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-rw-r--r--sysdeps/i386/fpu/libm-test-ulps14
-rw-r--r--sysdeps/ieee754/dbl-64/e_gamma_r.c9
-rw-r--r--sysdeps/ieee754/flt-32/e_gammaf_r.c9
-rw-r--r--sysdeps/ieee754/ldbl-96/e_gammal_r.c10
-rw-r--r--sysdeps/ieee754/ldbl-96/e_lgammal_r.c418
5 files changed, 452 insertions, 8 deletions
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 9845731..41d8d22 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 eff4046..9dc68f6 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 f0cd438..bbd1a35 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 1049924..376d2b9 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 0000000..f39ef35
--- /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;
+}
generated by cgit v1.1 at 2024-07-22 19:20:51 +0000