diff options
| -rw-r--r-- | ChangeLog | 10 | ||||
| -rw-r--r-- | sysdeps/i386/fpu/libm-test-ulps | 14 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_gamma_r.c | 9 | ||||
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_gammaf_r.c | 9 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/e_gammal_r.c | 10 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/e_lgammal_r.c | 418 |
6 files changed, 462 insertions, 8 deletions
diff --git a/ChangeLog b/ChangeLog index 273aadc21a..2fa1630b84 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,5 +1,15 @@ 2001-03-04 Ulrich Drepper <drepper@redhat.com> + * sysdeps/ieee754/ldbl-96/e_lgammal_r.c: New file. + Contributed by Stephen L. Moshier <moshier@na-net.ornl.gov>. + + * sysdeps/ieee754/ldbl-96/e_gammal_r.c: Fix handling of boundary cases. + + * sysdeps/ieee754/dbl-64/e_gamma_r.c: Always initialize sign variable. + * sysdeps/ieee754/flt-32/e_gammaf_r.c: Likewise. + + * sysdeps/i386/fpu/libm-test-ulps: Adjust after addition of lgammal. + * sysdeps/unix/sysv/linux/ia64/bits/siginfo.h: Fix typo in last change. 2001-03-04 Andreas Jaeger <aj@suse.de> diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index 984573109d..41d8d22665 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -598,6 +598,8 @@ ldouble: 4096 Test "gamma (-0.5) == log(2*sqrt(pi))": double: 1 idouble: 1 +ldouble: 1 +ildouble: 1 # hypot Test "hypot (-0.7, -12.4) == 12.419742348374220601176836866763271": @@ -772,6 +774,8 @@ ildouble: 1 Test "lgamma (-0.5) == log(2*sqrt(pi))": double: 1 idouble: 1 +ldouble: 1 +ildouble: 1 Test "lgamma (0.7) == 0.26086724653166651439": double: 1 float: 1 @@ -782,6 +786,8 @@ double: 1 float: 2 idouble: 1 ifloat: 2 +ldouble: 1 +ildouble: 1 # log Test "log (1.0 / M_El) == -1": @@ -906,6 +912,8 @@ double: 2 float: 1 idouble: 2 ifloat: 1 +ldouble: 2 +ildouble: 2 Test "tgamma (0.5) == sqrt (pi)": float: 1 ifloat: 1 @@ -1439,6 +1447,8 @@ ldouble: 4096 Function: "gamma": double: 1 idouble: 1 +ldouble: 1 +ildouble: 1 Function: "hypot": double: 1 @@ -1473,6 +1483,8 @@ double: 1 float: 2 idouble: 1 ifloat: 2 +ldouble: 1 +ildouble: 1 Function: "log": double: 1 @@ -1547,6 +1559,8 @@ double: 2 float: 1 idouble: 2 ifloat: 1 +ldouble: 2 +ildouble: 2 Function: "y0": double: 3 diff --git a/sysdeps/ieee754/dbl-64/e_gamma_r.c b/sysdeps/ieee754/dbl-64/e_gamma_r.c index eff40463be..9dc68f69b3 100644 --- a/sysdeps/ieee754/dbl-64/e_gamma_r.c +++ b/sysdeps/ieee754/dbl-64/e_gamma_r.c @@ -1,5 +1,5 @@ /* Implementation of gamma function according to ISO C. - Copyright (C) 1997, 1999 Free Software Foundation, Inc. + Copyright (C) 1997, 1999, 2001 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. @@ -46,8 +46,11 @@ __ieee754_gamma_r (double x, int *signgamp) return (x - x) / (x - x); } if ((unsigned int) hx == 0xfff00000 && lx==0) - /* x == -Inf. According to ISO this is NaN. */ - return x - x; + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } /* XXX FIXME. */ return __ieee754_exp (__ieee754_lgamma_r (x, signgamp)); diff --git a/sysdeps/ieee754/flt-32/e_gammaf_r.c b/sysdeps/ieee754/flt-32/e_gammaf_r.c index f0cd43840b..bbd1a35a95 100644 --- a/sysdeps/ieee754/flt-32/e_gammaf_r.c +++ b/sysdeps/ieee754/flt-32/e_gammaf_r.c @@ -1,5 +1,5 @@ /* Implementation of gamma function according to ISO C. - Copyright (C) 1997, 1999 Free Software Foundation, Inc. + Copyright (C) 1997, 1999, 2001 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. @@ -45,8 +45,11 @@ __ieee754_gammaf_r (float x, int *signgamp) return (x - x) / (x - x); } if (hx == 0xff800000) - /* x == -Inf. According to ISO this is NaN. */ - return x - x; + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } /* XXX FIXME. */ return __ieee754_expf (__ieee754_lgammaf_r (x, signgamp)); diff --git a/sysdeps/ieee754/ldbl-96/e_gammal_r.c b/sysdeps/ieee754/ldbl-96/e_gammal_r.c index 104992450b..376d2b9d94 100644 --- a/sysdeps/ieee754/ldbl-96/e_gammal_r.c +++ b/sysdeps/ieee754/ldbl-96/e_gammal_r.c @@ -1,5 +1,5 @@ /* Implementation of gamma function according to ISO C. - Copyright (C) 1997, 1999 Free Software Foundation, Inc. + Copyright (C) 1997, 1999, 2001 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. @@ -38,12 +38,18 @@ __ieee754_gammal_r (long double x, int *signgamp) *signgamp = 0; return x / x; } - if ((hx & 0x8000) != 0 && (hx & 0x7fff) != 0x7fff && __rintl (x) == x) + if ((es & 0x8000) != 0 && x < 0xffffffff && __rintl (x) == x) { /* Return value for integer x < 0 is NaN with invalid exception. */ *signgamp = 0; return (x - x) / (x - x); } + if (es == 0xffffffff && ((hx & 0x7fffffff) | lx) == 0) + { + /* x == -Inf. According to ISO this is NaN. */ + *signgamp = 0; + return x - x; + } /* XXX FIXME. */ return __ieee754_expl (__ieee754_lgammal_r (x, signgamp)); diff --git a/sysdeps/ieee754/ldbl-96/e_lgammal_r.c b/sysdeps/ieee754/ldbl-96/e_lgammal_r.c new file mode 100644 index 0000000000..f39ef355a1 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/e_lgammal_r.c @@ -0,0 +1,418 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Long double expansions contributed by + Stephen L. Moshier <moshier@na-net.ornl.gov> */ + +/* __ieee754_lgammal_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include "math.h" +#include "math_private.h" + +#ifdef __STDC__ +static const long double +#else +static long double +#endif + half = 0.5L, + one = 1.0L, + pi = 3.14159265358979323846264L, + + /* lgam(1+x) = 0.5 x + x a(x)/b(x) + -0.268402099609375 <= x <= 0 + peak relative error 6.6e-22 */ + a0 = -6.343246574721079391729402781192128239938E2L, + a1 = 1.856560238672465796768677717168371401378E3L, + a2 = 2.404733102163746263689288466865843408429E3L, + a3 = 8.804188795790383497379532868917517596322E2L, + a4 = 1.135361354097447729740103745999661157426E2L, + a5 = 3.766956539107615557608581581190400021285E0L, + + b0 = 8.214973713960928795704317259806842490498E3L, + b1 = 1.026343508841367384879065363925870888012E4L, + b2 = 4.553337477045763320522762343132210919277E3L, + b3 = 8.506975785032585797446253359230031874803E2L, + b4 = 6.042447899703295436820744186992189445813E1L, + /* b5 = 1.000000000000000000000000000000000000000E0 */ + + + tc = 1.4616321449683623412626595423257213284682E0L, + tf = -1.2148629053584961146050602565082954242826E-1,/* double precision */ +/* tt = (tail of tf), i.e. tf + tt has extended precision. */ + tt = 3.3649914684731379602768989080467587736363E-18L, + /* lgam ( 1.4616321449683623412626595423257213284682E0 ) = +-1.2148629053584960809551455717769158215135617312999903886372437313313530E-1 */ + + /* lgam (x + tc) = tf + tt + x g(x)/h(x) + - 0.230003726999612341262659542325721328468 <= x + <= 0.2699962730003876587373404576742786715318 + peak relative error 2.1e-21 */ + g0 = 3.645529916721223331888305293534095553827E-18L, + g1 = 5.126654642791082497002594216163574795690E3L, + g2 = 8.828603575854624811911631336122070070327E3L, + g3 = 5.464186426932117031234820886525701595203E3L, + g4 = 1.455427403530884193180776558102868592293E3L, + g5 = 1.541735456969245924860307497029155838446E2L, + g6 = 4.335498275274822298341872707453445815118E0L, + + h0 = 1.059584930106085509696730443974495979641E4L, + h1 = 2.147921653490043010629481226937850618860E4L, + h2 = 1.643014770044524804175197151958100656728E4L, + h3 = 5.869021995186925517228323497501767586078E3L, + h4 = 9.764244777714344488787381271643502742293E2L, + h5 = 6.442485441570592541741092969581997002349E1L, + /* h6 = 1.000000000000000000000000000000000000000E0 */ + + + /* lgam (x+1) = -0.5 x + x u(x)/v(x) + -0.100006103515625 <= x <= 0.231639862060546875 + peak relative error 1.3e-21 */ + u0 = -8.886217500092090678492242071879342025627E1L, + u1 = 6.840109978129177639438792958320783599310E2L, + u2 = 2.042626104514127267855588786511809932433E3L, + u3 = 1.911723903442667422201651063009856064275E3L, + u4 = 7.447065275665887457628865263491667767695E2L, + u5 = 1.132256494121790736268471016493103952637E2L, + u6 = 4.484398885516614191003094714505960972894E0L, + + v0 = 1.150830924194461522996462401210374632929E3L, + v1 = 3.399692260848747447377972081399737098610E3L, + v2 = 3.786631705644460255229513563657226008015E3L, + v3 = 1.966450123004478374557778781564114347876E3L, + v4 = 4.741359068914069299837355438370682773122E2L, + v5 = 4.508989649747184050907206782117647852364E1L, + /* v6 = 1.000000000000000000000000000000000000000E0 */ + + + /* lgam (x+2) = .5 x + x s(x)/r(x) + 0 <= x <= 1 + peak relative error 7.2e-22 */ + s0 = 1.454726263410661942989109455292824853344E6L, + s1 = -3.901428390086348447890408306153378922752E6L, + s2 = -6.573568698209374121847873064292963089438E6L, + s3 = -3.319055881485044417245964508099095984643E6L, + s4 = -7.094891568758439227560184618114707107977E5L, + s5 = -6.263426646464505837422314539808112478303E4L, + s6 = -1.684926520999477529949915657519454051529E3L, + + r0 = -1.883978160734303518163008696712983134698E7L, + r1 = -2.815206082812062064902202753264922306830E7L, + r2 = -1.600245495251915899081846093343626358398E7L, + r3 = -4.310526301881305003489257052083370058799E6L, + r4 = -5.563807682263923279438235987186184968542E5L, + r5 = -3.027734654434169996032905158145259713083E4L, + r6 = -4.501995652861105629217250715790764371267E2L, + /* r6 = 1.000000000000000000000000000000000000000E0 */ + + +/* lgam(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x w(1/x^2) + x >= 8 + Peak relative error 1.51e-21 + w0 = LS2PI - 0.5 */ + w0 = 4.189385332046727417803e-1L, + w1 = 8.333333333333331447505E-2L, + w2 = -2.777777777750349603440E-3L, + w3 = 7.936507795855070755671E-4L, + w4 = -5.952345851765688514613E-4L, + w5 = 8.412723297322498080632E-4L, + w6 = -1.880801938119376907179E-3L, + w7 = 4.885026142432270781165E-3L; + +#ifdef __STDC__ +static const long double zero = 0.0L; +#else +static long double zero = 0.0L; +#endif + +#ifdef __STDC__ +static long double +sin_pi (long double x) +#else +static long double +sin_pi (x) + long double x; +#endif +{ + long double y, z; + int n, ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + + i1 = (ix << 16) | (i0 >> 16); + if (ix < 0x3ffd8000) /* 0.25 */ + return __sinl (pi * x); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = __floorl (y); + if (z != y) + { /* inexact anyway */ + y *= half; + y = 2.0 * (y - __floorl (y)); /* y = |x| mod 2.0 */ + n = (int) (y * 4.0); + } + else + { + return (zero + zero); + } + + switch (n) + { + case 0: + y = __sinl (pi * y); + break; + case 1: + case 2: + y = __cosl (pi * (half - y)); + break; + case 3: + case 4: + y = __sinl (pi * (one - y)); + break; + case 5: + case 6: + y = -__cosl (pi * (y - 1.5)); + break; + default: + y = __sinl (pi * (y - 2.0)); + break; + } + return -y; +} + + +#ifdef __STDC__ +long double +__ieee754_lgammal_r (long double x, int *signgamp) +#else +long double +__ieee754_lgammal_r (x, signgamp) + long double x; + int *signgamp; +#endif +{ + long double t, y, z, nadj, p, p1, p2, q, r, w; + int i, ix; + u_int32_t se, i0, i1; + + GET_LDOUBLE_WORDS (se, i0, i1, x); + ix = se & 0x7fff; + + if ((ix | i0 | i1) == 0) + return one / fabsl (x); + + ix = (ix << 16) | (i0 >> 16); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + if (ix >= 0x7fff0000) + return x * x; + + if (ix < 0x3fc08000) /* 2^-63 */ + { /* |x|<2**-63, return -log(|x|) */ + if (se & 0x8000) + { + *signgamp = -1; + return -__ieee754_logl (-x); + } + else + return -__ieee754_logl (x); + } + if (se & 0x8000) + { + if (x == __floorl(x)) + return x / zero; + t = sin_pi (x); + if (t == zero) + return one / fabsl (t); /* -integer */ + nadj = __ieee754_logl (pi / fabsl (t * x)); + if (t < zero) + *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if ((((ix - 0x3fff8000) | i0 | i1) == 0) + || (((ix - 0x40008000) | i0 | i1) == 0)) + r = 0; + else if (ix < 0x40008000) /* 2.0 */ + { + /* x < 2.0 */ + if (ix <= 0x3ffee666) /* 8.99993896484375e-1 */ + { + /* lgamma(x) = lgamma(x+1) - log(x) */ + r = -__ieee754_logl (x); + if (ix >= 0x3ffebb4a) /* 7.31597900390625e-1 */ + { + y = x - one; + i = 0; + } + else if (ix >= 0x3ffced33)/* 2.31639862060546875e-1 */ + { + y = x - (tc - one); + i = 1; + } + else + { + /* x < 0.23 */ + y = x; + i = 2; + } + } + else + { + r = zero; + if (ix >= 0x3fffdda6) /* 1.73162841796875 */ + { + /* [1.7316,2] */ + y = x - 2.0; + i = 0; + } + else if (ix >= 0x3fff9da6)/* 1.23162841796875 */ + { + /* [1.23,1.73] */ + y = x - tc; + i = 1; + } + else + { + /* [0.9, 1.23] */ + y = x - one; + i = 2; + } + } + switch (i) + { + case 0: + p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5)))); + p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y)))); + r += half * y + y * p1/p2; + break; + case 1: + p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6))))); + p2 = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y))))); + p = tt + y * p1/p2; + r += (tf + p); + break; + case 2: + p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6)))))); + p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y))))); + r += (-half * y + p1 / p2); + } + } + else if (ix < 0x40028000) /* 8.0 */ + { + /* x < 8.0 */ + i = (int) x; + t = zero; + y = x - (double) i; + p = y * + (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6)))))); + q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y)))))); + r = half * y + p / q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch (i) + { + case 7: + z *= (y + 6.0); /* FALLTHRU */ + case 6: + z *= (y + 5.0); /* FALLTHRU */ + case 5: + z *= (y + 4.0); /* FALLTHRU */ + case 4: + z *= (y + 3.0); /* FALLTHRU */ + case 3: + z *= (y + 2.0); /* FALLTHRU */ + r += __ieee754_logl (z); + break; + } + } + else if (ix < 0x40418000) /* 2^66 */ + { + /* 8.0 <= x < 2**66 */ + t = __ieee754_logl (x); + z = one / x; + y = z * z; + w = w0 + z * (w1 + + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7)))))); + r = (x - half) * (t - one) + w; + } + else + /* 2**66 <= x <= inf */ + r = x * (__ieee754_logl (x) - one); + if (se & 0x8000) + r = nadj - r; + return r; +} |