diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-128')
49 files changed, 703 insertions, 339 deletions
diff --git a/sysdeps/ieee754/ldbl-128/e_exp10l.c b/sysdeps/ieee754/ldbl-128/e_exp10l.c index 503c1de3e8..3c5096379c 100644 --- a/sysdeps/ieee754/ldbl-128/e_exp10l.c +++ b/sysdeps/ieee754/ldbl-128/e_exp10l.c @@ -1,4 +1,4 @@ -/* Copyright (C) 2012 Free Software Foundation, Inc. +/* Copyright (C) 2012-2014 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or diff --git a/sysdeps/ieee754/ldbl-128/e_expl.c b/sysdeps/ieee754/ldbl-128/e_expl.c index 1559c2cecd..8259758cff 100644 --- a/sysdeps/ieee754/ldbl-128/e_expl.c +++ b/sysdeps/ieee754/ldbl-128/e_expl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point e^x. - Copyright (C) 1999, 2011 Free Software Foundation, Inc. + Copyright (C) 1999-2014 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 @@ -117,7 +117,7 @@ static const long double C[] = { #define TWO15 C[11] 32768.0L, -/* Chebyshev polynom coeficients for (exp(x)-1)/x */ +/* Chebyshev polynom coefficients for (exp(x)-1)/x */ #define P1 C[12] #define P2 C[13] #define P3 C[14] @@ -215,7 +215,7 @@ __ieee754_expl (long double x) ex3_u.d = (result - ex2_u.d) - x22 * ex2_u.d; ex2_u.d = result; ex3_u.ieee.exponent += LDBL_MANT_DIG + 15 + IEEE854_LONG_DOUBLE_BIAS - - ex2_u.ieee.exponent; + - ex2_u.ieee.exponent; n_i = abs (ex3_u.d); n_i = (n_i + 1) / 2; fesetenv (&oldenv); diff --git a/sysdeps/ieee754/ldbl-128/e_gammal_r.c b/sysdeps/ieee754/ldbl-128/e_gammal_r.c index e5a471e296..ffa27bc2b7 100644 --- a/sysdeps/ieee754/ldbl-128/e_gammal_r.c +++ b/sysdeps/ieee754/ldbl-128/e_gammal_r.c @@ -1,5 +1,5 @@ /* Implementation of gamma function according to ISO C. - Copyright (C) 1997, 1999, 2002, 2004, 2011 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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. @@ -20,14 +20,108 @@ #include <math.h> #include <math_private.h> +#include <float.h> +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const long double gamma_coeff[] = + { + 0x1.5555555555555555555555555555p-4L, + -0xb.60b60b60b60b60b60b60b60b60b8p-12L, + 0x3.4034034034034034034034034034p-12L, + -0x2.7027027027027027027027027028p-12L, + 0x3.72a3c5631fe46ae1d4e700dca8f2p-12L, + -0x7.daac36664f1f207daac36664f1f4p-12L, + 0x1.a41a41a41a41a41a41a41a41a41ap-8L, + -0x7.90a1b2c3d4e5f708192a3b4c5d7p-8L, + 0x2.dfd2c703c0cfff430edfd2c703cp-4L, + -0x1.6476701181f39edbdb9ce625987dp+0L, + 0xd.672219167002d3a7a9c886459cp+0L, + -0x9.cd9292e6660d55b3f712eb9e07c8p+4L, + 0x8.911a740da740da740da740da741p+8L, + -0x8.d0cc570e255bf59ff6eec24b49p+12L, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 1775, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static long double +gammal_positive (long double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam)); + } + else if (x < 12.5L) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + long double n = __ceill (x - 1.5L); + long double x_adj = x - n; + long double eps; + long double prod = __gamma_productl (x_adj, 0, n, &eps); + return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam)) + * prod * (1.0L + eps)); + } + else + { + long double eps = 0; + long double x_eps = 0; + long double x_adj = x; + long double prod = 1; + if (x < 24.0L) + { + /* Adjust into the range for applying Stirling's + approximation. */ + long double n = __ceill (24.0L - x); + x_adj = x + n; + x_eps = (x - (x_adj - n)); + prod = __gamma_productl (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + long double exp_adj = -eps; + long double x_adj_int = __roundl (x_adj); + long double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + long double x_adj_mant = __frexpl (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2l) + { + x_adj_log2--; + x_adj_mant *= 2.0L; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + long double ret = (__ieee754_powl (x_adj_mant, x_adj) + * __ieee754_exp2l (x_adj_log2 * x_adj_frac) + * __ieee754_expl (-x_adj) + * __ieee754_sqrtl (2 * M_PIl / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logl (x); + long double bsum = gamma_coeff[NCOEFF - 1]; + long double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1l (exp_adj); + } +} long double __ieee754_gammal_r (long double x, int *signgamp) { - /* We don't have a real gamma implementation now. We'll use lgamma - and the exp function. But due to the required boundary - conditions we must check some values separately. */ int64_t hx; u_int64_t lx; @@ -51,8 +145,49 @@ __ieee754_gammal_r (long double x, int *signgamp) *signgamp = 0; return x - x; } + if ((hx & 0x7fff000000000000ULL) == 0x7fff000000000000ULL) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } - /* XXX FIXME. */ - return __ieee754_expl (__ieee754_lgammal_r (x, signgamp)); + if (x >= 1756.0L) + { + /* Overflow. */ + *signgamp = 0; + return LDBL_MAX * LDBL_MAX; + } + else if (x > 0.0L) + { + *signgamp = 0; + int exp2_adj; + long double ret = gammal_positive (x, &exp2_adj); + return __scalbnl (ret, exp2_adj); + } + else if (x >= -LDBL_EPSILON / 4.0L) + { + *signgamp = 0; + return 1.0f / x; + } + else + { + long double tx = __truncl (x); + *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1; + if (x <= -1775.0L) + /* Underflow. */ + return LDBL_MIN * LDBL_MIN; + long double frac = tx - x; + if (frac > 0.5L) + frac = 1.0L - frac; + long double sinpix = (frac <= 0.25L + ? __sinl (M_PIl * frac) + : __cosl (M_PIl * (0.5L - frac))); + int exp2_adj; + long double ret = M_PIl / (-x * sinpix + * gammal_positive (-x, &exp2_adj)); + return __scalbnl (ret, -exp2_adj); + } } strong_alias (__ieee754_gammal_r, __gammal_r_finite) diff --git a/sysdeps/ieee754/ldbl-128/e_hypotl.c b/sysdeps/ieee754/ldbl-128/e_hypotl.c index f5ab901e6a..01444cfb4e 100644 --- a/sysdeps/ieee754/ldbl-128/e_hypotl.c +++ b/sysdeps/ieee754/ldbl-128/e_hypotl.c @@ -89,6 +89,17 @@ __ieee754_hypotl(long double x, long double y) b *= t1; a *= t1; k -= 16382; + GET_LDOUBLE_MSW64 (ha, a); + GET_LDOUBLE_MSW64 (hb, b); + if (hb > ha) + { + t1 = a; + a = b; + b = t1; + j = ha; + ha = hb; + hb = j; + } } else { /* scale a and b by 2^9600 */ ha += 0x2580000000000000LL; /* a *= 2^9600 */ hb += 0x2580000000000000LL; /* b *= 2^9600 */ diff --git a/sysdeps/ieee754/ldbl-128/e_j0l.c b/sysdeps/ieee754/ldbl-128/e_j0l.c index 112a8f3f9c..108eff4435 100644 --- a/sysdeps/ieee754/ldbl-128/e_j0l.c +++ b/sysdeps/ieee754/ldbl-128/e_j0l.c @@ -93,6 +93,7 @@ #include <math.h> #include <math_private.h> +#include <float.h> /* 1 / sqrt(pi) */ static const long double ONEOSQPI = 5.6418958354775628694807945156077258584405E-1L; @@ -700,6 +701,28 @@ __ieee754_j0l (long double x) 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 / 2.0L) + { + z = -__cosl (xx + xx); + if ((s * c) < 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > 0x1p256L) + return ONEOSQPI * cc / __ieee754_sqrtl (xx); + xinv = 1.0L / xx; z = xinv * xinv; if (xinv <= 0.25) @@ -761,21 +784,6 @@ __ieee754_j0l (long double x) p = 1.0L + z * p; q = z * xinv * q; q = q - 0.125L * xinv; - /* 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; - z = -__cosl (xx + xx); - if ((s * c) < 0) - cc = z / ss; - else - ss = z / cc; z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx); return z; } @@ -809,6 +817,7 @@ static long double Y0_2D[NY0_2D + 1] = { /* 1.000000000000000000000000000000000000000E0 */ }; +static const long double U0 = -7.3804295108687225274343927948483016310862e-02L; /* Bessel function of the second kind, order zero. */ @@ -831,6 +840,8 @@ long double return -HUGE_VALL + x; } xx = fabsl (x); + if (xx <= 0x1p-57) + return U0 + TWOOPI * __ieee754_logl (x); if (xx <= 2.0L) { /* 0 <= x <= 2 */ @@ -840,6 +851,28 @@ long double 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 / 2.0L) + { + z = -__cosl (x + x); + if ((s * c) < 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > 0x1p256L) + return ONEOSQPI * ss / __ieee754_sqrtl (x); + xinv = 1.0L / xx; z = xinv * xinv; if (xinv <= 0.25) @@ -901,21 +934,6 @@ long double p = 1.0L + z * p; q = z * xinv * q; q = q - 0.125L * xinv; - /* 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; - z = -__cosl (x + x); - if ((s * c) < 0) - cc = z / ss; - else - ss = z / cc; z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (x); return z; } diff --git a/sysdeps/ieee754/ldbl-128/e_j1l.c b/sysdeps/ieee754/ldbl-128/e_j1l.c index 1f62bd0920..70a1c86fd2 100644 --- a/sysdeps/ieee754/ldbl-128/e_j1l.c +++ b/sysdeps/ieee754/ldbl-128/e_j1l.c @@ -97,6 +97,7 @@ #include <math.h> #include <math_private.h> +#include <float.h> /* 1 / sqrt(pi) */ static const long double ONEOSQPI = 5.6418958354775628694807945156077258584405E-1L; @@ -706,6 +707,32 @@ __ieee754_j1l (long double x) 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 / 2.0L) + { + z = __cosl (xx + xx); + if ((s * c) > 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > 0x1p256L) + { + z = ONEOSQPI * cc / __ieee754_sqrtl (xx); + if (x < 0) + z = -z; + return z; + } + xinv = 1.0L / xx; z = xinv * xinv; if (xinv <= 0.25) @@ -767,20 +794,6 @@ __ieee754_j1l (long double x) p = 1.0L + z * p; q = z * q; q = q * xinv + 0.375L * xinv; - /* 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; - z = __cosl (xx + xx); - if ((s * c) > 0) - cc = z / ss; - else - ss = z / cc; z = ONEOSQPI * (p * cc - q * ss) / __ieee754_sqrtl (xx); if (x < 0) z = -z; @@ -838,6 +851,8 @@ __ieee754_y1l (long double x) return -HUGE_VALL + x; } xx = fabsl (x); + if (xx <= 0x1p-114) + return -TWOOPI / x; if (xx <= 2.0L) { /* 0 <= x <= 2 */ @@ -848,6 +863,27 @@ __ieee754_y1l (long double x) 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 / 2.0L) + { + z = __cosl (xx + xx); + if ((s * c) > 0) + cc = z / ss; + else + ss = z / cc; + } + + if (xx > 0x1p256L) + return ONEOSQPI * ss / __ieee754_sqrtl (xx); + xinv = 1.0L / xx; z = xinv * xinv; if (xinv <= 0.25) @@ -909,20 +945,6 @@ __ieee754_y1l (long double x) p = 1.0L + z * p; q = z * q; q = q * xinv + 0.375L * xinv; - /* 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; - z = __cosl (xx + xx); - if ((s * c) > 0) - cc = z / ss; - else - ss = z / cc; z = ONEOSQPI * (p * ss + q * cc) / __ieee754_sqrtl (xx); return z; } diff --git a/sysdeps/ieee754/ldbl-128/e_jnl.c b/sysdeps/ieee754/ldbl-128/e_jnl.c index 70d5672fd9..c2a49235c3 100644 --- a/sysdeps/ieee754/ldbl-128/e_jnl.c +++ b/sysdeps/ieee754/ldbl-128/e_jnl.c @@ -316,7 +316,7 @@ __ieee754_ynl (int n, long double x) if (x <= 0.0L) { if (x == 0.0L) - return -HUGE_VALL + x; + return ((n < 0 && (n & 1) != 0) ? 1.0L : -1.0L) / 0.0L; if (se & 0x80000000) return zero / (zero * x); } diff --git a/sysdeps/ieee754/ldbl-128/e_lgammal_r.c b/sysdeps/ieee754/ldbl-128/e_lgammal_r.c index 2b44afb759..1961355a73 100644 --- a/sysdeps/ieee754/ldbl-128/e_lgammal_r.c +++ b/sysdeps/ieee754/ldbl-128/e_lgammal_r.c @@ -782,6 +782,8 @@ __ieee754_lgammal_r (long double x, int *signgamp) *signgamp = -1; else *signgamp = 1; + if (q < 0x1p-120L) + return -__logl (q); z = q - p; if (z > 0.5L) { @@ -789,8 +791,6 @@ __ieee754_lgammal_r (long double x, int *signgamp) z = p - q; } z = q * __sinl (PIL * z); - if (z == 0.0L) - return (*signgamp * huge * huge); w = __ieee754_lgammal_r (q, &i); z = __logl (PIL / z) - w; return (z); @@ -805,7 +805,9 @@ __ieee754_lgammal_r (long double x, int *signgamp) { case 0: /* log gamma (x + 1) = log(x) + log gamma(x) */ - if (x <= 0.125) + if (x < 0x1p-120L) + return -__logl (x); + else if (x <= 0.125) { p = x * neval (x, RN1, NRN1) / deval (x, RD1, NRD1); } diff --git a/sysdeps/ieee754/ldbl-128/e_logl.c b/sysdeps/ieee754/ldbl-128/e_logl.c index 395a76302a..3d1034dd61 100644 --- a/sysdeps/ieee754/ldbl-128/e_logl.c +++ b/sysdeps/ieee754/ldbl-128/e_logl.c @@ -212,9 +212,8 @@ __ieee754_logl(long double x) } /* Extract exponent and reduce domain to 0.703125 <= u < 1.40625 */ - e = (int) (m >> 16) - (int) 0x3ffe; - m &= 0xffff; - u.parts32.w0 = m | 0x3ffe0000; + u.value = __frexpl (x, &e); + m = u.parts32.w0 & 0xffff; m |= 0x10000; /* Find lookup table index k from high order bits of the significand. */ if (m < 0x16800) diff --git a/sysdeps/ieee754/ldbl-128/e_powl.c b/sysdeps/ieee754/ldbl-128/e_powl.c index 40fc314730..d131750718 100644 --- a/sysdeps/ieee754/ldbl-128/e_powl.c +++ b/sysdeps/ieee754/ldbl-128/e_powl.c @@ -149,7 +149,7 @@ __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 s2, s_h, s_l, t_h, t_l; + long double s2, s_h, s_l, t_h, t_l, ay; int32_t i, j, k, yisint, n; u_int32_t ix, iy; int32_t hx, hy; @@ -282,6 +282,10 @@ __ieee754_powl (long double x, long double y) return (hy > 0) ? huge * huge : tiny * tiny; } + ay = y > 0 ? y : -y; + if (ay < 0x1p-128) + y = y < 0 ? -0x1p-128 : 0x1p-128; + n = 0; /* take care subnormal number */ if (ix < 0x00010000) diff --git a/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c b/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c index b8833ba137..81c2dd8944 100644 --- a/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c +++ b/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c @@ -1,5 +1,5 @@ /* Quad-precision floating point argument reduction. - Copyright (C) 1999 Free Software Foundation, Inc. + Copyright (C) 1999-2014 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jj@ultra.linux.cz> @@ -21,176 +21,176 @@ #include <math_private.h> /* - * Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi + * Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi */ static const int32_t two_over_pi[] = { -0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62, -0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a, -0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129, -0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41, -0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8, -0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf, -0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5, -0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08, -0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3, -0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880, -0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b, -0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6, -0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2, -0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35, -0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30, -0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c, -0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4, -0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770, -0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7, -0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19, -0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522, -0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16, -0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6, -0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e, -0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48, -0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3, -0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf, -0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55, -0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612, -0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929, -0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec, -0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b, -0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c, -0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4, -0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb, -0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc, -0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c, -0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f, -0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5, -0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437, -0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b, -0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea, -0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad, -0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3, -0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3, -0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717, -0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f, -0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61, -0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db, -0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51, -0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0, -0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c, -0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6, -0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc, -0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed, -0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328, -0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d, -0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0, -0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b, -0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4, -0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3, -0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f, -0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad, -0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b, -0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4, -0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761, -0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31, -0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30, -0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262, -0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e, -0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1, -0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c, -0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4, -0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08, -0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196, -0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9, -0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4, -0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc, -0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c, -0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0, -0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c, -0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0, -0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac, -0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22, -0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893, -0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7, -0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5, -0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f, -0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4, -0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf, -0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b, -0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2, -0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138, -0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e, -0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569, -0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34, -0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9, -0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d, -0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f, -0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855, -0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569, -0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b, -0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe, -0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41, -0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49, -0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f, -0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110, -0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8, -0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365, -0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a, -0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270, -0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5, -0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616, -0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b, -0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0, -0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb, -0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a, -0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e, -0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa, -0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5, -0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0, -0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2, -0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886, -0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142, -0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba, -0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4, -0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708, -0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555, -0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3, -0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55, -0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58, -0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5, -0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c, -0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe, -0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b, -0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8, -0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005, -0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7, -0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50, -0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604, -0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643, -0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485, -0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d, -0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6, -0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2, -0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02, -0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3, -0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412, -0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274, -0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755, -0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849, -0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce, -0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5, -0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba, -0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6, -0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d, -0x7b7b89, 0x483d38, +0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62, +0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a, +0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129, +0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41, +0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8, +0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf, +0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5, +0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08, +0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3, +0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880, +0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b, +0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6, +0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2, +0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35, +0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30, +0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c, +0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4, +0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770, +0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7, +0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19, +0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522, +0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16, +0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6, +0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e, +0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48, +0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3, +0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf, +0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55, +0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612, +0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929, +0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec, +0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b, +0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c, +0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4, +0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb, +0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc, +0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c, +0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f, +0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5, +0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437, +0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b, +0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea, +0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad, +0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3, +0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3, +0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717, +0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f, +0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61, +0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db, +0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51, +0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0, +0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c, +0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6, +0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc, +0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed, +0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328, +0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d, +0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0, +0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b, +0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4, +0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3, +0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f, +0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad, +0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b, +0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4, +0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761, +0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31, +0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30, +0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262, +0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e, +0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1, +0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c, +0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4, +0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08, +0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196, +0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9, +0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4, +0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc, +0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c, +0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0, +0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c, +0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0, +0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac, +0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22, +0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893, +0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7, +0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5, +0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f, +0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4, +0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf, +0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b, +0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2, +0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138, +0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e, +0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569, +0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34, +0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9, +0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d, +0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f, +0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855, +0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569, +0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b, +0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe, +0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41, +0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49, +0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f, +0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110, +0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8, +0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365, +0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a, +0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270, +0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5, +0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616, +0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b, +0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0, +0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb, +0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a, +0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e, +0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa, +0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5, +0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0, +0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2, +0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886, +0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142, +0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba, +0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4, +0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708, +0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555, +0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3, +0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55, +0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58, +0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5, +0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c, +0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe, +0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b, +0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8, +0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005, +0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7, +0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50, +0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604, +0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643, +0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485, +0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d, +0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6, +0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2, +0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02, +0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3, +0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412, +0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274, +0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755, +0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849, +0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce, +0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5, +0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba, +0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6, +0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d, +0x7b7b89, 0x483d38, }; static const long double c[] = { -/* 93 bits of pi/2 */ +/* 113 bits of pi/2 */ #define PI_2_1 c[0] - 1.57079632679489661923132169155131424e+00L, /* 3fff921fb54442d18469898cc5100000 */ + 0x1.921fb54442d18469898cc51701b8p+0L, /* pi/2 - PI_2_1 */ #define PI_2_1t c[1] - 8.84372056613570112025531863263659260e-29L, /* 3fa1c06e0e68948127044533e63a0106 */ + 0x3.9a252049c1114cf98e804177d4c8p-116L, }; int32_t __ieee754_rem_pio2l(long double x, long double *y) @@ -212,8 +212,8 @@ int32_t __ieee754_rem_pio2l(long double x, long double *y) if (ix < 0x40002d97c7f3321dLL) /* |x| in <pi/4, 3pi/4) */ { if (hx > 0) - { - /* 113 + 93 bit PI is ok */ + { + /* 113 + 113 bit PI is ok */ z = x - PI_2_1; y[0] = z - PI_2_1t; y[1] = (z - y[0]) - PI_2_1t; @@ -221,7 +221,7 @@ int32_t __ieee754_rem_pio2l(long double x, long double *y) } else { - /* 113 + 93 bit PI is ok */ + /* 113 + 113 bit PI is ok */ z = x + PI_2_1; y[0] = z + PI_2_1t; y[1] = (z - y[0]) + PI_2_1t; diff --git a/sysdeps/ieee754/ldbl-128/gamma_productl.c b/sysdeps/ieee754/ldbl-128/gamma_productl.c new file mode 100644 index 0000000000..2c87649677 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/gamma_productl.c @@ -0,0 +1,75 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013-2014 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 <float.h> + +/* Calculate X * Y exactly and store the result in *HI + *LO. It is + given that the values are small enough that no overflow occurs and + large enough (or zero) that no underflow occurs. */ + +static inline void +mul_split (long double *hi, long double *lo, long double x, long double y) +{ +#ifdef __FP_FAST_FMAL + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fmal (x, y, -*hi); +#elif defined FP_FAST_FMAL + /* Fast library fused multiply-add, compiler before GCC 4.6. */ + *hi = x * y; + *lo = __fmal (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) + long double x1 = x * C; + long double y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + long double x2 = x - x1; + long double y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +long double +__gamma_productl (long double x, long double x_eps, int n, long double *eps) +{ + SET_RESTORE_ROUNDL (FE_TONEAREST); + long double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + long double lo; + mul_split (&ret, &lo, ret, x + i); + *eps += lo / ret; + } + return ret; +} diff --git a/sysdeps/ieee754/ldbl-128/ieee754.h b/sysdeps/ieee754/ldbl-128/ieee754.h index 4a7a207a44..d77b83592f 100644 --- a/sysdeps/ieee754/ldbl-128/ieee754.h +++ b/sysdeps/ieee754/ldbl-128/ieee754.h @@ -1,4 +1,4 @@ -/* Copyright (C) 1992, 1995, 1996, 1999 Free Software Foundation, Inc. +/* Copyright (C) 1992-2014 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or diff --git a/sysdeps/ieee754/ldbl-128/k_cosl.c b/sysdeps/ieee754/ldbl-128/k_cosl.c index aa447ec1db..0c76332bcb 100644 --- a/sysdeps/ieee754/ldbl-128/k_cosl.c +++ b/sysdeps/ieee754/ldbl-128/k_cosl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point cosine on <-pi/4,pi/4>. - Copyright (C) 1999 Free Software Foundation, Inc. + Copyright (C) 1999-2014 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-128/k_sincosl.c b/sysdeps/ieee754/ldbl-128/k_sincosl.c index 00a21c45d1..038718a29f 100644 --- a/sysdeps/ieee754/ldbl-128/k_sincosl.c +++ b/sysdeps/ieee754/ldbl-128/k_sincosl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>. - Copyright (C) 1999 Free Software Foundation, Inc. + Copyright (C) 1999-2014 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-128/k_sinl.c b/sysdeps/ieee754/ldbl-128/k_sinl.c index 1f0ca8c7f9..1c9c7c7174 100644 --- a/sysdeps/ieee754/ldbl-128/k_sinl.c +++ b/sysdeps/ieee754/ldbl-128/k_sinl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point sine on <-pi/4,pi/4>. - Copyright (C) 1999 Free Software Foundation, Inc. + Copyright (C) 1999-2014 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-128/k_tanl.c b/sysdeps/ieee754/ldbl-128/k_tanl.c index cb2e9473d9..140ce959a6 100644 --- a/sysdeps/ieee754/ldbl-128/k_tanl.c +++ b/sysdeps/ieee754/ldbl-128/k_tanl.c @@ -12,9 +12,9 @@ /* Long double expansions are Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> - and are incorporated herein by permission of the author. The author + and are incorporated herein by permission of the author. The author reserves the right to distribute this material elsewhere under different - copying permissions. These modifications are distributed here under + copying permissions. These modifications are distributed here under the following terms: This library is free software; you can redistribute it and/or diff --git a/sysdeps/ieee754/ldbl-128/ldbl2mpn.c b/sysdeps/ieee754/ldbl-128/ldbl2mpn.c index 8d39d2bd28..6d6ee2a555 100644 --- a/sysdeps/ieee754/ldbl-128/ldbl2mpn.c +++ b/sysdeps/ieee754/ldbl-128/ldbl2mpn.c @@ -1,5 +1,4 @@ -/* Copyright (C) 1995,1996,1997,1998,1999,2002,2003 - Free Software Foundation, Inc. +/* Copyright (C) 1995-2014 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 @@ -70,7 +69,7 @@ __mpn_extract_long_double (mp_ptr res_ptr, mp_size_t size, else { /* It is a denormal number, meaning it has no implicit leading - one bit, and its exponent is in fact the format minimum. */ + one bit, and its exponent is in fact the format minimum. */ int cnt; #if N == 2 diff --git a/sysdeps/ieee754/ldbl-128/mpn2ldbl.c b/sysdeps/ieee754/ldbl-128/mpn2ldbl.c index 8de4fda6cb..6d17567fa7 100644 --- a/sysdeps/ieee754/ldbl-128/mpn2ldbl.c +++ b/sysdeps/ieee754/ldbl-128/mpn2ldbl.c @@ -1,5 +1,4 @@ -/* Copyright (C) 1995,1996,1997,1998,1999,2002,2003 - Free Software Foundation, Inc. +/* Copyright (C) 1995-2014 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or diff --git a/sysdeps/ieee754/ldbl-128/printf_fphex.c b/sysdeps/ieee754/ldbl-128/printf_fphex.c index 50f6598cfd..5bd1615105 100644 --- a/sysdeps/ieee754/ldbl-128/printf_fphex.c +++ b/sysdeps/ieee754/ldbl-128/printf_fphex.c @@ -1,6 +1,6 @@ /* Print floating point number in hexadecimal notation according to ISO C99. - Copyright (C) 1997, 1998, 1999, 2000, 2005 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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 @@ -24,13 +24,15 @@ do { \ digits we use only the implicit digits for the number before \ the decimal point. */ \ unsigned long long int num0, num1; \ + union ieee854_long_double u; \ + u.d = fpnum.ldbl; \ \ assert (sizeof (long double) == 16); \ \ - num0 = (((unsigned long long int) fpnum.ldbl.ieee.mantissa0) << 32 \ - | fpnum.ldbl.ieee.mantissa1); \ - num1 = (((unsigned long long int) fpnum.ldbl.ieee.mantissa2) << 32 \ - | fpnum.ldbl.ieee.mantissa3); \ + num0 = (((unsigned long long int) u.ieee.mantissa0) << 32 \ + | u.ieee.mantissa1); \ + num1 = (((unsigned long long int) u.ieee.mantissa2) << 32 \ + | u.ieee.mantissa3); \ \ zero_mantissa = (num0|num1) == 0; \ \ @@ -75,9 +77,9 @@ do { \ *--wnumstr = L'0'; \ } \ \ - leading = fpnum.ldbl.ieee.exponent == 0 ? '0' : '1'; \ + leading = u.ieee.exponent == 0 ? '0' : '1'; \ \ - exponent = fpnum.ldbl.ieee.exponent; \ + exponent = u.ieee.exponent; \ \ if (exponent == 0) \ { \ diff --git a/sysdeps/ieee754/ldbl-128/s_atanl.c b/sysdeps/ieee754/ldbl-128/s_atanl.c index 0138e792aa..dc5e7ef462 100644 --- a/sysdeps/ieee754/ldbl-128/s_atanl.c +++ b/sysdeps/ieee754/ldbl-128/s_atanl.c @@ -42,7 +42,7 @@ * */ -/* Copyright 2001 by Stephen L. Moshier <moshier@na-net.ornl.gov> +/* 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 @@ -167,6 +167,7 @@ static const long double q4 = 2.173623741810414221251136181221172551416E1L; /* q5 = 1.000000000000000000000000000000000000000E0 */ +static const long double huge = 1.0e4930L; long double __atanl (long double x) @@ -197,6 +198,22 @@ __atanl (long double x) return atantbl[83]; } + if (k <= 0x3fc50000) /* |x| < 2**-58 */ + { + /* Raise inexact. */ + if (huge + x > 0.0) + return x; + } + + if (k >= 0x40720000) /* |x| > 2**115 */ + { + /* Saturate result to {-,+}pi/2 */ + if (sign) + return -atantbl[83]; + else + return atantbl[83]; + } + if (sign) x = -x; diff --git a/sysdeps/ieee754/ldbl-128/s_erfl.c b/sysdeps/ieee754/ldbl-128/s_erfl.c index 85c6356373..ef65ed8922 100644 --- a/sysdeps/ieee754/ldbl-128/s_erfl.c +++ b/sysdeps/ieee754/ldbl-128/s_erfl.c @@ -11,9 +11,9 @@ /* Modifications and expansions for 128-bit long double are Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov> - and are incorporated herein by permission of the author. The author + and are incorporated herein by permission of the author. The author reserves the right to distribute this material elsewhere under different - copying permissions. These modifications are distributed here under + copying permissions. These modifications are distributed here under the following terms: This library is free software; you can redistribute it and/or @@ -96,6 +96,7 @@ * erfc/erf(NaN) is NaN */ +#include <errno.h> #include <math.h> #include <math_private.h> @@ -918,14 +919,22 @@ __erfcl (long double x) r = __ieee754_expl (-z * z - 0.5625) * __ieee754_expl ((z - x) * (z + x) + p); if ((sign & 0x80000000) == 0) - return r / x; + { + long double ret = r / x; + if (ret == 0) + __set_errno (ERANGE); + return ret; + } else return two - r / x; } else { if ((sign & 0x80000000) == 0) - return tiny * tiny; + { + __set_errno (ERANGE); + return tiny * tiny; + } else return two - tiny; } diff --git a/sysdeps/ieee754/ldbl-128/s_expm1l.c b/sysdeps/ieee754/ldbl-128/s_expm1l.c index ea63501819..1c12109511 100644 --- a/sysdeps/ieee754/ldbl-128/s_expm1l.c +++ b/sysdeps/ieee754/ldbl-128/s_expm1l.c @@ -35,7 +35,7 @@ * */ -/* Copyright 2001 by Stephen L. Moshier +/* Copyright 2001 by Stephen L. Moshier This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public diff --git a/sysdeps/ieee754/ldbl-128/s_fma.c b/sysdeps/ieee754/ldbl-128/s_fma.c index b08ff29c04..e3cae61cf9 100644 --- a/sysdeps/ieee754/ldbl-128/s_fma.c +++ b/sysdeps/ieee754/ldbl-128/s_fma.c @@ -1,5 +1,5 @@ /* Compute x * y + z as ternary operation. - Copyright (C) 2010-2012 Free Software Foundation, Inc. + Copyright (C) 2010-2014 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. diff --git a/sysdeps/ieee754/ldbl-128/s_fmal.c b/sysdeps/ieee754/ldbl-128/s_fmal.c index c6a3d71f1c..48b63ab51d 100644 --- a/sysdeps/ieee754/ldbl-128/s_fmal.c +++ b/sysdeps/ieee754/ldbl-128/s_fmal.c @@ -1,5 +1,5 @@ /* Compute x * y + z as ternary operation. - Copyright (C) 2010-2012 Free Software Foundation, Inc. + Copyright (C) 2010-2014 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jakub@redhat.com>, 2010. @@ -56,16 +56,18 @@ __fmal (long double x, long double y, long double z) underflows to 0. */ if (z == 0 && x != 0 && y != 0) return x * y; - /* If x or y or z is Inf/NaN, or if fma will certainly overflow, - or if x * y is zero, compute as x * y + z. */ + /* If x or y or z is Inf/NaN, or if x * y is zero, compute as + x * y + z. */ if (u.ieee.exponent == 0x7fff || v.ieee.exponent == 0x7fff || w.ieee.exponent == 0x7fff - || u.ieee.exponent + v.ieee.exponent - > 0x7fff + IEEE854_LONG_DOUBLE_BIAS || x == 0 || y == 0) return x * y + z; + /* If fma will certainly overflow, compute as x * y. */ + if (u.ieee.exponent + v.ieee.exponent + > 0x7fff + IEEE854_LONG_DOUBLE_BIAS) + return x * y; /* If x * y is less than 1/4 of LDBL_DENORM_MIN, neither the result nor whether there is underflow depends on its exact value, only on its sign. */ @@ -116,8 +118,17 @@ __fmal (long double x, long double y, long double z) { /* Similarly. If z exponent is very large and x and y exponents are - very small, it doesn't matter if we don't adjust it. */ - if (u.ieee.exponent > v.ieee.exponent) + very small, adjust them up to avoid spurious underflows, + rather than down. */ + if (u.ieee.exponent + v.ieee.exponent + <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) + { + if (u.ieee.exponent > v.ieee.exponent) + u.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + else + v.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + } + else if (u.ieee.exponent > v.ieee.exponent) { if (u.ieee.exponent > LDBL_MANT_DIG) u.ieee.exponent -= LDBL_MANT_DIG; @@ -147,15 +158,15 @@ __fmal (long double x, long double y, long double z) <= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */ { if (u.ieee.exponent > v.ieee.exponent) - u.ieee.exponent += 2 * LDBL_MANT_DIG; + u.ieee.exponent += 2 * LDBL_MANT_DIG + 2; else - v.ieee.exponent += 2 * LDBL_MANT_DIG; - if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 4) + v.ieee.exponent += 2 * LDBL_MANT_DIG + 2; + if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 6) { if (w.ieee.exponent) - w.ieee.exponent += 2 * LDBL_MANT_DIG; + w.ieee.exponent += 2 * LDBL_MANT_DIG + 2; else - w.d *= 0x1p226L; + w.d *= 0x1p228L; adjust = -1; } /* Otherwise x * y should just affect inexact @@ -170,6 +181,10 @@ __fmal (long double x, long double y, long double z) if (__builtin_expect ((x == 0 || y == 0) && z == 0, 0)) return x * y + z; + fenv_t env; + feholdexcept (&env); + fesetround (FE_TONEAREST); + /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */ #define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) long double x1 = x * C; @@ -188,9 +203,19 @@ __fmal (long double x, long double y, long double z) t1 = m1 - t1; t2 = z - t2; long double a2 = t1 + t2; + feclearexcept (FE_INEXACT); + + /* If the result is an exact zero, ensure it has the correct + sign. */ + if (a1 == 0 && m2 == 0) + { + feupdateenv (&env); + /* Ensure that round-to-nearest value of z + m1 is not + reused. */ + asm volatile ("" : "=m" (z) : "m" (z)); + return z + m1; + } - fenv_t env; - feholdexcept (&env); fesetround (FE_TOWARDZERO); /* Perform m2 + a2 addition with round to odd. */ u.d = a2 + m2; @@ -226,19 +251,19 @@ __fmal (long double x, long double y, long double z) /* If a1 + u.d is exact, the only rounding happens during scaling down. */ if (j == 0) - return v.d * 0x1p-226L; + return v.d * 0x1p-228L; /* If result rounded to zero is not subnormal, no double rounding will occur. */ - if (v.ieee.exponent > 226) - return (a1 + u.d) * 0x1p-226L; - /* If v.d * 0x1p-226L with round to zero is a subnormal above - or equal to LDBL_MIN / 2, then v.d * 0x1p-226L shifts mantissa + if (v.ieee.exponent > 228) + return (a1 + u.d) * 0x1p-228L; + /* If v.d * 0x1p-228L with round to zero is a subnormal above + or equal to LDBL_MIN / 2, then v.d * 0x1p-228L shifts mantissa down just by 1 bit, which means v.ieee.mantissa3 |= j would change the round bit, not sticky or guard bit. - v.d * 0x1p-226L never normalizes by shifting up, + v.d * 0x1p-228L never normalizes by shifting up, so round bit plus sticky bit should be already enough for proper rounding. */ - if (v.ieee.exponent == 226) + if (v.ieee.exponent == 228) { /* If the exponent would be in the normal range when rounding to normal precision with unbounded exponent @@ -248,8 +273,8 @@ __fmal (long double x, long double y, long double z) if (TININESS_AFTER_ROUNDING) { w.d = a1 + u.d; - if (w.ieee.exponent == 227) - return w.d * 0x1p-226L; + if (w.ieee.exponent == 229) + return w.d * 0x1p-228L; } /* v.ieee.mantissa3 & 2 is LSB bit of the result before rounding, v.ieee.mantissa3 & 1 is the round bit and j is our sticky @@ -258,12 +283,12 @@ __fmal (long double x, long double y, long double z) w.ieee.mantissa3 = ((v.ieee.mantissa3 & 3) << 1) | j; w.ieee.negative = v.ieee.negative; v.ieee.mantissa3 &= ~3U; - v.d *= 0x1p-226L; + v.d *= 0x1p-228L; w.d *= 0x1p-2L; return v.d + w.d; } v.ieee.mantissa3 |= j; - return v.d * 0x1p-226L; + return v.d * 0x1p-228L; } } weak_alias (__fmal, fmal) diff --git a/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c b/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c index a98f586f91..efe69f2d45 100644 --- a/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c +++ b/sysdeps/ieee754/ldbl-128/s_fpclassifyl.c @@ -1,8 +1,8 @@ /* Return classification value corresponding to argument. - Copyright (C) 1997, 1999, 2002 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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. + Jakub Jelinek <jj@ultra.linux.cz>, 1999. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public diff --git a/sysdeps/ieee754/ldbl-128/s_issignalingl.c b/sysdeps/ieee754/ldbl-128/s_issignalingl.c new file mode 100644 index 0000000000..c3d77aff78 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_issignalingl.c @@ -0,0 +1,45 @@ +/* Test for signaling NaN. + Copyright (C) 2013-2014 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> + +int +__issignalingl (long double x) +{ + u_int64_t hxi, lxi __attribute__ ((unused)); + GET_LDOUBLE_WORDS64 (hxi, lxi, x); +#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN + /* We only have to care about the high-order bit of x's significand, because + having it set (sNaN) already makes the significand different from that + used to designate infinity. */ + return ((hxi & UINT64_C (0x7fff800000000000)) + == UINT64_C (0x7fff800000000000)); +#else + /* To keep the following comparison simple, toggle the quiet/signaling bit, + so that it is set for sNaNs. This is inverse to IEEE 754-2008 (as well as + common practice for IEEE 754-1985). */ + hxi ^= UINT64_C (0x0000800000000000); + /* If lxi != 0, then set any suitable bit of the significand in hxi. */ + hxi |= (lxi | -lxi) >> 63; + /* We have to compare for greater (instead of greater or equal), because x's + significand being all-zero designates infinity not NaN. */ + return (hxi & UINT64_C (0x7fffffffffffffff)) > UINT64_C (0x7fff800000000000); +#endif +} +libm_hidden_def (__issignalingl) diff --git a/sysdeps/ieee754/ldbl-128/s_llrintl.c b/sysdeps/ieee754/ldbl-128/s_llrintl.c index be7cb5df11..b3a2124f23 100644 --- a/sysdeps/ieee754/ldbl-128/s_llrintl.c +++ b/sysdeps/ieee754/ldbl-128/s_llrintl.c @@ -1,9 +1,9 @@ /* Round argument to nearest integral value according to current rounding direction. - Copyright (C) 1997, 1999, 2006 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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. + Jakub Jelinek <jj@ultra.linux.cz>, 1999. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public diff --git a/sysdeps/ieee754/ldbl-128/s_llroundl.c b/sysdeps/ieee754/ldbl-128/s_llroundl.c index 16eea8f68a..8c2b48ea28 100644 --- a/sysdeps/ieee754/ldbl-128/s_llroundl.c +++ b/sysdeps/ieee754/ldbl-128/s_llroundl.c @@ -1,8 +1,8 @@ /* Round long double value to long long int. - Copyright (C) 1997, 1999, 2004 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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. + Jakub Jelinek <jj@ultra.linux.cz>, 1999. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public diff --git a/sysdeps/ieee754/ldbl-128/s_log1pl.c b/sysdeps/ieee754/ldbl-128/s_log1pl.c index 4ecea0fddd..d991e8a720 100644 --- a/sysdeps/ieee754/ldbl-128/s_log1pl.c +++ b/sysdeps/ieee754/ldbl-128/s_log1pl.c @@ -36,7 +36,7 @@ * IEEE -1, 8 100000 1.9e-34 4.3e-35 */ -/* Copyright 2001 by Stephen L. Moshier +/* Copyright 2001 by Stephen L. Moshier This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public @@ -138,6 +138,12 @@ __log1pl (long double xm1) && (u.parts32.w1 | u.parts32.w2 | u.parts32.w3) == 0) return xm1; + if ((hx & 0x7fffffff) < 0x3f8e0000) + { + if ((int) xm1 == 0) + return xm1; + } + x = xm1 + 1.0L; /* log1p(-1) = -inf */ diff --git a/sysdeps/ieee754/ldbl-128/s_lrintl.c b/sysdeps/ieee754/ldbl-128/s_lrintl.c index 11594a314f..7dbab5cc10 100644 --- a/sysdeps/ieee754/ldbl-128/s_lrintl.c +++ b/sysdeps/ieee754/ldbl-128/s_lrintl.c @@ -1,9 +1,9 @@ /* Round argument to nearest integral value according to current rounding direction. - Copyright (C) 1997, 1999, 2004, 2006 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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. + Jakub Jelinek <jj@ultra.linux.cz>, 1999. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public diff --git a/sysdeps/ieee754/ldbl-128/s_lroundl.c b/sysdeps/ieee754/ldbl-128/s_lroundl.c index efe71bc391..493592c4d5 100644 --- a/sysdeps/ieee754/ldbl-128/s_lroundl.c +++ b/sysdeps/ieee754/ldbl-128/s_lroundl.c @@ -1,8 +1,8 @@ /* Round long double value to long int. - Copyright (C) 1997, 1999, 2004 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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. + Jakub Jelinek <jj@ultra.linux.cz>, 1999. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public diff --git a/sysdeps/ieee754/ldbl-128/s_nearbyintl.c b/sysdeps/ieee754/ldbl-128/s_nearbyintl.c index b335adcaa1..2017c04207 100644 --- a/sysdeps/ieee754/ldbl-128/s_nearbyintl.c +++ b/sysdeps/ieee754/ldbl-128/s_nearbyintl.c @@ -37,7 +37,7 @@ long double __nearbyintl(long double x) { fenv_t env; int64_t i0,j0,sx; - u_int64_t i1; + u_int64_t i1 __attribute__ ((unused)); long double w,t; GET_LDOUBLE_WORDS64(i0,i1,x); sx = (((u_int64_t)i0)>>63); @@ -47,6 +47,7 @@ long double __nearbyintl(long double x) feholdexcept (&env); w = TWO112[sx]+x; t = w-TWO112[sx]; + math_force_eval (t); fesetenv (&env); GET_LDOUBLE_MSW64(i0,t); SET_LDOUBLE_MSW64(t,(i0&0x7fffffffffffffffLL)|(sx<<63)); @@ -59,6 +60,7 @@ long double __nearbyintl(long double x) feholdexcept (&env); w = TWO112[sx]+x; t = w-TWO112[sx]; + math_force_eval (t); fesetenv (&env); return t; } diff --git a/sysdeps/ieee754/ldbl-128/s_nexttoward.c b/sysdeps/ieee754/ldbl-128/s_nexttoward.c index 1ea0b64331..2cd2e58391 100644 --- a/sysdeps/ieee754/ldbl-128/s_nexttoward.c +++ b/sysdeps/ieee754/ldbl-128/s_nexttoward.c @@ -43,7 +43,7 @@ double __nexttoward(double x, long double y) if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ ((iy>=0x7fff000000000000LL)&&((iy-0x7fff000000000000LL)|ly)!=0)) - /* y is nan */ + /* y is nan */ return x+y; if((long double) x==y) return y; /* x=y, return y */ if((ix|lx)==0) { /* x == 0 */ diff --git a/sysdeps/ieee754/ldbl-128/s_nexttowardf.c b/sysdeps/ieee754/ldbl-128/s_nexttowardf.c index 02a14078af..ccd49d235d 100644 --- a/sysdeps/ieee754/ldbl-128/s_nexttowardf.c +++ b/sysdeps/ieee754/ldbl-128/s_nexttowardf.c @@ -26,7 +26,7 @@ float __nexttowardf(float x, long double y) int32_t hx,ix; int64_t hy,iy; u_int64_t ly; - + GET_FLOAT_WORD(hx,x); GET_LDOUBLE_WORDS64(hy,ly,y); ix = hx&0x7fffffff; /* |x| */ diff --git a/sysdeps/ieee754/ldbl-128/s_remquol.c b/sysdeps/ieee754/ldbl-128/s_remquol.c index a985546ea4..d7b1503857 100644 --- a/sysdeps/ieee754/ldbl-128/s_remquol.c +++ b/sysdeps/ieee754/ldbl-128/s_remquol.c @@ -1,5 +1,5 @@ /* Compute remainder and a congruent to the quotient. - Copyright (C) 1997, 1999, 2002 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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. @@ -50,7 +50,7 @@ __remquol (long double x, long double y, int *quo) if (hy <= 0x7ffbffffffffffffLL) x = __ieee754_fmodl (x, 8 * y); /* now x < 8y */ - + if (((hx - hy) | (lx - ly)) == 0) { *quo = qs ? -1 : 1; diff --git a/sysdeps/ieee754/ldbl-128/s_rintl.c b/sysdeps/ieee754/ldbl-128/s_rintl.c index 088d3c4d59..ae2142b2c9 100644 --- a/sysdeps/ieee754/ldbl-128/s_rintl.c +++ b/sysdeps/ieee754/ldbl-128/s_rintl.c @@ -39,7 +39,7 @@ TWO112[2]={ long double __rintl(long double x) { int64_t i0,j0,sx; - u_int64_t i1; + u_int64_t i1 __attribute__ ((unused)); long double w,t; GET_LDOUBLE_WORDS64(i0,i1,x); sx = (((u_int64_t)i0)>>63); diff --git a/sysdeps/ieee754/ldbl-128/s_roundl.c b/sysdeps/ieee754/ldbl-128/s_roundl.c index 1139d2781f..4be1ad8228 100644 --- a/sysdeps/ieee754/ldbl-128/s_roundl.c +++ b/sysdeps/ieee754/ldbl-128/s_roundl.c @@ -1,5 +1,5 @@ /* Round long double to integer away from zero. - Copyright (C) 1997, 1999 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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. diff --git a/sysdeps/ieee754/ldbl-128/s_scalblnl.c b/sysdeps/ieee754/ldbl-128/s_scalblnl.c index f0df2da9ea..f55239376d 100644 --- a/sysdeps/ieee754/ldbl-128/s_scalblnl.c +++ b/sysdeps/ieee754/ldbl-128/s_scalblnl.c @@ -1,7 +1,7 @@ /* s_scalblnl.c -- long double version of s_scalbn.c. * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. */ - + /* @(#)s_scalbn.c 5.1 93/09/24 */ /* * ==================================================== diff --git a/sysdeps/ieee754/ldbl-128/s_scalbnl.c b/sysdeps/ieee754/ldbl-128/s_scalbnl.c index a14848d8fd..8916dcbfdd 100644 --- a/sysdeps/ieee754/ldbl-128/s_scalbnl.c +++ b/sysdeps/ieee754/ldbl-128/s_scalbnl.c @@ -1,7 +1,7 @@ /* s_scalbnl.c -- long double version of s_scalbn.c. * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. */ - + /* @(#)s_scalbn.c 5.1 93/09/24 */ /* * ==================================================== diff --git a/sysdeps/ieee754/ldbl-128/s_signbitl.c b/sysdeps/ieee754/ldbl-128/s_signbitl.c index da74213075..434bc2ce64 100644 --- a/sysdeps/ieee754/ldbl-128/s_signbitl.c +++ b/sysdeps/ieee754/ldbl-128/s_signbitl.c @@ -1,5 +1,5 @@ /* Return nonzero value if number is negative. - Copyright (C) 1997, 1999 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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-128/s_sincosl.c b/sysdeps/ieee754/ldbl-128/s_sincosl.c index 5747ad464e..591867acd2 100644 --- a/sysdeps/ieee754/ldbl-128/s_sincosl.c +++ b/sysdeps/ieee754/ldbl-128/s_sincosl.c @@ -1,5 +1,5 @@ /* Compute sine and cosine of argument. - Copyright (C) 1997, 1999 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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-128/s_tanl.c b/sysdeps/ieee754/ldbl-128/s_tanl.c index c4bb8c80ec..c7d637402b 100644 --- a/sysdeps/ieee754/ldbl-128/s_tanl.c +++ b/sysdeps/ieee754/ldbl-128/s_tanl.c @@ -1,7 +1,7 @@ /* s_tanl.c -- long double version of s_tan.c. * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. */ - + /* @(#)s_tan.c 5.1 93/09/24 */ /* * ==================================================== diff --git a/sysdeps/ieee754/ldbl-128/s_truncl.c b/sysdeps/ieee754/ldbl-128/s_truncl.c index 092ff9cdf4..2395b5a152 100644 --- a/sysdeps/ieee754/ldbl-128/s_truncl.c +++ b/sysdeps/ieee754/ldbl-128/s_truncl.c @@ -1,8 +1,8 @@ /* Truncate argument to nearest integral value not larger than the argument. - Copyright (C) 1997, 1999 Free Software Foundation, Inc. + Copyright (C) 1997-2014 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. + Jakub Jelinek <jj@ultra.linux.cz>, 1999. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public diff --git a/sysdeps/ieee754/ldbl-128/strtold_l.c b/sysdeps/ieee754/ldbl-128/strtold_l.c index d2f6b0d8a2..b22cfe7651 100644 --- a/sysdeps/ieee754/ldbl-128/strtold_l.c +++ b/sysdeps/ieee754/ldbl-128/strtold_l.c @@ -1,4 +1,4 @@ -/* Copyright (C) 1999, 2004 Free Software Foundation, Inc. +/* Copyright (C) 1999-2014 Free Software Foundation, Inc. This file is part of the GNU C Library. The GNU C Library is free software; you can redistribute it and/or @@ -34,11 +34,13 @@ #define SET_MANTISSA(flt, mant) \ do { union ieee854_long_double u; \ u.d = (flt); \ - u.ieee.mantissa0 = 0x8000; \ - u.ieee.mantissa1 = 0; \ - u.ieee.mantissa2 = ((mant) >> 32); \ - u.ieee.mantissa3 = (mant) & 0xffffffff; \ - (flt) = u.d; \ + u.ieee_nan.mantissa0 = 0; \ + u.ieee_nan.mantissa1 = 0; \ + u.ieee_nan.mantissa2 = (mant) >> 32; \ + u.ieee_nan.mantissa3 = (mant); \ + if ((u.ieee.mantissa0 | u.ieee.mantissa1 \ + | u.ieee.mantissa2 | u.ieee.mantissa3) != 0) \ + (flt) = u.d; \ } while (0) #include <strtod_l.c> diff --git a/sysdeps/ieee754/ldbl-128/t_expl.h b/sysdeps/ieee754/ldbl-128/t_expl.h index b408229df6..6b94956ffe 100644 --- a/sysdeps/ieee754/ldbl-128/t_expl.h +++ b/sysdeps/ieee754/ldbl-128/t_expl.h @@ -1,5 +1,5 @@ /* Accurate table for expl(). - Copyright (C) 1999 Free Software Foundation, Inc. + Copyright (C) 1999-2014 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-128/t_sincosl.c b/sysdeps/ieee754/ldbl-128/t_sincosl.c index 129aae65cb..b04321dc12 100644 --- a/sysdeps/ieee754/ldbl-128/t_sincosl.c +++ b/sysdeps/ieee754/ldbl-128/t_sincosl.c @@ -1,5 +1,5 @@ /* Quad-precision floating point sine and cosine tables. - Copyright (C) 1999 Free Software Foundation, Inc. + Copyright (C) 1999-2014 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Jakub Jelinek <jj@ultra.linux.cz> @@ -34,7 +34,7 @@ const long double __sincosl_table[] = { /* sin(x) = 0.25dc50bc95711d0d9787d108fd438cf5959ee0bfb7a1e36e8b1a112968f356657420e9cc9ea */ 1.47892995873409608580026675734609314e-01L, /* 3ffc2ee285e4ab88e86cbc3e8847ea1c */ 9.74950446464233268291647449768590886e-36L, /* 3f8a9eb2b3dc17f6f43c6dd16342252d */ - + /* x = 1.56250000000000000000000000000000000e-01 3ffc4000000000000000000000000000 */ /* cos(x) = 0.fce1a053e621438b6d60c76e8c45bf0a9dc71aa16f922acc10e95144ec796a249813c9cb649 */ 9.87817783816471944100503034363211317e-01L, /* 3ffef9c340a7cc428716dac18edd188b */ diff --git a/sysdeps/ieee754/ldbl-128/w_expl.c b/sysdeps/ieee754/ldbl-128/w_expl.c index 10193befa9..f0b1f8e55f 100644 --- a/sysdeps/ieee754/ldbl-128/w_expl.c +++ b/sysdeps/ieee754/ldbl-128/w_expl.c @@ -25,24 +25,16 @@ static char rcsid[] = "$NetBSD: $"; #include <math.h> #include <math_private.h> -static const long double -o_threshold= 1.1356523406294143949491931077970763428449E4L, -u_threshold= -1.1433462743336297878837243843452621503410E4; - long double __expl(long double x) /* wrapper exp */ { #ifdef _IEEE_LIBM return __ieee754_expl(x); #else - long double z; - z = __ieee754_expl(x); - if(_LIB_VERSION == _IEEE_) return z; - if(__finitel(x)) { - if(x>o_threshold) - return __kernel_standard_l(x,x,206); /* exp overflow */ - else if(x<u_threshold) - return __kernel_standard_l(x,x,207); /* exp underflow */ - } + long double z = __ieee754_expl (x); + if (__glibc_unlikely (!__finitel (z) || z == 0) + && __finitel (x) && _LIB_VERSION != _IEEE_) + return __kernel_standard_l (x, x, 206 + !!__signbitl (x)); + return z; #endif } diff --git a/sysdeps/ieee754/ldbl-128/x2y2m1l.c b/sysdeps/ieee754/ldbl-128/x2y2m1l.c index a249cd3479..575bcd812d 100644 --- a/sysdeps/ieee754/ldbl-128/x2y2m1l.c +++ b/sysdeps/ieee754/ldbl-128/x2y2m1l.c @@ -1,5 +1,5 @@ /* Compute x^2 + y^2 - 1, without large cancellation error. - Copyright (C) 2012 Free Software Foundation, Inc. + Copyright (C) 2012-2014 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 |