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freebsd-skq/lib/msun/ld80/e_lgammal_r.c

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* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
/* @(#)e_lgamma_r.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
* See e_lgamma_r.c for complete comments.
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
*
* Converted to long double by Steven G. Kargl.
*/
#ifdef __i386__
#include <ieeefp.h>
#endif
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
static const volatile double vzero = 0;
static const double
zero= 0,
half= 0.5,
one = 1;
static const union IEEEl2bits
piu = LD80C(0xc90fdaa22168c235, 1, 3.14159265358979323851e+00L);
#define pi (piu.e)
/*
* Domain y in [0x1p-70, 0.27], range ~[-4.5264e-22, 4.5264e-22]:
* |(lgamma(2 - y) + y / 2) / y - a(y)| < 2**-70.9
*/
static const union IEEEl2bits
a0u = LD80C(0x9e233f1bed863d26, -4, 7.72156649015328606028e-02L),
a1u = LD80C(0xa51a6625307d3249, -2, 3.22467033424113218889e-01L),
a2u = LD80C(0x89f000d2abafda8c, -4, 6.73523010531979398946e-02L),
a3u = LD80C(0xa8991563eca75f26, -6, 2.05808084277991211934e-02L),
a4u = LD80C(0xf2027e10634ce6b6, -8, 7.38555102796070454026e-03L),
a5u = LD80C(0xbd6eb76dd22187f4, -9, 2.89051035162703932972e-03L),
a6u = LD80C(0x9c562ab05e0458ed, -10, 1.19275351624639999297e-03L),
a7u = LD80C(0x859baed93ee48e46, -11, 5.09674593842117925320e-04L),
a8u = LD80C(0xe9f28a4432949af2, -13, 2.23109648015769155122e-04L),
a9u = LD80C(0xd12ad0d9b93c6bb0, -14, 9.97387167479808509830e-05L),
a10u= LD80C(0xb7522643c78a219b, -15, 4.37071076331030136818e-05L),
a11u= LD80C(0xca024dcdece2cb79, -16, 2.40813493372040143061e-05L),
a12u= LD80C(0xbb90fb6968ebdbf9, -19, 2.79495621083634031729e-06L),
a13u= LD80C(0xba1c9ffeeae07b37, -17, 1.10931287015513924136e-05L);
#define a0 (a0u.e)
#define a1 (a1u.e)
#define a2 (a2u.e)
#define a3 (a3u.e)
#define a4 (a4u.e)
#define a5 (a5u.e)
#define a6 (a6u.e)
#define a7 (a7u.e)
#define a8 (a8u.e)
#define a9 (a9u.e)
#define a10 (a10u.e)
#define a11 (a11u.e)
#define a12 (a12u.e)
#define a13 (a13u.e)
/*
* Domain x in [tc-0.24, tc+0.28], range ~[-6.1205e-22, 6.1205e-22]:
* |(lgamma(x) - tf) - t(x - tc)| < 2**-70.5
*/
static const union IEEEl2bits
tcu = LD80C(0xbb16c31ab5f1fb71, 0, 1.46163214496836234128e+00L),
tfu = LD80C(0xf8cdcde61c520e0f, -4, -1.21486290535849608093e-01L),
ttu = LD80C(0xd46ee54b27d4de99, -69, -2.81152980996018785880e-21L),
t0u = LD80C(0x80b9406556a62a6b, -68, 3.40728634996055147231e-21L),
t1u = LD80C(0xc7e9c6f6df3f8c39, -67, -1.05833162742737073665e-20L),
t2u = LD80C(0xf7b95e4771c55d51, -2, 4.83836122723810583532e-01L),
t3u = LD80C(0x97213c6e35e119ff, -3, -1.47587722994530691476e-01L),
t4u = LD80C(0x845a14a6a81dc94b, -4, 6.46249402389135358063e-02L),
t5u = LD80C(0x864d46fa89997796, -5, -3.27885410884846056084e-02L),
t6u = LD80C(0x93373cbd00297438, -6, 1.79706751150707171293e-02L),
t7u = LD80C(0xa8fcfca7eddc8d1d, -7, -1.03142230361450732547e-02L),
t8u = LD80C(0xc7e7015ff4bc45af, -8, 6.10053603296546099193e-03L),
t9u = LD80C(0xf178d2247adc5093, -9, -3.68456964904901200152e-03L),
t10u = LD80C(0x94188d58f12e5e9f, -9, 2.25976420273774583089e-03L),
t11u = LD80C(0xb7cbaef14e1406f1, -10, -1.40224943666225639823e-03L),
t12u = LD80C(0xe63a671e6704ea4d, -11, 8.78250640744776944887e-04L),
t13u = LD80C(0x914b6c9cae61783e, -11, -5.54255012657716808811e-04L),
t14u = LD80C(0xb858f5bdb79276fe, -12, 3.51614951536825927370e-04L),
t15u = LD80C(0xea73e744c34b9591, -13, -2.23591563824520112236e-04L),
t16u = LD80C(0x99aeabb0d67ba835, -13, 1.46562869351659194136e-04L),
t17u = LD80C(0xd7c6938325db2024, -14, -1.02889866046435680588e-04L),
t18u = LD80C(0xe24cb1e3b0474775, -15, 5.39540265505221957652e-05L);
#define tc (tcu.e)
#define tf (tfu.e)
#define tt (ttu.e)
#define t0 (t0u.e)
#define t1 (t1u.e)
#define t2 (t2u.e)
#define t3 (t3u.e)
#define t4 (t4u.e)
#define t5 (t5u.e)
#define t6 (t6u.e)
#define t7 (t7u.e)
#define t8 (t8u.e)
#define t9 (t9u.e)
#define t10 (t10u.e)
#define t11 (t11u.e)
#define t12 (t12u.e)
#define t13 (t13u.e)
#define t14 (t14u.e)
#define t15 (t15u.e)
#define t16 (t16u.e)
#define t17 (t17u.e)
#define t18 (t18u.e)
/*
* Domain y in [-0.1, 0.232], range ~[-8.1938e-22, 8.3815e-22]:
* |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-71.2
*/
static const union IEEEl2bits
u0u = LD80C(0x9e233f1bed863d27, -4, -7.72156649015328606095e-02L),
u1u = LD80C(0x98280ee45e4ddd3d, -1, 5.94361239198682739769e-01L),
u2u = LD80C(0xe330c8ead4130733, 0, 1.77492629495841234275e+00L),
u3u = LD80C(0xd4a213f1a002ec52, 0, 1.66119622514818078064e+00L),
u4u = LD80C(0xa5a9ca6f5bc62163, -1, 6.47122051417476492989e-01L),
u5u = LD80C(0xc980e49cd5b019e6, -4, 9.83903751718671509455e-02L),
u6u = LD80C(0xff636a8bdce7025b, -9, 3.89691687802305743450e-03L),
v1u = LD80C(0xbd109c533a19fbf5, 1, 2.95413883330948556544e+00L),
v2u = LD80C(0xd295cbf96f31f099, 1, 3.29039286955665403176e+00L),
v3u = LD80C(0xdab8bcfee40496cb, 0, 1.70876276441416471410e+00L),
v4u = LD80C(0xd2f2dc3638567e9f, -2, 4.12009126299534668571e-01L),
v5u = LD80C(0xa07d9b0851070f41, -5, 3.91822868305682491442e-02L),
v6u = LD80C(0xe3cd8318f7adb2c4, -11, 8.68998648222144351114e-04L);
#define u0 (u0u.e)
#define u1 (u1u.e)
#define u2 (u2u.e)
#define u3 (u3u.e)
#define u4 (u4u.e)
#define u5 (u5u.e)
#define u6 (u6u.e)
#define v1 (v1u.e)
#define v2 (v2u.e)
#define v3 (v3u.e)
#define v4 (v4u.e)
#define v5 (v5u.e)
#define v6 (v6u.e)
/*
* Domain x in (2, 3], range ~[-3.3648e-22, 3.4416e-22]:
* |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-72.3
* with y = x - 2.
*/
static const union IEEEl2bits
s0u = LD80C(0x9e233f1bed863d27, -4, -7.72156649015328606095e-02L),
s1u = LD80C(0xd3ff0dcc7fa91f94, -3, 2.07027640921219389860e-01L),
s2u = LD80C(0xb2bb62782478ef31, -2, 3.49085881391362090549e-01L),
s3u = LD80C(0xb49f7438c4611a74, -3, 1.76389518704213357954e-01L),
s4u = LD80C(0x9a957008fa27ecf9, -5, 3.77401710862930008071e-02L),
s5u = LD80C(0xda9b389a6ca7a7ac, -9, 3.33566791452943399399e-03L),
s6u = LD80C(0xbc7a2263faf59c14, -14, 8.98728786745638844395e-05L),
r1u = LD80C(0xbf5cff5b11477d4d, 0, 1.49502555796294337722e+00L),
r2u = LD80C(0xd9aec89de08e3da6, -1, 8.50323236984473285866e-01L),
r3u = LD80C(0xeab7ae5057c443f9, -3, 2.29216312078225806131e-01L),
r4u = LD80C(0xf29707d9bd2b1e37, -6, 2.96130326586640089145e-02L),
r5u = LD80C(0xd376c2f09736c5a3, -10, 1.61334161411590662495e-03L),
r6u = LD80C(0xc985983d0cd34e3d, -16, 2.40232770710953450636e-05L),
r7u = LD80C(0xe5c7a4f7fc2ef13d, -25, -5.34997929289167573510e-08L);
#define s0 (s0u.e)
#define s1 (s1u.e)
#define s2 (s2u.e)
#define s3 (s3u.e)
#define s4 (s4u.e)
#define s5 (s5u.e)
#define s6 (s6u.e)
#define r1 (r1u.e)
#define r2 (r2u.e)
#define r3 (r3u.e)
#define r4 (r4u.e)
#define r5 (r5u.e)
#define r6 (r6u.e)
#define r7 (r7u.e)
/*
* Domain z in [8, 0x1p70], range ~[-3.0235e-22, 3.0563e-22]:
* |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-71.7
*/
static const union IEEEl2bits
w0u = LD80C(0xd67f1c864beb4a69, -2, 4.18938533204672741776e-01L),
w1u = LD80C(0xaaaaaaaaaaaaaaa1, -4, 8.33333333333333332678e-02L),
w2u = LD80C(0xb60b60b60b5491c9, -9, -2.77777777777760927870e-03L),
w3u = LD80C(0xd00d00cf58aede4c, -11, 7.93650793490637233668e-04L),
w4u = LD80C(0x9c09bf626783d4a5, -11, -5.95238023926039051268e-04L),
w5u = LD80C(0xdca7cadc5baa517b, -11, 8.41733700408000822962e-04L),
w6u = LD80C(0xfb060e361e1ffd07, -10, -1.91515849570245136604e-03L),
w7u = LD80C(0xcbd5101bb58d1f2b, -8, 6.22046743903262649294e-03L),
w8u = LD80C(0xad27a668d32c821b, -6, -2.11370706734662081843e-02L);
#define w0 (w0u.e)
#define w1 (w1u.e)
#define w2 (w2u.e)
#define w3 (w3u.e)
#define w4 (w4u.e)
#define w5 (w5u.e)
#define w6 (w6u.e)
#define w7 (w7u.e)
#define w8 (w8u.e)
static long double
sin_pil(long double x)
{
volatile long double vz;
long double y,z;
uint64_t n;
uint16_t hx;
y = -x;
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
vz = y+0x1p63;
z = vz-0x1p63;
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
if (z == y)
return zero;
vz = y+0x1p61;
EXTRACT_LDBL80_WORDS(hx,n,vz);
z = vz-0x1p61;
if (z > y) {
z -= 0.25; /* adjust to round down */
n--;
}
n &= 7; /* octant of y mod 2 */
y = y - z + n * 0.25; /* y mod 2 */
switch (n) {
case 0: y = __kernel_sinl(pi*y,zero,0); break;
case 1:
case 2: y = __kernel_cosl(pi*(0.5-y),zero); break;
case 3:
case 4: y = __kernel_sinl(pi*(one-y),zero,0); break;
case 5:
case 6: y = -__kernel_cosl(pi*(y-1.5),zero); break;
default: y = __kernel_sinl(pi*(y-2.0),zero,0); break;
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
}
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
return -y;
}
long double
lgammal_r(long double x, int *signgamp)
{
libm: remove unused variables Sponsored by: The FreeBSD Foundation
2016-10-05 17:04:58 +00:00
long double nadj,p,p1,p2,q,r,t,w,y,z;
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
uint64_t lx;
int i;
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
uint16_t hx,ix;
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
EXTRACT_LDBL80_WORDS(hx,lx,x);
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
/* purge +-Inf and NaNs */
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
*signgamp = 1;
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
ix = hx&0x7fff;
if(ix==0x7fff) return x*x;
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
ENTERI();
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
/* purge +-0 and tiny arguments */
*signgamp = 1-2*(hx>>15);
if(ix<0x3fff-67) { /* |x|<2**-(p+3), return -log(|x|) */
if((ix|lx)==0)
RETURNI(one/vzero);
RETURNI(-logl(fabsl(x)));
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
}
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
/* purge negative integers and start evaluation for other x < 0 */
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
if(hx&0x8000) {
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
*signgamp = 1;
if(ix>=0x3fff+63) /* |x|>=2**(p-1), must be -integer */
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
RETURNI(one/vzero);
t = sin_pil(x);
if(t==zero) RETURNI(one/vzero); /* -integer */
nadj = logl(pi/fabsl(t*x));
if(t<zero) *signgamp = -1;
x = -x;
}
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
/* purge 1 and 2 */
if((ix==0x3fff || ix==0x4000) && lx==0x8000000000000000ULL) r = 0;
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
/* for x < 2.0 */
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
else if(ix<0x4000) {
/*
* XXX Supposedly, one can use the following information to replace the
* XXX FP rational expressions. A similar approach is appropriate
* XXX for ld128, but one (may need?) needs to consider llx, too.
*
* 8.9999961853027344e-01 3ffe e666600000000000
* 7.3159980773925781e-01 3ffe bb4a200000000000
* 2.3163998126983643e-01 3ffc ed33080000000000
* 1.7316312789916992e+00 3fff dda6180000000000
* 1.2316322326660156e+00 3fff 9da6200000000000
*/
if(x<8.9999961853027344e-01) {
r = -logl(x);
if(x>=7.3159980773925781e-01) {y = 1-x; i= 0;}
else if(x>=2.3163998126983643e-01) {y= x-(tc-1); i=1;}
else {y = x; i=2;}
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
} else {
r = 0;
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
if(x>=1.7316312789916992e+00) {y=2-x;i=0;}
else if(x>=1.2316322326660156e+00) {y=x-tc;i=1;}
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
else {y=x-1;i=2;}
}
switch(i) {
case 0:
z = y*y;
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*(a10+z*a12)))));
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*(a11+z*a13))))));
p = y*p1+p2;
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
r += p-y/2; break;
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
case 1:
p = t0+y*t1+tt+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*(t7+y*(t8+
y*(t9+y*(t10+y*(t11+y*(t12+y*(t13+y*(t14+y*(t15+y*(t16+
y*(t17+y*t18))))))))))))))));
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
r += tf + p; break;
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
case 2:
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*(u5+y*u6))))));
p2 = 1+y*(v1+y*(v2+y*(v3+y*(v4+y*(v5+y*v6)))));
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
r += p1/p2-y/2;
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
}
}
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
/* x < 8.0 */
else if(ix<0x4002) {
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
i = x;
y = x-i;
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
q = 1+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*(r6+y*r7))))));
r = y/2+p/q;
z = 1; /* lgamma(1+s) = log(s) + lgamma(s) */
switch(i) {
case 7: z *= (y+6); /* FALLTHRU */
case 6: z *= (y+5); /* FALLTHRU */
case 5: z *= (y+4); /* FALLTHRU */
case 4: z *= (y+3); /* FALLTHRU */
case 3: z *= (y+2); /* FALLTHRU */
r += logl(z); break;
}
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
/* 8.0 <= x < 2**(p+3) */
} else if (ix<0x3fff+67) {
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
t = logl(x);
z = one/x;
y = z*z;
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*(w6+y*(w7+y*w8)))))));
r = (x-half)*(t-one)+w;
The value small=2**-(p+3), where p is the precision, can be determine from lgamma(x) = -log(x) - log(1+x) + x*(1-g) + x**2*P(x) with g = 0.57... being the Euler constant and P(x) a polynomial. Substitution of small into the RHS shows that the last 3 terms are negligible in comparison to the leading term. The choice of 3 may be conservative. The value large=2**(p+3) is detemined from Stirling's approximation lgamma(x) = x*(log(x)-1) - log(x)/2 + log(2*pi)/2 + P(1/x)/x Again, substitution of large into the RHS reveals the last 3 terms are negligible in comparison to the leading term. Move the x=+-0 special case into the |x|<small block. In the ld80 and ld128 implementaion, use fdlibm compatible comparisons involving ix, lx, and llx. This replaces several floating point comparisons (some involving fabsl()) and also fixes the special cases x=1 and x=2. While here . Remove unnecessary parentheses. . Fix/improve comments due to the above changes. . Fix nearby whitespace. * src/e_lgamma_r.c: . Sort declaration. . Remove unneeded explicit cast for type conversion. . Replace a double literal constant by an integer literal constant. * src/e_lgammaf_r.c: . Sort declaration. * ld128/e_lgammal_r.c: . Replace a long double literal constant by a double literal constant. * ld80/e_lgammal_r.c: . Remove unused '#include float.h' . Replace a long double literal constant by a double literal constant. Requested by: bde
2014-10-09 22:39:52 +00:00
/* 2**(p+3) <= x <= inf */
* Makefile: . Hook e_lgammal[_r].c to the build. . Create man page links for lgammal[-r].3. * Symbol.map: . Sort lgammal to its rightful place. . Add FBSD_1.4 section for the new lgamal_r symbol. * ld128/e_lgammal_r.c: . 128-bit implementataion of lgammal_r(). * ld80/e_lgammal_r.c: . Intel 80-bit format implementation of lgammal_r(). * src/e_lgamma.c: . Expose lgammal as a weak reference to lgamma for platforms where long double is mapped to double. * src/e_lgamma_r.c: . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. . Expose lgammal_r as a weak reference to lgamma_r for platforms where long double is mapped to double. * src/e_lgammaf_r.c: . Fixed the Cygnus Support conversion of e_lgamma_r.c to float. This includes the generation of new polynomial and rational approximations with fewer terms. For each approximation, include a comment on an estimate of the accuracy over the relevant domain. . Use integer literal constants instead of real literal constants. Let compiler(s) do the job of conversion to the appropriate type. This allows the removal of several explicit casts of double values to float. * src/e_lgammal.c: . Wrapper for lgammal() about lgammal_r(). * src/imprecise.c: . Remove the lgamma. * src/math.h: . Add a prototype for lgammal_r(). * man/lgamma.3: . Document the new functions. Reviewed by: bde
2014-09-15 23:21:57 +00:00
} else
r = x*(logl(x)-1);
if(hx&0x8000) r = nadj - r;
RETURNI(r);
}
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