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9090848d06
posix/wordexp-test.c used libc-internal.h for PTR_ALIGN_DOWN; similar
to what was done with libc-diag.h, I have split the definitions of
cast_to_integer, ALIGN_UP, ALIGN_DOWN, PTR_ALIGN_UP, and PTR_ALIGN_DOWN
to a new header, libc-pointer-arith.h.
It then occurred to me that the remaining declarations in libc-internal.h
are mostly to do with early initialization, and probably most of the
files including it, even in the core code, don't need it anymore. Indeed,
only 19 files actually need what remains of libc-internal.h. 23 others
need libc-diag.h instead, and 12 need libc-pointer-arith.h instead.
No file needs more than one of them, and 16 don't need any of them!
So, with this patch, libc-internal.h stops including libc-diag.h as
well as losing the pointer arithmetic macros, and all including files
are adjusted.
* include/libc-pointer-arith.h: New file. Define
cast_to_integer, ALIGN_UP, ALIGN_DOWN, PTR_ALIGN_UP, and
PTR_ALIGN_DOWN here.
* include/libc-internal.h: Definitions of above macros
moved from here. Don't include libc-diag.h anymore either.
* posix/wordexp-test.c: Include stdint.h and libc-pointer-arith.h.
Don't include libc-internal.h.
* debug/pcprofile.c, elf/dl-tunables.c, elf/soinit.c, io/openat.c
* io/openat64.c, misc/ptrace.c, nptl/pthread_clock_gettime.c
* nptl/pthread_clock_settime.c, nptl/pthread_cond_common.c
* string/strcoll_l.c, sysdeps/nacl/brk.c
* sysdeps/unix/clock_settime.c
* sysdeps/unix/sysv/linux/i386/get_clockfreq.c
* sysdeps/unix/sysv/linux/ia64/get_clockfreq.c
* sysdeps/unix/sysv/linux/powerpc/get_clockfreq.c
* sysdeps/unix/sysv/linux/sparc/sparc64/get_clockfreq.c:
Don't include libc-internal.h.
* elf/get-dynamic-info.h, iconv/loop.c
* iconvdata/iso-2022-cn-ext.c, locale/weight.h, locale/weightwc.h
* misc/reboot.c, nis/nis_table.c, nptl_db/thread_dbP.h
* nscd/connections.c, resolv/res_send.c, soft-fp/fmadf4.c
* soft-fp/fmasf4.c, soft-fp/fmatf4.c, stdio-common/vfscanf.c
* sysdeps/ieee754/dbl-64/e_lgamma_r.c
* sysdeps/ieee754/dbl-64/k_rem_pio2.c
* sysdeps/ieee754/flt-32/e_lgammaf_r.c
* sysdeps/ieee754/flt-32/k_rem_pio2f.c
* sysdeps/ieee754/ldbl-128/k_tanl.c
* sysdeps/ieee754/ldbl-128ibm/k_tanl.c
* sysdeps/ieee754/ldbl-96/e_lgammal_r.c
* sysdeps/ieee754/ldbl-96/k_tanl.c, sysdeps/nptl/futex-internal.h:
Include libc-diag.h instead of libc-internal.h.
* elf/dl-load.c, elf/dl-reloc.c, locale/programs/locarchive.c
* nptl/nptl-init.c, string/strcspn.c, string/strspn.c
* malloc/malloc.c, sysdeps/i386/nptl/tls.h
* sysdeps/nacl/dl-map-segments.h, sysdeps/x86_64/atomic-machine.h
* sysdeps/unix/sysv/linux/spawni.c
* sysdeps/x86_64/nptl/tls.h:
Include libc-pointer-arith.h instead of libc-internal.h.
* elf/get-dynamic-info.h, sysdeps/nacl/dl-map-segments.h
* sysdeps/x86_64/atomic-machine.h:
Add multiple include guard.
440 lines
13 KiB
C
440 lines
13 KiB
C
/*
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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 are
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Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
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and are incorporated herein by permission of the author. The author
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reserves the right to distribute this material elsewhere under different
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copying permissions. These modifications are distributed here under
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the following terms:
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This library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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This library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with this library; if not, see
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<http://www.gnu.org/licenses/>. */
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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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#include <libc-diag.h>
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static const long double
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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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two63 = 9.223372036854775808e18L,
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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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static const long double zero = 0.0L;
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static long double
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sin_pi (long double x)
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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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ix = (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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* argument reduction, make sure inexact flag not raised if input
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* is an integer
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*/
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z = __floorl (y);
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if (z != y)
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{ /* inexact anyway */
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y *= 0.5;
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y = 2.0*(y - __floorl(y)); /* y = |x| mod 2.0 */
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n = (int) (y*4.0);
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}
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else
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{
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if (ix >= 0x403f8000) /* 2^64 */
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{
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y = zero; n = 0; /* y must be even */
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}
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else
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{
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if (ix < 0x403e8000) /* 2^63 */
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z = y + two63; /* exact */
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GET_LDOUBLE_WORDS (se, i0, i1, z);
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n = i1 & 1;
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y = n;
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n <<= 2;
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}
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}
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switch (n)
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{
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case 0:
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y = __sinl (pi * y);
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break;
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case 1:
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case 2:
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y = __cosl (pi * (half - y));
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break;
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case 3:
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case 4:
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y = __sinl (pi * (one - y));
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break;
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case 5:
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case 6:
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y = -__cosl (pi * (y - 1.5));
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break;
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default:
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y = __sinl (pi * (y - 2.0));
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break;
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}
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return -y;
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}
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long double
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__ieee754_lgammal_r (long double x, int *signgamp)
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{
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long double t, y, z, nadj, p, p1, p2, q, r, w;
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int i, ix;
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u_int32_t se, i0, i1;
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*signgamp = 1;
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GET_LDOUBLE_WORDS (se, i0, i1, x);
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ix = se & 0x7fff;
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if (__builtin_expect((ix | i0 | i1) == 0, 0))
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{
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if (se & 0x8000)
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*signgamp = -1;
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return one / fabsl (x);
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}
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ix = (ix << 16) | (i0 >> 16);
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/* purge off +-inf, NaN, +-0, and negative arguments */
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if (__builtin_expect(ix >= 0x7fff0000, 0))
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return x * x;
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if (__builtin_expect(ix < 0x3fc08000, 0)) /* 2^-63 */
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{ /* |x|<2**-63, return -log(|x|) */
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if (se & 0x8000)
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{
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*signgamp = -1;
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return -__ieee754_logl (-x);
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}
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else
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return -__ieee754_logl (x);
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}
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if (se & 0x8000)
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{
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if (x < -2.0L && x > -33.0L)
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return __lgamma_negl (x, signgamp);
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t = sin_pi (x);
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if (t == zero)
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return one / fabsl (t); /* -integer */
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nadj = __ieee754_logl (pi / fabsl (t * x));
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if (t < zero)
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*signgamp = -1;
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x = -x;
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}
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/* purge off 1 and 2 */
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if ((((ix - 0x3fff8000) | i0 | i1) == 0)
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|| (((ix - 0x40008000) | i0 | i1) == 0))
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r = 0;
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else if (ix < 0x40008000) /* 2.0 */
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{
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/* x < 2.0 */
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if (ix <= 0x3ffee666) /* 8.99993896484375e-1 */
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{
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/* lgamma(x) = lgamma(x+1) - log(x) */
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r = -__ieee754_logl (x);
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if (ix >= 0x3ffebb4a) /* 7.31597900390625e-1 */
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{
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y = x - one;
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i = 0;
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}
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else if (ix >= 0x3ffced33)/* 2.31639862060546875e-1 */
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{
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y = x - (tc - one);
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i = 1;
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}
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else
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{
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/* x < 0.23 */
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y = x;
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i = 2;
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}
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}
|
|
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);
|
|
/* NADJ is set for negative arguments but not otherwise, resulting
|
|
in warnings that it may be used uninitialized although in the
|
|
cases where it is used it has always been set. */
|
|
DIAG_PUSH_NEEDS_COMMENT;
|
|
DIAG_IGNORE_NEEDS_COMMENT (4.9, "-Wmaybe-uninitialized");
|
|
if (se & 0x8000)
|
|
r = nadj - r;
|
|
DIAG_POP_NEEDS_COMMENT;
|
|
return r;
|
|
}
|
|
strong_alias (__ieee754_lgammal_r, __lgammal_r_finite)
|