, + { L(-0x1.4ffffffffffffffffa391c4248c3p+4), L(0x5.c63022b62b5484ba346524db607p-112) }, + { L(-0x1.500000000000000005c6e3bdb73dp+4), L(-0x5.c62f55ed5322b2685c5e9a51e6a8p-112) }, + { L(-0x1.5fffffffffffffffffbcc71a492p+4), L(-0x1.eb5aeb96c74d7ad25e060528fb5p-112) }, + { L(-0x1.6000000000000000004338e5b6ep+4), L(0x1.eb5aec04b2f2eb663e4e3d8a018cp-112) }, + { L(-0x1.6ffffffffffffffffffd13c97d9dp+4), L(-0x3.8fcc4d08d6fe5aa56ab04307ce7ep-112) }, + { L(-0x1.70000000000000000002ec368263p+4), L(0x3.8fcc4d090cee2f5d0b69a99c353cp-112) }, + { L(-0x1.7fffffffffffffffffffe0d30fe7p+4), L(0x7.2f577cca4b4c8cb1dc14001ac5ecp-112) }, + { L(-0x1.800000000000000000001f2cf019p+4), L(-0x7.2f577cca4b3442e35f0040b3b9e8p-112) }, + { L(-0x1.8ffffffffffffffffffffec0c332p+4), L(-0x2.e9a0572b1bb5b95f346a92d67a6p-112) }, + { L(-0x1.90000000000000000000013f3ccep+4), L(0x2.e9a0572b1bb5c371ddb3561705ap-112) }, + { L(-0x1.9ffffffffffffffffffffff3b8bdp+4), L(-0x1.cad8d32e386fd783e97296d63dcbp-116) }, + { L(-0x1.a0000000000000000000000c4743p+4), L(0x1.cad8d32e386fd7c1ab8c1fe34c0ep-116) }, + { L(-0x1.afffffffffffffffffffffff8b95p+4), L(-0x3.8f48cc5737d5979c39db806c5406p-112) }, + { L(-0x1.b00000000000000000000000746bp+4), L(0x3.8f48cc5737d5979c3b3a6bda06f6p-112) }, + { L(-0x1.bffffffffffffffffffffffffbd8p+4), L(0x6.2898d42174dcf171470d8c8c6028p-112) }, + { L(-0x1.c000000000000000000000000428p+4), L(-0x6.2898d42174dcf171470d18ba412cp-112) }, + { L(-0x1.cfffffffffffffffffffffffffdbp+4), L(-0x4.c0ce9794ea50a839e311320bde94p-112) }, + { L(-0x1.d000000000000000000000000025p+4), L(0x4.c0ce9794ea50a839e311322f7cf8p-112) }, + { L(-0x1.dfffffffffffffffffffffffffffp+4), L(0x3.932c5047d60e60caded4c298a174p-112) }, + { L(-0x1.e000000000000000000000000001p+4), L(-0x3.932c5047d60e60caded4c298973ap-112) }, + { L(-0x1.fp+4), L(0xa.1a6973c1fade2170f7237d35fe3p-116) }, + { L(-0x1.fp+4), L(-0xa.1a6973c1fade2170f7237d35fe08p-116) }, + { L(-0x2p+4), L(0x5.0d34b9e0fd6f10b87b91be9aff1p-120) }, + { L(-0x2p+4), L(-0x5.0d34b9e0fd6f10b87b91be9aff0cp-120) }, + { L(-0x2.1p+4), L(0x2.73024a9ba1aa36a7059bff52e844p-124) }, + { L(-0x2.1p+4), L(-0x2.73024a9ba1aa36a7059bff52e844p-124) }, + { L(-0x2.2p+4), L(0x1.2710231c0fd7a13f8a2b4af9d6b7p-128) }, + { L(-0x2.2p+4), L(-0x1.2710231c0fd7a13f8a2b4af9d6b7p-128) }, + { L(-0x2.3p+4), L(0x8.6e2ce38b6c8f9419e3fad3f0312p-136) }, + { L(-0x2.3p+4), L(-0x8.6e2ce38b6c8f9419e3fad3f0312p-136) }, + { L(-0x2.4p+4), L(0x3.bf30652185952560d71a254e4eb8p-140) }, + { L(-0x2.4p+4), L(-0x3.bf30652185952560d71a254e4eb8p-140) }, + { L(-0x2.5p+4), L(0x1.9ec8d1c94e85af4c78b15c3d89d3p-144) }, + { L(-0x2.5p+4), L(-0x1.9ec8d1c94e85af4c78b15c3d89d3p-144) }, + { L(-0x2.6p+4), L(0xa.ea565ce061d57489e9b85276274p-152) }, + { L(-0x2.6p+4), L(-0xa.ea565ce061d57489e9b85276274p-152) }, + { L(-0x2.7p+4), L(0x4.7a6512692eb37804111dabad30ecp-156) }, + { L(-0x2.7p+4), L(-0x4.7a6512692eb37804111dabad30ecp-156) }, + { L(-0x2.8p+4), L(0x1.ca8ed42a12ae3001a07244abad2bp-160) }, + { L(-0x2.8p+4), L(-0x1.ca8ed42a12ae3001a07244abad2bp-160) }, + { L(-0x2.9p+4), L(0xb.2f30e1ce812063f12e7e8d8d96e8p-168) }, + { L(-0x2.9p+4), L(-0xb.2f30e1ce812063f12e7e8d8d96e8p-168) }, + { L(-0x2.ap+4), L(0x4.42bd49d4c37a0db136489772e428p-172) }, + { L(-0x2.ap+4), L(-0x4.42bd49d4c37a0db136489772e428p-172) }, + { L(-0x2.bp+4), L(0x1.95db45257e5122dcbae56def372p-176) }, + { L(-0x2.bp+4), L(-0x1.95db45257e5122dcbae56def372p-176) }, + { L(-0x2.cp+4), L(0x9.3958d81ff63527ecf993f3fb6f48p-184) }, + { L(-0x2.cp+4), L(-0x9.3958d81ff63527ecf993f3fb6f48p-184) }, + { L(-0x2.dp+4), L(0x3.47970e4440c8f1c058bd238c9958p-188) }, + { L(-0x2.dp+4), L(-0x3.47970e4440c8f1c058bd238c9958p-188) }, + { L(-0x2.ep+4), L(0x1.240804f65951062ca46e4f25c608p-192) }, + { L(-0x2.ep+4), L(-0x1.240804f65951062ca46e4f25c608p-192) }, + { L(-0x2.fp+4), L(0x6.36a382849fae6de2d15362d8a394p-200) }, + { L(-0x2.fp+4), L(-0x6.36a382849fae6de2d15362d8a394p-200) }, + { L(-0x3p+4), L(0x2.123680d6dfe4cf4b9b1bcb9d8bdcp-204) }, + { L(-0x3p+4), L(-0x2.123680d6dfe4cf4b9b1bcb9d8bdcp-204) }, + { L(-0x3.1p+4), L(0xa.d21786ff5842eca51fea0870919p-212) }, + { L(-0x3.1p+4), L(-0xa.d21786ff5842eca51fea0870919p-212) }, + { L(-0x3.2p+4), L(0x3.766dedc259af040be140a68a6c04p-216) }, }; -static const long double e_hi = 0x2.b7e151628aed2a6abf7158809cf4p+0L; -static const long double e_lo = 0xf.3c762e7160f38b4da56a784d9048p-116L; +static const _Float128 e_hi = L(0x2.b7e151628aed2a6abf7158809cf4p+0); +static const _Float128 e_lo = L(0xf.3c762e7160f38b4da56a784d9048p-116); /* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) in Stirling's approximation to lgamma function. */ -static const long double lgamma_coeff[] = +static const _Float128 lgamma_coeff[] = { - 0x1.5555555555555555555555555555p-4L, - -0xb.60b60b60b60b60b60b60b60b60b8p-12L, - 0x3.4034034034034034034034034034p-12L, - -0x2.7027027027027027027027027028p-12L, - 0x3.72a3c5631fe46ae1d4e700dca8f2p-12L, - -0x7.daac36664f1f207daac36664f1f4p-12L, - 0x1.a41a41a41a41a41a41a41a41a41ap-8L, - -0x7.90a1b2c3d4e5f708192a3b4c5d7p-8L, - 0x2.dfd2c703c0cfff430edfd2c703cp-4L, - -0x1.6476701181f39edbdb9ce625987dp+0L, - 0xd.672219167002d3a7a9c886459cp+0L, - -0x9.cd9292e6660d55b3f712eb9e07c8p+4L, - 0x8.911a740da740da740da740da741p+8L, - -0x8.d0cc570e255bf59ff6eec24b49p+12L, - 0xa.8d1044d3708d1c219ee4fdc446ap+16L, - -0xe.8844d8a169abbc406169abbc406p+20L, - 0x1.6d29a0f6433b79890cede62433b8p+28L, - -0x2.88a233b3c8cddaba9809357125d8p+32L, - 0x5.0dde6f27500939a85c40939a85c4p+36L, - -0xb.4005bde03d4642a243581714af68p+40L, - 0x1.bc8cd6f8f1f755c78753cdb5d5c9p+48L, - -0x4.bbebb143bb94de5a0284fa7ec424p+52L, - 0xe.2e1337f5af0bed90b6b0a352d4fp+56L, - -0x2.e78250162b62405ad3e4bfe61b38p+64L, - 0xa.5f7eef9e71ac7c80326ab4cc8bfp+68L, - -0x2.83be0395e550213369924971b21ap+76L, - 0xa.8ebfe48da17dd999790760b0cep+80L, + L(0x1.5555555555555555555555555555p-4), + L(-0xb.60b60b60b60b60b60b60b60b60b8p-12), + L(0x3.4034034034034034034034034034p-12), + L(-0x2.7027027027027027027027027028p-12), + L(0x3.72a3c5631fe46ae1d4e700dca8f2p-12), + L(-0x7.daac36664f1f207daac36664f1f4p-12), + L(0x1.a41a41a41a41a41a41a41a41a41ap-8), + L(-0x7.90a1b2c3d4e5f708192a3b4c5d7p-8), + L(0x2.dfd2c703c0cfff430edfd2c703cp-4), + L(-0x1.6476701181f39edbdb9ce625987dp+0), + L(0xd.672219167002d3a7a9c886459cp+0), + L(-0x9.cd9292e6660d55b3f712eb9e07c8p+4), + L(0x8.911a740da740da740da740da741p+8), + L(-0x8.d0cc570e255bf59ff6eec24b49p+12), + L(0xa.8d1044d3708d1c219ee4fdc446ap+16), + L(-0xe.8844d8a169abbc406169abbc406p+20), + L(0x1.6d29a0f6433b79890cede62433b8p+28), + L(-0x2.88a233b3c8cddaba9809357125d8p+32), + L(0x5.0dde6f27500939a85c40939a85c4p+36), + L(-0xb.4005bde03d4642a243581714af68p+40), + L(0x1.bc8cd6f8f1f755c78753cdb5d5c9p+48), + L(-0x4.bbebb143bb94de5a0284fa7ec424p+52), + L(0xe.2e1337f5af0bed90b6b0a352d4fp+56), + L(-0x2.e78250162b62405ad3e4bfe61b38p+64), + L(0xa.5f7eef9e71ac7c80326ab4cc8bfp+68), + L(-0x2.83be0395e550213369924971b21ap+76), + L(0xa.8ebfe48da17dd999790760b0cep+80), }; #define NCOEFF (sizeof (lgamma_coeff) / sizeof (lgamma_coeff[0])) @@ -166,224 +166,224 @@ static const long double lgamma_coeff[] = polynomial is expressed in terms of x-xm, where xm is the midpoint of the interval for which the polynomial applies. */ -static const long double poly_coeff[] = +static const _Float128 poly_coeff[] = { /* Interval [-2.125, -2] (polynomial degree 23). */ - -0x1.0b71c5c54d42eb6c17f30b7aa8f5p+0L, - -0xc.73a1dc05f34951602554c6d7506p-4L, - -0x1.ec841408528b51473e6c425ee5ffp-4L, - -0xe.37c9da26fc3c9a3c1844c8c7f1cp-4L, - -0x1.03cd87c519305703b021fa33f827p-4L, - -0xe.ae9ada65e09aa7f1c75216128f58p-4L, - 0x9.b11855a4864b5731cf85736015a8p-8L, - -0xe.f28c133e697a95c28607c9701dep-4L, - 0x2.6ec14a1c586a72a7cc33ee569d6ap-4L, - -0xf.57cab973e14464a262fc24723c38p-4L, - 0x4.5b0fc25f16e52997b2886bbae808p-4L, - -0xf.f50e59f1a9b56e76e988dac9ccf8p-4L, - 0x6.5f5eae15e9a93369e1d85146c6fcp-4L, - -0x1.0d2422daac459e33e0994325ed23p+0L, - 0x8.82000a0e7401fb1117a0e6606928p-4L, - -0x1.1f492f178a3f1b19f58a2ca68e55p+0L, - 0xa.cb545f949899a04c160b19389abp-4L, - -0x1.36165a1b155ba3db3d1b77caf498p+0L, - 0xd.44c5d5576f74302e5cf79e183eep-4L, - -0x1.51f22e0cdd33d3d481e326c02f3ep+0L, - 0xf.f73a349c08244ac389c007779bfp-4L, - -0x1.73317bf626156ba716747c4ca866p+0L, - 0x1.379c3c97b9bc71e1c1c4802dd657p+0L, - -0x1.a72a351c54f902d483052000f5dfp+0L, + L(-0x1.0b71c5c54d42eb6c17f30b7aa8f5p+0), + L(-0xc.73a1dc05f34951602554c6d7506p-4), + L(-0x1.ec841408528b51473e6c425ee5ffp-4), + L(-0xe.37c9da26fc3c9a3c1844c8c7f1cp-4), + L(-0x1.03cd87c519305703b021fa33f827p-4), + L(-0xe.ae9ada65e09aa7f1c75216128f58p-4), + L(0x9.b11855a4864b5731cf85736015a8p-8), + L(-0xe.f28c133e697a95c28607c9701dep-4), + L(0x2.6ec14a1c586a72a7cc33ee569d6ap-4), + L(-0xf.57cab973e14464a262fc24723c38p-4), + L(0x4.5b0fc25f16e52997b2886bbae808p-4), + L(-0xf.f50e59f1a9b56e76e988dac9ccf8p-4), + L(0x6.5f5eae15e9a93369e1d85146c6fcp-4), + L(-0x1.0d2422daac459e33e0994325ed23p+0), + L(0x8.82000a0e7401fb1117a0e6606928p-4), + L(-0x1.1f492f178a3f1b19f58a2ca68e55p+0), + L(0xa.cb545f949899a04c160b19389abp-4), + L(-0x1.36165a1b155ba3db3d1b77caf498p+0), + L(0xd.44c5d5576f74302e5cf79e183eep-4), + L(-0x1.51f22e0cdd33d3d481e326c02f3ep+0), + L(0xf.f73a349c08244ac389c007779bfp-4), + L(-0x1.73317bf626156ba716747c4ca866p+0), + L(0x1.379c3c97b9bc71e1c1c4802dd657p+0), + L(-0x1.a72a351c54f902d483052000f5dfp+0), /* Interval [-2.25, -2.125] (polynomial degree 24). */ - -0xf.2930890d7d675a80c36afb0fd5e8p-4L, - -0xc.a5cfde054eab5c6770daeca577f8p-4L, - 0x3.9c9e0fdebb07cdf89c61d41c9238p-4L, - -0x1.02a5ad35605fcf4af65a6dbacb84p+0L, - 0x9.6e9b1185bb48be9de1918e00a2e8p-4L, - -0x1.4d8332f3cfbfa116fd611e9ce90dp+0L, - 0x1.1c0c8cb4d9f4b1d490e1a41fae4dp+0L, - -0x1.c9a6f5ae9130cd0299e293a42714p+0L, - 0x1.d7e9307fd58a2ea997f29573a112p+0L, - -0x2.921cb3473d96178ca2a11d2a8d46p+0L, - 0x2.e8d59113b6f3409ff8db226e9988p+0L, - -0x3.cbab931625a1ae2b26756817f264p+0L, - 0x4.7d9f0f05d5296d18663ca003912p+0L, - -0x5.ade9cba12a14ea485667b7135bbp+0L, - 0x6.dc983a5da74fb48e767b7fec0a3p+0L, - -0x8.8d9ed454ae31d9e138dd8ee0d1a8p+0L, - 0xa.6fa099d4e7c202e0c0fd6ed8492p+0L, - -0xc.ebc552a8090a0f0115e92d4ebbc8p+0L, - 0xf.d695e4772c0d829b53fba9ca5568p+0L, - -0x1.38c32ae38e5e9eb79b2a4c5570a9p+4L, - 0x1.8035145646cfab49306d0999a51bp+4L, - -0x1.d930adbb03dd342a4c2a8c4e1af6p+4L, - 0x2.45c2edb1b4943ddb3686cd9c6524p+4L, - -0x2.e818ebbfafe2f916fa21abf7756p+4L, - 0x3.9804ce51d0fb9a430a711fd7307p+4L, + L(-0xf.2930890d7d675a80c36afb0fd5e8p-4), + L(-0xc.a5cfde054eab5c6770daeca577f8p-4), + L(0x3.9c9e0fdebb07cdf89c61d41c9238p-4), + L(-0x1.02a5ad35605fcf4af65a6dbacb84p+0), + L(0x9.6e9b1185bb48be9de1918e00a2e8p-4), + L(-0x1.4d8332f3cfbfa116fd611e9ce90dp+0), + L(0x1.1c0c8cb4d9f4b1d490e1a41fae4dp+0), + L(-0x1.c9a6f5ae9130cd0299e293a42714p+0), + L(0x1.d7e9307fd58a2ea997f29573a112p+0), + L(-0x2.921cb3473d96178ca2a11d2a8d46p+0), + L(0x2.e8d59113b6f3409ff8db226e9988p+0), + L(-0x3.cbab931625a1ae2b26756817f264p+0), + L(0x4.7d9f0f05d5296d18663ca003912p+0), + L(-0x5.ade9cba12a14ea485667b7135bbp+0), + L(0x6.dc983a5da74fb48e767b7fec0a3p+0), + L(-0x8.8d9ed454ae31d9e138dd8ee0d1a8p+0), + L(0xa.6fa099d4e7c202e0c0fd6ed8492p+0), + L(-0xc.ebc552a8090a0f0115e92d4ebbc8p+0), + L(0xf.d695e4772c0d829b53fba9ca5568p+0), + L(-0x1.38c32ae38e5e9eb79b2a4c5570a9p+4), + L(0x1.8035145646cfab49306d0999a51bp+4), + L(-0x1.d930adbb03dd342a4c2a8c4e1af6p+4), + L(0x2.45c2edb1b4943ddb3686cd9c6524p+4), + L(-0x2.e818ebbfafe2f916fa21abf7756p+4), + L(0x3.9804ce51d0fb9a430a711fd7307p+4), /* Interval [-2.375, -2.25] (polynomial degree 25). */ - -0xd.7d28d505d6181218a25f31d5e45p-4L, - -0xe.69649a3040985140cdf946829fap-4L, - 0xb.0d74a2827d053a8d44595012484p-4L, - -0x1.924b0922853617cac181afbc08ddp+0L, - 0x1.d49b12bccf0a568582e2d3c410f3p+0L, - -0x3.0898bb7d8c4093e636279c791244p+0L, - 0x4.207a6cac711cb53868e8a5057eep+0L, - -0x6.39ee63ea4fb1dcab0c9144bf3ddcp+0L, - 0x8.e2e2556a797b649bf3f53bd26718p+0L, - -0xd.0e83ac82552ef12af508589e7a8p+0L, - 0x1.2e4525e0ce6670563c6484a82b05p+4L, - -0x1.b8e350d6a8f2b222fa390a57c23dp+4L, - 0x2.805cd69b919087d8a80295892c2cp+4L, - -0x3.a42585424a1b7e64c71743ab014p+4L, - 0x5.4b4f409f98de49f7bfb03c05f984p+4L, - -0x7.b3c5827fbe934bc820d6832fb9fcp+4L, - 0xb.33b7b90cc96c425526e0d0866e7p+4L, - -0x1.04b77047ac4f59ee3775ca10df0dp+8L, - 0x1.7b366f5e94a34f41386eac086313p+8L, - -0x2.2797338429385c9849ca6355bfc2p+8L, - 0x3.225273cf92a27c9aac1b35511256p+8L, - -0x4.8f078aa48afe6cb3a4e89690f898p+8L, - 0x6.9f311d7b6654fc1d0b5195141d04p+8L, - -0x9.a0c297b6b4621619ca9bacc48ed8p+8L, - 0xe.ce1f06b6f90d92138232a76e4cap+8L, - -0x1.5b0e6806fa064daf011613e43b17p+12L, + L(-0xd.7d28d505d6181218a25f31d5e45p-4), + L(-0xe.69649a3040985140cdf946829fap-4), + L(0xb.0d74a2827d053a8d44595012484p-4), + L(-0x1.924b0922853617cac181afbc08ddp+0), + L(0x1.d49b12bccf0a568582e2d3c410f3p+0), + L(-0x3.0898bb7d8c4093e636279c791244p+0), + L(0x4.207a6cac711cb53868e8a5057eep+0), + L(-0x6.39ee63ea4fb1dcab0c9144bf3ddcp+0), + L(0x8.e2e2556a797b649bf3f53bd26718p+0), + L(-0xd.0e83ac82552ef12af508589e7a8p+0), + L(0x1.2e4525e0ce6670563c6484a82b05p+4), + L(-0x1.b8e350d6a8f2b222fa390a57c23dp+4), + L(0x2.805cd69b919087d8a80295892c2cp+4), + L(-0x3.a42585424a1b7e64c71743ab014p+4), + L(0x5.4b4f409f98de49f7bfb03c05f984p+4), + L(-0x7.b3c5827fbe934bc820d6832fb9fcp+4), + L(0xb.33b7b90cc96c425526e0d0866e7p+4), + L(-0x1.04b77047ac4f59ee3775ca10df0dp+8), + L(0x1.7b366f5e94a34f41386eac086313p+8), + L(-0x2.2797338429385c9849ca6355bfc2p+8), + L(0x3.225273cf92a27c9aac1b35511256p+8), + L(-0x4.8f078aa48afe6cb3a4e89690f898p+8), + L(0x6.9f311d7b6654fc1d0b5195141d04p+8), + L(-0x9.a0c297b6b4621619ca9bacc48ed8p+8), + L(0xe.ce1f06b6f90d92138232a76e4cap+8), + L(-0x1.5b0e6806fa064daf011613e43b17p+12), /* Interval [-2.5, -2.375] (polynomial degree 27). */ - -0xb.74ea1bcfff94b2c01afba9daa7d8p-4L, - -0x1.2a82bd590c37538cab143308de4dp+0L, - 0x1.88020f828b966fec66b8649fd6fcp+0L, - -0x3.32279f040eb694970e9db24863dcp+0L, - 0x5.57ac82517767e68a721005853864p+0L, - -0x9.c2aedcfe22833de43834a0a6cc4p+0L, - 0x1.12c132f1f5577f99e1a0ed3538e1p+4L, - -0x1.ea94e26628a3de3597f7bb55a948p+4L, - 0x3.66b4ac4fa582f58b59f96b2f7c7p+4L, - -0x6.0cf746a9cf4cba8c39afcc73fc84p+4L, - 0xa.c102ef2c20d75a342197df7fedf8p+4L, - -0x1.31ebff06e8f14626782df58db3b6p+8L, - 0x2.1fd6f0c0e710994e059b9dbdb1fep+8L, - -0x3.c6d76040407f447f8b5074f07706p+8L, - 0x6.b6d18e0d8feb4c2ef5af6a40ed18p+8L, - -0xb.efaf542c529f91e34217f24ae6a8p+8L, - 0x1.53852d873210e7070f5d9eb2296p+12L, - -0x2.5b977c0ddc6d540717173ac29fc8p+12L, - 0x4.310d452ae05100eff1e02343a724p+12L, - -0x7.73a5d8f20c4f986a7dd1912b2968p+12L, - 0xd.3f5ea2484f3fca15eab1f4d1a218p+12L, - -0x1.78d18aac156d1d93a2ffe7e08d3fp+16L, - 0x2.9df49ca75e5b567f5ea3e47106cp+16L, - -0x4.a7149af8961a08aa7c3233b5bb94p+16L, - 0x8.3db10ffa742c707c25197d989798p+16L, - -0xe.a26d6dd023cadd02041a049ec368p+16L, - 0x1.c825d90514e7c57c7fa5316f947cp+20L, - -0x3.34bb81e5a0952df8ca1abdc6684cp+20L, + L(-0xb.74ea1bcfff94b2c01afba9daa7d8p-4), + L(-0x1.2a82bd590c37538cab143308de4dp+0), + L(0x1.88020f828b966fec66b8649fd6fcp+0), + L(-0x3.32279f040eb694970e9db24863dcp+0), + L(0x5.57ac82517767e68a721005853864p+0), + L(-0x9.c2aedcfe22833de43834a0a6cc4p+0), + L(0x1.12c132f1f5577f99e1a0ed3538e1p+4), + L(-0x1.ea94e26628a3de3597f7bb55a948p+4), + L(0x3.66b4ac4fa582f58b59f96b2f7c7p+4), + L(-0x6.0cf746a9cf4cba8c39afcc73fc84p+4), + L(0xa.c102ef2c20d75a342197df7fedf8p+4), + L(-0x1.31ebff06e8f14626782df58db3b6p+8), + L(0x2.1fd6f0c0e710994e059b9dbdb1fep+8), + L(-0x3.c6d76040407f447f8b5074f07706p+8), + L(0x6.b6d18e0d8feb4c2ef5af6a40ed18p+8), + L(-0xb.efaf542c529f91e34217f24ae6a8p+8), + L(0x1.53852d873210e7070f5d9eb2296p+12), + L(-0x2.5b977c0ddc6d540717173ac29fc8p+12), + L(0x4.310d452ae05100eff1e02343a724p+12), + L(-0x7.73a5d8f20c4f986a7dd1912b2968p+12), + L(0xd.3f5ea2484f3fca15eab1f4d1a218p+12), + L(-0x1.78d18aac156d1d93a2ffe7e08d3fp+16), + L(0x2.9df49ca75e5b567f5ea3e47106cp+16), + L(-0x4.a7149af8961a08aa7c3233b5bb94p+16), + L(0x8.3db10ffa742c707c25197d989798p+16), + L(-0xe.a26d6dd023cadd02041a049ec368p+16), + L(0x1.c825d90514e7c57c7fa5316f947cp+20), + L(-0x3.34bb81e5a0952df8ca1abdc6684cp+20), /* Interval [-2.625, -2.5] (polynomial degree 28). */ - -0x3.d10108c27ebafad533c20eac32bp-4L, - 0x1.cd557caff7d2b2085f41dbec5106p+0L, - 0x3.819b4856d399520dad9776ea2cacp+0L, - 0x6.8505cbad03dc34c5e42e8b12eb78p+0L, - 0xb.c1b2e653a9e38f82b399c94e7f08p+0L, - 0x1.50a53a38f148138105124df65419p+4L, - 0x2.57ae00cbe5232cbeeed34d89727ap+4L, - 0x4.2b156301b8604db85a601544bfp+4L, - 0x7.6989ed23ca3ca7579b3462592b5cp+4L, - 0xd.2dd2976557939517f831f5552cc8p+4L, - 0x1.76e1c3430eb860969bce40cd494p+8L, - 0x2.9a77bf5488742466db3a2c7c1ec6p+8L, - 0x4.a0d62ed7266e8eb36f725a8ebcep+8L, - 0x8.3a6184dd3021067df2f8b91e99c8p+8L, - 0xe.a0ade1538245bf55d39d7e436b1p+8L, - 0x1.a01359fae8617b5826dd74428e9p+12L, - 0x2.e3b0a32caae77251169acaca1ad4p+12L, - 0x5.2301257c81589f62b38fb5993ee8p+12L, - 0x9.21c9275db253d4e719b73b18cb9p+12L, - 0x1.03c104bc96141cda3f3fa4b112bcp+16L, - 0x1.cdc8ed65119196a08b0c78f1445p+16L, - 0x3.34f31d2eaacf34382cdb0073572ap+16L, - 0x5.b37628cadf12bf0000907d0ef294p+16L, - 0xa.22d8b332c0b1e6a616f425dfe5ap+16L, - 0x1.205b01444804c3ff922cd78b4c42p+20L, - 0x1.fe8f0cea9d1e0ff25be2470b4318p+20L, - 0x3.8872aebeb368399aee02b39340aep+20L, - 0x6.ebd560d351e84e26a4381f5b293cp+20L, - 0xc.c3644d094b0dae2fbcbf682cd428p+20L, + L(-0x3.d10108c27ebafad533c20eac32bp-4), + L(0x1.cd557caff7d2b2085f41dbec5106p+0), + L(0x3.819b4856d399520dad9776ea2cacp+0), + L(0x6.8505cbad03dc34c5e42e8b12eb78p+0), + L(0xb.c1b2e653a9e38f82b399c94e7f08p+0), + L(0x1.50a53a38f148138105124df65419p+4), + L(0x2.57ae00cbe5232cbeeed34d89727ap+4), + L(0x4.2b156301b8604db85a601544bfp+4), + L(0x7.6989ed23ca3ca7579b3462592b5cp+4), + L(0xd.2dd2976557939517f831f5552cc8p+4), + L(0x1.76e1c3430eb860969bce40cd494p+8), + L(0x2.9a77bf5488742466db3a2c7c1ec6p+8), + L(0x4.a0d62ed7266e8eb36f725a8ebcep+8), + L(0x8.3a6184dd3021067df2f8b91e99c8p+8), + L(0xe.a0ade1538245bf55d39d7e436b1p+8), + L(0x1.a01359fae8617b5826dd74428e9p+12), + L(0x2.e3b0a32caae77251169acaca1ad4p+12), + L(0x5.2301257c81589f62b38fb5993ee8p+12), + L(0x9.21c9275db253d4e719b73b18cb9p+12), + L(0x1.03c104bc96141cda3f3fa4b112bcp+16), + L(0x1.cdc8ed65119196a08b0c78f1445p+16), + L(0x3.34f31d2eaacf34382cdb0073572ap+16), + L(0x5.b37628cadf12bf0000907d0ef294p+16), + L(0xa.22d8b332c0b1e6a616f425dfe5ap+16), + L(0x1.205b01444804c3ff922cd78b4c42p+20), + L(0x1.fe8f0cea9d1e0ff25be2470b4318p+20), + L(0x3.8872aebeb368399aee02b39340aep+20), + L(0x6.ebd560d351e84e26a4381f5b293cp+20), + L(0xc.c3644d094b0dae2fbcbf682cd428p+20), /* Interval [-2.75, -2.625] (polynomial degree 26). */ - -0x6.b5d252a56e8a75458a27ed1c2dd4p-4L, - 0x1.28d60383da3ac721aed3c5794da9p+0L, - 0x1.db6513ada8a66ea77d87d9a8827bp+0L, - 0x2.e217118f9d348a27f7506a707e6ep+0L, - 0x4.450112c5cbf725a0fb9802396c9p+0L, - 0x6.4af99151eae7810a75df2a0303c4p+0L, - 0x9.2db598b4a97a7f69aeef32aec758p+0L, - 0xd.62bef9c22471f5ee47ea1b9c0b5p+0L, - 0x1.379f294e412bd62328326d4222f9p+4L, - 0x1.c5827349d8865f1e8825c37c31c6p+4L, - 0x2.93a7e7a75b7568cc8cbe8c016c12p+4L, - 0x3.bf9bb882afe57edb383d41879d3ap+4L, - 0x5.73c737828cee095c43a5566731c8p+4L, - 0x7.ee4653493a7f81e0442062b3823cp+4L, - 0xb.891c6b83fc8b55bd973b5d962d6p+4L, - 0x1.0c775d7de3bf9b246c0208e0207ep+8L, - 0x1.867ee43ec4bd4f4fd56abc05110ap+8L, - 0x2.37fe9ba6695821e9822d8c8af0a6p+8L, - 0x3.3a2c667e37c942f182cd3223a936p+8L, - 0x4.b1b500eb59f3f782c7ccec88754p+8L, - 0x6.d3efd3b65b3d0d8488d30b79fa4cp+8L, - 0x9.ee8224e65bed5ced8b75eaec609p+8L, - 0xe.72416e510cca77d53fc615c1f3dp+8L, - 0x1.4fb538b0a2dfe567a8904b7e0445p+12L, - 0x1.e7f56a9266cf525a5b8cf4cb76cep+12L, - 0x2.f0365c983f68c597ee49d099cce8p+12L, - 0x4.53aa229e1b9f5b5e59625265951p+12L, + L(-0x6.b5d252a56e8a75458a27ed1c2dd4p-4), + L(0x1.28d60383da3ac721aed3c5794da9p+0), + L(0x1.db6513ada8a66ea77d87d9a8827bp+0), + L(0x2.e217118f9d348a27f7506a707e6ep+0), + L(0x4.450112c5cbf725a0fb9802396c9p+0), + L(0x6.4af99151eae7810a75df2a0303c4p+0), + L(0x9.2db598b4a97a7f69aeef32aec758p+0), + L(0xd.62bef9c22471f5ee47ea1b9c0b5p+0), + L(0x1.379f294e412bd62328326d4222f9p+4), + L(0x1.c5827349d8865f1e8825c37c31c6p+4), + L(0x2.93a7e7a75b7568cc8cbe8c016c12p+4), + L(0x3.bf9bb882afe57edb383d41879d3ap+4), + L(0x5.73c737828cee095c43a5566731c8p+4), + L(0x7.ee4653493a7f81e0442062b3823cp+4), + L(0xb.891c6b83fc8b55bd973b5d962d6p+4), + L(0x1.0c775d7de3bf9b246c0208e0207ep+8), + L(0x1.867ee43ec4bd4f4fd56abc05110ap+8), + L(0x2.37fe9ba6695821e9822d8c8af0a6p+8), + L(0x3.3a2c667e37c942f182cd3223a936p+8), + L(0x4.b1b500eb59f3f782c7ccec88754p+8), + L(0x6.d3efd3b65b3d0d8488d30b79fa4cp+8), + L(0x9.ee8224e65bed5ced8b75eaec609p+8), + L(0xe.72416e510cca77d53fc615c1f3dp+8), + L(0x1.4fb538b0a2dfe567a8904b7e0445p+12), + L(0x1.e7f56a9266cf525a5b8cf4cb76cep+12), + L(0x2.f0365c983f68c597ee49d099cce8p+12), + L(0x4.53aa229e1b9f5b5e59625265951p+12), /* Interval [-2.875, -2.75] (polynomial degree 24). */ - -0x8.a41b1e4f36ff88dc820815607d68p-4L, - 0xc.da87d3b69dc0f2f9c6f368b8ca1p-4L, - 0x1.1474ad5c36158a7bea04fd2f98c6p+0L, - 0x1.761ecb90c555df6555b7dba955b6p+0L, - 0x1.d279bff9ae291caf6c4b4bcb3202p+0L, - 0x2.4e5d00559a6e2b9b5d7fe1f6689cp+0L, - 0x2.d57545a75cee8743ae2b17bc8d24p+0L, - 0x3.8514eee3aac88b89bec2307021bap+0L, - 0x4.5235e3b6e1891ffeb87fed9f8a24p+0L, - 0x5.562acdb10eef3c9a773b3e27a864p+0L, - 0x6.8ec8965c76efe03c26bff60b1194p+0L, - 0x8.15251aca144877af32658399f9b8p+0L, - 0x9.f08d56aba174d844138af782c0f8p+0L, - 0xc.3dbbeda2679e8a1346ccc3f6da88p+0L, - 0xf.0f5bfd5eacc26db308ffa0556fa8p+0L, - 0x1.28a6ccd84476fbc713d6bab49ac9p+4L, - 0x1.6d0a3ae2a3b1c8ff400641a3a21fp+4L, - 0x1.c15701b28637f87acfb6a91d33b5p+4L, - 0x2.28fbe0eccf472089b017651ca55ep+4L, - 0x2.a8a453004f6e8ffaacd1603bc3dp+4L, - 0x3.45ae4d9e1e7cd1a5dba0e4ec7f6cp+4L, - 0x4.065fbfacb7fad3e473cb577a61e8p+4L, - 0x4.f3d1473020927acac1944734a39p+4L, - 0x6.54bb091245815a36fb74e314dd18p+4L, - 0x7.d7f445129f7fb6c055e582d3f6ep+4L, + L(-0x8.a41b1e4f36ff88dc820815607d68p-4), + L(0xc.da87d3b69dc0f2f9c6f368b8ca1p-4), + L(0x1.1474ad5c36158a7bea04fd2f98c6p+0), + L(0x1.761ecb90c555df6555b7dba955b6p+0), + L(0x1.d279bff9ae291caf6c4b4bcb3202p+0), + L(0x2.4e5d00559a6e2b9b5d7fe1f6689cp+0), + L(0x2.d57545a75cee8743ae2b17bc8d24p+0), + L(0x3.8514eee3aac88b89bec2307021bap+0), + L(0x4.5235e3b6e1891ffeb87fed9f8a24p+0), + L(0x5.562acdb10eef3c9a773b3e27a864p+0), + L(0x6.8ec8965c76efe03c26bff60b1194p+0), + L(0x8.15251aca144877af32658399f9b8p+0), + L(0x9.f08d56aba174d844138af782c0f8p+0), + L(0xc.3dbbeda2679e8a1346ccc3f6da88p+0), + L(0xf.0f5bfd5eacc26db308ffa0556fa8p+0), + L(0x1.28a6ccd84476fbc713d6bab49ac9p+4), + L(0x1.6d0a3ae2a3b1c8ff400641a3a21fp+4), + L(0x1.c15701b28637f87acfb6a91d33b5p+4), + L(0x2.28fbe0eccf472089b017651ca55ep+4), + L(0x2.a8a453004f6e8ffaacd1603bc3dp+4), + L(0x3.45ae4d9e1e7cd1a5dba0e4ec7f6cp+4), + L(0x4.065fbfacb7fad3e473cb577a61e8p+4), + L(0x4.f3d1473020927acac1944734a39p+4), + L(0x6.54bb091245815a36fb74e314dd18p+4), + L(0x7.d7f445129f7fb6c055e582d3f6ep+4), /* Interval [-3, -2.875] (polynomial degree 23). */ - -0xa.046d667e468f3e44dcae1afcc648p-4L, - 0x9.70b88dcc006c214d8d996fdf5ccp-4L, - 0xa.a8a39421c86d3ff24931a0929fp-4L, - 0xd.2f4d1363f324da2b357c8b6ec94p-4L, - 0xd.ca9aa1a3a5c00de11bf60499a97p-4L, - 0xf.cf09c31eeb52a45dfa7ebe3778dp-4L, - 0x1.04b133a39ed8a09691205660468bp+0L, - 0x1.22b547a06edda944fcb12fd9b5ecp+0L, - 0x1.2c57fce7db86a91df09602d344b3p+0L, - 0x1.4aade4894708f84795212fe257eep+0L, - 0x1.579c8b7b67ec4afed5b28c8bf787p+0L, - 0x1.776820e7fc80ae5284239733078ap+0L, - 0x1.883ab28c7301fde4ca6b8ec26ec8p+0L, - 0x1.aa2ef6e1ae52eb42c9ee83b206e3p+0L, - 0x1.bf4ad50f0a9a9311300cf0c51ee7p+0L, - 0x1.e40206e0e96b1da463814dde0d09p+0L, - 0x1.fdcbcffef3a21b29719c2bd9feb1p+0L, - 0x2.25e2e8948939c4d42cf108fae4bep+0L, - 0x2.44ce14d2b59c1c0e6bf2cfa81018p+0L, - 0x2.70ee80bbd0387162be4861c43622p+0L, - 0x2.954b64d2c2ebf3489b949c74476p+0L, - 0x2.c616e133a811c1c9446105208656p+0L, - 0x3.05a69dfe1a9ba1079f90fcf26bd4p+0L, - 0x3.410d2ad16a0506de29736e6aafdap+0L, + L(-0xa.046d667e468f3e44dcae1afcc648p-4), + L(0x9.70b88dcc006c214d8d996fdf5ccp-4), + L(0xa.a8a39421c86d3ff24931a0929fp-4), + L(0xd.2f4d1363f324da2b357c8b6ec94p-4), + L(0xd.ca9aa1a3a5c00de11bf60499a97p-4), + L(0xf.cf09c31eeb52a45dfa7ebe3778dp-4), + L(0x1.04b133a39ed8a09691205660468bp+0), + L(0x1.22b547a06edda944fcb12fd9b5ecp+0), + L(0x1.2c57fce7db86a91df09602d344b3p+0), + L(0x1.4aade4894708f84795212fe257eep+0), + L(0x1.579c8b7b67ec4afed5b28c8bf787p+0), + L(0x1.776820e7fc80ae5284239733078ap+0), + L(0x1.883ab28c7301fde4ca6b8ec26ec8p+0), + L(0x1.aa2ef6e1ae52eb42c9ee83b206e3p+0), + L(0x1.bf4ad50f0a9a9311300cf0c51ee7p+0), + L(0x1.e40206e0e96b1da463814dde0d09p+0), + L(0x1.fdcbcffef3a21b29719c2bd9feb1p+0), + L(0x2.25e2e8948939c4d42cf108fae4bep+0), + L(0x2.44ce14d2b59c1c0e6bf2cfa81018p+0), + L(0x2.70ee80bbd0387162be4861c43622p+0), + L(0x2.954b64d2c2ebf3489b949c74476p+0), + L(0x2.c616e133a811c1c9446105208656p+0), + L(0x3.05a69dfe1a9ba1079f90fcf26bd4p+0), + L(0x3.410d2ad16a0506de29736e6aafdap+0), }; static const size_t poly_deg[] = @@ -412,30 +412,30 @@ static const size_t poly_end[] = /* Compute sin (pi * X) for -0.25 <= X <= 0.5. */ -static long double -lg_sinpi (long double x) +static _Float128 +lg_sinpi (_Float128 x) { - if (x <= 0.25L) + if (x <= L(0.25)) return __sinl (M_PIl * x); else - return __cosl (M_PIl * (0.5L - x)); + return __cosl (M_PIl * (L(0.5) - x)); } /* Compute cos (pi * X) for -0.25 <= X <= 0.5. */ -static long double -lg_cospi (long double x) +static _Float128 +lg_cospi (_Float128 x) { - if (x <= 0.25L) + if (x <= L(0.25)) return __cosl (M_PIl * x); else - return __sinl (M_PIl * (0.5L - x)); + return __sinl (M_PIl * (L(0.5) - x)); } /* Compute cot (pi * X) for -0.25 <= X <= 0.5. */ -static long double -lg_cotpi (long double x) +static _Float128 +lg_cotpi (_Float128 x) { return lg_cospi (x) / lg_sinpi (x); } @@ -443,34 +443,34 @@ lg_cotpi (long double x) /* Compute lgamma of a negative argument -50 < X < -2, setting *SIGNGAMP accordingly. */ -long double -__lgamma_negl (long double x, int *signgamp) +_Float128 +__lgamma_negl (_Float128 x, int *signgamp) { /* Determine the half-integer region X lies in, handle exact integers and determine the sign of the result. */ int i = __floorl (-2 * x); if ((i & 1) == 0 && i == -2 * x) - return 1.0L / 0.0L; - long double xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); + return L(1.0) / L(0.0); + _Float128 xn = ((i & 1) == 0 ? -i / 2 : (-i - 1) / 2); i -= 4; *signgamp = ((i & 2) == 0 ? -1 : 1); SET_RESTORE_ROUNDL (FE_TONEAREST); /* Expand around the zero X0 = X0_HI + X0_LO. */ - long double x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; - long double xdiff = x - x0_hi - x0_lo; + _Float128 x0_hi = lgamma_zeros[i][0], x0_lo = lgamma_zeros[i][1]; + _Float128 xdiff = x - x0_hi - x0_lo; /* For arguments in the range -3 to -2, use polynomial approximations to an adjusted version of the gamma function. */ if (i < 2) { int j = __floorl (-8 * x) - 16; - long double xm = (-33 - 2 * j) * 0.0625L; - long double x_adj = x - xm; + _Float128 xm = (-33 - 2 * j) * L(0.0625); + _Float128 x_adj = x - xm; size_t deg = poly_deg[j]; size_t end = poly_end[j]; - long double g = poly_coeff[end]; + _Float128 g = poly_coeff[end]; for (size_t j = 1; j <= deg; j++) g = g * x_adj + poly_coeff[end - j]; return __log1pl (g * xdiff / (x - xn)); @@ -478,9 +478,9 @@ __lgamma_negl (long double x, int *signgamp) /* The result we want is log (sinpi (X0) / sinpi (X)) + log (gamma (1 - X0) / gamma (1 - X)). */ - long double x_idiff = fabsl (xn - x), x0_idiff = fabsl (xn - x0_hi - x0_lo); - long double log_sinpi_ratio; - if (x0_idiff < x_idiff * 0.5L) + _Float128 x_idiff = fabsl (xn - x), x0_idiff = fabsl (xn - x0_hi - x0_lo); + _Float128 log_sinpi_ratio; + if (x0_idiff < x_idiff * L(0.5)) /* Use log not log1p to avoid inaccuracy from log1p of arguments close to -1. */ log_sinpi_ratio = __ieee754_logl (lg_sinpi (x0_idiff) @@ -490,29 +490,29 @@ __lgamma_negl (long double x, int *signgamp) /* Use log1p not log to avoid inaccuracy from log of arguments close to 1. X0DIFF2 has positive sign if X0 is further from XN than X is from XN, negative sign otherwise. */ - long double x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * 0.5L; - long double sx0d2 = lg_sinpi (x0diff2); - long double cx0d2 = lg_cospi (x0diff2); + _Float128 x0diff2 = ((i & 1) == 0 ? xdiff : -xdiff) * L(0.5); + _Float128 sx0d2 = lg_sinpi (x0diff2); + _Float128 cx0d2 = lg_cospi (x0diff2); log_sinpi_ratio = __log1pl (2 * sx0d2 * (-sx0d2 + cx0d2 * lg_cotpi (x_idiff))); } - long double log_gamma_ratio; - long double y0 = 1 - x0_hi; - long double y0_eps = -x0_hi + (1 - y0) - x0_lo; - long double y = 1 - x; - long double y_eps = -x + (1 - y); + _Float128 log_gamma_ratio; + _Float128 y0 = 1 - x0_hi; + _Float128 y0_eps = -x0_hi + (1 - y0) - x0_lo; + _Float128 y = 1 - x; + _Float128 y_eps = -x + (1 - y); /* We now wish to compute LOG_GAMMA_RATIO = log (gamma (Y0 + Y0_EPS) / gamma (Y + Y_EPS)). XDIFF accurately approximates the difference Y0 + Y0_EPS - Y - Y_EPS. Use Stirling's approximation. First, we may need to adjust into the range where Stirling's approximation is sufficiently accurate. */ - long double log_gamma_adj = 0; + _Float128 log_gamma_adj = 0; if (i < 20) { int n_up = (21 - i) / 2; - long double ny0, ny0_eps, ny, ny_eps; + _Float128 ny0, ny0_eps, ny, ny_eps; ny0 = y0 + n_up; ny0_eps = y0 - (ny0 - n_up) + y0_eps; y0 = ny0; @@ -521,28 +521,28 @@ __lgamma_negl (long double x, int *signgamp) ny_eps = y - (ny - n_up) + y_eps; y = ny; y_eps = ny_eps; - long double prodm1 = __lgamma_productl (xdiff, y - n_up, y_eps, n_up); + _Float128 prodm1 = __lgamma_productl (xdiff, y - n_up, y_eps, n_up); log_gamma_adj = -__log1pl (prodm1); } - long double log_gamma_high + _Float128 log_gamma_high = (xdiff * __log1pl ((y0 - e_hi - e_lo + y0_eps) / e_hi) - + (y - 0.5L + y_eps) * __log1pl (xdiff / y) + log_gamma_adj); + + (y - L(0.5) + y_eps) * __log1pl (xdiff / y) + log_gamma_adj); /* Compute the sum of (B_2k / 2k(2k-1))(Y0^-(2k-1) - Y^-(2k-1)). */ - long double y0r = 1 / y0, yr = 1 / y; - long double y0r2 = y0r * y0r, yr2 = yr * yr; - long double rdiff = -xdiff / (y * y0); - long double bterm[NCOEFF]; - long double dlast = rdiff, elast = rdiff * yr * (yr + y0r); + _Float128 y0r = 1 / y0, yr = 1 / y; + _Float128 y0r2 = y0r * y0r, yr2 = yr * yr; + _Float128 rdiff = -xdiff / (y * y0); + _Float128 bterm[NCOEFF]; + _Float128 dlast = rdiff, elast = rdiff * yr * (yr + y0r); bterm[0] = dlast * lgamma_coeff[0]; for (size_t j = 1; j < NCOEFF; j++) { - long double dnext = dlast * y0r2 + elast; - long double enext = elast * yr2; + _Float128 dnext = dlast * y0r2 + elast; + _Float128 enext = elast * yr2; bterm[j] = dnext * lgamma_coeff[j]; dlast = dnext; elast = enext; } - long double log_gamma_low = 0; + _Float128 log_gamma_low = 0; for (size_t j = 0; j < NCOEFF; j++) log_gamma_low += bterm[NCOEFF - 1 - j]; log_gamma_ratio = log_gamma_high + log_gamma_low; diff --git a/sysdeps/ieee754/ldbl-128/lgamma_productl.c b/sysdeps/ieee754/ldbl-128/lgamma_productl.c index de67cbe665..fa69603aee 100644 --- a/sysdeps/ieee754/ldbl-128/lgamma_productl.c +++ b/sysdeps/ieee754/ldbl-128/lgamma_productl.c @@ -1,5 +1,5 @@ /* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... - Copyright (C) 2015-2016 Free Software Foundation, Inc. + Copyright (C) 2015-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -18,37 +18,7 @@ #include <math.h> #include <math_private.h> -#include <float.h> - -/* Calculate X * Y exactly and store the result in *HI + *LO. It is - given that the values are small enough that no overflow occurs and - large enough (or zero) that no underflow occurs. */ - -static void -mul_split (long double *hi, long double *lo, long double x, long double y) -{ -#ifdef __FP_FAST_FMAL - /* Fast built-in fused multiply-add. */ - *hi = x * y; - *lo = __builtin_fmal (x, y, -*hi); -#elif defined FP_FAST_FMAL - /* Fast library fused multiply-add, compiler before GCC 4.6. */ - *hi = x * y; - *lo = __fmal (x, y, -*hi); -#else - /* Apply Dekker's algorithm. */ - *hi = x * y; -# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) - long double x1 = x * C; - long double y1 = y * C; -# undef C - x1 = (x - x1) + x1; - y1 = (y - y1) + y1; - long double x2 = x - x1; - long double y2 = y - y1; - *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; -#endif -} +#include <mul_splitl.h> /* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS + 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that @@ -56,24 +26,24 @@ mul_split (long double *hi, long double *lo, long double x, long double y) X_EPS / X is small enough that factors quadratic in it can be neglected. */ -long double -__lgamma_productl (long double t, long double x, long double x_eps, int n) +_Float128 +__lgamma_productl (_Float128 t, _Float128 x, _Float128 x_eps, int n) { - long double ret = 0, ret_eps = 0; + _Float128 ret = 0, ret_eps = 0; for (int i = 0; i < n; i++) { - long double xi = x + i; - long double quot = t / xi; - long double mhi, mlo; - mul_split (&mhi, &mlo, quot, xi); - long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi); + _Float128 xi = x + i; + _Float128 quot = t / xi; + _Float128 mhi, mlo; + mul_splitl (&mhi, &mlo, quot, xi); + _Float128 quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi); /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */ - long double rhi, rlo; - mul_split (&rhi, &rlo, ret, quot); - long double rpq = ret + quot; - long double rpq_eps = (ret - rpq) + quot; - long double nret = rpq + rhi; - long double nret_eps = (rpq - nret) + rhi; + _Float128 rhi, rlo; + mul_splitl (&rhi, &rlo, ret, quot); + _Float128 rpq = ret + quot; + _Float128 rpq_eps = (ret - rpq) + quot; + _Float128 nret = rpq + rhi; + _Float128 nret_eps = (rpq - nret) + rhi; ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot + quot_lo + quot_lo * (ret + ret_eps)); ret = nret; diff --git a/sysdeps/ieee754/ldbl-128/strtod_nan_ldouble.h b/sysdeps/ieee754/ldbl-128/math-nan-payload-ldouble.h index aed8953421..e2f092d3e1 100644 --- a/sysdeps/ieee754/ldbl-128/strtod_nan_ldouble.h +++ b/sysdeps/ieee754/ldbl-128/math-nan-payload-ldouble.h @@ -1,5 +1,5 @@ -/* Convert string for NaN payload to corresponding NaN. For ldbl-128. - Copyright (C) 1997-2016 Free Software Foundation, Inc. +/* NaN payload handling for ldbl-128. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -16,8 +16,7 @@ License along with the GNU C Library; if not, see <http://www.gnu.org/licenses/>. */ -#define FLOAT long double -#define SET_MANTISSA(flt, mant) \ +#define SET_NAN_PAYLOAD(flt, mant) \ do \ { \ union ieee854_long_double u; \ diff --git a/sysdeps/ieee754/ldbl-128/math_ldbl.h b/sysdeps/ieee754/ldbl-128/math_ldbl.h index b3faa04846..db2bc5e0c3 100644 --- a/sysdeps/ieee754/ldbl-128/math_ldbl.h +++ b/sysdeps/ieee754/ldbl-128/math_ldbl.h @@ -1,41 +1,61 @@ -#ifndef _MATH_PRIVATE_H_ -#error "Never use <math_ldbl.h> directly; include <math_private.h> instead." -#endif +/* Manipulation of the bit representation of 'long double' quantities. + Copyright (C) 1999-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#ifndef _MATH_LDBL_H_ +#define _MATH_LDBL_H_ 1 + +#include <stdint.h> +#include <endian.h> /* A union which permits us to convert between a long double and four 32 bit ints or two 64 bit ints. */ -#if __FLOAT_WORD_ORDER == BIG_ENDIAN +#if __FLOAT_WORD_ORDER == __BIG_ENDIAN typedef union { long double value; struct { - u_int64_t msw; - u_int64_t lsw; + uint64_t msw; + uint64_t lsw; } parts64; struct { - u_int32_t w0, w1, w2, w3; + uint32_t w0, w1, w2, w3; } parts32; } ieee854_long_double_shape_type; #endif -#if __FLOAT_WORD_ORDER == LITTLE_ENDIAN +#if __FLOAT_WORD_ORDER == __LITTLE_ENDIAN typedef union { long double value; struct { - u_int64_t lsw; - u_int64_t msw; + uint64_t lsw; + uint64_t msw; } parts64; struct { - u_int32_t w3, w2, w1, w0; + uint32_t w3, w2, w1, w0; } parts32; } ieee854_long_double_shape_type; @@ -88,3 +108,13 @@ do { \ sh_u.value = (d); \ (v) = sh_u.parts64.lsw; \ } while (0) + +/* + On a platform already supporting a binary128 long double, + _Float128 will alias to long double. This transformation + makes aliasing *l functions to *f128 trivial. +*/ +#define _Float128 long double +#define L(x) x##L + +#endif /* math_ldbl.h */ diff --git a/sysdeps/ieee754/ldbl-128/mpn2ldbl.c b/sysdeps/ieee754/ldbl-128/mpn2ldbl.c index f9e4a39f59..9fb9f5c3ad 100644 --- a/sysdeps/ieee754/ldbl-128/mpn2ldbl.c +++ b/sysdeps/ieee754/ldbl-128/mpn2ldbl.c @@ -1,4 +1,4 @@ -/* Copyright (C) 1995-2016 Free Software Foundation, Inc. +/* Copyright (C) 1995-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or diff --git a/sysdeps/ieee754/ldbl-128/printf_fphex.c b/sysdeps/ieee754/ldbl-128/printf_fphex.c index 83f8f39ae8..ec86afb6b1 100644 --- a/sysdeps/ieee754/ldbl-128/printf_fphex.c +++ b/sysdeps/ieee754/ldbl-128/printf_fphex.c @@ -1,6 +1,6 @@ /* Print floating point number in hexadecimal notation according to ISO C99. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -17,91 +17,9 @@ License along with the GNU C Library; if not, see <http://www.gnu.org/licenses/>. */ +#include <ldbl-128/printf_fphex_macros.h> #define PRINT_FPHEX_LONG_DOUBLE \ -do { \ - /* We have 112 bits of mantissa plus one implicit digit. Since \ - 112 bits are representable without rest using hexadecimal \ - digits we use only the implicit digits for the number before \ - the decimal point. */ \ - unsigned long long int num0, num1; \ - union ieee854_long_double u; \ - u.d = fpnum.ldbl; \ - \ - assert (sizeof (long double) == 16); \ - \ - num0 = (((unsigned long long int) u.ieee.mantissa0) << 32 \ - | u.ieee.mantissa1); \ - num1 = (((unsigned long long int) u.ieee.mantissa2) << 32 \ - | u.ieee.mantissa3); \ - \ - zero_mantissa = (num0|num1) == 0; \ - \ - if (sizeof (unsigned long int) > 6) \ - { \ - numstr = _itoa_word (num1, numbuf + sizeof numbuf, 16, \ - info->spec == 'A'); \ - wnumstr = _itowa_word (num1, \ - wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t),\ - 16, info->spec == 'A'); \ - } \ - else \ - { \ - numstr = _itoa (num1, numbuf + sizeof numbuf, 16, \ - info->spec == 'A'); \ - wnumstr = _itowa (num1, \ - wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t), \ - 16, info->spec == 'A'); \ - } \ - \ - while (numstr > numbuf + (sizeof numbuf - 64 / 4)) \ - { \ - *--numstr = '0'; \ - *--wnumstr = L'0'; \ - } \ - \ - if (sizeof (unsigned long int) > 6) \ - { \ - numstr = _itoa_word (num0, numstr, 16, info->spec == 'A'); \ - wnumstr = _itowa_word (num0, wnumstr, 16, info->spec == 'A'); \ - } \ - else \ - { \ - numstr = _itoa (num0, numstr, 16, info->spec == 'A'); \ - wnumstr = _itowa (num0, wnumstr, 16, info->spec == 'A'); \ - } \ - \ - /* Fill with zeroes. */ \ - while (numstr > numbuf + (sizeof numbuf - 112 / 4)) \ - { \ - *--numstr = '0'; \ - *--wnumstr = L'0'; \ - } \ - \ - leading = u.ieee.exponent == 0 ? '0' : '1'; \ - \ - exponent = u.ieee.exponent; \ - \ - if (exponent == 0) \ - { \ - if (zero_mantissa) \ - expnegative = 0; \ - else \ - { \ - /* This is a denormalized number. */ \ - expnegative = 1; \ - exponent = IEEE854_LONG_DOUBLE_BIAS - 1; \ - } \ - } \ - else if (exponent >= IEEE854_LONG_DOUBLE_BIAS) \ - { \ - expnegative = 0; \ - exponent -= IEEE854_LONG_DOUBLE_BIAS; \ - } \ - else \ - { \ - expnegative = 1; \ - exponent = -(exponent - IEEE854_LONG_DOUBLE_BIAS); \ - } \ -} while (0) + PRINT_FPHEX (long double, fpnum.ldbl, ieee854_long_double, \ + IEEE854_LONG_DOUBLE_BIAS) #include <stdio-common/printf_fphex.c> diff --git a/sysdeps/ieee754/ldbl-128/printf_fphex_macros.h b/sysdeps/ieee754/ldbl-128/printf_fphex_macros.h new file mode 100644 index 0000000000..4d3ba72004 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/printf_fphex_macros.h @@ -0,0 +1,104 @@ +/* Macro to print floating point numbers in hexadecimal notation. + Copyright (C) 2017-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define PRINT_FPHEX(FLOAT, VAR, IEEE854_UNION, IEEE854_BIAS) \ +do { \ + /* We have 112 bits of mantissa plus one implicit digit. Since \ + 112 bits are representable without rest using hexadecimal \ + digits we use only the implicit digits for the number before \ + the decimal point. */ \ + unsigned long long int num0, num1; \ + union IEEE854_UNION u; \ + u.d = VAR; \ + \ + assert (sizeof (FLOAT) == 16); \ + \ + num0 = (((unsigned long long int) u.ieee.mantissa0) << 32 \ + | u.ieee.mantissa1); \ + num1 = (((unsigned long long int) u.ieee.mantissa2) << 32 \ + | u.ieee.mantissa3); \ + \ + zero_mantissa = (num0|num1) == 0; \ + \ + if (sizeof (unsigned long int) > 6) \ + { \ + numstr = _itoa_word (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + wnumstr = _itowa_word (num1, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t),\ + 16, info->spec == 'A'); \ + } \ + else \ + { \ + numstr = _itoa (num1, numbuf + sizeof numbuf, 16, \ + info->spec == 'A'); \ + wnumstr = _itowa (num1, \ + wnumbuf + sizeof (wnumbuf) / sizeof (wchar_t), \ + 16, info->spec == 'A'); \ + } \ + \ + while (numstr > numbuf + (sizeof numbuf - 64 / 4)) \ + { \ + *--numstr = '0'; \ + *--wnumstr = L'0'; \ + } \ + \ + if (sizeof (unsigned long int) > 6) \ + { \ + numstr = _itoa_word (num0, numstr, 16, info->spec == 'A'); \ + wnumstr = _itowa_word (num0, wnumstr, 16, info->spec == 'A'); \ + } \ + else \ + { \ + numstr = _itoa (num0, numstr, 16, info->spec == 'A'); \ + wnumstr = _itowa (num0, wnumstr, 16, info->spec == 'A'); \ + } \ + \ + /* Fill with zeroes. */ \ + while (numstr > numbuf + (sizeof numbuf - 112 / 4)) \ + { \ + *--numstr = '0'; \ + *--wnumstr = L'0'; \ + } \ + \ + leading = u.ieee.exponent == 0 ? '0' : '1'; \ + \ + exponent = u.ieee.exponent; \ + \ + if (exponent == 0) \ + { \ + if (zero_mantissa) \ + expnegative = 0; \ + else \ + { \ + /* This is a denormalized number. */ \ + expnegative = 1; \ + exponent = IEEE854_BIAS - 1; \ + } \ + } \ + else if (exponent >= IEEE854_BIAS) \ + { \ + expnegative = 0; \ + exponent -= IEEE854_BIAS; \ + } \ + else \ + { \ + expnegative = 1; \ + exponent = -(exponent - IEEE854_BIAS); \ + } \ +} while (0) diff --git a/sysdeps/ieee754/ldbl-128/s_asinhl.c b/sysdeps/ieee754/ldbl-128/s_asinhl.c index 5f3b9f2c76..a733ee7695 100644 --- a/sysdeps/ieee754/ldbl-128/s_asinhl.c +++ b/sysdeps/ieee754/ldbl-128/s_asinhl.c @@ -32,16 +32,18 @@ static char rcsid[] = "$NetBSD: $"; #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> +#include <libm-alias-ldouble.h> -static const long double - one = 1.0L, - ln2 = 6.931471805599453094172321214581765681e-1L, - huge = 1.0e+4900L; +static const _Float128 + one = 1, + ln2 = L(6.931471805599453094172321214581765681e-1), + huge = L(1.0e+4900); -long double -__asinhl (long double x) +_Float128 +__asinhl (_Float128 x) { - long double t, w; + _Float128 t, w; int32_t ix, sign; ieee854_long_double_shape_type u; @@ -64,16 +66,16 @@ __asinhl (long double x) else if (ix >0x40000000) { /* 2^ 54 > |x| > 2.0 */ t = u.value; - w = __ieee754_logl (2.0 * t + one / (__ieee754_sqrtl (x * x + one) + t)); + w = __ieee754_logl (2.0 * t + one / (sqrtl (x * x + one) + t)); } else { /* 2.0 > |x| > 2 ^ -56 */ t = x * x; - w = __log1pl (u.value + t / (one + __ieee754_sqrtl (one + t))); + w = __log1pl (u.value + t / (one + sqrtl (one + t))); } if (sign & 0x80000000) return -w; else return w; } -weak_alias (__asinhl, asinhl) +libm_alias_ldouble (__asinh, asinh) diff --git a/sysdeps/ieee754/ldbl-128/s_atanl.c b/sysdeps/ieee754/ldbl-128/s_atanl.c index aaae701551..022ccf4c45 100644 --- a/sysdeps/ieee754/ldbl-128/s_atanl.c +++ b/sysdeps/ieee754/ldbl-128/s_atanl.c @@ -62,93 +62,95 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> +#include <libm-alias-ldouble.h> /* arctan(k/8), k = 0, ..., 82 */ -static const long double atantbl[84] = { - 0.0000000000000000000000000000000000000000E0L, - 1.2435499454676143503135484916387102557317E-1L, /* arctan(0.125) */ - 2.4497866312686415417208248121127581091414E-1L, - 3.5877067027057222039592006392646049977698E-1L, - 4.6364760900080611621425623146121440202854E-1L, - 5.5859931534356243597150821640166127034645E-1L, - 6.4350110879328438680280922871732263804151E-1L, - 7.1882999962162450541701415152590465395142E-1L, - 7.8539816339744830961566084581987572104929E-1L, - 8.4415398611317100251784414827164750652594E-1L, - 8.9605538457134395617480071802993782702458E-1L, - 9.4200004037946366473793717053459358607166E-1L, - 9.8279372324732906798571061101466601449688E-1L, - 1.0191413442663497346383429170230636487744E0L, - 1.0516502125483736674598673120862998296302E0L, - 1.0808390005411683108871567292171998202703E0L, - 1.1071487177940905030170654601785370400700E0L, - 1.1309537439791604464709335155363278047493E0L, - 1.1525719972156675180401498626127513797495E0L, - 1.1722738811284763866005949441337046149712E0L, - 1.1902899496825317329277337748293183376012E0L, - 1.2068173702852525303955115800565576303133E0L, - 1.2220253232109896370417417439225704908830E0L, - 1.2360594894780819419094519711090786987027E0L, - 1.2490457723982544258299170772810901230778E0L, - 1.2610933822524404193139408812473357720101E0L, - 1.2722973952087173412961937498224804940684E0L, - 1.2827408797442707473628852511364955306249E0L, - 1.2924966677897852679030914214070816845853E0L, - 1.3016288340091961438047858503666855921414E0L, - 1.3101939350475556342564376891719053122733E0L, - 1.3182420510168370498593302023271362531155E0L, - 1.3258176636680324650592392104284756311844E0L, - 1.3329603993374458675538498697331558093700E0L, - 1.3397056595989995393283037525895557411039E0L, - 1.3460851583802539310489409282517796256512E0L, - 1.3521273809209546571891479413898128509842E0L, - 1.3578579772154994751124898859640585287459E0L, - 1.3633001003596939542892985278250991189943E0L, - 1.3684746984165928776366381936948529556191E0L, - 1.3734007669450158608612719264449611486510E0L, - 1.3780955681325110444536609641291551522494E0L, - 1.3825748214901258580599674177685685125566E0L, - 1.3868528702577214543289381097042486034883E0L, - 1.3909428270024183486427686943836432060856E0L, - 1.3948567013423687823948122092044222644895E0L, - 1.3986055122719575950126700816114282335732E0L, - 1.4021993871854670105330304794336492676944E0L, - 1.4056476493802697809521934019958079881002E0L, - 1.4089588955564736949699075250792569287156E0L, - 1.4121410646084952153676136718584891599630E0L, - 1.4152014988178669079462550975833894394929E0L, - 1.4181469983996314594038603039700989523716E0L, - 1.4209838702219992566633046424614466661176E0L, - 1.4237179714064941189018190466107297503086E0L, - 1.4263547484202526397918060597281265695725E0L, - 1.4288992721907326964184700745371983590908E0L, - 1.4313562697035588982240194668401779312122E0L, - 1.4337301524847089866404719096698873648610E0L, - 1.4360250423171655234964275337155008780675E0L, - 1.4382447944982225979614042479354815855386E0L, - 1.4403930189057632173997301031392126865694E0L, - 1.4424730991091018200252920599377292525125E0L, - 1.4444882097316563655148453598508037025938E0L, - 1.4464413322481351841999668424758804165254E0L, - 1.4483352693775551917970437843145232637695E0L, - 1.4501726582147939000905940595923466567576E0L, - 1.4519559822271314199339700039142990228105E0L, - 1.4536875822280323362423034480994649820285E0L, - 1.4553696664279718992423082296859928222270E0L, - 1.4570043196511885530074841089245667532358E0L, - 1.4585935117976422128825857356750737658039E0L, - 1.4601391056210009726721818194296893361233E0L, - 1.4616428638860188872060496086383008594310E0L, - 1.4631064559620759326975975316301202111560E0L, - 1.4645314639038178118428450961503371619177E0L, - 1.4659193880646627234129855241049975398470E0L, - 1.4672716522843522691530527207287398276197E0L, - 1.4685896086876430842559640450619880951144E0L, - 1.4698745421276027686510391411132998919794E0L, - 1.4711276743037345918528755717617308518553E0L, - 1.4723501675822635384916444186631899205983E0L, - 1.4735431285433308455179928682541563973416E0L, /* arctan(10.25) */ - 1.5707963267948966192313216916397514420986E0L /* pi/2 */ +static const _Float128 atantbl[84] = { + L(0.0000000000000000000000000000000000000000E0), + L(1.2435499454676143503135484916387102557317E-1), /* arctan(0.125) */ + L(2.4497866312686415417208248121127581091414E-1), + L(3.5877067027057222039592006392646049977698E-1), + L(4.6364760900080611621425623146121440202854E-1), + L(5.5859931534356243597150821640166127034645E-1), + L(6.4350110879328438680280922871732263804151E-1), + L(7.1882999962162450541701415152590465395142E-1), + L(7.8539816339744830961566084581987572104929E-1), + L(8.4415398611317100251784414827164750652594E-1), + L(8.9605538457134395617480071802993782702458E-1), + L(9.4200004037946366473793717053459358607166E-1), + L(9.8279372324732906798571061101466601449688E-1), + L(1.0191413442663497346383429170230636487744E0), + L(1.0516502125483736674598673120862998296302E0), + L(1.0808390005411683108871567292171998202703E0), + L(1.1071487177940905030170654601785370400700E0), + L(1.1309537439791604464709335155363278047493E0), + L(1.1525719972156675180401498626127513797495E0), + L(1.1722738811284763866005949441337046149712E0), + L(1.1902899496825317329277337748293183376012E0), + L(1.2068173702852525303955115800565576303133E0), + L(1.2220253232109896370417417439225704908830E0), + L(1.2360594894780819419094519711090786987027E0), + L(1.2490457723982544258299170772810901230778E0), + L(1.2610933822524404193139408812473357720101E0), + L(1.2722973952087173412961937498224804940684E0), + L(1.2827408797442707473628852511364955306249E0), + L(1.2924966677897852679030914214070816845853E0), + L(1.3016288340091961438047858503666855921414E0), + L(1.3101939350475556342564376891719053122733E0), + L(1.3182420510168370498593302023271362531155E0), + L(1.3258176636680324650592392104284756311844E0), + L(1.3329603993374458675538498697331558093700E0), + L(1.3397056595989995393283037525895557411039E0), + L(1.3460851583802539310489409282517796256512E0), + L(1.3521273809209546571891479413898128509842E0), + L(1.3578579772154994751124898859640585287459E0), + L(1.3633001003596939542892985278250991189943E0), + L(1.3684746984165928776366381936948529556191E0), + L(1.3734007669450158608612719264449611486510E0), + L(1.3780955681325110444536609641291551522494E0), + L(1.3825748214901258580599674177685685125566E0), + L(1.3868528702577214543289381097042486034883E0), + L(1.3909428270024183486427686943836432060856E0), + L(1.3948567013423687823948122092044222644895E0), + L(1.3986055122719575950126700816114282335732E0), + L(1.4021993871854670105330304794336492676944E0), + L(1.4056476493802697809521934019958079881002E0), + L(1.4089588955564736949699075250792569287156E0), + L(1.4121410646084952153676136718584891599630E0), + L(1.4152014988178669079462550975833894394929E0), + L(1.4181469983996314594038603039700989523716E0), + L(1.4209838702219992566633046424614466661176E0), + L(1.4237179714064941189018190466107297503086E0), + L(1.4263547484202526397918060597281265695725E0), + L(1.4288992721907326964184700745371983590908E0), + L(1.4313562697035588982240194668401779312122E0), + L(1.4337301524847089866404719096698873648610E0), + L(1.4360250423171655234964275337155008780675E0), + L(1.4382447944982225979614042479354815855386E0), + L(1.4403930189057632173997301031392126865694E0), + L(1.4424730991091018200252920599377292525125E0), + L(1.4444882097316563655148453598508037025938E0), + L(1.4464413322481351841999668424758804165254E0), + L(1.4483352693775551917970437843145232637695E0), + L(1.4501726582147939000905940595923466567576E0), + L(1.4519559822271314199339700039142990228105E0), + L(1.4536875822280323362423034480994649820285E0), + L(1.4553696664279718992423082296859928222270E0), + L(1.4570043196511885530074841089245667532358E0), + L(1.4585935117976422128825857356750737658039E0), + L(1.4601391056210009726721818194296893361233E0), + L(1.4616428638860188872060496086383008594310E0), + L(1.4631064559620759326975975316301202111560E0), + L(1.4645314639038178118428450961503371619177E0), + L(1.4659193880646627234129855241049975398470E0), + L(1.4672716522843522691530527207287398276197E0), + L(1.4685896086876430842559640450619880951144E0), + L(1.4698745421276027686510391411132998919794E0), + L(1.4711276743037345918528755717617308518553E0), + L(1.4723501675822635384916444186631899205983E0), + L(1.4735431285433308455179928682541563973416E0), /* arctan(10.25) */ + L(1.5707963267948966192313216916397514420986E0) /* pi/2 */ }; @@ -156,26 +158,26 @@ static const long double atantbl[84] = { |t| <= 0.09375 peak relative error 5.3e-37 */ -static const long double - p0 = -4.283708356338736809269381409828726405572E1L, - p1 = -8.636132499244548540964557273544599863825E1L, - p2 = -5.713554848244551350855604111031839613216E1L, - p3 = -1.371405711877433266573835355036413750118E1L, - p4 = -8.638214309119210906997318946650189640184E-1L, - q0 = 1.285112506901621042780814422948906537959E2L, - q1 = 3.361907253914337187957855834229672347089E2L, - q2 = 3.180448303864130128268191635189365331680E2L, - q3 = 1.307244136980865800160844625025280344686E2L, - q4 = 2.173623741810414221251136181221172551416E1L; +static const _Float128 + p0 = L(-4.283708356338736809269381409828726405572E1), + p1 = L(-8.636132499244548540964557273544599863825E1), + p2 = L(-5.713554848244551350855604111031839613216E1), + p3 = L(-1.371405711877433266573835355036413750118E1), + p4 = L(-8.638214309119210906997318946650189640184E-1), + q0 = L(1.285112506901621042780814422948906537959E2), + q1 = L(3.361907253914337187957855834229672347089E2), + q2 = L(3.180448303864130128268191635189365331680E2), + q3 = L(1.307244136980865800160844625025280344686E2), + q4 = L(2.173623741810414221251136181221172551416E1); /* q5 = 1.000000000000000000000000000000000000000E0 */ -static const long double huge = 1.0e4930L; +static const _Float128 huge = L(1.0e4930); -long double -__atanl (long double x) +_Float128 +__atanl (_Float128 x) { int k, sign; - long double t, u, p, q; + _Float128 t, u, p, q; ieee854_long_double_shape_type s; s.value = x; @@ -231,7 +233,7 @@ __atanl (long double x) Roundoff to integer is asymmetrical to avoid cancellation when t < 0 (cf. fdlibm). */ k = 8.0 * x + 0.25; - u = 0.125 * k; + u = L(0.125) * k; /* Small arctan argument. */ t = (x - u) / (1.0 + x * u); } @@ -250,4 +252,4 @@ __atanl (long double x) return u; } -weak_alias (__atanl, atanl) +libm_alias_ldouble (__atan, atan) diff --git a/sysdeps/ieee754/ldbl-128/s_cbrtl.c b/sysdeps/ieee754/ldbl-128/s_cbrtl.c index c3ae96830e..526e850378 100644 --- a/sysdeps/ieee754/ldbl-128/s_cbrtl.c +++ b/sysdeps/ieee754/ldbl-128/s_cbrtl.c @@ -56,18 +56,19 @@ Adapted for glibc October, 2001. #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -static const long double CBRT2 = 1.259921049894873164767210607278228350570251L; -static const long double CBRT4 = 1.587401051968199474751705639272308260391493L; -static const long double CBRT2I = 0.7937005259840997373758528196361541301957467L; -static const long double CBRT4I = 0.6299605249474365823836053036391141752851257L; +static const _Float128 CBRT2 = L(1.259921049894873164767210607278228350570251); +static const _Float128 CBRT4 = L(1.587401051968199474751705639272308260391493); +static const _Float128 CBRT2I = L(0.7937005259840997373758528196361541301957467); +static const _Float128 CBRT4I = L(0.6299605249474365823836053036391141752851257); -long double -__cbrtl (long double x) +_Float128 +__cbrtl (_Float128 x) { int e, rem, sign; - long double z; + _Float128 z; if (!isfinite (x)) return x + x; @@ -89,11 +90,11 @@ __cbrtl (long double x) /* Approximate cube root of number between .5 and 1, peak relative error = 1.2e-6 */ - x = ((((1.3584464340920900529734e-1L * x - - 6.3986917220457538402318e-1L) * x - + 1.2875551670318751538055e0L) * x - - 1.4897083391357284957891e0L) * x - + 1.3304961236013647092521e0L) * x + 3.7568280825958912391243e-1L; + x = ((((L(1.3584464340920900529734e-1) * x + - L(6.3986917220457538402318e-1)) * x + + L(1.2875551670318751538055e0)) * x + - L(1.4897083391357284957891e0)) * x + + L(1.3304961236013647092521e0)) * x + L(3.7568280825958912391243e-1); /* exponent divided by 3 */ if (e >= 0) @@ -123,13 +124,13 @@ __cbrtl (long double x) x = __ldexpl (x, e); /* Newton iteration */ - x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L; - x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L; - x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L; + x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333); + x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333); + x -= (x - (z / (x * x))) * L(0.3333333333333333333333333333333333333333); if (sign < 0) x = -x; return (x); } -weak_alias (__cbrtl, cbrtl) +libm_alias_ldouble (__cbrt, cbrt) diff --git a/sysdeps/ieee754/ldbl-128/s_ceill.c b/sysdeps/ieee754/ldbl-128/s_ceill.c index 9f6bc4ce15..e6aba5f2af 100644 --- a/sysdeps/ieee754/ldbl-128/s_ceill.c +++ b/sysdeps/ieee754/ldbl-128/s_ceill.c @@ -22,34 +22,28 @@ static char rcsid[] = "$NetBSD: $"; * Return x rounded toward -inf to integral value * Method: * Bit twiddling. - * Exception: - * Inexact flag raised if x not equal to ceil(x). */ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -static const long double huge = 1.0e4930L; - -long double __ceill(long double x) +_Float128 __ceill(_Float128 x) { int64_t i0,i1,j0; - u_int64_t i,j; + uint64_t i,j; GET_LDOUBLE_WORDS64(i0,i1,x); j0 = ((i0>>48)&0x7fff)-0x3fff; if(j0<48) { - if(j0<0) { /* raise inexact if x != 0 */ - if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ - if(i0<0) {i0=0x8000000000000000ULL;i1=0;} - else if((i0|i1)!=0) { i0=0x3fff000000000000ULL;i1=0;} - } + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x8000000000000000ULL;i1=0;} + else if((i0|i1)!=0) { i0=0x3fff000000000000ULL;i1=0;} } else { i = (0x0000ffffffffffffULL)>>j0; if(((i0&i)|i1)==0) return x; /* x is integral */ - if(huge+x>0.0) { /* raise inexact flag */ - if(i0>0) i0 += (0x0001000000000000LL)>>j0; - i0 &= (~i); i1=0; - } + if(i0>0) i0 += (0x0001000000000000LL)>>j0; + i0 &= (~i); i1=0; } } else if (j0>111) { if(j0==0x4000) return x+x; /* inf or NaN */ @@ -57,19 +51,17 @@ long double __ceill(long double x) } else { i = -1ULL>>(j0-48); if((i1&i)==0) return x; /* x is integral */ - if(huge+x>0.0) { /* raise inexact flag */ - if(i0>0) { - if(j0==48) i0+=1; - else { - j = i1+(1LL<<(112-j0)); - if(j<i1) i0 +=1 ; /* got a carry */ - i1=j; - } + if(i0>0) { + if(j0==48) i0+=1; + else { + j = i1+(1LL<<(112-j0)); + if(j<i1) i0 +=1 ; /* got a carry */ + i1=j; } - i1 &= (~i); } + i1 &= (~i); } SET_LDOUBLE_WORDS64(x,i0,i1); return x; } -weak_alias (__ceill, ceill) +libm_alias_ldouble (__ceil, ceil) diff --git a/sysdeps/ieee754/ldbl-128/s_copysignl.c b/sysdeps/ieee754/ldbl-128/s_copysignl.c index 19b6880940..d23e0f72ea 100644 --- a/sysdeps/ieee754/ldbl-128/s_copysignl.c +++ b/sysdeps/ieee754/ldbl-128/s_copysignl.c @@ -25,14 +25,15 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -long double __copysignl(long double x, long double y) +_Float128 __copysignl(_Float128 x, _Float128 y) { - u_int64_t hx,hy; + uint64_t hx,hy; GET_LDOUBLE_MSW64(hx,x); GET_LDOUBLE_MSW64(hy,y); SET_LDOUBLE_MSW64(x,(hx&0x7fffffffffffffffULL) |(hy&0x8000000000000000ULL)); return x; } -weak_alias (__copysignl, copysignl) +libm_alias_ldouble (__copysign, copysign) diff --git a/sysdeps/ieee754/ldbl-128/s_cosl.c b/sysdeps/ieee754/ldbl-128/s_cosl.c index 2c3bff6e0f..b315abccc5 100644 --- a/sysdeps/ieee754/ldbl-128/s_cosl.c +++ b/sysdeps/ieee754/ldbl-128/s_cosl.c @@ -47,10 +47,11 @@ #include <errno.h> #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -long double __cosl(long double x) +_Float128 __cosl(_Float128 x) { - long double y[2],z=0.0L; + _Float128 y[2],z=0; int64_t n, ix; /* High word of x. */ @@ -83,4 +84,4 @@ long double __cosl(long double x) } } } -weak_alias (__cosl, cosl) +libm_alias_ldouble (__cos, cos) diff --git a/sysdeps/ieee754/ldbl-128/s_daddl.c b/sysdeps/ieee754/ldbl-128/s_daddl.c new file mode 100644 index 0000000000..81e8e2d3e1 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_daddl.c @@ -0,0 +1,37 @@ +/* Add long double (ldbl-128) values, narrowing the result to double. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define f32xaddf64x __hide_f32xaddf64x +#define f32xaddf128 __hide_f32xaddf128 +#define f64addf64x __hide_f64addf64x +#define f64addf128 __hide_f64addf128 +#include <math.h> +#undef f32xaddf64x +#undef f32xaddf128 +#undef f64addf64x +#undef f64addf128 + +#include <math-narrow.h> + +double +__daddl (_Float128 x, _Float128 y) +{ + NARROW_ADD_ROUND_TO_ODD (x, y, double, union ieee854_long_double, l, + mantissa3); +} +libm_alias_double_ldouble (add) diff --git a/sysdeps/ieee754/ldbl-128/s_ddivl.c b/sysdeps/ieee754/ldbl-128/s_ddivl.c new file mode 100644 index 0000000000..c76df92bfb --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_ddivl.c @@ -0,0 +1,37 @@ +/* Divide long double (ldbl-128) values, narrowing the result to double. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define f32xdivf64x __hide_f32xdivf64x +#define f32xdivf128 __hide_f32xdivf128 +#define f64divf64x __hide_f64divf64x +#define f64divf128 __hide_f64divf128 +#include <math.h> +#undef f32xdivf64x +#undef f32xdivf128 +#undef f64divf64x +#undef f64divf128 + +#include <math-narrow.h> + +double +__ddivl (_Float128 x, _Float128 y) +{ + NARROW_DIV_ROUND_TO_ODD (x, y, double, union ieee854_long_double, l, + mantissa3); +} +libm_alias_double_ldouble (div) diff --git a/sysdeps/ieee754/ldbl-128/s_dmull.c b/sysdeps/ieee754/ldbl-128/s_dmull.c new file mode 100644 index 0000000000..d32c4284e0 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_dmull.c @@ -0,0 +1,37 @@ +/* Multiply long double (ldbl-128) values, narrowing the result to double. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define f32xmulf64x __hide_f32xmulf64x +#define f32xmulf128 __hide_f32xmulf128 +#define f64mulf64x __hide_f64mulf64x +#define f64mulf128 __hide_f64mulf128 +#include <math.h> +#undef f32xmulf64x +#undef f32xmulf128 +#undef f64mulf64x +#undef f64mulf128 + +#include <math-narrow.h> + +double +__dmull (_Float128 x, _Float128 y) +{ + NARROW_MUL_ROUND_TO_ODD (x, y, double, union ieee854_long_double, l, + mantissa3); +} +libm_alias_double_ldouble (mul) diff --git a/sysdeps/ieee754/ldbl-128/s_dsubl.c b/sysdeps/ieee754/ldbl-128/s_dsubl.c new file mode 100644 index 0000000000..46d0f95b4c --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_dsubl.c @@ -0,0 +1,37 @@ +/* Subtract long double (ldbl-128) values, narrowing the result to double. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define f32xsubf64x __hide_f32xsubf64x +#define f32xsubf128 __hide_f32xsubf128 +#define f64subf64x __hide_f64subf64x +#define f64subf128 __hide_f64subf128 +#include <math.h> +#undef f32xsubf64x +#undef f32xsubf128 +#undef f64subf64x +#undef f64subf128 + +#include <math-narrow.h> + +double +__dsubl (_Float128 x, _Float128 y) +{ + NARROW_SUB_ROUND_TO_ODD (x, y, double, union ieee854_long_double, l, + mantissa3); +} +libm_alias_double_ldouble (sub) diff --git a/sysdeps/ieee754/ldbl-128/s_erfl.c b/sysdeps/ieee754/ldbl-128/s_erfl.c index dd275a7dd9..c0abfe2926 100644 --- a/sysdeps/ieee754/ldbl-128/s_erfl.c +++ b/sysdeps/ieee754/ldbl-128/s_erfl.c @@ -100,13 +100,15 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> +#include <libm-alias-ldouble.h> /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ -static long double -neval (long double x, const long double *p, int n) +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = *p--; @@ -121,10 +123,10 @@ neval (long double x, const long double *p, int n) /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ -static long double -deval (long double x, const long double *p, int n) +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = x + *p--; @@ -138,42 +140,42 @@ deval (long double x, const long double *p, int n) -static const long double -tiny = 1e-4931L, - one = 1.0L, - two = 2.0L, +static const _Float128 +tiny = L(1e-4931), + one = 1, + two = 2, /* 2/sqrt(pi) - 1 */ - efx = 1.2837916709551257389615890312154517168810E-1L; + efx = L(1.2837916709551257389615890312154517168810E-1); /* erf(x) = x + x R(x^2) 0 <= x <= 7/8 Peak relative error 1.8e-35 */ #define NTN1 8 -static const long double TN1[NTN1 + 1] = -{ - -3.858252324254637124543172907442106422373E10L, - 9.580319248590464682316366876952214879858E10L, - 1.302170519734879977595901236693040544854E10L, - 2.922956950426397417800321486727032845006E9L, - 1.764317520783319397868923218385468729799E8L, - 1.573436014601118630105796794840834145120E7L, - 4.028077380105721388745632295157816229289E5L, - 1.644056806467289066852135096352853491530E4L, - 3.390868480059991640235675479463287886081E1L +static const _Float128 TN1[NTN1 + 1] = +{ + L(-3.858252324254637124543172907442106422373E10), + L(9.580319248590464682316366876952214879858E10), + L(1.302170519734879977595901236693040544854E10), + L(2.922956950426397417800321486727032845006E9), + L(1.764317520783319397868923218385468729799E8), + L(1.573436014601118630105796794840834145120E7), + L(4.028077380105721388745632295157816229289E5), + L(1.644056806467289066852135096352853491530E4), + L(3.390868480059991640235675479463287886081E1) }; #define NTD1 8 -static const long double TD1[NTD1 + 1] = -{ - -3.005357030696532927149885530689529032152E11L, - -1.342602283126282827411658673839982164042E11L, - -2.777153893355340961288511024443668743399E10L, - -3.483826391033531996955620074072768276974E9L, - -2.906321047071299585682722511260895227921E8L, - -1.653347985722154162439387878512427542691E7L, - -6.245520581562848778466500301865173123136E5L, - -1.402124304177498828590239373389110545142E4L, - -1.209368072473510674493129989468348633579E2L +static const _Float128 TD1[NTD1 + 1] = +{ + L(-3.005357030696532927149885530689529032152E11), + L(-1.342602283126282827411658673839982164042E11), + L(-2.777153893355340961288511024443668743399E10), + L(-3.483826391033531996955620074072768276974E9), + L(-2.906321047071299585682722511260895227921E8), + L(-1.653347985722154162439387878512427542691E7), + L(-6.245520581562848778466500301865173123136E5), + L(-1.402124304177498828590239373389110545142E4), + L(-1.209368072473510674493129989468348633579E2) /* 1.0E0 */ }; @@ -181,32 +183,32 @@ static const long double TD1[NTD1 + 1] = /* erf(z+1) = erf_const + P(z)/Q(z) -.125 <= z <= 0 Peak relative error 7.3e-36 */ -static const long double erf_const = 0.845062911510467529296875L; +static const _Float128 erf_const = L(0.845062911510467529296875); #define NTN2 8 -static const long double TN2[NTN2 + 1] = -{ - -4.088889697077485301010486931817357000235E1L, - 7.157046430681808553842307502826960051036E3L, - -2.191561912574409865550015485451373731780E3L, - 2.180174916555316874988981177654057337219E3L, - 2.848578658049670668231333682379720943455E2L, - 1.630362490952512836762810462174798925274E2L, - 6.317712353961866974143739396865293596895E0L, - 2.450441034183492434655586496522857578066E1L, - 5.127662277706787664956025545897050896203E-1L +static const _Float128 TN2[NTN2 + 1] = +{ + L(-4.088889697077485301010486931817357000235E1), + L(7.157046430681808553842307502826960051036E3), + L(-2.191561912574409865550015485451373731780E3), + L(2.180174916555316874988981177654057337219E3), + L(2.848578658049670668231333682379720943455E2), + L(1.630362490952512836762810462174798925274E2), + L(6.317712353961866974143739396865293596895E0), + L(2.450441034183492434655586496522857578066E1), + L(5.127662277706787664956025545897050896203E-1) }; #define NTD2 8 -static const long double TD2[NTD2 + 1] = -{ - 1.731026445926834008273768924015161048885E4L, - 1.209682239007990370796112604286048173750E4L, - 1.160950290217993641320602282462976163857E4L, - 5.394294645127126577825507169061355698157E3L, - 2.791239340533632669442158497532521776093E3L, - 8.989365571337319032943005387378993827684E2L, - 2.974016493766349409725385710897298069677E2L, - 6.148192754590376378740261072533527271947E1L, - 1.178502892490738445655468927408440847480E1L +static const _Float128 TD2[NTD2 + 1] = +{ + L(1.731026445926834008273768924015161048885E4), + L(1.209682239007990370796112604286048173750E4), + L(1.160950290217993641320602282462976163857E4), + L(5.394294645127126577825507169061355698157E3), + L(2.791239340533632669442158497532521776093E3), + L(8.989365571337319032943005387378993827684E2), + L(2.974016493766349409725385710897298069677E2), + L(6.148192754590376378740261072533527271947E1), + L(1.178502892490738445655468927408440847480E1) /* 1.0E0 */ }; @@ -215,297 +217,297 @@ static const long double TD2[NTD2 + 1] = 0 <= x < 0.125 Peak relative error 1.4e-35 */ #define NRNr13 8 -static const long double RNr13[NRNr13 + 1] = -{ - -2.353707097641280550282633036456457014829E3L, - 3.871159656228743599994116143079870279866E2L, - -3.888105134258266192210485617504098426679E2L, - -2.129998539120061668038806696199343094971E1L, - -8.125462263594034672468446317145384108734E1L, - 8.151549093983505810118308635926270319660E0L, - -5.033362032729207310462422357772568553670E0L, - -4.253956621135136090295893547735851168471E-2L, - -8.098602878463854789780108161581050357814E-2L +static const _Float128 RNr13[NRNr13 + 1] = +{ + L(-2.353707097641280550282633036456457014829E3), + L(3.871159656228743599994116143079870279866E2), + L(-3.888105134258266192210485617504098426679E2), + L(-2.129998539120061668038806696199343094971E1), + L(-8.125462263594034672468446317145384108734E1), + L(8.151549093983505810118308635926270319660E0), + L(-5.033362032729207310462422357772568553670E0), + L(-4.253956621135136090295893547735851168471E-2), + L(-8.098602878463854789780108161581050357814E-2) }; #define NRDr13 7 -static const long double RDr13[NRDr13 + 1] = -{ - 2.220448796306693503549505450626652881752E3L, - 1.899133258779578688791041599040951431383E2L, - 1.061906712284961110196427571557149268454E3L, - 7.497086072306967965180978101974566760042E1L, - 2.146796115662672795876463568170441327274E2L, - 1.120156008362573736664338015952284925592E1L, - 2.211014952075052616409845051695042741074E1L, - 6.469655675326150785692908453094054988938E-1L +static const _Float128 RDr13[NRDr13 + 1] = +{ + L(2.220448796306693503549505450626652881752E3), + L(1.899133258779578688791041599040951431383E2), + L(1.061906712284961110196427571557149268454E3), + L(7.497086072306967965180978101974566760042E1), + L(2.146796115662672795876463568170441327274E2), + L(1.120156008362573736664338015952284925592E1), + L(2.211014952075052616409845051695042741074E1), + L(6.469655675326150785692908453094054988938E-1) /* 1.0E0 */ }; /* erfc(0.25) = C13a + C13b to extra precision. */ -static const long double C13a = 0.723663330078125L; -static const long double C13b = 1.0279753638067014931732235184287934646022E-5L; +static const _Float128 C13a = L(0.723663330078125); +static const _Float128 C13b = L(1.0279753638067014931732235184287934646022E-5); /* erfc(x + 0.375) = erfc(0.375) + x R(x) 0 <= x < 0.125 Peak relative error 1.2e-35 */ #define NRNr14 8 -static const long double RNr14[NRNr14 + 1] = -{ - -2.446164016404426277577283038988918202456E3L, - 6.718753324496563913392217011618096698140E2L, - -4.581631138049836157425391886957389240794E2L, - -2.382844088987092233033215402335026078208E1L, - -7.119237852400600507927038680970936336458E1L, - 1.313609646108420136332418282286454287146E1L, - -6.188608702082264389155862490056401365834E0L, - -2.787116601106678287277373011101132659279E-2L, - -2.230395570574153963203348263549700967918E-2L +static const _Float128 RNr14[NRNr14 + 1] = +{ + L(-2.446164016404426277577283038988918202456E3), + L(6.718753324496563913392217011618096698140E2), + L(-4.581631138049836157425391886957389240794E2), + L(-2.382844088987092233033215402335026078208E1), + L(-7.119237852400600507927038680970936336458E1), + L(1.313609646108420136332418282286454287146E1), + L(-6.188608702082264389155862490056401365834E0), + L(-2.787116601106678287277373011101132659279E-2), + L(-2.230395570574153963203348263549700967918E-2) }; #define NRDr14 7 -static const long double RDr14[NRDr14 + 1] = -{ - 2.495187439241869732696223349840963702875E3L, - 2.503549449872925580011284635695738412162E2L, - 1.159033560988895481698051531263861842461E3L, - 9.493751466542304491261487998684383688622E1L, - 2.276214929562354328261422263078480321204E2L, - 1.367697521219069280358984081407807931847E1L, - 2.276988395995528495055594829206582732682E1L, - 7.647745753648996559837591812375456641163E-1L +static const _Float128 RDr14[NRDr14 + 1] = +{ + L(2.495187439241869732696223349840963702875E3), + L(2.503549449872925580011284635695738412162E2), + L(1.159033560988895481698051531263861842461E3), + L(9.493751466542304491261487998684383688622E1), + L(2.276214929562354328261422263078480321204E2), + L(1.367697521219069280358984081407807931847E1), + L(2.276988395995528495055594829206582732682E1), + L(7.647745753648996559837591812375456641163E-1) /* 1.0E0 */ }; /* erfc(0.375) = C14a + C14b to extra precision. */ -static const long double C14a = 0.5958709716796875L; -static const long double C14b = 1.2118885490201676174914080878232469565953E-5L; +static const _Float128 C14a = L(0.5958709716796875); +static const _Float128 C14b = L(1.2118885490201676174914080878232469565953E-5); /* erfc(x + 0.5) = erfc(0.5) + x R(x) 0 <= x < 0.125 Peak relative error 4.7e-36 */ #define NRNr15 8 -static const long double RNr15[NRNr15 + 1] = -{ - -2.624212418011181487924855581955853461925E3L, - 8.473828904647825181073831556439301342756E2L, - -5.286207458628380765099405359607331669027E2L, - -3.895781234155315729088407259045269652318E1L, - -6.200857908065163618041240848728398496256E1L, - 1.469324610346924001393137895116129204737E1L, - -6.961356525370658572800674953305625578903E0L, - 5.145724386641163809595512876629030548495E-3L, - 1.990253655948179713415957791776180406812E-2L +static const _Float128 RNr15[NRNr15 + 1] = +{ + L(-2.624212418011181487924855581955853461925E3), + L(8.473828904647825181073831556439301342756E2), + L(-5.286207458628380765099405359607331669027E2), + L(-3.895781234155315729088407259045269652318E1), + L(-6.200857908065163618041240848728398496256E1), + L(1.469324610346924001393137895116129204737E1), + L(-6.961356525370658572800674953305625578903E0), + L(5.145724386641163809595512876629030548495E-3), + L(1.990253655948179713415957791776180406812E-2) }; #define NRDr15 7 -static const long double RDr15[NRDr15 + 1] = -{ - 2.986190760847974943034021764693341524962E3L, - 5.288262758961073066335410218650047725985E2L, - 1.363649178071006978355113026427856008978E3L, - 1.921707975649915894241864988942255320833E2L, - 2.588651100651029023069013885900085533226E2L, - 2.628752920321455606558942309396855629459E1L, - 2.455649035885114308978333741080991380610E1L, - 1.378826653595128464383127836412100939126E0L +static const _Float128 RDr15[NRDr15 + 1] = +{ + L(2.986190760847974943034021764693341524962E3), + L(5.288262758961073066335410218650047725985E2), + L(1.363649178071006978355113026427856008978E3), + L(1.921707975649915894241864988942255320833E2), + L(2.588651100651029023069013885900085533226E2), + L(2.628752920321455606558942309396855629459E1), + L(2.455649035885114308978333741080991380610E1), + L(1.378826653595128464383127836412100939126E0) /* 1.0E0 */ }; /* erfc(0.5) = C15a + C15b to extra precision. */ -static const long double C15a = 0.4794921875L; -static const long double C15b = 7.9346869534623172533461080354712635484242E-6L; +static const _Float128 C15a = L(0.4794921875); +static const _Float128 C15b = L(7.9346869534623172533461080354712635484242E-6); /* erfc(x + 0.625) = erfc(0.625) + x R(x) 0 <= x < 0.125 Peak relative error 5.1e-36 */ #define NRNr16 8 -static const long double RNr16[NRNr16 + 1] = -{ - -2.347887943200680563784690094002722906820E3L, - 8.008590660692105004780722726421020136482E2L, - -5.257363310384119728760181252132311447963E2L, - -4.471737717857801230450290232600243795637E1L, - -4.849540386452573306708795324759300320304E1L, - 1.140885264677134679275986782978655952843E1L, - -6.731591085460269447926746876983786152300E0L, - 1.370831653033047440345050025876085121231E-1L, - 2.022958279982138755020825717073966576670E-2L, +static const _Float128 RNr16[NRNr16 + 1] = +{ + L(-2.347887943200680563784690094002722906820E3), + L(8.008590660692105004780722726421020136482E2), + L(-5.257363310384119728760181252132311447963E2), + L(-4.471737717857801230450290232600243795637E1), + L(-4.849540386452573306708795324759300320304E1), + L(1.140885264677134679275986782978655952843E1), + L(-6.731591085460269447926746876983786152300E0), + L(1.370831653033047440345050025876085121231E-1), + L(2.022958279982138755020825717073966576670E-2), }; #define NRDr16 7 -static const long double RDr16[NRDr16 + 1] = -{ - 3.075166170024837215399323264868308087281E3L, - 8.730468942160798031608053127270430036627E2L, - 1.458472799166340479742581949088453244767E3L, - 3.230423687568019709453130785873540386217E2L, - 2.804009872719893612081109617983169474655E2L, - 4.465334221323222943418085830026979293091E1L, - 2.612723259683205928103787842214809134746E1L, - 2.341526751185244109722204018543276124997E0L, +static const _Float128 RDr16[NRDr16 + 1] = +{ + L(3.075166170024837215399323264868308087281E3), + L(8.730468942160798031608053127270430036627E2), + L(1.458472799166340479742581949088453244767E3), + L(3.230423687568019709453130785873540386217E2), + L(2.804009872719893612081109617983169474655E2), + L(4.465334221323222943418085830026979293091E1), + L(2.612723259683205928103787842214809134746E1), + L(2.341526751185244109722204018543276124997E0), /* 1.0E0 */ }; /* erfc(0.625) = C16a + C16b to extra precision. */ -static const long double C16a = 0.3767547607421875L; -static const long double C16b = 4.3570693945275513594941232097252997287766E-6L; +static const _Float128 C16a = L(0.3767547607421875); +static const _Float128 C16b = L(4.3570693945275513594941232097252997287766E-6); /* erfc(x + 0.75) = erfc(0.75) + x R(x) 0 <= x < 0.125 Peak relative error 1.7e-35 */ #define NRNr17 8 -static const long double RNr17[NRNr17 + 1] = -{ - -1.767068734220277728233364375724380366826E3L, - 6.693746645665242832426891888805363898707E2L, - -4.746224241837275958126060307406616817753E2L, - -2.274160637728782675145666064841883803196E1L, - -3.541232266140939050094370552538987982637E1L, - 6.988950514747052676394491563585179503865E0L, - -5.807687216836540830881352383529281215100E0L, - 3.631915988567346438830283503729569443642E-1L, - -1.488945487149634820537348176770282391202E-2L +static const _Float128 RNr17[NRNr17 + 1] = +{ + L(-1.767068734220277728233364375724380366826E3), + L(6.693746645665242832426891888805363898707E2), + L(-4.746224241837275958126060307406616817753E2), + L(-2.274160637728782675145666064841883803196E1), + L(-3.541232266140939050094370552538987982637E1), + L(6.988950514747052676394491563585179503865E0), + L(-5.807687216836540830881352383529281215100E0), + L(3.631915988567346438830283503729569443642E-1), + L(-1.488945487149634820537348176770282391202E-2) }; #define NRDr17 7 -static const long double RDr17[NRDr17 + 1] = -{ - 2.748457523498150741964464942246913394647E3L, - 1.020213390713477686776037331757871252652E3L, - 1.388857635935432621972601695296561952738E3L, - 3.903363681143817750895999579637315491087E2L, - 2.784568344378139499217928969529219886578E2L, - 5.555800830216764702779238020065345401144E1L, - 2.646215470959050279430447295801291168941E1L, - 2.984905282103517497081766758550112011265E0L, +static const _Float128 RDr17[NRDr17 + 1] = +{ + L(2.748457523498150741964464942246913394647E3), + L(1.020213390713477686776037331757871252652E3), + L(1.388857635935432621972601695296561952738E3), + L(3.903363681143817750895999579637315491087E2), + L(2.784568344378139499217928969529219886578E2), + L(5.555800830216764702779238020065345401144E1), + L(2.646215470959050279430447295801291168941E1), + L(2.984905282103517497081766758550112011265E0), /* 1.0E0 */ }; /* erfc(0.75) = C17a + C17b to extra precision. */ -static const long double C17a = 0.2888336181640625L; -static const long double C17b = 1.0748182422368401062165408589222625794046E-5L; +static const _Float128 C17a = L(0.2888336181640625); +static const _Float128 C17b = L(1.0748182422368401062165408589222625794046E-5); /* erfc(x + 0.875) = erfc(0.875) + x R(x) 0 <= x < 0.125 Peak relative error 2.2e-35 */ #define NRNr18 8 -static const long double RNr18[NRNr18 + 1] = -{ - -1.342044899087593397419622771847219619588E3L, - 6.127221294229172997509252330961641850598E2L, - -4.519821356522291185621206350470820610727E2L, - 1.223275177825128732497510264197915160235E1L, - -2.730789571382971355625020710543532867692E1L, - 4.045181204921538886880171727755445395862E0L, - -4.925146477876592723401384464691452700539E0L, - 5.933878036611279244654299924101068088582E-1L, - -5.557645435858916025452563379795159124753E-2L +static const _Float128 RNr18[NRNr18 + 1] = +{ + L(-1.342044899087593397419622771847219619588E3), + L(6.127221294229172997509252330961641850598E2), + L(-4.519821356522291185621206350470820610727E2), + L(1.223275177825128732497510264197915160235E1), + L(-2.730789571382971355625020710543532867692E1), + L(4.045181204921538886880171727755445395862E0), + L(-4.925146477876592723401384464691452700539E0), + L(5.933878036611279244654299924101068088582E-1), + L(-5.557645435858916025452563379795159124753E-2) }; #define NRDr18 7 -static const long double RDr18[NRDr18 + 1] = -{ - 2.557518000661700588758505116291983092951E3L, - 1.070171433382888994954602511991940418588E3L, - 1.344842834423493081054489613250688918709E3L, - 4.161144478449381901208660598266288188426E2L, - 2.763670252219855198052378138756906980422E2L, - 5.998153487868943708236273854747564557632E1L, - 2.657695108438628847733050476209037025318E1L, - 3.252140524394421868923289114410336976512E0L, +static const _Float128 RDr18[NRDr18 + 1] = +{ + L(2.557518000661700588758505116291983092951E3), + L(1.070171433382888994954602511991940418588E3), + L(1.344842834423493081054489613250688918709E3), + L(4.161144478449381901208660598266288188426E2), + L(2.763670252219855198052378138756906980422E2), + L(5.998153487868943708236273854747564557632E1), + L(2.657695108438628847733050476209037025318E1), + L(3.252140524394421868923289114410336976512E0), /* 1.0E0 */ }; /* erfc(0.875) = C18a + C18b to extra precision. */ -static const long double C18a = 0.215911865234375L; -static const long double C18b = 1.3073705765341685464282101150637224028267E-5L; +static const _Float128 C18a = L(0.215911865234375); +static const _Float128 C18b = L(1.3073705765341685464282101150637224028267E-5); /* erfc(x + 1.0) = erfc(1.0) + x R(x) 0 <= x < 0.125 Peak relative error 1.6e-35 */ #define NRNr19 8 -static const long double RNr19[NRNr19 + 1] = -{ - -1.139180936454157193495882956565663294826E3L, - 6.134903129086899737514712477207945973616E2L, - -4.628909024715329562325555164720732868263E2L, - 4.165702387210732352564932347500364010833E1L, - -2.286979913515229747204101330405771801610E1L, - 1.870695256449872743066783202326943667722E0L, - -4.177486601273105752879868187237000032364E0L, - 7.533980372789646140112424811291782526263E-1L, - -8.629945436917752003058064731308767664446E-2L +static const _Float128 RNr19[NRNr19 + 1] = +{ + L(-1.139180936454157193495882956565663294826E3), + L(6.134903129086899737514712477207945973616E2), + L(-4.628909024715329562325555164720732868263E2), + L(4.165702387210732352564932347500364010833E1), + L(-2.286979913515229747204101330405771801610E1), + L(1.870695256449872743066783202326943667722E0), + L(-4.177486601273105752879868187237000032364E0), + L(7.533980372789646140112424811291782526263E-1), + L(-8.629945436917752003058064731308767664446E-2) }; #define NRDr19 7 -static const long double RDr19[NRDr19 + 1] = -{ - 2.744303447981132701432716278363418643778E3L, - 1.266396359526187065222528050591302171471E3L, - 1.466739461422073351497972255511919814273E3L, - 4.868710570759693955597496520298058147162E2L, - 2.993694301559756046478189634131722579643E2L, - 6.868976819510254139741559102693828237440E1L, - 2.801505816247677193480190483913753613630E1L, - 3.604439909194350263552750347742663954481E0L, +static const _Float128 RDr19[NRDr19 + 1] = +{ + L(2.744303447981132701432716278363418643778E3), + L(1.266396359526187065222528050591302171471E3), + L(1.466739461422073351497972255511919814273E3), + L(4.868710570759693955597496520298058147162E2), + L(2.993694301559756046478189634131722579643E2), + L(6.868976819510254139741559102693828237440E1), + L(2.801505816247677193480190483913753613630E1), + L(3.604439909194350263552750347742663954481E0), /* 1.0E0 */ }; /* erfc(1.0) = C19a + C19b to extra precision. */ -static const long double C19a = 0.15728759765625L; -static const long double C19b = 1.1609394035130658779364917390740703933002E-5L; +static const _Float128 C19a = L(0.15728759765625); +static const _Float128 C19b = L(1.1609394035130658779364917390740703933002E-5); /* erfc(x + 1.125) = erfc(1.125) + x R(x) 0 <= x < 0.125 Peak relative error 3.6e-36 */ #define NRNr20 8 -static const long double RNr20[NRNr20 + 1] = -{ - -9.652706916457973956366721379612508047640E2L, - 5.577066396050932776683469951773643880634E2L, - -4.406335508848496713572223098693575485978E2L, - 5.202893466490242733570232680736966655434E1L, - -1.931311847665757913322495948705563937159E1L, - -9.364318268748287664267341457164918090611E-2L, - -3.306390351286352764891355375882586201069E0L, - 7.573806045289044647727613003096916516475E-1L, - -9.611744011489092894027478899545635991213E-2L +static const _Float128 RNr20[NRNr20 + 1] = +{ + L(-9.652706916457973956366721379612508047640E2), + L(5.577066396050932776683469951773643880634E2), + L(-4.406335508848496713572223098693575485978E2), + L(5.202893466490242733570232680736966655434E1), + L(-1.931311847665757913322495948705563937159E1), + L(-9.364318268748287664267341457164918090611E-2), + L(-3.306390351286352764891355375882586201069E0), + L(7.573806045289044647727613003096916516475E-1), + L(-9.611744011489092894027478899545635991213E-2) }; #define NRDr20 7 -static const long double RDr20[NRDr20 + 1] = -{ - 3.032829629520142564106649167182428189014E3L, - 1.659648470721967719961167083684972196891E3L, - 1.703545128657284619402511356932569292535E3L, - 6.393465677731598872500200253155257708763E2L, - 3.489131397281030947405287112726059221934E2L, - 8.848641738570783406484348434387611713070E1L, - 3.132269062552392974833215844236160958502E1L, - 4.430131663290563523933419966185230513168E0L +static const _Float128 RDr20[NRDr20 + 1] = +{ + L(3.032829629520142564106649167182428189014E3), + L(1.659648470721967719961167083684972196891E3), + L(1.703545128657284619402511356932569292535E3), + L(6.393465677731598872500200253155257708763E2), + L(3.489131397281030947405287112726059221934E2), + L(8.848641738570783406484348434387611713070E1), + L(3.132269062552392974833215844236160958502E1), + L(4.430131663290563523933419966185230513168E0) /* 1.0E0 */ }; /* erfc(1.125) = C20a + C20b to extra precision. */ -static const long double C20a = 0.111602783203125L; -static const long double C20b = 8.9850951672359304215530728365232161564636E-6L; +static const _Float128 C20a = L(0.111602783203125); +static const _Float128 C20b = L(8.9850951672359304215530728365232161564636E-6); /* erfc(1/x) = 1/x exp (-1/x^2 - 0.5625 + R(1/x^2)) 7/8 <= 1/x < 1 Peak relative error 1.4e-35 */ #define NRNr8 9 -static const long double RNr8[NRNr8 + 1] = -{ - 3.587451489255356250759834295199296936784E1L, - 5.406249749087340431871378009874875889602E2L, - 2.931301290625250886238822286506381194157E3L, - 7.359254185241795584113047248898753470923E3L, - 9.201031849810636104112101947312492532314E3L, - 5.749697096193191467751650366613289284777E3L, - 1.710415234419860825710780802678697889231E3L, - 2.150753982543378580859546706243022719599E2L, - 8.740953582272147335100537849981160931197E0L, - 4.876422978828717219629814794707963640913E-2L +static const _Float128 RNr8[NRNr8 + 1] = +{ + L(3.587451489255356250759834295199296936784E1), + L(5.406249749087340431871378009874875889602E2), + L(2.931301290625250886238822286506381194157E3), + L(7.359254185241795584113047248898753470923E3), + L(9.201031849810636104112101947312492532314E3), + L(5.749697096193191467751650366613289284777E3), + L(1.710415234419860825710780802678697889231E3), + L(2.150753982543378580859546706243022719599E2), + L(8.740953582272147335100537849981160931197E0), + L(4.876422978828717219629814794707963640913E-2) }; #define NRDr8 8 -static const long double RDr8[NRDr8 + 1] = -{ - 6.358593134096908350929496535931630140282E1L, - 9.900253816552450073757174323424051765523E2L, - 5.642928777856801020545245437089490805186E3L, - 1.524195375199570868195152698617273739609E4L, - 2.113829644500006749947332935305800887345E4L, - 1.526438562626465706267943737310282977138E4L, - 5.561370922149241457131421914140039411782E3L, - 9.394035530179705051609070428036834496942E2L, - 6.147019596150394577984175188032707343615E1L +static const _Float128 RDr8[NRDr8 + 1] = +{ + L(6.358593134096908350929496535931630140282E1), + L(9.900253816552450073757174323424051765523E2), + L(5.642928777856801020545245437089490805186E3), + L(1.524195375199570868195152698617273739609E4), + L(2.113829644500006749947332935305800887345E4), + L(1.526438562626465706267943737310282977138E4), + L(5.561370922149241457131421914140039411782E3), + L(9.394035530179705051609070428036834496942E2), + L(6.147019596150394577984175188032707343615E1) /* 1.0E0 */ }; @@ -513,32 +515,32 @@ static const long double RDr8[NRDr8 + 1] = 0.75 <= 1/x <= 0.875 Peak relative error 2.0e-36 */ #define NRNr7 9 -static const long double RNr7[NRNr7 + 1] = -{ - 1.686222193385987690785945787708644476545E1L, - 1.178224543567604215602418571310612066594E3L, - 1.764550584290149466653899886088166091093E4L, - 1.073758321890334822002849369898232811561E5L, - 3.132840749205943137619839114451290324371E5L, - 4.607864939974100224615527007793867585915E5L, - 3.389781820105852303125270837910972384510E5L, - 1.174042187110565202875011358512564753399E5L, - 1.660013606011167144046604892622504338313E4L, - 6.700393957480661937695573729183733234400E2L +static const _Float128 RNr7[NRNr7 + 1] = +{ + L(1.686222193385987690785945787708644476545E1), + L(1.178224543567604215602418571310612066594E3), + L(1.764550584290149466653899886088166091093E4), + L(1.073758321890334822002849369898232811561E5), + L(3.132840749205943137619839114451290324371E5), + L(4.607864939974100224615527007793867585915E5), + L(3.389781820105852303125270837910972384510E5), + L(1.174042187110565202875011358512564753399E5), + L(1.660013606011167144046604892622504338313E4), + L(6.700393957480661937695573729183733234400E2) }; #define NRDr7 9 -static const long double RDr7[NRDr7 + 1] = -{ --1.709305024718358874701575813642933561169E3L, --3.280033887481333199580464617020514788369E4L, --2.345284228022521885093072363418750835214E5L, --8.086758123097763971926711729242327554917E5L, --1.456900414510108718402423999575992450138E6L, --1.391654264881255068392389037292702041855E6L, --6.842360801869939983674527468509852583855E5L, --1.597430214446573566179675395199807533371E5L, --1.488876130609876681421645314851760773480E4L, --3.511762950935060301403599443436465645703E2L +static const _Float128 RDr7[NRDr7 + 1] = +{ +L(-1.709305024718358874701575813642933561169E3), +L(-3.280033887481333199580464617020514788369E4), +L(-2.345284228022521885093072363418750835214E5), +L(-8.086758123097763971926711729242327554917E5), +L(-1.456900414510108718402423999575992450138E6), +L(-1.391654264881255068392389037292702041855E6), +L(-6.842360801869939983674527468509852583855E5), +L(-1.597430214446573566179675395199807533371E5), +L(-1.488876130609876681421645314851760773480E4), +L(-3.511762950935060301403599443436465645703E2) /* 1.0E0 */ }; @@ -546,32 +548,32 @@ static const long double RDr7[NRDr7 + 1] = 5/8 <= 1/x < 3/4 Peak relative error 1.9e-35 */ #define NRNr6 9 -static const long double RNr6[NRNr6 + 1] = -{ - 1.642076876176834390623842732352935761108E0L, - 1.207150003611117689000664385596211076662E2L, - 2.119260779316389904742873816462800103939E3L, - 1.562942227734663441801452930916044224174E4L, - 5.656779189549710079988084081145693580479E4L, - 1.052166241021481691922831746350942786299E5L, - 9.949798524786000595621602790068349165758E4L, - 4.491790734080265043407035220188849562856E4L, - 8.377074098301530326270432059434791287601E3L, - 4.506934806567986810091824791963991057083E2L +static const _Float128 RNr6[NRNr6 + 1] = +{ + L(1.642076876176834390623842732352935761108E0), + L(1.207150003611117689000664385596211076662E2), + L(2.119260779316389904742873816462800103939E3), + L(1.562942227734663441801452930916044224174E4), + L(5.656779189549710079988084081145693580479E4), + L(1.052166241021481691922831746350942786299E5), + L(9.949798524786000595621602790068349165758E4), + L(4.491790734080265043407035220188849562856E4), + L(8.377074098301530326270432059434791287601E3), + L(4.506934806567986810091824791963991057083E2) }; #define NRDr6 9 -static const long double RDr6[NRDr6 + 1] = -{ --1.664557643928263091879301304019826629067E2L, --3.800035902507656624590531122291160668452E3L, --3.277028191591734928360050685359277076056E4L, --1.381359471502885446400589109566587443987E5L, --3.082204287382581873532528989283748656546E5L, --3.691071488256738343008271448234631037095E5L, --2.300482443038349815750714219117566715043E5L, --6.873955300927636236692803579555752171530E4L, --8.262158817978334142081581542749986845399E3L, --2.517122254384430859629423488157361983661E2L +static const _Float128 RDr6[NRDr6 + 1] = +{ +L(-1.664557643928263091879301304019826629067E2), +L(-3.800035902507656624590531122291160668452E3), +L(-3.277028191591734928360050685359277076056E4), +L(-1.381359471502885446400589109566587443987E5), +L(-3.082204287382581873532528989283748656546E5), +L(-3.691071488256738343008271448234631037095E5), +L(-2.300482443038349815750714219117566715043E5), +L(-6.873955300927636236692803579555752171530E4), +L(-8.262158817978334142081581542749986845399E3), +L(-2.517122254384430859629423488157361983661E2) /* 1.00 */ }; @@ -579,33 +581,33 @@ static const long double RDr6[NRDr6 + 1] = 1/2 <= 1/x < 5/8 Peak relative error 4.6e-36 */ #define NRNr5 10 -static const long double RNr5[NRNr5 + 1] = -{ --3.332258927455285458355550878136506961608E-3L, --2.697100758900280402659586595884478660721E-1L, --6.083328551139621521416618424949137195536E0L, --6.119863528983308012970821226810162441263E1L, --3.176535282475593173248810678636522589861E2L, --8.933395175080560925809992467187963260693E2L, --1.360019508488475978060917477620199499560E3L, --1.075075579828188621541398761300910213280E3L, --4.017346561586014822824459436695197089916E2L, --5.857581368145266249509589726077645791341E1L, --2.077715925587834606379119585995758954399E0L +static const _Float128 RNr5[NRNr5 + 1] = +{ +L(-3.332258927455285458355550878136506961608E-3), +L(-2.697100758900280402659586595884478660721E-1), +L(-6.083328551139621521416618424949137195536E0), +L(-6.119863528983308012970821226810162441263E1), +L(-3.176535282475593173248810678636522589861E2), +L(-8.933395175080560925809992467187963260693E2), +L(-1.360019508488475978060917477620199499560E3), +L(-1.075075579828188621541398761300910213280E3), +L(-4.017346561586014822824459436695197089916E2), +L(-5.857581368145266249509589726077645791341E1), +L(-2.077715925587834606379119585995758954399E0) }; #define NRDr5 9 -static const long double RDr5[NRDr5 + 1] = -{ - 3.377879570417399341550710467744693125385E-1L, - 1.021963322742390735430008860602594456187E1L, - 1.200847646592942095192766255154827011939E2L, - 7.118915528142927104078182863387116942836E2L, - 2.318159380062066469386544552429625026238E3L, - 4.238729853534009221025582008928765281620E3L, - 4.279114907284825886266493994833515580782E3L, - 2.257277186663261531053293222591851737504E3L, - 5.570475501285054293371908382916063822957E2L, - 5.142189243856288981145786492585432443560E1L +static const _Float128 RDr5[NRDr5 + 1] = +{ + L(3.377879570417399341550710467744693125385E-1), + L(1.021963322742390735430008860602594456187E1), + L(1.200847646592942095192766255154827011939E2), + L(7.118915528142927104078182863387116942836E2), + L(2.318159380062066469386544552429625026238E3), + L(4.238729853534009221025582008928765281620E3), + L(4.279114907284825886266493994833515580782E3), + L(2.257277186663261531053293222591851737504E3), + L(5.570475501285054293371908382916063822957E2), + L(5.142189243856288981145786492585432443560E1) /* 1.0E0 */ }; @@ -613,34 +615,34 @@ static const long double RDr5[NRDr5 + 1] = 3/8 <= 1/x < 1/2 Peak relative error 2.0e-36 */ #define NRNr4 10 -static const long double RNr4[NRNr4 + 1] = -{ - 3.258530712024527835089319075288494524465E-3L, - 2.987056016877277929720231688689431056567E-1L, - 8.738729089340199750734409156830371528862E0L, - 1.207211160148647782396337792426311125923E2L, - 8.997558632489032902250523945248208224445E2L, - 3.798025197699757225978410230530640879762E3L, - 9.113203668683080975637043118209210146846E3L, - 1.203285891339933238608683715194034900149E4L, - 8.100647057919140328536743641735339740855E3L, - 2.383888249907144945837976899822927411769E3L, - 2.127493573166454249221983582495245662319E2L +static const _Float128 RNr4[NRNr4 + 1] = +{ + L(3.258530712024527835089319075288494524465E-3), + L(2.987056016877277929720231688689431056567E-1), + L(8.738729089340199750734409156830371528862E0), + L(1.207211160148647782396337792426311125923E2), + L(8.997558632489032902250523945248208224445E2), + L(3.798025197699757225978410230530640879762E3), + L(9.113203668683080975637043118209210146846E3), + L(1.203285891339933238608683715194034900149E4), + L(8.100647057919140328536743641735339740855E3), + L(2.383888249907144945837976899822927411769E3), + L(2.127493573166454249221983582495245662319E2) }; #define NRDr4 10 -static const long double RDr4[NRDr4 + 1] = -{ --3.303141981514540274165450687270180479586E-1L, --1.353768629363605300707949368917687066724E1L, --2.206127630303621521950193783894598987033E2L, --1.861800338758066696514480386180875607204E3L, --8.889048775872605708249140016201753255599E3L, --2.465888106627948210478692168261494857089E4L, --3.934642211710774494879042116768390014289E4L, --3.455077258242252974937480623730228841003E4L, --1.524083977439690284820586063729912653196E4L, --2.810541887397984804237552337349093953857E3L, --1.343929553541159933824901621702567066156E2L +static const _Float128 RDr4[NRDr4 + 1] = +{ +L(-3.303141981514540274165450687270180479586E-1), +L(-1.353768629363605300707949368917687066724E1), +L(-2.206127630303621521950193783894598987033E2), +L(-1.861800338758066696514480386180875607204E3), +L(-8.889048775872605708249140016201753255599E3), +L(-2.465888106627948210478692168261494857089E4), +L(-3.934642211710774494879042116768390014289E4), +L(-3.455077258242252974937480623730228841003E4), +L(-1.524083977439690284820586063729912653196E4), +L(-2.810541887397984804237552337349093953857E3), +L(-1.343929553541159933824901621702567066156E2) /* 1.0E0 */ }; @@ -648,35 +650,35 @@ static const long double RDr4[NRDr4 + 1] = 1/4 <= 1/x < 3/8 Peak relative error 8.4e-37 */ #define NRNr3 11 -static const long double RNr3[NRNr3 + 1] = -{ --1.952401126551202208698629992497306292987E-6L, --2.130881743066372952515162564941682716125E-4L, --8.376493958090190943737529486107282224387E-3L, --1.650592646560987700661598877522831234791E-1L, --1.839290818933317338111364667708678163199E0L, --1.216278715570882422410442318517814388470E1L, --4.818759344462360427612133632533779091386E1L, --1.120994661297476876804405329172164436784E2L, --1.452850765662319264191141091859300126931E2L, --9.485207851128957108648038238656777241333E1L, --2.563663855025796641216191848818620020073E1L, --1.787995944187565676837847610706317833247E0L +static const _Float128 RNr3[NRNr3 + 1] = +{ +L(-1.952401126551202208698629992497306292987E-6), +L(-2.130881743066372952515162564941682716125E-4), +L(-8.376493958090190943737529486107282224387E-3), +L(-1.650592646560987700661598877522831234791E-1), +L(-1.839290818933317338111364667708678163199E0), +L(-1.216278715570882422410442318517814388470E1), +L(-4.818759344462360427612133632533779091386E1), +L(-1.120994661297476876804405329172164436784E2), +L(-1.452850765662319264191141091859300126931E2), +L(-9.485207851128957108648038238656777241333E1), +L(-2.563663855025796641216191848818620020073E1), +L(-1.787995944187565676837847610706317833247E0) }; #define NRDr3 10 -static const long double RDr3[NRDr3 + 1] = -{ - 1.979130686770349481460559711878399476903E-4L, - 1.156941716128488266238105813374635099057E-2L, - 2.752657634309886336431266395637285974292E-1L, - 3.482245457248318787349778336603569327521E0L, - 2.569347069372696358578399521203959253162E1L, - 1.142279000180457419740314694631879921561E2L, - 3.056503977190564294341422623108332700840E2L, - 4.780844020923794821656358157128719184422E2L, - 4.105972727212554277496256802312730410518E2L, - 1.724072188063746970865027817017067646246E2L, - 2.815939183464818198705278118326590370435E1L +static const _Float128 RDr3[NRDr3 + 1] = +{ + L(1.979130686770349481460559711878399476903E-4), + L(1.156941716128488266238105813374635099057E-2), + L(2.752657634309886336431266395637285974292E-1), + L(3.482245457248318787349778336603569327521E0), + L(2.569347069372696358578399521203959253162E1), + L(1.142279000180457419740314694631879921561E2), + L(3.056503977190564294341422623108332700840E2), + L(4.780844020923794821656358157128719184422E2), + L(4.105972727212554277496256802312730410518E2), + L(1.724072188063746970865027817017067646246E2), + L(2.815939183464818198705278118326590370435E1) /* 1.0E0 */ }; @@ -684,35 +686,35 @@ static const long double RDr3[NRDr3 + 1] = 1/8 <= 1/x < 1/4 Peak relative error 1.5e-36 */ #define NRNr2 11 -static const long double RNr2[NRNr2 + 1] = -{ --2.638914383420287212401687401284326363787E-8L, --3.479198370260633977258201271399116766619E-6L, --1.783985295335697686382487087502222519983E-4L, --4.777876933122576014266349277217559356276E-3L, --7.450634738987325004070761301045014986520E-2L, --7.068318854874733315971973707247467326619E-1L, --4.113919921935944795764071670806867038732E0L, --1.440447573226906222417767283691888875082E1L, --2.883484031530718428417168042141288943905E1L, --2.990886974328476387277797361464279931446E1L, --1.325283914915104866248279787536128997331E1L, --1.572436106228070195510230310658206154374E0L +static const _Float128 RNr2[NRNr2 + 1] = +{ +L(-2.638914383420287212401687401284326363787E-8), +L(-3.479198370260633977258201271399116766619E-6), +L(-1.783985295335697686382487087502222519983E-4), +L(-4.777876933122576014266349277217559356276E-3), +L(-7.450634738987325004070761301045014986520E-2), +L(-7.068318854874733315971973707247467326619E-1), +L(-4.113919921935944795764071670806867038732E0), +L(-1.440447573226906222417767283691888875082E1), +L(-2.883484031530718428417168042141288943905E1), +L(-2.990886974328476387277797361464279931446E1), +L(-1.325283914915104866248279787536128997331E1), +L(-1.572436106228070195510230310658206154374E0) }; #define NRDr2 10 -static const long double RDr2[NRDr2 + 1] = -{ - 2.675042728136731923554119302571867799673E-6L, - 2.170997868451812708585443282998329996268E-4L, - 7.249969752687540289422684951196241427445E-3L, - 1.302040375859768674620410563307838448508E-1L, - 1.380202483082910888897654537144485285549E0L, - 8.926594113174165352623847870299170069350E0L, - 3.521089584782616472372909095331572607185E1L, - 8.233547427533181375185259050330809105570E1L, - 1.072971579885803033079469639073292840135E2L, - 6.943803113337964469736022094105143158033E1L, - 1.775695341031607738233608307835017282662E1L +static const _Float128 RDr2[NRDr2 + 1] = +{ + L(2.675042728136731923554119302571867799673E-6), + L(2.170997868451812708585443282998329996268E-4), + L(7.249969752687540289422684951196241427445E-3), + L(1.302040375859768674620410563307838448508E-1), + L(1.380202483082910888897654537144485285549E0), + L(8.926594113174165352623847870299170069350E0), + L(3.521089584782616472372909095331572607185E1), + L(8.233547427533181375185259050330809105570E1), + L(1.072971579885803033079469639073292840135E2), + L(6.943803113337964469736022094105143158033E1), + L(1.775695341031607738233608307835017282662E1) /* 1.0E0 */ }; @@ -720,39 +722,39 @@ static const long double RDr2[NRDr2 + 1] = 1/128 <= 1/x < 1/8 Peak relative error 2.2e-36 */ #define NRNr1 9 -static const long double RNr1[NRNr1 + 1] = -{ --4.250780883202361946697751475473042685782E-8L, --5.375777053288612282487696975623206383019E-6L, --2.573645949220896816208565944117382460452E-4L, --6.199032928113542080263152610799113086319E-3L, --8.262721198693404060380104048479916247786E-2L, --6.242615227257324746371284637695778043982E-1L, --2.609874739199595400225113299437099626386E0L, --5.581967563336676737146358534602770006970E0L, --5.124398923356022609707490956634280573882E0L, --1.290865243944292370661544030414667556649E0L +static const _Float128 RNr1[NRNr1 + 1] = +{ +L(-4.250780883202361946697751475473042685782E-8), +L(-5.375777053288612282487696975623206383019E-6), +L(-2.573645949220896816208565944117382460452E-4), +L(-6.199032928113542080263152610799113086319E-3), +L(-8.262721198693404060380104048479916247786E-2), +L(-6.242615227257324746371284637695778043982E-1), +L(-2.609874739199595400225113299437099626386E0), +L(-5.581967563336676737146358534602770006970E0), +L(-5.124398923356022609707490956634280573882E0), +L(-1.290865243944292370661544030414667556649E0) }; #define NRDr1 8 -static const long double RDr1[NRDr1 + 1] = -{ - 4.308976661749509034845251315983612976224E-6L, - 3.265390126432780184125233455960049294580E-4L, - 9.811328839187040701901866531796570418691E-3L, - 1.511222515036021033410078631914783519649E-1L, - 1.289264341917429958858379585970225092274E0L, - 6.147640356182230769548007536914983522270E0L, - 1.573966871337739784518246317003956180750E1L, - 1.955534123435095067199574045529218238263E1L, - 9.472613121363135472247929109615785855865E0L +static const _Float128 RDr1[NRDr1 + 1] = +{ + L(4.308976661749509034845251315983612976224E-6), + L(3.265390126432780184125233455960049294580E-4), + L(9.811328839187040701901866531796570418691E-3), + L(1.511222515036021033410078631914783519649E-1), + L(1.289264341917429958858379585970225092274E0), + L(6.147640356182230769548007536914983522270E0), + L(1.573966871337739784518246317003956180750E1), + L(1.955534123435095067199574045529218238263E1), + L(9.472613121363135472247929109615785855865E0) /* 1.0E0 */ }; -long double -__erfl (long double x) +_Float128 +__erfl (_Float128 x) { - long double a, y, z; + _Float128 a, y, z; int32_t i, ix, sign; ieee854_long_double_shape_type u; @@ -763,7 +765,7 @@ __erfl (long double x) if (ix >= 0x7fff0000) { /* erf(nan)=nan */ i = ((sign & 0xffff0000) >> 31) << 1; - return (long double) (1 - i) + one / x; /* erf(+-inf)=+-1 */ + return (_Float128) (1 - i) + one / x; /* erf(+-inf)=+-1 */ } if (ix >= 0x3fff0000) /* |x| >= 1.0 */ @@ -784,7 +786,7 @@ __erfl (long double x) if (ix < 0x00080000) { /* Avoid spurious underflow. */ - long double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x); + _Float128 ret = 0.0625 * (16.0 * x + (16.0 * efx) * x); math_check_force_underflow (ret); return ret; } @@ -803,11 +805,11 @@ __erfl (long double x) return( y ); } -weak_alias (__erfl, erfl) -long double -__erfcl (long double x) +libm_alias_ldouble (__erf, erf) +_Float128 +__erfcl (_Float128 x) { - long double y, z, p, r; + _Float128 y, z, p, r; int32_t i, ix, sign; ieee854_long_double_shape_type u; @@ -819,7 +821,7 @@ __erfcl (long double x) if (ix >= 0x7fff0000) { /* erfc(nan)=nan */ /* erfc(+-inf)=0,2 */ - return (long double) (((u_int32_t) sign >> 31) << 1) + one / x; + return (_Float128) (((uint32_t) sign >> 31) << 1) + one / x; } if (ix < 0x3ffd0000) /* |x| <1/4 */ @@ -835,48 +837,48 @@ __erfcl (long double x) switch (i) { case 2: - z = x - 0.25L; + z = x - L(0.25); y = C13b + z * neval (z, RNr13, NRNr13) / deval (z, RDr13, NRDr13); y += C13a; break; case 3: - z = x - 0.375L; + z = x - L(0.375); y = C14b + z * neval (z, RNr14, NRNr14) / deval (z, RDr14, NRDr14); y += C14a; break; case 4: - z = x - 0.5L; + z = x - L(0.5); y = C15b + z * neval (z, RNr15, NRNr15) / deval (z, RDr15, NRDr15); y += C15a; break; case 5: - z = x - 0.625L; + z = x - L(0.625); y = C16b + z * neval (z, RNr16, NRNr16) / deval (z, RDr16, NRDr16); y += C16a; break; case 6: - z = x - 0.75L; + z = x - L(0.75); y = C17b + z * neval (z, RNr17, NRNr17) / deval (z, RDr17, NRDr17); y += C17a; break; case 7: - z = x - 0.875L; + z = x - L(0.875); y = C18b + z * neval (z, RNr18, NRNr18) / deval (z, RDr18, NRDr18); y += C18a; break; case 8: - z = x - 1.0L; + z = x - 1; y = C19b + z * neval (z, RNr19, NRNr19) / deval (z, RDr19, NRDr19); y += C19a; break; default: /* i == 9. */ - z = x - 1.125L; + z = x - L(1.125); y = C20b + z * neval (z, RNr20, NRNr20) / deval (z, RDr20, NRDr20); y += C20a; break; } if (sign & 0x80000000) - y = 2.0L - y; + y = 2 - y; return y; } /* 1.25 < |x| < 107 */ @@ -925,7 +927,7 @@ __erfcl (long double x) __ieee754_expl ((z - x) * (z + x) + p); if ((sign & 0x80000000) == 0) { - long double ret = r / x; + _Float128 ret = r / x; if (ret == 0) __set_errno (ERANGE); return ret; @@ -945,4 +947,4 @@ __erfcl (long double x) } } -weak_alias (__erfcl, erfcl) +libm_alias_ldouble (__erfc, erfc) diff --git a/sysdeps/ieee754/ldbl-128/s_expm1l.c b/sysdeps/ieee754/ldbl-128/s_expm1l.c index b1100a9d0e..66881af01a 100644 --- a/sysdeps/ieee754/ldbl-128/s_expm1l.c +++ b/sysdeps/ieee754/ldbl-128/s_expm1l.c @@ -57,41 +57,43 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> +#include <libm-alias-ldouble.h> /* exp(x) - 1 = x + 0.5 x^2 + x^3 P(x)/Q(x) -.5 ln 2 < x < .5 ln 2 Theoretical peak relative error = 8.1e-36 */ -static const long double - P0 = 2.943520915569954073888921213330863757240E8L, - P1 = -5.722847283900608941516165725053359168840E7L, - P2 = 8.944630806357575461578107295909719817253E6L, - P3 = -7.212432713558031519943281748462837065308E5L, - P4 = 4.578962475841642634225390068461943438441E4L, - P5 = -1.716772506388927649032068540558788106762E3L, - P6 = 4.401308817383362136048032038528753151144E1L, - P7 = -4.888737542888633647784737721812546636240E-1L, - Q0 = 1.766112549341972444333352727998584753865E9L, - Q1 = -7.848989743695296475743081255027098295771E8L, - Q2 = 1.615869009634292424463780387327037251069E8L, - Q3 = -2.019684072836541751428967854947019415698E7L, - Q4 = 1.682912729190313538934190635536631941751E6L, - Q5 = -9.615511549171441430850103489315371768998E4L, - Q6 = 3.697714952261803935521187272204485251835E3L, - Q7 = -8.802340681794263968892934703309274564037E1L, +static const _Float128 + P0 = L(2.943520915569954073888921213330863757240E8), + P1 = L(-5.722847283900608941516165725053359168840E7), + P2 = L(8.944630806357575461578107295909719817253E6), + P3 = L(-7.212432713558031519943281748462837065308E5), + P4 = L(4.578962475841642634225390068461943438441E4), + P5 = L(-1.716772506388927649032068540558788106762E3), + P6 = L(4.401308817383362136048032038528753151144E1), + P7 = L(-4.888737542888633647784737721812546636240E-1), + Q0 = L(1.766112549341972444333352727998584753865E9), + Q1 = L(-7.848989743695296475743081255027098295771E8), + Q2 = L(1.615869009634292424463780387327037251069E8), + Q3 = L(-2.019684072836541751428967854947019415698E7), + Q4 = L(1.682912729190313538934190635536631941751E6), + Q5 = L(-9.615511549171441430850103489315371768998E4), + Q6 = L(3.697714952261803935521187272204485251835E3), + Q7 = L(-8.802340681794263968892934703309274564037E1), /* Q8 = 1.000000000000000000000000000000000000000E0 */ /* C1 + C2 = ln 2 */ - C1 = 6.93145751953125E-1L, - C2 = 1.428606820309417232121458176568075500134E-6L, + C1 = L(6.93145751953125E-1), + C2 = L(1.428606820309417232121458176568075500134E-6), /* ln 2^-114 */ - minarg = -7.9018778583833765273564461846232128760607E1L, big = 1e4932L; + minarg = L(-7.9018778583833765273564461846232128760607E1), big = L(1e4932); -long double -__expm1l (long double x) +_Float128 +__expm1l (_Float128 x) { - long double px, qx, xx; + _Float128 px, qx, xx; int32_t ix, sign; ieee854_long_double_shape_type u; int k; @@ -110,9 +112,9 @@ __expm1l (long double x) { /* Infinity (which must be negative infinity). */ if (((ix & 0xffff) | u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) - return -1.0L; - /* NaN. No invalid exception. */ - return x; + return -1; + /* NaN. Invalid exception if signaling. */ + return x + x; } /* expm1(+- 0) = +- 0. */ @@ -121,12 +123,12 @@ __expm1l (long double x) /* Minimum value. */ if (x < minarg) - return (4.0/big - 1.0L); + return (4.0/big - 1); /* Avoid internal underflow when result does not underflow, while ensuring underflow (without returning a zero of the wrong sign) when the result does underflow. */ - if (fabsl (x) < 0x1p-113L) + if (fabsl (x) < L(0x1p-113)) { math_check_force_underflow (x); return x; @@ -158,9 +160,9 @@ __expm1l (long double x) exp(x) - 1 = 2^k (qx + 1) - 1 = 2^k qx + 2^k - 1. */ - px = __ldexpl (1.0L, k); + px = __ldexpl (1, k); x = px * qx + (px - 1.0); return x; } libm_hidden_def (__expm1l) -weak_alias (__expm1l, expm1l) +libm_alias_ldouble (__expm1, expm1) diff --git a/sysdeps/ieee754/ldbl-128/s_f64xaddf128.c b/sysdeps/ieee754/ldbl-128/s_f64xaddf128.c new file mode 100644 index 0000000000..545c7b93fd --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_f64xaddf128.c @@ -0,0 +1,38 @@ +/* Add _Float128 values, converting the result to _Float64x. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math-narrow.h> + +/* math_ldbl.h defines _Float128 to long double for this directory, + but when they are different, this function must be defined with + _Float128 arguments to avoid defining an alias with an incompatible + type. */ +#undef _Float128 + +_Float64x +__f64xaddf128 (_Float128 x, _Float128 y) +{ +#if __HAVE_FLOAT64X_LONG_DOUBLE && __HAVE_DISTINCT_FLOAT128 + NARROW_ADD_ROUND_TO_ODD (x, y, _Float64x, union ieee854_long_double, l, + mantissa3); +#else + NARROW_ADD_TRIVIAL (x, y, _Float64x); +#endif +} +libm_alias_float64x_float128 (add) diff --git a/sysdeps/ieee754/ldbl-128/s_f64xdivf128.c b/sysdeps/ieee754/ldbl-128/s_f64xdivf128.c new file mode 100644 index 0000000000..64356bbdd7 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_f64xdivf128.c @@ -0,0 +1,38 @@ +/* Divide _Float128 values, converting the result to _Float64x. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math-narrow.h> + +/* math_ldbl.h defines _Float128 to long double for this directory, + but when they are different, this function must be defined with + _Float128 arguments to avoid defining an alias with an incompatible + type. */ +#undef _Float128 + +_Float64x +__f64xdivf128 (_Float128 x, _Float128 y) +{ +#if __HAVE_FLOAT64X_LONG_DOUBLE && __HAVE_DISTINCT_FLOAT128 + NARROW_DIV_ROUND_TO_ODD (x, y, _Float64x, union ieee854_long_double, l, + mantissa3); +#else + NARROW_DIV_TRIVIAL (x, y, _Float64x); +#endif +} +libm_alias_float64x_float128 (div) diff --git a/sysdeps/ieee754/ldbl-128/s_f64xmulf128.c b/sysdeps/ieee754/ldbl-128/s_f64xmulf128.c new file mode 100644 index 0000000000..ed88eabe40 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_f64xmulf128.c @@ -0,0 +1,38 @@ +/* Multiply _Float128 values, converting the result to _Float64x. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math-narrow.h> + +/* math_ldbl.h defines _Float128 to long double for this directory, + but when they are different, this function must be defined with + _Float128 arguments to avoid defining an alias with an incompatible + type. */ +#undef _Float128 + +_Float64x +__f64xmulf128 (_Float128 x, _Float128 y) +{ +#if __HAVE_FLOAT64X_LONG_DOUBLE && __HAVE_DISTINCT_FLOAT128 + NARROW_MUL_ROUND_TO_ODD (x, y, _Float64x, union ieee854_long_double, l, + mantissa3); +#else + NARROW_MUL_TRIVIAL (x, y, _Float64x); +#endif +} +libm_alias_float64x_float128 (mul) diff --git a/sysdeps/ieee754/ldbl-128/s_f64xsubf128.c b/sysdeps/ieee754/ldbl-128/s_f64xsubf128.c new file mode 100644 index 0000000000..c9a63d9e84 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_f64xsubf128.c @@ -0,0 +1,38 @@ +/* Subtract _Float128 values, converting the result to _Float64x. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math-narrow.h> + +/* math_ldbl.h defines _Float128 to long double for this directory, + but when they are different, this function must be defined with + _Float128 arguments to avoid defining an alias with an incompatible + type. */ +#undef _Float128 + +_Float64x +__f64xsubf128 (_Float128 x, _Float128 y) +{ +#if __HAVE_FLOAT64X_LONG_DOUBLE && __HAVE_DISTINCT_FLOAT128 + NARROW_SUB_ROUND_TO_ODD (x, y, _Float64x, union ieee854_long_double, l, + mantissa3); +#else + NARROW_SUB_TRIVIAL (x, y, _Float64x); +#endif +} +libm_alias_float64x_float128 (sub) diff --git a/sysdeps/ieee754/ldbl-128/s_fabsl.c b/sysdeps/ieee754/ldbl-128/s_fabsl.c index a1bb6c5dff..8d554531be 100644 --- a/sysdeps/ieee754/ldbl-128/s_fabsl.c +++ b/sysdeps/ieee754/ldbl-128/s_fabsl.c @@ -23,12 +23,13 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -long double __fabsl(long double x) +_Float128 __fabsl(_Float128 x) { - u_int64_t hx; + uint64_t hx; GET_LDOUBLE_MSW64(hx,x); SET_LDOUBLE_MSW64(x,hx&0x7fffffffffffffffLL); return x; } -weak_alias (__fabsl, fabsl) +libm_alias_ldouble (__fabs, fabs) diff --git a/sysdeps/ieee754/ldbl-128/s_faddl.c b/sysdeps/ieee754/ldbl-128/s_faddl.c new file mode 100644 index 0000000000..edbaa2103b --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_faddl.c @@ -0,0 +1,33 @@ +/* Add long double (ldbl-128) values, narrowing the result to float. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define f32addf64x __hide_f32addf64x +#define f32addf128 __hide_f32addf128 +#include <math.h> +#undef f32addf64x +#undef f32addf128 + +#include <math-narrow.h> + +float +__faddl (_Float128 x, _Float128 y) +{ + NARROW_ADD_ROUND_TO_ODD (x, y, float, union ieee854_long_double, l, + mantissa3); +} +libm_alias_float_ldouble (add) diff --git a/sysdeps/ieee754/ldbl-128/s_fdivl.c b/sysdeps/ieee754/ldbl-128/s_fdivl.c new file mode 100644 index 0000000000..b00fdb4eaa --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_fdivl.c @@ -0,0 +1,33 @@ +/* Divide long double (ldbl-128) values, narrowing the result to float. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define f32divf64x __hide_f32divf64x +#define f32divf128 __hide_f32divf128 +#include <math.h> +#undef f32divf64x +#undef f32divf128 + +#include <math-narrow.h> + +float +__fdivl (_Float128 x, _Float128 y) +{ + NARROW_DIV_ROUND_TO_ODD (x, y, float, union ieee854_long_double, l, + mantissa3); +} +libm_alias_float_ldouble (div) diff --git a/sysdeps/ieee754/ldbl-128/s_finitel.c b/sysdeps/ieee754/ldbl-128/s_finitel.c index ea8a9ba379..d42b37815c 100644 --- a/sysdeps/ieee754/ldbl-128/s_finitel.c +++ b/sysdeps/ieee754/ldbl-128/s_finitel.c @@ -25,12 +25,12 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> -int __finitel(long double x) +int __finitel(_Float128 x) { int64_t hx; GET_LDOUBLE_MSW64(hx,x); - return (int)((u_int64_t)((hx&0x7fff000000000000LL) - -0x7fff000000000000LL)>>63); + return (int)((uint64_t)((hx&0x7fff000000000000LL) + -0x7fff000000000000LL)>>63); } -hidden_def (__finitel) +mathx_hidden_def (__finitel) weak_alias (__finitel, finitel) diff --git a/sysdeps/ieee754/ldbl-128/s_floorl.c b/sysdeps/ieee754/ldbl-128/s_floorl.c index c72d5d4330..f9c5e014f9 100644 --- a/sysdeps/ieee754/ldbl-128/s_floorl.c +++ b/sysdeps/ieee754/ldbl-128/s_floorl.c @@ -22,35 +22,29 @@ static char rcsid[] = "$NetBSD: $"; * Return x rounded toward -inf to integral value * Method: * Bit twiddling. - * Exception: - * Inexact flag raised if x not equal to floor(x). */ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -static const long double huge = 1.0e4930L; - -long double __floorl(long double x) +_Float128 __floorl(_Float128 x) { int64_t i0,i1,j0; - u_int64_t i,j; + uint64_t i,j; GET_LDOUBLE_WORDS64(i0,i1,x); j0 = ((i0>>48)&0x7fff)-0x3fff; if(j0<48) { - if(j0<0) { /* raise inexact if x != 0 */ - if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ - if(i0>=0) {i0=i1=0;} - else if(((i0&0x7fffffffffffffffLL)|i1)!=0) - { i0=0xbfff000000000000ULL;i1=0;} - } + if(j0<0) { + /* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffffffffffffLL)|i1)!=0) + { i0=0xbfff000000000000ULL;i1=0;} } else { i = (0x0000ffffffffffffULL)>>j0; if(((i0&i)|i1)==0) return x; /* x is integral */ - if(huge+x>0.0) { /* raise inexact flag */ - if(i0<0) i0 += (0x0001000000000000LL)>>j0; - i0 &= (~i); i1=0; - } + if(i0<0) i0 += (0x0001000000000000LL)>>j0; + i0 &= (~i); i1=0; } } else if (j0>111) { if(j0==0x4000) return x+x; /* inf or NaN */ @@ -58,19 +52,17 @@ long double __floorl(long double x) } else { i = -1ULL>>(j0-48); if((i1&i)==0) return x; /* x is integral */ - if(huge+x>0.0) { /* raise inexact flag */ - if(i0<0) { - if(j0==48) i0+=1; - else { - j = i1+(1LL<<(112-j0)); - if(j<i1) i0 +=1 ; /* got a carry */ - i1=j; - } + if(i0<0) { + if(j0==48) i0+=1; + else { + j = i1+(1LL<<(112-j0)); + if(j<i1) i0 +=1 ; /* got a carry */ + i1=j; } - i1 &= (~i); } + i1 &= (~i); } SET_LDOUBLE_WORDS64(x,i0,i1); return x; } -weak_alias (__floorl, floorl) +libm_alias_ldouble (__floor, floor) diff --git a/sysdeps/ieee754/ldbl-128/s_fma.c b/sysdeps/ieee754/ldbl-128/s_fma.c index cbe708f4b8..19620dca5c 100644 --- a/sysdeps/ieee754/ldbl-128/s_fma.c +++ b/sysdeps/ieee754/ldbl-128/s_fma.c @@ -1,5 +1,5 @@ /* Compute x * y + z as ternary operation. - Copyright (C) 2010-2016 Free Software Foundation, Inc. + Copyright (C) 2010-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. @@ -20,6 +20,7 @@ #include <math.h> #include <fenv.h> #include <ieee754.h> +#include <libm-alias-double.h> /* This implementation relies on long double being more than twice as precise as double and uses rounding to odd in order to avoid problems @@ -51,5 +52,5 @@ __fma (double x, double y, double z) return (double) u.d; } #ifndef __fma -weak_alias (__fma, fma) +libm_alias_double (__fma, fma) #endif diff --git a/sysdeps/ieee754/ldbl-128/s_fmal.c b/sysdeps/ieee754/ldbl-128/s_fmal.c index 728949c916..4eba9253df 100644 --- a/sysdeps/ieee754/ldbl-128/s_fmal.c +++ b/sysdeps/ieee754/ldbl-128/s_fmal.c @@ -1,5 +1,5 @@ /* Compute x * y + z as ternary operation. - Copyright (C) 2010-2016 Free Software Foundation, Inc. + Copyright (C) 2010-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. @@ -21,15 +21,17 @@ #include <math.h> #include <fenv.h> #include <ieee754.h> +#include <math-barriers.h> #include <math_private.h> +#include <libm-alias-ldouble.h> #include <tininess.h> /* This implementation uses rounding to odd to avoid problems with double rounding. See a paper by Boldo and Melquiond: http://www.lri.fr/~melquion/doc/08-tc.pdf */ -long double -__fmal (long double x, long double y, long double z) +_Float128 +__fmal (_Float128 x, _Float128 y, _Float128 z) { union ieee854_long_double u, v, w; int adjust = 0; @@ -75,7 +77,7 @@ __fmal (long double x, long double y, long double z) < IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2) { int neg = u.ieee.negative ^ v.ieee.negative; - long double tiny = neg ? -0x1p-16494L : 0x1p-16494L; + _Float128 tiny = neg ? L(-0x1p-16494) : L(0x1p-16494); if (w.ieee.exponent >= 3) return tiny + z; /* Scaling up, adding TINY and scaling down produces the @@ -83,7 +85,7 @@ __fmal (long double x, long double y, long double z) TINY has no effect and in other modes double rounding is harmless. But it may not produce required underflow exceptions. */ - v.d = z * 0x1p114L + tiny; + v.d = z * L(0x1p114) + tiny; if (TININESS_AFTER_ROUNDING ? v.ieee.exponent < 115 : (w.ieee.exponent == 0 @@ -94,10 +96,10 @@ __fmal (long double x, long double y, long double z) && w.ieee.mantissa1 == 0 && w.ieee.mantissa0 == 0))) { - long double force_underflow = x * y; + _Float128 force_underflow = x * y; math_force_eval (force_underflow); } - return v.d * 0x1p-114L; + return v.d * L(0x1p-114); } if (u.ieee.exponent + v.ieee.exponent >= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG) @@ -144,7 +146,7 @@ __fmal (long double x, long double y, long double z) if (v.ieee.exponent) v.ieee.exponent += LDBL_MANT_DIG; else - v.d *= 0x1p113L; + v.d *= L(0x1p113); } else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG) { @@ -152,7 +154,7 @@ __fmal (long double x, long double y, long double z) if (u.ieee.exponent) u.ieee.exponent += LDBL_MANT_DIG; else - u.d *= 0x1p113L; + u.d *= L(0x1p113); } else /* if (u.ieee.exponent + v.ieee.exponent <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */ @@ -166,7 +168,7 @@ __fmal (long double x, long double y, long double z) if (w.ieee.exponent) w.ieee.exponent += 2 * LDBL_MANT_DIG + 2; else - w.d *= 0x1p228L; + w.d *= L(0x1p228); adjust = -1; } /* Otherwise x * y should just affect inexact @@ -190,22 +192,22 @@ __fmal (long double x, long double y, long double z) /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ #define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) - long double x1 = x * C; - long double y1 = y * C; - long double m1 = x * y; + _Float128 x1 = x * C; + _Float128 y1 = y * C; + _Float128 m1 = x * y; x1 = (x - x1) + x1; y1 = (y - y1) + y1; - long double x2 = x - x1; - long double y2 = y - y1; - long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; + _Float128 x2 = x - x1; + _Float128 y2 = y - y1; + _Float128 m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2; /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */ - long double a1 = z + m1; - long double t1 = a1 - z; - long double t2 = a1 - t1; + _Float128 a1 = z + m1; + _Float128 t1 = a1 - z; + _Float128 t2 = a1 - t1; t1 = m1 - t1; t2 = z - t2; - long double a2 = t1 + t2; + _Float128 a2 = t1 + t2; /* Ensure the arithmetic is not scheduled after feclearexcept call. */ math_force_eval (m2); math_force_eval (a2); @@ -238,7 +240,7 @@ __fmal (long double x, long double y, long double z) u.ieee.mantissa3 |= fetestexcept (FE_INEXACT) != 0; feupdateenv (&env); /* Result is a1 + u.d, scaled up. */ - return (a1 + u.d) * 0x1p113L; + return (a1 + u.d) * L(0x1p113); } else { @@ -255,11 +257,11 @@ __fmal (long double x, long double y, long double z) /* If a1 + u.d is exact, the only rounding happens during scaling down. */ if (j == 0) - return v.d * 0x1p-228L; + return v.d * L(0x1p-228); /* If result rounded to zero is not subnormal, no double rounding will occur. */ if (v.ieee.exponent > 228) - return (a1 + u.d) * 0x1p-228L; + return (a1 + u.d) * L(0x1p-228); /* If v.d * 0x1p-228L with round to zero is a subnormal above or equal to LDBL_MIN / 2, then v.d * 0x1p-228L shifts mantissa down just by 1 bit, which means v.ieee.mantissa3 |= j would @@ -278,21 +280,21 @@ __fmal (long double x, long double y, long double z) { w.d = a1 + u.d; if (w.ieee.exponent == 229) - return w.d * 0x1p-228L; + return w.d * L(0x1p-228); } /* v.ieee.mantissa3 & 2 is LSB bit of the result before rounding, v.ieee.mantissa3 & 1 is the round bit and j is our sticky bit. */ - w.d = 0.0L; + w.d = 0; w.ieee.mantissa3 = ((v.ieee.mantissa3 & 3) << 1) | j; w.ieee.negative = v.ieee.negative; v.ieee.mantissa3 &= ~3U; - v.d *= 0x1p-228L; - w.d *= 0x1p-2L; + v.d *= L(0x1p-228); + w.d *= L(0x1p-2); return v.d + w.d; } v.ieee.mantissa3 |= j; - return v.d * 0x1p-228L; + return v.d * L(0x1p-228); } } -weak_alias (__fmal, fmal) +libm_alias_ldouble (__fma, fma) diff --git a/sysdeps/ieee754/ldbl-128/s_fmull.c b/sysdeps/ieee754/ldbl-128/s_fmull.c new file mode 100644 index 0000000000..dd399f9590 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_fmull.c @@ -0,0 +1,33 @@ +/* Multiply long double (ldbl-128) values, narrowing the result to float. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define f32mulf64x __hide_f32mulf64x +#define f32mulf128 __hide_f32mulf128 +#include <math.h> +#undef f32mulf64x +#undef f32mulf128 + +#include <math-narrow.h> + +float +__fmull (_Float128 x, _Float128 y) +{ + NARROW_MUL_ROUND_TO_ODD (x, y, float, union ieee854_long_double, l, + mantissa3); +} +libm_alias_float_ldouble (mul) diff --git a/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c b/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c index c89686f8f9..6deaa5cc45 100644 --- a/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c +++ b/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c @@ -1,5 +1,5 @@ /* Return classification value corresponding to argument. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz>, 1999. @@ -24,9 +24,9 @@ int -__fpclassifyl (long double x) +__fpclassifyl (_Float128 x) { - u_int64_t hx, lx; + uint64_t hx, lx; int retval = FP_NORMAL; GET_LDOUBLE_WORDS64 (hx, lx, x); diff --git a/sysdeps/ieee754/ldbl-128/s_frexpl.c b/sysdeps/ieee754/ldbl-128/s_frexpl.c index d61dddaaaa..bab0779e23 100644 --- a/sysdeps/ieee754/ldbl-128/s_frexpl.c +++ b/sysdeps/ieee754/ldbl-128/s_frexpl.c @@ -29,17 +29,18 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -static const long double -two114 = 2.0769187434139310514121985316880384E+34L; /* 0x4071000000000000, 0 */ +static const _Float128 +two114 = L(2.0769187434139310514121985316880384E+34); /* 0x4071000000000000, 0 */ -long double __frexpl(long double x, int *eptr) +_Float128 __frexpl(_Float128 x, int *eptr) { - u_int64_t hx, lx, ix; + uint64_t hx, lx, ix; GET_LDOUBLE_WORDS64(hx,lx,x); ix = 0x7fffffffffffffffULL&hx; *eptr = 0; - if(ix>=0x7fff000000000000ULL||((ix|lx)==0)) return x; /* 0,inf,nan */ + if(ix>=0x7fff000000000000ULL||((ix|lx)==0)) return x + x;/* 0,inf,nan */ if (ix<0x0001000000000000ULL) { /* subnormal */ x *= two114; GET_LDOUBLE_MSW64(hx,x); @@ -51,4 +52,4 @@ long double __frexpl(long double x, int *eptr) SET_LDOUBLE_MSW64(x,hx); return x; } -weak_alias (__frexpl, frexpl) +libm_alias_ldouble (__frexp, frexp) diff --git a/sysdeps/ieee754/ldbl-128/s_fromfpl.c b/sysdeps/ieee754/ldbl-128/s_fromfpl.c new file mode 100644 index 0000000000..bcedceea8e --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_fromfpl.c @@ -0,0 +1,5 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC __fromfpl +#include <s_fromfpl_main.c> +libm_alias_ldouble (__fromfp, fromfp) diff --git a/sysdeps/ieee754/ldbl-128/s_fromfpl_main.c b/sysdeps/ieee754/ldbl-128/s_fromfpl_main.c new file mode 100644 index 0000000000..5b9c1a84b2 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_fromfpl_main.c @@ -0,0 +1,91 @@ +/* Round to integer type. ldbl-128 version. + Copyright (C) 2016-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <errno.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <libm-alias-ldouble.h> +#include <stdbool.h> +#include <stdint.h> + +#define BIAS 0x3fff +#define MANT_DIG 113 + +#if UNSIGNED +# define RET_TYPE uintmax_t +#else +# define RET_TYPE intmax_t +#endif + +#include <fromfp.h> + +RET_TYPE +FUNC (_Float128 x, int round, unsigned int width) +{ + if (width > INTMAX_WIDTH) + width = INTMAX_WIDTH; + uint64_t hx, lx; + GET_LDOUBLE_WORDS64 (hx, lx, x); + bool negative = (hx & 0x8000000000000000ULL) != 0; + if (width == 0) + return fromfp_domain_error (negative, width); + hx &= 0x7fffffffffffffffULL; + if ((hx | lx) == 0) + return 0; + int exponent = hx >> (MANT_DIG - 1 - 64); + exponent -= BIAS; + int max_exponent = fromfp_max_exponent (negative, width); + if (exponent > max_exponent) + return fromfp_domain_error (negative, width); + + hx &= ((1ULL << (MANT_DIG - 1 - 64)) - 1); + hx |= 1ULL << (MANT_DIG - 1 - 64); + uintmax_t uret; + bool half_bit, more_bits; + /* The exponent is at most 63, so we are shifting right by at least + 49 bits. */ + if (exponent >= -1) + { + int shift = MANT_DIG - 1 - exponent; + if (shift <= 64) + { + uint64_t h = 1ULL << (shift - 1); + half_bit = (lx & h) != 0; + more_bits = (lx & (h - 1)) != 0; + uret = hx << (64 - shift); + if (shift != 64) + uret |= lx >> shift; + } + else + { + uint64_t h = 1ULL << (shift - 1 - 64); + half_bit = (hx & h) != 0; + more_bits = ((hx & (h - 1)) | lx) != 0; + uret = hx >> (shift - 64); + } + } + else + { + uret = 0; + half_bit = false; + more_bits = true; + } + return fromfp_round_and_return (negative, uret, half_bit, more_bits, round, + exponent, max_exponent, width); +} diff --git a/sysdeps/ieee754/ldbl-128/s_fromfpxl.c b/sysdeps/ieee754/ldbl-128/s_fromfpxl.c new file mode 100644 index 0000000000..0a342a22d1 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_fromfpxl.c @@ -0,0 +1,5 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC __fromfpxl +#include <s_fromfpl_main.c> +libm_alias_ldouble (__fromfpx, fromfpx) diff --git a/sysdeps/ieee754/ldbl-128/s_fsubl.c b/sysdeps/ieee754/ldbl-128/s_fsubl.c new file mode 100644 index 0000000000..6a5e6b3173 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_fsubl.c @@ -0,0 +1,33 @@ +/* Subtract long double (ldbl-128) values, narrowing the result to float. + Copyright (C) 2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#define f32subf64x __hide_f32subf64x +#define f32subf128 __hide_f32subf128 +#include <math.h> +#undef f32subf64x +#undef f32subf128 + +#include <math-narrow.h> + +float +__fsubl (_Float128 x, _Float128 y) +{ + NARROW_SUB_ROUND_TO_ODD (x, y, float, union ieee854_long_double, l, + mantissa3); +} +libm_alias_float_ldouble (sub) diff --git a/sysdeps/ieee754/ldbl-128/s_getpayloadl.c b/sysdeps/ieee754/ldbl-128/s_getpayloadl.c new file mode 100644 index 0000000000..3bdc429de6 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_getpayloadl.c @@ -0,0 +1,59 @@ +/* Get NaN payload. ldbl-128 version. + Copyright (C) 2016-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <libm-alias-ldouble.h> +#include <stdint.h> + +_Float128 +__getpayloadl (const _Float128 *x) +{ + uint64_t hx, lx; + GET_LDOUBLE_WORDS64 (hx, lx, *x); + hx &= 0x7fffffffffffULL; + /* Construct the representation of the return value directly, since + 128-bit integers may not be available. */ + int lz; + if (hx == 0) + { + if (lx == 0) + return 0.0L; + else + lz = __builtin_clzll (lx) + 64; + } + else + lz = __builtin_clzll (hx); + int shift = lz - 15; + if (shift >= 64) + { + hx = lx << (shift - 64); + lx = 0; + } + else + { + /* 2 <= SHIFT <= 63. */ + hx = (hx << shift) | (lx >> (64 - shift)); + lx <<= shift; + } + hx = (hx & 0xffffffffffffULL) | ((0x3fffULL + 127 - lz) << 48); + _Float128 ret; + SET_LDOUBLE_WORDS64 (ret, hx, lx); + return ret; +} +libm_alias_ldouble (__getpayload, getpayload) diff --git a/sysdeps/ieee754/ldbl-128/s_isinfl.c b/sysdeps/ieee754/ldbl-128/s_isinfl.c index 03e4d13371..a41e8cf44b 100644 --- a/sysdeps/ieee754/ldbl-128/s_isinfl.c +++ b/sysdeps/ieee754/ldbl-128/s_isinfl.c @@ -17,7 +17,7 @@ static char rcsid[] = "$NetBSD: $"; #include <math_private.h> int -__isinfl (long double x) +__isinfl (_Float128 x) { int64_t hx,lx; GET_LDOUBLE_WORDS64(hx,lx,x); @@ -25,5 +25,5 @@ __isinfl (long double x) lx |= -lx; return ~(lx >> 63) & (hx >> 62); } -hidden_def (__isinfl) +mathx_hidden_def (__isinfl) weak_alias (__isinfl, isinfl) diff --git a/sysdeps/ieee754/ldbl-128/s_isnanl.c b/sysdeps/ieee754/ldbl-128/s_isnanl.c index 74960e7ff2..8ebef00d24 100644 --- a/sysdeps/ieee754/ldbl-128/s_isnanl.c +++ b/sysdeps/ieee754/ldbl-128/s_isnanl.c @@ -25,14 +25,14 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> -int __isnanl(long double x) +int __isnanl(_Float128 x) { int64_t hx,lx; GET_LDOUBLE_WORDS64(hx,lx,x); hx &= 0x7fffffffffffffffLL; - hx |= (u_int64_t)(lx|(-lx))>>63; + hx |= (uint64_t)(lx|(-lx))>>63; hx = 0x7fff000000000000LL - hx; - return (int)((u_int64_t)hx>>63); + return (int)((uint64_t)hx>>63); } -hidden_def (__isnanl) +mathx_hidden_def (__isnanl) weak_alias (__isnanl, isnanl) diff --git a/sysdeps/ieee754/ldbl-128/s_issignalingl.c b/sysdeps/ieee754/ldbl-128/s_issignalingl.c index c06f14dd12..1893e80293 100644 --- a/sysdeps/ieee754/ldbl-128/s_issignalingl.c +++ b/sysdeps/ieee754/ldbl-128/s_issignalingl.c @@ -1,5 +1,5 @@ /* Test for signaling NaN. - Copyright (C) 2013-2016 Free Software Foundation, Inc. + Copyright (C) 2013-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -18,13 +18,14 @@ #include <math.h> #include <math_private.h> +#include <nan-high-order-bit.h> int -__issignalingl (long double x) +__issignalingl (_Float128 x) { - u_int64_t hxi, lxi __attribute__ ((unused)); + uint64_t hxi, lxi __attribute__ ((unused)); GET_LDOUBLE_WORDS64 (hxi, lxi, x); -#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN /* We only have to care about the high-order bit of x's significand, because having it set (sNaN) already makes the significand different from that used to designate infinity. */ diff --git a/sysdeps/ieee754/ldbl-128/s_llrintl.c b/sysdeps/ieee754/ldbl-128/s_llrintl.c index 84fc576ab6..ce17cf962a 100644 --- a/sysdeps/ieee754/ldbl-128/s_llrintl.c +++ b/sysdeps/ieee754/ldbl-128/s_llrintl.c @@ -1,6 +1,6 @@ /* Round argument to nearest integral value according to current rounding direction. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz>, 1999. @@ -24,21 +24,22 @@ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> #include <fix-fp-int-convert-overflow.h> -static const long double two112[2] = +static const _Float128 two112[2] = { - 5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */ - -5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */ + L(5.19229685853482762853049632922009600E+33), /* 0x406F000000000000, 0 */ + L(-5.19229685853482762853049632922009600E+33) /* 0xC06F000000000000, 0 */ }; long long int -__llrintl (long double x) +__llrintl (_Float128 x) { int32_t j0; - u_int64_t i0,i1; - long double w; - long double t; + uint64_t i0,i1; + _Float128 w; + _Float128 t; long long int result; int sx; @@ -52,7 +53,7 @@ __llrintl (long double x) { #if defined FE_INVALID || defined FE_INEXACT /* X < LLONG_MAX + 1 implied by J0 < 63. */ - if (x > (long double) LLONG_MAX) + if (x > (_Float128) LLONG_MAX) { /* In the event of overflow we must raise the "invalid" exception, but not "inexact". */ @@ -83,8 +84,8 @@ __llrintl (long double x) FE_INVALID must be raised and the return value is unspecified. */ #if defined FE_INVALID || defined FE_INEXACT - if (x < (long double) LLONG_MIN - && x > (long double) LLONG_MIN - 1.0L) + if (x < (_Float128) LLONG_MIN + && x > (_Float128) LLONG_MIN - 1) { /* If truncation produces LLONG_MIN, the cast will not raise the exception, but may raise "inexact". */ @@ -92,7 +93,7 @@ __llrintl (long double x) feraiseexcept (t == LLONG_MIN ? FE_INEXACT : FE_INVALID); return LLONG_MIN; } - else if (FIX_LDBL_LLONG_CONVERT_OVERFLOW && x != (long double) LLONG_MIN) + else if (FIX_LDBL_LLONG_CONVERT_OVERFLOW && x != (_Float128) LLONG_MIN) { feraiseexcept (FE_INVALID); return sx == 0 ? LLONG_MAX : LLONG_MIN; @@ -105,4 +106,4 @@ __llrintl (long double x) return sx ? -result : result; } -weak_alias (__llrintl, llrintl) +libm_alias_ldouble (__llrint, llrint) diff --git a/sysdeps/ieee754/ldbl-128/s_llroundl.c b/sysdeps/ieee754/ldbl-128/s_llroundl.c index bfc81cc534..1973e1bffd 100644 --- a/sysdeps/ieee754/ldbl-128/s_llroundl.c +++ b/sysdeps/ieee754/ldbl-128/s_llroundl.c @@ -1,5 +1,5 @@ /* Round long double value to long long int. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz>, 1999. @@ -23,13 +23,14 @@ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> #include <fix-fp-int-convert-overflow.h> long long int -__llroundl (long double x) +__llroundl (_Float128 x) { int64_t j0; - u_int64_t i1, i0; + uint64_t i1, i0; long long int result; int sign; @@ -55,7 +56,7 @@ __llroundl (long double x) result = ((long long int) i0 << (j0 - 48)) | (i1 << (j0 - 112)); else { - u_int64_t j = i1 + (0x8000000000000000ULL >> (j0 - 48)); + uint64_t j = i1 + (0x8000000000000000ULL >> (j0 - 48)); if (j < i1) ++i0; @@ -79,13 +80,13 @@ __llroundl (long double x) unspecified. */ #ifdef FE_INVALID if (FIX_LDBL_LLONG_CONVERT_OVERFLOW - && !(sign == -1 && x > (long double) LLONG_MIN - 0.5L)) + && !(sign == -1 && x > (_Float128) LLONG_MIN - L(0.5))) { feraiseexcept (FE_INVALID); return sign == 1 ? LLONG_MAX : LLONG_MIN; } else if (!FIX_LDBL_LLONG_CONVERT_OVERFLOW - && x <= (long double) LLONG_MIN - 0.5L) + && x <= (_Float128) LLONG_MIN - L(0.5)) { /* If truncation produces LLONG_MIN, the cast will not raise the exception, but may raise "inexact". */ @@ -99,4 +100,4 @@ __llroundl (long double x) return sign * result; } -weak_alias (__llroundl, llroundl) +libm_alias_ldouble (__llround, llround) diff --git a/sysdeps/ieee754/ldbl-128/s_log1pl.c b/sysdeps/ieee754/ldbl-128/s_log1pl.c index b348f41e55..f3181dbc8e 100644 --- a/sysdeps/ieee754/ldbl-128/s_log1pl.c +++ b/sysdeps/ieee754/ldbl-128/s_log1pl.c @@ -56,39 +56,40 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> /* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x) * 1/sqrt(2) <= 1+x < sqrt(2) * Theoretical peak relative error = 5.3e-37, * relative peak error spread = 2.3e-14 */ -static const long double - P12 = 1.538612243596254322971797716843006400388E-6L, - P11 = 4.998469661968096229986658302195402690910E-1L, - P10 = 2.321125933898420063925789532045674660756E1L, - P9 = 4.114517881637811823002128927449878962058E2L, - P8 = 3.824952356185897735160588078446136783779E3L, - P7 = 2.128857716871515081352991964243375186031E4L, - P6 = 7.594356839258970405033155585486712125861E4L, - P5 = 1.797628303815655343403735250238293741397E5L, - P4 = 2.854829159639697837788887080758954924001E5L, - P3 = 3.007007295140399532324943111654767187848E5L, - P2 = 2.014652742082537582487669938141683759923E5L, - P1 = 7.771154681358524243729929227226708890930E4L, - P0 = 1.313572404063446165910279910527789794488E4L, +static const _Float128 + P12 = L(1.538612243596254322971797716843006400388E-6), + P11 = L(4.998469661968096229986658302195402690910E-1), + P10 = L(2.321125933898420063925789532045674660756E1), + P9 = L(4.114517881637811823002128927449878962058E2), + P8 = L(3.824952356185897735160588078446136783779E3), + P7 = L(2.128857716871515081352991964243375186031E4), + P6 = L(7.594356839258970405033155585486712125861E4), + P5 = L(1.797628303815655343403735250238293741397E5), + P4 = L(2.854829159639697837788887080758954924001E5), + P3 = L(3.007007295140399532324943111654767187848E5), + P2 = L(2.014652742082537582487669938141683759923E5), + P1 = L(7.771154681358524243729929227226708890930E4), + P0 = L(1.313572404063446165910279910527789794488E4), /* Q12 = 1.000000000000000000000000000000000000000E0L, */ - Q11 = 4.839208193348159620282142911143429644326E1L, - Q10 = 9.104928120962988414618126155557301584078E2L, - Q9 = 9.147150349299596453976674231612674085381E3L, - Q8 = 5.605842085972455027590989944010492125825E4L, - Q7 = 2.248234257620569139969141618556349415120E5L, - Q6 = 6.132189329546557743179177159925690841200E5L, - Q5 = 1.158019977462989115839826904108208787040E6L, - Q4 = 1.514882452993549494932585972882995548426E6L, - Q3 = 1.347518538384329112529391120390701166528E6L, - Q2 = 7.777690340007566932935753241556479363645E5L, - Q1 = 2.626900195321832660448791748036714883242E5L, - Q0 = 3.940717212190338497730839731583397586124E4L; + Q11 = L(4.839208193348159620282142911143429644326E1), + Q10 = L(9.104928120962988414618126155557301584078E2), + Q9 = L(9.147150349299596453976674231612674085381E3), + Q8 = L(5.605842085972455027590989944010492125825E4), + Q7 = L(2.248234257620569139969141618556349415120E5), + Q6 = L(6.132189329546557743179177159925690841200E5), + Q5 = L(1.158019977462989115839826904108208787040E6), + Q4 = L(1.514882452993549494932585972882995548426E6), + Q3 = L(1.347518538384329112529391120390701166528E6), + Q2 = L(7.777690340007566932935753241556479363645E5), + Q1 = L(2.626900195321832660448791748036714883242E5), + Q0 = L(3.940717212190338497730839731583397586124E4); /* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2), * where z = 2(x-1)/(x+1) @@ -96,33 +97,33 @@ static const long double * Theoretical peak relative error = 1.1e-35, * relative peak error spread 1.1e-9 */ -static const long double - R5 = -8.828896441624934385266096344596648080902E-1L, - R4 = 8.057002716646055371965756206836056074715E1L, - R3 = -2.024301798136027039250415126250455056397E3L, - R2 = 2.048819892795278657810231591630928516206E4L, - R1 = -8.977257995689735303686582344659576526998E4L, - R0 = 1.418134209872192732479751274970992665513E5L, +static const _Float128 + R5 = L(-8.828896441624934385266096344596648080902E-1), + R4 = L(8.057002716646055371965756206836056074715E1), + R3 = L(-2.024301798136027039250415126250455056397E3), + R2 = L(2.048819892795278657810231591630928516206E4), + R1 = L(-8.977257995689735303686582344659576526998E4), + R0 = L(1.418134209872192732479751274970992665513E5), /* S6 = 1.000000000000000000000000000000000000000E0L, */ - S5 = -1.186359407982897997337150403816839480438E2L, - S4 = 3.998526750980007367835804959888064681098E3L, - S3 = -5.748542087379434595104154610899551484314E4L, - S2 = 4.001557694070773974936904547424676279307E5L, - S1 = -1.332535117259762928288745111081235577029E6L, - S0 = 1.701761051846631278975701529965589676574E6L; + S5 = L(-1.186359407982897997337150403816839480438E2), + S4 = L(3.998526750980007367835804959888064681098E3), + S3 = L(-5.748542087379434595104154610899551484314E4), + S2 = L(4.001557694070773974936904547424676279307E5), + S1 = L(-1.332535117259762928288745111081235577029E6), + S0 = L(1.701761051846631278975701529965589676574E6); /* C1 + C2 = ln 2 */ -static const long double C1 = 6.93145751953125E-1L; -static const long double C2 = 1.428606820309417232121458176568075500134E-6L; +static const _Float128 C1 = L(6.93145751953125E-1); +static const _Float128 C2 = L(1.428606820309417232121458176568075500134E-6); -static const long double sqrth = 0.7071067811865475244008443621048490392848L; +static const _Float128 sqrth = L(0.7071067811865475244008443621048490392848); /* ln (2^16384 * (1 - 2^-113)) */ -static const long double zero = 0.0L; +static const _Float128 zero = 0; -long double -__log1pl (long double xm1) +_Float128 +__log1pl (_Float128 xm1) { - long double x, y, z, r, s; + _Float128 x, y, z, r, s; ieee854_long_double_shape_type u; int32_t hx; int e; @@ -145,16 +146,16 @@ __log1pl (long double xm1) return xm1; } - if (xm1 >= 0x1p113L) + if (xm1 >= L(0x1p113)) x = xm1; else - x = xm1 + 1.0L; + x = xm1 + 1; /* log1p(-1) = -inf */ - if (x <= 0.0L) + if (x <= 0) { - if (x == 0.0L) - return (-1.0L / zero); /* log1p(-1) = -inf */ + if (x == 0) + return (-1 / zero); /* log1p(-1) = -inf */ else return (zero / (x - x)); } @@ -171,14 +172,14 @@ __log1pl (long double xm1) if (x < sqrth) { /* 2( 2x-1 )/( 2x+1 ) */ e -= 1; - z = x - 0.5L; - y = 0.5L * z + 0.5L; + z = x - L(0.5); + y = L(0.5) * z + L(0.5); } else { /* 2 (x-1)/(x+1) */ - z = x - 0.5L; - z -= 0.5L; - y = 0.5L * x + 0.5L; + z = x - L(0.5); + z -= L(0.5); + y = L(0.5) * x + L(0.5); } x = z / y; z = x * x; @@ -209,14 +210,14 @@ __log1pl (long double xm1) { e -= 1; if (e != 0) - x = 2.0L * x - 1.0L; /* 2x - 1 */ + x = 2 * x - 1; /* 2x - 1 */ else x = xm1; } else { if (e != 0) - x = x - 1.0L; + x = x - 1; else x = xm1; } @@ -249,7 +250,7 @@ __log1pl (long double xm1) + Q0; y = x * (z * r / s); y = y + e * C2; - z = y - 0.5L * z; + z = y - L(0.5) * z; z = z + x; z = z + e * C1; return (z); diff --git a/sysdeps/ieee754/ldbl-128/s_logbl.c b/sysdeps/ieee754/ldbl-128/s_logbl.c index 3ba67b7bd2..9264fe6616 100644 --- a/sysdeps/ieee754/ldbl-128/s_logbl.c +++ b/sysdeps/ieee754/ldbl-128/s_logbl.c @@ -25,16 +25,17 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -long double -__logbl (long double x) +_Float128 +__logbl (_Float128 x) { int64_t lx, hx, ex; GET_LDOUBLE_WORDS64 (hx, lx, x); hx &= 0x7fffffffffffffffLL; /* high |x| */ if ((hx | lx) == 0) - return -1.0 / fabs (x); + return -1.0 / fabsl (x); if (hx >= 0x7fff000000000000LL) return x * x; if ((ex = hx >> 48) == 0) /* IEEE 754 logb */ @@ -48,7 +49,7 @@ __logbl (long double x) ma = __builtin_clzll (hx); ex -= ma - 16; } - return (long double) (ex - 16383); + return (_Float128) (ex - 16383); } -weak_alias (__logbl, logbl) +libm_alias_ldouble (__logb, logb) diff --git a/sysdeps/ieee754/ldbl-128/s_lrintl.c b/sysdeps/ieee754/ldbl-128/s_lrintl.c index 23f828f862..c1233a45dc 100644 --- a/sysdeps/ieee754/ldbl-128/s_lrintl.c +++ b/sysdeps/ieee754/ldbl-128/s_lrintl.c @@ -1,6 +1,6 @@ /* Round argument to nearest integral value according to current rounding direction. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz>, 1999. @@ -24,21 +24,22 @@ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> #include <fix-fp-int-convert-overflow.h> -static const long double two112[2] = +static const _Float128 two112[2] = { - 5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */ - -5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */ + L(5.19229685853482762853049632922009600E+33), /* 0x406F000000000000, 0 */ + L(-5.19229685853482762853049632922009600E+33) /* 0xC06F000000000000, 0 */ }; long int -__lrintl (long double x) +__lrintl (_Float128 x) { int32_t j0; - u_int64_t i0,i1; - long double w; - long double t; + uint64_t i0,i1; + _Float128 w; + _Float128 t; long int result; int sx; @@ -55,7 +56,7 @@ __lrintl (long double x) #if defined FE_INVALID || defined FE_INEXACT /* X < LONG_MAX + 1 implied by J0 < 31. */ if (sizeof (long int) == 4 - && x > (long double) LONG_MAX) + && x > (_Float128) LONG_MAX) { /* In the event of overflow we must raise the "invalid" exception, but not "inexact". */ @@ -82,7 +83,7 @@ __lrintl (long double x) #if defined FE_INVALID || defined FE_INEXACT /* X < LONG_MAX + 1 implied by J0 < 63. */ if (sizeof (long int) == 8 - && x > (long double) LONG_MAX) + && x > (_Float128) LONG_MAX) { /* In the event of overflow we must raise the "invalid" exception, but not "inexact". */ @@ -112,8 +113,8 @@ __lrintl (long double x) FE_INVALID must be raised and the return value is unspecified. */ #if defined FE_INVALID || defined FE_INEXACT - if (x < (long double) LONG_MIN - && x > (long double) LONG_MIN - 1.0L) + if (x < (_Float128) LONG_MIN + && x > (_Float128) LONG_MIN - 1) { /* If truncation produces LONG_MIN, the cast will not raise the exception, but may raise "inexact". */ @@ -121,7 +122,7 @@ __lrintl (long double x) feraiseexcept (t == LONG_MIN ? FE_INEXACT : FE_INVALID); return LONG_MIN; } - else if (FIX_LDBL_LONG_CONVERT_OVERFLOW && x != (long double) LONG_MIN) + else if (FIX_LDBL_LONG_CONVERT_OVERFLOW && x != (_Float128) LONG_MIN) { feraiseexcept (FE_INVALID); return sx == 0 ? LONG_MAX : LONG_MIN; @@ -134,4 +135,4 @@ __lrintl (long double x) return sx ? -result : result; } -weak_alias (__lrintl, lrintl) +libm_alias_ldouble (__lrint, lrint) diff --git a/sysdeps/ieee754/ldbl-128/s_lroundl.c b/sysdeps/ieee754/ldbl-128/s_lroundl.c index f03262543f..f109157d67 100644 --- a/sysdeps/ieee754/ldbl-128/s_lroundl.c +++ b/sysdeps/ieee754/ldbl-128/s_lroundl.c @@ -1,5 +1,5 @@ /* Round long double value to long int. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz>, 1999. @@ -23,13 +23,14 @@ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> #include <fix-fp-int-convert-overflow.h> long int -__lroundl (long double x) +__lroundl (_Float128 x) { int64_t j0; - u_int64_t i1, i0; + uint64_t i1, i0; long int result; int sign; @@ -62,7 +63,7 @@ __lroundl (long double x) result = ((long int) i0 << (j0 - 48)) | (i1 << (j0 - 112)); else { - u_int64_t j = i1 + (0x8000000000000000ULL >> (j0 - 48)); + uint64_t j = i1 + (0x8000000000000000ULL >> (j0 - 48)); if (j < i1) ++i0; @@ -88,13 +89,13 @@ __lroundl (long double x) unspecified. */ #ifdef FE_INVALID if (FIX_LDBL_LONG_CONVERT_OVERFLOW - && !(sign == -1 && x > (long double) LONG_MIN - 0.5L)) + && !(sign == -1 && x > (_Float128) LONG_MIN - L(0.5))) { feraiseexcept (FE_INVALID); return sign == 1 ? LONG_MAX : LONG_MIN; } else if (!FIX_LDBL_LONG_CONVERT_OVERFLOW - && x <= (long double) LONG_MIN - 0.5L) + && x <= (_Float128) LONG_MIN - L(0.5)) { /* If truncation produces LONG_MIN, the cast will not raise the exception, but may raise "inexact". */ @@ -110,4 +111,4 @@ __lroundl (long double x) return sign * result; } -weak_alias (__lroundl, lroundl) +libm_alias_ldouble (__lround, lround) diff --git a/sysdeps/ieee754/ldbl-128/s_modfl.c b/sysdeps/ieee754/ldbl-128/s_modfl.c index 597a5c9a0c..2d0a2d739f 100644 --- a/sysdeps/ieee754/ldbl-128/s_modfl.c +++ b/sysdeps/ieee754/ldbl-128/s_modfl.c @@ -29,13 +29,14 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -static const long double one = 1.0; +static const _Float128 one = 1.0; -long double __modfl(long double x, long double *iptr) +_Float128 __modfl(_Float128 x, _Float128 *iptr) { int64_t i0,i1,j0; - u_int64_t i; + uint64_t i; GET_LDOUBLE_WORDS64(i0,i1,x); j0 = ((i0>>48)&0x7fff)-0x3fff; /* exponent of x */ if(j0<48) { /* integer part in high x */ @@ -76,4 +77,4 @@ long double __modfl(long double x, long double *iptr) } } } -weak_alias (__modfl, modfl) +libm_alias_ldouble (__modf, modf) diff --git a/sysdeps/ieee754/ldbl-128/s_nearbyintl.c b/sysdeps/ieee754/ldbl-128/s_nearbyintl.c index 2017c04207..f044cb4334 100644 --- a/sysdeps/ieee754/ldbl-128/s_nearbyintl.c +++ b/sysdeps/ieee754/ldbl-128/s_nearbyintl.c @@ -25,27 +25,29 @@ #include <fenv.h> #include <math.h> +#include <math-barriers.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -static const long double +static const _Float128 TWO112[2]={ - 5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */ - -5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */ + L(5.19229685853482762853049632922009600E+33), /* 0x406F000000000000, 0 */ + L(-5.19229685853482762853049632922009600E+33) /* 0xC06F000000000000, 0 */ }; -long double __nearbyintl(long double x) +_Float128 __nearbyintl(_Float128 x) { fenv_t env; int64_t i0,j0,sx; - u_int64_t i1 __attribute__ ((unused)); - long double w,t; + uint64_t i1 __attribute__ ((unused)); + _Float128 w,t; GET_LDOUBLE_WORDS64(i0,i1,x); - sx = (((u_int64_t)i0)>>63); + sx = (((uint64_t)i0)>>63); j0 = ((i0>>48)&0x7fff)-0x3fff; if(j0<112) { if(j0<0) { feholdexcept (&env); - w = TWO112[sx]+x; + w = TWO112[sx] + math_opt_barrier (x); t = w-TWO112[sx]; math_force_eval (t); fesetenv (&env); @@ -58,10 +60,10 @@ long double __nearbyintl(long double x) else return x; /* x is integral */ } feholdexcept (&env); - w = TWO112[sx]+x; + w = TWO112[sx] + math_opt_barrier (x); t = w-TWO112[sx]; math_force_eval (t); fesetenv (&env); return t; } -weak_alias (__nearbyintl, nearbyintl) +libm_alias_ldouble (__nearbyint, nearbyint) diff --git a/sysdeps/ieee754/ldbl-128/s_nextafterl.c b/sysdeps/ieee754/ldbl-128/s_nextafterl.c index 4e9a2ce520..60fdae648f 100644 --- a/sysdeps/ieee754/ldbl-128/s_nextafterl.c +++ b/sysdeps/ieee754/ldbl-128/s_nextafterl.c @@ -26,12 +26,14 @@ static char rcsid[] = "$NetBSD: $"; #include <errno.h> #include <math.h> +#include <math-barriers.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -long double __nextafterl(long double x, long double y) +_Float128 __nextafterl(_Float128 x, _Float128 y) { int64_t hx,hy,ix,iy; - u_int64_t lx,ly; + uint64_t lx,ly; GET_LDOUBLE_WORDS64(hx,lx,x); GET_LDOUBLE_WORDS64(hy,ly,y); @@ -43,7 +45,7 @@ long double __nextafterl(long double x, long double y) return x+y; if(x==y) return y; /* x=y, return y */ if((ix|lx)==0) { /* x == 0 */ - long double u; + _Float128 u; SET_LDOUBLE_WORDS64(x,hy&0x8000000000000000ULL,1);/* return +-minsubnormal */ u = math_opt_barrier (x); u = u * u; @@ -69,18 +71,18 @@ long double __nextafterl(long double x, long double y) } hy = hx&0x7fff000000000000LL; if(hy==0x7fff000000000000LL) { - long double u = x + x; /* overflow */ + _Float128 u = x + x; /* overflow */ math_force_eval (u); __set_errno (ERANGE); } if(hy==0) { - long double u = x*x; /* underflow */ + _Float128 u = x*x; /* underflow */ math_force_eval (u); /* raise underflow flag */ __set_errno (ERANGE); } SET_LDOUBLE_WORDS64(x,hx,lx); return x; } -weak_alias (__nextafterl, nextafterl) +libm_alias_ldouble (__nextafter, nextafter) strong_alias (__nextafterl, __nexttowardl) weak_alias (__nextafterl, nexttowardl) diff --git a/sysdeps/ieee754/ldbl-128/s_nexttoward.c b/sysdeps/ieee754/ldbl-128/s_nexttoward.c index 4343fe83f8..6db8b7f15f 100644 --- a/sysdeps/ieee754/ldbl-128/s_nexttoward.c +++ b/sysdeps/ieee754/ldbl-128/s_nexttoward.c @@ -27,6 +27,7 @@ static char rcsid[] = "$NetBSD: $"; #include <errno.h> #include <math.h> +#include <math-barriers.h> #include <math_private.h> #include <float.h> @@ -34,8 +35,8 @@ double __nexttoward(double x, long double y) { int32_t hx,ix; int64_t hy,iy; - u_int32_t lx; - u_int64_t ly; + uint32_t lx; + uint64_t ly; EXTRACT_WORDS(hx,lx,x); GET_LDOUBLE_WORDS64(hy,ly,y); @@ -49,7 +50,7 @@ double __nexttoward(double x, long double y) if((long double) x==y) return y; /* x=y, return y */ if((ix|lx)==0) { /* x == 0 */ double u; - INSERT_WORDS(x,(u_int32_t)((hy>>32)&0x80000000),1);/* return +-minsub */ + INSERT_WORDS(x,(uint32_t)((hy>>32)&0x80000000),1);/* return +-minsub */ u = math_opt_barrier (x); u = u * u; math_force_eval (u); /* raise underflow flag */ diff --git a/sysdeps/ieee754/ldbl-128/s_nexttowardf.c b/sysdeps/ieee754/ldbl-128/s_nexttowardf.c index 8703359d4f..7840cb382e 100644 --- a/sysdeps/ieee754/ldbl-128/s_nexttowardf.c +++ b/sysdeps/ieee754/ldbl-128/s_nexttowardf.c @@ -20,13 +20,14 @@ static char rcsid[] = "$NetBSD: $"; #include <errno.h> #include <math.h> +#include <math-barriers.h> #include <math_private.h> float __nexttowardf(float x, long double y) { int32_t hx,ix; int64_t hy,iy; - u_int64_t ly; + uint64_t ly; GET_FLOAT_WORD(hx,x); GET_LDOUBLE_WORDS64(hy,ly,y); @@ -40,7 +41,7 @@ float __nexttowardf(float x, long double y) if((long double) x==y) return y; /* x=y, return y */ if(ix==0) { /* x == 0 */ float u; - SET_FLOAT_WORD(x,(u_int32_t)((hy>>32)&0x80000000)|1);/* return +-minsub*/ + SET_FLOAT_WORD(x,(uint32_t)((hy>>32)&0x80000000)|1);/* return +-minsub*/ u = math_opt_barrier (x); u = u * u; math_force_eval (u); /* raise underflow flag */ diff --git a/sysdeps/ieee754/ldbl-128/s_nextupl.c b/sysdeps/ieee754/ldbl-128/s_nextupl.c new file mode 100644 index 0000000000..20827e6d09 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_nextupl.c @@ -0,0 +1,58 @@ +/* Return the least floating-point number greater than X. + Copyright (C) 2016-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <float.h> +#include <math.h> +#include <math_private.h> +#include <libm-alias-ldouble.h> + +/* Return the least floating-point number greater than X. */ +_Float128 +__nextupl (_Float128 x) +{ + int64_t hx, ix; + uint64_t lx; + + GET_LDOUBLE_WORDS64 (hx, lx, x); + ix = hx & 0x7fffffffffffffffLL; + + /* x is nan. */ + if (((ix >= 0x7fff000000000000LL) + && ((ix - 0x7fff000000000000LL) | lx) != 0)) + return x + x; + if ((ix | lx) == 0) + return LDBL_TRUE_MIN; + if (hx >= 0) + { /* x > 0. */ + if (isinf (x)) + return x; + lx++; + if (lx == 0) + hx++; + } + else + { /* x < 0. */ + if (lx == 0) + hx--; + lx--; + } + SET_LDOUBLE_WORDS64 (x, hx, lx); + return x; +} + +libm_alias_ldouble (__nextup, nextup) diff --git a/sysdeps/ieee754/ldbl-128/s_remquol.c b/sysdeps/ieee754/ldbl-128/s_remquol.c index 7356f5f4ef..2fcea6ecdf 100644 --- a/sysdeps/ieee754/ldbl-128/s_remquol.c +++ b/sysdeps/ieee754/ldbl-128/s_remquol.c @@ -1,5 +1,5 @@ /* Compute remainder and a congruent to the quotient. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz>, 1999. @@ -21,16 +21,17 @@ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -static const long double zero = 0.0; +static const _Float128 zero = 0.0; -long double -__remquol (long double x, long double y, int *quo) +_Float128 +__remquol (_Float128 x, _Float128 y, int *quo) { int64_t hx,hy; - u_int64_t sx,lx,ly,qs; + uint64_t sx,lx,ly,qs; int cquo; GET_LDOUBLE_WORDS64 (hx, lx, x); @@ -87,7 +88,7 @@ __remquol (long double x, long double y, int *quo) } else { - long double y_half = 0.5L * y; + _Float128 y_half = L(0.5) * y; if (x > y_half) { x -= y; @@ -103,10 +104,10 @@ __remquol (long double x, long double y, int *quo) *quo = qs ? -cquo : cquo; /* Ensure correct sign of zero result in round-downward mode. */ - if (x == 0.0L) - x = 0.0L; + if (x == 0) + x = 0; if (sx) x = -x; return x; } -weak_alias (__remquol, remquol) +libm_alias_ldouble (__remquo, remquo) diff --git a/sysdeps/ieee754/ldbl-128/s_rintl.c b/sysdeps/ieee754/ldbl-128/s_rintl.c index ae2142b2c9..9e6637a225 100644 --- a/sysdeps/ieee754/ldbl-128/s_rintl.c +++ b/sysdeps/ieee754/ldbl-128/s_rintl.c @@ -29,20 +29,21 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -static const long double +static const _Float128 TWO112[2]={ 5.19229685853482762853049632922009600E+33L, /* 0x406F000000000000, 0 */ -5.19229685853482762853049632922009600E+33L /* 0xC06F000000000000, 0 */ }; -long double __rintl(long double x) +_Float128 __rintl(_Float128 x) { int64_t i0,j0,sx; - u_int64_t i1 __attribute__ ((unused)); - long double w,t; + uint64_t i1 __attribute__ ((unused)); + _Float128 w,t; GET_LDOUBLE_WORDS64(i0,i1,x); - sx = (((u_int64_t)i0)>>63); + sx = (((uint64_t)i0)>>63); j0 = ((i0>>48)&0x7fff)-0x3fff; if(j0<112) { if(j0<0) { @@ -59,4 +60,4 @@ long double __rintl(long double x) w = TWO112[sx]+x; return w-TWO112[sx]; } -weak_alias (__rintl, rintl) +libm_alias_ldouble (__rint, rint) diff --git a/sysdeps/ieee754/ldbl-128/s_roundevenl.c b/sysdeps/ieee754/ldbl-128/s_roundevenl.c new file mode 100644 index 0000000000..5fc59af4ee --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_roundevenl.c @@ -0,0 +1,104 @@ +/* Round to nearest integer value, rounding halfway cases to even. + ldbl-128 version. + Copyright (C) 2016-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <libm-alias-ldouble.h> +#include <stdint.h> + +#define BIAS 0x3fff +#define MANT_DIG 113 +#define MAX_EXP (2 * BIAS + 1) + +_Float128 +__roundevenl (_Float128 x) +{ + uint64_t hx, lx, uhx; + GET_LDOUBLE_WORDS64 (hx, lx, x); + uhx = hx & 0x7fffffffffffffffULL; + int exponent = uhx >> (MANT_DIG - 1 - 64); + if (exponent >= BIAS + MANT_DIG - 1) + { + /* Integer, infinity or NaN. */ + if (exponent == MAX_EXP) + /* Infinity or NaN; quiet signaling NaNs. */ + return x + x; + else + return x; + } + else if (exponent >= BIAS + MANT_DIG - 64) + { + /* Not necessarily an integer; integer bit is in low word. + Locate the bits with exponents 0 and -1. */ + int int_pos = (BIAS + MANT_DIG - 1) - exponent; + int half_pos = int_pos - 1; + uint64_t half_bit = 1ULL << half_pos; + uint64_t int_bit = 1ULL << int_pos; + if ((lx & (int_bit | (half_bit - 1))) != 0) + { + /* Carry into the exponent works correctly. No need to test + whether HALF_BIT is set. */ + lx += half_bit; + hx += lx < half_bit; + } + lx &= ~(int_bit - 1); + } + else if (exponent == BIAS + MANT_DIG - 65) + { + /* Not necessarily an integer; integer bit is bottom of high + word, half bit is top of low word. */ + if (((hx & 1) | (lx & 0x7fffffffffffffffULL)) != 0) + { + lx += 0x8000000000000000ULL; + hx += lx < 0x8000000000000000ULL; + } + lx = 0; + } + else if (exponent >= BIAS) + { + /* At least 1; not necessarily an integer, integer bit and half + bit are in the high word. Locate the bits with exponents 0 + and -1 (when the unbiased exponent is 0, the bit with + exponent 0 is implicit, but as the bias is odd it is OK to + take it from the low bit of the exponent). */ + int int_pos = (BIAS + MANT_DIG - 65) - exponent; + int half_pos = int_pos - 1; + uint64_t half_bit = 1ULL << half_pos; + uint64_t int_bit = 1ULL << int_pos; + if (((hx & (int_bit | (half_bit - 1))) | lx) != 0) + hx += half_bit; + hx &= ~(int_bit - 1); + lx = 0; + } + else if (exponent == BIAS - 1 && (uhx > 0x3ffe000000000000ULL || lx != 0)) + { + /* Interval (0.5, 1). */ + hx = (hx & 0x8000000000000000ULL) | 0x3fff000000000000ULL; + lx = 0; + } + else + { + /* Rounds to 0. */ + hx &= 0x8000000000000000ULL; + lx = 0; + } + SET_LDOUBLE_WORDS64 (x, hx, lx); + return x; +} +libm_alias_ldouble (__roundeven, roundeven) diff --git a/sysdeps/ieee754/ldbl-128/s_roundl.c b/sysdeps/ieee754/ldbl-128/s_roundl.c index 98b448e4f3..22789cedf3 100644 --- a/sysdeps/ieee754/ldbl-128/s_roundl.c +++ b/sysdeps/ieee754/ldbl-128/s_roundl.c @@ -1,5 +1,5 @@ /* Round long double to integer away from zero. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz>, 1999. @@ -21,16 +21,14 @@ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -static const long double huge = 1.0E4930L; - - -long double -__roundl (long double x) +_Float128 +__roundl (_Float128 x) { int32_t j0; - u_int64_t i1, i0; + uint64_t i1, i0; GET_LDOUBLE_WORDS64 (i0, i1, x); j0 = ((i0 >> 48) & 0x7fff) - 0x3fff; @@ -38,27 +36,21 @@ __roundl (long double x) { if (j0 < 0) { - if (huge + x > 0.0) - { - i0 &= 0x8000000000000000ULL; - if (j0 == -1) - i0 |= 0x3fff000000000000LL; - i1 = 0; - } + i0 &= 0x8000000000000000ULL; + if (j0 == -1) + i0 |= 0x3fff000000000000LL; + i1 = 0; } else { - u_int64_t i = 0x0000ffffffffffffLL >> j0; + uint64_t i = 0x0000ffffffffffffLL >> j0; if (((i0 & i) | i1) == 0) /* X is integral. */ return x; - if (huge + x > 0.0) - { - /* Raise inexact if x != 0. */ - i0 += 0x0000800000000000LL >> j0; - i0 &= ~i; - i1 = 0; - } + + i0 += 0x0000800000000000LL >> j0; + i0 &= ~i; + i1 = 0; } } else if (j0 > 111) @@ -71,23 +63,19 @@ __roundl (long double x) } else { - u_int64_t i = -1ULL >> (j0 - 48); + uint64_t i = -1ULL >> (j0 - 48); if ((i1 & i) == 0) /* X is integral. */ return x; - if (huge + x > 0.0) - { - /* Raise inexact if x != 0. */ - u_int64_t j = i1 + (1LL << (111 - j0)); - if (j < i1) - i0 += 1; - i1 = j; - } + uint64_t j = i1 + (1LL << (111 - j0)); + if (j < i1) + i0 += 1; + i1 = j; i1 &= ~i; } SET_LDOUBLE_WORDS64 (x, i0, i1); return x; } -weak_alias (__roundl, roundl) +libm_alias_ldouble (__round, round) diff --git a/sysdeps/ieee754/ldbl-128/s_scalblnl.c b/sysdeps/ieee754/ldbl-128/s_scalblnl.c index 1e24197c63..5864eaf93c 100644 --- a/sysdeps/ieee754/ldbl-128/s_scalblnl.c +++ b/sysdeps/ieee754/ldbl-128/s_scalblnl.c @@ -28,13 +28,13 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> -static const long double -two114 = 2.0769187434139310514121985316880384E+34L, /* 0x4071000000000000, 0 */ -twom114 = 4.8148248609680896326399448564623183E-35L, /* 0x3F8D000000000000, 0 */ -huge = 1.0E+4900L, -tiny = 1.0E-4900L; +static const _Float128 +two114 = L(2.0769187434139310514121985316880384E+34), /* 0x4071000000000000, 0 */ +twom114 = L(4.8148248609680896326399448564623183E-35), /* 0x3F8D000000000000, 0 */ +huge = L(1.0E+4900), +tiny = L(1.0E-4900); -long double __scalblnl (long double x, long int n) +_Float128 __scalblnl (_Float128 x, long int n) { int64_t k,hx,lx; GET_LDOUBLE_WORDS64(hx,lx,x); diff --git a/sysdeps/ieee754/ldbl-128/s_scalbnl.c b/sysdeps/ieee754/ldbl-128/s_scalbnl.c index a5cbd0d9d2..e6fe796079 100644 --- a/sysdeps/ieee754/ldbl-128/s_scalbnl.c +++ b/sysdeps/ieee754/ldbl-128/s_scalbnl.c @@ -28,13 +28,13 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> -static const long double -two114 = 2.0769187434139310514121985316880384E+34L, /* 0x4071000000000000, 0 */ -twom114 = 4.8148248609680896326399448564623183E-35L, /* 0x3F8D000000000000, 0 */ -huge = 1.0E+4900L, -tiny = 1.0E-4900L; +static const _Float128 +two114 = L(2.0769187434139310514121985316880384E+34), /* 0x4071000000000000, 0 */ +twom114 = L(4.8148248609680896326399448564623183E-35), /* 0x3F8D000000000000, 0 */ +huge = L(1.0E+4900), +tiny = L(1.0E-4900); -long double __scalbnl (long double x, int n) +_Float128 __scalbnl (_Float128 x, int n) { int64_t k,hx,lx; GET_LDOUBLE_WORDS64(hx,lx,x); diff --git a/sysdeps/ieee754/ldbl-128/s_setpayloadl.c b/sysdeps/ieee754/ldbl-128/s_setpayloadl.c new file mode 100644 index 0000000000..9f43c259ec --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_setpayloadl.c @@ -0,0 +1,4 @@ +#define SIG 0 +#define FUNC __setpayloadl +#include <s_setpayloadl_main.c> +libm_alias_ldouble (__setpayload, setpayload) diff --git a/sysdeps/ieee754/ldbl-128/s_setpayloadl_main.c b/sysdeps/ieee754/ldbl-128/s_setpayloadl_main.c new file mode 100644 index 0000000000..bb3fc8d9fb --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_setpayloadl_main.c @@ -0,0 +1,70 @@ +/* Set NaN payload. ldbl-128 version. + Copyright (C) 2016-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <libm-alias-ldouble.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3fff +#define PAYLOAD_DIG 111 +#define EXPLICIT_MANT_DIG 112 + +int +FUNC (_Float128 *x, _Float128 payload) +{ + uint64_t hx, lx; + GET_LDOUBLE_WORDS64 (hx, lx, payload); + int exponent = hx >> (EXPLICIT_MANT_DIG - 64); + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. */ + if (exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && hx == 0 && lx == 0))) + { + SET_LDOUBLE_WORDS64 (*x, 0, 0); + return 1; + } + int shift = BIAS + EXPLICIT_MANT_DIG - exponent; + if (shift < 64 + ? (lx & ((1ULL << shift) - 1)) != 0 + : (lx != 0 || (hx & ((1ULL << (shift - 64)) - 1)) != 0)) + { + SET_LDOUBLE_WORDS64 (*x, 0, 0); + return 1; + } + if (exponent != 0) + { + hx &= (1ULL << (EXPLICIT_MANT_DIG - 64)) - 1; + hx |= 1ULL << (EXPLICIT_MANT_DIG - 64); + if (shift >= 64) + { + lx = hx >> (shift - 64); + hx = 0; + } + else if (shift != 0) + { + lx = (lx >> shift) | (hx << (64 - shift)); + hx >>= shift; + } + } + hx |= 0x7fff000000000000ULL | (SET_HIGH_BIT ? 0x800000000000ULL : 0); + SET_LDOUBLE_WORDS64 (*x, hx, lx); + return 0; +} diff --git a/sysdeps/ieee754/ldbl-128/s_setpayloadsigl.c b/sysdeps/ieee754/ldbl-128/s_setpayloadsigl.c new file mode 100644 index 0000000000..cd82f295aa --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_setpayloadsigl.c @@ -0,0 +1,4 @@ +#define SIG 1 +#define FUNC __setpayloadsigl +#include <s_setpayloadl_main.c> +libm_alias_ldouble (__setpayloadsig, setpayloadsig) diff --git a/sysdeps/ieee754/ldbl-128/s_signbitl.c b/sysdeps/ieee754/ldbl-128/s_signbitl.c index ee5d77e27a..1aa93f709d 100644 --- a/sysdeps/ieee754/ldbl-128/s_signbitl.c +++ b/sysdeps/ieee754/ldbl-128/s_signbitl.c @@ -1,5 +1,5 @@ /* Return nonzero value if number is negative. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. @@ -18,9 +18,10 @@ <http://www.gnu.org/licenses/>. */ #include <math.h> +#include <math_private.h> int -__signbitl (long double x) +__signbitl (_Float128 x) { return __builtin_signbitl (x); } diff --git a/sysdeps/ieee754/ldbl-128/s_sincosl.c b/sysdeps/ieee754/ldbl-128/s_sincosl.c index 1abdb4419e..dfcb0be301 100644 --- a/sysdeps/ieee754/ldbl-128/s_sincosl.c +++ b/sysdeps/ieee754/ldbl-128/s_sincosl.c @@ -1,5 +1,5 @@ /* Compute sine and cosine of argument. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz>. @@ -22,9 +22,10 @@ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> void -__sincosl (long double x, long double *sinx, long double *cosx) +__sincosl (_Float128 x, _Float128 *sinx, _Float128 *cosx) { int64_t ix; @@ -34,7 +35,7 @@ __sincosl (long double x, long double *sinx, long double *cosx) /* |x| ~< pi/4 */ ix &= 0x7fffffffffffffffLL; if (ix <= 0x3ffe921fb54442d1LL) - __kernel_sincosl (x, 0.0L, sinx, cosx, 0); + __kernel_sincosl (x, 0, sinx, cosx, 0); else if (ix >= 0x7fff000000000000LL) { /* sin(Inf or NaN) is NaN */ @@ -45,7 +46,7 @@ __sincosl (long double x, long double *sinx, long double *cosx) else { /* Argument reduction needed. */ - long double y[2]; + _Float128 y[2]; int n; n = __ieee754_rem_pio2l (x, y); @@ -70,4 +71,4 @@ __sincosl (long double x, long double *sinx, long double *cosx) } } } -weak_alias (__sincosl, sincosl) +libm_alias_ldouble (__sincos, sincos) diff --git a/sysdeps/ieee754/ldbl-128/s_sinl.c b/sysdeps/ieee754/ldbl-128/s_sinl.c index 582a53fd7a..773b2fa7ee 100644 --- a/sysdeps/ieee754/ldbl-128/s_sinl.c +++ b/sysdeps/ieee754/ldbl-128/s_sinl.c @@ -47,10 +47,11 @@ #include <errno.h> #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -long double __sinl(long double x) +_Float128 __sinl(_Float128 x) { - long double y[2],z=0.0L; + _Float128 y[2],z=0; int64_t n, ix; /* High word of x. */ @@ -83,4 +84,4 @@ long double __sinl(long double x) } } } -weak_alias (__sinl, sinl) +libm_alias_ldouble (__sin, sin) diff --git a/sysdeps/ieee754/ldbl-128/s_tanhl.c b/sysdeps/ieee754/ldbl-128/s_tanhl.c index f7a1d20f79..fc309dab0a 100644 --- a/sysdeps/ieee754/ldbl-128/s_tanhl.c +++ b/sysdeps/ieee754/ldbl-128/s_tanhl.c @@ -44,14 +44,16 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> +#include <libm-alias-ldouble.h> -static const long double one = 1.0, two = 2.0, tiny = 1.0e-4900L; +static const _Float128 one = 1.0, two = 2.0, tiny = L(1.0e-4900); -long double -__tanhl (long double x) +_Float128 +__tanhl (_Float128 x) { - long double t, z; - u_int32_t jx, ix; + _Float128 t, z; + uint32_t jx, ix; ieee854_long_double_shape_type u; /* Words of |x|. */ @@ -97,4 +99,4 @@ __tanhl (long double x) } return (jx & 0x80000000) ? -z : z; } -weak_alias (__tanhl, tanhl) +libm_alias_ldouble (__tanh, tanh) diff --git a/sysdeps/ieee754/ldbl-128/s_tanl.c b/sysdeps/ieee754/ldbl-128/s_tanl.c index c7d637402b..77db10f077 100644 --- a/sysdeps/ieee754/ldbl-128/s_tanl.c +++ b/sysdeps/ieee754/ldbl-128/s_tanl.c @@ -47,10 +47,11 @@ #include <errno.h> #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -long double __tanl(long double x) +_Float128 __tanl(_Float128 x) { - long double y[2],z=0.0L; + _Float128 y[2],z=0; int64_t n, ix; /* High word of x. */ @@ -77,4 +78,4 @@ long double __tanl(long double x) -1 -- n odd */ } } -weak_alias (__tanl, tanl) +libm_alias_ldouble (__tan, tan) diff --git a/sysdeps/ieee754/ldbl-128/s_totalorderl.c b/sysdeps/ieee754/ldbl-128/s_totalorderl.c new file mode 100644 index 0000000000..080c9597b9 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_totalorderl.c @@ -0,0 +1,56 @@ +/* Total order operation. ldbl-128 version. + Copyright (C) 2016-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <libm-alias-ldouble.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +__totalorderl (_Float128 x, _Float128 y) +{ + int64_t hx, hy; + uint64_t lx, ly; + GET_LDOUBLE_WORDS64 (hx, lx, x); + GET_LDOUBLE_WORDS64 (hy, ly, y); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + uint64_t uhx = hx & 0x7fffffffffffffffULL; + uint64_t uhy = hy & 0x7fffffffffffffffULL; + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the arguments interpreted as + sign-magnitude integers. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((uhx > 0x7fff000000000000ULL || (uhx == 0x7fff000000000000ULL + && lx != 0)) + && (uhy > 0x7fff000000000000ULL || (uhy == 0x7fff000000000000ULL + && ly != 0))) + { + hx ^= 0x0000800000000000ULL; + hy ^= 0x0000800000000000ULL; + } +#endif + uint64_t hx_sign = hx >> 63; + uint64_t hy_sign = hy >> 63; + hx ^= hx_sign >> 1; + lx ^= hx_sign; + hy ^= hy_sign >> 1; + ly ^= hy_sign; + return hx < hy || (hx == hy && lx <= ly); +} +libm_alias_ldouble (__totalorder, totalorder) diff --git a/sysdeps/ieee754/ldbl-128/s_totalordermagl.c b/sysdeps/ieee754/ldbl-128/s_totalordermagl.c new file mode 100644 index 0000000000..642c48e8f5 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_totalordermagl.c @@ -0,0 +1,50 @@ +/* Total order operation on absolute values. ldbl-128 version. + Copyright (C) 2016-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <libm-alias-ldouble.h> +#include <nan-high-order-bit.h> +#include <stdint.h> + +int +__totalordermagl (_Float128 x, _Float128 y) +{ + uint64_t hx, hy; + uint64_t lx, ly; + GET_LDOUBLE_WORDS64 (hx, lx, x); + GET_LDOUBLE_WORDS64 (hy, ly, y); + hx &= 0x7fffffffffffffffULL; + hy &= 0x7fffffffffffffffULL; +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* For the preferred quiet NaN convention, this operation is a + comparison of the representations of the absolute values of the + arguments. If both arguments are NaNs, invert the + quiet/signaling bit so comparing that way works. */ + if ((hx > 0x7fff000000000000ULL || (hx == 0x7fff000000000000ULL + && lx != 0)) + && (hy > 0x7fff000000000000ULL || (hy == 0x7fff000000000000ULL + && ly != 0))) + { + hx ^= 0x0000800000000000ULL; + hy ^= 0x0000800000000000ULL; + } +#endif + return hx < hy || (hx == hy && lx <= ly); +} +libm_alias_ldouble (__totalordermag, totalordermag) diff --git a/sysdeps/ieee754/ldbl-128/s_truncl.c b/sysdeps/ieee754/ldbl-128/s_truncl.c index c71f0aba92..f858ede3d2 100644 --- a/sysdeps/ieee754/ldbl-128/s_truncl.c +++ b/sysdeps/ieee754/ldbl-128/s_truncl.c @@ -1,5 +1,5 @@ /* Truncate argument to nearest integral value not larger than the argument. - Copyright (C) 1997-2016 Free Software Foundation, Inc. + Copyright (C) 1997-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997 and Jakub Jelinek <jj@ultra.linux.cz>, 1999. @@ -21,13 +21,14 @@ #include <math.h> #include <math_private.h> +#include <libm-alias-ldouble.h> -long double -__truncl (long double x) +_Float128 +__truncl (_Float128 x) { int32_t j0; - u_int64_t i0, i1, sx; + uint64_t i0, i1, sx; GET_LDOUBLE_WORDS64 (i0, i1, x); sx = i0 & 0x8000000000000000ULL; @@ -53,4 +54,4 @@ __truncl (long double x) return x; } -weak_alias (__truncl, truncl) +libm_alias_ldouble (__trunc, trunc) diff --git a/sysdeps/ieee754/ldbl-128/s_ufromfpl.c b/sysdeps/ieee754/ldbl-128/s_ufromfpl.c new file mode 100644 index 0000000000..22935e6ef7 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_ufromfpl.c @@ -0,0 +1,5 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC __ufromfpl +#include <s_fromfpl_main.c> +libm_alias_ldouble (__ufromfp, ufromfp) diff --git a/sysdeps/ieee754/ldbl-128/s_ufromfpxl.c b/sysdeps/ieee754/ldbl-128/s_ufromfpxl.c new file mode 100644 index 0000000000..77a5423de8 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_ufromfpxl.c @@ -0,0 +1,5 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC __ufromfpxl +#include <s_fromfpl_main.c> +libm_alias_ldouble (__ufromfpx, ufromfpx) diff --git a/sysdeps/ieee754/ldbl-128/strtold_l.c b/sysdeps/ieee754/ldbl-128/strtold_l.c index 12ccd93ee5..4b72ae1e33 100644 --- a/sysdeps/ieee754/ldbl-128/strtold_l.c +++ b/sysdeps/ieee754/ldbl-128/strtold_l.c @@ -1,4 +1,4 @@ -/* Copyright (C) 1999-2016 Free Software Foundation, Inc. +/* Copyright (C) 1999-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -34,4 +34,34 @@ #define MPN2FLOAT __mpn_construct_long_double #define FLOAT_HUGE_VAL HUGE_VALL +#if __HAVE_FLOAT128 && !__HAVE_DISTINCT_FLOAT128 +# define strtof128_l __hide_strtof128_l +# define wcstof128_l __hide_wcstof128_l +#endif + +#if __HAVE_FLOAT64X_LONG_DOUBLE +# define strtof64x_l __hide_strtof64x_l +# define wcstof64x_l __hide_wcstof64x_l +#endif + #include <strtod_l.c> + +#if __HAVE_FLOAT128 && !__HAVE_DISTINCT_FLOAT128 +# undef strtof128_l +# undef wcstof128_l +# ifdef USE_WIDE_CHAR +weak_alias (wcstold_l, wcstof128_l) +# else +weak_alias (strtold_l, strtof128_l) +# endif +#endif + +#if __HAVE_FLOAT64X_LONG_DOUBLE +# undef strtof64x_l +# undef wcstof64x_l +# ifdef USE_WIDE_CHAR +weak_alias (wcstold_l, wcstof64x_l) +# else +weak_alias (strtold_l, strtof64x_l) +# endif +#endif diff --git a/sysdeps/ieee754/ldbl-128/t_expl.h b/sysdeps/ieee754/ldbl-128/t_expl.h index a23d3d9344..b386fc1f54 100644 --- a/sysdeps/ieee754/ldbl-128/t_expl.h +++ b/sysdeps/ieee754/ldbl-128/t_expl.h @@ -1,5 +1,5 @@ /* Accurate table for expl(). - Copyright (C) 1999-2016 Free Software Foundation, Inc. + Copyright (C) 1999-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jj@ultra.linux.cz> @@ -29,942 +29,942 @@ __expl_table[T_EXPL_ARGN+2*i] == i/S+s where absl(s) <= 2^-54 and absl(r) <= 2^-212. */ -static const long double __expl_table [] = { - -3.47656250000000000584188889839535373E-01L, /* bffd640000000000002b1b04213cf000 */ - 6.90417668990715641167244540876988960E-32L, /* 3f97667c3fdb588a6ae1af8748357a17 */ - -3.43749999999999981853132895957607418E-01L, /* bffd5ffffffffffffac4ff5f4050b000 */ - -7.16021898043268093462818380603370350E-33L, /* bf94296c8219427edc1431ac2498583e */ - -3.39843750000000013418643523138766329E-01L, /* bffd5c000000000003de1f027a30e000 */ - 8.16920774283317801641347327589583265E-32L, /* 3f97a82b65774bdca1b4440d749ed8d3 */ - -3.35937500000000014998092453039303051E-01L, /* bffd5800000000000452a9f4d8857000 */ - -6.55865578425428447938248396879359670E-32L, /* bf97548b7d240f3d034b395e6eecfac8 */ - -3.32031250000000000981984049529998541E-01L, /* bffd540000000000004875277cda5000 */ - 6.91213046334032232108944519541512737E-32L, /* 3f9766e5f925338a19045c94443b66e1 */ - -3.28124999999999986646017645350399708E-01L, /* bffd4ffffffffffffc26a667bf44d000 */ - -6.16281060996110316602421505683742661E-32L, /* bf973ffdcdcffb6fbffc86b2b8d42f5d */ - -3.24218749999999991645717430645867963E-01L, /* bffd4bfffffffffffd97901063e48000 */ - -7.90797211087760527593856542417304137E-32L, /* bf979a9afaaca1ada6a8ed1c80584d60 */ - -3.20312499999999998918211610690789652E-01L, /* bffd47ffffffffffffb02d9856d71000 */ - 8.64024799457616856987630373786503376E-32L, /* 3f97c0a098623f95579d5d9b2b67342d */ - -3.16406249999999998153974811017181883E-01L, /* bffd43ffffffffffff77c991f1076000 */ - -2.73176610180696076418536105483668404E-32L, /* bf961baeccb32f9b1fcbb8e60468e95a */ - -3.12500000000000011420976192575972779E-01L, /* bffd400000000000034ab8240483d000 */ - 7.16573502812389453744433792609989420E-32L, /* 3f977410f4c2cfc4335f28446c0fb363 */ - -3.08593750000000001735496343854851414E-01L, /* bffd3c000000000000800e995c176000 */ - -1.56292999645122272621237565671593071E-32L, /* bf95449b9cbdaff6ac1246adb2c826ac */ - -3.04687499999999982592401295899221626E-01L, /* bffd37fffffffffffafb8bc1e061a000 */ - 6.48993208584888904958594509625158417E-32L, /* 3f9750f9fe8366d82d77afa0031a92e1 */ - -3.00781249999999999230616898937763959E-01L, /* bffd33ffffffffffffc73ac39da54000 */ - 6.57082437496961397305801409357792029E-32L, /* 3f97552d3cb598ea80135cf3feb27ec4 */ - -2.96874999999999998788769281703245722E-01L, /* bffd2fffffffffffffa6a07fa5021000 */ - -3.26588297198283968096426564544269170E-32L, /* bf9653260fc1802f46b629aee171809b */ - -2.92968750000000015318089182805941695E-01L, /* bffd2c0000000000046a468614bd6000 */ - -1.73291974845198589684358727559290718E-32L, /* bf9567e9d158f52e483c8d8dcb5961dd */ - -2.89062500000000007736778942676309681E-01L, /* bffd280000000000023adf9f4c3d3000 */ - -6.83629745986675744404029225571026236E-32L, /* bf9762f5face6281c1daf1c6aedbdb45 */ - -2.85156250000000001367091555763661937E-01L, /* bffd2400000000000064dfa11e3fb000 */ - -5.44898442619766878281110054067026237E-32L, /* bf971aed6d2db9f542986a785edae072 */ - -2.81249999999999986958718100227029406E-01L, /* bffd1ffffffffffffc3db9265ca9d000 */ - 1.13007318374506125723591889451107046E-32L, /* 3f94d569fe387f456a97902907ac3856 */ - -2.77343750000000000356078829380495179E-01L, /* bffd1c0000000000001a462390083000 */ - -4.98979365468978332358409063436543102E-32L, /* bf970315bbf3e0d14b5c94c900702d4c */ - -2.73437499999999990276993957508540484E-01L, /* bffd17fffffffffffd32919bcdc94000 */ - -8.79390484115892344533724650295100871E-32L, /* bf97c89b0b89cc19c3ab2b60da9bbbc3 */ - -2.69531250000000002434203866460082225E-01L, /* bffd14000000000000b39ccf9e130000 */ - 9.44060754687026590886751809927191596E-32L, /* 3f97ea2f32cfecca5c64a26137a9210f */ - -2.65624999999999997296320716986257179E-01L, /* bffd0fffffffffffff3880f13a2bc000 */ - 2.07142664067265697791007875348396921E-32L, /* 3f95ae37ee685b9122fbe377bd205ee4 */ - -2.61718750000000010237478733739017956E-01L, /* bffd0c000000000002f3648179d40000 */ - -6.10552936159265665298996309192680256E-32L, /* bf973d0467d31e407515a3cca0f3b4e2 */ - -2.57812500000000011948220522778370303E-01L, /* bffd08000000000003719f81275bd000 */ - 6.72477169058908902499239631466443836E-32L, /* 3f975d2b8c475d3160cf72d227d8e6f9 */ - -2.53906249999999991822993360536596860E-01L, /* bffd03fffffffffffda4a4b62f818000 */ - -2.44868296623215865054704392917190994E-32L, /* bf95fc92516c6d057d29fc2528855976 */ - -2.49999999999999986862019457428548084E-01L, /* bffcfffffffffffff86d2d20d5ff4000 */ - -3.85302898949105073614122724961613078E-32L, /* bf96901f147cb7d643af71b6129ce929 */ - -2.46093750000000000237554160737318435E-01L, /* bffcf8000000000000230e8ade26b000 */ - -1.52823675242678363494345369284988589E-32L, /* bf953d6700c5f3fc303f79d0ec8c680a */ - -2.42187500000000003023380963205457065E-01L, /* bffcf0000000000001be2c1a78bb0000 */ - -7.78402037952209709489481182714311699E-34L, /* bf9102ab1f3998e887f0ee4cf940faa5 */ - -2.38281249999999995309623303145485725E-01L, /* bffce7fffffffffffd4bd2940f43f000 */ - -3.54307216794236899443913216397197696E-32L, /* bf966fef03ab69c3f289436205b21d02 */ - -2.34374999999999998425804947623207526E-01L, /* bffcdfffffffffffff17b097a6092000 */ - -2.86038428948386602859761879407549696E-32L, /* bf96290a0eba0131efe3a05fe188f2e3 */ - -2.30468749999999993822207406785200832E-01L, /* bffcd7fffffffffffc70519834eae000 */ - -2.54339521031747516806893838749365762E-32L, /* bf96081f0ad7f9107ae6cddb32c178ab */ - -2.26562499999999997823524030344489884E-01L, /* bffccffffffffffffebecf10093df000 */ - 4.31904611473158635644635628922959401E-32L, /* 3f96c083f0b1faa7c4c686193e38d67c */ - -2.22656250000000004835132405125162742E-01L, /* bffcc8000000000002c98a233f19f000 */ - 2.54709791629335691650310168420597566E-33L, /* 3f92a735903f5eed07a716ab931e20d9 */ - -2.18749999999999988969454021829236626E-01L, /* bffcbffffffffffff9a42dc14ce36000 */ - -3.77236096429336082213752014054909454E-32L, /* bf9687be8e5b2fca54d3e81157eac660 */ - -2.14843750000000010613256919115758495E-01L, /* bffcb80000000000061e3d828ecac000 */ - -4.55194148712216691177097854305964738E-32L, /* bf96d8b35c776aa3e1a4768271380503 */ - -2.10937499999999993204656148110447201E-01L, /* bffcaffffffffffffc152f2aea118000 */ - -2.95044199165561453749332254271716417E-32L, /* bf96326433b00b2439094d9bef22ddd1 */ - -2.07031250000000012233944895423355677E-01L, /* bffca80000000000070d695ee0e94000 */ - 1.93146788688385419095981415411012357E-32L, /* 3f959126729135a5e390d4bb802a0bde */ - -2.03125000000000008030983633336321863E-01L, /* bffca0000000000004a129fbc51af000 */ - 2.37361904671826193563212931215900137E-32L, /* 3f95ecfb3c4ba1b97ea3ad45cbb1e68a */ - -1.99218750000000001763815712796132779E-01L, /* bffc98000000000001044b12d9950000 */ - -3.63171243370923753295192486732883239E-33L, /* bf932db5fb3f27c38e0fa7bbcfc64f55 */ - -1.95312500000000004883660234506677272E-01L, /* bffc90000000000002d0b3779d1f9000 */ - -3.19989507343607877747980892249711601E-33L, /* bf9309d63de96bb3ef744c865f22f1bd */ - -1.91406250000000013720152363227519348E-01L, /* bffc88000000000007e8bcb387121000 */ - -1.89295754093147174148371614722178860E-32L, /* bf958926e2e67dfe812c508290add2e7 */ - -1.87500000000000000182342082774432620E-01L, /* bffc800000000000001ae8b06a39f000 */ - -2.96812835183184815200854214892983927E-32L, /* bf96343a62d156bbe71f55d14ca4b6e5 */ - -1.83593750000000012410147185883290345E-01L, /* bffc78000000000007276a1adda8d000 */ - -2.02191931237489669058466239995304587E-32L, /* bf95a3efab92d26ec2df90df036a117f */ - -1.79687499999999997439177363346082917E-01L, /* bffc6ffffffffffffe8616db2927d000 */ - -9.92752326937775530007399526834009465E-33L, /* bf949c5f88ed17041e1a3f1829d543cd */ - -1.75781249999999995824373974504785174E-01L, /* bffc67fffffffffffd97c94f13ea3000 */ - 1.44184772065335613487885714828816178E-32L, /* 3f952b75c63476e7fcc2f5841c27bcce */ - -1.71874999999999986685050259043077809E-01L, /* bffc5ffffffffffff8530f6bc531a000 */ - -3.49007014971241147689894940544402482E-32L, /* bf966a6dfaa012aea8ffe6d90b02330f */ - -1.67968749999999997316058782350439701E-01L, /* bffc57fffffffffffe73eb914f2aa000 */ - 3.34025733574205019081305778794376391E-32L, /* 3f965adf4572561fd5456a6c13d8babf */ - -1.64062499999999993322730602128318480E-01L, /* bffc4ffffffffffffc269be4f68f3000 */ - -1.83345916769684984022099095506340635E-32L, /* bf957ccb69026cb2f6024c211576d5f4 */ - -1.60156249999999992419000744447607979E-01L, /* bffc47fffffffffffba13df21784a000 */ - 2.73442789798110494773517431626534726E-32L, /* 3f961bf58ff22c9b30f1e2b39f26d7d5 */ - -1.56249999999999987665010524130393080E-01L, /* bffc3ffffffffffff8e3ad45e7508000 */ - 2.02695576464836145806428118889332191E-32L, /* 3f95a4fb7435a4a2f71de81eb8ae75d1 */ - -1.52343749999999989905291167951491803E-01L, /* bffc37fffffffffffa2e48aecfc24000 */ - -3.61436631548815190395331054871041524E-32L, /* bf967756567ebd108075ae527cc2e7f0 */ - -1.48437500000000006686107754967759751E-01L, /* bffc30000000000003dab20261b3c000 */ - -2.15524270159131591469319477922198390E-32L, /* bf95bfa05b82ef3a708c4f0395e9fcf6 */ - -1.44531250000000005132889939177166485E-01L, /* bffc28000000000002f57b1969e7b000 */ - 2.74741116529653547935086189244019604E-32L, /* 3f961d4eb77c1185d34fe1b04a3f3cf5 */ - -1.40625000000000000707469094533647325E-01L, /* bffc2000000000000068676d3d5c4000 */ - 4.40607097220049957013547629906723266E-33L, /* 3f936e0ac425daf795b42913cf0ef881 */ - -1.36718749999999995713752139187543306E-01L, /* bffc17fffffffffffd87762255991000 */ - -3.73751317180116492404578048203389108E-32L, /* bf9684202491e9cbb7ceb67d9ff7e0c9 */ - -1.32812500000000007198453630478482191E-01L, /* bffc10000000000004264de3a4379000 */ - -3.97050085179660203884930593717220728E-32L, /* bf969c52048de14be3c9c1971e50869c */ - -1.28906250000000006070486371645733082E-01L, /* bffc080000000000037fd87db2cb0000 */ - 3.59610068058504988294019521946586131E-32L, /* 3f967570c10687cb8e9ebd0b280abf5a */ - -1.25000000000000003700729208608337966E-01L, /* bffc00000000000002222198bbc74000 */ - 3.23464851393124362331846965931995969E-33L, /* 3f930cb95da3bfc847e593716c91d57a */ - -1.21093750000000013729038501177102555E-01L, /* bffbf000000000000fd418d1f5fda000 */ - 2.45242487730722066611358741283977619E-32L, /* 3f95fd5945ad86a464292e26ac192a84 */ - -1.17187499999999999765305306880205578E-01L, /* bffbdfffffffffffffbabaf869845000 */ - -1.14557520298960389903199646350205537E-32L, /* bf94dbda735322179d9bcf392e1dd06d */ - -1.13281250000000009579647893740755690E-01L, /* bffbd000000000000b0b69bae7ab9000 */ - 2.37873962873837390105423621772752350E-32L, /* 3f95ee0b7e0bd5ac1f6fab1e2a71abc3 */ - -1.09375000000000008981153004560108539E-01L, /* bffbc000000000000a5ac4bc1d2c3000 */ - 1.53152444860014076105003555837231015E-32L, /* 3f953e15ce931e12ef9a152522e32bdd */ - -1.05468749999999992399063850363228723E-01L, /* bffbaffffffffffff73c998091408000 */ - -8.75920903597804862471749360196688834E-33L, /* bf946bd7e310a01bae5687ebdc47fcc5 */ - -1.01562500000000007685885179918350550E-01L, /* bffba0000000000008dc7910a648c000 */ - -4.63820993797174451904075397785059501E-33L, /* bf938153d0e54001a472da180fb5e8aa */ - -9.76562499999999887262211517861331814E-02L, /* bffb8ffffffffffff300915aa6fd6000 */ - -2.63767025974952608658936466715705903E-33L, /* bf92b64215bb8d520be5404620d38088 */ - -9.37499999999999939650246024457439795E-02L, /* bffb7ffffffffffff90aca26bd0fc000 */ - -1.72047822349322956713582039121348377E-32L, /* bf9565545015c5b9b56d02cfefca2c7d */ - -8.98437500000000033088896383977486369E-02L, /* bffb70000000000003d09ca1e3cbe000 */ - 3.04831994420989436248526129869697270E-33L, /* 3f92fa7d30d2ed90e7ebbd6231fd08b1 */ - -8.59374999999999947312400115121319225E-02L, /* bffb5ffffffffffff9ecefc03376e000 */ - 1.50416954438393392150792422537312281E-32L, /* 3f9538675ee99bd722fad0023c09c915 */ - -8.20312500000000054182280847004695514E-02L, /* bffb500000000000063f2dbd40200000 */ - 2.68399664523430004488075638997207289E-33L, /* 3f92bdf49766629882c49a3da88928ed */ - -7.81250000000000114767533968079748798E-02L, /* bffb4000000000000d3b56f81ba70000 */ - 1.72318124201659121296305402819694281E-32L, /* 3f9565e407aaabfb359e8a567d760de3 */ - -7.42187500000000035531829472486812869E-02L, /* bffb3000000000000418b6e9b5388000 */ - 2.09401756478514117051383998628099655E-32L, /* 3f95b2e91221fcd74be0a86d8ad658d2 */ - -7.03124999999999987474933134860732535E-02L, /* bffb1ffffffffffffe8e53453d2ac000 */ - 2.28515798224350800271565551341211666E-32L, /* 3f95da9bd6adf00894f05b5cc5530125 */ - -6.64062500000000042267533361089054159E-02L, /* bffb10000000000004df8473dbcf2000 */ - 1.97576478800281368377376002585430031E-32L, /* 3f959a59acbddb2f53bd3096b66370e9 */ - -6.25000000000000066329769382774201686E-02L, /* bffb00000000000007a5b5914e336000 */ - -1.46422615813786836245343723048221678E-33L, /* bf91e69295f069fc0c4a9db181ea25a3 */ - -5.85937500000000002823707957982406053E-02L, /* bffae0000000000000a6aeab10592000 */ - 9.25637741701318872896718218457555829E-33L, /* 3f94807eb021f1f40a37d4015b1eb76b */ - -5.46875000000000081586888005226044448E-02L, /* bffac0000000000012d00a3171e3a000 */ - -4.87144542459404765480424673678105050E-33L, /* bf9394b42faba6b7036fe7b36269daf3 */ - -5.07812499999999927720348253140567013E-02L, /* bffa9fffffffffffef555cc8dd914000 */ - -3.01901021987395945826043649523451725E-33L, /* bf92f59e7e3025691f290f8f67277faf */ - -4.68749999999999935349476738962633103E-02L, /* bffa7ffffffffffff117b4ea2b876000 */ - 1.21521638219189777347767475937119750E-32L, /* 3f94f8c7f88c5b56674b94d984ac8ecb */ - -4.29687500000000056305562847814228219E-02L, /* bffa6000000000000cfbb19be30c0000 */ - -1.18643699217679276275559592978275214E-32L, /* bf94ecd39f0833a876550e83eb012b99 */ - -3.90624999999999962692914526031373542E-02L, /* bffa3ffffffffffff765c743922f9000 */ - -4.91277156857520035712509544689973679E-33L, /* bf939823189996193872e58ac0dececb */ - -3.51562500000000108152468207687602886E-02L, /* bffa20000000000018f031e41177f000 */ - 1.18599806302656253755207072755609820E-32L, /* 3f94eca4f23e787fab73ce8f6b9b8d64 */ - -3.12500000000000077376981036742289578E-02L, /* bffa00000000000011d787e0b386f000 */ - 9.97730386477005171963635210799577079E-33L, /* 3f949e70e498c46a0173ac0d46c699fc */ - -2.73437500000000139436129596418623235E-02L, /* bff9c00000000000404db66e70a08000 */ - 2.25755321633070123579875157841633859E-33L, /* 3f927719b1a93074bdf9f3c2cb784785 */ - -2.34375000000000088003629211828324876E-02L, /* bff98000000000002895a27d45feb000 */ - 2.84374279216848803102126617873942975E-33L, /* 3f92d87f70e749d6da6c260b68dc210b */ - -1.95312500000000107408831063404855424E-02L, /* bff9400000000000318898ba69f71000 */ - 2.47348089686935458989103979140011912E-33L, /* 3f929afa3de45086fe909fdddb41edce */ - -1.56250000000000081443917555362290635E-02L, /* bff9000000000000258f335e9cdd6000 */ - -2.43379314483517422161458863218426254E-33L, /* bf9294621c8a9ccacf2b020ec19cad27 */ - -1.17187500000000051490597418161403184E-02L, /* bff88000000000002f7ddfa26221f000 */ - 1.83405297208145390679150568810924707E-33L, /* 3f9230bbfc5d5fe1b534fbcda0465bb9 */ - -7.81249999999999715861805208310174953E-03L, /* bff7ffffffffffffcb95f3fff157d000 */ - 3.51548384878710915171654413641872451E-34L, /* 3f8fd349b76c22966f77a39fc37ed704 */ - -3.90625000000000309326013918295097128E-03L, /* bff7000000000000390f820c8e153000 */ - 6.38058004651791109324060099097251911E-36L, /* 3f8a0f665d3ac25a1ac94d688273dbcd */ +static const _Float128 __expl_table [] = { + L(-3.47656250000000000584188889839535373E-01), /* bffd640000000000002b1b04213cf000 */ + L(6.90417668990715641167244540876988960E-32), /* 3f97667c3fdb588a6ae1af8748357a17 */ + L(-3.43749999999999981853132895957607418E-01), /* bffd5ffffffffffffac4ff5f4050b000 */ + L(-7.16021898043268093462818380603370350E-33), /* bf94296c8219427edc1431ac2498583e */ + L(-3.39843750000000013418643523138766329E-01), /* bffd5c000000000003de1f027a30e000 */ + L(8.16920774283317801641347327589583265E-32), /* 3f97a82b65774bdca1b4440d749ed8d3 */ + L(-3.35937500000000014998092453039303051E-01), /* bffd5800000000000452a9f4d8857000 */ + L(-6.55865578425428447938248396879359670E-32), /* bf97548b7d240f3d034b395e6eecfac8 */ + L(-3.32031250000000000981984049529998541E-01), /* bffd540000000000004875277cda5000 */ + L(6.91213046334032232108944519541512737E-32), /* 3f9766e5f925338a19045c94443b66e1 */ + L(-3.28124999999999986646017645350399708E-01), /* bffd4ffffffffffffc26a667bf44d000 */ + L(-6.16281060996110316602421505683742661E-32), /* bf973ffdcdcffb6fbffc86b2b8d42f5d */ + L(-3.24218749999999991645717430645867963E-01), /* bffd4bfffffffffffd97901063e48000 */ + L(-7.90797211087760527593856542417304137E-32), /* bf979a9afaaca1ada6a8ed1c80584d60 */ + L(-3.20312499999999998918211610690789652E-01), /* bffd47ffffffffffffb02d9856d71000 */ + L(8.64024799457616856987630373786503376E-32), /* 3f97c0a098623f95579d5d9b2b67342d */ + L(-3.16406249999999998153974811017181883E-01), /* bffd43ffffffffffff77c991f1076000 */ + L(-2.73176610180696076418536105483668404E-32), /* bf961baeccb32f9b1fcbb8e60468e95a */ + L(-3.12500000000000011420976192575972779E-01), /* bffd400000000000034ab8240483d000 */ + L(7.16573502812389453744433792609989420E-32), /* 3f977410f4c2cfc4335f28446c0fb363 */ + L(-3.08593750000000001735496343854851414E-01), /* bffd3c000000000000800e995c176000 */ + L(-1.56292999645122272621237565671593071E-32), /* bf95449b9cbdaff6ac1246adb2c826ac */ + L(-3.04687499999999982592401295899221626E-01), /* bffd37fffffffffffafb8bc1e061a000 */ + L(6.48993208584888904958594509625158417E-32), /* 3f9750f9fe8366d82d77afa0031a92e1 */ + L(-3.00781249999999999230616898937763959E-01), /* bffd33ffffffffffffc73ac39da54000 */ + L(6.57082437496961397305801409357792029E-32), /* 3f97552d3cb598ea80135cf3feb27ec4 */ + L(-2.96874999999999998788769281703245722E-01), /* bffd2fffffffffffffa6a07fa5021000 */ + L(-3.26588297198283968096426564544269170E-32), /* bf9653260fc1802f46b629aee171809b */ + L(-2.92968750000000015318089182805941695E-01), /* bffd2c0000000000046a468614bd6000 */ + L(-1.73291974845198589684358727559290718E-32), /* bf9567e9d158f52e483c8d8dcb5961dd */ + L(-2.89062500000000007736778942676309681E-01), /* bffd280000000000023adf9f4c3d3000 */ + L(-6.83629745986675744404029225571026236E-32), /* bf9762f5face6281c1daf1c6aedbdb45 */ + L(-2.85156250000000001367091555763661937E-01), /* bffd2400000000000064dfa11e3fb000 */ + L(-5.44898442619766878281110054067026237E-32), /* bf971aed6d2db9f542986a785edae072 */ + L(-2.81249999999999986958718100227029406E-01), /* bffd1ffffffffffffc3db9265ca9d000 */ + L(1.13007318374506125723591889451107046E-32), /* 3f94d569fe387f456a97902907ac3856 */ + L(-2.77343750000000000356078829380495179E-01), /* bffd1c0000000000001a462390083000 */ + L(-4.98979365468978332358409063436543102E-32), /* bf970315bbf3e0d14b5c94c900702d4c */ + L(-2.73437499999999990276993957508540484E-01), /* bffd17fffffffffffd32919bcdc94000 */ + L(-8.79390484115892344533724650295100871E-32), /* bf97c89b0b89cc19c3ab2b60da9bbbc3 */ + L(-2.69531250000000002434203866460082225E-01), /* bffd14000000000000b39ccf9e130000 */ + L(9.44060754687026590886751809927191596E-32), /* 3f97ea2f32cfecca5c64a26137a9210f */ + L(-2.65624999999999997296320716986257179E-01), /* bffd0fffffffffffff3880f13a2bc000 */ + L(2.07142664067265697791007875348396921E-32), /* 3f95ae37ee685b9122fbe377bd205ee4 */ + L(-2.61718750000000010237478733739017956E-01), /* bffd0c000000000002f3648179d40000 */ + L(-6.10552936159265665298996309192680256E-32), /* bf973d0467d31e407515a3cca0f3b4e2 */ + L(-2.57812500000000011948220522778370303E-01), /* bffd08000000000003719f81275bd000 */ + L(6.72477169058908902499239631466443836E-32), /* 3f975d2b8c475d3160cf72d227d8e6f9 */ + L(-2.53906249999999991822993360536596860E-01), /* bffd03fffffffffffda4a4b62f818000 */ + L(-2.44868296623215865054704392917190994E-32), /* bf95fc92516c6d057d29fc2528855976 */ + L(-2.49999999999999986862019457428548084E-01), /* bffcfffffffffffff86d2d20d5ff4000 */ + L(-3.85302898949105073614122724961613078E-32), /* bf96901f147cb7d643af71b6129ce929 */ + L(-2.46093750000000000237554160737318435E-01), /* bffcf8000000000000230e8ade26b000 */ + L(-1.52823675242678363494345369284988589E-32), /* bf953d6700c5f3fc303f79d0ec8c680a */ + L(-2.42187500000000003023380963205457065E-01), /* bffcf0000000000001be2c1a78bb0000 */ + L(-7.78402037952209709489481182714311699E-34), /* bf9102ab1f3998e887f0ee4cf940faa5 */ + L(-2.38281249999999995309623303145485725E-01), /* bffce7fffffffffffd4bd2940f43f000 */ + L(-3.54307216794236899443913216397197696E-32), /* bf966fef03ab69c3f289436205b21d02 */ + L(-2.34374999999999998425804947623207526E-01), /* bffcdfffffffffffff17b097a6092000 */ + L(-2.86038428948386602859761879407549696E-32), /* bf96290a0eba0131efe3a05fe188f2e3 */ + L(-2.30468749999999993822207406785200832E-01), /* bffcd7fffffffffffc70519834eae000 */ + L(-2.54339521031747516806893838749365762E-32), /* bf96081f0ad7f9107ae6cddb32c178ab */ + L(-2.26562499999999997823524030344489884E-01), /* bffccffffffffffffebecf10093df000 */ + L(4.31904611473158635644635628922959401E-32), /* 3f96c083f0b1faa7c4c686193e38d67c */ + L(-2.22656250000000004835132405125162742E-01), /* bffcc8000000000002c98a233f19f000 */ + L(2.54709791629335691650310168420597566E-33), /* 3f92a735903f5eed07a716ab931e20d9 */ + L(-2.18749999999999988969454021829236626E-01), /* bffcbffffffffffff9a42dc14ce36000 */ + L(-3.77236096429336082213752014054909454E-32), /* bf9687be8e5b2fca54d3e81157eac660 */ + L(-2.14843750000000010613256919115758495E-01), /* bffcb80000000000061e3d828ecac000 */ + L(-4.55194148712216691177097854305964738E-32), /* bf96d8b35c776aa3e1a4768271380503 */ + L(-2.10937499999999993204656148110447201E-01), /* bffcaffffffffffffc152f2aea118000 */ + L(-2.95044199165561453749332254271716417E-32), /* bf96326433b00b2439094d9bef22ddd1 */ + L(-2.07031250000000012233944895423355677E-01), /* bffca80000000000070d695ee0e94000 */ + L(1.93146788688385419095981415411012357E-32), /* 3f959126729135a5e390d4bb802a0bde */ + L(-2.03125000000000008030983633336321863E-01), /* bffca0000000000004a129fbc51af000 */ + L(2.37361904671826193563212931215900137E-32), /* 3f95ecfb3c4ba1b97ea3ad45cbb1e68a */ + L(-1.99218750000000001763815712796132779E-01), /* bffc98000000000001044b12d9950000 */ + L(-3.63171243370923753295192486732883239E-33), /* bf932db5fb3f27c38e0fa7bbcfc64f55 */ + L(-1.95312500000000004883660234506677272E-01), /* bffc90000000000002d0b3779d1f9000 */ + L(-3.19989507343607877747980892249711601E-33), /* bf9309d63de96bb3ef744c865f22f1bd */ + L(-1.91406250000000013720152363227519348E-01), /* bffc88000000000007e8bcb387121000 */ + L(-1.89295754093147174148371614722178860E-32), /* bf958926e2e67dfe812c508290add2e7 */ + L(-1.87500000000000000182342082774432620E-01), /* bffc800000000000001ae8b06a39f000 */ + L(-2.96812835183184815200854214892983927E-32), /* bf96343a62d156bbe71f55d14ca4b6e5 */ + L(-1.83593750000000012410147185883290345E-01), /* bffc78000000000007276a1adda8d000 */ + L(-2.02191931237489669058466239995304587E-32), /* bf95a3efab92d26ec2df90df036a117f */ + L(-1.79687499999999997439177363346082917E-01), /* bffc6ffffffffffffe8616db2927d000 */ + L(-9.92752326937775530007399526834009465E-33), /* bf949c5f88ed17041e1a3f1829d543cd */ + L(-1.75781249999999995824373974504785174E-01), /* bffc67fffffffffffd97c94f13ea3000 */ + L(1.44184772065335613487885714828816178E-32), /* 3f952b75c63476e7fcc2f5841c27bcce */ + L(-1.71874999999999986685050259043077809E-01), /* bffc5ffffffffffff8530f6bc531a000 */ + L(-3.49007014971241147689894940544402482E-32), /* bf966a6dfaa012aea8ffe6d90b02330f */ + L(-1.67968749999999997316058782350439701E-01), /* bffc57fffffffffffe73eb914f2aa000 */ + L(3.34025733574205019081305778794376391E-32), /* 3f965adf4572561fd5456a6c13d8babf */ + L(-1.64062499999999993322730602128318480E-01), /* bffc4ffffffffffffc269be4f68f3000 */ + L(-1.83345916769684984022099095506340635E-32), /* bf957ccb69026cb2f6024c211576d5f4 */ + L(-1.60156249999999992419000744447607979E-01), /* bffc47fffffffffffba13df21784a000 */ + L(2.73442789798110494773517431626534726E-32), /* 3f961bf58ff22c9b30f1e2b39f26d7d5 */ + L(-1.56249999999999987665010524130393080E-01), /* bffc3ffffffffffff8e3ad45e7508000 */ + L(2.02695576464836145806428118889332191E-32), /* 3f95a4fb7435a4a2f71de81eb8ae75d1 */ + L(-1.52343749999999989905291167951491803E-01), /* bffc37fffffffffffa2e48aecfc24000 */ + L(-3.61436631548815190395331054871041524E-32), /* bf967756567ebd108075ae527cc2e7f0 */ + L(-1.48437500000000006686107754967759751E-01), /* bffc30000000000003dab20261b3c000 */ + L(-2.15524270159131591469319477922198390E-32), /* bf95bfa05b82ef3a708c4f0395e9fcf6 */ + L(-1.44531250000000005132889939177166485E-01), /* bffc28000000000002f57b1969e7b000 */ + L(2.74741116529653547935086189244019604E-32), /* 3f961d4eb77c1185d34fe1b04a3f3cf5 */ + L(-1.40625000000000000707469094533647325E-01), /* bffc2000000000000068676d3d5c4000 */ + L(4.40607097220049957013547629906723266E-33), /* 3f936e0ac425daf795b42913cf0ef881 */ + L(-1.36718749999999995713752139187543306E-01), /* bffc17fffffffffffd87762255991000 */ + L(-3.73751317180116492404578048203389108E-32), /* bf9684202491e9cbb7ceb67d9ff7e0c9 */ + L(-1.32812500000000007198453630478482191E-01), /* bffc10000000000004264de3a4379000 */ + L(-3.97050085179660203884930593717220728E-32), /* bf969c52048de14be3c9c1971e50869c */ + L(-1.28906250000000006070486371645733082E-01), /* bffc080000000000037fd87db2cb0000 */ + L(3.59610068058504988294019521946586131E-32), /* 3f967570c10687cb8e9ebd0b280abf5a */ + L(-1.25000000000000003700729208608337966E-01), /* bffc00000000000002222198bbc74000 */ + L(3.23464851393124362331846965931995969E-33), /* 3f930cb95da3bfc847e593716c91d57a */ + L(-1.21093750000000013729038501177102555E-01), /* bffbf000000000000fd418d1f5fda000 */ + L(2.45242487730722066611358741283977619E-32), /* 3f95fd5945ad86a464292e26ac192a84 */ + L(-1.17187499999999999765305306880205578E-01), /* bffbdfffffffffffffbabaf869845000 */ + L(-1.14557520298960389903199646350205537E-32), /* bf94dbda735322179d9bcf392e1dd06d */ + L(-1.13281250000000009579647893740755690E-01), /* bffbd000000000000b0b69bae7ab9000 */ + L(2.37873962873837390105423621772752350E-32), /* 3f95ee0b7e0bd5ac1f6fab1e2a71abc3 */ + L(-1.09375000000000008981153004560108539E-01), /* bffbc000000000000a5ac4bc1d2c3000 */ + L(1.53152444860014076105003555837231015E-32), /* 3f953e15ce931e12ef9a152522e32bdd */ + L(-1.05468749999999992399063850363228723E-01), /* bffbaffffffffffff73c998091408000 */ + L(-8.75920903597804862471749360196688834E-33), /* bf946bd7e310a01bae5687ebdc47fcc5 */ + L(-1.01562500000000007685885179918350550E-01), /* bffba0000000000008dc7910a648c000 */ + L(-4.63820993797174451904075397785059501E-33), /* bf938153d0e54001a472da180fb5e8aa */ + L(-9.76562499999999887262211517861331814E-02), /* bffb8ffffffffffff300915aa6fd6000 */ + L(-2.63767025974952608658936466715705903E-33), /* bf92b64215bb8d520be5404620d38088 */ + L(-9.37499999999999939650246024457439795E-02), /* bffb7ffffffffffff90aca26bd0fc000 */ + L(-1.72047822349322956713582039121348377E-32), /* bf9565545015c5b9b56d02cfefca2c7d */ + L(-8.98437500000000033088896383977486369E-02), /* bffb70000000000003d09ca1e3cbe000 */ + L(3.04831994420989436248526129869697270E-33), /* 3f92fa7d30d2ed90e7ebbd6231fd08b1 */ + L(-8.59374999999999947312400115121319225E-02), /* bffb5ffffffffffff9ecefc03376e000 */ + L(1.50416954438393392150792422537312281E-32), /* 3f9538675ee99bd722fad0023c09c915 */ + L(-8.20312500000000054182280847004695514E-02), /* bffb500000000000063f2dbd40200000 */ + L(2.68399664523430004488075638997207289E-33), /* 3f92bdf49766629882c49a3da88928ed */ + L(-7.81250000000000114767533968079748798E-02), /* bffb4000000000000d3b56f81ba70000 */ + L(1.72318124201659121296305402819694281E-32), /* 3f9565e407aaabfb359e8a567d760de3 */ + L(-7.42187500000000035531829472486812869E-02), /* bffb3000000000000418b6e9b5388000 */ + L(2.09401756478514117051383998628099655E-32), /* 3f95b2e91221fcd74be0a86d8ad658d2 */ + L(-7.03124999999999987474933134860732535E-02), /* bffb1ffffffffffffe8e53453d2ac000 */ + L(2.28515798224350800271565551341211666E-32), /* 3f95da9bd6adf00894f05b5cc5530125 */ + L(-6.64062500000000042267533361089054159E-02), /* bffb10000000000004df8473dbcf2000 */ + L(1.97576478800281368377376002585430031E-32), /* 3f959a59acbddb2f53bd3096b66370e9 */ + L(-6.25000000000000066329769382774201686E-02), /* bffb00000000000007a5b5914e336000 */ + L(-1.46422615813786836245343723048221678E-33), /* bf91e69295f069fc0c4a9db181ea25a3 */ + L(-5.85937500000000002823707957982406053E-02), /* bffae0000000000000a6aeab10592000 */ + L(9.25637741701318872896718218457555829E-33), /* 3f94807eb021f1f40a37d4015b1eb76b */ + L(-5.46875000000000081586888005226044448E-02), /* bffac0000000000012d00a3171e3a000 */ + L(-4.87144542459404765480424673678105050E-33), /* bf9394b42faba6b7036fe7b36269daf3 */ + L(-5.07812499999999927720348253140567013E-02), /* bffa9fffffffffffef555cc8dd914000 */ + L(-3.01901021987395945826043649523451725E-33), /* bf92f59e7e3025691f290f8f67277faf */ + L(-4.68749999999999935349476738962633103E-02), /* bffa7ffffffffffff117b4ea2b876000 */ + L(1.21521638219189777347767475937119750E-32), /* 3f94f8c7f88c5b56674b94d984ac8ecb */ + L(-4.29687500000000056305562847814228219E-02), /* bffa6000000000000cfbb19be30c0000 */ + L(-1.18643699217679276275559592978275214E-32), /* bf94ecd39f0833a876550e83eb012b99 */ + L(-3.90624999999999962692914526031373542E-02), /* bffa3ffffffffffff765c743922f9000 */ + L(-4.91277156857520035712509544689973679E-33), /* bf939823189996193872e58ac0dececb */ + L(-3.51562500000000108152468207687602886E-02), /* bffa20000000000018f031e41177f000 */ + L(1.18599806302656253755207072755609820E-32), /* 3f94eca4f23e787fab73ce8f6b9b8d64 */ + L(-3.12500000000000077376981036742289578E-02), /* bffa00000000000011d787e0b386f000 */ + L(9.97730386477005171963635210799577079E-33), /* 3f949e70e498c46a0173ac0d46c699fc */ + L(-2.73437500000000139436129596418623235E-02), /* bff9c00000000000404db66e70a08000 */ + L(2.25755321633070123579875157841633859E-33), /* 3f927719b1a93074bdf9f3c2cb784785 */ + L(-2.34375000000000088003629211828324876E-02), /* bff98000000000002895a27d45feb000 */ + L(2.84374279216848803102126617873942975E-33), /* 3f92d87f70e749d6da6c260b68dc210b */ + L(-1.95312500000000107408831063404855424E-02), /* bff9400000000000318898ba69f71000 */ + L(2.47348089686935458989103979140011912E-33), /* 3f929afa3de45086fe909fdddb41edce */ + L(-1.56250000000000081443917555362290635E-02), /* bff9000000000000258f335e9cdd6000 */ + L(-2.43379314483517422161458863218426254E-33), /* bf9294621c8a9ccacf2b020ec19cad27 */ + L(-1.17187500000000051490597418161403184E-02), /* bff88000000000002f7ddfa26221f000 */ + L(1.83405297208145390679150568810924707E-33), /* 3f9230bbfc5d5fe1b534fbcda0465bb9 */ + L(-7.81249999999999715861805208310174953E-03), /* bff7ffffffffffffcb95f3fff157d000 */ + L(3.51548384878710915171654413641872451E-34), /* 3f8fd349b76c22966f77a39fc37ed704 */ + L(-3.90625000000000309326013918295097128E-03), /* bff7000000000000390f820c8e153000 */ + L(6.38058004651791109324060099097251911E-36), /* 3f8a0f665d3ac25a1ac94d688273dbcd */ #define T_EXPL_ARG1 (2*89) - 0.00000000000000000000000000000000000E+00L, /* 00000000000000000000000000000000 */ - 0.00000000000000000000000000000000000E+00L, /* 00000000000000000000000000000000 */ - 3.90625000000000245479958859972588985E-03L, /* 3ff70000000000002d48769ac9874000 */ - -6.58439598384342854976169982902779828E-36L, /* bf8a1811b923e6c626b07ef29761482a */ - 7.81250000000001311374391093664996358E-03L, /* 3ff800000000000078f3f3cd89111000 */ - 2.60265650555493781464273319671555602E-33L, /* 3f92b070c3b635b87af426735a71fc87 */ - 1.17187500000000269581156218247101912E-02L, /* 3ff8800000000000f8a50d02fe20d000 */ - 1.00961747974945520631836275894919326E-33L, /* 3f914f80c1a4f8042044fe3b757b030b */ - 1.56249999999999797878275270751825475E-02L, /* 3ff8ffffffffffff45935b69da62e000 */ - 2.03174577741375590087897353146748580E-33L, /* 3f925194e863496e0f6e91cbf6b22e26 */ - 1.95312499999999760319884511789111533E-02L, /* 3ff93fffffffffff917790ff9a8f4000 */ - 4.62788519658803722282100289809515007E-33L, /* 3f9380783ba81295feeb3e4879d7d52d */ - 2.34374999999999822953909016349145918E-02L, /* 3ff97fffffffffffae5a163bd3cd5000 */ - -3.19499956304699705390404384504876533E-33L, /* bf93096e2037ced8194cf344c692f8d6 */ - 2.73437500000000137220327275871555682E-02L, /* 3ff9c000000000003f481dea5dd51000 */ - -2.25757776523031994464630107442723424E-33L, /* bf92771abcf988a02b414bf2614e3734 */ - 3.12499999999999790857640618332718621E-02L, /* 3ff9ffffffffffff9f8cd40b51509000 */ - -4.22479470489989916319395454536511458E-33L, /* bf935efb7245612f371deca17cb7b30c */ - 3.51562499999999840753382405747597346E-02L, /* 3ffa1fffffffffffdb47bd275f722000 */ - 1.08459658374118041980976756063083500E-34L, /* 3f8e2055d18b7117c9db1c318b1e889b */ - 3.90624999999999989384433621470426757E-02L, /* 3ffa3ffffffffffffd8d5e18b042e000 */ - -7.41674226146122000759491297811091830E-33L, /* bf94341454e48029e5b0205d91baffdc */ - 4.29687500000000107505739500500200462E-02L, /* 3ffa60000000000018ca04cd9085c000 */ - -4.74689012756713017494437969420919847E-34L, /* bf903b7c268103c6f7fbaaa24142e287 */ - 4.68749999999999978700749928325717352E-02L, /* 3ffa7ffffffffffffb16b6d5479e3000 */ - -1.06208165308448830117773486334902917E-32L, /* bf94b92be4b3b5b5a596a0a5187cc955 */ - 5.07812499999999815072625435955786253E-02L, /* 3ffa9fffffffffffd55bd086d5cbc000 */ - -9.37038897148383660401929567549111394E-33L, /* bf94853b111b0175b491c80d00419416 */ - 5.46874999999999809511553152189867394E-02L, /* 3ffabfffffffffffd4138bfa74a61000 */ - 1.06642963074562437340498606682822123E-32L, /* 3f94bafa3fe991b39255d563dfa05d89 */ - 5.85937500000000184331996330905145551E-02L, /* 3ffae000000000002a810a5f2f8bf000 */ - -1.76639977694797200820296641773791945E-34L, /* bf8ed596f07ce4408f1705c8ec16864c */ - 6.25000000000000021544696744852045001E-02L, /* 3ffb000000000000027be32045e2b000 */ - 1.68616371995798354366633034788947149E-32L, /* 3f955e33d7440794d8a1b25233d086ab */ - 6.64062499999999965563110718495802889E-02L, /* 3ffb0ffffffffffffc079a38a3fed000 */ - -1.82463217667830160048872113565316215E-32L, /* bf957af6163bcdb97cefab44a942482a */ - 7.03124999999999759989183341261898222E-02L, /* 3ffb1fffffffffffe454218acea05000 */ - -1.07843770101525495515646940862541503E-32L, /* bf94bff72aada26d94e76e71c07e0580 */ - 7.42187499999999898968873730710101412E-02L, /* 3ffb2ffffffffffff45a166496dc1000 */ - 1.28629441689592874462780757154138223E-32L, /* 3f950b2724597b8b93ce1e9d1cf4d035 */ - 7.81249999999999957198938523510804668E-02L, /* 3ffb3ffffffffffffb10bc52adbc5000 */ - 1.13297573459968118467100063135856856E-33L, /* 3f91787eea895b3c245899cf34ad0abd */ - 8.20312500000000199911640621145851159E-02L, /* 3ffb500000000000170c59a661a89000 */ - -1.51161335208135146756554123073528707E-32L, /* bf9539f326c5ca84e7db5401566f3775 */ - 8.59375000000000134175373433347670743E-02L, /* 3ffb6000000000000f78287547af0000 */ - 1.09763629458404270323909815379924900E-32L, /* 3f94c7f0b61b6e3e27d44b9f5bbc7e9d */ - 8.98437500000000036533922600308306335E-02L, /* 3ffb70000000000004364a83b7a14000 */ - 3.11459653680110433194288029777718358E-33L, /* 3f9302c0248136d65cebeab69488d949 */ - 9.37500000000000184977946245216914691E-02L, /* 3ffb800000000000155395d870b17000 */ - -4.66656154468277949130395786965043927E-33L, /* bf9383aec9b993b6db492b1ede786d8a */ - 9.76562500000000237839723100419376084E-02L, /* 3ffb9000000000001b6bca237f6c4000 */ - -1.03028043424658760249140747856831301E-32L, /* bf94abf6352e3d2bb398e47919a343fb */ - 1.01562500000000012345545575236836572E-01L, /* 3ffba000000000000e3bc30cd9a1f000 */ - 2.15755372310795701322789783729456319E-32L, /* 3f95c01b3b819edd9d07548fafd61550 */ - 1.05468749999999976493840484471911438E-01L, /* 3ffbafffffffffffe4e634cd77985000 */ - 1.78771847038773333029677216592309083E-32L, /* 3f95734b6ae650f33dd43c49a1df9fc0 */ - 1.09375000000000002267015055992785402E-01L, /* 3ffbc00000000000029d1ad08de7b000 */ - 6.23263106693943817730045115112427717E-33L, /* 3f9402e4b39ce2198a45e1d045868cd6 */ - 1.13281250000000022354208618429577398E-01L, /* 3ffbd0000000000019c5cc3f9d2b5000 */ - 5.40514416644786448581426756221178868E-33L, /* 3f93c10ab4021472c662f69435de9269 */ - 1.17187500000000013252367133076817603E-01L, /* 3ffbe000000000000f47688cc561b000 */ - -7.12412585457324989451327215568641325E-33L, /* bf9427ecb343a8d1758990565fcfbf45 */ - 1.21093750000000020759863992944300792E-01L, /* 3ffbf0000000000017ef3af97bf04000 */ - 6.26591408357572503875647872077266444E-33L, /* 3f940446a09a2da771b45fc075514d12 */ - 1.25000000000000004739659392396765618E-01L, /* 3ffc00000000000002bb7344ecd89000 */ - -1.55611398459729463981000080101758830E-32L, /* bf95433135febefa9e6aa4db39e263d2 */ - 1.28906249999999982360888081057894783E-01L, /* 3ffc07fffffffffff5d4ed3154361000 */ - -1.77531518652835570781208599686606474E-32L, /* bf9570b7f225ea076f97f418d11359c1 */ - 1.32812500000000010568583998727400436E-01L, /* 3ffc1000000000000617a5d09526a000 */ - 2.12104021624990594668286391598300893E-32L, /* 3f95b885d767a1048d93055927a27adc */ - 1.36718749999999998434125157367005292E-01L, /* 3ffc17ffffffffffff18eaebc7970000 */ - 2.50454798592543203967309921276955297E-32L, /* 3f9604164e5598528a76faff26cd1c97 */ - 1.40625000000000015550032422969330356E-01L, /* 3ffc20000000000008f6c79d8928c000 */ - 7.80972982879849783680252962992639832E-33L, /* 3f9444674acf2b3225c7647e0d95edf3 */ - 1.44531250000000012402535562111122522E-01L, /* 3ffc28000000000007264a8bc1ff1000 */ - 2.79662468716455159585514763921671876E-32L, /* 3f96226b095bd78aa650faf95a221993 */ - 1.48437500000000007761020440087419948E-01L, /* 3ffc3000000000000479530ff8fe3000 */ - 2.15518492972728435680556239996258527E-32L, /* 3f95bf9d49295e73a957906a029768cb */ - 1.52343750000000001733189947520484032E-01L, /* 3ffc38000000000000ffc6109f71f000 */ - 8.34032236093545825619420380704500188E-33L, /* 3f945a71851226a1d0ce5e656693153e */ - 1.56249999999999988073295321246958484E-01L, /* 3ffc3ffffffffffff91fedd62ae0f000 */ - 2.44119337150624789345260194989620908E-32L, /* 3f95fb041a57bc1c1280680ac1620bea */ - 1.60156250000000002076894210913572460E-01L, /* 3ffc48000000000001327ed84a199000 */ - -7.36124501128859978061216696286151753E-33L, /* bf9431c62f01e59d2c1e00f195a0037f */ - 1.64062500000000000950861276373482172E-01L, /* 3ffc500000000000008c5285fba85000 */ - -4.80566184447001164583855800470217373E-33L, /* bf938f3d1fcafd390f22f80e6c19421f */ - 1.67968749999999989878071706155265999E-01L, /* 3ffc57fffffffffffa2a445c548c5000 */ - -4.42154428718618459799673088733365064E-32L, /* bf96cb28cf1c1b28006d53ffe633b22a */ - 1.71874999999999999459734108403218175E-01L, /* 3ffc5fffffffffffffb04554e9dd4000 */ - -3.29736288190321377985697972236270628E-32L, /* bf96566af0ebc852e84be12859b24a31 */ - 1.75781249999999997987525759778901845E-01L, /* 3ffc67fffffffffffed702df6ffff000 */ - -1.28800728638468399687523924685844352E-32L, /* bf950b8236b88ca0c1b739dc91a7e3fc */ - 1.79687500000000004929565820437175783E-01L, /* 3ffc70000000000002d779bb32d2e000 */ - 1.60624461317978482424582320675174225E-32L, /* 3f954d9a9cc0c963fd081f3dc922d04e */ - 1.83593750000000016873727045739708856E-01L, /* 3ffc78000000000009ba1f6263c9a000 */ - -3.83390389582056606880506003118452558E-32L, /* bf968e22a5d826f77f19ee788474df22 */ - 1.87500000000000013443068740761666872E-01L, /* 3ffc80000000000007bfd8c72a1bf000 */ - -2.74141662712926256150154726565203091E-32L, /* bf961caf5ac59c7f941f928e324c2cc1 */ - 1.91406249999999981494101786848611970E-01L, /* 3ffc87fffffffffff55502eeae001000 */ - 3.68992437075565165346469517256118001E-32L, /* 3f967f2f03f9096793372a27b92ad79d */ - 1.95312499999999989069921848800501648E-01L, /* 3ffc8ffffffffffff9b3015280394000 */ - 3.69712249337856518452988332367785220E-32L, /* 3f967fee5fdb5bd501ff93516999faa0 */ - 1.99218750000000021148042946919300804E-01L, /* 3ffc9800000000000c30e67939095000 */ - 2.50142536781142175091322844848566649E-32L, /* 3f9603c34ae58e10b300b07137ee618a */ - 2.03124999999999977732559198825437141E-01L, /* 3ffc9ffffffffffff329e7df079e4000 */ - -2.41951877287895024779300892731537816E-32L, /* bf95f683aefe6965f080df8f59dd34a1 */ - 2.07031249999999996744030653771913124E-01L, /* 3ffca7fffffffffffe1f80f4b73ca000 */ - -1.94346475904454000031592792989765585E-32L, /* bf9593a44f87870a3d100d498501ecc7 */ - 2.10937500000000000251399259834392298E-01L, /* 3ffcb000000000000025199873310000 */ - -1.33528748788094249098998693871759411E-33L, /* bf91bbb9b25c813668d6103d08acac35 */ - 2.14843749999999993936323609611875097E-01L, /* 3ffcb7fffffffffffc8128c866236000 */ - 1.14839877977014974625242788556545292E-32L, /* 3f94dd06b4655c9b83a1305b240e7a42 */ - 2.18750000000000015181732784749663837E-01L, /* 3ffcc0000000000008c06da5fff24000 */ - 1.42689085313142539755499441881408391E-32L, /* 3f95285a87dfa7ea7dad5b3be8c669f4 */ - 2.22656249999999992172647770539596569E-01L, /* 3ffcc7fffffffffffb7ce2fe531f6000 */ - -3.34421462850496887359128610229650547E-32L, /* bf965b487962b5c2d9056ca6ac0c2e5c */ - 2.26562499999999989595607223847082419E-01L, /* 3ffccffffffffffffa0095277be5c000 */ - -3.08983588107248752517344356508205569E-32L, /* bf9640dded57157f8eded311213bdbcd */ - 2.30468749999999979130462438434567117E-01L, /* 3ffcd7fffffffffff3f8332996560000 */ - -3.01407539802851697849105682795217019E-32L, /* bf9638ffde35dbdfe1a1ffe45185de5d */ - 2.34375000000000012194252337217891971E-01L, /* 3ffce0000000000007078dd402c86000 */ - -8.46879710915628592284714319904522657E-33L, /* bf945fc7b29a2ac6c9eff9eb258a510f */ - 2.38281249999999982991877076137149870E-01L, /* 3ffce7fffffffffff6320b486eece000 */ - -2.93563878880439245627127095245798544E-32L, /* bf9630daaa4f40ff05caf29ace2ea7d4 */ - 2.42187499999999981447559841442773990E-01L, /* 3ffceffffffffffff54e24a09a8d5000 */ - -4.56766746558806021264215486909850481E-32L, /* bf96da556dee11f3113e5a3467b908e6 */ - 2.46093749999999991067720539980207318E-01L, /* 3ffcf7fffffffffffad9d405dcb5d000 */ - 2.14033004219908074003010247652128251E-32L, /* 3f95bc8776e8f9ae098884aa664cc3df */ - 2.50000000000000016613825838126835953E-01L, /* 3ffd00000000000004c9e24c12bb3000 */ - 2.57617532593749185996714235009382870E-32L, /* 3f960b867cc01178c0ec68226c6cb47d */ - 2.53906250000000013372004437827044321E-01L, /* 3ffd04000000000003daae05b3168000 */ - 7.20177123439204414298152646284640101E-32L, /* 3f9775eff59ddad7e7530b83934af87f */ - 2.57812499999999995765234725413886085E-01L, /* 3ffd07fffffffffffec7878bad9d5000 */ - 6.51253187532920882777046064603770602E-32L, /* 3f975226659ca241402e71c2011583b0 */ - 2.61718750000000007647689994011222248E-01L, /* 3ffd0c000000000002344cc793a0f000 */ - 3.02370610028725823590045201871491395E-32L, /* 3f9639ffe55fa2fa011674448b4e5b96 */ - 2.65624999999999986893899042596554269E-01L, /* 3ffd0ffffffffffffc38f0c0a1e9f000 */ - -2.07683715950724761146070082510569258E-32L, /* bf95af579a92e872fef81abfdf06bae8 */ - 2.69531249999999979842788204900639327E-01L, /* 3ffd13fffffffffffa30a908d67db000 */ - 8.71465252506557329027658736641075706E-32L, /* 3f97c47d99e19830447a42b1c0ffac61 */ - 2.73437500000000006712165837793818271E-01L, /* 3ffd18000000000001ef453a58edb000 */ - -6.62704045767568912140550474455810301E-32L, /* bf9758187a204dcb06ece46588aeeaba */ - 2.77343749999999994411329302988535617E-01L, /* 3ffd1bfffffffffffe63a0fec9c9e000 */ - -4.87273466291944117406493607771338767E-32L, /* bf96fa0381b0844a0be46bac2d673f0c */ - 2.81250000000000012677892447379453135E-01L, /* 3ffd20000000000003a7769e125d6000 */ - -8.55871796664700790726282049552906783E-32L, /* bf97bc64e01332cf7616b0091b8dff2c */ - 2.85156249999999998558643013736363981E-01L, /* 3ffd23ffffffffffff95a5894bccf000 */ - -1.33068334720606220176455289635046875E-32L, /* bf95145f43290ecf5b7adcb24697bc73 */ - 2.89062500000000008831431235621753924E-01L, /* 3ffd280000000000028ba504fac59000 */ - -9.34157398616814623985483776710704237E-32L, /* bf97e50ad1115b941fcb5f0c88a428f7 */ - 2.92968750000000019840235286110877063E-01L, /* 3ffd2c000000000005b7f372d184f000 */ - 4.99302093775173155906059132992249671E-33L, /* 3f939ecdcfb97bad3f8dbec5df5ec67d */ - 2.96875000000000015867911730971630513E-01L, /* 3ffd3000000000000492d860c79db000 */ - 7.86107787827057767235127454590866211E-33L, /* 3f944689517ee8f16cdb97d6a6938f32 */ - 3.00781250000000015814100002286124758E-01L, /* 3ffd340000000000048edfe73a17d000 */ - -1.65419431293024229981937172317171504E-32L, /* bf9557900e3efca16c89646b57f68dc0 */ - 3.04687499999999985213157159965287195E-01L, /* 3ffd37fffffffffffbbcec6f99b36000 */ - 9.68753602893894024018934325652944198E-32L, /* 3f97f70170e5458660c33a7e8d43d049 */ - 3.08593749999999989969324338045156215E-01L, /* 3ffd3bfffffffffffd1bdde4d0fb1000 */ - 7.10268609610294706092252562643261106E-32L, /* 3f9770cae45cdf615010401a4b37d8d4 */ - 3.12500000000000002971606591018488854E-01L, /* 3ffd40000000000000db440fbc06b000 */ - 6.38924218802905979887732294952782964E-32L, /* 3f974bbf988bb5622bd8fbaa46e8b811 */ - 3.16406250000000006594921047402056305E-01L, /* 3ffd44000000000001e69e8954814000 */ - 3.96079878754651470094149874444850097E-32L, /* 3f969b5017b9fa7a1e86975258c73d3d */ - 3.20312500000000006713799366908329147E-01L, /* 3ffd48000000000001ef64159c065000 */ - -1.86401314975634286055150437995880517E-32L, /* bf958323f0434911794e5fb8bfe136ba */ - 3.24218749999999987061246567584951210E-01L, /* 3ffd4bfffffffffffc4549db9b928000 */ - -3.18643523744758601387071062700407431E-32L, /* bf964ae5fa7e26c2c3981bed12e14372 */ - 3.28124999999999991782776266707412953E-01L, /* 3ffd4ffffffffffffda1ad0840ca8000 */ - -4.46964199751314296839915534813144652E-32L, /* bf96d0277729ffd74727150df6d15547 */ - 3.32031250000000000393816557756032682E-01L, /* 3ffd540000000000001d0efc04fad000 */ - -9.03246333902065439930373230002688649E-33L, /* bf947731a008748cc6dee948839ef7ae */ - 3.35937499999999983810482995064392173E-01L, /* 3ffd57fffffffffffb556cab8ae61000 */ - 5.27742727066129518825981597650621794E-32L, /* 3f9712050a6ddbf1cabf1b971f4b5d0b */ - 3.39843750000000004310441349760912471E-01L, /* 3ffd5c0000000000013e0def5ddc4000 */ - -3.85927263474732591932884416445586106E-32L, /* bf9690c51088ef3db9ca000829c450c2 */ - 3.43749999999999990248130003997484364E-01L, /* 3ffd5ffffffffffffd3070624a0af000 */ - 9.62005170171527308106468341512327487E-34L, /* 3f913fae595cea84432eb01430817fca */ - 3.47656250000000004085726414568625697E-01L, /* 3ffd640000000000012d79309e291000 */ - -6.59664093705705297250259434519072507E-32L, /* bf97568465eafb0e662e64a5dbfaf35f */ + L(0.00000000000000000000000000000000000E+00), /* 00000000000000000000000000000000 */ + L(0.00000000000000000000000000000000000E+00), /* 00000000000000000000000000000000 */ + L(3.90625000000000245479958859972588985E-03), /* 3ff70000000000002d48769ac9874000 */ + L(-6.58439598384342854976169982902779828E-36), /* bf8a1811b923e6c626b07ef29761482a */ + L(7.81250000000001311374391093664996358E-03), /* 3ff800000000000078f3f3cd89111000 */ + L(2.60265650555493781464273319671555602E-33), /* 3f92b070c3b635b87af426735a71fc87 */ + L(1.17187500000000269581156218247101912E-02), /* 3ff8800000000000f8a50d02fe20d000 */ + L(1.00961747974945520631836275894919326E-33), /* 3f914f80c1a4f8042044fe3b757b030b */ + L(1.56249999999999797878275270751825475E-02), /* 3ff8ffffffffffff45935b69da62e000 */ + L(2.03174577741375590087897353146748580E-33), /* 3f925194e863496e0f6e91cbf6b22e26 */ + L(1.95312499999999760319884511789111533E-02), /* 3ff93fffffffffff917790ff9a8f4000 */ + L(4.62788519658803722282100289809515007E-33), /* 3f9380783ba81295feeb3e4879d7d52d */ + L(2.34374999999999822953909016349145918E-02), /* 3ff97fffffffffffae5a163bd3cd5000 */ + L(-3.19499956304699705390404384504876533E-33), /* bf93096e2037ced8194cf344c692f8d6 */ + L(2.73437500000000137220327275871555682E-02), /* 3ff9c000000000003f481dea5dd51000 */ + L(-2.25757776523031994464630107442723424E-33), /* bf92771abcf988a02b414bf2614e3734 */ + L(3.12499999999999790857640618332718621E-02), /* 3ff9ffffffffffff9f8cd40b51509000 */ + L(-4.22479470489989916319395454536511458E-33), /* bf935efb7245612f371deca17cb7b30c */ + L(3.51562499999999840753382405747597346E-02), /* 3ffa1fffffffffffdb47bd275f722000 */ + L(1.08459658374118041980976756063083500E-34), /* 3f8e2055d18b7117c9db1c318b1e889b */ + L(3.90624999999999989384433621470426757E-02), /* 3ffa3ffffffffffffd8d5e18b042e000 */ + L(-7.41674226146122000759491297811091830E-33), /* bf94341454e48029e5b0205d91baffdc */ + L(4.29687500000000107505739500500200462E-02), /* 3ffa60000000000018ca04cd9085c000 */ + L(-4.74689012756713017494437969420919847E-34), /* bf903b7c268103c6f7fbaaa24142e287 */ + L(4.68749999999999978700749928325717352E-02), /* 3ffa7ffffffffffffb16b6d5479e3000 */ + L(-1.06208165308448830117773486334902917E-32), /* bf94b92be4b3b5b5a596a0a5187cc955 */ + L(5.07812499999999815072625435955786253E-02), /* 3ffa9fffffffffffd55bd086d5cbc000 */ + L(-9.37038897148383660401929567549111394E-33), /* bf94853b111b0175b491c80d00419416 */ + L(5.46874999999999809511553152189867394E-02), /* 3ffabfffffffffffd4138bfa74a61000 */ + L(1.06642963074562437340498606682822123E-32), /* 3f94bafa3fe991b39255d563dfa05d89 */ + L(5.85937500000000184331996330905145551E-02), /* 3ffae000000000002a810a5f2f8bf000 */ + L(-1.76639977694797200820296641773791945E-34), /* bf8ed596f07ce4408f1705c8ec16864c */ + L(6.25000000000000021544696744852045001E-02), /* 3ffb000000000000027be32045e2b000 */ + L(1.68616371995798354366633034788947149E-32), /* 3f955e33d7440794d8a1b25233d086ab */ + L(6.64062499999999965563110718495802889E-02), /* 3ffb0ffffffffffffc079a38a3fed000 */ + L(-1.82463217667830160048872113565316215E-32), /* bf957af6163bcdb97cefab44a942482a */ + L(7.03124999999999759989183341261898222E-02), /* 3ffb1fffffffffffe454218acea05000 */ + L(-1.07843770101525495515646940862541503E-32), /* bf94bff72aada26d94e76e71c07e0580 */ + L(7.42187499999999898968873730710101412E-02), /* 3ffb2ffffffffffff45a166496dc1000 */ + L(1.28629441689592874462780757154138223E-32), /* 3f950b2724597b8b93ce1e9d1cf4d035 */ + L(7.81249999999999957198938523510804668E-02), /* 3ffb3ffffffffffffb10bc52adbc5000 */ + L(1.13297573459968118467100063135856856E-33), /* 3f91787eea895b3c245899cf34ad0abd */ + L(8.20312500000000199911640621145851159E-02), /* 3ffb500000000000170c59a661a89000 */ + L(-1.51161335208135146756554123073528707E-32), /* bf9539f326c5ca84e7db5401566f3775 */ + L(8.59375000000000134175373433347670743E-02), /* 3ffb6000000000000f78287547af0000 */ + L(1.09763629458404270323909815379924900E-32), /* 3f94c7f0b61b6e3e27d44b9f5bbc7e9d */ + L(8.98437500000000036533922600308306335E-02), /* 3ffb70000000000004364a83b7a14000 */ + L(3.11459653680110433194288029777718358E-33), /* 3f9302c0248136d65cebeab69488d949 */ + L(9.37500000000000184977946245216914691E-02), /* 3ffb800000000000155395d870b17000 */ + L(-4.66656154468277949130395786965043927E-33), /* bf9383aec9b993b6db492b1ede786d8a */ + L(9.76562500000000237839723100419376084E-02), /* 3ffb9000000000001b6bca237f6c4000 */ + L(-1.03028043424658760249140747856831301E-32), /* bf94abf6352e3d2bb398e47919a343fb */ + L(1.01562500000000012345545575236836572E-01), /* 3ffba000000000000e3bc30cd9a1f000 */ + L(2.15755372310795701322789783729456319E-32), /* 3f95c01b3b819edd9d07548fafd61550 */ + L(1.05468749999999976493840484471911438E-01), /* 3ffbafffffffffffe4e634cd77985000 */ + L(1.78771847038773333029677216592309083E-32), /* 3f95734b6ae650f33dd43c49a1df9fc0 */ + L(1.09375000000000002267015055992785402E-01), /* 3ffbc00000000000029d1ad08de7b000 */ + L(6.23263106693943817730045115112427717E-33), /* 3f9402e4b39ce2198a45e1d045868cd6 */ + L(1.13281250000000022354208618429577398E-01), /* 3ffbd0000000000019c5cc3f9d2b5000 */ + L(5.40514416644786448581426756221178868E-33), /* 3f93c10ab4021472c662f69435de9269 */ + L(1.17187500000000013252367133076817603E-01), /* 3ffbe000000000000f47688cc561b000 */ + L(-7.12412585457324989451327215568641325E-33), /* bf9427ecb343a8d1758990565fcfbf45 */ + L(1.21093750000000020759863992944300792E-01), /* 3ffbf0000000000017ef3af97bf04000 */ + L(6.26591408357572503875647872077266444E-33), /* 3f940446a09a2da771b45fc075514d12 */ + L(1.25000000000000004739659392396765618E-01), /* 3ffc00000000000002bb7344ecd89000 */ + L(-1.55611398459729463981000080101758830E-32), /* bf95433135febefa9e6aa4db39e263d2 */ + L(1.28906249999999982360888081057894783E-01), /* 3ffc07fffffffffff5d4ed3154361000 */ + L(-1.77531518652835570781208599686606474E-32), /* bf9570b7f225ea076f97f418d11359c1 */ + L(1.32812500000000010568583998727400436E-01), /* 3ffc1000000000000617a5d09526a000 */ + L(2.12104021624990594668286391598300893E-32), /* 3f95b885d767a1048d93055927a27adc */ + L(1.36718749999999998434125157367005292E-01), /* 3ffc17ffffffffffff18eaebc7970000 */ + L(2.50454798592543203967309921276955297E-32), /* 3f9604164e5598528a76faff26cd1c97 */ + L(1.40625000000000015550032422969330356E-01), /* 3ffc20000000000008f6c79d8928c000 */ + L(7.80972982879849783680252962992639832E-33), /* 3f9444674acf2b3225c7647e0d95edf3 */ + L(1.44531250000000012402535562111122522E-01), /* 3ffc28000000000007264a8bc1ff1000 */ + L(2.79662468716455159585514763921671876E-32), /* 3f96226b095bd78aa650faf95a221993 */ + L(1.48437500000000007761020440087419948E-01), /* 3ffc3000000000000479530ff8fe3000 */ + L(2.15518492972728435680556239996258527E-32), /* 3f95bf9d49295e73a957906a029768cb */ + L(1.52343750000000001733189947520484032E-01), /* 3ffc38000000000000ffc6109f71f000 */ + L(8.34032236093545825619420380704500188E-33), /* 3f945a71851226a1d0ce5e656693153e */ + L(1.56249999999999988073295321246958484E-01), /* 3ffc3ffffffffffff91fedd62ae0f000 */ + L(2.44119337150624789345260194989620908E-32), /* 3f95fb041a57bc1c1280680ac1620bea */ + L(1.60156250000000002076894210913572460E-01), /* 3ffc48000000000001327ed84a199000 */ + L(-7.36124501128859978061216696286151753E-33), /* bf9431c62f01e59d2c1e00f195a0037f */ + L(1.64062500000000000950861276373482172E-01), /* 3ffc500000000000008c5285fba85000 */ + L(-4.80566184447001164583855800470217373E-33), /* bf938f3d1fcafd390f22f80e6c19421f */ + L(1.67968749999999989878071706155265999E-01), /* 3ffc57fffffffffffa2a445c548c5000 */ + L(-4.42154428718618459799673088733365064E-32), /* bf96cb28cf1c1b28006d53ffe633b22a */ + L(1.71874999999999999459734108403218175E-01), /* 3ffc5fffffffffffffb04554e9dd4000 */ + L(-3.29736288190321377985697972236270628E-32), /* bf96566af0ebc852e84be12859b24a31 */ + L(1.75781249999999997987525759778901845E-01), /* 3ffc67fffffffffffed702df6ffff000 */ + L(-1.28800728638468399687523924685844352E-32), /* bf950b8236b88ca0c1b739dc91a7e3fc */ + L(1.79687500000000004929565820437175783E-01), /* 3ffc70000000000002d779bb32d2e000 */ + L(1.60624461317978482424582320675174225E-32), /* 3f954d9a9cc0c963fd081f3dc922d04e */ + L(1.83593750000000016873727045739708856E-01), /* 3ffc78000000000009ba1f6263c9a000 */ + L(-3.83390389582056606880506003118452558E-32), /* bf968e22a5d826f77f19ee788474df22 */ + L(1.87500000000000013443068740761666872E-01), /* 3ffc80000000000007bfd8c72a1bf000 */ + L(-2.74141662712926256150154726565203091E-32), /* bf961caf5ac59c7f941f928e324c2cc1 */ + L(1.91406249999999981494101786848611970E-01), /* 3ffc87fffffffffff55502eeae001000 */ + L(3.68992437075565165346469517256118001E-32), /* 3f967f2f03f9096793372a27b92ad79d */ + L(1.95312499999999989069921848800501648E-01), /* 3ffc8ffffffffffff9b3015280394000 */ + L(3.69712249337856518452988332367785220E-32), /* 3f967fee5fdb5bd501ff93516999faa0 */ + L(1.99218750000000021148042946919300804E-01), /* 3ffc9800000000000c30e67939095000 */ + L(2.50142536781142175091322844848566649E-32), /* 3f9603c34ae58e10b300b07137ee618a */ + L(2.03124999999999977732559198825437141E-01), /* 3ffc9ffffffffffff329e7df079e4000 */ + L(-2.41951877287895024779300892731537816E-32), /* bf95f683aefe6965f080df8f59dd34a1 */ + L(2.07031249999999996744030653771913124E-01), /* 3ffca7fffffffffffe1f80f4b73ca000 */ + L(-1.94346475904454000031592792989765585E-32), /* bf9593a44f87870a3d100d498501ecc7 */ + L(2.10937500000000000251399259834392298E-01), /* 3ffcb000000000000025199873310000 */ + L(-1.33528748788094249098998693871759411E-33), /* bf91bbb9b25c813668d6103d08acac35 */ + L(2.14843749999999993936323609611875097E-01), /* 3ffcb7fffffffffffc8128c866236000 */ + L(1.14839877977014974625242788556545292E-32), /* 3f94dd06b4655c9b83a1305b240e7a42 */ + L(2.18750000000000015181732784749663837E-01), /* 3ffcc0000000000008c06da5fff24000 */ + L(1.42689085313142539755499441881408391E-32), /* 3f95285a87dfa7ea7dad5b3be8c669f4 */ + L(2.22656249999999992172647770539596569E-01), /* 3ffcc7fffffffffffb7ce2fe531f6000 */ + L(-3.34421462850496887359128610229650547E-32), /* bf965b487962b5c2d9056ca6ac0c2e5c */ + L(2.26562499999999989595607223847082419E-01), /* 3ffccffffffffffffa0095277be5c000 */ + L(-3.08983588107248752517344356508205569E-32), /* bf9640dded57157f8eded311213bdbcd */ + L(2.30468749999999979130462438434567117E-01), /* 3ffcd7fffffffffff3f8332996560000 */ + L(-3.01407539802851697849105682795217019E-32), /* bf9638ffde35dbdfe1a1ffe45185de5d */ + L(2.34375000000000012194252337217891971E-01), /* 3ffce0000000000007078dd402c86000 */ + L(-8.46879710915628592284714319904522657E-33), /* bf945fc7b29a2ac6c9eff9eb258a510f */ + L(2.38281249999999982991877076137149870E-01), /* 3ffce7fffffffffff6320b486eece000 */ + L(-2.93563878880439245627127095245798544E-32), /* bf9630daaa4f40ff05caf29ace2ea7d4 */ + L(2.42187499999999981447559841442773990E-01), /* 3ffceffffffffffff54e24a09a8d5000 */ + L(-4.56766746558806021264215486909850481E-32), /* bf96da556dee11f3113e5a3467b908e6 */ + L(2.46093749999999991067720539980207318E-01), /* 3ffcf7fffffffffffad9d405dcb5d000 */ + L(2.14033004219908074003010247652128251E-32), /* 3f95bc8776e8f9ae098884aa664cc3df */ + L(2.50000000000000016613825838126835953E-01), /* 3ffd00000000000004c9e24c12bb3000 */ + L(2.57617532593749185996714235009382870E-32), /* 3f960b867cc01178c0ec68226c6cb47d */ + L(2.53906250000000013372004437827044321E-01), /* 3ffd04000000000003daae05b3168000 */ + L(7.20177123439204414298152646284640101E-32), /* 3f9775eff59ddad7e7530b83934af87f */ + L(2.57812499999999995765234725413886085E-01), /* 3ffd07fffffffffffec7878bad9d5000 */ + L(6.51253187532920882777046064603770602E-32), /* 3f975226659ca241402e71c2011583b0 */ + L(2.61718750000000007647689994011222248E-01), /* 3ffd0c000000000002344cc793a0f000 */ + L(3.02370610028725823590045201871491395E-32), /* 3f9639ffe55fa2fa011674448b4e5b96 */ + L(2.65624999999999986893899042596554269E-01), /* 3ffd0ffffffffffffc38f0c0a1e9f000 */ + L(-2.07683715950724761146070082510569258E-32), /* bf95af579a92e872fef81abfdf06bae8 */ + L(2.69531249999999979842788204900639327E-01), /* 3ffd13fffffffffffa30a908d67db000 */ + L(8.71465252506557329027658736641075706E-32), /* 3f97c47d99e19830447a42b1c0ffac61 */ + L(2.73437500000000006712165837793818271E-01), /* 3ffd18000000000001ef453a58edb000 */ + L(-6.62704045767568912140550474455810301E-32), /* bf9758187a204dcb06ece46588aeeaba */ + L(2.77343749999999994411329302988535617E-01), /* 3ffd1bfffffffffffe63a0fec9c9e000 */ + L(-4.87273466291944117406493607771338767E-32), /* bf96fa0381b0844a0be46bac2d673f0c */ + L(2.81250000000000012677892447379453135E-01), /* 3ffd20000000000003a7769e125d6000 */ + L(-8.55871796664700790726282049552906783E-32), /* bf97bc64e01332cf7616b0091b8dff2c */ + L(2.85156249999999998558643013736363981E-01), /* 3ffd23ffffffffffff95a5894bccf000 */ + L(-1.33068334720606220176455289635046875E-32), /* bf95145f43290ecf5b7adcb24697bc73 */ + L(2.89062500000000008831431235621753924E-01), /* 3ffd280000000000028ba504fac59000 */ + L(-9.34157398616814623985483776710704237E-32), /* bf97e50ad1115b941fcb5f0c88a428f7 */ + L(2.92968750000000019840235286110877063E-01), /* 3ffd2c000000000005b7f372d184f000 */ + L(4.99302093775173155906059132992249671E-33), /* 3f939ecdcfb97bad3f8dbec5df5ec67d */ + L(2.96875000000000015867911730971630513E-01), /* 3ffd3000000000000492d860c79db000 */ + L(7.86107787827057767235127454590866211E-33), /* 3f944689517ee8f16cdb97d6a6938f32 */ + L(3.00781250000000015814100002286124758E-01), /* 3ffd340000000000048edfe73a17d000 */ + L(-1.65419431293024229981937172317171504E-32), /* bf9557900e3efca16c89646b57f68dc0 */ + L(3.04687499999999985213157159965287195E-01), /* 3ffd37fffffffffffbbcec6f99b36000 */ + L(9.68753602893894024018934325652944198E-32), /* 3f97f70170e5458660c33a7e8d43d049 */ + L(3.08593749999999989969324338045156215E-01), /* 3ffd3bfffffffffffd1bdde4d0fb1000 */ + L(7.10268609610294706092252562643261106E-32), /* 3f9770cae45cdf615010401a4b37d8d4 */ + L(3.12500000000000002971606591018488854E-01), /* 3ffd40000000000000db440fbc06b000 */ + L(6.38924218802905979887732294952782964E-32), /* 3f974bbf988bb5622bd8fbaa46e8b811 */ + L(3.16406250000000006594921047402056305E-01), /* 3ffd44000000000001e69e8954814000 */ + L(3.96079878754651470094149874444850097E-32), /* 3f969b5017b9fa7a1e86975258c73d3d */ + L(3.20312500000000006713799366908329147E-01), /* 3ffd48000000000001ef64159c065000 */ + L(-1.86401314975634286055150437995880517E-32), /* bf958323f0434911794e5fb8bfe136ba */ + L(3.24218749999999987061246567584951210E-01), /* 3ffd4bfffffffffffc4549db9b928000 */ + L(-3.18643523744758601387071062700407431E-32), /* bf964ae5fa7e26c2c3981bed12e14372 */ + L(3.28124999999999991782776266707412953E-01), /* 3ffd4ffffffffffffda1ad0840ca8000 */ + L(-4.46964199751314296839915534813144652E-32), /* bf96d0277729ffd74727150df6d15547 */ + L(3.32031250000000000393816557756032682E-01), /* 3ffd540000000000001d0efc04fad000 */ + L(-9.03246333902065439930373230002688649E-33), /* bf947731a008748cc6dee948839ef7ae */ + L(3.35937499999999983810482995064392173E-01), /* 3ffd57fffffffffffb556cab8ae61000 */ + L(5.27742727066129518825981597650621794E-32), /* 3f9712050a6ddbf1cabf1b971f4b5d0b */ + L(3.39843750000000004310441349760912471E-01), /* 3ffd5c0000000000013e0def5ddc4000 */ + L(-3.85927263474732591932884416445586106E-32), /* bf9690c51088ef3db9ca000829c450c2 */ + L(3.43749999999999990248130003997484364E-01), /* 3ffd5ffffffffffffd3070624a0af000 */ + L(9.62005170171527308106468341512327487E-34), /* 3f913fae595cea84432eb01430817fca */ + L(3.47656250000000004085726414568625697E-01), /* 3ffd640000000000012d79309e291000 */ + L(-6.59664093705705297250259434519072507E-32), /* bf97568465eafb0e662e64a5dbfaf35f */ - -1.98364257812501251077851763965418372E-03L, /* bff6040000000001cd90f658cf0b1000 */ - -3.71984513103117734260309047540278737E-34L, /* bf8fee73c54483194782aac4a6154d11 */ - -1.95312500000000378520649630233891879E-03L, /* bff60000000000008ba643bb5e2e8000 */ - -1.12194202736719050440745599339855038E-34L, /* bf8e2a436aeff7bc529873354f47a3f5 */ - -1.92260742187499397430259771221991482E-03L, /* bff5f7fffffffffe4361cb51170da000 */ - -2.30068299876822157331268484824540848E-34L, /* bf8f31d02f85cfe8c0cc02276ce0f437 */ - -1.89208984375001137424603270262074989E-03L, /* bff5f0000000000347456ed490c23000 */ - -1.15012507244426243338260435466985403E-34L, /* bf8e31c174d5677a937a34ad8d2a70b4 */ - -1.86157226562500172319250342061336738E-03L, /* bff5e800000000007f262fa3617b4000 */ - -3.12438344643346437509767736937785561E-34L, /* bf8f9f4d426a2457c273d34ef7d9bde9 */ - -1.83105468749999505256246872355430379E-03L, /* bff5dffffffffffe92f18c1c2b6fa000 */ - -5.91130415288336591179087455220308942E-35L, /* bf8d3a4c80b42dc036bae446c9807f78 */ - -1.80053710937499445182387245573120522E-03L, /* bff5d7fffffffffe669dea82b4a4c000 */ - -1.92396289352411531324908916321392100E-34L, /* bf8eff7a2123fb573ba9778550d669bd */ - -1.77001953125000387737631542516323906E-03L, /* bff5d000000000011e19915c3ddb7000 */ - 7.91101758977203355387806553469731354E-36L, /* 3f8a507f5a70faaccf469e3461873dea */ - -1.73950195312500034854670281415554486E-03L, /* bff5c8000000000019b7dc6ef97bd000 */ - 1.55906551582436824067407021178835755E-34L, /* 3f8e9e7880333e34955aebcde3cfb053 */ - -1.70898437499998955782591472611429852E-03L, /* bff5bffffffffffcfd80e88aa6b96000 */ - 8.22951661962611381718215899498500357E-35L, /* 3f8db58e6031a779b59f6ece191de7cc */ - -1.67846679687500586652037711131708544E-03L, /* bff5b80000000001b0df6fd21c133000 */ - -8.96642618848426299713145894522897419E-35L, /* bf8ddcbcab46d531801bfae4121f2f8a */ - -1.64794921875000109499161354039904782E-03L, /* bff5b0000000000050cbce8915575000 */ - -2.88077905394253859590587789680486639E-34L, /* bf8f7eebd4dd860ef73b674d5e707959 */ - -1.61743164062501133830507079150388351E-03L, /* bff5a80000000003449e8700c3e82000 */ - -3.68271725851639066312899986829350273E-34L, /* bf8fe9845fe20a5fe74059e0cae185d6 */ - -1.58691406249999015546015764131101956E-03L, /* bff59ffffffffffd2999e668cdd28000 */ - 8.48197657099957029953716507898788812E-35L, /* 3f8dc2faaebb97392e451b07b28c4b12 */ - -1.55639648437500317366570219290722587E-03L, /* bff5980000000000ea2cd9a40d256000 */ - -3.45156704719737676412949957712570373E-36L, /* bf8925a079505516c8e317ac1ff53255 */ - -1.52587890625000568759013197767046039E-03L, /* bff5900000000001a3ab8a3f6b698000 */ - -1.01902948542497496574967177677556729E-34L, /* bf8e0ee78d94d9b5ad3d63ae35c9b554 */ - -1.49536132812500945889014955936485340E-03L, /* bff5880000000002b9f1621b57743000 */ - -3.32264697086631598830366079048117140E-34L, /* bf8fb9a7d14c32289204fbb0c9eb20e0 */ - -1.46484374999999931883259902869504725E-03L, /* bff57fffffffffffcdbd1c90e1b4a000 */ - -1.76487524793892929381101031660811433E-34L, /* bf8ed52f2f724bc1ae870b18356337b4 */ - -1.43432617187498876325946983333888768E-03L, /* bff577fffffffffcc2dff8faa5570000 */ - -3.54550084538495708816233114576143814E-34L, /* bf8fd74724576915868c1e8ce9f430f1 */ - -1.40380859374999215367421282192718062E-03L, /* bff56ffffffffffdbd0b18aac65ed000 */ - -1.90585907028351204486765167064669639E-34L, /* bf8efaaa0c0e23e50c11b2120348054f */ - -1.37329101562499692341771212945644892E-03L, /* bff567ffffffffff1cfd00f1b0577000 */ - -3.59631150411372589637918252836880320E-34L, /* bf8fde08239ac74942a46298ea4fb715 */ - -1.34277343749999137467356674296739172E-03L, /* bff55ffffffffffd839030b05d53d000 */ - -1.49571076125940368185068762485268117E-35L, /* bf8b3e1a3d5c684b27a9f835b1d8d3c9 */ - -1.31225585937499247038404301859788734E-03L, /* bff557fffffffffdd469936e691e3000 */ - 3.10375845385355395586146533282311300E-34L, /* 3f8f9c8f6d63b7a4145716ffd92491fb */ - -1.28173828124999024755581675764821898E-03L, /* bff54ffffffffffd306589b0ab21d000 */ - -1.98541096105909793397376077900810019E-34L, /* bf8f07e808bbb1e35106c294ffbb9687 */ - -1.25122070312500340204619591143332523E-03L, /* bff5480000000000fb06d5f16ad2c000 */ - 3.62884195935761446237911443317457521E-34L, /* 3f8fe25b17d623178a386a6fa6c5afb2 */ - -1.22070312499999591578388993012071279E-03L, /* bff53ffffffffffed2a356c440074000 */ - -2.96756662615653130862526710937493307E-35L, /* bf8c3b90d8ff2a991e5bd16718fb0645 */ - -1.19018554687498821966212632349422735E-03L, /* bff537fffffffffc9ac3b585dda89000 */ - 1.44659971891167323357060028901142644E-34L, /* 3f8e809279ab249edf1dad9fe13fb0bf */ - -1.15966796875000160938908064907298384E-03L, /* bff530000000000076c0800db9639000 */ - 2.50088010538742402346270685365928513E-34L, /* 3f8f4c6c8a483b60201d30c1a83c3cb7 */ - -1.12915039062500267151512523291939657E-03L, /* bff5280000000000c51f7e7315137000 */ - 7.56402096465615210500092443924888831E-35L, /* 3f8d922c1e485d99aea2668ed32b55a6 */ - -1.09863281249998665006360103291051571E-03L, /* bff51ffffffffffc26f2d4c9ce2ba000 */ - 1.43982174467233642713619821353592061E-34L, /* 3f8e7ec530b3d92b6303bec1c81214d1 */ - -1.06811523437500522742248711752028025E-03L, /* bff518000000000181b7380f10446000 */ - 5.41265133745862349181293024531133174E-35L, /* 3f8d1fc9313d018b30e790e06b6be723 */ - -1.03759765624999980942114138999770552E-03L, /* bff50ffffffffffff1f01130490e1000 */ - 1.21525139612685854366189534669623436E-34L, /* 3f8e4311b96b6fcde412caf3f0d86fb9 */ - -1.00708007812499602697537601515759439E-03L, /* bff507fffffffffedad7afcce7051000 */ - 1.00020246351201558505328236381833392E-34L, /* 3f8e09e640992512b1300744a7e984ed */ - -9.76562499999992592487302113340463694E-04L, /* bff4fffffffffffbbad8151f8adf6000 */ - -1.64984406575162932060422892046851002E-34L, /* bf8eb69a919986e8054b86fc34300f24 */ - -9.46044921874989085824996924138179594E-04L, /* bff4effffffffff9b55a204fd9792000 */ - -9.29539174108308550334255350011347171E-35L, /* bf8dee3a50ed896b4656fa577a1df3d7 */ - -9.15527343750013735214860599791540029E-04L, /* bff4e00000000007eaf5bf103f82d000 */ - 3.07557018309280519949818825519490586E-35L, /* 3f8c470cfbef77d32c74cb8042f6ee81 */ - -8.85009765625012292294986105781516428E-04L, /* bff4d000000000071605c65403b97000 */ - 4.77499983783821950338363358545463558E-35L, /* 3f8cfbc3dc18884c4c4f9e07d90d7bd3 */ - -8.54492187499986941239470706817188192E-04L, /* bff4bffffffffff878ddf9cab264a000 */ - -1.60128240346239526958630011447901568E-34L, /* bf8ea9b1a21e19e2d5bd84b0fbffcf95 */ - -8.23974609374996290174598690241743810E-04L, /* bff4affffffffffddc86c249ebe06000 */ - 1.61677540391961912631535763471935882E-34L, /* 3f8eadd00841366b0dc2bc262c2c8c36 */ - -7.93457031249988696952538334288757473E-04L, /* bff49ffffffffff97bf6f0aa85a5f000 */ - 1.22318577008381887076634753347515709E-34L, /* 3f8e452db5b5d250878f71040da06d14 */ - -7.62939453124996723316499040007097041E-04L, /* bff48ffffffffffe1c7265b431108000 */ - -1.03845161748762410745671891558398468E-34L, /* bf8e14115ad884c96d1a820c73647220 */ - -7.32421874999998242520117923997325794E-04L, /* bff47ffffffffffefca4498b7aa8a000 */ - 5.64005211953031009549514026639438083E-35L, /* 3f8d2be06950f68f1a6d8ff829a6928e */ - -7.01904296874999772890934814265622012E-04L, /* bff46fffffffffffde7c0fe5d8041000 */ - 5.90245467325173644235991233229525762E-35L, /* 3f8d39d40cc49002189243c194b1db0e */ - -6.71386718750008699269643939210658742E-04L, /* bff460000000000503c91d798b60c000 */ - -5.20515801723324452151498579012322191E-35L, /* bf8d14c0f08a6a9285b32b8bda003eb5 */ - -6.40869140625005499535275057463709988E-04L, /* bff45000000000032b969184e9751000 */ - -6.69469163285461870099846471658294534E-35L, /* bf8d63f36bab7b24d936c9380e3d3fa6 */ - -6.10351562499999293780097329596079841E-04L, /* bff43fffffffffff97c7c433e35ed000 */ - -1.16941808547394177991845382085515086E-34L, /* bf8e36e27886f10b234a7dd8fc588bf0 */ - -5.79833984375000068291972326409994795E-04L, /* bff43000000000000a13ff6dcf2bf000 */ - 1.17885044988246219185041488459766001E-34L, /* 3f8e3964677e001a00412aab52790842 */ - -5.49316406249990904622170867910987793E-04L, /* bff41ffffffffffac1c25739c716b000 */ - -3.31875702128137033065075734368960972E-35L, /* bf8c60e928d8982c3c99aef4f885a121 */ - -5.18798828125011293653756992177727236E-04L, /* bff410000000000682a62cff36775000 */ - -5.69971237642088463334239430962628187E-35L, /* bf8d2f0c76f8757d61cd1abc7ea7d066 */ - -4.88281249999990512232251384917893121E-04L, /* bff3fffffffffff50fb48992320df000 */ - 1.02144616714408655325510171265051108E-35L, /* 3f8ab279a3626612710b9b3ac71734ac */ - -4.57763671874997554564967307956493434E-04L, /* bff3dffffffffffd2e3c272e3cca9000 */ - -8.25484058867957231164162481843653503E-35L, /* bf8db6e71158e7bf93e2e683f07aa841 */ - -4.27246093749991203999790346349633286E-04L, /* bff3bffffffffff5dbe103cba0eb2000 */ - -3.51191203319375193921924105905691755E-35L, /* bf8c757356d0f3dd7fbefc0dd419ab50 */ - -3.96728515624986649402960638705483281E-04L, /* bff39ffffffffff09b996882706ec000 */ - -5.51925962073095883016589497244931171E-36L, /* bf89d586d49f22289cfc860bebb99056 */ - -3.66210937499999945095511981300980754E-04L, /* bff37fffffffffffefcb88bfc7df6000 */ - -2.11696465278144529364423332249588595E-35L, /* bf8bc23a84d28e5496c874ef9833be25 */ - -3.35693359374992480958458008559640163E-04L, /* bff35ffffffffff754c548a8798f2000 */ - -8.58941791799705081104736787493668352E-35L, /* bf8dc8b1192fb7c3662826d43acb7c68 */ - -3.05175781250009811036303273640122156E-04L, /* bff340000000000b4fb4f1aad1c76000 */ - -8.61173897858769926480551302277426632E-35L, /* bf8dc9e0eabb1c0b33051011b64769fa */ - -2.74658203124987298321920308390303850E-04L, /* bff31ffffffffff15b2056ac252fd000 */ - 3.35152809454778381053519808988046631E-37L, /* 3f85c82fb59ff8d7c80d44e635420ab1 */ - -2.44140624999999992770514819575735516E-04L, /* bff2fffffffffffffbbb82d6a7636000 */ - 3.54445837111124472730013879165516908E-35L, /* 3f8c78e955b01378be647b1c92aa9a77 */ - -2.13623046875012756463165168672749438E-04L, /* bff2c0000000001d6a1635fea6bbf000 */ - 1.50050816288650121729916777279129473E-35L, /* 3f8b3f1f6f616a61129a58e131cbd31d */ - -1.83105468749991323078784464300306893E-04L, /* bff27fffffffffebfe0cbd0c82399000 */ - -9.14919506501448661140572099029756008E-37L, /* bf873754bacaa9d9513b6127e791eb47 */ - -1.52587890625013337032336300236461546E-04L, /* bff240000000001ec0cb57f2cc995000 */ - 2.84906084373176180870418394956384516E-35L, /* 3f8c2ef6d03a7e6ab087c4f099e4de89 */ - -1.22070312499990746786116828458007518E-04L, /* bff1ffffffffffd553bbb49f35a34000 */ - 6.71618008964968339584520728412444537E-36L, /* 3f8a1dacb99c60071fc9cd2349495bf0 */ - -9.15527343750029275602791047595142231E-05L, /* bff180000000000d8040cd6ecde28000 */ - -1.95753652091078750312541716951402172E-35L, /* bf8ba0526cfb24d8d59122f1c7a09a14 */ - -6.10351562499913258461494008080572701E-05L, /* bff0ffffffffffaffebbb92d7f6a9000 */ - 5.69868489273961111703398456218119973E-36L, /* 3f89e4ca5df09ef4a4386dd5b3bf0331 */ - -3.05175781250092882818419203884960853E-05L, /* bff0000000000055ab55de88fac1d000 */ - 9.03341100018476837609128961872915953E-36L, /* 3f8a803d229fa3a0e834a63abb06662b */ + L(-1.98364257812501251077851763965418372E-03), /* bff6040000000001cd90f658cf0b1000 */ + L(-3.71984513103117734260309047540278737E-34), /* bf8fee73c54483194782aac4a6154d11 */ + L(-1.95312500000000378520649630233891879E-03), /* bff60000000000008ba643bb5e2e8000 */ + L(-1.12194202736719050440745599339855038E-34), /* bf8e2a436aeff7bc529873354f47a3f5 */ + L(-1.92260742187499397430259771221991482E-03), /* bff5f7fffffffffe4361cb51170da000 */ + L(-2.30068299876822157331268484824540848E-34), /* bf8f31d02f85cfe8c0cc02276ce0f437 */ + L(-1.89208984375001137424603270262074989E-03), /* bff5f0000000000347456ed490c23000 */ + L(-1.15012507244426243338260435466985403E-34), /* bf8e31c174d5677a937a34ad8d2a70b4 */ + L(-1.86157226562500172319250342061336738E-03), /* bff5e800000000007f262fa3617b4000 */ + L(-3.12438344643346437509767736937785561E-34), /* bf8f9f4d426a2457c273d34ef7d9bde9 */ + L(-1.83105468749999505256246872355430379E-03), /* bff5dffffffffffe92f18c1c2b6fa000 */ + L(-5.91130415288336591179087455220308942E-35), /* bf8d3a4c80b42dc036bae446c9807f78 */ + L(-1.80053710937499445182387245573120522E-03), /* bff5d7fffffffffe669dea82b4a4c000 */ + L(-1.92396289352411531324908916321392100E-34), /* bf8eff7a2123fb573ba9778550d669bd */ + L(-1.77001953125000387737631542516323906E-03), /* bff5d000000000011e19915c3ddb7000 */ + L(7.91101758977203355387806553469731354E-36), /* 3f8a507f5a70faaccf469e3461873dea */ + L(-1.73950195312500034854670281415554486E-03), /* bff5c8000000000019b7dc6ef97bd000 */ + L(1.55906551582436824067407021178835755E-34), /* 3f8e9e7880333e34955aebcde3cfb053 */ + L(-1.70898437499998955782591472611429852E-03), /* bff5bffffffffffcfd80e88aa6b96000 */ + L(8.22951661962611381718215899498500357E-35), /* 3f8db58e6031a779b59f6ece191de7cc */ + L(-1.67846679687500586652037711131708544E-03), /* bff5b80000000001b0df6fd21c133000 */ + L(-8.96642618848426299713145894522897419E-35), /* bf8ddcbcab46d531801bfae4121f2f8a */ + L(-1.64794921875000109499161354039904782E-03), /* bff5b0000000000050cbce8915575000 */ + L(-2.88077905394253859590587789680486639E-34), /* bf8f7eebd4dd860ef73b674d5e707959 */ + L(-1.61743164062501133830507079150388351E-03), /* bff5a80000000003449e8700c3e82000 */ + L(-3.68271725851639066312899986829350273E-34), /* bf8fe9845fe20a5fe74059e0cae185d6 */ + L(-1.58691406249999015546015764131101956E-03), /* bff59ffffffffffd2999e668cdd28000 */ + L(8.48197657099957029953716507898788812E-35), /* 3f8dc2faaebb97392e451b07b28c4b12 */ + L(-1.55639648437500317366570219290722587E-03), /* bff5980000000000ea2cd9a40d256000 */ + L(-3.45156704719737676412949957712570373E-36), /* bf8925a079505516c8e317ac1ff53255 */ + L(-1.52587890625000568759013197767046039E-03), /* bff5900000000001a3ab8a3f6b698000 */ + L(-1.01902948542497496574967177677556729E-34), /* bf8e0ee78d94d9b5ad3d63ae35c9b554 */ + L(-1.49536132812500945889014955936485340E-03), /* bff5880000000002b9f1621b57743000 */ + L(-3.32264697086631598830366079048117140E-34), /* bf8fb9a7d14c32289204fbb0c9eb20e0 */ + L(-1.46484374999999931883259902869504725E-03), /* bff57fffffffffffcdbd1c90e1b4a000 */ + L(-1.76487524793892929381101031660811433E-34), /* bf8ed52f2f724bc1ae870b18356337b4 */ + L(-1.43432617187498876325946983333888768E-03), /* bff577fffffffffcc2dff8faa5570000 */ + L(-3.54550084538495708816233114576143814E-34), /* bf8fd74724576915868c1e8ce9f430f1 */ + L(-1.40380859374999215367421282192718062E-03), /* bff56ffffffffffdbd0b18aac65ed000 */ + L(-1.90585907028351204486765167064669639E-34), /* bf8efaaa0c0e23e50c11b2120348054f */ + L(-1.37329101562499692341771212945644892E-03), /* bff567ffffffffff1cfd00f1b0577000 */ + L(-3.59631150411372589637918252836880320E-34), /* bf8fde08239ac74942a46298ea4fb715 */ + L(-1.34277343749999137467356674296739172E-03), /* bff55ffffffffffd839030b05d53d000 */ + L(-1.49571076125940368185068762485268117E-35), /* bf8b3e1a3d5c684b27a9f835b1d8d3c9 */ + L(-1.31225585937499247038404301859788734E-03), /* bff557fffffffffdd469936e691e3000 */ + L(3.10375845385355395586146533282311300E-34), /* 3f8f9c8f6d63b7a4145716ffd92491fb */ + L(-1.28173828124999024755581675764821898E-03), /* bff54ffffffffffd306589b0ab21d000 */ + L(-1.98541096105909793397376077900810019E-34), /* bf8f07e808bbb1e35106c294ffbb9687 */ + L(-1.25122070312500340204619591143332523E-03), /* bff5480000000000fb06d5f16ad2c000 */ + L(3.62884195935761446237911443317457521E-34), /* 3f8fe25b17d623178a386a6fa6c5afb2 */ + L(-1.22070312499999591578388993012071279E-03), /* bff53ffffffffffed2a356c440074000 */ + L(-2.96756662615653130862526710937493307E-35), /* bf8c3b90d8ff2a991e5bd16718fb0645 */ + L(-1.19018554687498821966212632349422735E-03), /* bff537fffffffffc9ac3b585dda89000 */ + L(1.44659971891167323357060028901142644E-34), /* 3f8e809279ab249edf1dad9fe13fb0bf */ + L(-1.15966796875000160938908064907298384E-03), /* bff530000000000076c0800db9639000 */ + L(2.50088010538742402346270685365928513E-34), /* 3f8f4c6c8a483b60201d30c1a83c3cb7 */ + L(-1.12915039062500267151512523291939657E-03), /* bff5280000000000c51f7e7315137000 */ + L(7.56402096465615210500092443924888831E-35), /* 3f8d922c1e485d99aea2668ed32b55a6 */ + L(-1.09863281249998665006360103291051571E-03), /* bff51ffffffffffc26f2d4c9ce2ba000 */ + L(1.43982174467233642713619821353592061E-34), /* 3f8e7ec530b3d92b6303bec1c81214d1 */ + L(-1.06811523437500522742248711752028025E-03), /* bff518000000000181b7380f10446000 */ + L(5.41265133745862349181293024531133174E-35), /* 3f8d1fc9313d018b30e790e06b6be723 */ + L(-1.03759765624999980942114138999770552E-03), /* bff50ffffffffffff1f01130490e1000 */ + L(1.21525139612685854366189534669623436E-34), /* 3f8e4311b96b6fcde412caf3f0d86fb9 */ + L(-1.00708007812499602697537601515759439E-03), /* bff507fffffffffedad7afcce7051000 */ + L(1.00020246351201558505328236381833392E-34), /* 3f8e09e640992512b1300744a7e984ed */ + L(-9.76562499999992592487302113340463694E-04), /* bff4fffffffffffbbad8151f8adf6000 */ + L(-1.64984406575162932060422892046851002E-34), /* bf8eb69a919986e8054b86fc34300f24 */ + L(-9.46044921874989085824996924138179594E-04), /* bff4effffffffff9b55a204fd9792000 */ + L(-9.29539174108308550334255350011347171E-35), /* bf8dee3a50ed896b4656fa577a1df3d7 */ + L(-9.15527343750013735214860599791540029E-04), /* bff4e00000000007eaf5bf103f82d000 */ + L(3.07557018309280519949818825519490586E-35), /* 3f8c470cfbef77d32c74cb8042f6ee81 */ + L(-8.85009765625012292294986105781516428E-04), /* bff4d000000000071605c65403b97000 */ + L(4.77499983783821950338363358545463558E-35), /* 3f8cfbc3dc18884c4c4f9e07d90d7bd3 */ + L(-8.54492187499986941239470706817188192E-04), /* bff4bffffffffff878ddf9cab264a000 */ + L(-1.60128240346239526958630011447901568E-34), /* bf8ea9b1a21e19e2d5bd84b0fbffcf95 */ + L(-8.23974609374996290174598690241743810E-04), /* bff4affffffffffddc86c249ebe06000 */ + L(1.61677540391961912631535763471935882E-34), /* 3f8eadd00841366b0dc2bc262c2c8c36 */ + L(-7.93457031249988696952538334288757473E-04), /* bff49ffffffffff97bf6f0aa85a5f000 */ + L(1.22318577008381887076634753347515709E-34), /* 3f8e452db5b5d250878f71040da06d14 */ + L(-7.62939453124996723316499040007097041E-04), /* bff48ffffffffffe1c7265b431108000 */ + L(-1.03845161748762410745671891558398468E-34), /* bf8e14115ad884c96d1a820c73647220 */ + L(-7.32421874999998242520117923997325794E-04), /* bff47ffffffffffefca4498b7aa8a000 */ + L(5.64005211953031009549514026639438083E-35), /* 3f8d2be06950f68f1a6d8ff829a6928e */ + L(-7.01904296874999772890934814265622012E-04), /* bff46fffffffffffde7c0fe5d8041000 */ + L(5.90245467325173644235991233229525762E-35), /* 3f8d39d40cc49002189243c194b1db0e */ + L(-6.71386718750008699269643939210658742E-04), /* bff460000000000503c91d798b60c000 */ + L(-5.20515801723324452151498579012322191E-35), /* bf8d14c0f08a6a9285b32b8bda003eb5 */ + L(-6.40869140625005499535275057463709988E-04), /* bff45000000000032b969184e9751000 */ + L(-6.69469163285461870099846471658294534E-35), /* bf8d63f36bab7b24d936c9380e3d3fa6 */ + L(-6.10351562499999293780097329596079841E-04), /* bff43fffffffffff97c7c433e35ed000 */ + L(-1.16941808547394177991845382085515086E-34), /* bf8e36e27886f10b234a7dd8fc588bf0 */ + L(-5.79833984375000068291972326409994795E-04), /* bff43000000000000a13ff6dcf2bf000 */ + L(1.17885044988246219185041488459766001E-34), /* 3f8e3964677e001a00412aab52790842 */ + L(-5.49316406249990904622170867910987793E-04), /* bff41ffffffffffac1c25739c716b000 */ + L(-3.31875702128137033065075734368960972E-35), /* bf8c60e928d8982c3c99aef4f885a121 */ + L(-5.18798828125011293653756992177727236E-04), /* bff410000000000682a62cff36775000 */ + L(-5.69971237642088463334239430962628187E-35), /* bf8d2f0c76f8757d61cd1abc7ea7d066 */ + L(-4.88281249999990512232251384917893121E-04), /* bff3fffffffffff50fb48992320df000 */ + L(1.02144616714408655325510171265051108E-35), /* 3f8ab279a3626612710b9b3ac71734ac */ + L(-4.57763671874997554564967307956493434E-04), /* bff3dffffffffffd2e3c272e3cca9000 */ + L(-8.25484058867957231164162481843653503E-35), /* bf8db6e71158e7bf93e2e683f07aa841 */ + L(-4.27246093749991203999790346349633286E-04), /* bff3bffffffffff5dbe103cba0eb2000 */ + L(-3.51191203319375193921924105905691755E-35), /* bf8c757356d0f3dd7fbefc0dd419ab50 */ + L(-3.96728515624986649402960638705483281E-04), /* bff39ffffffffff09b996882706ec000 */ + L(-5.51925962073095883016589497244931171E-36), /* bf89d586d49f22289cfc860bebb99056 */ + L(-3.66210937499999945095511981300980754E-04), /* bff37fffffffffffefcb88bfc7df6000 */ + L(-2.11696465278144529364423332249588595E-35), /* bf8bc23a84d28e5496c874ef9833be25 */ + L(-3.35693359374992480958458008559640163E-04), /* bff35ffffffffff754c548a8798f2000 */ + L(-8.58941791799705081104736787493668352E-35), /* bf8dc8b1192fb7c3662826d43acb7c68 */ + L(-3.05175781250009811036303273640122156E-04), /* bff340000000000b4fb4f1aad1c76000 */ + L(-8.61173897858769926480551302277426632E-35), /* bf8dc9e0eabb1c0b33051011b64769fa */ + L(-2.74658203124987298321920308390303850E-04), /* bff31ffffffffff15b2056ac252fd000 */ + L(3.35152809454778381053519808988046631E-37), /* 3f85c82fb59ff8d7c80d44e635420ab1 */ + L(-2.44140624999999992770514819575735516E-04), /* bff2fffffffffffffbbb82d6a7636000 */ + L(3.54445837111124472730013879165516908E-35), /* 3f8c78e955b01378be647b1c92aa9a77 */ + L(-2.13623046875012756463165168672749438E-04), /* bff2c0000000001d6a1635fea6bbf000 */ + L(1.50050816288650121729916777279129473E-35), /* 3f8b3f1f6f616a61129a58e131cbd31d */ + L(-1.83105468749991323078784464300306893E-04), /* bff27fffffffffebfe0cbd0c82399000 */ + L(-9.14919506501448661140572099029756008E-37), /* bf873754bacaa9d9513b6127e791eb47 */ + L(-1.52587890625013337032336300236461546E-04), /* bff240000000001ec0cb57f2cc995000 */ + L(2.84906084373176180870418394956384516E-35), /* 3f8c2ef6d03a7e6ab087c4f099e4de89 */ + L(-1.22070312499990746786116828458007518E-04), /* bff1ffffffffffd553bbb49f35a34000 */ + L(6.71618008964968339584520728412444537E-36), /* 3f8a1dacb99c60071fc9cd2349495bf0 */ + L(-9.15527343750029275602791047595142231E-05), /* bff180000000000d8040cd6ecde28000 */ + L(-1.95753652091078750312541716951402172E-35), /* bf8ba0526cfb24d8d59122f1c7a09a14 */ + L(-6.10351562499913258461494008080572701E-05), /* bff0ffffffffffaffebbb92d7f6a9000 */ + L(5.69868489273961111703398456218119973E-36), /* 3f89e4ca5df09ef4a4386dd5b3bf0331 */ + L(-3.05175781250092882818419203884960853E-05), /* bff0000000000055ab55de88fac1d000 */ + L(9.03341100018476837609128961872915953E-36), /* 3f8a803d229fa3a0e834a63abb06662b */ #define T_EXPL_ARG2 (2*T_EXPL_ARG1 + 2 + 2*65) - 0.00000000000000000000000000000000000E+00L, /* 00000000000000000000000000000000 */ - 0.00000000000000000000000000000000000E+00L, /* 00000000000000000000000000000000 */ - 3.05175781249814607084128277672749162E-05L, /* 3feffffffffffeaa02abb9102f499000 */ - 1.00271855391179733380665816525889949E-36L, /* 3f8755351afa042ac3f58114824d4c10 */ - 6.10351562500179243748093427073421439E-05L, /* 3ff1000000000052a95de07a4c26d000 */ - 1.67231624299180373502350811501181670E-36L, /* 3f881c87a53691cae9d77f4e40d66616 */ - 9.15527343749970728685313252158399200E-05L, /* 3ff17ffffffffff28040cc2acde28000 */ - 2.43665747834893104318707597514407880E-36L, /* 3f889e9366c7c6c6a2ecb78dc9b0509e */ - 1.22070312500027751961838150070880064E-04L, /* 3ff200000000003ffddde6c153b53000 */ - -1.73322146370624186623546452226755405E-35L, /* bf8b709d8d658ed5dbbe943de56ee84e */ - 1.52587890624995916105682628143179430E-04L, /* 3ff23ffffffffff6954b56e285d23000 */ - 1.23580432650945898349135528000443828E-35L, /* 3f8b06d396601dde16de7d7bc27346e6 */ - 1.83105468750008670314358488289621794E-04L, /* 3ff2800000000013fe0cdc8c823b7000 */ - 4.30446229148833293310207915930740796E-35L, /* 3f8cc9ba9bfe554a4f7f2fece291eb23 */ - 2.13623046875005741337455947623248132E-04L, /* 3ff2c0000000000d3d1662de21a3f000 */ - -3.96110759869520786681660669615255057E-35L, /* bf8ca5379b04ff4a31aab0ceacc917e6 */ - 2.44140624999981493573336463433440506E-04L, /* 3ff2ffffffffffd553bbdf48e0534000 */ - -1.39617373942387888957350179316792928E-35L, /* bf8b28eeedc286015802b63f96b8c5cd */ - 2.74658203124984920706309918754626834E-04L, /* 3ff31fffffffffee9d60c8439ec1d000 */ - -3.16168080483901830349738314447356223E-36L, /* bf890cf74f81c77a611abc1243812444 */ - 3.05175781250008648918265055410966055E-04L, /* 3ff3400000000009f8b5c9a346636000 */ - 8.54421306185008998867856704677221443E-35L, /* 3f8dc649cd40922fc08adc6b6b20ead0 */ - 3.35693359374988945462612499316774515E-04L, /* 3ff35ffffffffff34146c540f15b2000 */ - 7.96443137431639500475160850431097078E-35L, /* 3f8da77638ed3148fc4d99d1c9e13446 */ - 3.66210937500027690542093987739604535E-04L, /* 3ff380000000001fecce34bea89c4000 */ - 2.14507323877752361258862577769090367E-35L, /* 3f8bc834e554d38894cf91957b0253d3 */ - 3.96728515625003928083564943615052121E-04L, /* 3ff3a00000000004875d9a4acf6ab000 */ - 4.88358523466632050664019922448605508E-35L, /* 3f8d03a7eaeef1a9f78c71a12c44dd28 */ - 4.27246093750017799227172345607351585E-04L, /* 3ff3c00000000014856794c3ee850000 */ - 6.66520494592631402182216588784828935E-35L, /* 3f8d6262118fcdb59b8f16108f5f1a6c */ - 4.57763671875002108342364320152138181E-04L, /* 3ff3e000000000026e45d855410b9000 */ - 7.21799615960261390920033272189522298E-35L, /* 3f8d7fc645cff8879462296af975c9fd */ - 4.88281249999999768797631616370963356E-04L, /* 3ff3ffffffffffffbbc2d7cc004df000 */ - -5.30564629906905979452258114088325361E-35L, /* bf8d1a18b71929a30d67a217a27ae851 */ - 5.18798828124997339054881383202487041E-04L, /* 3ff40ffffffffffe775055eea5851000 */ - -4.03682911253647925867848180522846377E-35L, /* bf8cad44f0f3e5199d8a589d9332acad */ - 5.49316406249980511907933706754958501E-04L, /* 3ff41ffffffffff4c410b29bb62fb000 */ - -2.08166843948323917121806956728438051E-35L, /* bf8bbab8cf691403249fe5b699e25143 */ - 5.79833984374989593561576568548497165E-04L, /* 3ff42ffffffffffa0047df328d817000 */ - -1.72745033420153042445343706432627539E-34L, /* bf8ecb3c2d7d3a9e6e960576be901fdf */ - 6.10351562500008540711511259540838154E-04L, /* 3ff4400000000004ec62f54f8c271000 */ - 7.41889382604319545724663095428976499E-35L, /* 3f8d8a74c002c81a47c93b8e05d15f8e */ - 6.40869140625020444702875407535884986E-04L, /* 3ff450000000000bc91b09718515d000 */ - -4.47321009727305792048065440180490107E-35L, /* bf8cdbac5c8fe70822081d8993eb5cb6 */ - 6.71386718750007531635964622352684074E-04L, /* 3ff460000000000457792973db05c000 */ - 5.13698959677949336513874456684462092E-35L, /* 3f8d112114436949c5ef38d8049004ab */ - 7.01904296875006634673332887754430334E-04L, /* 3ff4700000000003d31adf2cb8b1d000 */ - -8.25665755717729437292989870760751482E-35L, /* bf8db6ffcc8ef71f8e648e3a8b160f5a */ - 7.32421874999998244664170215504673504E-04L, /* 3ff47ffffffffffefcf5498bd5c8a000 */ - -5.64005234937832153139057628112753364E-35L, /* bf8d2be06a1dfe90e7bf90fba7c12a98 */ - 7.62939453125017456345986752604096408E-04L, /* 3ff490000000000a101a1b093d4a8000 */ - -1.11084094120417622468550608896588329E-34L, /* bf8e274feabd2d94f6694507a46accb1 */ - 7.93457031249987558617598988993908016E-04L, /* 3ff49ffffffffff8d3f9dcab74bbf000 */ - -1.22966480225449015129079129940978828E-34L, /* bf8e46e6a65eef8fa9e42eddf3da305e */ - 8.23974609374997378723747633335135819E-04L, /* 3ff4affffffffffe7d2afbaa55b26000 */ - -1.62270010016794279091906973366704963E-34L, /* bf8eaf633f057ebdb664a34566401c4e */ - 8.54492187500023938282350821569920958E-04L, /* 3ff4c0000000000dccaabce399e59000 */ - -1.39076361712838158775374263169606160E-34L, /* bf8e71ba779364b3bbdba7841f2c4ca1 */ - 8.85009765624987932362186815286691297E-04L, /* 3ff4cffffffffff90b218886edc2a000 */ - 4.07328275060905585228261577392403980E-35L, /* 3f8cb1254dbb6ea4b8cfa5ed4cf28d24 */ - 9.15527343749975579461305518559161974E-04L, /* 3ff4dffffffffff1ec2a21f25df33000 */ - 1.16855112459192484947855553716334015E-35L, /* 3f8af10bf319e9f5270cf249eeffbe5c */ - 9.46044921875016761584725882821122521E-04L, /* 3ff4f00000000009a992c46c16d71000 */ - 9.51660680007524262741115611071680436E-35L, /* 3f8df9fd56e81f8edf133843910ee831 */ - 9.76562499999974118878133088548272636E-04L, /* 3ff4fffffffffff1149edc46a6df6000 */ - -5.65271128977550656964071208289181661E-36L, /* bf89e0e12689dd721aa2314c81eb6429 */ - 1.00708007812498671732140389760347830E-03L, /* 3ff507fffffffffc2be94b90ed091000 */ - -1.43355074891483635310132767255371379E-34L, /* bf8e7d1a688c247b16022daab1316d55 */ - 1.03759765625002637786192745235343007E-03L, /* 3ff51000000000079a57b966bc158000 */ - 2.95905815240957629366749917020106928E-34L, /* 3f8f895387fc73bb38f8a1b254c01a60 */ - 1.06811523437500860568717813047520763E-03L, /* 3ff51800000000027afcd5b35f5e6000 */ - -5.98328495358586628195372356742878314E-35L, /* bf8d3e204130013bf6328f1b70ff8c76 */ - 1.09863281250001439958487251556220070E-03L, /* 3ff5200000000004268077c6c66bd000 */ - 2.41371837889426603334113000868144760E-34L, /* 3f8f40d6948edf864054ccf151f9815e */ - 1.12915039062501298413451613770002366E-03L, /* 3ff5280000000003be0f5dd8fe81b000 */ - -1.28815268997394164973472617519705703E-34L, /* bf8e567321172ea089dce4bc8354ecb7 */ - 1.15966796874997272036339054191407232E-03L, /* 3ff52ffffffffff8231e3bcfff1e8000 */ - 1.02996064554316248496839462594377804E-34L, /* 3f8e11cf7d402789244f68e2d4f985b1 */ - 1.19018554687502744121802585360546796E-03L, /* 3ff5380000000007e8cdf3f8f6c20000 */ - -1.43453217726255628994625761307322163E-34L, /* bf8e7d5d3370d85a374f5f4802fc517a */ - 1.22070312499997743541996266398850614E-03L, /* 3ff53ffffffffff97f0722561f454000 */ - -1.41086259180534339713692694428211646E-34L, /* bf8e77125519ff76244dfec5fbd58402 */ - 1.25122070312501024092560690174507039E-03L, /* 3ff5480000000002f3a59d8820691000 */ - 3.84102646020099293168698506729765213E-34L, /* 3f8ffe8f5b86f9c3569c8f26e19b1f50 */ - 1.28173828124997986521442660131425390E-03L, /* 3ff54ffffffffffa3250a764439d9000 */ - 1.44644589735033114377952806106652650E-34L, /* 3f8e808801b80dcf38323cdbfdca2549 */ - 1.31225585937501665804856968749058137E-03L, /* 3ff5580000000004cd25a414c6d62000 */ - 1.67474574742200577294563576414361377E-34L, /* 3f8ebd394a151dbda4f81d5d83c0f1e9 */ - 1.34277343749997290265837386401818888E-03L, /* 3ff55ffffffffff83091b042cfd59000 */ - -1.55650565030381326742591837551559103E-34L, /* bf8e9dca490d7fecfadba9625ffb91c5 */ - 1.37329101562497720784949380297774268E-03L, /* 3ff567fffffffff96e3c7312f5ccf000 */ - 1.65279335325630026116581677369221748E-34L, /* 3f8eb763496f5bd7404f2298b402074f */ - 1.40380859374999099958354100336136647E-03L, /* 3ff56ffffffffffd67e2f09f2a381000 */ - 1.89919944388961890195706641264717076E-34L, /* 3f8ef8e4d0ffdfeba982aa8829501389 */ - 1.43432617187497484122173130998160625E-03L, /* 3ff577fffffffff8bf9c1d71af8a8000 */ - 2.57638517142061429772064578590009568E-34L, /* 3f8f5675d82c1cc4ada70fd3a957b89a */ - 1.46484374999999929342158925502052945E-03L, /* 3ff57fffffffffffcbdd1c7671b46000 */ - 1.76487201934184070490166772482073801E-34L, /* 3f8ed52ef732458f6e4c5c07504f33cc */ - 1.49536132812502318451070466256902933E-03L, /* 3ff5880000000006aeb7066c8ad43000 */ - 2.38068367275295804321313550609246656E-34L, /* 3f8f3c7277ae6fc390ace5e06c0b025b */ - 1.52587890625000448053340248672949543E-03L, /* 3ff59000000000014a9ae2104b3bc000 */ - 1.01174455568392813258454590274740959E-34L, /* 3f8e0cf7c434762991bb38e12acee215 */ - 1.55639648437501113499837053523090913E-03L, /* 3ff5980000000003359e2c204355e000 */ - -2.82398418808099749023517211651363693E-35L, /* bf8c2c4c2971d88caa95e15fb1ccb1a1 */ - 1.58691406249999937955142588308171026E-03L, /* 3ff59fffffffffffd2380ecbc87c2000 */ - -1.27361695572422741562701199136538047E-34L, /* bf8e5295e0e206dfb0f0266c07225448 */ - 1.61743164062498000531048954475329309E-03L, /* 3ff5a7fffffffffa3ca6fe61ed94c000 */ - -1.22606548862580061633942923016222044E-34L, /* bf8e45f1b17bb61039d21a351bb207b8 */ - 1.64794921875001835451453858682255576E-03L, /* 3ff5b000000000054a52fa20f6565000 */ - 1.39132339594152335892305491425264583E-34L, /* 3f8e71e0904c5449b414ee49b191cef2 */ - 1.67846679687501263995029340691547953E-03L, /* 3ff5b80000000003a4a9e912c910b000 */ - 6.67245854693585315412242764786197029E-35L, /* 3f8d62c4ccac1e7511a617d469468ccd */ - 1.70898437500002646861403514115369655E-03L, /* 3ff5c00000000007a109fbaa7e015000 */ - 6.87367172354719289559624829652240928E-36L, /* 3f8a245fa835eceb42bae8128d9336db */ - 1.73950195312501174308226096992992128E-03L, /* 3ff5c80000000003627c8d637a005000 */ - -2.20824271875474985927385878948759352E-34L, /* bf8f25869b1cbefb25e735992f232f57 */ - 1.77001953124997491747605207736194513E-03L, /* 3ff5cffffffffff8c53c84b6883b8000 */ - 3.43123048533596296514343180408963705E-34L, /* 3f8fc816b91d173ddadbbf09b1287906 */ - 1.80053710937497698911127570705069398E-03L, /* 3ff5d7fffffffff95e1899f4a8430000 */ - 3.99231237340890073475077494556136100E-35L, /* 3f8ca889148f62fa854da5674df41279 */ - 1.83105468750002267094899598630423914E-03L, /* 3ff5e0000000000688d21e62ba674000 */ - -3.22274595655810623999007524769365273E-34L, /* bf8fac605cb9ae01eb719675ced25560 */ - 1.86157226562500499224728040579690330E-03L, /* 3ff5e80000000001705ce28a6d89e000 */ - 3.07094985075881613489605622068441083E-34L, /* 3f8f98330225ec7e2c8f3c0d1c432b91 */ - 1.89208984374998234666824993196980949E-03L, /* 3ff5effffffffffae969fdc7cd8cf000 */ - -3.06287628722973914692165056776495733E-34L, /* bf8f9720477d9cfa10e464df7f91020c */ - 1.92260742187501225343755557292811682E-03L, /* 3ff5f800000000038824e428ed49a000 */ - 6.30049124729794620592961282769623368E-35L, /* 3f8d4efdd7cd4336d88a6aa49e1e96bc */ - 1.95312499999998514894032051116231258E-03L, /* 3ff5fffffffffffbb82f6a04f1ae0000 */ - -6.14610057507500948543216998736262902E-35L, /* bf8d46c862d39255370e7974d48daa7e */ - 1.98364257812501222021119324146882732E-03L, /* 3ff6040000000001c2d8a1aa5188d000 */ - 3.71942298418113774118754986159801984E-34L, /* 3f8fee6567d9940495519ffe62cbc9a4 */ + L(0.00000000000000000000000000000000000E+00), /* 00000000000000000000000000000000 */ + L(0.00000000000000000000000000000000000E+00), /* 00000000000000000000000000000000 */ + L(3.05175781249814607084128277672749162E-05), /* 3feffffffffffeaa02abb9102f499000 */ + L(1.00271855391179733380665816525889949E-36), /* 3f8755351afa042ac3f58114824d4c10 */ + L(6.10351562500179243748093427073421439E-05), /* 3ff1000000000052a95de07a4c26d000 */ + L(1.67231624299180373502350811501181670E-36), /* 3f881c87a53691cae9d77f4e40d66616 */ + L(9.15527343749970728685313252158399200E-05), /* 3ff17ffffffffff28040cc2acde28000 */ + L(2.43665747834893104318707597514407880E-36), /* 3f889e9366c7c6c6a2ecb78dc9b0509e */ + L(1.22070312500027751961838150070880064E-04), /* 3ff200000000003ffddde6c153b53000 */ + L(-1.73322146370624186623546452226755405E-35), /* bf8b709d8d658ed5dbbe943de56ee84e */ + L(1.52587890624995916105682628143179430E-04), /* 3ff23ffffffffff6954b56e285d23000 */ + L(1.23580432650945898349135528000443828E-35), /* 3f8b06d396601dde16de7d7bc27346e6 */ + L(1.83105468750008670314358488289621794E-04), /* 3ff2800000000013fe0cdc8c823b7000 */ + L(4.30446229148833293310207915930740796E-35), /* 3f8cc9ba9bfe554a4f7f2fece291eb23 */ + L(2.13623046875005741337455947623248132E-04), /* 3ff2c0000000000d3d1662de21a3f000 */ + L(-3.96110759869520786681660669615255057E-35), /* bf8ca5379b04ff4a31aab0ceacc917e6 */ + L(2.44140624999981493573336463433440506E-04), /* 3ff2ffffffffffd553bbdf48e0534000 */ + L(-1.39617373942387888957350179316792928E-35), /* bf8b28eeedc286015802b63f96b8c5cd */ + L(2.74658203124984920706309918754626834E-04), /* 3ff31fffffffffee9d60c8439ec1d000 */ + L(-3.16168080483901830349738314447356223E-36), /* bf890cf74f81c77a611abc1243812444 */ + L(3.05175781250008648918265055410966055E-04), /* 3ff3400000000009f8b5c9a346636000 */ + L(8.54421306185008998867856704677221443E-35), /* 3f8dc649cd40922fc08adc6b6b20ead0 */ + L(3.35693359374988945462612499316774515E-04), /* 3ff35ffffffffff34146c540f15b2000 */ + L(7.96443137431639500475160850431097078E-35), /* 3f8da77638ed3148fc4d99d1c9e13446 */ + L(3.66210937500027690542093987739604535E-04), /* 3ff380000000001fecce34bea89c4000 */ + L(2.14507323877752361258862577769090367E-35), /* 3f8bc834e554d38894cf91957b0253d3 */ + L(3.96728515625003928083564943615052121E-04), /* 3ff3a00000000004875d9a4acf6ab000 */ + L(4.88358523466632050664019922448605508E-35), /* 3f8d03a7eaeef1a9f78c71a12c44dd28 */ + L(4.27246093750017799227172345607351585E-04), /* 3ff3c00000000014856794c3ee850000 */ + L(6.66520494592631402182216588784828935E-35), /* 3f8d6262118fcdb59b8f16108f5f1a6c */ + L(4.57763671875002108342364320152138181E-04), /* 3ff3e000000000026e45d855410b9000 */ + L(7.21799615960261390920033272189522298E-35), /* 3f8d7fc645cff8879462296af975c9fd */ + L(4.88281249999999768797631616370963356E-04), /* 3ff3ffffffffffffbbc2d7cc004df000 */ + L(-5.30564629906905979452258114088325361E-35), /* bf8d1a18b71929a30d67a217a27ae851 */ + L(5.18798828124997339054881383202487041E-04), /* 3ff40ffffffffffe775055eea5851000 */ + L(-4.03682911253647925867848180522846377E-35), /* bf8cad44f0f3e5199d8a589d9332acad */ + L(5.49316406249980511907933706754958501E-04), /* 3ff41ffffffffff4c410b29bb62fb000 */ + L(-2.08166843948323917121806956728438051E-35), /* bf8bbab8cf691403249fe5b699e25143 */ + L(5.79833984374989593561576568548497165E-04), /* 3ff42ffffffffffa0047df328d817000 */ + L(-1.72745033420153042445343706432627539E-34), /* bf8ecb3c2d7d3a9e6e960576be901fdf */ + L(6.10351562500008540711511259540838154E-04), /* 3ff4400000000004ec62f54f8c271000 */ + L(7.41889382604319545724663095428976499E-35), /* 3f8d8a74c002c81a47c93b8e05d15f8e */ + L(6.40869140625020444702875407535884986E-04), /* 3ff450000000000bc91b09718515d000 */ + L(-4.47321009727305792048065440180490107E-35), /* bf8cdbac5c8fe70822081d8993eb5cb6 */ + L(6.71386718750007531635964622352684074E-04), /* 3ff460000000000457792973db05c000 */ + L(5.13698959677949336513874456684462092E-35), /* 3f8d112114436949c5ef38d8049004ab */ + L(7.01904296875006634673332887754430334E-04), /* 3ff4700000000003d31adf2cb8b1d000 */ + L(-8.25665755717729437292989870760751482E-35), /* bf8db6ffcc8ef71f8e648e3a8b160f5a */ + L(7.32421874999998244664170215504673504E-04), /* 3ff47ffffffffffefcf5498bd5c8a000 */ + L(-5.64005234937832153139057628112753364E-35), /* bf8d2be06a1dfe90e7bf90fba7c12a98 */ + L(7.62939453125017456345986752604096408E-04), /* 3ff490000000000a101a1b093d4a8000 */ + L(-1.11084094120417622468550608896588329E-34), /* bf8e274feabd2d94f6694507a46accb1 */ + L(7.93457031249987558617598988993908016E-04), /* 3ff49ffffffffff8d3f9dcab74bbf000 */ + L(-1.22966480225449015129079129940978828E-34), /* bf8e46e6a65eef8fa9e42eddf3da305e */ + L(8.23974609374997378723747633335135819E-04), /* 3ff4affffffffffe7d2afbaa55b26000 */ + L(-1.62270010016794279091906973366704963E-34), /* bf8eaf633f057ebdb664a34566401c4e */ + L(8.54492187500023938282350821569920958E-04), /* 3ff4c0000000000dccaabce399e59000 */ + L(-1.39076361712838158775374263169606160E-34), /* bf8e71ba779364b3bbdba7841f2c4ca1 */ + L(8.85009765624987932362186815286691297E-04), /* 3ff4cffffffffff90b218886edc2a000 */ + L(4.07328275060905585228261577392403980E-35), /* 3f8cb1254dbb6ea4b8cfa5ed4cf28d24 */ + L(9.15527343749975579461305518559161974E-04), /* 3ff4dffffffffff1ec2a21f25df33000 */ + L(1.16855112459192484947855553716334015E-35), /* 3f8af10bf319e9f5270cf249eeffbe5c */ + L(9.46044921875016761584725882821122521E-04), /* 3ff4f00000000009a992c46c16d71000 */ + L(9.51660680007524262741115611071680436E-35), /* 3f8df9fd56e81f8edf133843910ee831 */ + L(9.76562499999974118878133088548272636E-04), /* 3ff4fffffffffff1149edc46a6df6000 */ + L(-5.65271128977550656964071208289181661E-36), /* bf89e0e12689dd721aa2314c81eb6429 */ + L(1.00708007812498671732140389760347830E-03), /* 3ff507fffffffffc2be94b90ed091000 */ + L(-1.43355074891483635310132767255371379E-34), /* bf8e7d1a688c247b16022daab1316d55 */ + L(1.03759765625002637786192745235343007E-03), /* 3ff51000000000079a57b966bc158000 */ + L(2.95905815240957629366749917020106928E-34), /* 3f8f895387fc73bb38f8a1b254c01a60 */ + L(1.06811523437500860568717813047520763E-03), /* 3ff51800000000027afcd5b35f5e6000 */ + L(-5.98328495358586628195372356742878314E-35), /* bf8d3e204130013bf6328f1b70ff8c76 */ + L(1.09863281250001439958487251556220070E-03), /* 3ff5200000000004268077c6c66bd000 */ + L(2.41371837889426603334113000868144760E-34), /* 3f8f40d6948edf864054ccf151f9815e */ + L(1.12915039062501298413451613770002366E-03), /* 3ff5280000000003be0f5dd8fe81b000 */ + L(-1.28815268997394164973472617519705703E-34), /* bf8e567321172ea089dce4bc8354ecb7 */ + L(1.15966796874997272036339054191407232E-03), /* 3ff52ffffffffff8231e3bcfff1e8000 */ + L(1.02996064554316248496839462594377804E-34), /* 3f8e11cf7d402789244f68e2d4f985b1 */ + L(1.19018554687502744121802585360546796E-03), /* 3ff5380000000007e8cdf3f8f6c20000 */ + L(-1.43453217726255628994625761307322163E-34), /* bf8e7d5d3370d85a374f5f4802fc517a */ + L(1.22070312499997743541996266398850614E-03), /* 3ff53ffffffffff97f0722561f454000 */ + L(-1.41086259180534339713692694428211646E-34), /* bf8e77125519ff76244dfec5fbd58402 */ + L(1.25122070312501024092560690174507039E-03), /* 3ff5480000000002f3a59d8820691000 */ + L(3.84102646020099293168698506729765213E-34), /* 3f8ffe8f5b86f9c3569c8f26e19b1f50 */ + L(1.28173828124997986521442660131425390E-03), /* 3ff54ffffffffffa3250a764439d9000 */ + L(1.44644589735033114377952806106652650E-34), /* 3f8e808801b80dcf38323cdbfdca2549 */ + L(1.31225585937501665804856968749058137E-03), /* 3ff5580000000004cd25a414c6d62000 */ + L(1.67474574742200577294563576414361377E-34), /* 3f8ebd394a151dbda4f81d5d83c0f1e9 */ + L(1.34277343749997290265837386401818888E-03), /* 3ff55ffffffffff83091b042cfd59000 */ + L(-1.55650565030381326742591837551559103E-34), /* bf8e9dca490d7fecfadba9625ffb91c5 */ + L(1.37329101562497720784949380297774268E-03), /* 3ff567fffffffff96e3c7312f5ccf000 */ + L(1.65279335325630026116581677369221748E-34), /* 3f8eb763496f5bd7404f2298b402074f */ + L(1.40380859374999099958354100336136647E-03), /* 3ff56ffffffffffd67e2f09f2a381000 */ + L(1.89919944388961890195706641264717076E-34), /* 3f8ef8e4d0ffdfeba982aa8829501389 */ + L(1.43432617187497484122173130998160625E-03), /* 3ff577fffffffff8bf9c1d71af8a8000 */ + L(2.57638517142061429772064578590009568E-34), /* 3f8f5675d82c1cc4ada70fd3a957b89a */ + L(1.46484374999999929342158925502052945E-03), /* 3ff57fffffffffffcbdd1c7671b46000 */ + L(1.76487201934184070490166772482073801E-34), /* 3f8ed52ef732458f6e4c5c07504f33cc */ + L(1.49536132812502318451070466256902933E-03), /* 3ff5880000000006aeb7066c8ad43000 */ + L(2.38068367275295804321313550609246656E-34), /* 3f8f3c7277ae6fc390ace5e06c0b025b */ + L(1.52587890625000448053340248672949543E-03), /* 3ff59000000000014a9ae2104b3bc000 */ + L(1.01174455568392813258454590274740959E-34), /* 3f8e0cf7c434762991bb38e12acee215 */ + L(1.55639648437501113499837053523090913E-03), /* 3ff5980000000003359e2c204355e000 */ + L(-2.82398418808099749023517211651363693E-35), /* bf8c2c4c2971d88caa95e15fb1ccb1a1 */ + L(1.58691406249999937955142588308171026E-03), /* 3ff59fffffffffffd2380ecbc87c2000 */ + L(-1.27361695572422741562701199136538047E-34), /* bf8e5295e0e206dfb0f0266c07225448 */ + L(1.61743164062498000531048954475329309E-03), /* 3ff5a7fffffffffa3ca6fe61ed94c000 */ + L(-1.22606548862580061633942923016222044E-34), /* bf8e45f1b17bb61039d21a351bb207b8 */ + L(1.64794921875001835451453858682255576E-03), /* 3ff5b000000000054a52fa20f6565000 */ + L(1.39132339594152335892305491425264583E-34), /* 3f8e71e0904c5449b414ee49b191cef2 */ + L(1.67846679687501263995029340691547953E-03), /* 3ff5b80000000003a4a9e912c910b000 */ + L(6.67245854693585315412242764786197029E-35), /* 3f8d62c4ccac1e7511a617d469468ccd */ + L(1.70898437500002646861403514115369655E-03), /* 3ff5c00000000007a109fbaa7e015000 */ + L(6.87367172354719289559624829652240928E-36), /* 3f8a245fa835eceb42bae8128d9336db */ + L(1.73950195312501174308226096992992128E-03), /* 3ff5c80000000003627c8d637a005000 */ + L(-2.20824271875474985927385878948759352E-34), /* bf8f25869b1cbefb25e735992f232f57 */ + L(1.77001953124997491747605207736194513E-03), /* 3ff5cffffffffff8c53c84b6883b8000 */ + L(3.43123048533596296514343180408963705E-34), /* 3f8fc816b91d173ddadbbf09b1287906 */ + L(1.80053710937497698911127570705069398E-03), /* 3ff5d7fffffffff95e1899f4a8430000 */ + L(3.99231237340890073475077494556136100E-35), /* 3f8ca889148f62fa854da5674df41279 */ + L(1.83105468750002267094899598630423914E-03), /* 3ff5e0000000000688d21e62ba674000 */ + L(-3.22274595655810623999007524769365273E-34), /* bf8fac605cb9ae01eb719675ced25560 */ + L(1.86157226562500499224728040579690330E-03), /* 3ff5e80000000001705ce28a6d89e000 */ + L(3.07094985075881613489605622068441083E-34), /* 3f8f98330225ec7e2c8f3c0d1c432b91 */ + L(1.89208984374998234666824993196980949E-03), /* 3ff5effffffffffae969fdc7cd8cf000 */ + L(-3.06287628722973914692165056776495733E-34), /* bf8f9720477d9cfa10e464df7f91020c */ + L(1.92260742187501225343755557292811682E-03), /* 3ff5f800000000038824e428ed49a000 */ + L(6.30049124729794620592961282769623368E-35), /* 3f8d4efdd7cd4336d88a6aa49e1e96bc */ + L(1.95312499999998514894032051116231258E-03), /* 3ff5fffffffffffbb82f6a04f1ae0000 */ + L(-6.14610057507500948543216998736262902E-35), /* bf8d46c862d39255370e7974d48daa7e */ + L(1.98364257812501222021119324146882732E-03), /* 3ff6040000000001c2d8a1aa5188d000 */ + L(3.71942298418113774118754986159801984E-34), /* 3f8fee6567d9940495519ffe62cbc9a4 */ - 7.06341639425619532977052017486130353E-01L, /* 3ffe69a59c8245a9ac00000000000000 */ - 7.09106182437398424589503065362805501E-01L, /* 3ffe6b0ff72deb89d000000000000000 */ - 7.11881545564596485142772053222870454E-01L, /* 3ffe6c7bbce9a6d93000000000000000 */ - 7.14667771155948150507697391731198877E-01L, /* 3ffe6de8ef213d71e000000000000000 */ - 7.17464901725936049503573599395167548E-01L, /* 3ffe6f578f41e1a9e400000000000000 */ - 7.20272979955439790478166628417966422E-01L, /* 3ffe70c79eba33c06c00000000000000 */ - 7.23092048692387218133958981525211129E-01L, /* 3ffe72391efa434c7400000000000000 */ - 7.25922150952408251622927082280511968E-01L, /* 3ffe73ac117390acd800000000000000 */ - 7.28763329919491220643124052003258839E-01L, /* 3ffe752077990e79d000000000000000 */ - 7.31615628946641782803794740175362676E-01L, /* 3ffe769652df22f7e000000000000000 */ - 7.34479091556544505525749855223693885E-01L, /* 3ffe780da4bba98c4800000000000000 */ - 7.37353761442226890432394270646909717E-01L, /* 3ffe79866ea5f432d400000000000000 */ - 7.40239682467726090031590047146892175E-01L, /* 3ffe7b00b216ccf53000000000000000 */ - 7.43136898668758316688354170764796436E-01L, /* 3ffe7c7c70887763c000000000000000 */ - 7.46045454253390638577059235103661194E-01L, /* 3ffe7df9ab76b20fd000000000000000 */ - 7.48965393602715662213498148958024103E-01L, /* 3ffe7f78645eb8076400000000000000 */ - 7.51896761271528629722027403659012634E-01L, /* 3ffe80f89cbf42526400000000000000 */ - 7.54839601989007347171423134568613023E-01L, /* 3ffe827a561889716000000000000000 */ - 7.57793960659394638668118204805068672E-01L, /* 3ffe83fd91ec46ddc000000000000000 */ - 7.60759882362683631518152083117456641E-01L, /* 3ffe858251bdb68b8c00000000000000 */ - 7.63737412355305483879774897104653064E-01L, /* 3ffe87089711986c9400000000000000 */ - 7.66726596070820082262642358728044201E-01L, /* 3ffe8890636e31f54400000000000000 */ - 7.69727479120609181517664865168626420E-01L, /* 3ffe8a19b85b4fa2d800000000000000 */ - 7.72740107294572486917871856348938309E-01L, /* 3ffe8ba4976246833800000000000000 */ - 7.75764526561826289752232810315035749E-01L, /* 3ffe8d31020df5be4400000000000000 */ - 7.78800783071404878477039801509818062E-01L, /* 3ffe8ebef9eac820b000000000000000 */ - 7.81848923152964780936002853195532225E-01L, /* 3ffe904e8086b5a87800000000000000 */ - 7.84908993317491698871180005880887620E-01L, /* 3ffe91df97714512d800000000000000 */ - 7.87981040258010162480317717381694820E-01L, /* 3ffe9372403b8d6bcc00000000000000 */ - 7.91065110850296016042904057030682452E-01L, /* 3ffe95067c78379f2800000000000000 */ - 7.94161252153591734614934694036492147E-01L, /* 3ffe969c4dbb800b4800000000000000 */ - 7.97269511411324433014513601847284008E-01L, /* 3ffe9833b59b38154400000000000000 */ - 8.00389936051826789142893403550260700E-01L, /* 3ffe99ccb5aec7bec800000000000000 */ - 8.03522573689060742863077280162542593E-01L, /* 3ffe9b674f8f2f3d7c00000000000000 */ - 8.06667472123343942680406826184480451E-01L, /* 3ffe9d0384d70893f800000000000000 */ - 8.09824679342079301047618855591281317E-01L, /* 3ffe9ea15722892c7800000000000000 */ - 8.12994243520486992160556383169023320E-01L, /* 3ffea040c80f8374f000000000000000 */ - 8.16176213022339780422953481320291758E-01L, /* 3ffea1e1d93d687d0000000000000000 */ - 8.19370636400700819157449927843117621E-01L, /* 3ffea3848c4d49954c00000000000000 */ - 8.22577562398664585696650419777142815E-01L, /* 3ffea528e2e1d9f09800000000000000 */ - 8.25797039950100647542896581398963463E-01L, /* 3ffea6cede9f70467c00000000000000 */ - 8.29029118180400342863478613253391813E-01L, /* 3ffea876812c0877bc00000000000000 */ - 8.32273846407226292054559735333896242E-01L, /* 3ffeaa1fcc2f45343800000000000000 */ - 8.35531274141265073440720811959181447E-01L, /* 3ffeabcac15271a2a400000000000000 */ - 8.38801451086982535754188461396552157E-01L, /* 3ffead7762408309bc00000000000000 */ - 8.42084427143382358016410194068157580E-01L, /* 3ffeaf25b0a61a7b4c00000000000000 */ - 8.45380252404767357221615498019673396E-01L, /* 3ffeb0d5ae318680c400000000000000 */ - 8.48688977161503960155997106085123960E-01L, /* 3ffeb2875c92c4c99400000000000000 */ - 8.52010651900789478530029441571969073E-01L, /* 3ffeb43abd7b83db1c00000000000000 */ - 8.55345327307422548246407245642330963E-01L, /* 3ffeb5efd29f24c26400000000000000 */ - 8.58693054264576483003423845730139874E-01L, /* 3ffeb7a69db2bcc77800000000000000 */ - 8.62053883854575708767242758767679334E-01L, /* 3ffeb95f206d17228000000000000000 */ - 8.65427867359675251357487013592617586E-01L, /* 3ffebb195c86b6b29000000000000000 */ - 8.68815056262843166123843730019871145E-01L, /* 3ffebcd553b9d7b62000000000000000 */ - 8.72215502248546159513864495238522068E-01L, /* 3ffebe9307c271855000000000000000 */ - 8.75629257203538208242932228131394368E-01L, /* 3ffec0527a5e384ddc00000000000000 */ - 8.79056373217652342599848225290770642E-01L, /* 3ffec213ad4c9ed0d800000000000000 */ - 8.82496902584595399599010079327854328E-01L, /* 3ffec3d6a24ed8221800000000000000 */ - 8.85950897802745995779361010136199184E-01L, /* 3ffec59b5b27d9696800000000000000 */ - 8.89418411575955636383383762222365476E-01L, /* 3ffec761d99c5ba58800000000000000 */ - 8.92899496814352794382685374330321793E-01L, /* 3ffec92a1f72dd70d400000000000000 */ - 8.96394206635150403439382671422208659E-01L, /* 3ffecaf42e73a4c7d800000000000000 */ - 8.99902594363456265202927397695020773E-01L, /* 3ffeccc00868c0d18800000000000000 */ - 9.03424713533086704009278378180169966E-01L, /* 3ffece8daf1e0ba94c00000000000000 */ - 9.06960617887383580004723171441582963E-01L, /* 3ffed05d24612c2af000000000000000 */ - 9.10510361380034133338412516422977205E-01L, /* 3ffed22e6a0197c02c00000000000000 */ - 9.14073998175894436579724811053893063E-01L, /* 3ffed40181d094303400000000000000 */ - 9.17651582651815816982221463149471674E-01L, /* 3ffed5d66da13970f400000000000000 */ - 9.21243169397474526149949269893113524E-01L, /* 3ffed7ad2f48737a2000000000000000 */ - 9.24848813216204823639543519675498828E-01L, /* 3ffed985c89d041a3000000000000000 */ - 9.28468569125835141431224428743007593E-01L, /* 3ffedb603b7784cd1800000000000000 */ - 9.32102492359527579068867453315760940E-01L, /* 3ffedd3c89b26894e000000000000000 */ - 9.35750638366620729469147477175283711E-01L, /* 3ffedf1ab529fdd41c00000000000000 */ - 9.39413062813475779888605643463961314E-01L, /* 3ffee0fabfbc702a3c00000000000000 */ - 9.43089821584325888048638830696290825E-01L, /* 3ffee2dcab49ca51b400000000000000 */ - 9.46780970782128888929563004239753354E-01L, /* 3ffee4c079b3f8000400000000000000 */ - 9.50486566729423443256052905780961737E-01L, /* 3ffee6a62cdec7c7b000000000000000 */ - 9.54206665969188322362626308859034907E-01L, /* 3ffee88dc6afecfbfc00000000000000 */ - 9.57941325265705301283958306157728657E-01L, /* 3ffeea77490f0196b000000000000000 */ - 9.61690601605425299247542625380447134E-01L, /* 3ffeec62b5e5881fb000000000000000 */ - 9.65454552197837823079851204965962097E-01L, /* 3ffeee500f1eed967000000000000000 */ - 9.69233234476344074348475032820715569E-01L, /* 3ffef03f56a88b5d7800000000000000 */ - 9.73026706099133165128733935489435680E-01L, /* 3ffef2308e71a927a800000000000000 */ - 9.76835024950062025261843245971249416E-01L, /* 3ffef423b86b7ee79000000000000000 */ - 9.80658249139538557015427500118676107E-01L, /* 3ffef618d68936c09c00000000000000 */ - 9.84496437005408397968864164795377292E-01L, /* 3ffef80feabfeefa4800000000000000 */ - 9.88349647113845042323276857132441364E-01L, /* 3ffefa08f706bbf53800000000000000 */ - 9.92217938260243514925207364285597578E-01L, /* 3ffefc03fd56aa225000000000000000 */ - 9.96101369470117486981664001177705359E-01L, /* 3ffefe00ffaabffbbc00000000000000 */ + L(7.06341639425619532977052017486130353E-01), /* 3ffe69a59c8245a9ac00000000000000 */ + L(7.09106182437398424589503065362805501E-01), /* 3ffe6b0ff72deb89d000000000000000 */ + L(7.11881545564596485142772053222870454E-01), /* 3ffe6c7bbce9a6d93000000000000000 */ + L(7.14667771155948150507697391731198877E-01), /* 3ffe6de8ef213d71e000000000000000 */ + L(7.17464901725936049503573599395167548E-01), /* 3ffe6f578f41e1a9e400000000000000 */ + L(7.20272979955439790478166628417966422E-01), /* 3ffe70c79eba33c06c00000000000000 */ + L(7.23092048692387218133958981525211129E-01), /* 3ffe72391efa434c7400000000000000 */ + L(7.25922150952408251622927082280511968E-01), /* 3ffe73ac117390acd800000000000000 */ + L(7.28763329919491220643124052003258839E-01), /* 3ffe752077990e79d000000000000000 */ + L(7.31615628946641782803794740175362676E-01), /* 3ffe769652df22f7e000000000000000 */ + L(7.34479091556544505525749855223693885E-01), /* 3ffe780da4bba98c4800000000000000 */ + L(7.37353761442226890432394270646909717E-01), /* 3ffe79866ea5f432d400000000000000 */ + L(7.40239682467726090031590047146892175E-01), /* 3ffe7b00b216ccf53000000000000000 */ + L(7.43136898668758316688354170764796436E-01), /* 3ffe7c7c70887763c000000000000000 */ + L(7.46045454253390638577059235103661194E-01), /* 3ffe7df9ab76b20fd000000000000000 */ + L(7.48965393602715662213498148958024103E-01), /* 3ffe7f78645eb8076400000000000000 */ + L(7.51896761271528629722027403659012634E-01), /* 3ffe80f89cbf42526400000000000000 */ + L(7.54839601989007347171423134568613023E-01), /* 3ffe827a561889716000000000000000 */ + L(7.57793960659394638668118204805068672E-01), /* 3ffe83fd91ec46ddc000000000000000 */ + L(7.60759882362683631518152083117456641E-01), /* 3ffe858251bdb68b8c00000000000000 */ + L(7.63737412355305483879774897104653064E-01), /* 3ffe87089711986c9400000000000000 */ + L(7.66726596070820082262642358728044201E-01), /* 3ffe8890636e31f54400000000000000 */ + L(7.69727479120609181517664865168626420E-01), /* 3ffe8a19b85b4fa2d800000000000000 */ + L(7.72740107294572486917871856348938309E-01), /* 3ffe8ba4976246833800000000000000 */ + L(7.75764526561826289752232810315035749E-01), /* 3ffe8d31020df5be4400000000000000 */ + L(7.78800783071404878477039801509818062E-01), /* 3ffe8ebef9eac820b000000000000000 */ + L(7.81848923152964780936002853195532225E-01), /* 3ffe904e8086b5a87800000000000000 */ + L(7.84908993317491698871180005880887620E-01), /* 3ffe91df97714512d800000000000000 */ + L(7.87981040258010162480317717381694820E-01), /* 3ffe9372403b8d6bcc00000000000000 */ + L(7.91065110850296016042904057030682452E-01), /* 3ffe95067c78379f2800000000000000 */ + L(7.94161252153591734614934694036492147E-01), /* 3ffe969c4dbb800b4800000000000000 */ + L(7.97269511411324433014513601847284008E-01), /* 3ffe9833b59b38154400000000000000 */ + L(8.00389936051826789142893403550260700E-01), /* 3ffe99ccb5aec7bec800000000000000 */ + L(8.03522573689060742863077280162542593E-01), /* 3ffe9b674f8f2f3d7c00000000000000 */ + L(8.06667472123343942680406826184480451E-01), /* 3ffe9d0384d70893f800000000000000 */ + L(8.09824679342079301047618855591281317E-01), /* 3ffe9ea15722892c7800000000000000 */ + L(8.12994243520486992160556383169023320E-01), /* 3ffea040c80f8374f000000000000000 */ + L(8.16176213022339780422953481320291758E-01), /* 3ffea1e1d93d687d0000000000000000 */ + L(8.19370636400700819157449927843117621E-01), /* 3ffea3848c4d49954c00000000000000 */ + L(8.22577562398664585696650419777142815E-01), /* 3ffea528e2e1d9f09800000000000000 */ + L(8.25797039950100647542896581398963463E-01), /* 3ffea6cede9f70467c00000000000000 */ + L(8.29029118180400342863478613253391813E-01), /* 3ffea876812c0877bc00000000000000 */ + L(8.32273846407226292054559735333896242E-01), /* 3ffeaa1fcc2f45343800000000000000 */ + L(8.35531274141265073440720811959181447E-01), /* 3ffeabcac15271a2a400000000000000 */ + L(8.38801451086982535754188461396552157E-01), /* 3ffead7762408309bc00000000000000 */ + L(8.42084427143382358016410194068157580E-01), /* 3ffeaf25b0a61a7b4c00000000000000 */ + L(8.45380252404767357221615498019673396E-01), /* 3ffeb0d5ae318680c400000000000000 */ + L(8.48688977161503960155997106085123960E-01), /* 3ffeb2875c92c4c99400000000000000 */ + L(8.52010651900789478530029441571969073E-01), /* 3ffeb43abd7b83db1c00000000000000 */ + L(8.55345327307422548246407245642330963E-01), /* 3ffeb5efd29f24c26400000000000000 */ + L(8.58693054264576483003423845730139874E-01), /* 3ffeb7a69db2bcc77800000000000000 */ + L(8.62053883854575708767242758767679334E-01), /* 3ffeb95f206d17228000000000000000 */ + L(8.65427867359675251357487013592617586E-01), /* 3ffebb195c86b6b29000000000000000 */ + L(8.68815056262843166123843730019871145E-01), /* 3ffebcd553b9d7b62000000000000000 */ + L(8.72215502248546159513864495238522068E-01), /* 3ffebe9307c271855000000000000000 */ + L(8.75629257203538208242932228131394368E-01), /* 3ffec0527a5e384ddc00000000000000 */ + L(8.79056373217652342599848225290770642E-01), /* 3ffec213ad4c9ed0d800000000000000 */ + L(8.82496902584595399599010079327854328E-01), /* 3ffec3d6a24ed8221800000000000000 */ + L(8.85950897802745995779361010136199184E-01), /* 3ffec59b5b27d9696800000000000000 */ + L(8.89418411575955636383383762222365476E-01), /* 3ffec761d99c5ba58800000000000000 */ + L(8.92899496814352794382685374330321793E-01), /* 3ffec92a1f72dd70d400000000000000 */ + L(8.96394206635150403439382671422208659E-01), /* 3ffecaf42e73a4c7d800000000000000 */ + L(8.99902594363456265202927397695020773E-01), /* 3ffeccc00868c0d18800000000000000 */ + L(9.03424713533086704009278378180169966E-01), /* 3ffece8daf1e0ba94c00000000000000 */ + L(9.06960617887383580004723171441582963E-01), /* 3ffed05d24612c2af000000000000000 */ + L(9.10510361380034133338412516422977205E-01), /* 3ffed22e6a0197c02c00000000000000 */ + L(9.14073998175894436579724811053893063E-01), /* 3ffed40181d094303400000000000000 */ + L(9.17651582651815816982221463149471674E-01), /* 3ffed5d66da13970f400000000000000 */ + L(9.21243169397474526149949269893113524E-01), /* 3ffed7ad2f48737a2000000000000000 */ + L(9.24848813216204823639543519675498828E-01), /* 3ffed985c89d041a3000000000000000 */ + L(9.28468569125835141431224428743007593E-01), /* 3ffedb603b7784cd1800000000000000 */ + L(9.32102492359527579068867453315760940E-01), /* 3ffedd3c89b26894e000000000000000 */ + L(9.35750638366620729469147477175283711E-01), /* 3ffedf1ab529fdd41c00000000000000 */ + L(9.39413062813475779888605643463961314E-01), /* 3ffee0fabfbc702a3c00000000000000 */ + L(9.43089821584325888048638830696290825E-01), /* 3ffee2dcab49ca51b400000000000000 */ + L(9.46780970782128888929563004239753354E-01), /* 3ffee4c079b3f8000400000000000000 */ + L(9.50486566729423443256052905780961737E-01), /* 3ffee6a62cdec7c7b000000000000000 */ + L(9.54206665969188322362626308859034907E-01), /* 3ffee88dc6afecfbfc00000000000000 */ + L(9.57941325265705301283958306157728657E-01), /* 3ffeea77490f0196b000000000000000 */ + L(9.61690601605425299247542625380447134E-01), /* 3ffeec62b5e5881fb000000000000000 */ + L(9.65454552197837823079851204965962097E-01), /* 3ffeee500f1eed967000000000000000 */ + L(9.69233234476344074348475032820715569E-01), /* 3ffef03f56a88b5d7800000000000000 */ + L(9.73026706099133165128733935489435680E-01), /* 3ffef2308e71a927a800000000000000 */ + L(9.76835024950062025261843245971249416E-01), /* 3ffef423b86b7ee79000000000000000 */ + L(9.80658249139538557015427500118676107E-01), /* 3ffef618d68936c09c00000000000000 */ + L(9.84496437005408397968864164795377292E-01), /* 3ffef80feabfeefa4800000000000000 */ + L(9.88349647113845042323276857132441364E-01), /* 3ffefa08f706bbf53800000000000000 */ + L(9.92217938260243514925207364285597578E-01), /* 3ffefc03fd56aa225000000000000000 */ + L(9.96101369470117486981664001177705359E-01), /* 3ffefe00ffaabffbbc00000000000000 */ #define T_EXPL_RES1 (T_EXPL_ARG2 + 2 + 2*65 + 89) - 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ - 1.00391388933834757590801700644078664E+00L, /* 3fff0100802ab5577800000000000000 */ - 1.00784309720644799091004983893071767E+00L, /* 3fff0202015600445c00000000000000 */ - 1.01178768355933151879000320150225889E+00L, /* 3fff0304848362076c00000000000000 */ - 1.01574770858668572692806719715008512E+00L, /* 3fff04080ab55de39000000000000000 */ - 1.01972323271377413034244341361045372E+00L, /* 3fff050c94ef7a206c00000000000000 */ - 1.02371431660235789884438872832106426E+00L, /* 3fff06122436410dd000000000000000 */ - 1.02772102115162167201845022646011785E+00L, /* 3fff0718b98f42085000000000000000 */ - 1.03174340749910264936062276319717057E+00L, /* 3fff08205601127ec800000000000000 */ - 1.03578153702162378824169763902318664E+00L, /* 3fff0928fa934ef90800000000000000 */ - 1.03983547133622999947277776300325058E+00L, /* 3fff0a32a84e9c1f5800000000000000 */ - 1.04390527230112850620713516036630608E+00L, /* 3fff0b3d603ca7c32800000000000000 */ - 1.04799100201663270004459604933799710E+00L, /* 3fff0c49236829e8bc00000000000000 */ - 1.05209272282610977189420964350574650E+00L, /* 3fff0d55f2dce5d1e800000000000000 */ - 1.05621049731693195106174698594259098E+00L, /* 3fff0e63cfa7ab09d000000000000000 */ - 1.06034438832143151909548350886325352E+00L, /* 3fff0f72bad65671b800000000000000 */ - 1.06449445891785943185681162503897212E+00L, /* 3fff1082b577d34ed800000000000000 */ - 1.06866077243134810492719566354935523E+00L, /* 3fff1193c09c1c595c00000000000000 */ - 1.07284339243487741866189821848820429E+00L, /* 3fff12a5dd543ccc4c00000000000000 */ - 1.07704238275024494209120007326419000E+00L, /* 3fff13b90cb25176a400000000000000 */ - 1.08125780744903959851299646288680378E+00L, /* 3fff14cd4fc989cd6400000000000000 */ - 1.08548973085361949442173568058933597E+00L, /* 3fff15e2a7ae28fecc00000000000000 */ - 1.08973821753809324563988525369495619E+00L, /* 3fff16f9157587069400000000000000 */ - 1.09400333232930546678574046381982043E+00L, /* 3fff18109a3611c35000000000000000 */ - 1.09828514030782586896606289883493446E+00L, /* 3fff192937074e0cd800000000000000 */ - 1.10258370680894224324930519287590869E+00L, /* 3fff1a42ed01d8cbc800000000000000 */ - 1.10689909742365749645287564817408565E+00L, /* 3fff1b5dbd3f68122400000000000000 */ - 1.11123137799969046168868658241990488E+00L, /* 3fff1c79a8dacc350c00000000000000 */ - 1.11558061464248076122274255794764031E+00L, /* 3fff1d96b0eff0e79400000000000000 */ - 1.11994687371619722204840741142106708E+00L, /* 3fff1eb4d69bde569c00000000000000 */ - 1.12433022184475073235176978414529003E+00L, /* 3fff1fd41afcba45e800000000000000 */ - 1.12873072591281087273529237791080959E+00L, /* 3fff20f47f31c92e4800000000000000 */ - 1.13314845306682632219974493636982515E+00L, /* 3fff2216045b6f5cd000000000000000 */ - 1.13758347071604959399593326452304609E+00L, /* 3fff2338ab9b32134800000000000000 */ - 1.14203584653356560174586320499656722E+00L, /* 3fff245c7613b8a9b000000000000000 */ - 1.14650564845732405583333957110880874E+00L, /* 3fff258164e8cdb0d800000000000000 */ - 1.15099294469117646722011727433709893E+00L, /* 3fff26a7793f60164400000000000000 */ - 1.15549780370591653744227755851170514E+00L, /* 3fff27ceb43d84490400000000000000 */ - 1.16002029424032515603215642840950750E+00L, /* 3fff28f7170a755fd800000000000000 */ - 1.16456048530221917269855680387991015E+00L, /* 3fff2a20a2ce96406400000000000000 */ - 1.16911844616950438835445424956560601E+00L, /* 3fff2b4b58b372c79400000000000000 */ - 1.17369424639123270948104504896036815E+00L, /* 3fff2c7739e3c0f32c00000000000000 */ - 1.17828795578866324378353169777255971E+00L, /* 3fff2da4478b620c7400000000000000 */ - 1.18289964445632783673900689791480545E+00L, /* 3fff2ed282d763d42400000000000000 */ - 1.18752938276310060494722620205720887E+00L, /* 3fff3001ecf601af7000000000000000 */ - 1.19217724135327157730657177125976887E+00L, /* 3fff31328716a5d63c00000000000000 */ - 1.19684329114762477708211463323095813E+00L, /* 3fff32645269ea829000000000000000 */ - 1.20152760334452030077656559114984702E+00L, /* 3fff339750219b212c00000000000000 */ - 1.20623024942098072687102217059873510E+00L, /* 3fff34cb8170b5835400000000000000 */ - 1.21095130113378179892436037334846333E+00L, /* 3fff3600e78b6b11d000000000000000 */ - 1.21569083052054743854242246925423387E+00L, /* 3fff373783a722012400000000000000 */ - 1.22044890990084875515009343871497549E+00L, /* 3fff386f56fa7686e800000000000000 */ - 1.22522561187730755216662714701669756E+00L, /* 3fff39a862bd3c106400000000000000 */ - 1.23002100933670455162882717559114099E+00L, /* 3fff3ae2a8287e7a8000000000000000 */ - 1.23483517545109100499445276000187732E+00L, /* 3fff3c1e2876834aa800000000000000 */ - 1.23966818367890557750499169742397498E+00L, /* 3fff3d5ae4e2cae92c00000000000000 */ - 1.24452010776609517384017067342938390E+00L, /* 3fff3e98deaa11dcbc00000000000000 */ - 1.24939102174724003813111039562500082E+00L, /* 3fff3fd8170a52071800000000000000 */ - 1.25428099994668373895478907797951251E+00L, /* 3fff41188f42c3e32000000000000000 */ - 1.25919011697966698459794088194030337E+00L, /* 3fff425a4893dfc3f800000000000000 */ - 1.26411844775346637881341393949696794E+00L, /* 3fff439d443f5f159000000000000000 */ - 1.26906606746853711786826579555054195E+00L, /* 3fff44e183883d9e4800000000000000 */ - 1.27403305161966090564007458851847332E+00L, /* 3fff462707b2bac20c00000000000000 */ - 1.27901947599709753244923149395617656E+00L, /* 3fff476dd2045ac67800000000000000 */ - 1.28402541668774150540599521264084615E+00L, /* 3fff48b5e3c3e8186800000000000000 */ - 1.28905095007628295311619126550795045E+00L, /* 3fff49ff3e397492bc00000000000000 */ - 1.29409615284637330434591717676084954E+00L, /* 3fff4b49e2ae5ac67400000000000000 */ - 1.29916110198179535206719492634874769E+00L, /* 3fff4c95d26d3f440800000000000000 */ - 1.30424587476763775839572190307080746E+00L, /* 3fff4de30ec211e60000000000000000 */ - 1.30935054879147461104338390214252286E+00L, /* 3fff4f3198fa0f1cf800000000000000 */ - 1.31447520194454914310711046709911898E+00L, /* 3fff50817263c13cd000000000000000 */ - 1.31961991242296217130558488861424848E+00L, /* 3fff51d29c4f01cb3000000000000000 */ - 1.32478475872886558573071624778094701E+00L, /* 3fff5325180cfacf7800000000000000 */ - 1.32996981967165983640200010995613411E+00L, /* 3fff5478e6f02823d000000000000000 */ - 1.33517517436919680440254865061433520E+00L, /* 3fff55ce0a4c58c7bc00000000000000 */ - 1.34040090224898678084031189428060316E+00L, /* 3fff57248376b033d800000000000000 */ - 1.34564708304941055283521222918352578E+00L, /* 3fff587c53c5a7af0400000000000000 */ - 1.35091379682093615244298234756570309E+00L, /* 3fff59d57c910fa4e000000000000000 */ - 1.35620112392734021300455538039386738E+00L, /* 3fff5b2fff3210fd9400000000000000 */ - 1.36150914504693443252136830778908916E+00L, /* 3fff5c8bdd032e770800000000000000 */ - 1.36683794117379636690046140756749082E+00L, /* 3fff5de9176045ff5400000000000000 */ - 1.37218759361900544124779344201670028E+00L, /* 3fff5f47afa69210a800000000000000 */ - 1.37755818401188367960941150158760138E+00L, /* 3fff60a7a734ab0e8800000000000000 */ - 1.38294979430124120867162673675920814E+00L, /* 3fff6208ff6a88a46000000000000000 */ - 1.38836250675662681297595213436579797E+00L, /* 3fff636bb9a983258400000000000000 */ - 1.39379640396958309755959248832368758E+00L, /* 3fff64cfd75454ee7c00000000000000 */ - 1.39925156885490681313299887733592186E+00L, /* 3fff663559cf1bc7c400000000000000 */ - 1.40472808465191417726103395580139477E+00L, /* 3fff679c427f5a49f400000000000000 */ - 1.41022603492571069194738697660795879E+00L, /* 3fff690492cbf9432c00000000000000 */ - 1.41574550356846662335641440222389065E+00L, /* 3fff6a6e4c1d491e1800000000000000 */ + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ + L(1.00391388933834757590801700644078664E+00), /* 3fff0100802ab5577800000000000000 */ + L(1.00784309720644799091004983893071767E+00), /* 3fff0202015600445c00000000000000 */ + L(1.01178768355933151879000320150225889E+00), /* 3fff0304848362076c00000000000000 */ + L(1.01574770858668572692806719715008512E+00), /* 3fff04080ab55de39000000000000000 */ + L(1.01972323271377413034244341361045372E+00), /* 3fff050c94ef7a206c00000000000000 */ + L(1.02371431660235789884438872832106426E+00), /* 3fff06122436410dd000000000000000 */ + L(1.02772102115162167201845022646011785E+00), /* 3fff0718b98f42085000000000000000 */ + L(1.03174340749910264936062276319717057E+00), /* 3fff08205601127ec800000000000000 */ + L(1.03578153702162378824169763902318664E+00), /* 3fff0928fa934ef90800000000000000 */ + L(1.03983547133622999947277776300325058E+00), /* 3fff0a32a84e9c1f5800000000000000 */ + L(1.04390527230112850620713516036630608E+00), /* 3fff0b3d603ca7c32800000000000000 */ + L(1.04799100201663270004459604933799710E+00), /* 3fff0c49236829e8bc00000000000000 */ + L(1.05209272282610977189420964350574650E+00), /* 3fff0d55f2dce5d1e800000000000000 */ + L(1.05621049731693195106174698594259098E+00), /* 3fff0e63cfa7ab09d000000000000000 */ + L(1.06034438832143151909548350886325352E+00), /* 3fff0f72bad65671b800000000000000 */ + L(1.06449445891785943185681162503897212E+00), /* 3fff1082b577d34ed800000000000000 */ + L(1.06866077243134810492719566354935523E+00), /* 3fff1193c09c1c595c00000000000000 */ + L(1.07284339243487741866189821848820429E+00), /* 3fff12a5dd543ccc4c00000000000000 */ + L(1.07704238275024494209120007326419000E+00), /* 3fff13b90cb25176a400000000000000 */ + L(1.08125780744903959851299646288680378E+00), /* 3fff14cd4fc989cd6400000000000000 */ + L(1.08548973085361949442173568058933597E+00), /* 3fff15e2a7ae28fecc00000000000000 */ + L(1.08973821753809324563988525369495619E+00), /* 3fff16f9157587069400000000000000 */ + L(1.09400333232930546678574046381982043E+00), /* 3fff18109a3611c35000000000000000 */ + L(1.09828514030782586896606289883493446E+00), /* 3fff192937074e0cd800000000000000 */ + L(1.10258370680894224324930519287590869E+00), /* 3fff1a42ed01d8cbc800000000000000 */ + L(1.10689909742365749645287564817408565E+00), /* 3fff1b5dbd3f68122400000000000000 */ + L(1.11123137799969046168868658241990488E+00), /* 3fff1c79a8dacc350c00000000000000 */ + L(1.11558061464248076122274255794764031E+00), /* 3fff1d96b0eff0e79400000000000000 */ + L(1.11994687371619722204840741142106708E+00), /* 3fff1eb4d69bde569c00000000000000 */ + L(1.12433022184475073235176978414529003E+00), /* 3fff1fd41afcba45e800000000000000 */ + L(1.12873072591281087273529237791080959E+00), /* 3fff20f47f31c92e4800000000000000 */ + L(1.13314845306682632219974493636982515E+00), /* 3fff2216045b6f5cd000000000000000 */ + L(1.13758347071604959399593326452304609E+00), /* 3fff2338ab9b32134800000000000000 */ + L(1.14203584653356560174586320499656722E+00), /* 3fff245c7613b8a9b000000000000000 */ + L(1.14650564845732405583333957110880874E+00), /* 3fff258164e8cdb0d800000000000000 */ + L(1.15099294469117646722011727433709893E+00), /* 3fff26a7793f60164400000000000000 */ + L(1.15549780370591653744227755851170514E+00), /* 3fff27ceb43d84490400000000000000 */ + L(1.16002029424032515603215642840950750E+00), /* 3fff28f7170a755fd800000000000000 */ + L(1.16456048530221917269855680387991015E+00), /* 3fff2a20a2ce96406400000000000000 */ + L(1.16911844616950438835445424956560601E+00), /* 3fff2b4b58b372c79400000000000000 */ + L(1.17369424639123270948104504896036815E+00), /* 3fff2c7739e3c0f32c00000000000000 */ + L(1.17828795578866324378353169777255971E+00), /* 3fff2da4478b620c7400000000000000 */ + L(1.18289964445632783673900689791480545E+00), /* 3fff2ed282d763d42400000000000000 */ + L(1.18752938276310060494722620205720887E+00), /* 3fff3001ecf601af7000000000000000 */ + L(1.19217724135327157730657177125976887E+00), /* 3fff31328716a5d63c00000000000000 */ + L(1.19684329114762477708211463323095813E+00), /* 3fff32645269ea829000000000000000 */ + L(1.20152760334452030077656559114984702E+00), /* 3fff339750219b212c00000000000000 */ + L(1.20623024942098072687102217059873510E+00), /* 3fff34cb8170b5835400000000000000 */ + L(1.21095130113378179892436037334846333E+00), /* 3fff3600e78b6b11d000000000000000 */ + L(1.21569083052054743854242246925423387E+00), /* 3fff373783a722012400000000000000 */ + L(1.22044890990084875515009343871497549E+00), /* 3fff386f56fa7686e800000000000000 */ + L(1.22522561187730755216662714701669756E+00), /* 3fff39a862bd3c106400000000000000 */ + L(1.23002100933670455162882717559114099E+00), /* 3fff3ae2a8287e7a8000000000000000 */ + L(1.23483517545109100499445276000187732E+00), /* 3fff3c1e2876834aa800000000000000 */ + L(1.23966818367890557750499169742397498E+00), /* 3fff3d5ae4e2cae92c00000000000000 */ + L(1.24452010776609517384017067342938390E+00), /* 3fff3e98deaa11dcbc00000000000000 */ + L(1.24939102174724003813111039562500082E+00), /* 3fff3fd8170a52071800000000000000 */ + L(1.25428099994668373895478907797951251E+00), /* 3fff41188f42c3e32000000000000000 */ + L(1.25919011697966698459794088194030337E+00), /* 3fff425a4893dfc3f800000000000000 */ + L(1.26411844775346637881341393949696794E+00), /* 3fff439d443f5f159000000000000000 */ + L(1.26906606746853711786826579555054195E+00), /* 3fff44e183883d9e4800000000000000 */ + L(1.27403305161966090564007458851847332E+00), /* 3fff462707b2bac20c00000000000000 */ + L(1.27901947599709753244923149395617656E+00), /* 3fff476dd2045ac67800000000000000 */ + L(1.28402541668774150540599521264084615E+00), /* 3fff48b5e3c3e8186800000000000000 */ + L(1.28905095007628295311619126550795045E+00), /* 3fff49ff3e397492bc00000000000000 */ + L(1.29409615284637330434591717676084954E+00), /* 3fff4b49e2ae5ac67400000000000000 */ + L(1.29916110198179535206719492634874769E+00), /* 3fff4c95d26d3f440800000000000000 */ + L(1.30424587476763775839572190307080746E+00), /* 3fff4de30ec211e60000000000000000 */ + L(1.30935054879147461104338390214252286E+00), /* 3fff4f3198fa0f1cf800000000000000 */ + L(1.31447520194454914310711046709911898E+00), /* 3fff50817263c13cd000000000000000 */ + L(1.31961991242296217130558488861424848E+00), /* 3fff51d29c4f01cb3000000000000000 */ + L(1.32478475872886558573071624778094701E+00), /* 3fff5325180cfacf7800000000000000 */ + L(1.32996981967165983640200010995613411E+00), /* 3fff5478e6f02823d000000000000000 */ + L(1.33517517436919680440254865061433520E+00), /* 3fff55ce0a4c58c7bc00000000000000 */ + L(1.34040090224898678084031189428060316E+00), /* 3fff57248376b033d800000000000000 */ + L(1.34564708304941055283521222918352578E+00), /* 3fff587c53c5a7af0400000000000000 */ + L(1.35091379682093615244298234756570309E+00), /* 3fff59d57c910fa4e000000000000000 */ + L(1.35620112392734021300455538039386738E+00), /* 3fff5b2fff3210fd9400000000000000 */ + L(1.36150914504693443252136830778908916E+00), /* 3fff5c8bdd032e770800000000000000 */ + L(1.36683794117379636690046140756749082E+00), /* 3fff5de9176045ff5400000000000000 */ + L(1.37218759361900544124779344201670028E+00), /* 3fff5f47afa69210a800000000000000 */ + L(1.37755818401188367960941150158760138E+00), /* 3fff60a7a734ab0e8800000000000000 */ + L(1.38294979430124120867162673675920814E+00), /* 3fff6208ff6a88a46000000000000000 */ + L(1.38836250675662681297595213436579797E+00), /* 3fff636bb9a983258400000000000000 */ + L(1.39379640396958309755959248832368758E+00), /* 3fff64cfd75454ee7c00000000000000 */ + L(1.39925156885490681313299887733592186E+00), /* 3fff663559cf1bc7c400000000000000 */ + L(1.40472808465191417726103395580139477E+00), /* 3fff679c427f5a49f400000000000000 */ + L(1.41022603492571069194738697660795879E+00), /* 3fff690492cbf9432c00000000000000 */ + L(1.41574550356846662335641440222389065E+00), /* 3fff6a6e4c1d491e1800000000000000 */ - 9.98018323540573404351050612604012713E-01L, /* 3ffefefc41f8d4bdb000000000000000 */ - 9.98048781107475468932221929208026268E-01L, /* 3ffeff003ff556aa8800000000000000 */ - 9.98079239603882895082165305211674422E-01L, /* 3ffeff043df9d4986000000000000000 */ - 9.98109699029824021243584297735651489E-01L, /* 3ffeff083c064e972c00000000000000 */ - 9.98140159385327269125909310787392315E-01L, /* 3ffeff0c3a1ac4b6ec00000000000000 */ - 9.98170620670420977171843901487591211E-01L, /* 3ffeff10383737079400000000000000 */ - 9.98201082885133511579667242585856002E-01L, /* 3ffeff14365ba5991c00000000000000 */ - 9.98231546029493238547658506831794512E-01L, /* 3ffeff183488107b7c00000000000000 */ - 9.98262010103528552029672482603928074E-01L, /* 3ffeff1c32bc77beb000000000000000 */ - 9.98292475107267818223988342651864514E-01L, /* 3ffeff2030f8db72b000000000000000 */ - 9.98322941040739375573309644096298143E-01L, /* 3ffeff242f3d3ba77000000000000000 */ - 9.98353407903971645787066790944663808E-01L, /* 3ffeff282d89986cf000000000000000 */ - 9.98383875696992967307963340317655820E-01L, /* 3ffeff2c2bddf1d32400000000000000 */ - 9.98414344419831761845429696222709026E-01L, /* 3ffeff302a3a47ea0c00000000000000 */ - 9.98444814072516340086593800151604228E-01L, /* 3ffeff34289e9ac19800000000000000 */ - 9.98475284655075123740886056111776270E-01L, /* 3ffeff38270aea69c800000000000000 */ - 9.98505756167536479006585636852832977E-01L, /* 3ffeff3c257f36f29400000000000000 */ - 9.98536228609928799837547330753295682E-01L, /* 3ffeff4023fb806bf800000000000000 */ - 9.98566701982280452432050310562772211E-01L, /* 3ffeff44227fc6e5ec00000000000000 */ - 9.98597176284619802988373749030870385E-01L, /* 3ffeff48210c0a706800000000000000 */ - 9.98627651516975245460372434536111541E-01L, /* 3ffeff4c1fa04b1b6800000000000000 */ - 9.98658127679375173801901155457017012E-01L, /* 3ffeff501e3c88f6e800000000000000 */ - 9.98688604771847954211239084543194622E-01L, /* 3ffeff541ce0c412e000000000000000 */ - 9.98719082794421980642241010173165705E-01L, /* 3ffeff581b8cfc7f4c00000000000000 */ - 9.98749561747125619293186105096538085E-01L, /* 3ffeff5c1a41324c2400000000000000 */ - 9.98780041629987291873504773320746608E-01L, /* 3ffeff6018fd65896800000000000000 */ - 9.98810522443035364581476187595399097E-01L, /* 3ffeff6417c196471000000000000000 */ - 9.98841004186298203615379520670103375E-01L, /* 3ffeff68168dc4951400000000000000 */ - 9.98871486859804230684645176552294288E-01L, /* 3ffeff6c1561f0837400000000000000 */ - 9.98901970463581839743127943620493170E-01L, /* 3ffeff70143e1a222c00000000000000 */ - 9.98932454997659369233531378995394334E-01L, /* 3ffeff74132241813000000000000000 */ - 9.98962940462065268620861502313346136E-01L, /* 3ffeff78120e66b08400000000000000 */ - 9.98993426856827904103397486323956400E-01L, /* 3ffeff7c110289c02000000000000000 */ - 9.99023914181975669634994119405746460E-01L, /* 3ffeff800ffeaac00000000000000000 */ - 9.99054402437536959169506189937237650E-01L, /* 3ffeff840f02c9c02000000000000000 */ - 9.99084891623540138905212870668037795E-01L, /* 3ffeff880e0ee6d07800000000000000 */ - 9.99115381740013658307120181234495249E-01L, /* 3ffeff8c0d2302010c00000000000000 */ - 9.99145872786985911329082910015131347E-01L, /* 3ffeff900c3f1b61d800000000000000 */ - 9.99176364764485236413804614130640402E-01L, /* 3ffeff940b633302d000000000000000 */ - 9.99206857672540083026291313217370771E-01L, /* 3ffeff980a8f48f3f800000000000000 */ - 9.99237351511178817364822180024930276E-01L, /* 3ffeff9c09c35d454800000000000000 */ - 9.99267846280429861138827618560753763E-01L, /* 3ffeffa008ff7006c000000000000000 */ - 9.99298341980321608302162417203362565E-01L, /* 3ffeffa4084381485c00000000000000 */ - 9.99328838610882452808681364331278019E-01L, /* 3ffeffa8078f911a1800000000000000 */ - 9.99359336172140816367814863951934967E-01L, /* 3ffeffac06e39f8bf400000000000000 */ - 9.99389834664125092933417704443854745E-01L, /* 3ffeffb0063facadec00000000000000 */ - 9.99420334086863676459344674185558688E-01L, /* 3ffeffb405a3b88ffc00000000000000 */ - 9.99450834440384988655026177184481639E-01L, /* 3ffeffb8050fc3422400000000000000 */ - 9.99481335724717395718741386190231424E-01L, /* 3ffeffbc0483ccd45c00000000000000 */ - 9.99511837939889374871071936468069907E-01L, /* 3ffeffc003ffd556ac00000000000000 */ - 9.99542341085929264554721385138691403E-01L, /* 3ffeffc40383dcd90800000000000000 */ - 9.99572845162865514234695751838444266E-01L, /* 3ffeffc8030fe36b7400000000000000 */ - 9.99603350170726517864849824945849832E-01L, /* 3ffeffcc02a3e91dec00000000000000 */ - 9.99633856109540669399038392839429434E-01L, /* 3ffeffd0023fee006c00000000000000 */ - 9.99664362979336418302267475155531429E-01L, /* 3ffeffd401e3f222f800000000000000 */ - 9.99694870780142130772816244643763639E-01L, /* 3ffeffd8018ff5958800000000000000 */ - 9.99725379511986284031266336569387931E-01L, /* 3ffeffdc0143f8682400000000000000 */ - 9.99755889174897216520321308053098619E-01L, /* 3ffeffe000fffaaac000000000000000 */ - 9.99786399768903377704987178731244057E-01L, /* 3ffeffe400c3fc6d6000000000000000 */ - 9.99816911294033217050269968240172602E-01L, /* 3ffeffe8008ffdc00800000000000000 */ - 9.99847423750315072998873233700578567E-01L, /* 3ffeffec0063feb2ac00000000000000 */ - 9.99877937137777450526954226006637327E-01L, /* 3ffefff0003fff555800000000000000 */ - 9.99908451456448688077216502279043198E-01L, /* 3ffefff40023ffb80000000000000000 */ - 9.99938966706357262870241697783058044E-01L, /* 3ffefff8000fffeaac00000000000000 */ - 9.99969482887531541104308985268289689E-01L, /* 3ffefffc0003fffd5400000000000000 */ + L(9.98018323540573404351050612604012713E-01), /* 3ffefefc41f8d4bdb000000000000000 */ + L(9.98048781107475468932221929208026268E-01), /* 3ffeff003ff556aa8800000000000000 */ + L(9.98079239603882895082165305211674422E-01), /* 3ffeff043df9d4986000000000000000 */ + L(9.98109699029824021243584297735651489E-01), /* 3ffeff083c064e972c00000000000000 */ + L(9.98140159385327269125909310787392315E-01), /* 3ffeff0c3a1ac4b6ec00000000000000 */ + L(9.98170620670420977171843901487591211E-01), /* 3ffeff10383737079400000000000000 */ + L(9.98201082885133511579667242585856002E-01), /* 3ffeff14365ba5991c00000000000000 */ + L(9.98231546029493238547658506831794512E-01), /* 3ffeff183488107b7c00000000000000 */ + L(9.98262010103528552029672482603928074E-01), /* 3ffeff1c32bc77beb000000000000000 */ + L(9.98292475107267818223988342651864514E-01), /* 3ffeff2030f8db72b000000000000000 */ + L(9.98322941040739375573309644096298143E-01), /* 3ffeff242f3d3ba77000000000000000 */ + L(9.98353407903971645787066790944663808E-01), /* 3ffeff282d89986cf000000000000000 */ + L(9.98383875696992967307963340317655820E-01), /* 3ffeff2c2bddf1d32400000000000000 */ + L(9.98414344419831761845429696222709026E-01), /* 3ffeff302a3a47ea0c00000000000000 */ + L(9.98444814072516340086593800151604228E-01), /* 3ffeff34289e9ac19800000000000000 */ + L(9.98475284655075123740886056111776270E-01), /* 3ffeff38270aea69c800000000000000 */ + L(9.98505756167536479006585636852832977E-01), /* 3ffeff3c257f36f29400000000000000 */ + L(9.98536228609928799837547330753295682E-01), /* 3ffeff4023fb806bf800000000000000 */ + L(9.98566701982280452432050310562772211E-01), /* 3ffeff44227fc6e5ec00000000000000 */ + L(9.98597176284619802988373749030870385E-01), /* 3ffeff48210c0a706800000000000000 */ + L(9.98627651516975245460372434536111541E-01), /* 3ffeff4c1fa04b1b6800000000000000 */ + L(9.98658127679375173801901155457017012E-01), /* 3ffeff501e3c88f6e800000000000000 */ + L(9.98688604771847954211239084543194622E-01), /* 3ffeff541ce0c412e000000000000000 */ + L(9.98719082794421980642241010173165705E-01), /* 3ffeff581b8cfc7f4c00000000000000 */ + L(9.98749561747125619293186105096538085E-01), /* 3ffeff5c1a41324c2400000000000000 */ + L(9.98780041629987291873504773320746608E-01), /* 3ffeff6018fd65896800000000000000 */ + L(9.98810522443035364581476187595399097E-01), /* 3ffeff6417c196471000000000000000 */ + L(9.98841004186298203615379520670103375E-01), /* 3ffeff68168dc4951400000000000000 */ + L(9.98871486859804230684645176552294288E-01), /* 3ffeff6c1561f0837400000000000000 */ + L(9.98901970463581839743127943620493170E-01), /* 3ffeff70143e1a222c00000000000000 */ + L(9.98932454997659369233531378995394334E-01), /* 3ffeff74132241813000000000000000 */ + L(9.98962940462065268620861502313346136E-01), /* 3ffeff78120e66b08400000000000000 */ + L(9.98993426856827904103397486323956400E-01), /* 3ffeff7c110289c02000000000000000 */ + L(9.99023914181975669634994119405746460E-01), /* 3ffeff800ffeaac00000000000000000 */ + L(9.99054402437536959169506189937237650E-01), /* 3ffeff840f02c9c02000000000000000 */ + L(9.99084891623540138905212870668037795E-01), /* 3ffeff880e0ee6d07800000000000000 */ + L(9.99115381740013658307120181234495249E-01), /* 3ffeff8c0d2302010c00000000000000 */ + L(9.99145872786985911329082910015131347E-01), /* 3ffeff900c3f1b61d800000000000000 */ + L(9.99176364764485236413804614130640402E-01), /* 3ffeff940b633302d000000000000000 */ + L(9.99206857672540083026291313217370771E-01), /* 3ffeff980a8f48f3f800000000000000 */ + L(9.99237351511178817364822180024930276E-01), /* 3ffeff9c09c35d454800000000000000 */ + L(9.99267846280429861138827618560753763E-01), /* 3ffeffa008ff7006c000000000000000 */ + L(9.99298341980321608302162417203362565E-01), /* 3ffeffa4084381485c00000000000000 */ + L(9.99328838610882452808681364331278019E-01), /* 3ffeffa8078f911a1800000000000000 */ + L(9.99359336172140816367814863951934967E-01), /* 3ffeffac06e39f8bf400000000000000 */ + L(9.99389834664125092933417704443854745E-01), /* 3ffeffb0063facadec00000000000000 */ + L(9.99420334086863676459344674185558688E-01), /* 3ffeffb405a3b88ffc00000000000000 */ + L(9.99450834440384988655026177184481639E-01), /* 3ffeffb8050fc3422400000000000000 */ + L(9.99481335724717395718741386190231424E-01), /* 3ffeffbc0483ccd45c00000000000000 */ + L(9.99511837939889374871071936468069907E-01), /* 3ffeffc003ffd556ac00000000000000 */ + L(9.99542341085929264554721385138691403E-01), /* 3ffeffc40383dcd90800000000000000 */ + L(9.99572845162865514234695751838444266E-01), /* 3ffeffc8030fe36b7400000000000000 */ + L(9.99603350170726517864849824945849832E-01), /* 3ffeffcc02a3e91dec00000000000000 */ + L(9.99633856109540669399038392839429434E-01), /* 3ffeffd0023fee006c00000000000000 */ + L(9.99664362979336418302267475155531429E-01), /* 3ffeffd401e3f222f800000000000000 */ + L(9.99694870780142130772816244643763639E-01), /* 3ffeffd8018ff5958800000000000000 */ + L(9.99725379511986284031266336569387931E-01), /* 3ffeffdc0143f8682400000000000000 */ + L(9.99755889174897216520321308053098619E-01), /* 3ffeffe000fffaaac000000000000000 */ + L(9.99786399768903377704987178731244057E-01), /* 3ffeffe400c3fc6d6000000000000000 */ + L(9.99816911294033217050269968240172602E-01), /* 3ffeffe8008ffdc00800000000000000 */ + L(9.99847423750315072998873233700578567E-01), /* 3ffeffec0063feb2ac00000000000000 */ + L(9.99877937137777450526954226006637327E-01), /* 3ffefff0003fff555800000000000000 */ + L(9.99908451456448688077216502279043198E-01), /* 3ffefff40023ffb80000000000000000 */ + L(9.99938966706357262870241697783058044E-01), /* 3ffefff8000fffeaac00000000000000 */ + L(9.99969482887531541104308985268289689E-01), /* 3ffefffc0003fffd5400000000000000 */ #define T_EXPL_RES2 (T_EXPL_RES1 + 1 + 89 + 65) - 1.00000000000000000000000000000000000E+00L, /* 3fff0000000000000000000000000000 */ - 1.00003051804379100575559391472779680E+00L, /* 3fff0002000200015400000000000000 */ - 1.00006103701893306334724798034585547E+00L, /* 3fff00040008000aac00000000000000 */ - 1.00009155692545448346209013834595680E+00L, /* 3fff0006001200240000000000000000 */ - 1.00012207776338379883185325525118969E+00L, /* 3fff0008002000555800000000000000 */ - 1.00015259953274932014366527255333494E+00L, /* 3fff000a003200a6ac00000000000000 */ - 1.00018312223357958012925905677548144E+00L, /* 3fff000c004801200400000000000000 */ - 1.00021364586590294498691378066723701E+00L, /* 3fff000e006201c95c00000000000000 */ - 1.00024417042974783642605984823603649E+00L, /* 3fff0010008002aab400000000000000 */ - 1.00027469592514273166727889474714175E+00L, /* 3fff001200a203cc1000000000000000 */ - 1.00030522235211605242000132420798764E+00L, /* 3fff001400c805357000000000000000 */ - 1.00033574971069616488250630936818197E+00L, /* 3fff001600f206eed000000000000000 */ - 1.00036627800091160178652671675081365E+00L, /* 3fff0018012009003800000000000000 */ - 1.00039680722279067381919048784766346E+00L, /* 3fff001a01520b71a000000000000000 */ - 1.00042733737636191371223048918182030E+00L, /* 3fff001c01880e4b1000000000000000 */ - 1.00045786846165368766392589350289200E+00L, /* 3fff001e01c211948400000000000000 */ - 1.00048840047869447289485833607614040E+00L, /* 3fff0020020015560000000000000000 */ - 1.00051893342751269111445822090900037E+00L, /* 3fff0022024219978400000000000000 */ - 1.00054946730813676403215595200890675E+00L, /* 3fff002402881e611000000000000000 */ - 1.00058000212059516886853316464112140E+00L, /* 3fff002602d223baa800000000000000 */ - 1.00061053786491632733302026281307917E+00L, /* 3fff0028032029ac4c00000000000000 */ - 1.00064107454112866113504765053221490E+00L, /* 3fff002a0372303dfc00000000000000 */ - 1.00067161214926059198404573180596344E+00L, /* 3fff002c03c83777b800000000000000 */ - 1.00070215068934059710059614189958666E+00L, /* 3fff002e04223f618400000000000000 */ - 1.00073269016139709819412928482051939E+00L, /* 3fff0030048048036000000000000000 */ - 1.00076323056545857248522679583402351E+00L, /* 3fff003204e251655000000000000000 */ - 1.00079377190155338617216784768970683E+00L, /* 3fff003405485b8f5000000000000000 */ - 1.00082431416971007198668530691065826E+00L, /* 3fff003605b266896800000000000000 */ - 1.00085485736995705163820957750431262E+00L, /* 3fff00380620725b9800000000000000 */ - 1.00088540150232269132501983222027775E+00L, /* 3fff003a06927f0ddc00000000000000 */ - 1.00091594656683552377884893758164253E+00L, /* 3fff003c07088ca83c00000000000000 */ - 1.00094649256352402622027852885366883E+00L, /* 3fff003e07829b32bc00000000000000 */ - 1.00097703949241650933643654752813745E+00L, /* 3fff00400800aab55400000000000000 */ - 1.00100758735354156137020709138596430E+00L, /* 3fff00420882bb381000000000000000 */ - 1.00103813614692760403102056443458423E+00L, /* 3fff00440908ccc2f000000000000000 */ - 1.00106868587260300351715613942360505E+00L, /* 3fff00460992df5df000000000000000 */ - 1.00109923653059629256034668287611566E+00L, /* 3fff00480a20f3111800000000000000 */ - 1.00112978812093589287002259879955091E+00L, /* 3fff004a0ab307e46800000000000000 */ - 1.00116034064365022615561429120134562E+00L, /* 3fff004c0b491ddfe000000000000000 */ - 1.00119089409876788066000585786241572E+00L, /* 3fff004e0be3350b8c00000000000000 */ - 1.00122144848631711155917400901671499E+00L, /* 3fff00500c814d6f6000000000000000 */ - 1.00125200380632656260715407370298635E+00L, /* 3fff00520d2367136c00000000000000 */ - 1.00128256005882454449107399341301061E+00L, /* 3fff00540dc981ffa800000000000000 */ - 1.00131311724383964545381786592770368E+00L, /* 3fff00560e739e3c2000000000000000 */ - 1.00134367536140017618251363273884635E+00L, /* 3fff00580f21bbd0cc00000000000000 */ - 1.00137423441153472492004539162735455E+00L, /* 3fff005a0fd3dac5b800000000000000 */ - 1.00140479439427171337584354660066310E+00L, /* 3fff005c1089fb22e400000000000000 */ - 1.00143535530963956325933850166620687E+00L, /* 3fff005e11441cf05000000000000000 */ - 1.00146591715766680730226312334707472E+00L, /* 3fff0060120240360400000000000000 */ - 1.00149647993838186721404781565070152E+00L, /* 3fff006212c464fc0000000000000000 */ - 1.00152704365181316470412298258452211E+00L, /* 3fff0064138a8b4a4400000000000000 */ - 1.00155760829798923250422149067162536E+00L, /* 3fff00661454b328d800000000000000 */ - 1.00158817387693849232377374391944613E+00L, /* 3fff00681522dc9fbc00000000000000 */ - 1.00161874038868942138336137759324629E+00L, /* 3fff006a15f507b6f400000000000000 */ - 1.00164930783327055241471725821611471E+00L, /* 3fff006c16cb34768800000000000000 */ - 1.00167987621071025161612055853765924E+00L, /* 3fff006e17a562e67400000000000000 */ - 1.00171044552103705171930414508096874E+00L, /* 3fff00701883930ec000000000000000 */ - 1.00174101576427937443369842185347807E+00L, /* 3fff00721965c4f76c00000000000000 */ - 1.00177158694046569697988502412044909E+00L, /* 3fff00741a4bf8a87c00000000000000 */ - 1.00180215904962455208959681840497069E+00L, /* 3fff00761b362e29f800000000000000 */ - 1.00183273209178441698341543997230474E+00L, /* 3fff00781c246583e400000000000000 */ - 1.00186330606697365785962006157205906E+00L, /* 3fff007a1d169ebe3c00000000000000 */ - 1.00189388097522080744994354972732253E+00L, /* 3fff007c1e0cd9e10800000000000000 */ - 1.00192445681655439848611877096118405E+00L, /* 3fff007e1f0716f45000000000000000 */ - 1.00195503359100279716642489802325144E+00L, /* 3fff0080200556001000000000000000 */ - 1.00198561129859459173374602869444061E+00L, /* 3fff00822107970c5400000000000000 */ + L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */ + L(1.00003051804379100575559391472779680E+00), /* 3fff0002000200015400000000000000 */ + L(1.00006103701893306334724798034585547E+00), /* 3fff00040008000aac00000000000000 */ + L(1.00009155692545448346209013834595680E+00), /* 3fff0006001200240000000000000000 */ + L(1.00012207776338379883185325525118969E+00), /* 3fff0008002000555800000000000000 */ + L(1.00015259953274932014366527255333494E+00), /* 3fff000a003200a6ac00000000000000 */ + L(1.00018312223357958012925905677548144E+00), /* 3fff000c004801200400000000000000 */ + L(1.00021364586590294498691378066723701E+00), /* 3fff000e006201c95c00000000000000 */ + L(1.00024417042974783642605984823603649E+00), /* 3fff0010008002aab400000000000000 */ + L(1.00027469592514273166727889474714175E+00), /* 3fff001200a203cc1000000000000000 */ + L(1.00030522235211605242000132420798764E+00), /* 3fff001400c805357000000000000000 */ + L(1.00033574971069616488250630936818197E+00), /* 3fff001600f206eed000000000000000 */ + L(1.00036627800091160178652671675081365E+00), /* 3fff0018012009003800000000000000 */ + L(1.00039680722279067381919048784766346E+00), /* 3fff001a01520b71a000000000000000 */ + L(1.00042733737636191371223048918182030E+00), /* 3fff001c01880e4b1000000000000000 */ + L(1.00045786846165368766392589350289200E+00), /* 3fff001e01c211948400000000000000 */ + L(1.00048840047869447289485833607614040E+00), /* 3fff0020020015560000000000000000 */ + L(1.00051893342751269111445822090900037E+00), /* 3fff0022024219978400000000000000 */ + L(1.00054946730813676403215595200890675E+00), /* 3fff002402881e611000000000000000 */ + L(1.00058000212059516886853316464112140E+00), /* 3fff002602d223baa800000000000000 */ + L(1.00061053786491632733302026281307917E+00), /* 3fff0028032029ac4c00000000000000 */ + L(1.00064107454112866113504765053221490E+00), /* 3fff002a0372303dfc00000000000000 */ + L(1.00067161214926059198404573180596344E+00), /* 3fff002c03c83777b800000000000000 */ + L(1.00070215068934059710059614189958666E+00), /* 3fff002e04223f618400000000000000 */ + L(1.00073269016139709819412928482051939E+00), /* 3fff0030048048036000000000000000 */ + L(1.00076323056545857248522679583402351E+00), /* 3fff003204e251655000000000000000 */ + L(1.00079377190155338617216784768970683E+00), /* 3fff003405485b8f5000000000000000 */ + L(1.00082431416971007198668530691065826E+00), /* 3fff003605b266896800000000000000 */ + L(1.00085485736995705163820957750431262E+00), /* 3fff00380620725b9800000000000000 */ + L(1.00088540150232269132501983222027775E+00), /* 3fff003a06927f0ddc00000000000000 */ + L(1.00091594656683552377884893758164253E+00), /* 3fff003c07088ca83c00000000000000 */ + L(1.00094649256352402622027852885366883E+00), /* 3fff003e07829b32bc00000000000000 */ + L(1.00097703949241650933643654752813745E+00), /* 3fff00400800aab55400000000000000 */ + L(1.00100758735354156137020709138596430E+00), /* 3fff00420882bb381000000000000000 */ + L(1.00103813614692760403102056443458423E+00), /* 3fff00440908ccc2f000000000000000 */ + L(1.00106868587260300351715613942360505E+00), /* 3fff00460992df5df000000000000000 */ + L(1.00109923653059629256034668287611566E+00), /* 3fff00480a20f3111800000000000000 */ + L(1.00112978812093589287002259879955091E+00), /* 3fff004a0ab307e46800000000000000 */ + L(1.00116034064365022615561429120134562E+00), /* 3fff004c0b491ddfe000000000000000 */ + L(1.00119089409876788066000585786241572E+00), /* 3fff004e0be3350b8c00000000000000 */ + L(1.00122144848631711155917400901671499E+00), /* 3fff00500c814d6f6000000000000000 */ + L(1.00125200380632656260715407370298635E+00), /* 3fff00520d2367136c00000000000000 */ + L(1.00128256005882454449107399341301061E+00), /* 3fff00540dc981ffa800000000000000 */ + L(1.00131311724383964545381786592770368E+00), /* 3fff00560e739e3c2000000000000000 */ + L(1.00134367536140017618251363273884635E+00), /* 3fff00580f21bbd0cc00000000000000 */ + L(1.00137423441153472492004539162735455E+00), /* 3fff005a0fd3dac5b800000000000000 */ + L(1.00140479439427171337584354660066310E+00), /* 3fff005c1089fb22e400000000000000 */ + L(1.00143535530963956325933850166620687E+00), /* 3fff005e11441cf05000000000000000 */ + L(1.00146591715766680730226312334707472E+00), /* 3fff0060120240360400000000000000 */ + L(1.00149647993838186721404781565070152E+00), /* 3fff006212c464fc0000000000000000 */ + L(1.00152704365181316470412298258452211E+00), /* 3fff0064138a8b4a4400000000000000 */ + L(1.00155760829798923250422149067162536E+00), /* 3fff00661454b328d800000000000000 */ + L(1.00158817387693849232377374391944613E+00), /* 3fff00681522dc9fbc00000000000000 */ + L(1.00161874038868942138336137759324629E+00), /* 3fff006a15f507b6f400000000000000 */ + L(1.00164930783327055241471725821611471E+00), /* 3fff006c16cb34768800000000000000 */ + L(1.00167987621071025161612055853765924E+00), /* 3fff006e17a562e67400000000000000 */ + L(1.00171044552103705171930414508096874E+00), /* 3fff00701883930ec000000000000000 */ + L(1.00174101576427937443369842185347807E+00), /* 3fff00721965c4f76c00000000000000 */ + L(1.00177158694046569697988502412044909E+00), /* 3fff00741a4bf8a87c00000000000000 */ + L(1.00180215904962455208959681840497069E+00), /* 3fff00761b362e29f800000000000000 */ + L(1.00183273209178441698341543997230474E+00), /* 3fff00781c246583e400000000000000 */ + L(1.00186330606697365785962006157205906E+00), /* 3fff007a1d169ebe3c00000000000000 */ + L(1.00189388097522080744994354972732253E+00), /* 3fff007c1e0cd9e10800000000000000 */ + L(1.00192445681655439848611877096118405E+00), /* 3fff007e1f0716f45000000000000000 */ + L(1.00195503359100279716642489802325144E+00), /* 3fff0080200556001000000000000000 */ + L(1.00198561129859459173374602869444061E+00), /* 3fff00822107970c5400000000000000 */ }; diff --git a/sysdeps/ieee754/ldbl-128/t_sincosl.c b/sysdeps/ieee754/ldbl-128/t_sincosl.c index de5fe0d9e9..7d65c5fcb0 100644 --- a/sysdeps/ieee754/ldbl-128/t_sincosl.c +++ b/sysdeps/ieee754/ldbl-128/t_sincosl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point sine and cosine tables. - Copyright (C) 1999-2016 Free Software Foundation, Inc. + Copyright (C) 1999-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jj@ultra.linux.cz> @@ -25,669 +25,672 @@ Computed using gmp. */ -const long double __sincosl_table[] = { +/* Include to grab typedefs and wrappers for _Float128 and such. */ +#include <math_private.h> + +const _Float128 __sincosl_table[] = { /* x = 1.48437500000000000000000000000000000e-01L 3ffc3000000000000000000000000000 */ /* cos(x) = 0.fd2f5320e1b790209b4dda2f98f79caaa7b873aff1014b0fbc5243766d03cb006bc837c4358 */ - 9.89003367927322909016887196069562069e-01L, /* 3ffefa5ea641c36f2041369bb45f31ef */ - 2.15663692029265697782289400027743703e-35L, /* 3f8bcaaa7b873aff1014b0fbc5243767 */ + L(9.89003367927322909016887196069562069e-01), /* 3ffefa5ea641c36f2041369bb45f31ef */ + L(2.15663692029265697782289400027743703e-35), /* 3f8bcaaa7b873aff1014b0fbc5243767 */ /* sin(x) = 0.25dc50bc95711d0d9787d108fd438cf5959ee0bfb7a1e36e8b1a112968f356657420e9cc9ea */ - 1.47892995873409608580026675734609314e-01L, /* 3ffc2ee285e4ab88e86cbc3e8847ea1c */ - 9.74950446464233268291647449768590886e-36L, /* 3f8a9eb2b3dc17f6f43c6dd16342252d */ + L(1.47892995873409608580026675734609314e-01), /* 3ffc2ee285e4ab88e86cbc3e8847ea1c */ + L(9.74950446464233268291647449768590886e-36), /* 3f8a9eb2b3dc17f6f43c6dd16342252d */ /* x = 1.56250000000000000000000000000000000e-01 3ffc4000000000000000000000000000 */ /* cos(x) = 0.fce1a053e621438b6d60c76e8c45bf0a9dc71aa16f922acc10e95144ec796a249813c9cb649 */ - 9.87817783816471944100503034363211317e-01L, /* 3ffef9c340a7cc428716dac18edd188b */ - 4.74271307836705897892468107620526395e-35L, /* 3f8cf854ee38d50b7c915660874a8a27 */ + L(9.87817783816471944100503034363211317e-01), /* 3ffef9c340a7cc428716dac18edd188b */ + L(4.74271307836705897892468107620526395e-35), /* 3f8cf854ee38d50b7c915660874a8a27 */ /* sin(x) = 0.27d66258bacd96a3eb335b365c87d59438c5142bb56a489e9b8db9d36234ffdebb6bdc22d8e */ - 1.55614992773556041209920643203516258e-01L, /* 3ffc3eb312c5d66cb51f599ad9b2e43f */ --7.83989563419287980121718050629497270e-36L, /* bf8a4d78e75d7a8952b6ec2c8e48c594 */ + L(1.55614992773556041209920643203516258e-01), /* 3ffc3eb312c5d66cb51f599ad9b2e43f */ +L(-7.83989563419287980121718050629497270e-36), /* bf8a4d78e75d7a8952b6ec2c8e48c594 */ /* x = 1.64062500000000000000000000000000000e-01 3ffc5000000000000000000000000000 */ /* cos(x) = 0.fc8ffa01ba6807417e05962b0d9fdf1fddb0cc4c07d22e19e08019bffa50a6c7acdb40307a3 */ - 9.86571908399497588757337407495308409e-01L, /* 3ffef91ff40374d00e82fc0b2c561b40 */ --2.47327949936985362476252401212720725e-35L, /* bf8c070112799d9fc16e8f30fbff3200 */ + L(9.86571908399497588757337407495308409e-01), /* 3ffef91ff40374d00e82fc0b2c561b40 */ +L(-2.47327949936985362476252401212720725e-35), /* bf8c070112799d9fc16e8f30fbff3200 */ /* sin(x) = 0.29cfd49b8be4f665276cab01cbf0426934906c3dd105473b226e410b1450f62e53ff7c6cce1 */ - 1.63327491736612850846866172454354370e-01L, /* 3ffc4e7ea4dc5f27b3293b65580e5f82 */ - 1.81380344301155485770367902300754350e-36L, /* 3f88349a48361ee882a39d913720858a */ + L(1.63327491736612850846866172454354370e-01), /* 3ffc4e7ea4dc5f27b3293b65580e5f82 */ + L(1.81380344301155485770367902300754350e-36), /* 3f88349a48361ee882a39d913720858a */ /* x = 1.71875000000000000000000000000000000e-01 3ffc6000000000000000000000000000 */ /* cos(x) = 0.fc3a6170f767ac735d63d99a9d439e1db5e59d3ef153a4265d5855850ed82b536bf361b80e3 */ - 9.85265817718213816204294709759578994e-01L, /* 3ffef874c2e1eecf58e6bac7b3353a87 */ - 2.26568029505818066141517497778527952e-35L, /* 3f8be1db5e59d3ef153a4265d5855851 */ + L(9.85265817718213816204294709759578994e-01), /* 3ffef874c2e1eecf58e6bac7b3353a87 */ + L(2.26568029505818066141517497778527952e-35), /* 3f8be1db5e59d3ef153a4265d5855851 */ /* sin(x) = 0.2bc89f9f424de5485de7ce03b2514952b9faf5648c3244d4736feb95dbb9da49f3b58a9253b */ - 1.71030022031395019281347969239834331e-01L, /* 3ffc5e44fcfa126f2a42ef3e701d928a */ - 7.01395875187487608875416030203241317e-36L, /* 3f8a2a573f5eac9186489a8e6dfd72bb */ + L(1.71030022031395019281347969239834331e-01), /* 3ffc5e44fcfa126f2a42ef3e701d928a */ + L(7.01395875187487608875416030203241317e-36), /* 3f8a2a573f5eac9186489a8e6dfd72bb */ /* x = 1.79687500000000000000000000000000000e-01 3ffc7000000000000000000000000000 */ /* cos(x) = 0.fbe0d7f7fef11e70aa43b8abf4f6a457cea20c8f3f676b47781f9821bbe9ce04b3c7b981c0b */ - 9.83899591489663972178309351416487245e-01L, /* 3ffef7c1afeffde23ce154877157e9ed */ - 2.73414318948066207810486330723761265e-35L, /* 3f8c22be75106479fb3b5a3bc0fcc10e */ + L(9.83899591489663972178309351416487245e-01), /* 3ffef7c1afeffde23ce154877157e9ed */ + L(2.73414318948066207810486330723761265e-35), /* 3f8c22be75106479fb3b5a3bc0fcc10e */ /* sin(x) = 0.2dc0bb80b49a97ffb34e8dd1f8db9df7af47ed2dcf58b12c8e7827e048cae929da02c04ecac */ - 1.78722113535153659375356241864180724e-01L, /* 3ffc6e05dc05a4d4bffd9a746e8fc6dd */ --1.52906926517265103202547561260594148e-36L, /* bf8804285c09691853a769b8c3ec0fdc */ + L(1.78722113535153659375356241864180724e-01), /* 3ffc6e05dc05a4d4bffd9a746e8fc6dd */ +L(-1.52906926517265103202547561260594148e-36), /* bf8804285c09691853a769b8c3ec0fdc */ /* x = 1.87500000000000000000000000000000000e-01 3ffc8000000000000000000000000000 */ /* cos(x) = 0.fb835efcf670dd2ce6fe7924697eea13ea358867e9cdb3899b783f4f9f43aa5626e8b67b3bc */ - 9.82473313101255257487327683243622495e-01L, /* 3ffef706bdf9ece1ba59cdfcf248d2fe */ --1.64924358891557584625463868014230342e-35L, /* bf8b5ec15ca779816324c766487c0b06 */ + L(9.82473313101255257487327683243622495e-01), /* 3ffef706bdf9ece1ba59cdfcf248d2fe */ +L(-1.64924358891557584625463868014230342e-35), /* bf8b5ec15ca779816324c766487c0b06 */ /* sin(x) = 0.2fb8205f75e56a2b56a1c4792f856258769af396e0189ef72c05e4df59a6b00e4b44a6ea515 */ - 1.86403296762269884552379983103205261e-01L, /* 3ffc7dc102fbaf2b515ab50e23c97c2b */ - 1.76460304806826780010586715975331753e-36L, /* 3f882c3b4d79cb700c4f7b9602f26fad */ + L(1.86403296762269884552379983103205261e-01), /* 3ffc7dc102fbaf2b515ab50e23c97c2b */ + L(1.76460304806826780010586715975331753e-36), /* 3f882c3b4d79cb700c4f7b9602f26fad */ /* x = 1.95312500000000000000000000000000000e-01 3ffc9000000000000000000000000000 */ /* cos(x) = 0.fb21f7f5c156696b00ac1fe28ac5fd76674a92b4df80d9c8a46c684399005deccc41386257c */ - 9.80987069605669190469329896435309665e-01L, /* 3ffef643efeb82acd2d601583fc5158c */ --1.90899259410096419886996331536278461e-36L, /* bf8844cc5ab6a5903f931badc9cbde34 */ + L(9.80987069605669190469329896435309665e-01), /* 3ffef643efeb82acd2d601583fc5158c */ +L(-1.90899259410096419886996331536278461e-36), /* bf8844cc5ab6a5903f931badc9cbde34 */ /* sin(x) = 0.31aec65df552876f82ece9a2356713246eba6799983d7011b0b3698d6e1da919c15d57c30c1 */ - 1.94073102892909791156055200214145404e-01L, /* 3ffc8d7632efaa943b7c17674d11ab39 */ --9.67304741051998267208945242944928999e-36L, /* bf8a9b7228b30cccf851fdc9e992ce52 */ + L(1.94073102892909791156055200214145404e-01), /* 3ffc8d7632efaa943b7c17674d11ab39 */ +L(-9.67304741051998267208945242944928999e-36), /* bf8a9b7228b30cccf851fdc9e992ce52 */ /* x = 2.03125000000000000000000000000000000e-01 3ffca000000000000000000000000000 */ /* cos(x) = 0.fabca467fb3cb8f1d069f01d8ea33ade5bfd68296ecd1cc9f7b7609bbcf3676e726c3301334 */ - 9.79440951715548359998530954502987493e-01L, /* 3ffef57948cff67971e3a0d3e03b1d46 */ - 4.42878056591560757066844797290067990e-35L, /* 3f8cd6f2dfeb414b7668e64fbdbb04de */ + L(9.79440951715548359998530954502987493e-01), /* 3ffef57948cff67971e3a0d3e03b1d46 */ + L(4.42878056591560757066844797290067990e-35), /* 3f8cd6f2dfeb414b7668e64fbdbb04de */ /* sin(x) = 0.33a4a5a19d86246710f602c44df4fa513f4639ce938477aeeabb82e8e0a7ed583a188879fd4 */ - 2.01731063801638804725038151164000971e-01L, /* 3ffc9d252d0cec31233887b016226fa8 */ --4.27513434754966978435151290617384120e-36L, /* bf896bb02e718c5b1ee21445511f45c8 */ + L(2.01731063801638804725038151164000971e-01), /* 3ffc9d252d0cec31233887b016226fa8 */ +L(-4.27513434754966978435151290617384120e-36), /* bf896bb02e718c5b1ee21445511f45c8 */ /* x = 2.10937500000000000000000000000000000e-01 3ffcb000000000000000000000000000 */ /* cos(x) = 0.fa5365e8f1d3ca27be1db5d76ae64d983d7470a4ab0f4ccf65a2b8c67a380df949953a09bc1 */ - 9.77835053797959793331971572944454549e-01L, /* 3ffef4a6cbd1e3a7944f7c3b6baed5cd */ --3.79207422905180416937210853779192702e-35L, /* bf8c933e145c7adaa7859984d2ea39cc */ + L(9.77835053797959793331971572944454549e-01), /* 3ffef4a6cbd1e3a7944f7c3b6baed5cd */ +L(-3.79207422905180416937210853779192702e-35), /* bf8c933e145c7adaa7859984d2ea39cc */ /* sin(x) = 0.3599b652f40ec999df12a0a4c8561de159c98d4e54555de518b97f48886f715d8df5f4f093e */ - 2.09376712085993643711890752724881652e-01L, /* 3ffcaccdb297a0764ccef895052642b1 */ --1.59470287344329449965314638482515925e-36L, /* bf880f531b3958d5d5510d73a3405bbc */ + L(2.09376712085993643711890752724881652e-01), /* 3ffcaccdb297a0764ccef895052642b1 */ +L(-1.59470287344329449965314638482515925e-36), /* bf880f531b3958d5d5510d73a3405bbc */ /* x = 2.18750000000000000000000000000000000e-01 3ffcc000000000000000000000000000 */ /* cos(x) = 0.f9e63e1d9e8b6f6f2e296bae5b5ed9c11fd7fa2fe11e09fc7bde901abed24b6365e72f7db4e */ - 9.76169473868635276723989035435135534e-01L, /* 3ffef3cc7c3b3d16dede5c52d75cb6be */ --2.87727974249481583047944860626985460e-35L, /* bf8c31f701402e80f70fb01c210b7f2a */ + L(9.76169473868635276723989035435135534e-01), /* 3ffef3cc7c3b3d16dede5c52d75cb6be */ +L(-2.87727974249481583047944860626985460e-35), /* bf8c31f701402e80f70fb01c210b7f2a */ /* sin(x) = 0.378df09db8c332ce0d2b53d865582e4526ea336c768f68c32b496c6d11c1cd241bb9f1da523 */ - 2.17009581095010156760578095826055396e-01L, /* 3ffcbc6f84edc6199670695a9ec32ac1 */ - 1.07356488794216831812829549198201194e-35L, /* 3f8ac8a4dd466d8ed1ed1865692d8da2 */ + L(2.17009581095010156760578095826055396e-01), /* 3ffcbc6f84edc6199670695a9ec32ac1 */ + L(1.07356488794216831812829549198201194e-35), /* 3f8ac8a4dd466d8ed1ed1865692d8da2 */ /* x = 2.26562500000000000000000000000000000e-01 3ffcd000000000000000000000000000 */ /* cos(x) = 0.f9752eba9fff6b98842beadab054a932fb0f8d5b875ae63d6b2288d09b148921aeb6e52f61b */ - 9.74444313585988980349711056045434344e-01L, /* 3ffef2ea5d753ffed7310857d5b560a9 */ - 3.09947905955053419304514538592548333e-35L, /* 3f8c4997d87c6adc3ad731eb59144685 */ + L(9.74444313585988980349711056045434344e-01), /* 3ffef2ea5d753ffed7310857d5b560a9 */ + L(3.09947905955053419304514538592548333e-35), /* 3f8c4997d87c6adc3ad731eb59144685 */ /* sin(x) = 0.39814cb10513453cb97b21bc1ca6a337b150c21a675ab85503bc09a436a10ab1473934e20c8 */ - 2.24629204957705292350428549796424820e-01L, /* 3ffccc0a6588289a29e5cbd90de0e535 */ - 2.42061510849297469844695751870058679e-36L, /* 3f889bd8a8610d33ad5c2a81de04d21b */ + L(2.24629204957705292350428549796424820e-01), /* 3ffccc0a6588289a29e5cbd90de0e535 */ + L(2.42061510849297469844695751870058679e-36), /* 3f889bd8a8610d33ad5c2a81de04d21b */ /* x = 2.34375000000000000000000000000000000e-01 3ffce000000000000000000000000000 */ /* cos(x) = 0.f90039843324f9b940416c1984b6cbed1fc733d97354d4265788a86150493ce657cae032674 */ - 9.72659678244912752670913058267565260e-01L, /* 3ffef20073086649f3728082d833096e */ --3.91759231819314904966076958560252735e-35L, /* bf8ca09701c6613465595ecd43babcf5 */ + L(9.72659678244912752670913058267565260e-01), /* 3ffef20073086649f3728082d833096e */ +L(-3.91759231819314904966076958560252735e-35), /* bf8ca09701c6613465595ecd43babcf5 */ /* sin(x) = 0.3b73c2bf6b4b9f668ef9499c81f0d965087f1753fa64b086e58cb8470515c18c1412f8c2e02 */ - 2.32235118611511462413930877746235872e-01L, /* 3ffcdb9e15fb5a5cfb3477ca4ce40f87 */ --4.96930483364191020075024624332928910e-36L, /* bf89a6bde03a2b0166d3de469cd1ee3f */ + L(2.32235118611511462413930877746235872e-01), /* 3ffcdb9e15fb5a5cfb3477ca4ce40f87 */ +L(-4.96930483364191020075024624332928910e-36), /* bf89a6bde03a2b0166d3de469cd1ee3f */ /* x = 2.42187500000000000000000000000000000e-01 3ffcf000000000000000000000000000 */ /* cos(x) = 0.f887604e2c39dbb20e4ec5825059a789ffc95b275ad9954078ba8a28d3fcfe9cc2c1d49697b */ - 9.70815676770349462947490545785046027e-01L, /* 3ffef10ec09c5873b7641c9d8b04a0b3 */ - 2.97458820972393859125277682021202860e-35L, /* 3f8c3c4ffe4ad93ad6ccaa03c5d45147 */ + L(9.70815676770349462947490545785046027e-01), /* 3ffef10ec09c5873b7641c9d8b04a0b3 */ + L(2.97458820972393859125277682021202860e-35), /* 3f8c3c4ffe4ad93ad6ccaa03c5d45147 */ /* sin(x) = 0.3d654aff15cb457a0fca854698aba33039a8a40626609204472d9d40309b626eccc6dff0ffa */ - 2.39826857830661564441369251810886574e-01L, /* 3ffceb2a57f8ae5a2bd07e542a34c55d */ - 2.39867036569896287240938444445071448e-36L, /* 3f88981cd45203133049022396cea018 */ + L(2.39826857830661564441369251810886574e-01), /* 3ffceb2a57f8ae5a2bd07e542a34c55d */ + L(2.39867036569896287240938444445071448e-36), /* 3f88981cd45203133049022396cea018 */ /* x = 2.50000000000000000000000000000000000e-01 3ffd0000000000000000000000000000 */ /* cos(x) = 0.f80aa4fbef750ba783d33cb95f94f8a41426dbe79edc4a023ef9ec13c944551c0795b84fee1 */ - 9.68912421710644784144595449494189205e-01L, /* 3ffef01549f7deea174f07a67972bf2a */ --5.53634706113461989398873287749326500e-36L, /* bf89d6faf649061848ed7f704184fb0e */ + L(9.68912421710644784144595449494189205e-01), /* 3ffef01549f7deea174f07a67972bf2a */ +L(-5.53634706113461989398873287749326500e-36), /* bf89d6faf649061848ed7f704184fb0e */ /* sin(x) = 0.3f55dda9e62aed7513bd7b8e6a3d1635dd5676648d7db525898d7086af9330f03c7f285442a */ - 2.47403959254522929596848704849389203e-01L, /* 3ffcfaaeed4f31576ba89debdc7351e9 */ --7.36487001108599532943597115275811618e-36L, /* bf8a39445531336e50495b4ece51ef2a */ + L(2.47403959254522929596848704849389203e-01), /* 3ffcfaaeed4f31576ba89debdc7351e9 */ +L(-7.36487001108599532943597115275811618e-36), /* bf8a39445531336e50495b4ece51ef2a */ /* x = 2.57812500000000000000000000000000000e-01 3ffd0800000000000000000000000000 */ /* cos(x) = 0.f78a098069792daabc9ee42591b7c5a68cb1ab822aeb446b3311b4ba5371b8970e2c1547ad7 */ - 9.66950029230677822008341623610531503e-01L, /* 3ffeef141300d2f25b55793dc84b2370 */ --4.38972214432792412062088059990480514e-35L, /* bf8cd2cb9a72a3eea8a5dca667725a2d */ + L(9.66950029230677822008341623610531503e-01), /* 3ffeef141300d2f25b55793dc84b2370 */ +L(-4.38972214432792412062088059990480514e-35), /* bf8cd2cb9a72a3eea8a5dca667725a2d */ /* sin(x) = 0.414572fd94556e6473d620271388dd47c0ba050cdb5270112e3e370e8c4705ae006426fb5d5 */ - 2.54965960415878467487556574864872628e-01L, /* 3ffd0515cbf65155b991cf58809c4e23 */ - 2.20280377918534721005071688328074154e-35L, /* 3f8bd47c0ba050cdb5270112e3e370e9 */ + L(2.54965960415878467487556574864872628e-01), /* 3ffd0515cbf65155b991cf58809c4e23 */ + L(2.20280377918534721005071688328074154e-35), /* 3f8bd47c0ba050cdb5270112e3e370e9 */ /* x = 2.65625000000000000000000000000000000e-01 3ffd1000000000000000000000000000 */ /* cos(x) = 0.f7058fde0788dfc805b8fe88789e4f4253e3c50afe8b22f41159620ab5940ff7df9557c0d1f */ - 9.64928619104771009581074665315748371e-01L, /* 3ffeee0b1fbc0f11bf900b71fd10f13d */ --3.66685832670820775002475545602761113e-35L, /* bf8c85ed60e1d7a80ba6e85f7534efaa */ + L(9.64928619104771009581074665315748371e-01), /* 3ffeee0b1fbc0f11bf900b71fd10f13d */ +L(-3.66685832670820775002475545602761113e-35), /* bf8c85ed60e1d7a80ba6e85f7534efaa */ /* sin(x) = 0.4334033bcd90d6604f5f36c1d4b84451a87150438275b77470b50e5b968fa7962b5ffb379b7 */ - 2.62512399769153281450949626395692931e-01L, /* 3ffd0cd00cef364359813d7cdb0752e1 */ - 3.24923677072031064673177178571821843e-36L, /* 3f89146a1c5410e09d6ddd1c2d4396e6 */ + L(2.62512399769153281450949626395692931e-01), /* 3ffd0cd00cef364359813d7cdb0752e1 */ + L(3.24923677072031064673177178571821843e-36), /* 3f89146a1c5410e09d6ddd1c2d4396e6 */ /* x = 2.73437500000000000000000000000000000e-01 3ffd1800000000000000000000000000 */ /* cos(x) = 0.f67d3a26af7d07aa4bd6d42af8c0067fefb96d5b46c031eff53627f215ea3242edc3f2e13eb */ - 9.62848314709379699899701093480214365e-01L, /* 3ffeecfa744d5efa0f5497ada855f180 */ - 4.88986966383343450799422013051821394e-36L, /* 3f899ffbee5b56d1b00c7bfd4d89fc85 */ + L(9.62848314709379699899701093480214365e-01), /* 3ffeecfa744d5efa0f5497ada855f180 */ + L(4.88986966383343450799422013051821394e-36), /* 3f899ffbee5b56d1b00c7bfd4d89fc85 */ /* sin(x) = 0.452186aa5377ab20bbf2524f52e3a06a969f47166ab88cf88c111ad12c55941021ef3317a1a */ - 2.70042816718585031552755063618827102e-01L, /* 3ffd14861aa94ddeac82efc9493d4b8f */ --2.37608892440611310321138680065803162e-35L, /* bf8bf956960b8e99547730773eee52ed */ + L(2.70042816718585031552755063618827102e-01), /* 3ffd14861aa94ddeac82efc9493d4b8f */ +L(-2.37608892440611310321138680065803162e-35), /* bf8bf956960b8e99547730773eee52ed */ /* x = 2.81250000000000000000000000000000000e-01 3ffd2000000000000000000000000000 */ /* cos(x) = 0.f5f10a7bb77d3dfa0c1da8b57842783280d01ce3c0f82bae3b9d623c168d2e7c29977994451 */ - 9.60709243015561903066659350581313472e-01L, /* 3ffeebe214f76efa7bf4183b516af085 */ --5.87011558231583960712013351601221840e-36L, /* bf89f35fcbf8c70fc1f5147118a770fa */ + L(9.60709243015561903066659350581313472e-01), /* 3ffeebe214f76efa7bf4183b516af085 */ +L(-5.87011558231583960712013351601221840e-36), /* bf89f35fcbf8c70fc1f5147118a770fa */ /* sin(x) = 0.470df5931ae1d946076fe0dcff47fe31bb2ede618ebc607821f8462b639e1f4298b5ae87fd3 */ - 2.77556751646336325922023446828128568e-01L, /* 3ffd1c37d64c6b8765181dbf8373fd20 */ --1.35848595468998128214344668770082997e-36L, /* bf87ce44d1219e71439f87de07b9d49c */ + L(2.77556751646336325922023446828128568e-01), /* 3ffd1c37d64c6b8765181dbf8373fd20 */ +L(-1.35848595468998128214344668770082997e-36), /* bf87ce44d1219e71439f87de07b9d49c */ /* x = 2.89062500000000000000000000000000000e-01 3ffd2800000000000000000000000000 */ /* cos(x) = 0.f561030ddd7a78960ea9f4a32c6521554995667f5547bafee9ec48b3155cdb0f7fd00509713 */ - 9.58511534581228627301969408154919822e-01L, /* 3ffeeac2061bbaf4f12c1d53e94658ca */ - 2.50770779371636481145735089393154404e-35L, /* 3f8c0aaa4cab33faaa3dd7f74f624599 */ + L(9.58511534581228627301969408154919822e-01), /* 3ffeeac2061bbaf4f12c1d53e94658ca */ + L(2.50770779371636481145735089393154404e-35), /* 3f8c0aaa4cab33faaa3dd7f74f624599 */ /* sin(x) = 0.48f948446abcd6b0f7fccb100e7a1b26eccad880b0d24b59948c7cdd49514d44b933e6985c2 */ - 2.85053745940547424587763033323252561e-01L, /* 3ffd23e52111aaf35ac3dff32c4039e8 */ - 2.04269325885902918802700123680403749e-35L, /* 3f8bb26eccad880b0d24b59948c7cdd5 */ + L(2.85053745940547424587763033323252561e-01), /* 3ffd23e52111aaf35ac3dff32c4039e8 */ + L(2.04269325885902918802700123680403749e-35), /* 3f8bb26eccad880b0d24b59948c7cdd5 */ /* x = 2.96875000000000000000000000000000000e-01 3ffd3000000000000000000000000000 */ /* cos(x) = 0.f4cd261d3e6c15bb369c8758630d2ac00b7ace2a51c0631bfeb39ed158ba924cc91e259c195 */ - 9.56255323543175296975599942263028361e-01L, /* 3ffee99a4c3a7cd82b766d390eb0c61a */ - 3.21616572190865997051103645135837207e-35L, /* 3f8c56005bd671528e0318dff59cf68b */ + L(9.56255323543175296975599942263028361e-01), /* 3ffee99a4c3a7cd82b766d390eb0c61a */ + L(3.21616572190865997051103645135837207e-35), /* 3f8c56005bd671528e0318dff59cf68b */ /* sin(x) = 0.4ae37710fad27c8aa9c4cf96c03519b9ce07dc08a1471775499f05c29f86190aaebaeb9716e */ - 2.92533342023327543624702326493913423e-01L, /* 3ffd2b8ddc43eb49f22aa7133e5b00d4 */ - 1.93539408668704450308003687950685128e-35L, /* 3f8b9b9ce07dc08a1471775499f05c2a */ + L(2.92533342023327543624702326493913423e-01), /* 3ffd2b8ddc43eb49f22aa7133e5b00d4 */ + L(1.93539408668704450308003687950685128e-35), /* 3f8b9b9ce07dc08a1471775499f05c2a */ /* x = 3.04687500000000000000000000000000000e-01 3ffd3800000000000000000000000000 */ /* cos(x) = 0.f43575f94d4f6b272f5fb76b14d2a64ab52df1ee8ddf7c651034e5b2889305a9ea9015d758a */ - 9.53940747608894733981324795987611623e-01L, /* 3ffee86aebf29a9ed64e5ebf6ed629a5 */ - 2.88075689052478602008395972924657164e-35L, /* 3f8c3255a96f8f746efbe32881a72d94 */ + L(9.53940747608894733981324795987611623e-01), /* 3ffee86aebf29a9ed64e5ebf6ed629a5 */ + L(2.88075689052478602008395972924657164e-35), /* 3f8c3255a96f8f746efbe32881a72d94 */ /* sin(x) = 0.4ccc7a50127e1de0cb6b40c302c651f7bded4f9e7702b0471ae0288d091a37391950907202f */ - 2.99995083378683051163248282011699944e-01L, /* 3ffd3331e94049f877832dad030c0b19 */ - 1.35174265535697850139283361475571050e-35L, /* 3f8b1f7bded4f9e7702b0471ae0288d1 */ + L(2.99995083378683051163248282011699944e-01), /* 3ffd3331e94049f877832dad030c0b19 */ + L(1.35174265535697850139283361475571050e-35), /* 3f8b1f7bded4f9e7702b0471ae0288d1 */ /* x = 3.12500000000000000000000000000000000e-01 3ffd4000000000000000000000000000 */ /* cos(x) = 0.f399f500c9e9fd37ae9957263dab8877102beb569f101ee4495350868e5847d181d50d3cca2 */ - 9.51567948048172202145488217364270962e-01L, /* 3ffee733ea0193d3fa6f5d32ae4c7b57 */ - 6.36842628598115658308749288799884606e-36L, /* 3f8a0ee2057d6ad3e203dc892a6a10d2 */ + L(9.51567948048172202145488217364270962e-01), /* 3ffee733ea0193d3fa6f5d32ae4c7b57 */ + L(6.36842628598115658308749288799884606e-36), /* 3f8a0ee2057d6ad3e203dc892a6a10d2 */ /* sin(x) = 0.4eb44a5da74f600207aaa090f0734e288603ffadb3eb2542a46977b105f8547128036dcf7f0 */ - 3.07438514580380850670502958201982091e-01L, /* 3ffd3ad129769d3d80081eaa8243c1cd */ - 1.06515172423204645839241099453417152e-35L, /* 3f8ac510c07ff5b67d64a8548d2ef621 */ + L(3.07438514580380850670502958201982091e-01), /* 3ffd3ad129769d3d80081eaa8243c1cd */ + L(1.06515172423204645839241099453417152e-35), /* 3f8ac510c07ff5b67d64a8548d2ef621 */ /* x = 3.20312500000000000000000000000000000e-01 3ffd4800000000000000000000000000 */ /* cos(x) = 0.f2faa5a1b74e82fd61fa05f9177380e8e69b7b15a945e8e5ae1124bf3d12b0617e03af4fab5 */ - 9.49137069684463027665847421762105623e-01L, /* 3ffee5f54b436e9d05fac3f40bf22ee7 */ - 6.84433965991637152250309190468859701e-37L, /* 3f86d1cd36f62b528bd1cb5c22497e7a */ + L(9.49137069684463027665847421762105623e-01), /* 3ffee5f54b436e9d05fac3f40bf22ee7 */ + L(6.84433965991637152250309190468859701e-37), /* 3f86d1cd36f62b528bd1cb5c22497e7a */ /* sin(x) = 0.509adf9a7b9a5a0f638a8fa3a60a199418859f18b37169a644fdb986c21ecb00133853bc35b */ - 3.14863181319745250865036315126939016e-01L, /* 3ffd426b7e69ee69683d8e2a3e8e9828 */ - 1.92431240212432926993057705062834160e-35L, /* 3f8b99418859f18b37169a644fdb986c */ + L(3.14863181319745250865036315126939016e-01), /* 3ffd426b7e69ee69683d8e2a3e8e9828 */ + L(1.92431240212432926993057705062834160e-35), /* 3f8b99418859f18b37169a644fdb986c */ /* x = 3.28125000000000000000000000000000000e-01 3ffd5000000000000000000000000000 */ /* cos(x) = 0.f2578a595224dd2e6bfa2eb2f99cc674f5ea6f479eae2eb580186897ae3f893df1113ca06b8 */ - 9.46648260886053321846099507295532976e-01L, /* 3ffee4af14b2a449ba5cd7f45d65f33a */ --4.32906339663000890941529420498824645e-35L, /* bf8ccc5850ac85c30a8e8a53ff3cbb43 */ + L(9.46648260886053321846099507295532976e-01), /* 3ffee4af14b2a449ba5cd7f45d65f33a */ +L(-4.32906339663000890941529420498824645e-35), /* bf8ccc5850ac85c30a8e8a53ff3cbb43 */ /* sin(x) = 0.5280326c3cf481823ba6bb08eac82c2093f2bce3c4eb4ee3dec7df41c92c8a4226098616075 */ - 3.22268630433386625687745919893188031e-01L, /* 3ffd4a00c9b0f3d20608ee9aec23ab21 */ --1.49505897804759263483853908335500228e-35L, /* bf8b3df6c0d431c3b14b11c213820be3 */ + L(3.22268630433386625687745919893188031e-01), /* 3ffd4a00c9b0f3d20608ee9aec23ab21 */ +L(-1.49505897804759263483853908335500228e-35), /* bf8b3df6c0d431c3b14b11c213820be3 */ /* x = 3.35937500000000000000000000000000000e-01 3ffd5800000000000000000000000000 */ /* cos(x) = 0.f1b0a5b406b526d886c55feadc8d0dcc8eb9ae2ac707051771b48e05b25b000009660bdb3e3 */ - 9.44101673557004345630017691253124860e-01L, /* 3ffee3614b680d6a4db10d8abfd5b91a */ - 1.03812535240120229609822461172145584e-35L, /* 3f8ab991d735c558e0e0a2ee3691c0b6 */ + L(9.44101673557004345630017691253124860e-01), /* 3ffee3614b680d6a4db10d8abfd5b91a */ + L(1.03812535240120229609822461172145584e-35), /* 3f8ab991d735c558e0e0a2ee3691c0b6 */ /* sin(x) = 0.54643b3da29de9b357155eef0f332fb3e66c83bf4dddd9491c5eb8e103ccd92d6175220ed51 */ - 3.29654409930860171914317725126463176e-01L, /* 3ffd5190ecf68a77a6cd5c557bbc3ccd */ --1.22606996784743214973082192294232854e-35L, /* bf8b04c19937c40b22226b6e3a1471f0 */ + L(3.29654409930860171914317725126463176e-01), /* 3ffd5190ecf68a77a6cd5c557bbc3ccd */ +L(-1.22606996784743214973082192294232854e-35), /* bf8b04c19937c40b22226b6e3a1471f0 */ /* x = 3.43750000000000000000000000000000000e-01 3ffd6000000000000000000000000000 */ /* cos(x) = 0.f105fa4d66b607a67d44e042725204435142ac8ad54dfb0907a4f6b56b06d98ee60f19e557a */ - 9.41497463127881068644511236053670815e-01L, /* 3ffee20bf49acd6c0f4cfa89c084e4a4 */ - 3.20709366603165602071590241054884900e-36L, /* 3f8910d450ab22b5537ec241e93dad5b */ + L(9.41497463127881068644511236053670815e-01), /* 3ffee20bf49acd6c0f4cfa89c084e4a4 */ + L(3.20709366603165602071590241054884900e-36), /* 3f8910d450ab22b5537ec241e93dad5b */ /* sin(x) = 0.5646f27e8bd65cbe3a5d61ff06572290ee826d9674a00246b05ae26753cdfc90d9ce81a7d02 */ - 3.37020069022253076261281754173810024e-01L, /* 3ffd591bc9fa2f5972f8e97587fc195d */ --2.21435756148839473677777545049890664e-35L, /* bf8bd6f117d92698b5ffdb94fa51d98b */ + L(3.37020069022253076261281754173810024e-01), /* 3ffd591bc9fa2f5972f8e97587fc195d */ +L(-2.21435756148839473677777545049890664e-35), /* bf8bd6f117d92698b5ffdb94fa51d98b */ /* x = 3.51562500000000000000000000000000000e-01 3ffd6800000000000000000000000000 */ /* cos(x) = 0.f0578ad01ede707fa39c09dc6b984afef74f3dc8d0efb0f4c5a6b13771145b3e0446fe33887 */ - 9.38835788546265488632578305984712554e-01L, /* 3ffee0af15a03dbce0ff473813b8d731 */ --3.98758068773974031348585072752245458e-35L, /* bf8ca808458611b978827859d2ca7644 */ + L(9.38835788546265488632578305984712554e-01), /* 3ffee0af15a03dbce0ff473813b8d731 */ +L(-3.98758068773974031348585072752245458e-35), /* bf8ca808458611b978827859d2ca7644 */ /* sin(x) = 0.582850a41e1dd46c7f602ea244cdbbbfcdfa8f3189be794dda427ce090b5f85164f1f80ac13 */ - 3.44365158145698408207172046472223747e-01L, /* 3ffd60a14290787751b1fd80ba891337 */ --3.19791885005480924937758467594051927e-36L, /* bf89100c815c339d9061ac896f60c7dc */ + L(3.44365158145698408207172046472223747e-01), /* 3ffd60a14290787751b1fd80ba891337 */ +L(-3.19791885005480924937758467594051927e-36), /* bf89100c815c339d9061ac896f60c7dc */ /* x = 3.59375000000000000000000000000000000e-01 3ffd7000000000000000000000000000 */ /* cos(x) = 0.efa559f5ec3aec3a4eb03319278a2d41fcf9189462261125fe6147b078f1daa0b06750a1654 */ - 9.36116812267055290294237411019508588e-01L, /* 3ffedf4ab3ebd875d8749d6066324f14 */ - 3.40481591236710658435409862439032162e-35L, /* 3f8c6a0fe7c8c4a31130892ff30a3d84 */ + L(9.36116812267055290294237411019508588e-01), /* 3ffedf4ab3ebd875d8749d6066324f14 */ + L(3.40481591236710658435409862439032162e-35), /* 3f8c6a0fe7c8c4a31130892ff30a3d84 */ /* sin(x) = 0.5a084e28e35fda2776dfdbbb5531d74ced2b5d17c0b1afc4647529d50c295e36d8ceec126c1 */ - 3.51689228994814059222584896955547016e-01L, /* 3ffd682138a38d7f689ddb7f6eed54c7 */ - 1.75293433418270210567525412802083294e-35L, /* 3f8b74ced2b5d17c0b1afc4647529d51 */ + L(3.51689228994814059222584896955547016e-01), /* 3ffd682138a38d7f689ddb7f6eed54c7 */ + L(1.75293433418270210567525412802083294e-35), /* 3f8b74ced2b5d17c0b1afc4647529d51 */ /* x = 3.67187500000000000000000000000000000e-01 3ffd7800000000000000000000000000 */ /* cos(x) = 0.eeef6a879146af0bf9b95ea2ea0ac0d3e2e4d7e15d93f48cbd41bf8e4fded40bef69e19eafa */ - 9.33340700242548435655299229469995527e-01L, /* 3ffeddded50f228d5e17f372bd45d416 */ --4.75255707251679831124800898831382223e-35L, /* bf8cf960e8d940f513605b9a15f2038e */ + L(9.33340700242548435655299229469995527e-01), /* 3ffeddded50f228d5e17f372bd45d416 */ +L(-4.75255707251679831124800898831382223e-35), /* bf8cf960e8d940f513605b9a15f2038e */ /* sin(x) = 0.5be6e38ce8095542bc14ee9da0d36483e6734bcab2e07624188af5653f114eeb46738fa899d */ - 3.58991834546065053677710299152868941e-01L, /* 3ffd6f9b8e33a025550af053ba76834e */ --2.06772389262723368139416970257112089e-35L, /* bf8bb7c198cb4354d1f89dbe7750a9ac */ + L(3.58991834546065053677710299152868941e-01), /* 3ffd6f9b8e33a025550af053ba76834e */ +L(-2.06772389262723368139416970257112089e-35), /* bf8bb7c198cb4354d1f89dbe7750a9ac */ /* x = 3.75000000000000000000000000000000000e-01 3ffd8000000000000000000000000000 */ /* cos(x) = 0.ee35bf5ccac89052cd91ddb734d3a47e262e3b609db604e217053803be0091e76daf28a89b7 */ - 9.30507621912314291149476792229555481e-01L, /* 3ffedc6b7eb9959120a59b23bb6e69a7 */ - 2.74541088551732982573335285685416092e-35L, /* 3f8c23f13171db04edb02710b829c01e */ + L(9.30507621912314291149476792229555481e-01), /* 3ffedc6b7eb9959120a59b23bb6e69a7 */ + L(2.74541088551732982573335285685416092e-35), /* 3f8c23f13171db04edb02710b829c01e */ /* sin(x) = 0.5dc40955d9084f48a94675a2498de5d851320ff5528a6afb3f2e24de240fce6cbed1ba0ccd6 */ - 3.66272529086047561372909351716264177e-01L, /* 3ffd7710255764213d22a519d6892638 */ --1.96768433534936592675897818253108989e-35L, /* bf8ba27aecdf00aad759504c0d1db21e */ + L(3.66272529086047561372909351716264177e-01), /* 3ffd7710255764213d22a519d6892638 */ +L(-1.96768433534936592675897818253108989e-35), /* bf8ba27aecdf00aad759504c0d1db21e */ /* x = 3.82812500000000000000000000000000000e-01 3ffd8800000000000000000000000000 */ /* cos(x) = 0.ed785b5c44741b4493c56bcb9d338a151c6f6b85d8f8aca658b28572c162b199680eb9304da */ - 9.27617750192851909628030798799961350e-01L, /* 3ffedaf0b6b888e83689278ad7973a67 */ - 7.58520371916345756281201167126854712e-36L, /* 3f8a42a38ded70bb1f1594cb1650ae58 */ + L(9.27617750192851909628030798799961350e-01), /* 3ffedaf0b6b888e83689278ad7973a67 */ + L(7.58520371916345756281201167126854712e-36), /* 3f8a42a38ded70bb1f1594cb1650ae58 */ /* sin(x) = 0.5f9fb80f21b53649c432540a50e22c53057ff42ae0fdf1307760dc0093f99c8efeb2fbd7073 */ - 3.73530868238692946416839752660848112e-01L, /* 3ffd7e7ee03c86d4d92710c950294389 */ --1.48023494778986556048879113411517128e-35L, /* bf8b3acfa800bd51f020ecf889f23ff7 */ + L(3.73530868238692946416839752660848112e-01), /* 3ffd7e7ee03c86d4d92710c950294389 */ +L(-1.48023494778986556048879113411517128e-35), /* bf8b3acfa800bd51f020ecf889f23ff7 */ /* x = 3.90625000000000000000000000000000000e-01 3ffd9000000000000000000000000000 */ /* cos(x) = 0.ecb7417b8d4ee3fec37aba4073aa48f1f14666006fb431d9671303c8100d10190ec8179c41d */ - 9.24671261467036098502113014560138771e-01L, /* 3ffed96e82f71a9dc7fd86f57480e755 */ --4.14187124860031825108649347251175815e-35L, /* bf8cb87075cccffc825e7134c767e1bf */ + L(9.24671261467036098502113014560138771e-01), /* 3ffed96e82f71a9dc7fd86f57480e755 */ +L(-4.14187124860031825108649347251175815e-35), /* bf8cb87075cccffc825e7134c767e1bf */ /* sin(x) = 0.6179e84a09a5258a40e9b5face03e525f8b5753cd0105d93fe6298010c3458e84d75fe420e9 */ - 3.80766408992390192057200703388896675e-01L, /* 3ffd85e7a1282694962903a6d7eb3810 */ --2.02009541175208636336924533372496107e-35L, /* bf8bada074a8ac32fefa26c019d67fef */ + L(3.80766408992390192057200703388896675e-01), /* 3ffd85e7a1282694962903a6d7eb3810 */ +L(-2.02009541175208636336924533372496107e-35), /* bf8bada074a8ac32fefa26c019d67fef */ /* x = 3.98437500000000000000000000000000000e-01 3ffd9800000000000000000000000000 */ /* cos(x) = 0.ebf274bf0bda4f62447e56a093626798d3013b5942b1abfd155aacc9dc5c6d0806a20d6b9c1 */ - 9.21668335573351918175411368202712714e-01L, /* 3ffed7e4e97e17b49ec488fcad4126c5 */ --1.83587995433957622948710263541479322e-35L, /* bf8b8672cfec4a6bd4e5402eaa553362 */ + L(9.21668335573351918175411368202712714e-01), /* 3ffed7e4e97e17b49ec488fcad4126c5 */ +L(-1.83587995433957622948710263541479322e-35), /* bf8b8672cfec4a6bd4e5402eaa553362 */ /* sin(x) = 0.6352929dd264bd44a02ea766325d8aa8bd9695fc8def3caefba5b94c9a3c873f7b2d3776ead */ - 3.87978709727025046051079690813741960e-01L, /* 3ffd8d4a4a774992f51280ba9d98c976 */ - 8.01904783870935075844443278617586301e-36L, /* 3f8a5517b2d2bf91bde795df74b72993 */ + L(3.87978709727025046051079690813741960e-01), /* 3ffd8d4a4a774992f51280ba9d98c976 */ + L(8.01904783870935075844443278617586301e-36), /* 3f8a5517b2d2bf91bde795df74b72993 */ /* x = 4.06250000000000000000000000000000000e-01 3ffda000000000000000000000000000 */ /* cos(x) = 0.eb29f839f201fd13b93796827916a78f15c85230a4e8ea4b21558265a14367e1abb4c30695a */ - 9.18609155794918267837824977718549863e-01L, /* 3ffed653f073e403fa27726f2d04f22d */ - 2.97608282778274433460057745798409849e-35L, /* 3f8c3c78ae429185274752590aac132d */ + L(9.18609155794918267837824977718549863e-01), /* 3ffed653f073e403fa27726f2d04f22d */ + L(2.97608282778274433460057745798409849e-35), /* 3f8c3c78ae429185274752590aac132d */ /* sin(x) = 0.6529afa7d51b129631ec197c0a840a11d7dc5368b0a47956feb285caa8371c4637ef17ef01b */ - 3.95167330240934236244832640419653657e-01L, /* 3ffd94a6be9f546c4a58c7b065f02a10 */ - 7.57560031388312550940040194042627704e-36L, /* 3f8a423afb8a6d16148f2adfd650b955 */ + L(3.95167330240934236244832640419653657e-01), /* 3ffd94a6be9f546c4a58c7b065f02a10 */ + L(7.57560031388312550940040194042627704e-36), /* 3f8a423afb8a6d16148f2adfd650b955 */ /* x = 4.14062500000000000000000000000000000e-01 3ffda800000000000000000000000000 */ /* cos(x) = 0.ea5dcf0e30cf03e6976ef0b1ec26515fba47383855c3b4055a99b5e86824b2cd1a691fdca7b */ - 9.15493908848301228563917732180221882e-01L, /* 3ffed4bb9e1c619e07cd2edde163d84d */ --3.50775517955306954815090901168305659e-35L, /* bf8c75022dc63e3d51e25fd52b3250bd */ + L(9.15493908848301228563917732180221882e-01), /* 3ffed4bb9e1c619e07cd2edde163d84d */ +L(-3.50775517955306954815090901168305659e-35), /* bf8c75022dc63e3d51e25fd52b3250bd */ /* sin(x) = 0.66ff380ba0144109e39a320b0a3fa5fd65ea0585bcbf9b1a769a9b0334576c658139e1a1cbe */ - 4.02331831777773111217105598880982387e-01L, /* 3ffd9bfce02e805104278e68c82c28ff */ --1.95678722882848174723569916504871563e-35L, /* bf8ba029a15fa7a434064e5896564fcd */ + L(4.02331831777773111217105598880982387e-01), /* 3ffd9bfce02e805104278e68c82c28ff */ +L(-1.95678722882848174723569916504871563e-35), /* bf8ba029a15fa7a434064e5896564fcd */ /* x = 4.21875000000000000000000000000000000e-01 3ffdb000000000000000000000000000 */ /* cos(x) = 0.e98dfc6c6be031e60dd3089cbdd18a75b1f6b2c1e97f79225202f03dbea45b07a5ec4efc062 */ - 9.12322784872117846492029542047341734e-01L, /* 3ffed31bf8d8d7c063cc1ba611397ba3 */ - 7.86903886556373674267948132178845568e-36L, /* 3f8a4eb63ed6583d2fef244a405e07b8 */ + L(9.12322784872117846492029542047341734e-01), /* 3ffed31bf8d8d7c063cc1ba611397ba3 */ + L(7.86903886556373674267948132178845568e-36), /* 3f8a4eb63ed6583d2fef244a405e07b8 */ /* sin(x) = 0.68d32473143327973bc712bcc4ccddc47630d755850c0655243b205934dc49ffed8eb76adcb */ - 4.09471777053295066122694027011452236e-01L, /* 3ffda34c91cc50cc9e5cef1c4af31333 */ - 2.23945241468457597921655785729821354e-35L, /* 3f8bdc47630d755850c0655243b20593 */ + L(4.09471777053295066122694027011452236e-01), /* 3ffda34c91cc50cc9e5cef1c4af31333 */ + L(2.23945241468457597921655785729821354e-35), /* 3f8bdc47630d755850c0655243b20593 */ /* x = 4.29687500000000000000000000000000000e-01 3ffdb800000000000000000000000000 */ /* cos(x) = 0.e8ba8393eca7821aa563d83491b6101189b3b101c3677f73d7bad7c10f9ee02b7ab4009739a */ - 9.09095977415431051650381735684476417e-01L, /* 3ffed1750727d94f04354ac7b069236c */ - 1.20886014028444155733776025085677953e-35L, /* 3f8b01189b3b101c3677f73d7bad7c11 */ + L(9.09095977415431051650381735684476417e-01), /* 3ffed1750727d94f04354ac7b069236c */ + L(1.20886014028444155733776025085677953e-35), /* 3f8b01189b3b101c3677f73d7bad7c11 */ /* sin(x) = 0.6aa56d8e8249db4eb60a761fe3f9e559be456b9e13349ca99b0bfb787f22b95db3b70179615 */ - 4.16586730282041119259112448831069657e-01L, /* 3ffdaa95b63a09276d3ad829d87f8fe8 */ --2.00488106831998813675438269796963612e-35L, /* bf8baa641ba9461eccb635664f404878 */ + L(4.16586730282041119259112448831069657e-01), /* 3ffdaa95b63a09276d3ad829d87f8fe8 */ +L(-2.00488106831998813675438269796963612e-35), /* bf8baa641ba9461eccb635664f404878 */ /* x = 4.37500000000000000000000000000000000e-01 3ffdc000000000000000000000000000 */ /* cos(x) = 0.e7e367d2956cfb16b6aa11e5419cd0057f5c132a6455bf064297e6a76fe2b72bb630d6d50ff */ - 9.05813683425936420744516660652700258e-01L, /* 3ffecfc6cfa52ad9f62d6d5423ca833a */ --3.60950307605941169775676563004467163e-35L, /* bf8c7fd4051f66acdd5207cdeb40cac5 */ + L(9.05813683425936420744516660652700258e-01), /* 3ffecfc6cfa52ad9f62d6d5423ca833a */ +L(-3.60950307605941169775676563004467163e-35), /* bf8c7fd4051f66acdd5207cdeb40cac5 */ /* sin(x) = 0.6c760c14c8585a51dbd34660ae6c52ac7036a0b40887a0b63724f8b4414348c3063a637f457 */ - 4.23676257203938010361683988031102480e-01L, /* 3ffdb1d83053216169476f4d1982b9b1 */ - 1.40484456388654470329473096579312595e-35L, /* 3f8b2ac7036a0b40887a0b63724f8b44 */ + L(4.23676257203938010361683988031102480e-01), /* 3ffdb1d83053216169476f4d1982b9b1 */ + L(1.40484456388654470329473096579312595e-35), /* 3f8b2ac7036a0b40887a0b63724f8b44 */ /* x = 4.45312500000000000000000000000000000e-01 3ffdc800000000000000000000000000 */ /* cos(x) = 0.e708ac84d4172a3e2737662213429e14021074d7e702e77d72a8f1101a7e70410df8273e9aa */ - 9.02476103237941504925183272675895999e-01L, /* 3ffece115909a82e547c4e6ecc442685 */ - 2.26282899501344419018306295680210602e-35L, /* 3f8be14021074d7e702e77d72a8f1102 */ + L(9.02476103237941504925183272675895999e-01), /* 3ffece115909a82e547c4e6ecc442685 */ + L(2.26282899501344419018306295680210602e-35), /* 3f8be14021074d7e702e77d72a8f1102 */ /* sin(x) = 0.6e44f8c36eb10a1c752d093c00f4d47ba446ac4c215d26b0316442f168459e677d06e7249e3 */ - 4.30739925110803197216321517850849190e-01L, /* 3ffdb913e30dbac42871d4b424f003d3 */ - 1.54096780001629398850891218396761548e-35L, /* 3f8b47ba446ac4c215d26b0316442f17 */ + L(4.30739925110803197216321517850849190e-01), /* 3ffdb913e30dbac42871d4b424f003d3 */ + L(1.54096780001629398850891218396761548e-35), /* 3f8b47ba446ac4c215d26b0316442f17 */ /* x = 4.53125000000000000000000000000000000e-01 3ffdd000000000000000000000000000 */ /* cos(x) = 0.e62a551594b970a770b15d41d4c0e483e47aca550111df6966f9e7ac3a94ae49e6a71eb031e */ - 8.99083440560138456216544929209379307e-01L, /* 3ffecc54aa2b2972e14ee162ba83a982 */ --2.06772615490904370666670275154751976e-35L, /* bf8bb7c1b8535aafeee209699061853c */ + L(8.99083440560138456216544929209379307e-01), /* 3ffecc54aa2b2972e14ee162ba83a982 */ +L(-2.06772615490904370666670275154751976e-35), /* bf8bb7c1b8535aafeee209699061853c */ /* sin(x) = 0.70122c5ec5028c8cff33abf4fd340ccc382e038379b09cf04f9a52692b10b72586060cbb001 */ - 4.37777302872755132861618974702796680e-01L, /* 3ffdc048b17b140a3233fcceafd3f4d0 */ - 9.62794364503442612477117426033922467e-36L, /* 3f8a998705c0706f36139e09f34a4d25 */ + L(4.37777302872755132861618974702796680e-01), /* 3ffdc048b17b140a3233fcceafd3f4d0 */ + L(9.62794364503442612477117426033922467e-36), /* 3f8a998705c0706f36139e09f34a4d25 */ /* x = 4.60937500000000000000000000000000000e-01 3ffdd800000000000000000000000000 */ /* cos(x) = 0.e54864fe33e8575cabf5bd0e5cf1b1a8bc7c0d5f61702450fa6b6539735820dd2603ae355d5 */ - 8.95635902463170698900570000446256350e-01L, /* 3ffeca90c9fc67d0aeb957eb7a1cb9e3 */ - 3.73593741659866883088620495542311808e-35L, /* 3f8c8d45e3e06afb0b812287d35b29cc */ + L(8.95635902463170698900570000446256350e-01), /* 3ffeca90c9fc67d0aeb957eb7a1cb9e3 */ + L(3.73593741659866883088620495542311808e-35), /* 3f8c8d45e3e06afb0b812287d35b29cc */ /* sin(x) = 0.71dd9fb1ff4677853acb970a9f6729c6e3aac247b1c57cea66c77413f1f98e8b9e98e49d851 */ - 4.44787960964527211433056012529525211e-01L, /* 3ffdc7767ec7fd19de14eb2e5c2a7d9d */ --1.67187936511493678007508371613954899e-35L, /* bf8b6391c553db84e3a831599388bec1 */ + L(4.44787960964527211433056012529525211e-01), /* 3ffdc7767ec7fd19de14eb2e5c2a7d9d */ +L(-1.67187936511493678007508371613954899e-35), /* bf8b6391c553db84e3a831599388bec1 */ /* x = 4.68750000000000000000000000000000000e-01 3ffde000000000000000000000000000 */ /* cos(x) = 0.e462dfc670d421ab3d1a15901228f146a0547011202bf5ab01f914431859aef577966bc4fa4 */ - 8.92133699366994404723900253723788575e-01L, /* 3ffec8c5bf8ce1a843567a342b202452 */ --1.10771937602567314732693079264692504e-35L, /* bf8ad72bf571fddbfa814a9fc0dd779d */ + L(8.92133699366994404723900253723788575e-01), /* 3ffec8c5bf8ce1a843567a342b202452 */ +L(-1.10771937602567314732693079264692504e-35), /* bf8ad72bf571fddbfa814a9fc0dd779d */ /* sin(x) = 0.73a74b8f52947b681baf6928eb3fb021769bf4779bad0e3aa9b1cdb75ec60aad9fc63ff19d5 */ - 4.51771471491683776581688750134062870e-01L, /* 3ffdce9d2e3d4a51eda06ebda4a3acff */ --1.19387223016472295893794387275284505e-35L, /* bf8afbd12c81710c8a5e38aac9c64914 */ + L(4.51771471491683776581688750134062870e-01), /* 3ffdce9d2e3d4a51eda06ebda4a3acff */ +L(-1.19387223016472295893794387275284505e-35), /* bf8afbd12c81710c8a5e38aac9c64914 */ /* x = 4.76562500000000000000000000000000000e-01 3ffde800000000000000000000000000 */ /* cos(x) = 0.e379c9045f29d517c4808aa497c2057b2b3d109e76c0dc302d4d0698b36e3f0bdbf33d8e952 */ - 8.88577045028035543317609023116020980e-01L, /* 3ffec6f39208be53aa2f890115492f84 */ - 4.12354278954664731443813655177022170e-36L, /* 3f895ecacf44279db0370c0b5341a62d */ + L(8.88577045028035543317609023116020980e-01), /* 3ffec6f39208be53aa2f890115492f84 */ + L(4.12354278954664731443813655177022170e-36), /* 3f895ecacf44279db0370c0b5341a62d */ /* sin(x) = 0.756f28d011d98528a44a75fc29c779bd734ecdfb582fdb74b68a4c4c4be54cfd0b2d3ad292f */ - 4.58727408216736592377295028972874773e-01L, /* 3ffdd5bca340476614a29129d7f0a71e */ --4.70946994194182908929251719575431779e-36L, /* bf8990a32c4c8129f40922d25d6ceced */ + L(4.58727408216736592377295028972874773e-01), /* 3ffdd5bca340476614a29129d7f0a71e */ +L(-4.70946994194182908929251719575431779e-36), /* bf8990a32c4c8129f40922d25d6ceced */ /* x = 4.84375000000000000000000000000000000e-01 3ffdf000000000000000000000000000 */ /* cos(x) = 0.e28d245c58baef72225e232abc003c4366acd9eb4fc2808c2ab7fe7676cf512ac7f945ae5fb */ - 8.84966156526143291697296536966647926e-01L, /* 3ffec51a48b8b175dee444bc46557800 */ - 4.53370570288325630442037826313462165e-35L, /* 3f8ce21b3566cf5a7e14046155bff3b4 */ + L(8.84966156526143291697296536966647926e-01), /* 3ffec51a48b8b175dee444bc46557800 */ + L(4.53370570288325630442037826313462165e-35), /* 3f8ce21b3566cf5a7e14046155bff3b4 */ /* sin(x) = 0.77353054ca72690d4c6e171fd99e6b39fa8e1ede5f052fd2964534c75340970a3a9cd3c5c32 */ - 4.65655346585160182681199512507546779e-01L, /* 3ffddcd4c15329c9a43531b85c7f667a */ --1.56282598978971872478619772155305961e-35L, /* bf8b4c60571e121a0fad02d69bacb38b */ + L(4.65655346585160182681199512507546779e-01), /* 3ffddcd4c15329c9a43531b85c7f667a */ +L(-1.56282598978971872478619772155305961e-35), /* bf8b4c60571e121a0fad02d69bacb38b */ /* x = 4.92187500000000000000000000000000000e-01 3ffdf800000000000000000000000000 */ /* cos(x) = 0.e19cf580eeec046aa1422fa74807ecefb2a1911c94e7b5f20a00f70022d940193691e5bd790 */ - 8.81301254251340599140161908298100173e-01L, /* 3ffec339eb01ddd808d542845f4e9010 */ --1.43419192312116687783945619009629445e-35L, /* bf8b3104d5e6ee36b184a0df5ff08ffe */ + L(8.81301254251340599140161908298100173e-01), /* 3ffec339eb01ddd808d542845f4e9010 */ +L(-1.43419192312116687783945619009629445e-35), /* bf8b3104d5e6ee36b184a0df5ff08ffe */ /* sin(x) = 0.78f95b0560a9a3bd6df7bd981dc38c61224d08bc20631ea932e605e53b579e9e0767dfcbbcb */ - 4.72554863751304451146551317808516942e-01L, /* 3ffde3e56c1582a68ef5b7def660770e */ - 9.31324774957768018850224267625371204e-36L, /* 3f8a8c2449a117840c63d5265cc0bca7 */ + L(4.72554863751304451146551317808516942e-01), /* 3ffde3e56c1582a68ef5b7def660770e */ + L(9.31324774957768018850224267625371204e-36), /* 3f8a8c2449a117840c63d5265cc0bca7 */ /* x = 5.00000000000000000000000000000000000e-01 3ffe0000000000000000000000000000 */ /* cos(x) = 0.e0a94032dbea7cedbddd9da2fafad98556566b3a89f43eabd72350af3e8b19e801204d8fe2e */ - 8.77582561890372716116281582603829681e-01L, /* 3ffec1528065b7d4f9db7bbb3b45f5f6 */ --2.89484960181363924855192538540698851e-35L, /* bf8c33d54d4ca62bb05e0aa146e57a86 */ + L(8.77582561890372716116281582603829681e-01), /* 3ffec1528065b7d4f9db7bbb3b45f5f6 */ +L(-2.89484960181363924855192538540698851e-35), /* bf8c33d54d4ca62bb05e0aa146e57a86 */ /* sin(x) = 0.7abba1d12c17bfa1d92f0d93f60ded9992f45b4fcaf13cd58b303693d2a0db47db35ae8a3a9 */ - 4.79425538604203000273287935215571402e-01L, /* 3ffdeaee8744b05efe8764bc364fd838 */ --1.38426977616718318950175848639381926e-35L, /* bf8b2666d0ba4b0350ec32a74cfc96c3 */ + L(4.79425538604203000273287935215571402e-01), /* 3ffdeaee8744b05efe8764bc364fd838 */ +L(-1.38426977616718318950175848639381926e-35), /* bf8b2666d0ba4b0350ec32a74cfc96c3 */ /* x = 5.07812500000000000000000000000000000e-01 3ffe0400000000000000000000000000 */ /* cos(x) = 0.dfb20840f3a9b36f7ae2c515342890b5ec583b8366cc2b55029e95094d31112383f2553498b */ - 8.73810306413054508282556837071377159e-01L, /* 3ffebf641081e75366def5c58a2a6851 */ - 1.25716864497849302237218128599994785e-35L, /* 3f8b0b5ec583b8366cc2b55029e95095 */ + L(8.73810306413054508282556837071377159e-01), /* 3ffebf641081e75366def5c58a2a6851 */ + L(1.25716864497849302237218128599994785e-35), /* 3f8b0b5ec583b8366cc2b55029e95095 */ /* sin(x) = 0.7c7bfdaf13e5ed17212f8a7525bfb113aba6c0741b5362bb8d59282a850b63716bca0c910f0 */ - 4.86266951793275574311011306895834993e-01L, /* 3ffdf1eff6bc4f97b45c84be29d496ff */ --1.12269393250914752644352376448094271e-35L, /* bf8add8a8b27f17c9593a88e54dafaaf */ + L(4.86266951793275574311011306895834993e-01), /* 3ffdf1eff6bc4f97b45c84be29d496ff */ +L(-1.12269393250914752644352376448094271e-35), /* bf8add8a8b27f17c9593a88e54dafaaf */ /* x = 5.15625000000000000000000000000000000e-01 3ffe0800000000000000000000000000 */ /* cos(x) = 0.deb7518814a7a931bbcc88c109cd41c50bf8bb48f20ae8c36628d1d3d57574f7dc58f27d91c */ - 8.69984718058417388828915599901466243e-01L, /* 3ffebd6ea310294f526377991182139b */ --4.68168638300575626782741319792183837e-35L, /* bf8cf1d7a03a25b86fa8b9e4ceb97161 */ + L(8.69984718058417388828915599901466243e-01), /* 3ffebd6ea310294f526377991182139b */ +L(-4.68168638300575626782741319792183837e-35), /* bf8cf1d7a03a25b86fa8b9e4ceb97161 */ /* sin(x) = 0.7e3a679daaf25c676542bcb4028d0964172961c921823a4ef0c3a9070d886dbd073f6283699 */ - 4.93078685753923057265136552753487121e-01L, /* 3ffdf8e99e76abc9719d950af2d00a34 */ - 7.06498693112535056352301101088624950e-36L, /* 3f8a2c82e52c3924304749de187520e2 */ + L(4.93078685753923057265136552753487121e-01), /* 3ffdf8e99e76abc9719d950af2d00a34 */ + L(7.06498693112535056352301101088624950e-36), /* 3f8a2c82e52c3924304749de187520e2 */ /* x = 5.23437500000000000000000000000000000e-01 3ffe0c00000000000000000000000000 */ /* cos(x) = 0.ddb91ff318799172bd2452d0a3889f5169c64a0094bcf0b8aa7dcf0d7640a2eba68955a80be */ - 8.66106030320656714696616831654267220e-01L, /* 3ffebb723fe630f322e57a48a5a14711 */ - 2.35610597588322493119667003904687628e-35L, /* 3f8bf5169c64a0094bcf0b8aa7dcf0d7 */ + L(8.66106030320656714696616831654267220e-01), /* 3ffebb723fe630f322e57a48a5a14711 */ + L(2.35610597588322493119667003904687628e-35), /* 3f8bf5169c64a0094bcf0b8aa7dcf0d7 */ /* sin(x) = 0.7ff6d8a34bd5e8fa54c97482db5159df1f24e8038419c0b448b9eea8939b5d4dfcf40900257 */ - 4.99860324733013463819556536946425724e-01L, /* 3ffdffdb628d2f57a3e95325d20b6d45 */ - 1.94636052312235297538564591686645139e-35L, /* 3f8b9df1f24e8038419c0b448b9eea89 */ + L(4.99860324733013463819556536946425724e-01), /* 3ffdffdb628d2f57a3e95325d20b6d45 */ + L(1.94636052312235297538564591686645139e-35), /* 3f8b9df1f24e8038419c0b448b9eea89 */ /* x = 5.31250000000000000000000000000000000e-01 3ffe1000000000000000000000000000 */ /* cos(x) = 0.dcb7777ac420705168f31e3eb780ce9c939ecada62843b54522f5407eb7f21e556059fcd734 */ - 8.62174479934880504367162510253324274e-01L, /* 3ffeb96eeef58840e0a2d1e63c7d6f02 */ --3.71556818317533582234562471835771823e-35L, /* bf8c8b1b6309a92cebde255d6e855fc1 */ + L(8.62174479934880504367162510253324274e-01), /* 3ffeb96eeef58840e0a2d1e63c7d6f02 */ +L(-3.71556818317533582234562471835771823e-35), /* bf8c8b1b6309a92cebde255d6e855fc1 */ /* sin(x) = 0.81b149ce34caa5a4e650f8d09fd4d6aa74206c32ca951a93074c83b2d294d25dbb0f7fdfad2 */ - 5.06611454814257367642296000893867192e-01L, /* 3ffe0362939c69954b49cca1f1a13faa */ --3.10963699824274155702706043065967062e-35L, /* bf8c4aac5efc9e69ab572b67c59be269 */ + L(5.06611454814257367642296000893867192e-01), /* 3ffe0362939c69954b49cca1f1a13faa */ +L(-3.10963699824274155702706043065967062e-35), /* bf8c4aac5efc9e69ab572b67c59be269 */ /* x = 5.39062500000000000000000000000000000e-01 3ffe1400000000000000000000000000 */ /* cos(x) = 0.dbb25c25b8260c14f6e7bc98ec991b70c65335198b0ab628bad20cc7b229d4dd62183cfa055 */ - 8.58190306862660347046629564970494649e-01L, /* 3ffeb764b84b704c1829edcf7931d932 */ - 2.06439574601190798155563653000684861e-35L, /* 3f8bb70c65335198b0ab628bad20cc7b */ + L(8.58190306862660347046629564970494649e-01), /* 3ffeb764b84b704c1829edcf7931d932 */ + L(2.06439574601190798155563653000684861e-35), /* 3f8bb70c65335198b0ab628bad20cc7b */ /* sin(x) = 0.8369b434a372da7eb5c8a71fe36ce1e0b2b493f6f5cb2e38bcaec2a556b3678c401940d1c3c */ - 5.13331663943471218288801270215706878e-01L, /* 3ffe06d3686946e5b4fd6b914e3fc6da */ --2.26614796466671970772244932848067224e-35L, /* bf8be1f4d4b6c090a34d1c743513d5ab */ + L(5.13331663943471218288801270215706878e-01), /* 3ffe06d3686946e5b4fd6b914e3fc6da */ +L(-2.26614796466671970772244932848067224e-35), /* bf8be1f4d4b6c090a34d1c743513d5ab */ /* x = 5.46875000000000000000000000000000000e-01 3ffe1800000000000000000000000000 */ /* cos(x) = 0.daa9d20860827063fde51c09e855e9932e1b17143e7244fd267a899d41ae1f3bc6a0ec42e27 */ - 8.54153754277385385143451785105103176e-01L, /* 3ffeb553a410c104e0c7fbca3813d0ac */ --1.68707534013095152873222061722573172e-35L, /* bf8b66cd1e4e8ebc18dbb02d9857662c */ + L(8.54153754277385385143451785105103176e-01), /* 3ffeb553a410c104e0c7fbca3813d0ac */ +L(-1.68707534013095152873222061722573172e-35), /* bf8b66cd1e4e8ebc18dbb02d9857662c */ /* sin(x) = 0.852010f4f0800521378bd8dd614753d080c2e9e0775ffc609947b9132f5357404f464f06a58 */ - 5.20020541953727004760213699874674730e-01L, /* 3ffe0a4021e9e1000a426f17b1bac28f */ --3.32415021330884924833711842866896734e-35L, /* bf8c617bf9e8b0fc45001cfb35c23767 */ + L(5.20020541953727004760213699874674730e-01), /* 3ffe0a4021e9e1000a426f17b1bac28f */ +L(-3.32415021330884924833711842866896734e-35), /* bf8c617bf9e8b0fc45001cfb35c23767 */ /* x = 5.54687500000000000000000000000000000e-01 3ffe1c00000000000000000000000000 */ /* cos(x) = 0.d99ddd44e44a43d4d4a3a3ed95204106fd54d78e8c7684545c0da0b7c2c72be7a89b7c182ad */ - 8.50065068549420263957072899177793617e-01L, /* 3ffeb33bba89c89487a9a94747db2a41 */ --4.73753917078785974356016104842568442e-35L, /* bf8cf7c81559438b9c4bdd5d1f92fa42 */ + L(8.50065068549420263957072899177793617e-01), /* 3ffeb33bba89c89487a9a94747db2a41 */ +L(-4.73753917078785974356016104842568442e-35), /* bf8cf7c81559438b9c4bdd5d1f92fa42 */ /* sin(x) = 0.86d45935ab396cb4e421e822dee54f3562dfcefeaa782184c23401d231f5ad981a1cc195b18 */ - 5.26677680590386730710789410624833901e-01L, /* 3ffe0da8b26b5672d969c843d045bdcb */ --3.67066148195515214077582496518566735e-35L, /* bf8c8654e901880aac3ef3d9ee5ff16e */ + L(5.26677680590386730710789410624833901e-01), /* 3ffe0da8b26b5672d969c843d045bdcb */ +L(-3.67066148195515214077582496518566735e-35), /* bf8c8654e901880aac3ef3d9ee5ff16e */ /* x = 5.62500000000000000000000000000000000e-01 3ffe2000000000000000000000000000 */ /* cos(x) = 0.d88e820b1526311dd561efbc0c1a9a5375eb26f65d246c5744b13ca26a7e0fd42556da843c8 */ - 8.45924499231067954459723078597493262e-01L, /* 3ffeb11d04162a4c623baac3df781835 */ - 1.98054947141989878179164342925274053e-35L, /* 3f8ba5375eb26f65d246c5744b13ca27 */ + L(8.45924499231067954459723078597493262e-01), /* 3ffeb11d04162a4c623baac3df781835 */ + L(1.98054947141989878179164342925274053e-35), /* 3f8ba5375eb26f65d246c5744b13ca27 */ /* sin(x) = 0.88868625b4e1dbb2313310133022527200c143a5cb16637cb7daf8ade82459ff2e98511f40f */ - 5.33302673536020173329131103308161529e-01L, /* 3ffe110d0c4b69c3b764626620266045 */ --3.42715291319551615996993795226755157e-35L, /* bf8c6c6ff9f5e2d1a74ce41a41283a91 */ + L(5.33302673536020173329131103308161529e-01), /* 3ffe110d0c4b69c3b764626620266045 */ +L(-3.42715291319551615996993795226755157e-35), /* bf8c6c6ff9f5e2d1a74ce41a41283a91 */ /* x = 5.70312500000000000000000000000000000e-01 3ffe2400000000000000000000000000 */ /* cos(x) = 0.d77bc4985e93a607c9d868b906bbc6bbe3a04258814acb0358468b826fc91bd4d814827f65e */ - 8.41732299041338366963111794309701085e-01L, /* 3ffeaef78930bd274c0f93b0d1720d78 */ --4.30821936750410026005408345400225948e-35L, /* bf8cca20e2fded3bf5a9a7e53dcba3ed */ + L(8.41732299041338366963111794309701085e-01), /* 3ffeaef78930bd274c0f93b0d1720d78 */ +L(-4.30821936750410026005408345400225948e-35), /* bf8cca20e2fded3bf5a9a7e53dcba3ed */ /* sin(x) = 0.8a3690fc5bfc11bf9535e2739a8512f448a41251514bbed7fc18d530f9b4650fcbb2861b0aa */ - 5.39895116435204405041660709903993340e-01L, /* 3ffe146d21f8b7f8237f2a6bc4e7350a */ - 1.42595803521626714477253741404712093e-35L, /* 3f8b2f448a41251514bbed7fc18d5310 */ + L(5.39895116435204405041660709903993340e-01), /* 3ffe146d21f8b7f8237f2a6bc4e7350a */ + L(1.42595803521626714477253741404712093e-35), /* 3f8b2f448a41251514bbed7fc18d5310 */ /* x = 5.78125000000000000000000000000000000e-01 3ffe2800000000000000000000000000 */ /* cos(x) = 0.d665a937b4ef2b1f6d51bad6d988a4419c1d7051faf31a9efa151d7631117efac03713f950a */ - 8.37488723850523685315353348917240617e-01L, /* 3ffeaccb526f69de563edaa375adb311 */ - 2.72761997872084533045777718677326179e-35L, /* 3f8c220ce0eb828fd798d4f7d0a8ebb2 */ + L(8.37488723850523685315353348917240617e-01), /* 3ffeaccb526f69de563edaa375adb311 */ + L(2.72761997872084533045777718677326179e-35), /* 3f8c220ce0eb828fd798d4f7d0a8ebb2 */ /* sin(x) = 0.8be472f9776d809af2b88171243d63d66dfceeeb739cc894e023fbc165a0e3f26ff729c5d57 */ - 5.46454606919203564403349553749411001e-01L, /* 3ffe17c8e5f2eedb0135e57102e2487b */ --2.11870230730160315420936523771864858e-35L, /* bf8bc29920311148c63376b1fdc043ea */ + L(5.46454606919203564403349553749411001e-01), /* 3ffe17c8e5f2eedb0135e57102e2487b */ +L(-2.11870230730160315420936523771864858e-35), /* bf8bc29920311148c63376b1fdc043ea */ /* x = 5.85937500000000000000000000000000000e-01 3ffe2c00000000000000000000000000 */ /* cos(x) = 0.d54c3441844897fc8f853f0655f1ba695eba9fbfd7439dbb1171d862d9d9146ca5136f825ac */ - 8.33194032664581363070224042208032321e-01L, /* 3ffeaa98688308912ff91f0a7e0cabe3 */ - 4.39440050052045486567668031751259899e-35L, /* 3f8cd34af5d4fdfeba1cedd88b8ec317 */ + L(8.33194032664581363070224042208032321e-01), /* 3ffeaa98688308912ff91f0a7e0cabe3 */ + L(4.39440050052045486567668031751259899e-35), /* 3f8cd34af5d4fdfeba1cedd88b8ec317 */ /* sin(x) = 0.8d902565817ee7839bce3cd128060119492cd36d42d82ada30d7f8bde91324808377ddbf5d4 */ - 5.52980744630527369849695082681623667e-01L, /* 3ffe1b204acb02fdcf07379c79a2500c */ - 8.26624790417342895897164123189984127e-37L, /* 3f8719492cd36d42d82ada30d7f8bde9 */ + L(5.52980744630527369849695082681623667e-01), /* 3ffe1b204acb02fdcf07379c79a2500c */ + L(8.26624790417342895897164123189984127e-37), /* 3f8719492cd36d42d82ada30d7f8bde9 */ /* x = 5.93750000000000000000000000000000000e-01 3ffe3000000000000000000000000000 */ /* cos(x) = 0.d42f6a1b9f0168cdf031c2f63c8d9304d86f8d34cb1d5fccb68ca0f2241427fc18d1fd5bbdf */ - 8.28848487609325734810171790119116638e-01L, /* 3ffea85ed4373e02d19be06385ec791b */ - 1.43082508100496581719048175506239770e-35L, /* 3f8b304d86f8d34cb1d5fccb68ca0f22 */ + L(8.28848487609325734810171790119116638e-01), /* 3ffea85ed4373e02d19be06385ec791b */ + L(1.43082508100496581719048175506239770e-35), /* 3f8b304d86f8d34cb1d5fccb68ca0f22 */ /* sin(x) = 0.8f39a191b2ba6122a3fa4f41d5a3ffd421417d46f19a22230a14f7fcc8fce5c75b4b28b29d1 */ - 5.59473131247366877384844006003116688e-01L, /* 3ffe1e7343236574c24547f49e83ab48 */ --1.28922620524163922306886952100992796e-37L, /* bf845ef5f415c8732eeee7af584019b8 */ + L(5.59473131247366877384844006003116688e-01), /* 3ffe1e7343236574c24547f49e83ab48 */ +L(-1.28922620524163922306886952100992796e-37), /* bf845ef5f415c8732eeee7af584019b8 */ /* x = 6.01562500000000000000000000000000000e-01 3ffe3400000000000000000000000000 */ /* cos(x) = 0.d30f4f392c357ab0661c5fa8a7d9b26627846fef214b1d19a22379ff9eddba087cf410eb097 */ - 8.24452353914429207485643598212356053e-01L, /* 3ffea61e9e72586af560cc38bf514fb3 */ - 3.79160239225080026987031418939026741e-35L, /* 3f8c93313c237f790a58e8cd111bcffd */ + L(8.24452353914429207485643598212356053e-01), /* 3ffea61e9e72586af560cc38bf514fb3 */ + L(3.79160239225080026987031418939026741e-35), /* 3f8c93313c237f790a58e8cd111bcffd */ /* sin(x) = 0.90e0e0d81ca678796cc92c8ea8c2815bc72ca78abe571bfa8576aacc571e096a33237e0e830 */ - 5.65931370507905990773159095689276114e-01L, /* 3ffe21c1c1b0394cf0f2d992591d5185 */ - 1.02202775968053982310991962521535027e-36L, /* 3f875bc72ca78abe571bfa8576aacc57 */ + L(5.65931370507905990773159095689276114e-01), /* 3ffe21c1c1b0394cf0f2d992591d5185 */ + L(1.02202775968053982310991962521535027e-36), /* 3f875bc72ca78abe571bfa8576aacc57 */ /* x = 6.09375000000000000000000000000000000e-01 3ffe3800000000000000000000000000 */ /* cos(x) = 0.d1ebe81a95ee752e48a26bcd32d6e922d7eb44b8ad2232f6930795e84b56317269b9dd1dfa6 */ - 8.20005899897234008255550633876556043e-01L, /* 3ffea3d7d0352bdcea5c9144d79a65ae */ --1.72008811955230823416724332297991247e-35L, /* bf8b6dd2814bb4752ddcd096cf86a17b */ + L(8.20005899897234008255550633876556043e-01), /* 3ffea3d7d0352bdcea5c9144d79a65ae */ +L(-1.72008811955230823416724332297991247e-35), /* bf8b6dd2814bb4752ddcd096cf86a17b */ /* sin(x) = 0.9285dc9bc45dd9ea3d02457bcce59c4175aab6ff7929a8d287195525fdace200dba032874fb */ - 5.72355068234507240384953706824503608e-01L, /* 3ffe250bb93788bbb3d47a048af799cb */ - 2.12572273479933123944580199464514529e-35L, /* 3f8bc4175aab6ff7929a8d2871955260 */ + L(5.72355068234507240384953706824503608e-01), /* 3ffe250bb93788bbb3d47a048af799cb */ + L(2.12572273479933123944580199464514529e-35), /* 3f8bc4175aab6ff7929a8d2871955260 */ /* x = 6.17187500000000000000000000000000000e-01 3ffe3c00000000000000000000000000 */ /* cos(x) = 0.d0c5394d772228195e25736c03574707de0af1ca344b13bd3914bfe27518e9e426f5deff1e1 */ - 8.15509396946375476876345384201386217e-01L, /* 3ffea18a729aee445032bc4ae6d806af */ --4.28589138410712954051679139949341961e-35L, /* bf8cc7c10fa871ae5da76216375a00ec */ + L(8.15509396946375476876345384201386217e-01), /* 3ffea18a729aee445032bc4ae6d806af */ +L(-4.28589138410712954051679139949341961e-35), /* bf8cc7c10fa871ae5da76216375a00ec */ /* sin(x) = 0.94288e48bd0335fc41c4cbd2920497a8f5d1d8185c99fa0081f90c27e2a53ffdd208a0dbe69 */ - 5.78743832357770354521111378581385347e-01L, /* 3ffe28511c917a066bf8838997a52409 */ - 1.77998063432551282609698670002456093e-35L, /* 3f8b7a8f5d1d8185c99fa0081f90c27e */ + L(5.78743832357770354521111378581385347e-01), /* 3ffe28511c917a066bf8838997a52409 */ + L(1.77998063432551282609698670002456093e-35), /* 3f8b7a8f5d1d8185c99fa0081f90c27e */ /* x = 6.25000000000000000000000000000000000e-01 3ffe4000000000000000000000000000 */ /* cos(x) = 0.cf9b476c897c25c5bfe750dd3f308eaf7bcc1ed00179a256870f4200445043dcdb1974b5878 */ - 8.10963119505217902189534803941080724e-01L, /* 3ffe9f368ed912f84b8b7fcea1ba7e61 */ - 1.10481292856794436426051402418804358e-35L, /* 3f8ad5ef7983da002f344ad0e1e84009 */ + L(8.10963119505217902189534803941080724e-01), /* 3ffe9f368ed912f84b8b7fcea1ba7e61 */ + L(1.10481292856794436426051402418804358e-35), /* 3f8ad5ef7983da002f344ad0e1e84009 */ /* sin(x) = 0.95c8ef544210ec0b91c49bd2aa09e8515fa61a156ebb10f5f8c232a6445b61ebf3c2ec268f9 */ - 5.85097272940462154805399314150080459e-01L, /* 3ffe2b91dea88421d817238937a55414 */ --1.78164576278056195136525335403380464e-35L, /* bf8b7aea059e5ea9144ef0a073dcd59c */ + L(5.85097272940462154805399314150080459e-01), /* 3ffe2b91dea88421d817238937a55414 */ +L(-1.78164576278056195136525335403380464e-35), /* bf8b7aea059e5ea9144ef0a073dcd59c */ /* x = 6.32812500000000000000000000000000000e-01 3ffe4400000000000000000000000000 */ /* cos(x) = 0.ce6e171f92f2e27f32225327ec440ddaefae248413efc0e58ceee1ae369aabe73f88c87ed1a */ - 8.06367345055103913698795406077297399e-01L, /* 3ffe9cdc2e3f25e5c4fe6444a64fd888 */ - 1.04235088143133625463876245029180850e-35L, /* 3f8abb5df5c490827df81cb19ddc35c7 */ + L(8.06367345055103913698795406077297399e-01), /* 3ffe9cdc2e3f25e5c4fe6444a64fd888 */ + L(1.04235088143133625463876245029180850e-35), /* 3f8abb5df5c490827df81cb19ddc35c7 */ /* sin(x) = 0.9766f93cd18413a6aafc1cfc6fc28abb6817bf94ce349901ae3f48c3215d3eb60acc5f78903 */ - 5.91415002201316315087000225758031236e-01L, /* 3ffe2ecdf279a308274d55f839f8df85 */ - 8.07390238063560077355762466502569603e-36L, /* 3f8a576d02f7f299c6932035c7e91864 */ + L(5.91415002201316315087000225758031236e-01), /* 3ffe2ecdf279a308274d55f839f8df85 */ + L(8.07390238063560077355762466502569603e-36), /* 3f8a576d02f7f299c6932035c7e91864 */ /* x = 6.40625000000000000000000000000000000e-01 3ffe4800000000000000000000000000 */ /* cos(x) = 0.cd3dad1b5328a2e459f993f4f5108819faccbc4eeba9604e81c7adad51cc8a2561631a06826 */ - 8.01722354098418450607492605652964208e-01L, /* 3ffe9a7b5a36a65145c8b3f327e9ea21 */ - 6.09487851305233089325627939458963741e-36L, /* 3f8a033f599789dd752c09d038f5b5aa */ + L(8.01722354098418450607492605652964208e-01), /* 3ffe9a7b5a36a65145c8b3f327e9ea21 */ + L(6.09487851305233089325627939458963741e-36), /* 3f8a033f599789dd752c09d038f5b5aa */ /* sin(x) = 0.9902a58a45e27bed68412b426b675ed503f54d14c8172e0d373f42cadf04daf67319a7f94be */ - 5.97696634538701531238647618967334337e-01L, /* 3ffe32054b148bc4f7dad0825684d6cf */ --2.49527608940873714527427941350461554e-35L, /* bf8c0957e0559759bf468f964605e9a9 */ + L(5.97696634538701531238647618967334337e-01), /* 3ffe32054b148bc4f7dad0825684d6cf */ +L(-2.49527608940873714527427941350461554e-35), /* bf8c0957e0559759bf468f964605e9a9 */ /* x = 6.48437500000000000000000000000000000e-01 3ffe4c00000000000000000000000000 */ /* cos(x) = 0.cc0a0e21709883a3ff00911e11a07ee3bd7ea2b04e081be99be0264791170761ae64b8b744a */ - 7.97028430141468342004642741431945296e-01L, /* 3ffe98141c42e1310747fe01223c2341 */ --8.35364432831812599727083251866305534e-37L, /* bf871c42815d4fb1f7e416641fd9b86f */ + L(7.97028430141468342004642741431945296e-01), /* 3ffe98141c42e1310747fe01223c2341 */ +L(-8.35364432831812599727083251866305534e-37), /* bf871c42815d4fb1f7e416641fd9b86f */ /* sin(x) = 0.9a9bedcdf01b38d993f3d7820781de292033ead73b89e28f39313dbe3a6e463f845b5fa8490 */ - 6.03941786554156657267270287527367726e-01L, /* 3ffe3537db9be03671b327e7af040f04 */ --2.54578992328947177770363936132309779e-35L, /* bf8c0eb6fe60a94623b0eb863676120e */ + L(6.03941786554156657267270287527367726e-01), /* 3ffe3537db9be03671b327e7af040f04 */ +L(-2.54578992328947177770363936132309779e-35), /* bf8c0eb6fe60a94623b0eb863676120e */ /* x = 6.56250000000000000000000000000000000e-01 3ffe5000000000000000000000000000 */ /* cos(x) = 0.cad33f00658fe5e8204bbc0f3a66a0e6a773f87987a780b243d7be83b3db1448ca0e0e62787 */ - 7.92285859677178543141501323781709399e-01L, /* 3ffe95a67e00cb1fcbd04097781e74cd */ - 2.47519558228473167879248891673807645e-35L, /* 3f8c07353b9fc3cc3d3c05921ebdf41e */ + L(7.92285859677178543141501323781709399e-01), /* 3ffe95a67e00cb1fcbd04097781e74cd */ + L(2.47519558228473167879248891673807645e-35), /* 3f8c07353b9fc3cc3d3c05921ebdf41e */ /* sin(x) = 0.9c32cba2b14156ef05256c4f857991ca6a547cd7ceb1ac8a8e62a282bd7b9183648a462bd04 */ - 6.10150077075791371273742393566183220e-01L, /* 3ffe386597456282adde0a4ad89f0af3 */ - 1.33842237929938963780969418369150532e-35L, /* 3f8b1ca6a547cd7ceb1ac8a8e62a282c */ + L(6.10150077075791371273742393566183220e-01), /* 3ffe386597456282adde0a4ad89f0af3 */ + L(1.33842237929938963780969418369150532e-35), /* 3f8b1ca6a547cd7ceb1ac8a8e62a282c */ /* x = 6.64062500000000000000000000000000000e-01 3ffe5400000000000000000000000000 */ /* cos(x) = 0.c99944936cf48c8911ff93fe64b3ddb7981e414bdaf6aae1203577de44878c62bc3bc9cf7b9 */ - 7.87494932167606083931328295965533034e-01L, /* 3ffe93328926d9e9191223ff27fcc968 */ --2.57915385618070637156514241185180920e-35L, /* bf8c12433f0df5a1284aa8f6fe54410e */ + L(7.87494932167606083931328295965533034e-01), /* 3ffe93328926d9e9191223ff27fcc968 */ +L(-2.57915385618070637156514241185180920e-35), /* bf8c12433f0df5a1284aa8f6fe54410e */ /* sin(x) = 0.9dc738ad14204e689ac582d0f85826590feece34886cfefe2e08cf2bb8488d55424dc9d3525 */ - 6.16321127181550943005700433761731837e-01L, /* 3ffe3b8e715a28409cd1358b05a1f0b0 */ - 2.88497530050197716298085892460478666e-35L, /* 3f8c32c87f7671a44367f7f17046795e */ + L(6.16321127181550943005700433761731837e-01), /* 3ffe3b8e715a28409cd1358b05a1f0b0 */ + L(2.88497530050197716298085892460478666e-35), /* 3f8c32c87f7671a44367f7f17046795e */ /* x = 6.71875000000000000000000000000000000e-01 3ffe5800000000000000000000000000 */ /* cos(x) = 0.c85c23c26ed7b6f014ef546c47929682122876bfbf157de0aff3c4247d820c746e32cd4174f */ - 7.82655940026272796930787447428139026e-01L, /* 3ffe90b84784ddaf6de029dea8d88f25 */ - 1.69332045679237919427807771288506254e-35L, /* 3f8b682122876bfbf157de0aff3c4248 */ + L(7.82655940026272796930787447428139026e-01), /* 3ffe90b84784ddaf6de029dea8d88f25 */ + L(1.69332045679237919427807771288506254e-35), /* 3f8b682122876bfbf157de0aff3c4248 */ /* sin(x) = 0.9f592e9b66a9cf906a3c7aa3c10199849040c45ec3f0a747597311038101780c5f266059dbf */ - 6.22454560222343683041926705090443330e-01L, /* 3ffe3eb25d36cd539f20d478f5478203 */ - 1.91974786921147072717621236192269859e-35L, /* 3f8b9849040c45ec3f0a747597311038 */ + L(6.22454560222343683041926705090443330e-01), /* 3ffe3eb25d36cd539f20d478f5478203 */ + L(1.91974786921147072717621236192269859e-35), /* 3f8b9849040c45ec3f0a747597311038 */ /* x = 6.79687500000000000000000000000000000e-01 3ffe5c00000000000000000000000000 */ /* cos(x) = 0.c71be181ecd6875ce2da5615a03cca207d9adcb9dfb0a1d6c40a4f0056437f1a59ccddd06ee */ - 7.77769178600317903122203513685412863e-01L, /* 3ffe8e37c303d9ad0eb9c5b4ac2b407a */ --4.05296033424632846931240580239929672e-35L, /* bf8caefc13291a31027af149dfad87fd */ + L(7.77769178600317903122203513685412863e-01), /* 3ffe8e37c303d9ad0eb9c5b4ac2b407a */ +L(-4.05296033424632846931240580239929672e-35), /* bf8caefc13291a31027af149dfad87fd */ /* sin(x) = 0.a0e8a725d33c828c11fa50fd9e9a15ffecfad43f3e534358076b9b0f6865694842b1e8c67dc */ - 6.28550001845029662028004327939032867e-01L, /* 3ffe41d14e4ba679051823f4a1fb3d34 */ - 1.65507421184028099672784511397428852e-35L, /* 3f8b5ffecfad43f3e534358076b9b0f7 */ + L(6.28550001845029662028004327939032867e-01), /* 3ffe41d14e4ba679051823f4a1fb3d34 */ + L(1.65507421184028099672784511397428852e-35), /* 3f8b5ffecfad43f3e534358076b9b0f7 */ /* x = 6.87500000000000000000000000000000000e-01 3ffe6000000000000000000000000000 */ /* cos(x) = 0.c5d882d2ee48030c7c07d28e981e34804f82ed4cf93655d2365389b716de6ad44676a1cc5da */ - 7.72834946152471544810851845913425178e-01L, /* 3ffe8bb105a5dc900618f80fa51d303c */ - 3.94975229341211664237241534741146939e-35L, /* 3f8ca4027c176a67c9b2ae91b29c4db9 */ + L(7.72834946152471544810851845913425178e-01), /* 3ffe8bb105a5dc900618f80fa51d303c */ + L(3.94975229341211664237241534741146939e-35), /* 3f8ca4027c176a67c9b2ae91b29c4db9 */ /* sin(x) = 0.a2759c0e79c35582527c32b55f5405c182c66160cb1d9eb7bb0b7cdf4ad66f317bda4332914 */ - 6.34607080015269296850309914203671436e-01L, /* 3ffe44eb381cf386ab04a4f8656abea8 */ - 4.33025916939968369326060156455927002e-36L, /* 3f897060b1985832c767adeec2df37d3 */ + L(6.34607080015269296850309914203671436e-01), /* 3ffe44eb381cf386ab04a4f8656abea8 */ + L(4.33025916939968369326060156455927002e-36), /* 3f897060b1985832c767adeec2df37d3 */ /* x = 6.95312500000000000000000000000000000e-01 3ffe6400000000000000000000000000 */ /* cos(x) = 0.c4920cc2ec38fb891b38827db08884fc66371ac4c2052ca8885b981bbcfd3bb7b093ee31515 */ - 7.67853543842850365879920759114193964e-01L, /* 3ffe89241985d871f712367104fb6111 */ - 3.75100035267325597157244776081706979e-36L, /* 3f893f198dc6b130814b2a2216e606ef */ + L(7.67853543842850365879920759114193964e-01), /* 3ffe89241985d871f712367104fb6111 */ + L(3.75100035267325597157244776081706979e-36), /* 3f893f198dc6b130814b2a2216e606ef */ /* sin(x) = 0.a400072188acf49cd6b173825e038346f105e1301afe642bcc364cea455e21e506e3e927ed8 */ - 6.40625425040230409188409779413961021e-01L, /* 3ffe48000e431159e939ad62e704bc07 */ - 2.46542747294664049615806500747173281e-36L, /* 3f88a37882f0980d7f3215e61b267523 */ + L(6.40625425040230409188409779413961021e-01), /* 3ffe48000e431159e939ad62e704bc07 */ + L(2.46542747294664049615806500747173281e-36), /* 3f88a37882f0980d7f3215e61b267523 */ /* x = 7.03125000000000000000000000000000000e-01 3ffe6800000000000000000000000000 */ /* cos(x) = 0.c348846bbd3631338ffe2bfe9dd1381a35b4e9c0c51b4c13fe376bad1bf5caacc4542be0aa9 */ - 7.62825275710576250507098753625429792e-01L, /* 3ffe869108d77a6c62671ffc57fd3ba2 */ - 4.22067411888601505004748939382325080e-35L, /* 3f8cc0d1ada74e0628da609ff1bb5d69 */ + L(7.62825275710576250507098753625429792e-01), /* 3ffe869108d77a6c62671ffc57fd3ba2 */ + L(4.22067411888601505004748939382325080e-35), /* 3f8cc0d1ada74e0628da609ff1bb5d69 */ /* sin(x) = 0.a587e23555bb08086d02b9c662cdd29316c3e9bd08d93793634a21b1810cce73bdb97a99b9e */ - 6.46604669591152370524042159882800763e-01L, /* 3ffe4b0fc46aab761010da05738cc59c */ --3.41742981816219412415674365946079826e-35L, /* bf8c6b6749e0b217b9364364e5aef274 */ + L(6.46604669591152370524042159882800763e-01), /* 3ffe4b0fc46aab761010da05738cc59c */ +L(-3.41742981816219412415674365946079826e-35), /* bf8c6b6749e0b217b9364364e5aef274 */ /* x = 7.10937500000000000000000000000000000e-01 3ffe6c00000000000000000000000000 */ /* cos(x) = 0.c1fbeef380e4ffdd5a613ec8722f643ffe814ec2343e53adb549627224fdc9f2a7b77d3d69f */ - 7.57750448655219342240234832230493361e-01L, /* 3ffe83f7dde701c9ffbab4c27d90e45f */ --2.08767968311222650582659938787920125e-35L, /* bf8bbc0017eb13dcbc1ac524ab69d8de */ + L(7.57750448655219342240234832230493361e-01), /* 3ffe83f7dde701c9ffbab4c27d90e45f */ +L(-2.08767968311222650582659938787920125e-35), /* bf8bbc0017eb13dcbc1ac524ab69d8de */ /* sin(x) = 0.a70d272a76a8d4b6da0ec90712bb748b96dabf88c3079246f3db7eea6e58ead4ed0e2843303 */ - 6.52544448725765956407573982284767763e-01L, /* 3ffe4e1a4e54ed51a96db41d920e2577 */ --8.61758060284379660697102362141557170e-36L, /* bf8a6e8d24a80ee79f0db721849022b2 */ + L(6.52544448725765956407573982284767763e-01), /* 3ffe4e1a4e54ed51a96db41d920e2577 */ +L(-8.61758060284379660697102362141557170e-36), /* bf8a6e8d24a80ee79f0db721849022b2 */ /* x = 7.18750000000000000000000000000000000e-01 3ffe7000000000000000000000000000 */ /* cos(x) = 0.c0ac518c8b6ae710ba37a3eeb90cb15aebcb8bed4356fb507a48a6e97de9aa6d9660116b436 */ - 7.52629372418066476054541324847143116e-01L, /* 3ffe8158a31916d5ce21746f47dd7219 */ - 3.71306958657663189665450864311104571e-35L, /* 3f8c8ad75e5c5f6a1ab7da83d245374c */ + L(7.52629372418066476054541324847143116e-01), /* 3ffe8158a31916d5ce21746f47dd7219 */ + L(3.71306958657663189665450864311104571e-35), /* 3f8c8ad75e5c5f6a1ab7da83d245374c */ /* sin(x) = 0.a88fcfebd9a8dd47e2f3c76ef9e2439920f7e7fbe735f8bcc985491ec6f12a2d4214f8cfa99 */ - 6.58444399910567541589583954884041989e-01L, /* 3ffe511f9fd7b351ba8fc5e78eddf3c5 */ --4.54412944084300330523721391865787219e-35L, /* bf8ce336f840c020c6503a19b3d5b70a */ + L(6.58444399910567541589583954884041989e-01), /* 3ffe511f9fd7b351ba8fc5e78eddf3c5 */ +L(-4.54412944084300330523721391865787219e-35), /* bf8ce336f840c020c6503a19b3d5b70a */ /* x = 7.26562500000000000000000000000000000e-01 3ffe7400000000000000000000000000 */ /* cos(x) = 0.bf59b17550a4406875969296567cf3e3b4e483061877c02811c6cae85fad5a6c3da58f49292 */ - 7.47462359563216166669700384714767552e-01L, /* 3ffe7eb362eaa14880d0eb2d252cacfa */ --9.11094340926220027288083639048016945e-36L, /* bf8a8389636f9f3cf107fafdc726a2f4 */ + L(7.47462359563216166669700384714767552e-01), /* 3ffe7eb362eaa14880d0eb2d252cacfa */ +L(-9.11094340926220027288083639048016945e-36), /* bf8a8389636f9f3cf107fafdc726a2f4 */ /* sin(x) = 0.aa0fd66eddb921232c28520d3911b8a03193b47f187f1471ac216fbcd5bb81029294d3a73f1 */ - 6.64304163042946276515506587432846246e-01L, /* 3ffe541facddbb7242465850a41a7223 */ - 4.26004843895378210155889028714676019e-35L, /* 3f8cc5018c9da3f8c3f8a38d610b7de7 */ + L(6.64304163042946276515506587432846246e-01), /* 3ffe541facddbb7242465850a41a7223 */ + L(4.26004843895378210155889028714676019e-35), /* 3f8cc5018c9da3f8c3f8a38d610b7de7 */ /* x = 7.34375000000000000000000000000000000e-01 3ffe7800000000000000000000000000 */ /* cos(x) = 0.be0413f84f2a771c614946a88cbf4da1d75a5560243de8f2283fefa0ea4a48468a52d51d8b3 */ - 7.42249725458501306991347253449610537e-01L, /* 3ffe7c0827f09e54ee38c2928d51197f */ --3.78925270049800913539923473871287550e-35L, /* bf8c92f1452d54fede10b86ebe0082f9 */ + L(7.42249725458501306991347253449610537e-01), /* 3ffe7c0827f09e54ee38c2928d51197f */ +L(-3.78925270049800913539923473871287550e-35), /* bf8c92f1452d54fede10b86ebe0082f9 */ /* sin(x) = 0.ab8d34b36acd987210ed343ec65d7e3adc2e7109fce43d55c8d57dfdf55b9e01d2cc1f1b9ec */ - 6.70123380473162894654531583500648495e-01L, /* 3ffe571a6966d59b30e421da687d8cbb */ --1.33165852952743729897634069393684656e-36L, /* bf87c523d18ef6031bc2aa372a82020b */ + L(6.70123380473162894654531583500648495e-01), /* 3ffe571a6966d59b30e421da687d8cbb */ +L(-1.33165852952743729897634069393684656e-36), /* bf87c523d18ef6031bc2aa372a82020b */ /* x = 7.42187500000000000000000000000000000e-01 3ffe7c00000000000000000000000000 */ /* cos(x) = 0.bcab7e6bfb2a14a9b122c574a376bec98ab14808c64a4e731b34047e217611013ac99c0f25d */ - 7.36991788256240741057089385586450844e-01L, /* 3ffe7956fcd7f654295362458ae946ed */ - 4.72358938637974850573747497460125519e-35L, /* 3f8cf64c558a404632527398d9a023f1 */ + L(7.36991788256240741057089385586450844e-01), /* 3ffe7956fcd7f654295362458ae946ed */ + L(4.72358938637974850573747497460125519e-35), /* 3f8cf64c558a404632527398d9a023f1 */ /* sin(x) = 0.ad07e4c409d08c4fa3a9057bb0ac24b8636e74e76f51e09bd6b2319707cbd9f5e254643897a */ - 6.75901697026178809189642203142423973e-01L, /* 3ffe5a0fc98813a1189f47520af76158 */ - 2.76252586616364878801928456702948857e-35L, /* 3f8c25c31b73a73b7a8f04deb5918cb8 */ + L(6.75901697026178809189642203142423973e-01), /* 3ffe5a0fc98813a1189f47520af76158 */ + L(2.76252586616364878801928456702948857e-35), /* 3f8c25c31b73a73b7a8f04deb5918cb8 */ /* x = 7.50000000000000000000000000000000000e-01 3ffe8000000000000000000000000000 */ /* cos(x) = 0.bb4ff632a908f73ec151839cb9d993b4e0bfb8f20e7e44e6e4aee845e35575c3106dbe6fd06 */ - 7.31688868873820886311838753000084529e-01L, /* 3ffe769fec655211ee7d82a3073973b3 */ - 1.48255637548931697184991710293198620e-35L, /* 3f8b3b4e0bfb8f20e7e44e6e4aee845e */ + L(7.31688868873820886311838753000084529e-01), /* 3ffe769fec655211ee7d82a3073973b3 */ + L(1.48255637548931697184991710293198620e-35), /* 3f8b3b4e0bfb8f20e7e44e6e4aee845e */ /* sin(x) = 0.ae7fe0b5fc786b2d966e1d6af140a488476747c2646425fc7533f532cd044cb10a971a49a6a */ - 6.81638760023334166733241952779893908e-01L, /* 3ffe5cffc16bf8f0d65b2cdc3ad5e281 */ - 2.74838775935027549024224114338667371e-35L, /* 3f8c24423b3a3e1323212fe3a99fa996 */ + L(6.81638760023334166733241952779893908e-01), /* 3ffe5cffc16bf8f0d65b2cdc3ad5e281 */ + L(2.74838775935027549024224114338667371e-35), /* 3f8c24423b3a3e1323212fe3a99fa996 */ /* x = 7.57812500000000000000000000000000000e-01 3ffe8400000000000000000000000000 */ /* cos(x) = 0.b9f180ba77dd0751628e135a9508299012230f14becacdd14c3f8862d122de5b56d55b53360 */ - 7.26341290974108590410147630237598973e-01L, /* 3ffe73e30174efba0ea2c51c26b52a10 */ - 3.12683579338351123545814364980658990e-35L, /* 3f8c4c80911878a5f6566e8a61fc4317 */ + L(7.26341290974108590410147630237598973e-01), /* 3ffe73e30174efba0ea2c51c26b52a10 */ + L(3.12683579338351123545814364980658990e-35), /* 3f8c4c80911878a5f6566e8a61fc4317 */ /* sin(x) = 0.aff522a954f2ba16d9defdc416e33f5e9a5dfd5a6c228e0abc4d521327ff6e2517a7b3851dd */ - 6.87334219303873534951703613035647220e-01L, /* 3ffe5fea4552a9e5742db3bdfb882dc6 */ - 4.76739454455410744997012795035529128e-35L, /* 3f8cfaf4d2efead361147055e26a9099 */ + L(6.87334219303873534951703613035647220e-01), /* 3ffe5fea4552a9e5742db3bdfb882dc6 */ + L(4.76739454455410744997012795035529128e-35), /* 3f8cfaf4d2efead361147055e26a9099 */ /* x = 7.65625000000000000000000000000000000e-01 3ffe8800000000000000000000000000 */ /* cos(x) = 0.b890237d3bb3c284b614a0539016bfa1053730bbdf940fa895e185f8e58884d3dda15e63371 */ - 7.20949380945696418043812784148447688e-01L, /* 3ffe712046fa776785096c2940a7202d */ - 4.78691285733673379499536326050811832e-35L, /* 3f8cfd0829b985defca07d44af0c2fc7 */ + L(7.20949380945696418043812784148447688e-01), /* 3ffe712046fa776785096c2940a7202d */ + L(4.78691285733673379499536326050811832e-35), /* 3f8cfd0829b985defca07d44af0c2fc7 */ /* sin(x) = 0.b167a4c90d63c4244cf5493b7cc23bd3c3c1225e078baa0c53d6d400b926281f537a1a260e6 */ - 6.92987727246317910281815490823048210e-01L, /* 3ffe62cf49921ac7884899ea9276f984 */ - 4.50089871077663557180849219529189918e-35L, /* 3f8cde9e1e0912f03c5d50629eb6a006 */ + L(6.92987727246317910281815490823048210e-01), /* 3ffe62cf49921ac7884899ea9276f984 */ + L(4.50089871077663557180849219529189918e-35), /* 3f8cde9e1e0912f03c5d50629eb6a006 */ /* x = 7.73437500000000000000000000000000000e-01 3ffe8c00000000000000000000000000 */ /* cos(x) = 0.b72be40067aaf2c050dbdb7a14c3d7d4f203f6b3f0224a4afe55d6ec8e92b508fd5c5984b3b */ - 7.15513467882981573520620561289896903e-01L, /* 3ffe6e57c800cf55e580a1b7b6f42988 */ --3.02191815581445336509438104625489192e-35L, /* bf8c41586fe04a607eedada80d51489c */ + L(7.15513467882981573520620561289896903e-01), /* 3ffe6e57c800cf55e580a1b7b6f42988 */ +L(-3.02191815581445336509438104625489192e-35), /* bf8c41586fe04a607eedada80d51489c */ /* sin(x) = 0.b2d7614b1f3aaa24df2d6e20a77e1ca3e6d838c03e29c1bcb026e6733324815fadc9eb89674 */ - 6.98598938789681741301929277107891591e-01L, /* 3ffe65aec2963e755449be5adc414efc */ - 2.15465226809256290914423429408722521e-35L, /* 3f8bca3e6d838c03e29c1bcb026e6733 */ + L(6.98598938789681741301929277107891591e-01), /* 3ffe65aec2963e755449be5adc414efc */ + L(2.15465226809256290914423429408722521e-35), /* 3f8bca3e6d838c03e29c1bcb026e6733 */ /* x = 7.81250000000000000000000000000000000e-01 3ffe9000000000000000000000000000 */ /* cos(x) = 0.b5c4c7d4f7dae915ac786ccf4b1a498d3e73b6e5e74fe7519d9c53ee6d6b90e881bddfc33e1 */ - 7.10033883566079674974121643959490219e-01L, /* 3ffe6b898fa9efb5d22b58f0d99e9635 */ --4.09623224763692443220896752907902465e-35L, /* bf8cb3960c6248d0c580c573131d608d */ + L(7.10033883566079674974121643959490219e-01), /* 3ffe6b898fa9efb5d22b58f0d99e9635 */ +L(-4.09623224763692443220896752907902465e-35), /* bf8cb3960c6248d0c580c573131d608d */ /* sin(x) = 0.b44452709a59752905913765434a59d111f0433eb2b133f7d103207e2aeb4aae111ddc385b3 */ - 7.04167511454533672780059509973942844e-01L, /* 3ffe6888a4e134b2ea520b226eca8695 */ --2.87259372740393348676633610275598640e-35L, /* bf8c3177707de60a6a76604177e6fc0f */ + L(7.04167511454533672780059509973942844e-01), /* 3ffe6888a4e134b2ea520b226eca8695 */ +L(-2.87259372740393348676633610275598640e-35), /* bf8c3177707de60a6a76604177e6fc0f */ /* x = 7.89062500000000000000000000000000000e-01 3ffe9400000000000000000000000000 */ /* cos(x) = 0.b45ad4975b1294cadca4cf40ec8f22a68cd14b175835239a37e63acb85e8e9505215df18140 */ - 7.04510962440574606164129481545916976e-01L, /* 3ffe68b5a92eb6252995b9499e81d91e */ - 2.60682037357042658395360726992048803e-35L, /* 3f8c1534668a58bac1a91cd1bf31d65c */ + L(7.04510962440574606164129481545916976e-01), /* 3ffe68b5a92eb6252995b9499e81d91e */ + L(2.60682037357042658395360726992048803e-35), /* 3f8c1534668a58bac1a91cd1bf31d65c */ /* sin(x) = 0.b5ae7285bc10cf515753847e8f8b7a30e0a580d929d770103509880680f7b8b0e8ad23b65d8 */ - 7.09693105363899724959669028139035515e-01L, /* 3ffe6b5ce50b78219ea2aea708fd1f17 */ --4.37026016974122945368562319136420097e-36L, /* bf8973c7d69fc9b58a23fbf2bd9dfe60 */ + L(7.09693105363899724959669028139035515e-01), /* 3ffe6b5ce50b78219ea2aea708fd1f17 */ +L(-4.37026016974122945368562319136420097e-36), /* bf8973c7d69fc9b58a23fbf2bd9dfe60 */ }; diff --git a/sysdeps/ieee754/ldbl-128/w_expl.c b/sysdeps/ieee754/ldbl-128/w_expl.c deleted file mode 100644 index c32616e504..0000000000 --- a/sysdeps/ieee754/ldbl-128/w_expl.c +++ /dev/null @@ -1,42 +0,0 @@ -/* w_expl.c -- long double version of w_exp.c. - * Conversion to long double by Ulrich Drepper, - * Cygnus Support, drepper@cygnus.com. - */ - -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: $"; -#endif - -/* - * wrapper expl(x) - */ - -#include <math.h> -#include <math_private.h> - -long double __expl(long double x) /* wrapper exp */ -{ -#ifdef _IEEE_LIBM - return __ieee754_expl(x); -#else - long double z = __ieee754_expl (x); - if (__glibc_unlikely (!isfinite (z) || z == 0) - && isfinite (x) && _LIB_VERSION != _IEEE_) - return __kernel_standard_l (x, x, 206 + !!signbit (x)); - - return z; -#endif -} -hidden_def (__expl) -weak_alias (__expl, expl) diff --git a/sysdeps/ieee754/ldbl-128/x2y2m1l.c b/sysdeps/ieee754/ldbl-128/x2y2m1l.c index 733742da04..390163fbc4 100644 --- a/sysdeps/ieee754/ldbl-128/x2y2m1l.c +++ b/sysdeps/ieee754/ldbl-128/x2y2m1l.c @@ -1,5 +1,5 @@ /* Compute x^2 + y^2 - 1, without large cancellation error. - Copyright (C) 2012-2016 Free Software Foundation, Inc. + Copyright (C) 2012-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -18,59 +18,30 @@ #include <math.h> #include <math_private.h> -#include <float.h> +#include <mul_splitl.h> #include <stdlib.h> + /* Calculate X + Y exactly and store the result in *HI + *LO. It is given that |X| >= |Y| and the values are small enough that no overflow occurs. */ static inline void -add_split (long double *hi, long double *lo, long double x, long double y) +add_split (_Float128 *hi, _Float128 *lo, _Float128 x, _Float128 y) { /* Apply Dekker's algorithm. */ *hi = x + y; *lo = (x - *hi) + y; } -/* Calculate X * Y exactly and store the result in *HI + *LO. It is - given that the values are small enough that no overflow occurs and - large enough (or zero) that no underflow occurs. */ - -static inline void -mul_split (long double *hi, long double *lo, long double x, long double y) -{ -#ifdef __FP_FAST_FMAL - /* Fast built-in fused multiply-add. */ - *hi = x * y; - *lo = __builtin_fmal (x, y, -*hi); -#elif defined FP_FAST_FMAL - /* Fast library fused multiply-add, compiler before GCC 4.6. */ - *hi = x * y; - *lo = __fmal (x, y, -*hi); -#else - /* Apply Dekker's algorithm. */ - *hi = x * y; -# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) - long double x1 = x * C; - long double y1 = y * C; -# undef C - x1 = (x - x1) + x1; - y1 = (y - y1) + y1; - long double x2 = x - x1; - long double y2 = y - y1; - *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; -#endif -} - /* Compare absolute values of floating-point values pointed to by P and Q for qsort. */ static int compare (const void *p, const void *q) { - long double pld = fabsl (*(const long double *) p); - long double qld = fabsl (*(const long double *) q); + _Float128 pld = fabsl (*(const _Float128 *) p); + _Float128 qld = fabsl (*(const _Float128 *) q); if (pld < qld) return -1; else if (pld == qld) @@ -83,22 +54,22 @@ compare (const void *p, const void *q) It is given that 1 > X >= Y >= epsilon / 2, and that X^2 + Y^2 >= 0.5. */ -long double -__x2y2m1l (long double x, long double y) +_Float128 +__x2y2m1l (_Float128 x, _Float128 y) { - long double vals[5]; + _Float128 vals[5]; SET_RESTORE_ROUNDL (FE_TONEAREST); - mul_split (&vals[1], &vals[0], x, x); - mul_split (&vals[3], &vals[2], y, y); - vals[4] = -1.0L; - qsort (vals, 5, sizeof (long double), compare); + mul_splitl (&vals[1], &vals[0], x, x); + mul_splitl (&vals[3], &vals[2], y, y); + vals[4] = -1; + qsort (vals, 5, sizeof (_Float128), compare); /* Add up the values so that each element of VALS has absolute value at most equal to the last set bit of the next nonzero element. */ for (size_t i = 0; i <= 3; i++) { add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]); - qsort (vals + i + 1, 4 - i, sizeof (long double), compare); + qsort (vals + i + 1, 4 - i, sizeof (_Float128), compare); } /* Now any error from this addition will be small. */ return vals[4] + vals[3] + vals[2] + vals[1] + vals[0]; |