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Update.
* 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.
This commit is contained in:
Ulrich Drepper
parent
73807ef933
commit
3bde1a69c1
10
ChangeLog
10
ChangeLog
@ -1,5 +1,15 @@
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2001-03-04 Ulrich Drepper <drepper@redhat.com>
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* sysdeps/ieee754/ldbl-96/e_lgammal_r.c: New file.
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Contributed by Stephen L. Moshier <moshier@na-net.ornl.gov>.
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* sysdeps/ieee754/ldbl-96/e_gammal_r.c: Fix handling of boundary cases.
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* sysdeps/ieee754/dbl-64/e_gamma_r.c: Always initialize sign variable.
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* sysdeps/ieee754/flt-32/e_gammaf_r.c: Likewise.
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* sysdeps/i386/fpu/libm-test-ulps: Adjust after addition of lgammal.
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* sysdeps/unix/sysv/linux/ia64/bits/siginfo.h: Fix typo in last change.
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2001-03-04 Andreas Jaeger <aj@suse.de>
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@ -598,6 +598,8 @@ ldouble: 4096
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Test "gamma (-0.5) == log(2*sqrt(pi))":
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double: 1
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idouble: 1
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ldouble: 1
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ildouble: 1
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# hypot
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Test "hypot (-0.7, -12.4) == 12.419742348374220601176836866763271":
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@ -772,6 +774,8 @@ ildouble: 1
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Test "lgamma (-0.5) == log(2*sqrt(pi))":
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double: 1
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idouble: 1
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ldouble: 1
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ildouble: 1
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Test "lgamma (0.7) == 0.26086724653166651439":
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double: 1
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float: 1
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@ -782,6 +786,8 @@ double: 1
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float: 2
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idouble: 1
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ifloat: 2
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ldouble: 1
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ildouble: 1
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# log
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Test "log (1.0 / M_El) == -1":
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@ -906,6 +912,8 @@ double: 2
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float: 1
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idouble: 2
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ifloat: 1
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ldouble: 2
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ildouble: 2
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Test "tgamma (0.5) == sqrt (pi)":
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float: 1
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ifloat: 1
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@ -1439,6 +1447,8 @@ ldouble: 4096
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Function: "gamma":
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double: 1
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idouble: 1
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ldouble: 1
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ildouble: 1
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Function: "hypot":
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double: 1
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@ -1473,6 +1483,8 @@ double: 1
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float: 2
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idouble: 1
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ifloat: 2
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ldouble: 1
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ildouble: 1
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Function: "log":
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double: 1
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@ -1547,6 +1559,8 @@ double: 2
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float: 1
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idouble: 2
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ifloat: 1
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ldouble: 2
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ildouble: 2
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Function: "y0":
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double: 3
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@ -1,5 +1,5 @@
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/* Implementation of gamma function according to ISO C.
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Copyright (C) 1997, 1999 Free Software Foundation, Inc.
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Copyright (C) 1997, 1999, 2001 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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@ -46,8 +46,11 @@ __ieee754_gamma_r (double x, int *signgamp)
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return (x - x) / (x - x);
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}
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if ((unsigned int) hx == 0xfff00000 && lx==0)
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/* x == -Inf. According to ISO this is NaN. */
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return x - x;
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{
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/* x == -Inf. According to ISO this is NaN. */
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*signgamp = 0;
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return x - x;
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}
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/* XXX FIXME. */
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return __ieee754_exp (__ieee754_lgamma_r (x, signgamp));
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@ -1,5 +1,5 @@
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/* Implementation of gamma function according to ISO C.
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Copyright (C) 1997, 1999 Free Software Foundation, Inc.
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Copyright (C) 1997, 1999, 2001 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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@ -45,8 +45,11 @@ __ieee754_gammaf_r (float x, int *signgamp)
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return (x - x) / (x - x);
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}
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if (hx == 0xff800000)
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/* x == -Inf. According to ISO this is NaN. */
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return x - x;
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{
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/* x == -Inf. According to ISO this is NaN. */
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*signgamp = 0;
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return x - x;
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}
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/* XXX FIXME. */
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return __ieee754_expf (__ieee754_lgammaf_r (x, signgamp));
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@ -1,5 +1,5 @@
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/* Implementation of gamma function according to ISO C.
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Copyright (C) 1997, 1999 Free Software Foundation, Inc.
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Copyright (C) 1997, 1999, 2001 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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@ -38,12 +38,18 @@ __ieee754_gammal_r (long double x, int *signgamp)
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*signgamp = 0;
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return x / x;
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}
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if ((hx & 0x8000) != 0 && (hx & 0x7fff) != 0x7fff && __rintl (x) == x)
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if ((es & 0x8000) != 0 && x < 0xffffffff && __rintl (x) == x)
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{
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/* Return value for integer x < 0 is NaN with invalid exception. */
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*signgamp = 0;
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return (x - x) / (x - x);
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}
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if (es == 0xffffffff && ((hx & 0x7fffffff) | lx) == 0)
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{
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/* x == -Inf. According to ISO this is NaN. */
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*signgamp = 0;
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return x - x;
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}
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/* XXX FIXME. */
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return __ieee754_expl (__ieee754_lgammal_r (x, signgamp));
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418
sysdeps/ieee754/ldbl-96/e_lgammal_r.c
Normal file
418
sysdeps/ieee754/ldbl-96/e_lgammal_r.c
Normal file
@ -0,0 +1,418 @@
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* Long double expansions contributed by
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Stephen L. Moshier <moshier@na-net.ornl.gov> */
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/* __ieee754_lgammal_r(x, signgamp)
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* Reentrant version of the logarithm of the Gamma function
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* with user provide pointer for the sign of Gamma(x).
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*
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* Method:
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* 1. Argument Reduction for 0 < x <= 8
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* Since gamma(1+s)=s*gamma(s), for x in [0,8], we may
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* reduce x to a number in [1.5,2.5] by
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* lgamma(1+s) = log(s) + lgamma(s)
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* for example,
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* lgamma(7.3) = log(6.3) + lgamma(6.3)
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* = log(6.3*5.3) + lgamma(5.3)
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* = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3)
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* 2. Polynomial approximation of lgamma around its
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* minimun ymin=1.461632144968362245 to maintain monotonicity.
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* On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use
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* Let z = x-ymin;
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* lgamma(x) = -1.214862905358496078218 + z^2*poly(z)
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* 2. Rational approximation in the primary interval [2,3]
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* We use the following approximation:
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* s = x-2.0;
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* lgamma(x) = 0.5*s + s*P(s)/Q(s)
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* Our algorithms are based on the following observation
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*
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* zeta(2)-1 2 zeta(3)-1 3
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* lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ...
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* 2 3
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*
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* where Euler = 0.5771... is the Euler constant, which is very
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* close to 0.5.
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*
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* 3. For x>=8, we have
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* lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+....
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* (better formula:
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* lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...)
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* Let z = 1/x, then we approximation
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* f(z) = lgamma(x) - (x-0.5)(log(x)-1)
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* by
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* 3 5 11
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* w = w0 + w1*z + w2*z + w3*z + ... + w6*z
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*
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* 4. For negative x, since (G is gamma function)
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* -x*G(-x)*G(x) = pi/sin(pi*x),
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* we have
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* G(x) = pi/(sin(pi*x)*(-x)*G(-x))
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* since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0
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* Hence, for x<0, signgam = sign(sin(pi*x)) and
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* lgamma(x) = log(|Gamma(x)|)
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* = log(pi/(|x*sin(pi*x)|)) - lgamma(-x);
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* Note: one should avoid compute pi*(-x) directly in the
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* computation of sin(pi*(-x)).
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*
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* 5. Special Cases
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* lgamma(2+s) ~ s*(1-Euler) for tiny s
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* lgamma(1)=lgamma(2)=0
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* lgamma(x) ~ -log(x) for tiny x
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* lgamma(0) = lgamma(inf) = inf
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* lgamma(-integer) = +-inf
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*
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*/
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#include "math.h"
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#include "math_private.h"
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#ifdef __STDC__
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static const long double
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#else
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static long double
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#endif
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half = 0.5L,
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one = 1.0L,
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pi = 3.14159265358979323846264L,
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/* lgam(1+x) = 0.5 x + x a(x)/b(x)
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-0.268402099609375 <= x <= 0
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peak relative error 6.6e-22 */
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a0 = -6.343246574721079391729402781192128239938E2L,
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a1 = 1.856560238672465796768677717168371401378E3L,
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a2 = 2.404733102163746263689288466865843408429E3L,
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a3 = 8.804188795790383497379532868917517596322E2L,
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a4 = 1.135361354097447729740103745999661157426E2L,
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a5 = 3.766956539107615557608581581190400021285E0L,
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b0 = 8.214973713960928795704317259806842490498E3L,
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b1 = 1.026343508841367384879065363925870888012E4L,
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b2 = 4.553337477045763320522762343132210919277E3L,
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b3 = 8.506975785032585797446253359230031874803E2L,
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b4 = 6.042447899703295436820744186992189445813E1L,
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/* b5 = 1.000000000000000000000000000000000000000E0 */
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tc = 1.4616321449683623412626595423257213284682E0L,
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tf = -1.2148629053584961146050602565082954242826E-1,/* double precision */
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/* tt = (tail of tf), i.e. tf + tt has extended precision. */
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tt = 3.3649914684731379602768989080467587736363E-18L,
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/* lgam ( 1.4616321449683623412626595423257213284682E0 ) =
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-1.2148629053584960809551455717769158215135617312999903886372437313313530E-1 */
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/* lgam (x + tc) = tf + tt + x g(x)/h(x)
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- 0.230003726999612341262659542325721328468 <= x
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<= 0.2699962730003876587373404576742786715318
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peak relative error 2.1e-21 */
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g0 = 3.645529916721223331888305293534095553827E-18L,
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g1 = 5.126654642791082497002594216163574795690E3L,
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g2 = 8.828603575854624811911631336122070070327E3L,
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g3 = 5.464186426932117031234820886525701595203E3L,
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g4 = 1.455427403530884193180776558102868592293E3L,
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g5 = 1.541735456969245924860307497029155838446E2L,
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g6 = 4.335498275274822298341872707453445815118E0L,
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h0 = 1.059584930106085509696730443974495979641E4L,
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h1 = 2.147921653490043010629481226937850618860E4L,
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h2 = 1.643014770044524804175197151958100656728E4L,
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h3 = 5.869021995186925517228323497501767586078E3L,
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h4 = 9.764244777714344488787381271643502742293E2L,
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h5 = 6.442485441570592541741092969581997002349E1L,
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/* h6 = 1.000000000000000000000000000000000000000E0 */
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/* lgam (x+1) = -0.5 x + x u(x)/v(x)
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-0.100006103515625 <= x <= 0.231639862060546875
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peak relative error 1.3e-21 */
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u0 = -8.886217500092090678492242071879342025627E1L,
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u1 = 6.840109978129177639438792958320783599310E2L,
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u2 = 2.042626104514127267855588786511809932433E3L,
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u3 = 1.911723903442667422201651063009856064275E3L,
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u4 = 7.447065275665887457628865263491667767695E2L,
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u5 = 1.132256494121790736268471016493103952637E2L,
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u6 = 4.484398885516614191003094714505960972894E0L,
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v0 = 1.150830924194461522996462401210374632929E3L,
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v1 = 3.399692260848747447377972081399737098610E3L,
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v2 = 3.786631705644460255229513563657226008015E3L,
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v3 = 1.966450123004478374557778781564114347876E3L,
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v4 = 4.741359068914069299837355438370682773122E2L,
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v5 = 4.508989649747184050907206782117647852364E1L,
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/* v6 = 1.000000000000000000000000000000000000000E0 */
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/* lgam (x+2) = .5 x + x s(x)/r(x)
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0 <= x <= 1
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peak relative error 7.2e-22 */
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s0 = 1.454726263410661942989109455292824853344E6L,
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s1 = -3.901428390086348447890408306153378922752E6L,
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s2 = -6.573568698209374121847873064292963089438E6L,
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s3 = -3.319055881485044417245964508099095984643E6L,
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s4 = -7.094891568758439227560184618114707107977E5L,
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s5 = -6.263426646464505837422314539808112478303E4L,
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s6 = -1.684926520999477529949915657519454051529E3L,
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r0 = -1.883978160734303518163008696712983134698E7L,
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r1 = -2.815206082812062064902202753264922306830E7L,
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r2 = -1.600245495251915899081846093343626358398E7L,
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r3 = -4.310526301881305003489257052083370058799E6L,
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r4 = -5.563807682263923279438235987186184968542E5L,
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r5 = -3.027734654434169996032905158145259713083E4L,
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r6 = -4.501995652861105629217250715790764371267E2L,
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/* r6 = 1.000000000000000000000000000000000000000E0 */
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/* lgam(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x w(1/x^2)
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x >= 8
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Peak relative error 1.51e-21
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w0 = LS2PI - 0.5 */
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w0 = 4.189385332046727417803e-1L,
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w1 = 8.333333333333331447505E-2L,
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w2 = -2.777777777750349603440E-3L,
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w3 = 7.936507795855070755671E-4L,
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w4 = -5.952345851765688514613E-4L,
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w5 = 8.412723297322498080632E-4L,
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w6 = -1.880801938119376907179E-3L,
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w7 = 4.885026142432270781165E-3L;
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#ifdef __STDC__
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static const long double zero = 0.0L;
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#else
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static long double zero = 0.0L;
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#endif
|
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#ifdef __STDC__
|
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static long double
|
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sin_pi (long double x)
|
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#else
|
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static long double
|
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sin_pi (x)
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long double x;
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#endif
|
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{
|
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long double y, z;
|
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int n, ix;
|
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u_int32_t se, i0, i1;
|
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GET_LDOUBLE_WORDS (se, i0, i1, x);
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ix = se & 0x7fff;
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i1 = (ix << 16) | (i0 >> 16);
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if (ix < 0x3ffd8000) /* 0.25 */
|
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return __sinl (pi * x);
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y = -x; /* x is assume negative */
|
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|
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/*
|
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* argument reduction, make sure inexact flag not raised if input
|
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* is an integer
|
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*/
|
||||
z = __floorl (y);
|
||||
if (z != y)
|
||||
{ /* inexact anyway */
|
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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;
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user