diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm')
100 files changed, 5713 insertions, 471 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/Makefile b/sysdeps/ieee754/ldbl-128ibm/Makefile index 5591814824..bdba6cc6b5 100644 --- a/sysdeps/ieee754/ldbl-128ibm/Makefile +++ b/sysdeps/ieee754/ldbl-128ibm/Makefile @@ -8,3 +8,9 @@ ifeq ($(subdir),stdlib) tests += tst-strtold-ldbl-128ibm $(objpfx)tst-strtold-ldbl-128ibm: $(libm) endif + +ifeq ($(subdir),math) +tests += test-fmodl-ldbl-128ibm test-remainderl-ldbl-128ibm \ + test-remquol-ldbl-128ibm test-canonical-ldbl-128ibm \ + test-totalorderl-ldbl-128ibm +endif diff --git a/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h b/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h new file mode 100644 index 0000000000..60c54cca46 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h @@ -0,0 +1,58 @@ +/* Define iscanonical macro. ldbl-128ibm 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/>. */ + +#ifndef _MATH_H +# error "Never use <bits/iscanonical.h> directly; include <math.h> instead." +#endif + +#ifdef __NO_LONG_DOUBLE_MATH +# define iscanonical(x) ((void) (__typeof (x)) (x), 1) +#else +extern int __iscanonicall (long double __x) + __THROW __attribute__ ((__const__)); +# define __iscanonicalf(x) ((void) (__typeof (x)) (x), 1) +# define __iscanonical(x) ((void) (__typeof (x)) (x), 1) +# if __HAVE_DISTINCT_FLOAT128 +# define __iscanonicalf128(x) ((void) (__typeof (x)) (x), 1) +# endif + +/* Return nonzero value if X is canonical. In IEEE interchange binary + formats, all values are canonical, but the argument must still be + converted to its semantic type for any exceptions arising from the + conversion, before being discarded; in IBM long double, there are + encodings that are not consistently handled as corresponding to any + particular value of the type, and we return 0 for those. */ +# ifndef __cplusplus +# define iscanonical(x) __MATH_TG ((x), __iscanonical, (x)) +# else +/* In C++ mode, __MATH_TG cannot be used, because it relies on + __builtin_types_compatible_p, which is a C-only builtin. On the + other hand, overloading provides the means to distinguish between + the floating-point types. The overloading resolution will match + the correct parameter (regardless of type qualifiers (i.e.: const + and volatile)). */ +extern "C++" { +inline int iscanonical (float __val) { return __iscanonicalf (__val); } +inline int iscanonical (double __val) { return __iscanonical (__val); } +inline int iscanonical (long double __val) { return __iscanonicall (__val); } +# if __HAVE_DISTINCT_FLOAT128 +inline int iscanonical (_Float128 __val) { return __iscanonicalf128 (__val); } +# endif +} +# endif /* __cplusplus */ +#endif /* __NO_LONG_DOUBLE_MATH */ diff --git a/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c b/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c index cab1da9995..f85fe678ba 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_acoshl.c @@ -53,10 +53,10 @@ __ieee754_acoshl(long double x) return 0.0; /* acosh(1) = 0 */ } else if (hx > 0x4000000000000000LL) { /* 2**56 > x > 2 */ t=x*x; - return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one))); + return __ieee754_logl(2.0*x-one/(x+sqrtl(t-one))); } else { /* 1<x<2 */ t = x-one; - return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t)); + return __log1pl(t+sqrtl(2.0*t+t*t)); } } strong_alias (__ieee754_acoshl, __acoshl_finite) diff --git a/sysdeps/ieee754/ldbl-128ibm/e_acosl.c b/sysdeps/ieee754/ldbl-128ibm/e_acosl.c index 5974ee1338..1f8e405c9b 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_acosl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_acosl.c @@ -51,7 +51,7 @@ * 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> @@ -268,7 +268,7 @@ __ieee754_acosl (long double x) double shi, slo; z = (one - a) * 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-128ibm/e_asinl.c b/sysdeps/ieee754/ldbl-128ibm/e_asinl.c index 6ed5e8d68d..e8b0221a92 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_asinl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_asinl.c @@ -61,8 +61,9 @@ #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, @@ -226,7 +227,7 @@ __ieee754_asinl (long double x) return x + x * w; } - s = __ieee754_sqrtl (t); + s = sqrtl (t); if (a > 0.975L) { w = p / q; diff --git a/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c b/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c index b576f42030..25c286b8ff 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_atanhl.c @@ -31,6 +31,7 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> static const long double one = 1.0L, huge = 1e300L; diff --git a/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c b/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c index 5699b8e53d..b4c17856b2 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_exp10l.c +++ b/sysdeps/ieee754/ldbl-128ibm/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 diff --git a/sysdeps/ieee754/ldbl-128ibm/e_expl.c b/sysdeps/ieee754/ldbl-128ibm/e_expl.c index ca3cbb53af..16d4205465 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_expl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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 @@ -65,7 +65,9 @@ #include <fenv.h> #include <inttypes.h> #include <math_private.h> -#include <sysdeps/ieee754/ldbl-128/t_expl.h> + + +#include "t_expl.h" static const long double C[] = { /* Smallest integer x for which e^x overflows. */ diff --git a/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c b/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c index 205097d38f..fae7dbe888 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_fmodl.c @@ -55,6 +55,13 @@ __ieee754_fmodl (long double x, long double y) return x; /* At this point the absolute value of the high doubles of x and y must be equal. */ + if ((lx & 0x7fffffffffffffffLL) == 0 + && (ly & 0x7fffffffffffffffLL) == 0) + /* Both low parts are zero. The result should be an + appropriately signed zero, but the subsequent logic + could treat them as unequal, depending on the signs + of the low parts. */ + return Zero[(uint64_t) sx >> 63]; /* If the low double of y is the same sign as the high double of y (ie. the low double increases |y|)... */ if (((ly ^ sy) & 0x8000000000000000LL) == 0 @@ -112,7 +119,7 @@ __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; } } @@ -121,7 +128,7 @@ __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; @@ -130,15 +137,11 @@ __ieee754_fmodl (long double x, long double y) x = ldbl_insert_mantissa((sx>>63), iy, hx, lx); } else { /* subnormal output */ n = -1022 - iy; - if(n<=48) { - lx = (lx>>n)|((u_int64_t)hx<<(64-n)); - hx >>= n; - } else if (n<=63) { - lx = (hx<<(64-n))|(lx>>n); hx = sx; - } else { - lx = hx>>(n-64); hx = sx; - } - x = ldbl_insert_mantissa((sx>>63), iy, hx, lx); + /* We know 1 <= N <= 52, and that there are no nonzero + bits in places below 2^-1074. */ + lx = (lx >> n) | ((uint64_t) hx << (64 - n)); + hx >>= n; + x = ldbl_insert_mantissa((sx>>63), -1023, hx, lx); x *= one; /* create necessary signal */ } return x; /* exact output */ diff --git a/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c b/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c index 8dbb131f93..84ea7ee0f5 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c +++ b/sysdeps/ieee754/ldbl-128ibm/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. @@ -20,6 +20,7 @@ #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 @@ -106,7 +107,7 @@ gammal_positive (long double x, int *exp2_adj) 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) + * sqrtl (2 * M_PIl / x_adj) / prod); exp_adj += x_eps * __ieee754_logl (x_adj); long double bsum = gamma_coeff[NCOEFF - 1]; @@ -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 < 0xfff0000000000000ULL && __rintl (x) == x) + if (hx < 0 && (uint64_t) hx < 0xfff0000000000000ULL && __rintl (x) == x) { /* Return value for integer x < 0 is NaN with invalid exception. */ *signgamp = 0; diff --git a/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c b/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c index c68dac03b0..842f77b7ed 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_hypotl.c @@ -44,6 +44,7 @@ #include <math.h> #include <math_private.h> +#include <math-underflow.h> long double __ieee754_hypotl(long double x, long double y) @@ -67,6 +68,8 @@ __ieee754_hypotl(long double x, long double y) if(ha > 0x5f30000000000000LL) { /* a>2**500 */ if(ha >= 0x7ff0000000000000LL) { /* Inf or NaN */ w = a+b; /* for sNaN */ + if (issignaling (a) || issignaling (b)) + return w; if(ha == 0x7ff0000000000000LL) w = a; if(hb == 0x7ff0000000000000LL) @@ -105,7 +108,7 @@ __ieee754_hypotl(long double x, long double y) = a1*(a1+a2) + a2*a + b*b = a1*a1 + a1*a2 + a2*a + b*b = a1*a1 + a2*(a+a1) + b*b */ - w = __ieee754_sqrtl(a1*a1-(b*(-b)-a2*(a+a1))); + w = sqrtl(a1*a1-(b*(-b)-a2*(a+a1))); } else { a = a+a; ldbl_unpack (b, &hi, &lo); @@ -122,7 +125,7 @@ __ieee754_hypotl(long double x, long double y) = w*w + a1*b + a2*b = w*w + a1*(b1+b2) + a2*b = w*w + a1*b1 + a1*b2 + a2*b */ - w = __ieee754_sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b))); + w = sqrtl(a1*b1-(w*(-w)-(a1*b2+a2*b))); } if(k!=0) { diff --git a/sysdeps/ieee754/ldbl-128ibm/e_j0l.c b/sysdeps/ieee754/ldbl-128ibm/e_j0l.c index 39a238aa9b..448cfb63fe 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_j0l.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_j0l.c @@ -1,3 +1,864 @@ -/* Looks like we can use ieee854 e_j0l.c as is for IBM extended format. */ -#include <sysdeps/ieee754/ldbl-128/e_j0l.c> +/* Bessel function of order zero. IBM Extended Precision version. + Copyright 2001 by Stephen L. Moshier (moshier@na-net.ornl.gov). + This 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. + + This 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 this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This file was copied from sysdeps/ieee754/ldbl-128/e_j0l.c. */ + + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* 1 / sqrt(pi) */ +static const long double ONEOSQPI = 5.6418958354775628694807945156077258584405E-1L; +/* 2 / pi */ +static const long double TWOOPI = 6.3661977236758134307553505349005744813784E-1L; +static const long double 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J0(x)cosX + Y0(x)sinX = sqrt( 2/(pi x)) P0(x), P0(x) = 1 + 1/x^2 R(1/x^2) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ + }; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0*/ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y0(x)cosX - J0(x)sinX = sqrt( 2/(pi x)) Q0(x), + Q0(x) = 1/x (-.125 + 1/x^2 R(1/x^2)) + 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, +}; +#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, + /* 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) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* 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) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Bessel function of the first kind, order zero. */ + +long double +__ieee754_j0l (long double x) +{ + long double xx, xinv, z, p, q, c, s, cc, ss; + + if (! isfinite (x)) + { + if (x != x) + return x + x; + else + return 0; + } + if (x == 0) + return 1; + + xx = fabsl (x); + if (xx <= 2) + { + if (xx < 0x1p-57L) + 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; + return p; + } + + /* X = x - pi/4 + cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4) + = 1/sqrt(2) * (cos(x) + sin(x)) + sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) + = 1/sqrt(2) * (sin(x) - cos(x)) + sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + cf. Fdlibm. */ + __sincosl (xx, &s, &c); + ss = s - c; + cc = s + c; + if (xx <= LDBL_MAX / 2) + { + z = -__cosl (xx + xx); + if ((s * c) < 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > 0x1p256L) + return ONEOSQPI * cc / sqrtl (xx); + + xinv = 1 / xx; + z = xinv * xinv; + if (xinv <= 0.25) + { + if (xinv <= 0.125) + { + if (xinv <= 0.0625) + { + p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID); + q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID); + } + else + { + p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D); + q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D); + } + } + else if (xinv <= 0.1875) + { + p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D); + q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D); + } + else + { + p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D); + q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D); + } + } /* .25 */ + else /* if (xinv <= 0.5) */ + { + if (xinv <= 0.375) + { + if (xinv <= 0.3125) + { + p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D); + q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D); + } + else + { + p = neval (z, P2r7_3r2N, NP2r7_3r2N) + / deval (z, P2r7_3r2D, NP2r7_3r2D); + q = neval (z, Q2r7_3r2N, NQ2r7_3r2N) + / deval (z, Q2r7_3r2D, NQ2r7_3r2D); + } + } + else if (xinv <= 0.4375) + { + p = neval (z, P2r3_2r7N, NP2r3_2r7N) + / deval (z, P2r3_2r7D, NP2r3_2r7D); + q = neval (z, Q2r3_2r7N, NQ2r3_2r7N) + / deval (z, Q2r3_2r7D, NQ2r3_2r7D); + } + else + { + p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D); + q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); + } + } + p = 1 + z * p; + q = z * xinv * q; + q = q - 0.125L * xinv; + z = ONEOSQPI * (p * cc - q * ss) / sqrtl (xx); + return z; +} +strong_alias (__ieee754_j0l, __j0l_finite) + + +/* Y0(x) = 2/pi * log(x) * J0(x) + R(x^2) + Peak absolute error 1.7e-36 (relative where Y0 > 1) + 0 <= x <= 2 */ +#define NY0_2N 7 +static const long double Y0_2N[NY0_2N + 1] = { + -1.062023609591350692692296993537002558155E19L, + 2.542000883190248639104127452714966858866E19L, + -1.984190771278515324281415820316054696545E18L, + 4.982586044371592942465373274440222033891E16L, + -5.529326354780295177243773419090123407550E14L, + 3.013431465522152289279088265336861140391E12L, + -7.959436160727126750732203098982718347785E9L, + 8.230845651379566339707130644134372793322E6L, +}; +#define NY0_2D 7 +static const long double Y0_2D[NY0_2D + 1] = { + 1.438972634353286978700329883122253752192E20L, + 1.856409101981569254247700169486907405500E18L, + 1.219693352678218589553725579802986255614E16L, + 5.389428943282838648918475915779958097958E13L, + 1.774125762108874864433872173544743051653E11L, + 4.522104832545149534808218252434693007036E8L, + 8.872187401232943927082914504125234454930E5L, + 1.251945613186787532055610876304669413955E3L, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +static const long double U0 = -7.3804295108687225274343927948483016310862e-02L; + +/* Bessel function of the second kind, order zero. */ + +long double + __ieee754_y0l(long double x) +{ + long double xx, xinv, z, p, q, c, s, cc, ss; + + if (! isfinite (x)) + return 1 / (x + x * x); + if (x <= 0) + { + if (x < 0) + return (zero / (zero * 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) + { + /* 0 <= x <= 2 */ + z = xx * xx; + p = neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D); + p = TWOOPI * __ieee754_logl (x) * __ieee754_j0l (x) + p; + return p; + } + + /* X = x - pi/4 + cos(X) = cos(x) cos(pi/4) + sin(x) sin(pi/4) + = 1/sqrt(2) * (cos(x) + sin(x)) + sin(X) = sin(x) cos(pi/4) - cos(x) sin(pi/4) + = 1/sqrt(2) * (sin(x) - cos(x)) + sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + cf. Fdlibm. */ + __sincosl (x, &s, &c); + ss = s - c; + cc = s + c; + if (xx <= LDBL_MAX / 2) + { + z = -__cosl (x + x); + if ((s * c) < 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > 0x1p256L) + return ONEOSQPI * ss / sqrtl (x); + + xinv = 1 / xx; + z = xinv * xinv; + if (xinv <= 0.25) + { + if (xinv <= 0.125) + { + if (xinv <= 0.0625) + { + p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID); + q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID); + } + else + { + p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D); + q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D); + } + } + else if (xinv <= 0.1875) + { + p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D); + q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D); + } + else + { + p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D); + q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D); + } + } /* .25 */ + else /* if (xinv <= 0.5) */ + { + if (xinv <= 0.375) + { + if (xinv <= 0.3125) + { + p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D); + q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D); + } + else + { + p = neval (z, P2r7_3r2N, NP2r7_3r2N) + / deval (z, P2r7_3r2D, NP2r7_3r2D); + q = neval (z, Q2r7_3r2N, NQ2r7_3r2N) + / deval (z, Q2r7_3r2D, NQ2r7_3r2D); + } + } + else if (xinv <= 0.4375) + { + p = neval (z, P2r3_2r7N, NP2r3_2r7N) + / deval (z, P2r3_2r7D, NP2r3_2r7D); + q = neval (z, Q2r3_2r7N, NQ2r3_2r7N) + / deval (z, Q2r3_2r7D, NQ2r3_2r7D); + } + else + { + p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D); + q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); + } + } + p = 1 + z * p; + q = z * xinv * q; + q = q - 0.125L * xinv; + z = ONEOSQPI * (p * ss + q * cc) / sqrtl (x); + return z; +} +strong_alias (__ieee754_y0l, __y0l_finite) diff --git a/sysdeps/ieee754/ldbl-128ibm/e_j1l.c b/sysdeps/ieee754/ldbl-128ibm/e_j1l.c index c86e24f7c0..5126900f96 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_j1l.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_j1l.c @@ -1,2 +1,885 @@ -/* Looks like we can use ieee854 e_j1l.c as is for IBM extended format. */ -#include <sysdeps/ieee754/ldbl-128/e_j1l.c> +/* Bessel function of order one. IBM Extended Precision version. + Copyright 2001 by Stephen L. Moshier (moshier@na-net.onrl.gov). + + This 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. + + This 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 this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This file was copied from sysdeps/ieee754/ldbl-128/e_j0l.c. */ + + +#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; +/* 2 / pi */ +static const long double TWOOPI = 6.3661977236758134307553505349005744813784E-1L; +static const long double 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 +}; +#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, + /* 1.000000000000000000000000000000000000000E0L */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 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 +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* J1(x)cosX + Y1(x)sinX = sqrt( 2/(pi x)) P1(x), P1(x) = 1 + 1/x^2 R(1/x^2), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ + }; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + 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, +}; +#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, + /* 1.000000000000000000000000000000000000000E0 */ +}; + +/* Y1(x)cosX - J1(x)sinX = sqrt( 2/(pi x)) Q1(x), + Q1(x) = 1/x (.375 + 1/x^2 R(1/x^2)), + 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, +}; +#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, + /* 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) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* 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) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* Bessel function of the first kind, order one. */ + +long double +__ieee754_j1l (long double x) +{ + long double xx, xinv, z, p, q, c, s, cc, ss; + + if (! isfinite (x)) + { + if (x != x) + return x + x; + else + return 0; + } + if (x == 0) + return x; + xx = fabsl (x); + if (xx <= 0x1p-58L) + { + long double ret = x * 0.5L; + math_check_force_underflow (ret); + if (ret == 0) + __set_errno (ERANGE); + return ret; + } + 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; + if (x < 0) + p = -p; + return p; + } + + /* X = x - 3 pi/4 + cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4) + = 1/sqrt(2) * (-cos(x) + sin(x)) + sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4) + = -1/sqrt(2) * (sin(x) + cos(x)) + cf. Fdlibm. */ + __sincosl (xx, &s, &c); + ss = -s - c; + cc = s - c; + if (xx <= LDBL_MAX / 2) + { + z = __cosl (xx + xx); + if ((s * c) > 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > 0x1p256L) + { + z = ONEOSQPI * cc / sqrtl (xx); + if (x < 0) + z = -z; + return z; + } + + xinv = 1 / xx; + z = xinv * xinv; + if (xinv <= 0.25) + { + if (xinv <= 0.125) + { + if (xinv <= 0.0625) + { + p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID); + q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID); + } + else + { + p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D); + q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D); + } + } + else if (xinv <= 0.1875) + { + p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D); + q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D); + } + else + { + p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D); + q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D); + } + } /* .25 */ + else /* if (xinv <= 0.5) */ + { + if (xinv <= 0.375) + { + if (xinv <= 0.3125) + { + p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D); + q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D); + } + else + { + p = neval (z, P2r7_3r2N, NP2r7_3r2N) + / deval (z, P2r7_3r2D, NP2r7_3r2D); + q = neval (z, Q2r7_3r2N, NQ2r7_3r2N) + / deval (z, Q2r7_3r2D, NQ2r7_3r2D); + } + } + else if (xinv <= 0.4375) + { + p = neval (z, P2r3_2r7N, NP2r3_2r7N) + / deval (z, P2r3_2r7D, NP2r3_2r7D); + q = neval (z, Q2r3_2r7N, NQ2r3_2r7N) + / deval (z, Q2r3_2r7D, NQ2r3_2r7D); + } + else + { + p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D); + q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); + } + } + p = 1 + z * p; + q = z * q; + q = q * xinv + 0.375L * xinv; + z = ONEOSQPI * (p * cc - q * ss) / sqrtl (xx); + if (x < 0) + z = -z; + return z; +} +strong_alias (__ieee754_j1l, __j1l_finite) + + +/* Y1(x) = 2/pi * (log(x) * J1(x) - 1/x) + x R(x^2) + Peak relative error 6.2e-38 + 0 <= x <= 2 */ +#define NY0_2N 7 +static const long double Y0_2N[NY0_2N + 1] = { + -6.804415404830253804408698161694720833249E19L, + 1.805450517967019908027153056150465849237E19L, + -8.065747497063694098810419456383006737312E17L, + 1.401336667383028259295830955439028236299E16L, + -1.171654432898137585000399489686629680230E14L, + 5.061267920943853732895341125243428129150E11L, + -1.096677850566094204586208610960870217970E9L, + 9.541172044989995856117187515882879304461E5L, +}; +#define NY0_2D 7 +static const long double Y0_2D[NY0_2D + 1] = { + 3.470629591820267059538637461549677594549E20L, + 4.120796439009916326855848107545425217219E18L, + 2.477653371652018249749350657387030814542E16L, + 9.954678543353888958177169349272167762797E13L, + 2.957927997613630118216218290262851197754E11L, + 6.748421382188864486018861197614025972118E8L, + 1.173453425218010888004562071020305709319E6L, + 1.450335662961034949894009554536003377187E3L, + /* 1.000000000000000000000000000000000000000E0 */ +}; + + +/* Bessel function of the second kind, order one. */ + +long double +__ieee754_y1l (long double x) +{ + long double xx, xinv, z, p, q, c, s, cc, ss; + + if (! isfinite (x)) + return 1 / (x + x * x); + if (x <= 0) + { + if (x < 0) + return (zero / (zero * x)); + return -1 / zero; /* -inf and divide by zero exception. */ + } + xx = fabsl (x); + if (xx <= 0x1p-114) + { + z = -TWOOPI / x; + if (isinf (z)) + __set_errno (ERANGE); + return z; + } + if (xx <= 2) + { + /* 0 <= x <= 2 */ + SET_RESTORE_ROUNDL (FE_TONEAREST); + z = xx * xx; + p = xx * neval (z, Y0_2N, NY0_2N) / deval (z, Y0_2D, NY0_2D); + p = -TWOOPI / xx + p; + p = TWOOPI * __ieee754_logl (x) * __ieee754_j1l (x) + p; + return p; + } + + /* X = x - 3 pi/4 + cos(X) = cos(x) cos(3 pi/4) + sin(x) sin(3 pi/4) + = 1/sqrt(2) * (-cos(x) + sin(x)) + sin(X) = sin(x) cos(3 pi/4) - cos(x) sin(3 pi/4) + = -1/sqrt(2) * (sin(x) + cos(x)) + cf. Fdlibm. */ + __sincosl (xx, &s, &c); + ss = -s - c; + cc = s - c; + if (xx <= LDBL_MAX / 2) + { + z = __cosl (xx + xx); + if ((s * c) > 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > 0x1p256L) + return ONEOSQPI * ss / sqrtl (xx); + + xinv = 1 / xx; + z = xinv * xinv; + if (xinv <= 0.25) + { + if (xinv <= 0.125) + { + if (xinv <= 0.0625) + { + p = neval (z, P16_IN, NP16_IN) / deval (z, P16_ID, NP16_ID); + q = neval (z, Q16_IN, NQ16_IN) / deval (z, Q16_ID, NQ16_ID); + } + else + { + p = neval (z, P8_16N, NP8_16N) / deval (z, P8_16D, NP8_16D); + q = neval (z, Q8_16N, NQ8_16N) / deval (z, Q8_16D, NQ8_16D); + } + } + else if (xinv <= 0.1875) + { + p = neval (z, P5_8N, NP5_8N) / deval (z, P5_8D, NP5_8D); + q = neval (z, Q5_8N, NQ5_8N) / deval (z, Q5_8D, NQ5_8D); + } + else + { + p = neval (z, P4_5N, NP4_5N) / deval (z, P4_5D, NP4_5D); + q = neval (z, Q4_5N, NQ4_5N) / deval (z, Q4_5D, NQ4_5D); + } + } /* .25 */ + else /* if (xinv <= 0.5) */ + { + if (xinv <= 0.375) + { + if (xinv <= 0.3125) + { + p = neval (z, P3r2_4N, NP3r2_4N) / deval (z, P3r2_4D, NP3r2_4D); + q = neval (z, Q3r2_4N, NQ3r2_4N) / deval (z, Q3r2_4D, NQ3r2_4D); + } + else + { + p = neval (z, P2r7_3r2N, NP2r7_3r2N) + / deval (z, P2r7_3r2D, NP2r7_3r2D); + q = neval (z, Q2r7_3r2N, NQ2r7_3r2N) + / deval (z, Q2r7_3r2D, NQ2r7_3r2D); + } + } + else if (xinv <= 0.4375) + { + p = neval (z, P2r3_2r7N, NP2r3_2r7N) + / deval (z, P2r3_2r7D, NP2r3_2r7D); + q = neval (z, Q2r3_2r7N, NQ2r3_2r7N) + / deval (z, Q2r3_2r7D, NQ2r3_2r7D); + } + else + { + p = neval (z, P2_2r3N, NP2_2r3N) / deval (z, P2_2r3D, NP2_2r3D); + q = neval (z, Q2_2r3N, NQ2_2r3N) / deval (z, Q2_2r3D, NQ2_2r3D); + } + } + p = 1 + z * p; + q = z * q; + q = q * xinv + 0.375L * xinv; + z = ONEOSQPI * (p * ss + q * cc) / sqrtl (xx); + return z; +} +strong_alias (__ieee754_y1l, __y1l_finite) diff --git a/sysdeps/ieee754/ldbl-128ibm/e_jnl.c b/sysdeps/ieee754/ldbl-128ibm/e_jnl.c index 4a8ccb044e..71b3addfba 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_jnl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_jnl.c @@ -60,6 +60,7 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> static const long double invsqrtpi = 5.6418958354775628694807945156077258584405E-1L, @@ -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 { @@ -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 { diff --git a/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c b/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c index 9bcaaf765a..5b628bedc1 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c @@ -1,3 +1,992 @@ -/* Looks like we can use ieee854 e_lgammal_r.c as is for IBM extended format. */ -#include <sysdeps/ieee754/ldbl-128/e_lgammal_r.c> +/* Natural logarithm of gamma function. IBM Extended Precision version. + Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> + This 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. + + This 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 this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This file was copied from sysdeps/ieee754/ldbl-128/e_lgammal_r.c. */ + + +#include <math.h> +#include <math_private.h> +#include <float.h> + +static const long double PIL = 3.1415926535897932384626433832795028841972E0L; +static const long double MAXLGM = 0x5.d53649e2d469dbc1f01e99fd66p+1012L; +static const long double one = 1; +static const long double 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; +#define NRASY 12 +static const long double 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 +}; + + +/* log gamma(x+13) = log gamma(13) + x P(x)/Q(x) + -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; +#define NRN13 7 +static const long double RN13[NRN13 + 1] = +{ + 8.591478354823578150238226576156275285700E11L, + 2.347931159756482741018258864137297157668E11L, + 2.555408396679352028680662433943000804616E10L, + 1.408581709264464345480765758902967123937E9L, + 4.126759849752613822953004114044451046321E7L, + 6.133298899622688505854211579222889943778E5L, + 3.929248056293651597987893340755876578072E3L, + 6.850783280018706668924952057996075215223E0L +}; +#define NRD13 6 +static const long double RD13[NRD13 + 1] = +{ + 3.401225382297342302296607039352935541669E11L, + 8.756765276918037910363513243563234551784E10L, + 8.873913342866613213078554180987647243903E9L, + 4.483797255342763263361893016049310017973E8L, + 1.178186288833066430952276702931512870676E7L, + 1.519928623743264797939103740132278337476E5L, + 7.989298844938119228411117593338850892311E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+12) = log gamma(12) + x P(x)/Q(x) + -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; +#define NRN12 7 +static const long double RN12[NRN12 + 1] = +{ + 4.709859662695606986110997348630997559137E11L, + 1.398713878079497115037857470168777995230E11L, + 1.654654931821564315970930093932954900867E10L, + 9.916279414876676861193649489207282144036E8L, + 3.159604070526036074112008954113411389879E7L, + 5.109099197547205212294747623977502492861E5L, + 3.563054878276102790183396740969279826988E3L, + 6.769610657004672719224614163196946862747E0L +}; +#define NRD12 6 +static const long double RD12[NRD12 + 1] = +{ + 1.928167007860968063912467318985802726613E11L, + 5.383198282277806237247492369072266389233E10L, + 5.915693215338294477444809323037871058363E9L, + 3.241438287570196713148310560147925781342E8L, + 9.236680081763754597872713592701048455890E6L, + 1.292246897881650919242713651166596478850E5L, + 7.366532445427159272584194816076600211171E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+11) = log gamma(11) + x P(x)/Q(x) + -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; +#define NRN11 7 +static const long double RN11[NRN11 + 1] = +{ + 2.446960438029415837384622675816736622795E11L, + 7.955444974446413315803799763901729640350E10L, + 1.030555327949159293591618473447420338444E10L, + 6.765022131195302709153994345470493334946E8L, + 2.361892792609204855279723576041468347494E7L, + 4.186623629779479136428005806072176490125E5L, + 3.202506022088912768601325534149383594049E3L, + 6.681356101133728289358838690666225691363E0L +}; +#define NRD11 6 +static const long double RD11[NRD11 + 1] = +{ + 1.040483786179428590683912396379079477432E11L, + 3.172251138489229497223696648369823779729E10L, + 3.806961885984850433709295832245848084614E9L, + 2.278070344022934913730015420611609620171E8L, + 7.089478198662651683977290023829391596481E6L, + 1.083246385105903533237139380509590158658E5L, + 6.744420991491385145885727942219463243597E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+10) = log gamma(10) + x P(x)/Q(x) + -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; +#define NRN10 7 +static const long double RN10[NRN10 + 1] = +{ + -1.239059737177249934158597996648808363783E14L, + -4.725899566371458992365624673357356908719E13L, + -7.283906268647083312042059082837754850808E12L, + -5.802855515464011422171165179767478794637E11L, + -2.532349691157548788382820303182745897298E10L, + -5.884260178023777312587193693477072061820E8L, + -6.437774864512125749845840472131829114906E6L, + -2.350975266781548931856017239843273049384E4L +}; +#define NRD10 7 +static const long double RD10[NRD10 + 1] = +{ + -5.502645997581822567468347817182347679552E13L, + -1.970266640239849804162284805400136473801E13L, + -2.819677689615038489384974042561531409392E12L, + -2.056105863694742752589691183194061265094E11L, + -8.053670086493258693186307810815819662078E9L, + -1.632090155573373286153427982504851867131E8L, + -1.483575879240631280658077826889223634921E6L, + -4.002806669713232271615885826373550502510E3L + /* 1.0E0L */ +}; + + +/* log gamma(x+9) = log gamma(9) + x P(x)/Q(x) + -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; +#define NRN9 7 +static const long double RN9[NRN9 + 1] = +{ + -4.936332264202687973364500998984608306189E13L, + -2.101372682623700967335206138517766274855E13L, + -3.615893404644823888655732817505129444195E12L, + -3.217104993800878891194322691860075472926E11L, + -1.568465330337375725685439173603032921399E10L, + -4.073317518162025744377629219101510217761E8L, + -4.983232096406156139324846656819246974500E6L, + -2.036280038903695980912289722995505277253E4L +}; +#define NRD9 7 +static const long double RD9[NRD9 + 1] = +{ + -2.306006080437656357167128541231915480393E13L, + -9.183606842453274924895648863832233799950E12L, + -1.461857965935942962087907301194381010380E12L, + -1.185728254682789754150068652663124298303E11L, + -5.166285094703468567389566085480783070037E9L, + -1.164573656694603024184768200787835094317E8L, + -1.177343939483908678474886454113163527909E6L, + -3.529391059783109732159524500029157638736E3L + /* 1.0E0L */ +}; + + +/* log gamma(x+8) = log gamma(8) + x P(x)/Q(x) + -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; +#define NRN8 8 +static const long double RN8[NRN8 + 1] = +{ + 6.600775438203423546565361176829139703289E11L, + 3.406361267593790705240802723914281025800E11L, + 7.222460928505293914746983300555538432830E10L, + 8.102984106025088123058747466840656458342E9L, + 5.157620015986282905232150979772409345927E8L, + 1.851445288272645829028129389609068641517E7L, + 3.489261702223124354745894067468953756656E5L, + 2.892095396706665774434217489775617756014E3L, + 6.596977510622195827183948478627058738034E0L +}; +#define NRD8 7 +static const long double RD8[NRD8 + 1] = +{ + 3.274776546520735414638114828622673016920E11L, + 1.581811207929065544043963828487733970107E11L, + 3.108725655667825188135393076860104546416E10L, + 3.193055010502912617128480163681842165730E9L, + 1.830871482669835106357529710116211541839E8L, + 5.790862854275238129848491555068073485086E6L, + 9.305213264307921522842678835618803553589E4L, + 6.216974105861848386918949336819572333622E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+7) = log gamma(7) + x P(x)/Q(x) + -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; +#define NRN7 8 +static const long double RN7[NRN7 + 1] = +{ + 2.065019306969459407636744543358209942213E11L, + 1.226919919023736909889724951708796532847E11L, + 2.996157990374348596472241776917953749106E10L, + 3.873001919306801037344727168434909521030E9L, + 2.841575255593761593270885753992732145094E8L, + 1.176342515359431913664715324652399565551E7L, + 2.558097039684188723597519300356028511547E5L, + 2.448525238332609439023786244782810774702E3L, + 6.460280377802030953041566617300902020435E0L +}; +#define NRD7 7 +static const long double RD7[NRD7 + 1] = +{ + 1.102646614598516998880874785339049304483E11L, + 6.099297512712715445879759589407189290040E10L, + 1.372898136289611312713283201112060238351E10L, + 1.615306270420293159907951633566635172343E9L, + 1.061114435798489135996614242842561967459E8L, + 3.845638971184305248268608902030718674691E6L, + 7.081730675423444975703917836972720495507E4L, + 5.423122582741398226693137276201344096370E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+6) = log gamma(6) + x P(x)/Q(x) + -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; +#define NRN6 8 +static const long double RN6[NRN6 + 1] = +{ + -3.538412754670746879119162116819571823643E13L, + -2.613432593406849155765698121483394257148E13L, + -8.020670732770461579558867891923784753062E12L, + -1.322227822931250045347591780332435433420E12L, + -1.262809382777272476572558806855377129513E11L, + -7.015006277027660872284922325741197022467E9L, + -2.149320689089020841076532186783055727299E8L, + -3.167210585700002703820077565539658995316E6L, + -1.576834867378554185210279285358586385266E4L +}; +#define NRD6 8 +static const long double RD6[NRD6 + 1] = +{ + -2.073955870771283609792355579558899389085E13L, + -1.421592856111673959642750863283919318175E13L, + -4.012134994918353924219048850264207074949E12L, + -6.013361045800992316498238470888523722431E11L, + -5.145382510136622274784240527039643430628E10L, + -2.510575820013409711678540476918249524123E9L, + -6.564058379709759600836745035871373240904E7L, + -7.861511116647120540275354855221373571536E5L, + -2.821943442729620524365661338459579270561E3L + /* 1.0E0L */ +}; + + +/* log gamma(x+5) = log gamma(5) + x P(x)/Q(x) + -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; +#define NRN5 9 +static const long double RN5[NRN5 + 1] = +{ + 2.010952885441805899580403215533972172098E11L, + 1.916132681242540921354921906708215338584E11L, + 7.679102403710581712903937970163206882492E10L, + 1.680514903671382470108010973615268125169E10L, + 2.181011222911537259440775283277711588410E9L, + 1.705361119398837808244780667539728356096E8L, + 7.792391565652481864976147945997033946360E6L, + 1.910741381027985291688667214472560023819E5L, + 2.088138241893612679762260077783794329559E3L, + 6.330318119566998299106803922739066556550E0L +}; +#define NRD5 8 +static const long double RD5[NRD5 + 1] = +{ + 1.335189758138651840605141370223112376176E11L, + 1.174130445739492885895466097516530211283E11L, + 4.308006619274572338118732154886328519910E10L, + 8.547402888692578655814445003283720677468E9L, + 9.934628078575618309542580800421370730906E8L, + 6.847107420092173812998096295422311820672E7L, + 2.698552646016599923609773122139463150403E6L, + 5.526516251532464176412113632726150253215E4L, + 4.772343321713697385780533022595450486932E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+4) = log gamma(4) + x P(x)/Q(x) + -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; +#define NRN4 9 +static const long double RN4[NRN4 + 1] = +{ + -1.026583408246155508572442242188887829208E13L, + -1.306476685384622809290193031208776258809E13L, + -7.051088602207062164232806511992978915508E12L, + -2.100849457735620004967624442027793656108E12L, + -3.767473790774546963588549871673843260569E11L, + -4.156387497364909963498394522336575984206E10L, + -2.764021460668011732047778992419118757746E9L, + -1.036617204107109779944986471142938641399E8L, + -1.895730886640349026257780896972598305443E6L, + -1.180509051468390914200720003907727988201E4L +}; +#define NRD4 9 +static const long double RD4[NRD4 + 1] = +{ + -8.172669122056002077809119378047536240889E12L, + -9.477592426087986751343695251801814226960E12L, + -4.629448850139318158743900253637212801682E12L, + -1.237965465892012573255370078308035272942E12L, + -1.971624313506929845158062177061297598956E11L, + -1.905434843346570533229942397763361493610E10L, + -1.089409357680461419743730978512856675984E9L, + -3.416703082301143192939774401370222822430E7L, + -4.981791914177103793218433195857635265295E5L, + -2.192507743896742751483055798411231453733E3L + /* 1.0E0L */ +}; + + +/* log gamma(x+3) = log gamma(3) + x P(x)/Q(x) + -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; + +#define NRN3 9 +static const long double RN3[NRN3 + 1] = +{ + -4.813901815114776281494823863935820876670E11L, + -8.425592975288250400493910291066881992620E11L, + -6.228685507402467503655405482985516909157E11L, + -2.531972054436786351403749276956707260499E11L, + -6.170200796658926701311867484296426831687E10L, + -9.211477458528156048231908798456365081135E9L, + -8.251806236175037114064561038908691305583E8L, + -4.147886355917831049939930101151160447495E7L, + -1.010851868928346082547075956946476932162E6L, + -8.333374463411801009783402800801201603736E3L +}; +#define NRD3 9 +static const long double RD3[NRD3 + 1] = +{ + -5.216713843111675050627304523368029262450E11L, + -8.014292925418308759369583419234079164391E11L, + -5.180106858220030014546267824392678611990E11L, + -1.830406975497439003897734969120997840011E11L, + -3.845274631904879621945745960119924118925E10L, + -4.891033385370523863288908070309417710903E9L, + -3.670172254411328640353855768698287474282E8L, + -1.505316381525727713026364396635522516989E7L, + -2.856327162923716881454613540575964890347E5L, + -1.622140448015769906847567212766206894547E3L + /* 1.0E0L */ +}; + + +/* 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; +#define NRN2r5 8 +static const long double RN2r5[NRN2r5 + 1] = +{ + -4.676454313888335499356699817678862233205E9L, + -9.361888347911187924389905984624216340639E9L, + -7.695353600835685037920815799526540237703E9L, + -3.364370100981509060441853085968900734521E9L, + -8.449902011848163568670361316804900559863E8L, + -1.225249050950801905108001246436783022179E8L, + -9.732972931077110161639900388121650470926E6L, + -3.695711763932153505623248207576425983573E5L, + -4.717341584067827676530426007495274711306E3L +}; +#define NRD2r5 8 +static const long double RD2r5[NRD2r5 + 1] = +{ + -6.650657966618993679456019224416926875619E9L, + -1.099511409330635807899718829033488771623E10L, + -7.482546968307837168164311101447116903148E9L, + -2.702967190056506495988922973755870557217E9L, + -5.570008176482922704972943389590409280950E8L, + -6.536934032192792470926310043166993233231E7L, + -4.101991193844953082400035444146067511725E6L, + -1.174082735875715802334430481065526664020E5L, + -9.932840389994157592102947657277692978511E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+2) = x P(x)/Q(x) + -0.125 <= x <= +0.375 + 1.875 <= x+2 <= 2.375 + Peak relative error 4.6e-36 */ +#define NRN2 9 +static const long double RN2[NRN2 + 1] = +{ + -3.716661929737318153526921358113793421524E9L, + -1.138816715030710406922819131397532331321E10L, + -1.421017419363526524544402598734013569950E10L, + -9.510432842542519665483662502132010331451E9L, + -3.747528562099410197957514973274474767329E9L, + -8.923565763363912474488712255317033616626E8L, + -1.261396653700237624185350402781338231697E8L, + -9.918402520255661797735331317081425749014E6L, + -3.753996255897143855113273724233104768831E5L, + -4.778761333044147141559311805999540765612E3L +}; +#define NRD2 9 +static const long double RD2[NRD2 + 1] = +{ + -8.790916836764308497770359421351673950111E9L, + -2.023108608053212516399197678553737477486E10L, + -1.958067901852022239294231785363504458367E10L, + -1.035515043621003101254252481625188704529E10L, + -3.253884432621336737640841276619272224476E9L, + -6.186383531162456814954947669274235815544E8L, + -6.932557847749518463038934953605969951466E7L, + -4.240731768287359608773351626528479703758E6L, + -1.197343995089189188078944689846348116630E5L, + -1.004622911670588064824904487064114090920E3L +/* 1.0E0 */ +}; + + +/* log gamma(x+1.75) = log gamma(1.75) + x P(x)/Q(x) + -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; +#define NRN1r75 8 +static const long double RN1r75[NRN1r75 + 1] = +{ + -5.221061693929833937710891646275798251513E7L, + -2.052466337474314812817883030472496436993E8L, + -2.952718275974940270675670705084125640069E8L, + -2.132294039648116684922965964126389017840E8L, + -8.554103077186505960591321962207519908489E7L, + -1.940250901348870867323943119132071960050E7L, + -2.379394147112756860769336400290402208435E6L, + -1.384060879999526222029386539622255797389E5L, + -2.698453601378319296159355612094598695530E3L +}; +#define NRD1r75 8 +static const long double RD1r75[NRD1r75 + 1] = +{ + -2.109754689501705828789976311354395393605E8L, + -5.036651829232895725959911504899241062286E8L, + -4.954234699418689764943486770327295098084E8L, + -2.589558042412676610775157783898195339410E8L, + -7.731476117252958268044969614034776883031E7L, + -1.316721702252481296030801191240867486965E7L, + -1.201296501404876774861190604303728810836E6L, + -5.007966406976106636109459072523610273928E4L, + -6.155817990560743422008969155276229018209E2L + /* 1.0E0L */ +}; + + +/* log gamma(x+x0) = y0 + x^2 P(x)/Q(x) + -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; +#define NRN1r5 8 +static const long double RN1r5[NRN1r5 + 1] = +{ + 6.827103657233705798067415468881313128066E5L, + 1.910041815932269464714909706705242148108E6L, + 2.194344176925978377083808566251427771951E6L, + 1.332921400100891472195055269688876427962E6L, + 4.589080973377307211815655093824787123508E5L, + 8.900334161263456942727083580232613796141E4L, + 9.053840838306019753209127312097612455236E3L, + 4.053367147553353374151852319743594873771E2L, + 5.040631576303952022968949605613514584950E0L +}; +#define NRD1r5 8 +static const long double RD1r5[NRD1r5 + 1] = +{ + 1.411036368843183477558773688484699813355E6L, + 4.378121767236251950226362443134306184849E6L, + 5.682322855631723455425929877581697918168E6L, + 3.999065731556977782435009349967042222375E6L, + 1.653651390456781293163585493620758410333E6L, + 4.067774359067489605179546964969435858311E5L, + 5.741463295366557346748361781768833633256E4L, + 4.226404539738182992856094681115746692030E3L, + 1.316980975410327975566999780608618774469E2L, + /* 1.0E0L */ +}; + + +/* log gamma(x+1.25) = log gamma(1.25) + x P(x)/Q(x) + -.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; +#define NRN1r25 9 +static const long double RN1r25[NRN1r25 + 1] = +{ + -9.054787275312026472896002240379580536760E4L, + -8.685076892989927640126560802094680794471E4L, + 2.797898965448019916967849727279076547109E5L, + 6.175520827134342734546868356396008898299E5L, + 5.179626599589134831538516906517372619641E5L, + 2.253076616239043944538380039205558242161E5L, + 5.312653119599957228630544772499197307195E4L, + 6.434329437514083776052669599834938898255E3L, + 3.385414416983114598582554037612347549220E2L, + 4.907821957946273805080625052510832015792E0L +}; +#define NRD1r25 8 +static const long double RD1r25[NRD1r25 + 1] = +{ + 3.980939377333448005389084785896660309000E5L, + 1.429634893085231519692365775184490465542E6L, + 2.145438946455476062850151428438668234336E6L, + 1.743786661358280837020848127465970357893E6L, + 8.316364251289743923178092656080441655273E5L, + 2.355732939106812496699621491135458324294E5L, + 3.822267399625696880571810137601310855419E4L, + 3.228463206479133236028576845538387620856E3L, + 1.152133170470059555646301189220117965514E2L + /* 1.0E0L */ +}; + + +/* log gamma(x + 1) = x P(x)/Q(x) + 0.0 <= x <= +0.125 + 1.0 <= x+1 <= 1.125 + Peak relative error 1.1e-35 */ +#define NRN1 8 +static const long double RN1[NRN1 + 1] = +{ + -9.987560186094800756471055681088744738818E3L, + -2.506039379419574361949680225279376329742E4L, + -1.386770737662176516403363873617457652991E4L, + 1.439445846078103202928677244188837130744E4L, + 2.159612048879650471489449668295139990693E4L, + 1.047439813638144485276023138173676047079E4L, + 2.250316398054332592560412486630769139961E3L, + 1.958510425467720733041971651126443864041E2L, + 4.516830313569454663374271993200291219855E0L +}; +#define NRD1 7 +static const long double RD1[NRD1 + 1] = +{ + 1.730299573175751778863269333703788214547E4L, + 6.807080914851328611903744668028014678148E4L, + 1.090071629101496938655806063184092302439E5L, + 9.124354356415154289343303999616003884080E4L, + 4.262071638655772404431164427024003253954E4L, + 1.096981664067373953673982635805821283581E4L, + 1.431229503796575892151252708527595787588E3L, + 7.734110684303689320830401788262295992921E1L + /* 1.0E0 */ +}; + + +/* log gamma(x + 1) = x P(x)/Q(x) + -0.125 <= x <= 0 + 0.875 <= x+1 <= 1.0 + Peak relative error 7.0e-37 */ +#define NRNr9 8 +static const long double RNr9[NRNr9 + 1] = +{ + 4.441379198241760069548832023257571176884E5L, + 1.273072988367176540909122090089580368732E6L, + 9.732422305818501557502584486510048387724E5L, + -5.040539994443998275271644292272870348684E5L, + -1.208719055525609446357448132109723786736E6L, + -7.434275365370936547146540554419058907156E5L, + -2.075642969983377738209203358199008185741E5L, + -2.565534860781128618589288075109372218042E4L, + -1.032901669542994124131223797515913955938E3L, +}; +#define NRDr9 8 +static const long double RDr9[NRDr9 + 1] = +{ + -7.694488331323118759486182246005193998007E5L, + -3.301918855321234414232308938454112213751E6L, + -5.856830900232338906742924836032279404702E6L, + -5.540672519616151584486240871424021377540E6L, + -3.006530901041386626148342989181721176919E6L, + -9.350378280513062139466966374330795935163E5L, + -1.566179100031063346901755685375732739511E5L, + -1.205016539620260779274902967231510804992E4L, + -2.724583156305709733221564484006088794284E2L +/* 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) +{ + long double y; + + p += n; + y = *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +/* 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) +{ + long double y; + + p += n; + y = x + *p--; + do + { + y = y * x + *p--; + } + while (--n > 0); + return y; +} + + +long double +__ieee754_lgammal_r (long double x, int *signgamp) +{ + long double p, q, w, z, nx; + int i, nn; + + *signgamp = 1; + + if (! isfinite (x)) + return x * x; + + if (x == 0) + { + if (signbit (x)) + *signgamp = -1; + } + + if (x < 0) + { + if (x < -2 && x > -48) + return __lgamma_negl (x, signgamp); + q = -x; + p = __floorl (q); + if (p == q) + return (one / fabsl (p - p)); + long double halfp = p * 0.5L; + if (halfp == __floorl (halfp)) + *signgamp = -1; + else + *signgamp = 1; + if (q < 0x1p-120L) + return -__logl (q); + z = q - p; + if (z > 0.5L) + { + p += 1; + z = p - q; + } + z = q * __sinl (PIL * z); + w = __ieee754_lgammal_r (q, &i); + z = __logl (PIL / z) - w; + return (z); + } + + if (x < 13.5L) + { + p = 0; + nx = __floorl (x + 0.5L); + nn = nx; + switch (nn) + { + case 0: + /* log gamma (x + 1) = log(x) + log gamma(x) */ + if (x < 0x1p-120L) + return -__logl (x); + else if (x <= 0.125) + { + p = x * neval (x, RN1, NRN1) / deval (x, RD1, NRD1); + } + else if (x <= 0.375) + { + z = x - 0.25L; + p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); + p += lgam1r25b; + p += lgam1r25a; + } + else if (x <= 0.625) + { + z = x + (1 - x0a); + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + else if (x <= 0.875) + { + z = x - 0.75L; + p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); + p += lgam1r75b; + p += lgam1r75a; + } + else + { + 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 <= 0.625) + { + z = x + (1 - x0a); + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + else if (x <= 0.875) + { + z = x - 0.75L; + p = z * neval (z, RN1r75, NRN1r75) + / deval (z, RD1r75, NRD1r75); + p += lgam1r75b; + p += lgam1r75a; + } + else + { + z = x - 1; + p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); + } + p = p - __logl (x); + } + else if (x < 1) + { + z = x - 1; + p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9); + } + else if (x == 1) + p = 0; + else if (x <= 1.125L) + { + z = x - 1; + p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1); + } + else if (x <= 1.375) + { + z = x - 1.25L; + p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); + p += lgam1r25b; + p += lgam1r25a; + } + else + { + /* 1.375 <= x+x0 <= 1.625 */ + z = x - x0a; + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + break; + + case 2: + if (x < 1.625L) + { + z = x - x0a; + z = z - x0b; + p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); + p = p * z * z; + p = p + y0b; + p = p + y0a; + } + else if (x < 1.875L) + { + z = x - 1.75L; + p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); + p += lgam1r75b; + p += lgam1r75a; + } + else if (x == 2) + p = 0; + else if (x < 2.375L) + { + z = x - 2; + p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); + } + else + { + z = x - 2.5L; + p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); + p += lgam2r5b; + p += lgam2r5a; + } + break; + + case 3: + if (x < 2.75) + { + z = x - 2.5L; + p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); + p += lgam2r5b; + p += lgam2r5a; + } + else + { + z = x - 3; + p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3); + p += lgam3b; + p += lgam3a; + } + break; + + case 4: + z = x - 4; + p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4); + p += lgam4b; + p += lgam4a; + break; + + case 5: + z = x - 5; + p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5); + p += lgam5b; + p += lgam5a; + break; + + case 6: + z = x - 6; + p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6); + p += lgam6b; + p += lgam6a; + break; + + case 7: + z = x - 7; + p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7); + p += lgam7b; + p += lgam7a; + break; + + case 8: + z = x - 8; + p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8); + p += lgam8b; + p += lgam8a; + break; + + case 9: + z = x - 9; + p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9); + p += lgam9b; + p += lgam9a; + break; + + case 10: + z = x - 10; + p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10); + p += lgam10b; + p += lgam10a; + break; + + case 11: + z = x - 11; + p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11); + p += lgam11b; + p += lgam11a; + break; + + case 12: + z = x - 12; + p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12); + p += lgam12b; + p += lgam12a; + break; + + case 13: + z = x - 13; + p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13); + p += lgam13b; + p += lgam13a; + break; + } + return p; + } + + if (x > MAXLGM) + return (*signgamp * huge * huge); + + if (x > 0x1p120L) + return x * (__logl (x) - 1); + q = ls2pi - x; + q = (x - 0.5L) * __logl (x) + q; + if (x > 1.0e18L) + return (q); + + p = 1 / (x * x); + q += neval (p, RASY, NRASY) / x; + return (q); +} +strong_alias (__ieee754_lgammal_r, __lgammal_r_finite) diff --git a/sysdeps/ieee754/ldbl-128ibm/e_log10l.c b/sysdeps/ieee754/ldbl-128ibm/e_log10l.c index 7477791b77..62e3214ca4 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_log10l.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_log10l.c @@ -189,7 +189,7 @@ __ieee754_log10l (long double x) xhi = ldbl_high (x); EXTRACT_WORDS64 (hx, xhi); if ((hx & 0x7fffffffffffffffLL) == 0) - return (-1.0L / (x - x)); + return (-1.0L / fabsl (x)); /* log10l(+-0)=-inf */ if (hx < 0) return (x - x) / (x - x); if (hx >= 0x7ff0000000000000LL) diff --git a/sysdeps/ieee754/ldbl-128ibm/e_log2l.c b/sysdeps/ieee754/ldbl-128ibm/e_log2l.c index e39eaba72a..1f8b6e9d7f 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_log2l.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_log2l.c @@ -183,7 +183,7 @@ __ieee754_log2l (long double x) xhi = ldbl_high (x); EXTRACT_WORDS64 (hx, xhi); if ((hx & 0x7fffffffffffffffLL) == 0) - return (-1.0L / (x - x)); + return (-1.0L / fabsl (x)); /* log2l(+-0)=-inf */ if (hx < 0) return (x - x) / (x - x); if (hx >= 0x7ff0000000000000LL) diff --git a/sysdeps/ieee754/ldbl-128ibm/e_logl.c b/sysdeps/ieee754/ldbl-128ibm/e_logl.c index 14acfc2db7..c44feca65b 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_logl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_logl.c @@ -58,6 +58,7 @@ 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) diff --git a/sysdeps/ieee754/ldbl-128ibm/e_powl.c b/sysdeps/ieee754/ldbl-128ibm/e_powl.c index 90340e890e..f59ad4e113 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_powl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_powl.c @@ -66,6 +66,7 @@ #include <math.h> #include <math_private.h> +#include <math-underflow.h> static const long double bp[] = { 1.0L, @@ -148,7 +149,7 @@ long double __ieee754_powl (long double x, long double y) { long double z, ax, z_h, z_l, p_h, p_l; - long double y1, t1, t2, r, s, t, u, v, w; + long double y1, t1, t2, r, s, sgn, t, u, v, w; long double s2, s_h, s_l, t_h, t_l, ay; int32_t i, j, k, yisint, n; uint32_t ix, iy; @@ -165,11 +166,11 @@ __ieee754_powl (long double x, long double y) iy = hy & 0x7fffffff; /* y==zero: x**0 = 1 */ - if ((iy | ly) == 0) + if ((iy | ly) == 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 - 0x7ff00000) | ly) == 0) return one; @@ -233,7 +234,7 @@ __ieee754_powl (long double x, long double y) if (hy == 0x3fe00000) { /* y is 0.5 */ if (hx >= 0) /* x >= +0 */ - return __ieee754_sqrtl (x); + return sqrtl (x); } } } @@ -260,9 +261,14 @@ __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 (((((uint32_t) hx >> 31) - 1) | (yisint - 1)) == 0) + sgn = -one; /* (-ve)**(odd int) */ + /* |y| is huge. 2^-16495 = 1/2 of smallest representable value. If (1 - 1/131072)^y underflows, y > 1.4986e9 */ @@ -272,15 +278,15 @@ __ieee754_powl (long double x, long double y) if (iy > 0x47d654b0) { if (ix <= 0x3fefffff) - return (hy < 0) ? huge * huge : tiny * tiny; + return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny; if (ix >= 0x3ff00000) - return (hy > 0) ? huge * huge : tiny * tiny; + return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny; } /* over/underflow if x is not close to one */ if (ix < 0x3fefffff) - return (hy < 0) ? huge * huge : tiny * tiny; + return (hy < 0) ? sgn * huge * huge : sgn * tiny * tiny; if (ix > 0x3ff00000) - return (hy > 0) ? huge * huge : tiny * tiny; + return (hy > 0) ? sgn * huge * huge : sgn * tiny * tiny; } ay = y > 0 ? y : -y; @@ -351,11 +357,6 @@ __ieee754_powl (long double x, long double y) t1 = ldbl_high (t1); t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); - /* s (sign of result -ve**odd) = -1 else = 1 */ - s = one; - if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) - s = -one; /* (-ve)**(odd int) */ - /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ y1 = ldbl_high (y); p_l = (y - y1) * t1 + y * t2; @@ -367,22 +368,22 @@ __ieee754_powl (long double x, long double y) { /* if z > 16384 */ if (((j - 0x40d00000) | lj) != 0) - return s * huge * huge; /* overflow */ + return sgn * huge * huge; /* overflow */ else { if (p_l + ovt > z - p_h) - return s * huge * huge; /* overflow */ + return sgn * huge * huge; /* overflow */ } } else if ((j & 0x7fffffff) >= 0x40d01b90) /* z <= -16495 */ { /* z < -16495 */ if (((j - 0xc0d01bc0) | lj) != 0) - return s * tiny * tiny; /* underflow */ + return sgn * tiny * tiny; /* underflow */ else { if (p_l <= z - p_h) - return s * tiny * tiny; /* underflow */ + return sgn * tiny * tiny; /* underflow */ } } /* compute 2**(p_h+p_l) */ @@ -408,8 +409,8 @@ __ieee754_powl (long double x, long double y) t1 = z - t * u / v; r = (z * t1) / (t1 - two) - (w + z * w); z = one - (r - z); - z = __scalbnl (z, n); - math_check_force_underflow_nonneg (z); - return s * z; + z = __scalbnl (sgn * z, n); + math_check_force_underflow (z); + return z; } strong_alias (__ieee754_powl, __powl_finite) diff --git a/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c b/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c index cc2b235534..07cb1e8b4c 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c +++ b/sysdeps/ieee754/ldbl-128ibm/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> @@ -200,7 +200,7 @@ int32_t __ieee754_rem_pio2l(long double x, long double *y) double tx[8]; int exp; int64_t n, ix, hx, ixd; - u_int64_t lxd; + uint64_t lxd; double xhi; xhi = ldbl_high (x); diff --git a/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c b/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c index 800416f29a..efa83bdab7 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_remainderl.c @@ -31,7 +31,7 @@ long double __ieee754_remainderl(long double x, long double p) { int64_t hx,hp; - u_int64_t sx,lx,lp; + uint64_t sx,lx,lp; long double p_half; double xhi, xlo, phi, plo; @@ -42,8 +42,14 @@ __ieee754_remainderl(long double x, long double p) EXTRACT_WORDS64 (hp, phi); EXTRACT_WORDS64 (lp, plo); sx = hx&0x8000000000000000ULL; + lp ^= hp & 0x8000000000000000ULL; hp &= 0x7fffffffffffffffLL; + lx ^= sx; hx &= 0x7fffffffffffffffLL; + if (lp == 0x8000000000000000ULL) + lp = 0; + if (lx == 0x8000000000000000ULL) + lx = 0; /* purge off exception values */ if(hp==0) return (x*p)/(x*p); /* p = 0 */ diff --git a/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c b/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c index 67d9d24ce7..f869fb068c 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_sinhl.c @@ -31,6 +31,7 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> static const long double one = 1.0, shuge = 1.0e307; diff --git a/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c b/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c index 96845fe5f8..28b208883d 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c @@ -1,7 +1,7 @@ /* * IBM Accurate Mathematical Library * written by International Business Machines Corp. - * Copyright (C) 2001-2016 Free Software Foundation, Inc. + * Copyright (C) 2001-2018 Free Software Foundation, Inc. * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU Lesser General Public License as published by @@ -91,11 +91,9 @@ long double __ieee754_sqrtl(long double x) return c.x * i; } else { - if (k>=INT64_C(0x7ff0000000000000)) { - if (a.i[0] == INT64_C(0xfff0000000000000)) - return (big1-big1)/(big-big); /* sqrt (-Inf) = NaN. */ - return x; /* sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */ - } + if (k>=INT64_C(0x7ff0000000000000)) + /* sqrt (-Inf) = NaN, sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */ + return x * x + x; if (x == 0) return x; if (x < 0) return (big1-big1)/(big-big); return tm256*__ieee754_sqrtl(x*t512); diff --git a/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c b/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c index b631f90a44..e4d9887b6c 100644 --- a/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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 diff --git a/sysdeps/ieee754/ldbl-128ibm/ieee754.h b/sysdeps/ieee754/ldbl-128ibm/ieee754.h index c07a6def4b..8017d9846f 100644 --- a/sysdeps/ieee754/ldbl-128ibm/ieee754.h +++ b/sysdeps/ieee754/ldbl-128ibm/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-128ibm/include/bits/iscanonical.h b/sysdeps/ieee754/ldbl-128ibm/include/bits/iscanonical.h new file mode 100644 index 0000000000..bee080bd29 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/include/bits/iscanonical.h @@ -0,0 +1,5 @@ +#include_next <bits/iscanonical.h> + +#ifndef _ISOMAC +libm_hidden_proto (__iscanonicall) +#endif diff --git a/sysdeps/ieee754/ldbl-128ibm/k_cosl.c b/sysdeps/ieee754/ldbl-128ibm/k_cosl.c index 2a3189ad36..e40c53cad3 100644 --- a/sysdeps/ieee754/ldbl-128ibm/k_cosl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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> @@ -86,7 +86,7 @@ __kernel_cosl(long double x, long double y) xhi = ldbl_high (x); EXTRACT_WORDS64 (ix, xhi); - tix = ((u_int64_t)ix) >> 32; + tix = ((uint64_t)ix) >> 32; tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ if (tix < 0x3fc30000) /* |x| < 0.1484375 */ { diff --git a/sysdeps/ieee754/ldbl-128ibm/k_sincosl.c b/sysdeps/ieee754/ldbl-128ibm/k_sincosl.c index 4e43c8622e..ba95337c31 100644 --- a/sysdeps/ieee754/ldbl-128ibm/k_sincosl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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> @@ -20,6 +20,7 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> static const long double c[] = { #define ONE c[0] diff --git a/sysdeps/ieee754/ldbl-128ibm/k_sinl.c b/sysdeps/ieee754/ldbl-128ibm/k_sinl.c index 44da02b0f3..46d1d7b52a 100644 --- a/sysdeps/ieee754/ldbl-128ibm/k_sinl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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> @@ -20,6 +20,7 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> static const long double c[] = { #define ONE c[0] @@ -82,12 +83,12 @@ __kernel_sinl(long double x, long double y, int iy) { long double h, l, z, sin_l, cos_l_m1; int64_t ix; - u_int32_t tix, hix, index; + uint32_t tix, hix, index; double xhi, hhi; xhi = ldbl_high (x); EXTRACT_WORDS64 (ix, xhi); - tix = ((u_int64_t)ix) >> 32; + tix = ((uint64_t)ix) >> 32; tix &= ~0x80000000; /* tix = |x|'s high 32 bits */ if (tix < 0x3fc30000) /* |x| < 0.1484375 */ { diff --git a/sysdeps/ieee754/ldbl-128ibm/k_tanl.c b/sysdeps/ieee754/ldbl-128ibm/k_tanl.c index 3c1bf32af9..3927fca25c 100644 --- a/sysdeps/ieee754/ldbl-128ibm/k_tanl.c +++ b/sysdeps/ieee754/ldbl-128ibm/k_tanl.c @@ -57,9 +57,11 @@ */ #include <float.h> -#include <libc-internal.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> +#include <libc-diag.h> + static const long double one = 1.0L, pio4hi = 7.8539816339744830961566084581987569936977E-1L, diff --git a/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c b/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c index 4f550ef47c..0e265ff5b2 100644 --- a/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c +++ b/sysdeps/ieee754/ldbl-128ibm/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 @@ -28,6 +28,12 @@ bits (106 for long double) and an integral power of two (MPN frexpl). */ + +/* When signs differ, the actual value is the difference between the + significant double and the less significant double. Sometimes a + bit can be lost when we borrow from the significant mantissa. */ +#define EXTRA_INTERNAL_PRECISION (7) + mp_size_t __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, int *expt, int *is_neg, @@ -45,10 +51,15 @@ __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, lo = ((long long) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1; hi = ((long long) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1; + /* Hold 7 extra bits of precision in the mantissa. This allows + the normalizing shifts below to prevent losing precision when + the signs differ and the exponents are sufficiently far apart. */ + lo <<= EXTRA_INTERNAL_PRECISION; + /* If the lower double is not a denormal or zero then set the hidden 53rd bit. */ if (u.d[1].ieee.exponent != 0) - lo |= 1ULL << 52; + lo |= 1ULL << (52 + EXTRA_INTERNAL_PRECISION); else lo = lo << 1; @@ -72,12 +83,12 @@ __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, if (u.d[0].ieee.negative != u.d[1].ieee.negative && lo != 0) { - lo = (1ULL << 53) - lo; + lo = (1ULL << (53 + EXTRA_INTERNAL_PRECISION)) - lo; if (hi == 0) { /* we have a borrow from the hidden bit, so shift left 1. */ - hi = 0x0ffffffffffffeLL | (lo >> 51); - lo = 0x1fffffffffffffLL & (lo << 1); + hi = 0x000ffffffffffffeLL | (lo >> (52 + EXTRA_INTERNAL_PRECISION)); + lo = 0x0fffffffffffffffLL & (lo << 1); (*expt)--; } else @@ -85,14 +96,14 @@ __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, } #if BITS_PER_MP_LIMB == 32 /* Combine the mantissas to be contiguous. */ - res_ptr[0] = lo; - res_ptr[1] = (hi << (53 - 32)) | (lo >> 32); + res_ptr[0] = lo >> EXTRA_INTERNAL_PRECISION; + res_ptr[1] = (hi << (53 - 32)) | (lo >> (32 + EXTRA_INTERNAL_PRECISION)); res_ptr[2] = hi >> 11; res_ptr[3] = hi >> (32 + 11); #define N 4 #elif BITS_PER_MP_LIMB == 64 /* Combine the two mantissas to be contiguous. */ - res_ptr[0] = (hi << 53) | lo; + res_ptr[0] = (hi << 53) | (lo >> EXTRA_INTERNAL_PRECISION); res_ptr[1] = hi >> 11; #define N 2 #else diff --git a/sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c b/sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c index c2a5cd29b6..e00f7b9889 100644 --- a/sysdeps/ieee754/ldbl-128ibm/lgamma_negl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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 diff --git a/sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c b/sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c index c5fa81be8e..dc0e8dd723 100644 --- a/sysdeps/ieee754/ldbl-128ibm/lgamma_productl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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 diff --git a/sysdeps/ieee754/ldbl-128ibm/strtod_nan_ldouble.h b/sysdeps/ieee754/ldbl-128ibm/math-nan-payload-ldouble.h index d827112446..653407597f 100644 --- a/sysdeps/ieee754/ldbl-128ibm/strtod_nan_ldouble.h +++ b/sysdeps/ieee754/ldbl-128ibm/math-nan-payload-ldouble.h @@ -1,5 +1,5 @@ -/* Convert string for NaN payload to corresponding NaN. For ldbl-128ibm. - Copyright (C) 1997-2016 Free Software Foundation, Inc. +/* NaN payload handling or ldbl-128ibm. + 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 ibm_extended_long_double u; \ diff --git a/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h b/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h index 051352f9f7..ccb646620e 100644 --- a/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h +++ b/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h @@ -1,6 +1,23 @@ -#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) 2006-2018 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 <ieee754.h> #include <stdint.h> @@ -230,3 +247,44 @@ ldbl_nearbyint (double a) } return a; } + +/* Canonicalize a result from an integer rounding function, in any + rounding mode. *A and *AA are finite and integers, with *A being + nonzero; if the result is not already canonical, *AA is plus or + minus a power of 2 that does not exceed the least set bit in + *A. */ +static inline void +ldbl_canonicalize_int (double *a, double *aa) +{ + /* Previously we used EXTRACT_WORDS64 from math_private.h, but in order + to avoid including internal headers we duplicate that code here. */ + uint64_t ax, aax; + union { double value; uint64_t word; } extractor; + extractor.value = *a; + ax = extractor.word; + extractor.value = *aa; + aax = extractor.word; + + int expdiff = ((ax >> 52) & 0x7ff) - ((aax >> 52) & 0x7ff); + if (expdiff <= 53) + { + if (expdiff == 53) + { + /* Half way between two double values; noncanonical iff the + low bit of A's mantissa is 1. */ + if ((ax & 1) != 0) + { + *a += 2 * *aa; + *aa = -*aa; + } + } + else + { + /* The sum can be represented in a single double. */ + *a += *aa; + *aa = 0; + } + } +} + +#endif /* math_ldbl.h */ diff --git a/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c b/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c index 42f5e6a02d..ff9f6496bd 100644 --- a/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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-128ibm/printf_fphex.c b/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c index 06be1c52d4..2908e8a819 100644 --- a/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c +++ b/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c @@ -1,5 +1,5 @@ /* 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. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. diff --git a/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c b/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c index aa9a9ba213..d4977e5414 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_asinhl.c @@ -28,6 +28,7 @@ static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $"; #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> #include <math_ldbl_opt.h> static const long double @@ -53,10 +54,10 @@ long double __asinhl(long double x) w = __ieee754_logl(fabsl(x))+ln2; } else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */ t = fabs(x); - 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(fabsl(x)+t/(one+__ieee754_sqrtl(one+t))); + w =__log1pl(fabsl(x)+t/(one+sqrtl(one+t))); } if(hx>0) return w; else return -w; } diff --git a/sysdeps/ieee754/ldbl-128ibm/s_atanl.c b/sysdeps/ieee754/ldbl-128ibm/s_atanl.c index 0560d820ae..32cf36c65d 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_atanl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_atanl.c @@ -62,6 +62,7 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> #include <math_ldbl_opt.h> /* arctan(k/8), k = 0, ..., 82 */ diff --git a/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c b/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c index 010a671dce..317d238057 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c @@ -1,6 +1,102 @@ -/* Looks like we can use ieee854 s_cbrtl.c as is for IBM extended format. */ +/* Implementation of cbrtl. IBM Extended Precision version. + Cephes Math Library Release 2.2: January, 1991 + Copyright 1984, 1991 by Stephen L. Moshier + Adapted for glibc October, 2001. + + This 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. + + This 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 this library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* This file was copied from sysdeps/ieee754/ldbl-128/e_j0l.c. */ + + #include <math_ldbl_opt.h> -#undef weak_alias -#define weak_alias(n,a) -#include <sysdeps/ieee754/ldbl-128/s_cbrtl.c> +#include <math.h> +#include <math_private.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; + + +long double +__cbrtl (long double x) +{ + int e, rem, sign; + long double z; + + if (!isfinite (x)) + return x + x; + + if (x == 0) + return (x); + + if (x > 0) + sign = 1; + else + { + sign = -1; + x = -x; + } + + z = x; + /* extract power of 2, leaving mantissa between 0.5 and 1 */ + x = __frexpl (x, &e); + + /* 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; + + /* exponent divided by 3 */ + if (e >= 0) + { + rem = e; + e /= 3; + rem -= 3 * e; + if (rem == 1) + x *= CBRT2; + else if (rem == 2) + x *= CBRT4; + } + else + { /* argument less than 1 */ + e = -e; + rem = e; + e /= 3; + rem -= 3 * e; + if (rem == 1) + x *= CBRT2I; + else if (rem == 2) + x *= CBRT4I; + e = -e; + } + + /* multiply by power of 2 */ + 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; + + if (sign < 0) + x = -x; + return (x); +} + long_double_symbol (libm, __cbrtl, cbrtl); diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ceill.c b/sysdeps/ieee754/ldbl-128ibm/s_ceill.c index ac649b7215..7dcff021c4 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_ceill.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_ceill.c @@ -1,6 +1,6 @@ /* Ceil (round to +inf) long double floating-point values. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ -18,6 +18,7 @@ <http://www.gnu.org/licenses/>. */ #include <math.h> +#include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> #include <ieee754.h> @@ -35,43 +36,26 @@ __ceill (long double x) && __builtin_isless (__builtin_fabs (xh), __builtin_inf ()), 1)) { - double orig_xh; - - /* Long double arithmetic, including the canonicalisation below, - only works in round-to-nearest mode. */ - - /* Convert the high double to integer. */ - orig_xh = xh; - hi = ldbl_nearbyint (xh); - - /* Subtract integral high part from the value. */ - xh -= hi; - ldbl_canonicalize (&xh, &xl); - - /* Now convert the low double, adjusted for any remainder from the - high double. */ - lo = ldbl_nearbyint (xh); - - /* Adjust the result when the remainder is non-zero. nearbyint - rounds values to the nearest integer, and values halfway - between integers to the nearest even integer. ceill must - round towards +Inf. */ - xh -= lo; - ldbl_canonicalize (&xh, &xl); - - if (xh > 0.0 || (xh == 0.0 && xl > 0.0)) - lo += 1.0; - - /* Ensure the final value is canonical. In certain cases, - rounding causes hi,lo calculated so far to be non-canonical. */ - xh = hi; - xl = lo; - ldbl_canonicalize (&xh, &xl); - - /* Ensure we return -0 rather than +0 when appropriate. */ - if (orig_xh < 0.0) - xh = -__builtin_fabs (xh); + hi = __ceil (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part does not + affect the result. */ + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = __ceil (xl); + xh = hi; + xl = lo; + ldbl_canonicalize_int (&xh, &xl); + } } + else + /* Quiet signaling NaN arguments. */ + xh += xh; return ldbl_pack (xh, xl); } diff --git a/sysdeps/ieee754/ldbl-128ibm/s_daddl.c b/sysdeps/ieee754/ldbl-128ibm/s_daddl.c new file mode 100644 index 0000000000..28b7e06ace --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_daddl.c @@ -0,0 +1,27 @@ +/* Add long double (ldbl-128ibm) 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/>. */ + +#include <math.h> +#include <math-narrow.h> + +double +__daddl (long double x, long double y) +{ + NARROW_ADD_TRIVIAL (x, y, double); +} +libm_alias_double_ldouble (add) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ddivl.c b/sysdeps/ieee754/ldbl-128ibm/s_ddivl.c new file mode 100644 index 0000000000..6bbbbcf09d --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_ddivl.c @@ -0,0 +1,27 @@ +/* Divide long double (ldbl-128ibm) 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/>. */ + +#include <math.h> +#include <math-narrow.h> + +double +__ddivl (long double x, long double y) +{ + NARROW_DIV_TRIVIAL (x, y, double); +} +libm_alias_double_ldouble (div) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_dmull.c b/sysdeps/ieee754/ldbl-128ibm/s_dmull.c new file mode 100644 index 0000000000..7b75b2b0f1 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_dmull.c @@ -0,0 +1,27 @@ +/* Multiply long double (ldbl-128ibm) 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/>. */ + +#include <math.h> +#include <math-narrow.h> + +double +__dmull (long double x, long double y) +{ + NARROW_MUL_TRIVIAL (x, y, double); +} +libm_alias_double_ldouble (mul) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_dsubl.c b/sysdeps/ieee754/ldbl-128ibm/s_dsubl.c new file mode 100644 index 0000000000..e0e80f26a4 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_dsubl.c @@ -0,0 +1,27 @@ +/* Subtract long double (ldbl-128ibm) 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/>. */ + +#include <math.h> +#include <math-narrow.h> + +double +__dsubl (long double x, long double y) +{ + NARROW_SUB_TRIVIAL (x, y, double); +} +libm_alias_double_ldouble (sub) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_erfl.c b/sysdeps/ieee754/ldbl-128ibm/s_erfl.c index 7b761b0afa..5302fee522 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_erfl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_erfl.c @@ -105,6 +105,7 @@ #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> #include <math_ldbl_opt.h> #include <fix-int-fp-convert-zero.h> diff --git a/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c b/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c index 66f75e1c80..42d57c6eec 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_expm1l.c @@ -106,8 +106,8 @@ __expm1l (long double x) /* Infinity (which must be negative infinity). */ if (((ix - 0x7ff00000) | lx) == 0) return -1.0L; - /* NaN. No invalid exception. */ - return x; + /* NaN. Invalid exception if signaling. */ + return x + x; } /* expm1(+- 0) = +- 0. */ diff --git a/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c b/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c index c801c97065..54bf9b9cc1 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_fabsl.c @@ -28,7 +28,7 @@ static char rcsid[] = "$NetBSD: $"; long double __fabsl(long double x) { - u_int64_t hx, lx; + uint64_t hx, lx; double xhi, xlo; ldbl_unpack (x, &xhi, &xlo); diff --git a/sysdeps/ieee754/ldbl-128ibm/s_faddl.c b/sysdeps/ieee754/ldbl-128ibm/s_faddl.c new file mode 100644 index 0000000000..55a391885c --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_faddl.c @@ -0,0 +1,27 @@ +/* Add long double (ldbl-128ibm) 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/>. */ + +#include <math.h> +#include <math-narrow.h> + +float +__faddl (long double x, long double y) +{ + NARROW_ADD_TRIVIAL (x, y, float); +} +libm_alias_float_ldouble (add) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_fdivl.c b/sysdeps/ieee754/ldbl-128ibm/s_fdivl.c new file mode 100644 index 0000000000..dd34c05502 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_fdivl.c @@ -0,0 +1,27 @@ +/* Divide long double (ldbl-128ibm) 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/>. */ + +#include <math.h> +#include <math-narrow.h> + +float +__fdivl (long double x, long double y) +{ + NARROW_DIV_TRIVIAL (x, y, float); +} +libm_alias_float_ldouble (div) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_floorl.c b/sysdeps/ieee754/ldbl-128ibm/s_floorl.c index 912230870a..4aae5ae608 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_floorl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_floorl.c @@ -1,6 +1,6 @@ /* Round to int long double floating-point values. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ -18,6 +18,7 @@ <http://www.gnu.org/licenses/>. */ #include <math.h> +#include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> #include <ieee754.h> @@ -35,36 +36,26 @@ __floorl (long double x) && __builtin_isless (__builtin_fabs (xh), __builtin_inf ()), 1)) { - /* Long double arithmetic, including the canonicalisation below, - only works in round-to-nearest mode. */ - - /* Convert the high double to integer. */ - hi = ldbl_nearbyint (xh); - - /* Subtract integral high part from the value. */ - xh -= hi; - ldbl_canonicalize (&xh, &xl); - - /* Now convert the low double, adjusted for any remainder from the - high double. */ - lo = ldbl_nearbyint (xh); - - /* Adjust the result when the remainder is non-zero. nearbyint - rounds values to the nearest integer, and values halfway - between integers to the nearest even integer. floorl must - round towards -Inf. */ - xh -= lo; - ldbl_canonicalize (&xh, &xl); - - if (xh < 0.0 || (xh == 0.0 && xl < 0.0)) - lo += -1.0; - - /* Ensure the final value is canonical. In certain cases, - rounding causes hi,lo calculated so far to be non-canonical. */ - xh = hi; - xl = lo; - ldbl_canonicalize (&xh, &xl); + hi = __floor (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part does not + affect the result. */ + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. */ + lo = __floor (xl); + xh = hi; + xl = lo; + ldbl_canonicalize_int (&xh, &xl); + } } + else + /* Quiet signaling NaN arguments. */ + xh += xh; return ldbl_pack (xh, xl); } diff --git a/sysdeps/ieee754/ldbl-128ibm/s_fmal.c b/sysdeps/ieee754/ldbl-128ibm/s_fmal.c index eb3ee3cfb8..e72a3e4d59 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_fmal.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_fmal.c @@ -1,5 +1,5 @@ /* Compute x * y + z as ternary operation. - Copyright (C) 2011-2016 Free Software Foundation, Inc. + Copyright (C) 2011-2018 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by David Flaherty <flaherty@linux.vnet.ibm.com>. @@ -17,25 +17,240 @@ License along with the GNU C Library; if not, see <http://www.gnu.org/licenses/>. */ +#include <fenv.h> +#include <float.h> #include <math.h> +#include <math-barriers.h> +#include <math_private.h> +#include <math-underflow.h> #include <math_ldbl_opt.h> +#include <mul_split.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 void +add_split (double *hi, double *lo, double x, double y) +{ + /* Apply Dekker's algorithm. */ + *hi = x + y; + *lo = (x - *hi) + y; +} + +/* Value with extended range, used in intermediate computations. */ +typedef struct +{ + /* Value in [0.5, 1), as from frexp, or 0. */ + double val; + /* Exponent of power of 2 it is multiplied by, or 0 for zero. */ + int exp; +} ext_val; + +/* Store D as an ext_val value. */ + +static void +store_ext_val (ext_val *v, double d) +{ + v->val = __frexp (d, &v->exp); +} + +/* Store X * Y as ext_val values *V0 and *V1. */ + +static void +mul_ext_val (ext_val *v0, ext_val *v1, double x, double y) +{ + int xexp, yexp; + x = __frexp (x, &xexp); + y = __frexp (y, &yexp); + double hi, lo; + mul_split (&hi, &lo, x, y); + store_ext_val (v0, hi); + if (hi != 0) + v0->exp += xexp + yexp; + store_ext_val (v1, lo); + if (lo != 0) + v1->exp += xexp + yexp; +} + +/* Compare absolute values of ext_val values pointed to by P and Q for + qsort. */ + +static int +compare (const void *p, const void *q) +{ + const ext_val *pe = p; + const ext_val *qe = q; + if (pe->val == 0) + return qe->val == 0 ? 0 : -1; + else if (qe->val == 0) + return 1; + else if (pe->exp < qe->exp) + return -1; + else if (pe->exp > qe->exp) + return 1; + else + { + double pd = fabs (pe->val); + double qd = fabs (qe->val); + if (pd < qd) + return -1; + else if (pd == qd) + return 0; + else + return 1; + } +} + +/* Calculate *X + *Y exactly, storing the high part in *X (rounded to + nearest) and the low part in *Y. It is given that |X| >= |Y|. */ + +static void +add_split_ext (ext_val *x, ext_val *y) +{ + int xexp = x->exp, yexp = y->exp; + if (y->val == 0 || xexp - yexp > 53) + return; + double hi = x->val; + double lo = __scalbn (y->val, yexp - xexp); + add_split (&hi, &lo, hi, lo); + store_ext_val (x, hi); + if (hi != 0) + x->exp += xexp; + store_ext_val (y, lo); + if (lo != 0) + y->exp += xexp; +} long double __fmal (long double x, long double y, long double z) { - /* An IBM long double 128 is really just 2 IEEE64 doubles, and in - * the case of inf/nan only the first double counts. So we use the - * (double) cast to avoid any data movement. */ - if ((isfinite ((double)x) && isfinite ((double)y)) && isinf ((double)z)) - return (z); - - /* If z is zero and x are y are nonzero, compute the result - as x * y to avoid the wrong sign of a zero result if x * y - underflows to 0. */ - if (z == 0 && x != 0 && y != 0) - return x * y; - - return (x * y) + z; + double xhi, xlo, yhi, ylo, zhi, zlo; + int64_t hx, hy, hz; + int xexp, yexp, zexp; + double scale_val; + int scale_exp; + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + xexp = (hx & 0x7ff0000000000000LL) >> 52; + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); + yexp = (hy & 0x7ff0000000000000LL) >> 52; + ldbl_unpack (z, &zhi, &zlo); + EXTRACT_WORDS64 (hz, zhi); + zexp = (hz & 0x7ff0000000000000LL) >> 52; + + /* If z is Inf or NaN, but x and y are finite, avoid any exceptions + from computing x * y. */ + if (zexp == 0x7ff && xexp != 0x7ff && yexp != 0x7ff) + return (z + x) + y; + + /* If z is zero and x are y are nonzero, compute the result as x * y + to avoid the wrong sign of a zero result if x * y underflows to + 0. */ + if (z == 0 && x != 0 && y != 0) + return x * y; + + /* If x or y or z is Inf/NaN, or if x * y is zero, compute as x * y + + z. */ + if (xexp == 0x7ff || yexp == 0x7ff || zexp == 0x7ff + || x == 0 || y == 0) + return (x * y) + z; + + { + SET_RESTORE_ROUND (FE_TONEAREST); + + ext_val vals[10]; + store_ext_val (&vals[0], zhi); + store_ext_val (&vals[1], zlo); + mul_ext_val (&vals[2], &vals[3], xhi, yhi); + mul_ext_val (&vals[4], &vals[5], xhi, ylo); + mul_ext_val (&vals[6], &vals[7], xlo, yhi); + mul_ext_val (&vals[8], &vals[9], xlo, ylo); + qsort (vals, 10, sizeof (ext_val), 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 <= 8; i++) + { + add_split_ext (&vals[i + 1], &vals[i]); + qsort (vals + i + 1, 9 - i, sizeof (ext_val), compare); + } + /* Add up the values in the other direction, so that each element + of VALS has absolute value less than 5ulp of the next + value. */ + size_t dstpos = 9; + for (size_t i = 1; i <= 9; i++) + { + if (vals[dstpos].val == 0) + { + vals[dstpos] = vals[9 - i]; + vals[9 - i].val = 0; + vals[9 - i].exp = 0; + } + else + { + add_split_ext (&vals[dstpos], &vals[9 - i]); + if (vals[9 - i].val != 0) + { + if (9 - i < dstpos - 1) + { + vals[dstpos - 1] = vals[9 - i]; + vals[9 - i].val = 0; + vals[9 - i].exp = 0; + } + dstpos--; + } + } + } + /* If the result is an exact zero, it results from adding two + values with opposite signs; recompute in the original rounding + mode. */ + if (vals[9].val == 0) + goto zero_out; + /* Adding the top three values will now give a result as accurate + as the underlying long double arithmetic. */ + add_split_ext (&vals[9], &vals[8]); + if (compare (&vals[8], &vals[7]) < 0) + { + ext_val tmp = vals[7]; + vals[7] = vals[8]; + vals[8] = tmp; + } + add_split_ext (&vals[8], &vals[7]); + add_split_ext (&vals[9], &vals[8]); + if (vals[9].exp > DBL_MAX_EXP || vals[9].exp < DBL_MIN_EXP) + { + /* Overflow or underflow, with the result depending on the + original rounding mode, but not on the low part computed + here. */ + scale_val = vals[9].val; + scale_exp = vals[9].exp; + goto scale_out; + } + double hi = __scalbn (vals[9].val, vals[9].exp); + double lo = __scalbn (vals[8].val, vals[8].exp); + /* It is possible that the low part became subnormal and was + rounded so that the result is no longer canonical. */ + ldbl_canonicalize (&hi, &lo); + long double ret = ldbl_pack (hi, lo); + math_check_force_underflow (ret); + return ret; + } + + scale_out: + scale_val = math_opt_barrier (scale_val); + scale_val = __scalbn (scale_val, scale_exp); + if (fabs (scale_val) == DBL_MAX) + return __copysignl (LDBL_MAX, scale_val); + math_check_force_underflow (scale_val); + return scale_val; + + zero_out:; + double zero = 0.0; + zero = math_opt_barrier (zero); + return zero - zero; } #if IS_IN (libm) long_double_symbol (libm, __fmal, fmal); diff --git a/sysdeps/ieee754/ldbl-128ibm/s_fmull.c b/sysdeps/ieee754/ldbl-128ibm/s_fmull.c new file mode 100644 index 0000000000..d1988f168d --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_fmull.c @@ -0,0 +1,27 @@ +/* Multiply long double (ldbl-128ibm) 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/>. */ + +#include <math.h> +#include <math-narrow.h> + +float +__fmull (long double x, long double y) +{ + NARROW_MUL_TRIVIAL (x, y, float); +} +libm_alias_float_ldouble (mul) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c b/sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c index 83c3a8dc51..92c08cc995 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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. @@ -44,7 +44,7 @@ int ___fpclassifyl (long double x) { - u_int64_t hx, lx; + uint64_t hx, lx; int retval = FP_NORMAL; double xhi, xlo; diff --git a/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c b/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c index 52d2d3ea90..210c5d2ed4 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_frexpl.c @@ -47,7 +47,7 @@ long double __frexpl(long double x, int *eptr) { /* 0,inf,nan. */ *eptr = expon; - return x; + return x + x; } expon = ix >> 52; if (expon == 0) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c b/sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c new file mode 100644 index 0000000000..f3fdba33c1 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_fromfpl.c @@ -0,0 +1,5 @@ +#define UNSIGNED 0 +#define INEXACT 0 +#define FUNC __fromfpl +#include <s_fromfpl_main.c> +weak_alias (__fromfpl, fromfpl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c b/sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c new file mode 100644 index 0000000000..76287c33dc --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_fromfpl_main.c @@ -0,0 +1,147 @@ +/* Round to integer type. ldbl-128ibm 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 <stdbool.h> +#include <stdint.h> + +#define BIAS 0x3ff +#define MANT_DIG 53 + +#if UNSIGNED +# define RET_TYPE uintmax_t +#else +# define RET_TYPE intmax_t +#endif + +#include <fromfp.h> + +RET_TYPE +FUNC (long double x, int round, unsigned int width) +{ + double hi, lo; + if (width > INTMAX_WIDTH) + width = INTMAX_WIDTH; + uint64_t hx, lx; + ldbl_unpack (x, &hi, &lo); + EXTRACT_WORDS64 (hx, hi); + EXTRACT_WORDS64 (lx, lo); + bool negative = (hx & 0x8000000000000000ULL) != 0; + bool lo_negative = (lx & 0x8000000000000000ULL) != 0; + if (width == 0) + return fromfp_domain_error (negative, width); + hx &= 0x7fffffffffffffffULL; + lx &= 0x7fffffffffffffffULL; + if ((hx | lx) == 0) + return 0; + int hi_exponent = hx >> (MANT_DIG - 1); + hi_exponent -= BIAS; + int exponent = hi_exponent; + hx &= ((1ULL << (MANT_DIG - 1)) - 1); + if (hx == 0 && lx != 0 && lo_negative != negative) + exponent--; + int max_exponent = fromfp_max_exponent (negative, width); + if (exponent > max_exponent) + return fromfp_domain_error (negative, width); + int lo_exponent = lx >> (MANT_DIG - 1); + lo_exponent -= BIAS; + + /* Convert the high part to integer. */ + hx |= 1ULL << (MANT_DIG - 1); + uintmax_t uret; + bool half_bit, more_bits; + if (hi_exponent >= MANT_DIG - 1) + { + uret = hx; + uret <<= hi_exponent - (MANT_DIG - 1); + half_bit = false; + more_bits = false; + } + else if (hi_exponent >= -1) + { + uint64_t h = 1ULL << (MANT_DIG - 2 - hi_exponent); + half_bit = (hx & h) != 0; + more_bits = (hx & (h - 1)) != 0; + uret = hx >> (MANT_DIG - 1 - hi_exponent); + } + else + { + uret = 0; + half_bit = false; + more_bits = true; + } + + /* Likewise, the low part. */ + if (lx != 0) + { + uintmax_t lo_uret; + bool lo_half_bit, lo_more_bits; + lx &= ((1ULL << (MANT_DIG - 1)) - 1); + lx |= 1ULL << (MANT_DIG - 1); + /* The high part exponent is at most 64, so the low part + exponent is at most 11. */ + if (lo_exponent >= -1) + { + uint64_t h = 1ULL << (MANT_DIG - 2 - lo_exponent); + lo_half_bit = (lx & h) != 0; + lo_more_bits = (lx & (h - 1)) != 0; + lo_uret = lx >> (MANT_DIG - 1 - lo_exponent); + } + else + { + lo_uret = 0; + lo_half_bit = false; + lo_more_bits = true; + } + if (lo_negative == negative) + { + uret += lo_uret; + half_bit |= lo_half_bit; + more_bits |= lo_more_bits; + } + else + { + uret -= lo_uret; + if (lo_half_bit) + { + uret--; + half_bit = true; + } + if (lo_more_bits && !more_bits) + { + if (half_bit) + { + half_bit = false; + more_bits = true; + } + else + { + uret--; + half_bit = true; + 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-128ibm/s_fromfpxl.c b/sysdeps/ieee754/ldbl-128ibm/s_fromfpxl.c new file mode 100644 index 0000000000..9477cc2ea7 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_fromfpxl.c @@ -0,0 +1,5 @@ +#define UNSIGNED 0 +#define INEXACT 1 +#define FUNC __fromfpxl +#include <s_fromfpl_main.c> +weak_alias (__fromfpxl, fromfpxl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_fsubl.c b/sysdeps/ieee754/ldbl-128ibm/s_fsubl.c new file mode 100644 index 0000000000..aa6662de05 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_fsubl.c @@ -0,0 +1,27 @@ +/* Subtract long double (ldbl-128ibm) 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/>. */ + +#include <math.h> +#include <math-narrow.h> + +float +__fsubl (long double x, long double y) +{ + NARROW_SUB_TRIVIAL (x, y, float); +} +libm_alias_float_ldouble (sub) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_getpayloadl.c b/sysdeps/ieee754/ldbl-128ibm/s_getpayloadl.c new file mode 100644 index 0000000000..5b24955353 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_getpayloadl.c @@ -0,0 +1,35 @@ +/* Get NaN payload. ldbl-128ibm 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 <fix-int-fp-convert-zero.h> +#include <math.h> +#include <math_private.h> +#include <stdint.h> + +long double +__getpayloadl (const long double *x) +{ + double xhi = ldbl_high (*x); + uint64_t ix; + EXTRACT_WORDS64 (ix, xhi); + ix &= 0x7ffffffffffffULL; + if (FIX_INT_FP_CONVERT_ZERO && ix == 0) + return 0.0L; + return (long double) ix; +} +weak_alias (__getpayloadl, getpayloadl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c b/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c new file mode 100644 index 0000000000..91ce417992 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c @@ -0,0 +1,60 @@ +/* Test whether long double value is canonical. ldbl-128ibm 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 <stdint.h> + +int +__iscanonicall (long double x) +{ + double xhi, xlo; + uint64_t hx, lx; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + int64_t ix = hx & 0x7fffffffffffffffULL; + int64_t iy = lx & 0x7fffffffffffffffULL; + int hexp = (ix & 0x7ff0000000000000LL) >> 52; + int lexp = (iy & 0x7ff0000000000000LL) >> 52; + + if (iy == 0) + /* Low part 0 is always OK. */ + return 1; + + if (hexp == 0x7ff) + /* If a NaN, the low part does not matter. If an infinity, the + low part must be 0, in which case we have already returned. */ + return ix != 0x7ff0000000000000LL; + + /* The high part is finite and the low part is nonzero. There must + be sufficient difference between the exponents. */ + bool low_p2; + if (lexp == 0) + { + /* Adjust the exponent for subnormal low part. */ + lexp = 12 - __builtin_clzll (iy); + low_p2 = iy == (1LL << (51 + lexp)); + } + else + low_p2 = (iy & 0xfffffffffffffLL) == 0; + int expdiff = hexp - lexp; + return expdiff > 53 || (expdiff == 53 && low_p2 && (ix & 1) == 0); +} +libm_hidden_def (__iscanonicall) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c b/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c index 091513908b..126abce2de 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_issignalingl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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 @@ -18,6 +18,7 @@ #include <math.h> #include <math_private.h> +#include <nan-high-order-bit.h> int __issignalingl (long double x) @@ -29,7 +30,7 @@ __issignalingl (long double x) xhi = ldbl_high (x); EXTRACT_WORDS64 (xi, xhi); -#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN # error untested /* 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 diff --git a/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c b/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c index 860ede1e0b..9d4535103e 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_llrintl.c @@ -1,6 +1,6 @@ /* Round to long long int long double floating-point values. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ -19,6 +19,7 @@ #include <math.h> #include <fenv.h> +#include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> #include <ieee754.h> diff --git a/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c b/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c index 9fba087d5b..de6a7b5be2 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_llroundl.c @@ -1,6 +1,6 @@ /* Round to long long int long double floating-point values. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ -19,6 +19,7 @@ #include <math.h> #include <fenv.h> +#include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> #include <ieee754.h> diff --git a/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c b/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c index 743693bfd6..e499c9f604 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c @@ -131,8 +131,8 @@ __log1pl (long double xm1) /* Test for NaN or infinity input. */ xhi = ldbl_high (xm1); EXTRACT_WORDS (hx, lx, xhi); - if (hx >= 0x7ff00000) - return xm1; + if ((hx & 0x7fffffff) >= 0x7ff00000) + return xm1 + xm1 * xm1; /* log1p(+- 0) = +- 0. */ if (((hx & 0x7fffffff) | lx) == 0) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c b/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c index 988de70c5a..05fe7fefdf 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_lrintl.c @@ -1,6 +1,6 @@ /* Round to long int long double floating-point values. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ -19,6 +19,7 @@ #include <math.h> #include <fenv.h> +#include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> #include <ieee754.h> @@ -84,7 +85,7 @@ __lrintl (long double x) /* Peg at max/min values, assuming that the above conversions do so. Strictly speaking, we can return anything for values that overflow, but this is more useful. */ - res = hi + lo; + res = (long int) ((unsigned long int) hi + (unsigned long int) lo); /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) @@ -105,27 +106,27 @@ __lrintl (long double x) return res; if (xh < 0.0) - res -= 1; + res -= 1UL; else - res += 1; + res += 1UL; break; case FE_TOWARDZERO: if (res > 0 && (xh < 0.0 || (xh == 0.0 && xl < 0.0))) - res -= 1; + res -= 1UL; else if (res < 0 && (xh > 0.0 || (xh == 0.0 && xl > 0.0))) - res += 1; + res += 1UL; return res; break; case FE_UPWARD: if (xh > 0.0 || (xh == 0.0 && xl > 0.0)) - res += 1; + res += 1UL; break; case FE_DOWNWARD: if (xh < 0.0 || (xh == 0.0 && xl < 0.0)) - res -= 1; + res -= 1UL; break; } diff --git a/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c b/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c index aa48f680d4..bc8dda4c1d 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_lroundl.c @@ -1,6 +1,6 @@ /* Round to long int long double floating-point values. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ -19,6 +19,7 @@ #include <math.h> #include <fenv.h> +#include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> #include <ieee754.h> @@ -80,7 +81,7 @@ __lroundl (long double x) /* Peg at max/min values, assuming that the above conversions do so. Strictly speaking, we can return anything for values that overflow, but this is more useful. */ - res = hi + lo; + res = (long int) ((unsigned long int) hi + (unsigned long int) lo); /* This is just sign(hi) == sign(lo) && sign(res) != sign(hi). */ if (__glibc_unlikely (((~(hi ^ lo) & (res ^ hi)) < 0))) @@ -92,21 +93,21 @@ __lroundl (long double x) hi = res; if (xh > 0.5) { - res += 1; + res += 1UL; } else if (xh == 0.5) { if (xl > 0.0 || (xl == 0.0 && res >= 0)) - res += 1; + res += 1UL; } else if (-xh > 0.5) { - res -= 1; + res -= 1UL; } else if (-xh == 0.5) { if (xl < 0.0 || (xl == 0.0 && res <= 0)) - res -= 1; + res -= 1UL; } if (__glibc_unlikely (((~(hi ^ (res - hi)) & (res ^ hi)) < 0))) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_modfl.c b/sysdeps/ieee754/ldbl-128ibm/s_modfl.c index 260cc3e33c..1dc6c40e9c 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_modfl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_modfl.c @@ -36,7 +36,7 @@ static const long double one = 1.0; long double __modfl(long double x, long double *iptr) { int64_t i0,i1,j0; - u_int64_t i; + uint64_t i; double xhi, xlo; ldbl_unpack (x, &xhi, &xlo); diff --git a/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c b/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c index 08134edd10..bd691f3310 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c @@ -1,6 +1,6 @@ /* Round to int long double floating-point values without raising inexact. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ -17,110 +17,5 @@ License along with the GNU C Library; if not, see <http://www.gnu.org/licenses/>. */ -/* This has been coded in assembler because GCC makes such a mess of it - when it's coded in C. */ - -#include <math.h> -#include <math_private.h> -#include <fenv.h> -#include <math_ldbl_opt.h> -#include <float.h> -#include <ieee754.h> - - -long double -__nearbyintl (long double x) -{ - fenv_t env; - static const long double TWO52 = 4503599627370496.0L; - union ibm_extended_long_double u; - u.ld = x; - - if (!isfinite (u.d[0].d)) - return x; - else if (fabs (u.d[0].d) < TWO52) - { - double xh = u.d[0].d; - double high = u.d[0].d; - feholdexcept (&env); - if (high > 0.0) - { - high += TWO52; - high -= TWO52; - if (high == -0.0) high = 0.0; - } - else if (high < 0.0) - { - high -= TWO52; - high += TWO52; - if (high == 0.0) high = -0.0; - } - if (u.d[1].d > 0.0 && (xh - high == 0.5)) - high += 1.0; - else if (u.d[1].d < 0.0 && (-(xh - high) == 0.5)) - high -= 1.0; - u.d[0].d = high; - u.d[1].d = 0.0; - math_force_eval (u.d[0]); - math_force_eval (u.d[1]); - fesetenv (&env); - } - else if (fabs (u.d[1].d) < TWO52 && u.d[1].d != 0.0) - { - double high = u.d[0].d, low = u.d[1].d, tau; - /* In this case we have to round the low double and handle any - adjustment to the high double that may be caused by rounding - (up). This is complicated by the fact that the high double - may already be rounded and the low double may have the - opposite sign to compensate. */ - feholdexcept (&env); - if (u.d[0].d > 0.0) - { - if (u.d[1].d > 0.0) - { - /* If the high/low doubles are the same sign then simply - round the low double. */ - } - else if (u.d[1].d < 0.0) - { - /* Else the high double is pre rounded and we need to - adjust for that. */ - - tau = __nextafter (u.d[0].d, 0.0); - tau = (u.d[0].d - tau) * 2.0; - high -= tau; - low += tau; - } - low += TWO52; - low -= TWO52; - } - else if (u.d[0].d < 0.0) - { - if (u.d[1].d < 0.0) - { - /* If the high/low doubles are the same sign then simply - round the low double. */ - } - else if (u.d[1].d > 0.0) - { - /* Else the high double is pre rounded and we need to - adjust for that. */ - tau = __nextafter (u.d[0].d, 0.0); - tau = (u.d[0].d - tau) * 2.0; - high -= tau; - low += tau; - } - low = TWO52 - low; - low = -(low - TWO52); - } - u.d[0].d = high + low; - u.d[1].d = high - u.d[0].d + low; - math_force_eval (u.d[0]); - math_force_eval (u.d[1]); - fesetenv (&env); - } - - return u.ld; -} - -long_double_symbol (libm, __nearbyintl, nearbyintl); +#define USE_AS_NEARBYINTL +#include "s_rintl.c" diff --git a/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c b/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c index 515aa1ef5b..e29f7d60a3 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c @@ -27,6 +27,7 @@ static char rcsid[] = "$NetBSD: $"; #include <errno.h> #include <float.h> #include <math.h> +#include <math-barriers.h> #include <math_private.h> #include <math_ldbl_opt.h> @@ -87,6 +88,9 @@ long double __nextafterl(long double x, long double y) math_force_eval (u); /* raise underflow flag */ __set_errno (ERANGE); } + /* Avoid returning -0 in FE_DOWNWARD mode. */ + if (x == 0.0L) + return 0.0L; return x; } /* If the high double is an exact power of two and the low diff --git a/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c b/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c index d8f4fc6523..8456bd5145 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c @@ -27,6 +27,7 @@ static char rcsid[] = "$NetBSD: $"; #include <errno.h> #include <math.h> +#include <math-barriers.h> #include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> diff --git a/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c b/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c index 7c5d1cc112..960ffd9aee 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c @@ -20,6 +20,7 @@ static char rcsid[] = "$NetBSD: $"; #include <errno.h> #include <math.h> +#include <math-barriers.h> #include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> @@ -43,7 +44,7 @@ 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-128ibm/s_nextupl.c b/sysdeps/ieee754/ldbl-128ibm/s_nextupl.c new file mode 100644 index 0000000000..9b532a3a25 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_nextupl.c @@ -0,0 +1,79 @@ +/* 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 <math_ldbl_opt.h> + +/* Return the least floating-point number greater than X. */ +long double +__nextupl (long double x) +{ + int64_t hx, ihx, lx; + double xhi, xlo, yhi; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + EXTRACT_WORDS64 (lx, xlo); + ihx = hx & 0x7fffffffffffffffLL; + + if (ihx > 0x7ff0000000000000LL) /* x is nan. */ + return x + x; /* Signal the nan. */ + if (ihx == 0) + return LDBL_TRUE_MIN; + + long double u; + if ((hx == 0x7fefffffffffffffLL) && (lx == 0x7c8ffffffffffffeLL)) + return INFINITY; + if ((uint64_t) hx >= 0xfff0000000000000ULL) + { + u = -0x1.fffffffffffff7ffffffffffff8p+1023L; + return u; + } + if (ihx <= 0x0360000000000000LL) + { /* x <= LDBL_MIN. */ + x += LDBL_TRUE_MIN; + if (x == 0.0L) /* Handle negative LDBL_TRUE_MIN case. */ + x = -0.0L; + return x; + } + /* If the high double is an exact power of two and the low + double is the opposite sign, then 1ulp is one less than + what we might determine from the high double. Similarly + if X is an exact power of two, and negative, because + making it a little larger will result in the exponent + decreasing by one and normalisation of the mantissa. */ + if ((hx & 0x000fffffffffffffLL) == 0 + && ((lx != 0 && lx != 0x8000000000000000LL && (hx ^ lx) < 0) + || ((lx == 0 || lx == 0x8000000000000000LL) && hx < 0))) + ihx -= 1LL << 52; + if (ihx < (106LL << 52)) + { /* ulp will denormal. */ + INSERT_WORDS64 (yhi, ihx & (0x7ffLL << 52)); + u = yhi * 0x1p-105; + } + else + { + INSERT_WORDS64 (yhi, (ihx & (0x7ffLL << 52)) - (105LL << 52)); + u = yhi; + } + return x + u; +} + +weak_alias (__nextupl, nextupl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_remquol.c b/sysdeps/ieee754/ldbl-128ibm/s_remquol.c index 20e17cc823..d87bce7982 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_remquol.c +++ b/sysdeps/ieee754/ldbl-128ibm/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. @@ -31,7 +31,7 @@ long double __remquol (long double x, long double y, int *quo) { int64_t hx,hy; - u_int64_t sx,lx,ly,qs; + uint64_t sx,lx,ly,qs; int cquo; double xhi, xlo, yhi, ylo; @@ -43,7 +43,9 @@ __remquol (long double x, long double y, int *quo) EXTRACT_WORDS64 (ly, ylo); sx = hx & 0x8000000000000000ULL; qs = sx ^ (hy & 0x8000000000000000ULL); + ly ^= hy & 0x8000000000000000ULL; hy &= 0x7fffffffffffffffLL; + lx ^= sx; hx &= 0x7fffffffffffffffLL; /* Purge off exception values. */ diff --git a/sysdeps/ieee754/ldbl-128ibm/s_rintl.c b/sysdeps/ieee754/ldbl-128ibm/s_rintl.c index 8c51ded1d6..f003609d95 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_rintl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_rintl.c @@ -1,6 +1,6 @@ /* Round to int long double floating-point values. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ -22,10 +22,17 @@ #include <math.h> #include <fenv.h> +#include <math-barriers.h> +#include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> #include <ieee754.h> +#ifdef USE_AS_NEARBYINTL +# define rintl nearbyintl +# define __rintl __nearbyintl +#endif + long double __rintl (long double x) @@ -44,7 +51,11 @@ __rintl (long double x) /* Long double arithmetic, including the canonicalisation below, only works in round-to-nearest mode. */ +#ifdef USE_AS_NEARBYINTL + SET_RESTORE_ROUND_NOEX (FE_TONEAREST); +#else fesetround (FE_TONEAREST); +#endif /* Convert the high double to integer. */ orig_xh = xh; @@ -103,8 +114,16 @@ __rintl (long double x) if (orig_xh < 0.0) xh = -__builtin_fabs (xh); +#ifdef USE_AS_NEARBYINTL + math_force_eval (xh); + math_force_eval (xl); +#else fesetround (save_round); +#endif } + else + /* Quiet signaling NaN arguments. */ + xh += xh; return ldbl_pack (xh, xl); } diff --git a/sysdeps/ieee754/ldbl-128ibm/s_roundevenl.c b/sysdeps/ieee754/ldbl-128ibm/s_roundevenl.c new file mode 100644 index 0000000000..84950e215f --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_roundevenl.c @@ -0,0 +1,70 @@ +/* Round to nearest integer value, rounding halfway cases to even. + ldbl-128ibm 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> + +long double +__roundevenl (long double x) +{ + double xh, xl, hi; + + ldbl_unpack (x, &xh, &xl); + + if (xh != 0 && isfinite (xh)) + { + hi = __roundeven (xh); + if (hi != xh) + { + /* The high part is not an integer; the low part only + affects the result if the high part is exactly half way + between two integers and the low part is nonzero in the + opposite direction to the rounding of the high part. */ + double diff = hi - xh; + if (fabs (diff) == 0.5) + { + if (xl < 0 && diff > 0) + xh = hi - 1; + else if (xl > 0 && diff < 0) + xh = hi + 1; + else + xh = hi; + } + else + xh = hi; + xl = 0; + } + else + { + /* The high part is a nonzero integer. Rounding the low + part to nearest, ties round to even, is always correct, + as a high part that is an odd integer together with a low + part with magnitude 0.5 is not a valid long double. */ + xl = __roundeven (xl); + xh = hi; + ldbl_canonicalize_int (&xh, &xl); + } + } + else + /* Quiet signaling NaN arguments. */ + xh += xh; + + return ldbl_pack (xh, xl); +} +weak_alias (__roundevenl, roundevenl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_roundl.c b/sysdeps/ieee754/ldbl-128ibm/s_roundl.c index 20813ed366..94a62dcd6c 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_roundl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_roundl.c @@ -1,6 +1,6 @@ /* Round to int long double floating-point values. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ when it's coded in C. */ #include <math.h> +#include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> #include <ieee754.h> @@ -38,47 +39,48 @@ __roundl (long double x) && __builtin_isless (__builtin_fabs (xh), __builtin_inf ()), 1)) { - double orig_xh; - - /* Long double arithmetic, including the canonicalisation below, - only works in round-to-nearest mode. */ - - /* Convert the high double to integer. */ - orig_xh = xh; - hi = ldbl_nearbyint (xh); - - /* Subtract integral high part from the value. */ - xh -= hi; - ldbl_canonicalize (&xh, &xl); - - /* Now convert the low double, adjusted for any remainder from the - high double. */ - lo = ldbl_nearbyint (xh); - - /* Adjust the result when the remainder is exactly 0.5. nearbyint - rounds values halfway between integers to the nearest even - integer. roundl must round away from zero. - Also correct cases where nearbyint returns an incorrect value - for LO. */ - xh -= lo; - ldbl_canonicalize (&xh, &xl); - if (xh == 0.5) + hi = __round (xh); + if (hi != xh) { - if (xl > 0.0 || (xl == 0.0 && orig_xh > 0.0)) - lo += 1.0; + /* The high part is not an integer; the low part only + affects the result if the high part is exactly half way + between two integers and the low part is nonzero with the + opposite sign. */ + if (fabs (hi - xh) == 0.5) + { + if (xh > 0 && xl < 0) + xh = hi - 1; + else if (xh < 0 && xl > 0) + xh = hi + 1; + else + xh = hi; + } + else + xh = hi; + xl = 0; } - else if (-xh == 0.5) + else { - if (xl < 0.0 || (xl == 0.0 && orig_xh < 0.0)) - lo -= 1.0; + /* The high part is a nonzero integer. */ + lo = __round (xl); + if (fabs (lo - xl) == 0.5) + { + if (xh > 0 && xl < 0) + xl = lo + 1; + else if (xh < 0 && lo > 0) + xl = lo - 1; + else + xl = lo; + } + else + xl = lo; + xh = hi; + ldbl_canonicalize_int (&xh, &xl); } - - /* Ensure the final value is canonical. In certain cases, - rounding causes hi,lo calculated so far to be non-canonical. */ - xh = hi; - xl = lo; - ldbl_canonicalize (&xh, &xl); } + else + /* Quiet signaling NaN arguments. */ + xh += xh; return ldbl_pack (xh, xl); } diff --git a/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl.c b/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl.c new file mode 100644 index 0000000000..bb07a3533a --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl.c @@ -0,0 +1,4 @@ +#define SIG 0 +#define FUNC __setpayloadl +#include <s_setpayloadl_main.c> +weak_alias (__setpayloadl, setpayloadl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl_main.c b/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl_main.c new file mode 100644 index 0000000000..e5b49d03a2 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_setpayloadl_main.c @@ -0,0 +1,60 @@ +/* Set NaN payload. ldbl-128ibm 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 <nan-high-order-bit.h> +#include <stdint.h> + +#define SET_HIGH_BIT (HIGH_ORDER_BIT_IS_SET_FOR_SNAN ? SIG : !SIG) +#define BIAS 0x3ff +#define PAYLOAD_DIG 51 +#define EXPLICIT_MANT_DIG 52 + +int +FUNC (long double *x, long double payload) +{ + double hi, lo; + uint64_t hx, lx; + + ldbl_unpack (payload, &hi, &lo); + EXTRACT_WORDS64 (hx, hi); + EXTRACT_WORDS64 (lx, lo); + int exponent = hx >> EXPLICIT_MANT_DIG; + /* Test if argument is (a) negative or too large; (b) too small, + except for 0 when allowed; (c) not an integer. All valid + arguments have the low part zero. */ + if ((lx & 0x7fffffffffffffffULL) != 0 + || exponent >= BIAS + PAYLOAD_DIG + || (exponent < BIAS && !(SET_HIGH_BIT && hx == 0)) + || (hx & ((1ULL << (BIAS + EXPLICIT_MANT_DIG - exponent)) - 1)) != 0) + { + *x = 0.0L; + return 1; + } + if (hx != 0) + { + hx &= (1ULL << EXPLICIT_MANT_DIG) - 1; + hx |= 1ULL << EXPLICIT_MANT_DIG; + hx >>= BIAS + EXPLICIT_MANT_DIG - exponent; + } + hx |= 0x7ff0000000000000ULL | (SET_HIGH_BIT ? 0x8000000000000ULL : 0); + INSERT_WORDS64 (hi, hx); + *x = ldbl_pack (hi, 0.0); + return 0; +} diff --git a/sysdeps/ieee754/ldbl-128ibm/s_setpayloadsigl.c b/sysdeps/ieee754/ldbl-128ibm/s_setpayloadsigl.c new file mode 100644 index 0000000000..4e920360d4 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_setpayloadsigl.c @@ -0,0 +1,4 @@ +#define SIG 1 +#define FUNC __setpayloadsigl +#include <s_setpayloadl_main.c> +weak_alias (__setpayloadsigl, setpayloadsigl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_signbitl.c b/sysdeps/ieee754/ldbl-128ibm/s_signbitl.c index b4e8256329..2f7eb62ee8 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_signbitl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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. diff --git a/sysdeps/ieee754/ldbl-128ibm/s_sincosl.c b/sysdeps/ieee754/ldbl-128ibm/s_sincosl.c index fae4020a7b..ca4f9dff2f 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_sincosl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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>. diff --git a/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c b/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c index e6457a1c1c..3504862402 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_tanhl.c @@ -41,6 +41,7 @@ static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $"; #include <float.h> #include <math.h> #include <math_private.h> +#include <math-underflow.h> #include <math_ldbl_opt.h> static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L; diff --git a/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c b/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c new file mode 100644 index 0000000000..9f20e01adc --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c @@ -0,0 +1,63 @@ +/* Total order operation. ldbl-128ibm 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 <nan-high-order-bit.h> +#include <stdint.h> + +int +__totalorderl (long double x, long double y) +{ + double xhi, xlo, yhi, ylo; + int64_t hx, hy, lx, ly; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error not implemented +#endif + uint64_t hx_sign = hx >> 63; + uint64_t hy_sign = hy >> 63; + int64_t hx_adj = hx ^ (hx_sign >> 1); + int64_t hy_adj = hy ^ (hy_sign >> 1); + if (hx_adj < hy_adj) + return 1; + else if (hx_adj > hy_adj) + return 0; + + /* The high doubles are identical. If they are NaNs or both the low + parts are zero, the low parts are not significant (and if they + are infinities, both the low parts must be zero). */ + if ((hx & 0x7fffffffffffffffULL) >= 0x7ff0000000000000ULL) + return 1; + EXTRACT_WORDS64 (lx, xlo); + EXTRACT_WORDS64 (ly, ylo); + if (((lx | ly) & 0x7fffffffffffffffULL) == 0) + return 1; + + /* Otherwise compare the low parts. */ + uint64_t lx_sign = lx >> 63; + uint64_t ly_sign = ly >> 63; + lx ^= lx_sign >> 1; + ly ^= ly_sign >> 1; + return lx <= ly; +} +weak_alias (__totalorderl, totalorderl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c b/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c new file mode 100644 index 0000000000..d8027ffbb0 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_totalordermagl.c @@ -0,0 +1,65 @@ +/* Total order operation on absolute values. ldbl-128ibm 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 <nan-high-order-bit.h> +#include <stdint.h> + +int +__totalordermagl (long double x, long double y) +{ + double xhi, xlo, yhi, ylo; + int64_t hx, hy, lx, ly; + + ldbl_unpack (x, &xhi, &xlo); + EXTRACT_WORDS64 (hx, xhi); + ldbl_unpack (y, &yhi, &ylo); + EXTRACT_WORDS64 (hy, yhi); +#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN +# error not implemented +#endif + uint64_t x_sign = hx & 0x8000000000000000ULL; + uint64_t y_sign = hy & 0x8000000000000000ULL; + hx ^= x_sign; + hy ^= y_sign; + if (hx < hy) + return 1; + else if (hx > hy) + return 0; + + /* The high doubles are identical. If they are NaNs or both the low + parts are zero, the low parts are not significant (and if they + are infinities, both the low parts must be zero). */ + if (hx >= 0x7ff0000000000000ULL) + return 1; + EXTRACT_WORDS64 (lx, xlo); + EXTRACT_WORDS64 (ly, ylo); + if (((lx | ly) & 0x7fffffffffffffffULL) == 0) + return 1; + lx ^= x_sign; + ly ^= y_sign; + + /* Otherwise compare the low parts. */ + uint64_t lx_sign = lx >> 63; + uint64_t ly_sign = ly >> 63; + lx ^= lx_sign >> 1; + ly ^= ly_sign >> 1; + return lx <= ly; +} +weak_alias (__totalordermagl, totalordermagl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_truncl.c b/sysdeps/ieee754/ldbl-128ibm/s_truncl.c index df58b64b53..a915a01ac6 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_truncl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_truncl.c @@ -1,6 +1,6 @@ /* Truncate (toward zero) long double floating-point values. IBM extended format long double version. - Copyright (C) 2006-2016 Free Software Foundation, Inc. + Copyright (C) 2006-2018 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 @@ -18,6 +18,7 @@ <http://www.gnu.org/licenses/>. */ #include <math.h> +#include <math_private.h> #include <math_ldbl_opt.h> #include <float.h> #include <ieee754.h> @@ -35,51 +36,26 @@ __truncl (long double x) && __builtin_isless (__builtin_fabs (xh), __builtin_inf ()), 1)) { - double orig_xh; - - /* Long double arithmetic, including the canonicalisation below, - only works in round-to-nearest mode. */ - - /* Convert the high double to integer. */ - orig_xh = xh; - hi = ldbl_nearbyint (xh); - - /* Subtract integral high part from the value. */ - xh -= hi; - ldbl_canonicalize (&xh, &xl); - - /* Now convert the low double, adjusted for any remainder from the - high double. */ - lo = ldbl_nearbyint (xh); - - /* Adjust the result when the remainder is non-zero. nearbyint - rounds values to the nearest integer, and values halfway - between integers to the nearest even integer. floorl must - round towards -Inf. */ - xh -= lo; - ldbl_canonicalize (&xh, &xl); - - if (orig_xh < 0.0) + hi = __trunc (xh); + if (hi != xh) { - if (xh > 0.0 || (xh == 0.0 && xl > 0.0)) - lo += 1.0; + /* The high part is not an integer; the low part does not + affect the result. */ + xh = hi; + xl = 0; } else { - if (xh < 0.0 || (xh == 0.0 && xl < 0.0)) - lo -= 1.0; + /* The high part is a nonzero integer. */ + lo = xh > 0 ? __floor (xl) : __ceil (xl); + xh = hi; + xl = lo; + ldbl_canonicalize_int (&xh, &xl); } - - /* Ensure the final value is canonical. In certain cases, - rounding causes hi,lo calculated so far to be non-canonical. */ - xh = hi; - xl = lo; - ldbl_canonicalize (&xh, &xl); - - /* Ensure we return -0 rather than +0 when appropriate. */ - if (orig_xh < 0.0) - xh = -__builtin_fabs (xh); } + else + /* Quiet signaling NaN arguments. */ + xh += xh; return ldbl_pack (xh, xl); } diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c b/sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c new file mode 100644 index 0000000000..2176aa0cdd --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_ufromfpl.c @@ -0,0 +1,5 @@ +#define UNSIGNED 1 +#define INEXACT 0 +#define FUNC __ufromfpl +#include <s_fromfpl_main.c> +weak_alias (__ufromfpl, ufromfpl) diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c b/sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c new file mode 100644 index 0000000000..2901151312 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/s_ufromfpxl.c @@ -0,0 +1,5 @@ +#define UNSIGNED 1 +#define INEXACT 1 +#define FUNC __ufromfpxl +#include <s_fromfpl_main.c> +weak_alias (__ufromfpxl, ufromfpxl) diff --git a/sysdeps/ieee754/ldbl-128ibm/strtold_l.c b/sysdeps/ieee754/ldbl-128ibm/strtold_l.c index a8181740a8..862fd533be 100644 --- a/sysdeps/ieee754/ldbl-128ibm/strtold_l.c +++ b/sysdeps/ieee754/ldbl-128ibm/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 @@ -18,7 +18,6 @@ #include <math.h> #include <stdlib.h> #include <wchar.h> -#include <xlocale.h> /* The actual implementation for all floating point sizes is in strtod.c. These macros tell it to produce the `long double' version, `strtold'. */ @@ -26,13 +25,13 @@ #define FLOAT long double #define FLT LDBL #ifdef USE_WIDE_CHAR -extern long double ____new_wcstold_l (const wchar_t *, wchar_t **, __locale_t); +extern long double ____new_wcstold_l (const wchar_t *, wchar_t **, locale_t); # define STRTOF __new_wcstold_l # define __STRTOF ____new_wcstold_l # define ____STRTOF_INTERNAL ____wcstold_l_internal # define STRTOF_NAN __wcstold_nan #else -extern long double ____new_strtold_l (const char *, char **, __locale_t); +extern long double ____new_strtold_l (const char *, char **, locale_t); # define STRTOF __new_strtold_l # define __STRTOF ____new_strtold_l # define ____STRTOF_INTERNAL ____strtold_l_internal diff --git a/sysdeps/ieee754/ldbl-128ibm/t_expl.h b/sysdeps/ieee754/ldbl-128ibm/t_expl.h new file mode 100644 index 0000000000..ca2481caa1 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/t_expl.h @@ -0,0 +1,970 @@ +/* Accurate table for expl(). + 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/>. */ + +/* __expl_table basically consists of four tables, T_EXPL_ARG{1,2} and + T_EXPL_RES{1,2}. All tables use positive and negative indexes, the 0 points + are marked by T_EXPL_* defines. + For ARG1 and RES1 tables lets B be 89 and S 256.0, for ARG2 and RES2 B is 65 + and S 32768.0. + These table have the property that, for all integers -B <= i <= B + expl(__expl_table[T_EXPL_ARGN+2*i]+__expl_table[T_EXPL_ARGN+2*i+1]+r) == + __expl_table[T_EXPL_RESN+i], __expl_table[T_EXPL_RESN+i] is some exact number + with the low 58 bits of the mantissa 0, + __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 */ +#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 */ + + -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 */ +#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 */ + + 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 */ +#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 */ + + 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 */ +#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 */ +}; diff --git a/sysdeps/ieee754/ldbl-128ibm/t_sincosl.c b/sysdeps/ieee754/ldbl-128ibm/t_sincosl.c index 737c7c73fa..daeba17942 100644 --- a/sysdeps/ieee754/ldbl-128ibm/t_sincosl.c +++ b/sysdeps/ieee754/ldbl-128ibm/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> diff --git a/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c b/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c new file mode 100644 index 0000000000..a2571649ec --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c @@ -0,0 +1,230 @@ +/* Test iscanonical and canonicalizel for ldbl-128ibm. + 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_ldbl.h> +#include <stdbool.h> +#include <stdio.h> + +struct test +{ + double hi, lo; + bool canonical; +}; + +static const struct test tests[] = + { + { __builtin_nan (""), 0.0, true }, + { __builtin_nan (""), DBL_MAX, true }, + { __builtin_nan (""), __builtin_inf (), true }, + { __builtin_nan (""), __builtin_nan (""), true }, + { __builtin_nan (""), __builtin_nans (""), true }, + { __builtin_nans (""), 0.0, true }, + { __builtin_nans (""), DBL_MAX, true }, + { __builtin_nans (""), __builtin_inf (), true }, + { __builtin_nans (""), __builtin_nan (""), true }, + { __builtin_nans (""), __builtin_nans (""), true }, + { __builtin_inf (), 0.0, true }, + { __builtin_inf (), -0.0, true }, + { -__builtin_inf (), 0.0, true }, + { -__builtin_inf (), -0.0, true }, + { __builtin_inf (), DBL_TRUE_MIN, false }, + { __builtin_inf (), -DBL_TRUE_MIN, false }, + { -__builtin_inf (), DBL_TRUE_MIN, false }, + { -__builtin_inf (), -DBL_TRUE_MIN, false }, + { __builtin_inf (), DBL_MIN, false }, + { __builtin_inf (), -DBL_MIN, false }, + { -__builtin_inf (), DBL_MIN, false }, + { -__builtin_inf (), -DBL_MIN, false }, + { __builtin_inf (), __builtin_inf (), false }, + { __builtin_inf (), -__builtin_inf (), false }, + { -__builtin_inf (), __builtin_inf (), false }, + { -__builtin_inf (), -__builtin_inf (), false }, + { __builtin_inf (), __builtin_nan (""), false }, + { __builtin_inf (), -__builtin_nan (""), false }, + { -__builtin_inf (), __builtin_nan (""), false }, + { -__builtin_inf (), -__builtin_nan (""), false }, + { 0.0, 0.0, true }, + { 0.0, -0.0, true }, + { -0.0, 0.0, true }, + { -0.0, -0.0, true }, + { 0.0, DBL_TRUE_MIN, false }, + { 0.0, -DBL_TRUE_MIN, false }, + { -0.0, DBL_TRUE_MIN, false }, + { -0.0, -DBL_TRUE_MIN, false }, + { 0.0, DBL_MAX, false }, + { 0.0, -DBL_MAX, false }, + { -0.0, DBL_MAX, false }, + { -0.0, -DBL_MAX, false }, + { 0.0, __builtin_inf (), false }, + { 0.0, -__builtin_inf (), false }, + { -0.0, __builtin_inf (), false }, + { -0.0, -__builtin_inf (), false }, + { 0.0, __builtin_nan (""), false }, + { 0.0, -__builtin_nan (""), false }, + { -0.0, __builtin_nan (""), false }, + { -0.0, -__builtin_nan (""), false }, + { 1.0, 0.0, true }, + { 1.0, -0.0, true }, + { -1.0, 0.0, true }, + { -1.0, -0.0, true }, + { 1.0, DBL_TRUE_MIN, true }, + { 1.0, -DBL_TRUE_MIN, true }, + { -1.0, DBL_TRUE_MIN, true }, + { -1.0, -DBL_TRUE_MIN, true }, + { 1.0, DBL_MAX, false }, + { 1.0, -DBL_MAX, false }, + { -1.0, DBL_MAX, false }, + { -1.0, -DBL_MAX, false }, + { 1.0, __builtin_inf (), false }, + { 1.0, -__builtin_inf (), false }, + { -1.0, __builtin_inf (), false }, + { -1.0, -__builtin_inf (), false }, + { 1.0, __builtin_nan (""), false }, + { 1.0, -__builtin_nan (""), false }, + { -1.0, __builtin_nan (""), false }, + { -1.0, -__builtin_nan (""), false }, + { 0x1p1023, 0x1.1p969, true }, + { 0x1p1023, -0x1.1p969, true }, + { -0x1p1023, 0x1.1p969, true }, + { -0x1p1023, -0x1.1p969, true }, + { 0x1p1023, 0x1.1p970, false }, + { 0x1p1023, -0x1.1p970, false }, + { -0x1p1023, 0x1.1p970, false }, + { -0x1p1023, -0x1.1p970, false }, + { 0x1p1023, 0x1p970, true }, + { 0x1p1023, -0x1p970, true }, + { -0x1p1023, 0x1p970, true }, + { -0x1p1023, -0x1p970, true }, + { 0x1.0000000000001p1023, 0x1p970, false }, + { 0x1.0000000000001p1023, -0x1p970, false }, + { -0x1.0000000000001p1023, 0x1p970, false }, + { -0x1.0000000000001p1023, -0x1p970, false }, + { 0x1p-969, 0x1.1p-1023, true }, + { 0x1p-969, -0x1.1p-1023, true }, + { -0x1p-969, 0x1.1p-1023, true }, + { -0x1p-969, -0x1.1p-1023, true }, + { 0x1p-969, 0x1.1p-1022, false }, + { 0x1p-969, -0x1.1p-1022, false }, + { -0x1p-969, 0x1.1p-1022, false }, + { -0x1p-969, -0x1.1p-1022, false }, + { 0x1p-969, 0x1p-1022, true }, + { 0x1p-969, -0x1p-1022, true }, + { -0x1p-969, 0x1p-1022, true }, + { -0x1p-969, -0x1p-1022, true }, + { 0x1.0000000000001p-969, 0x1p-1022, false }, + { 0x1.0000000000001p-969, -0x1p-1022, false }, + { -0x1.0000000000001p-969, 0x1p-1022, false }, + { -0x1.0000000000001p-969, -0x1p-1022, false }, + { 0x1p-970, 0x1.1p-1024, true }, + { 0x1p-970, -0x1.1p-1024, true }, + { -0x1p-970, 0x1.1p-1024, true }, + { -0x1p-970, -0x1.1p-1024, true }, + { 0x1p-970, 0x1.1p-1023, false }, + { 0x1p-970, -0x1.1p-1023, false }, + { -0x1p-970, 0x1.1p-1023, false }, + { -0x1p-970, -0x1.1p-1023, false }, + { 0x1p-970, 0x1p-1023, true }, + { 0x1p-970, -0x1p-1023, true }, + { -0x1p-970, 0x1p-1023, true }, + { -0x1p-970, -0x1p-1023, true }, + { 0x1.0000000000001p-970, 0x1p-1023, false }, + { 0x1.0000000000001p-970, -0x1p-1023, false }, + { -0x1.0000000000001p-970, 0x1p-1023, false }, + { -0x1.0000000000001p-970, -0x1p-1023, false }, + { 0x1p-1000, 0x1.1p-1054, true }, + { 0x1p-1000, -0x1.1p-1054, true }, + { -0x1p-1000, 0x1.1p-1054, true }, + { -0x1p-1000, -0x1.1p-1054, true }, + { 0x1p-1000, 0x1.1p-1053, false }, + { 0x1p-1000, -0x1.1p-1053, false }, + { -0x1p-1000, 0x1.1p-1053, false }, + { -0x1p-1000, -0x1.1p-1053, false }, + { 0x1p-1000, 0x1p-1053, true }, + { 0x1p-1000, -0x1p-1053, true }, + { -0x1p-1000, 0x1p-1053, true }, + { -0x1p-1000, -0x1p-1053, true }, + { 0x1.0000000000001p-1000, 0x1p-1053, false }, + { 0x1.0000000000001p-1000, -0x1p-1053, false }, + { -0x1.0000000000001p-1000, 0x1p-1053, false }, + { -0x1.0000000000001p-1000, -0x1p-1053, false }, + { 0x1p-1021, 0x1p-1074, true }, + { 0x1p-1021, -0x1p-1074, true }, + { -0x1p-1021, 0x1p-1074, true }, + { -0x1p-1021, -0x1p-1074, true }, + { 0x1.0000000000001p-1021, 0x1p-1074, false }, + { 0x1.0000000000001p-1021, -0x1p-1074, false }, + { -0x1.0000000000001p-1021, 0x1p-1074, false }, + { -0x1.0000000000001p-1021, -0x1p-1074, false }, + { 0x1p-1022, 0x1p-1074, false }, + { 0x1p-1022, -0x1p-1074, false }, + { -0x1p-1022, 0x1p-1074, false }, + { -0x1p-1022, -0x1p-1074, false }, + }; + +static int +do_test (void) +{ + int result = 0; + + for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++) + { + long double ld = ldbl_pack (tests[i].hi, tests[i].lo); + bool canonical = iscanonical (ld); + if (canonical == tests[i].canonical) + { + printf ("PASS: iscanonical test %zu\n", i); + long double ldc = 12345.0L; + bool canonicalize_ret = canonicalizel (&ldc, &ld); + if (canonicalize_ret == !canonical) + { + printf ("PASS: canonicalizel test %zu\n", i); + bool canon_ok; + if (!canonical) + canon_ok = ldc == 12345.0L; + else if (isnan (ld)) + canon_ok = isnan (ldc) && !issignaling (ldc); + else + canon_ok = ldc == ld; + if (canon_ok) + printf ("PASS: canonicalized value test %zu\n", i); + else + { + printf ("FAIL: canonicalized value test %zu\n", i); + result = 1; + } + } + else + { + printf ("FAIL: canonicalizel test %zu\n", i); + result = 1; + } + } + else + { + printf ("FAIL: iscanonical test %zu\n", i); + result = 1; + } + } + + return result; +} + +#define TEST_FUNCTION do_test () +#include "../test-skeleton.c" diff --git a/sysdeps/ieee754/ldbl-128ibm/w_log1pl.c b/sysdeps/ieee754/ldbl-128ibm/test-fmodl-ldbl-128ibm.c index 969fadc205..c717616e3c 100644 --- a/sysdeps/ieee754/ldbl-128ibm/w_log1pl.c +++ b/sysdeps/ieee754/ldbl-128ibm/test-fmodl-ldbl-128ibm.c @@ -1,5 +1,5 @@ -/* Wrapper for __log1pl that handles setting errno. - Copyright (C) 2015-2016 Free Software Foundation, Inc. +/* Test for ldbl-128ibm fmodl handling of equal values (bug 19602). + 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 @@ -16,8 +16,6 @@ License along with the GNU C Library; if not, see <http://www.gnu.org/licenses/>. */ -#include <math_ldbl_opt.h> -#undef weak_alias -#define weak_alias(n,a) -#include <math/w_log1pl.c> -long_double_symbol (libm, __w_log1pl, log1pl); +#define FUNC fmodl +#define SETUP +#include "test-fmodrem-ldbl-128ibm.c" diff --git a/sysdeps/ieee754/ldbl-128ibm/test-fmodrem-ldbl-128ibm.c b/sysdeps/ieee754/ldbl-128ibm/test-fmodrem-ldbl-128ibm.c new file mode 100644 index 0000000000..ce959faf90 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/test-fmodrem-ldbl-128ibm.c @@ -0,0 +1,84 @@ +/* Test for ldbl-128ibm fmodl etc. handling of equal values. + 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 <fenv.h> +#include <float.h> +#include <math.h> +#include <stdio.h> + +/* FUNC is defined to be the name of the function to test. */ +#define STRX(x) #x +#define STR(x) STRX (x) +#define SFUNC STR (FUNC) + +union u +{ + long double ld; + double d[2]; +}; + +volatile union u p1 = { .d = { DBL_MIN, 0.0 } }; +volatile union u p2 = { .d = { DBL_MIN, -0.0 } }; +volatile union u m1 = { .d = { -DBL_MIN, 0.0 } }; +volatile union u m2 = { .d = { -DBL_MIN, -0.0 } }; + +static int +test_func (const char *s, long double x, long double y, long double expected) +{ + volatile long double r; + r = FUNC (x, y); + if (r != expected || copysignl (1.0, r) != copysignl (1.0, expected)) + { + printf ("FAIL: " SFUNC " (%s)\n", s); + return 1; + } + else + { + printf ("PASS: " SFUNC " (%s)\n", s); + return 0; + } +} + +#define TEST_FUNC(a, b, e) test_func (#a ", " #b, a, b, e) + +static int +do_test (void) +{ + int result = 0; + SETUP; + result |= TEST_FUNC (p1.ld, p1.ld, 0.0L); + result |= TEST_FUNC (p1.ld, p2.ld, 0.0L); + result |= TEST_FUNC (p1.ld, m1.ld, 0.0L); + result |= TEST_FUNC (p1.ld, m2.ld, 0.0L); + result |= TEST_FUNC (p2.ld, p1.ld, 0.0L); + result |= TEST_FUNC (p2.ld, p2.ld, 0.0L); + result |= TEST_FUNC (p2.ld, m1.ld, 0.0L); + result |= TEST_FUNC (p2.ld, m2.ld, 0.0L); + result |= TEST_FUNC (m1.ld, p1.ld, -0.0L); + result |= TEST_FUNC (m1.ld, p2.ld, -0.0L); + result |= TEST_FUNC (m1.ld, m1.ld, -0.0L); + result |= TEST_FUNC (m1.ld, m2.ld, -0.0L); + result |= TEST_FUNC (m2.ld, p1.ld, -0.0L); + result |= TEST_FUNC (m2.ld, p2.ld, -0.0L); + result |= TEST_FUNC (m2.ld, m1.ld, -0.0L); + result |= TEST_FUNC (m2.ld, m2.ld, -0.0L); + return result; +} + +#define TEST_FUNCTION do_test () +#include "../../../test-skeleton.c" diff --git a/sysdeps/ieee754/ldbl-128ibm/w_scalblnl.c b/sysdeps/ieee754/ldbl-128ibm/test-remainderl-ldbl-128ibm.c index 7e73c9abf8..829cf48c89 100644 --- a/sysdeps/ieee754/ldbl-128ibm/w_scalblnl.c +++ b/sysdeps/ieee754/ldbl-128ibm/test-remainderl-ldbl-128ibm.c @@ -1,5 +1,5 @@ -/* Wrapper for __scalblnl handles setting errno. - Copyright (C) 2014-2016 Free Software Foundation, Inc. +/* Test for ldbl-128ibm remainderl handling of equal values (bug 19677). + 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 @@ -16,8 +16,6 @@ License along with the GNU C Library; if not, see <http://www.gnu.org/licenses/>. */ -#include <math_ldbl_opt.h> -#undef weak_alias -#define weak_alias(name, alias) -#include <math/w_scalblnl.c> -long_double_symbol (libm, __w_scalblnl, scalblnl); +#define FUNC remainderl +#define SETUP fesetround (FE_DOWNWARD) +#include "test-fmodrem-ldbl-128ibm.c" diff --git a/sysdeps/ieee754/ldbl-128ibm/test-remquol-ldbl-128ibm.c b/sysdeps/ieee754/ldbl-128ibm/test-remquol-ldbl-128ibm.c new file mode 100644 index 0000000000..446e84146d --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/test-remquol-ldbl-128ibm.c @@ -0,0 +1,30 @@ +/* Test for ldbl-128ibm remquol handling of equal values (bug 19677). + 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> + +static long double +wrap_remquol (long double x, long double y) +{ + int quo; + return remquol (x, y, &quo); +} + +#define FUNC wrap_remquol +#define SETUP fesetround (FE_DOWNWARD) +#include "test-fmodrem-ldbl-128ibm.c" diff --git a/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c b/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c new file mode 100644 index 0000000000..6412e1781d --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c @@ -0,0 +1,73 @@ +/* Test totalorderl and totalordermagl for ldbl-128ibm. + 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_ldbl.h> +#include <stdbool.h> +#include <stdio.h> + +struct test +{ + double hi, lo1, lo2; +}; + +static const struct test tests[] = + { + { __builtin_nan (""), 1, __builtin_nans ("") }, + { -__builtin_nan (""), 1, __builtin_nans ("") }, + { __builtin_nans (""), 1, __builtin_nan ("") }, + { -__builtin_nans (""), 1, __builtin_nan ("") }, + { __builtin_inf (), 0.0, -0.0 }, + { -__builtin_inf (), 0.0, -0.0 }, + { 1.5, 0.0, -0.0 }, + }; + +static int +do_test (void) +{ + int result = 0; + + for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++) + { + long double ldx = ldbl_pack (tests[i].hi, tests[i].lo1); + long double ldy = ldbl_pack (tests[i].hi, tests[i].lo2); + bool to1 = totalorderl (ldx, ldy); + bool to2 = totalorderl (ldy, ldx); + if (to1 && to2) + printf ("PASS: test %zu\n", i); + else + { + printf ("FAIL: test %zu\n", i); + result = 1; + } + to1 = totalordermagl (ldx, ldy); + to2 = totalordermagl (ldy, ldx); + if (to1 && to2) + printf ("PASS: test %zu (totalordermagl)\n", i); + else + { + printf ("FAIL: test %zu (totalordermagl)\n", i); + result = 1; + } + } + + return result; +} + +#define TEST_FUNCTION do_test () +#include "../test-skeleton.c" diff --git a/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c b/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c index 14dc683619..1893c04dda 100644 --- a/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c +++ b/sysdeps/ieee754/ldbl-128ibm/tst-strtold-ldbl-128ibm.c @@ -1,5 +1,5 @@ /* Test for ldbl-128ibm strtold overflow to infinity (bug 14551). - 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 diff --git a/sysdeps/ieee754/ldbl-128ibm/w_expl.c b/sysdeps/ieee754/ldbl-128ibm/w_expl.c deleted file mode 100644 index c9d44b61dd..0000000000 --- a/sysdeps/ieee754/ldbl-128ibm/w_expl.c +++ /dev/null @@ -1,21 +0,0 @@ -#include <math.h> -#include <math_private.h> -#include <math_ldbl_opt.h> - -long double __expl(long double x) /* wrapper exp */ -{ - long double z; - z = __ieee754_expl(x); - if (_LIB_VERSION == _IEEE_) - return z; - if (isfinite(x)) - { - if (!isfinite (z)) - return __kernel_standard_l(x,x,206); /* exp overflow */ - else if (z == 0.0L) - return __kernel_standard_l(x,x,207); /* exp underflow */ - } - return z; -} -hidden_def (__expl) -long_double_symbol (libm, __expl, expl); diff --git a/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c b/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c index da2e929175..e299c48748 100644 --- a/sysdeps/ieee754/ldbl-128ibm/x2y2m1l.c +++ b/sysdeps/ieee754/ldbl-128ibm/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 @@ -18,7 +18,7 @@ #include <math.h> #include <math_private.h> -#include <float.h> +#include <mul_split.h> #include <stdlib.h> /* Calculate X + Y exactly and store the result in *HI + *LO. It is @@ -33,36 +33,6 @@ add_split (double *hi, double *lo, double x, double 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 (double *hi, double *lo, double x, double y) -{ -#ifdef __FP_FAST_FMA - /* Fast built-in fused multiply-add. */ - *hi = x * y; - *lo = __builtin_fma (x, y, -*hi); -#elif defined FP_FAST_FMA - /* Fast library fused multiply-add, compiler before GCC 4.6. */ - *hi = x * y; - *lo = __fma (x, y, -*hi); -#else - /* Apply Dekker's algorithm. */ - *hi = x * y; -# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1) - double x1 = x * C; - double y1 = y * C; -# undef C - x1 = (x - x1) + x1; - y1 = (y - y1) + y1; - double x2 = x - x1; - 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. */ |