Mercurial > hg > octave-nkf > gnulib-hg
changeset 16581:8e7ddab445f4
New module 'expm1'.
* lib/math.in.h (expm1): New declaration.
* lib/expm1.c: New file.
* m4/expm1.m4: New file.
* m4/math_h.m4 (gl_MATH_H): Test whether expm1 is declared.
(gl_MATH_H_DEFAULTS): Initialize GNULIB_EXPM1, HAVE_EXPM1.
* modules/math (Makefile.am): Substitute GNULIB_EXPM1, HAVE_EXPM1.
* modules/expm1: New file.
* tests/test-math-c++.cc: Check the declaration of expm1.
* doc/posix-functions/expm1.texi: Mention the new module.
| author | Bruno Haible <bruno@clisp.org> |
|---|---|
| date | Tue, 06 Mar 2012 17:55:54 +0100 |
| parents | fdbe3125f81a |
| children | 199ab6e5373c |
| files | ChangeLog doc/posix-functions/expm1.texi lib/expm1.c lib/math.in.h m4/expm1.m4 m4/math_h.m4 modules/expm1 modules/math tests/test-math-c++.cc |
| diffstat | 9 files changed, 587 insertions(+), 7 deletions(-) [+] |
line wrap: on
line diff
--- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,16 @@ +2012-03-06 Bruno Haible <bruno@clisp.org> + + New module 'expm1'. + * lib/math.in.h (expm1): New declaration. + * lib/expm1.c: New file. + * m4/expm1.m4: New file. + * m4/math_h.m4 (gl_MATH_H): Test whether expm1 is declared. + (gl_MATH_H_DEFAULTS): Initialize GNULIB_EXPM1, HAVE_EXPM1. + * modules/math (Makefile.am): Substitute GNULIB_EXPM1, HAVE_EXPM1. + * modules/expm1: New file. + * tests/test-math-c++.cc: Check the declaration of expm1. + * doc/posix-functions/expm1.texi: Mention the new module. + 2012-03-06 Bruno Haible <bruno@clisp.org> math: Ensure declarations of math functions.
--- a/doc/posix-functions/expm1.texi +++ b/doc/posix-functions/expm1.texi @@ -4,15 +4,15 @@ POSIX specification:@* @url{http://www.opengroup.org/onlinepubs/9699919799/functions/expm1.html} -Gnulib module: --- +Gnulib module: expm1 Portability problems fixed by Gnulib: @itemize -@end itemize - -Portability problems not fixed by Gnulib: -@itemize @item This function is missing on some platforms: Minix 3.1.8, mingw, MSVC 9. @end itemize + +Portability problems not fixed by Gnulib: +@itemize +@end itemize
new file mode 100644 --- /dev/null +++ b/lib/expm1.c @@ -0,0 +1,422 @@ +/* Exponential function minus one. + Copyright (C) 2012 Free Software Foundation, Inc. + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation; either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see <http://www.gnu.org/licenses/>. */ + +#include <config.h> + +/* Specification. */ +#include <math.h> + +#include <float.h> + +/* A value slightly larger than log(2). */ +#define LOG2_PLUS_EPSILON 0.6931471805599454 + +/* Best possible approximation of log(2) as a 'double'. */ +#define LOG2 0.693147180559945309417232121458176568075 + +/* Best possible approximation of 1/log(2) as a 'double'. */ +#define LOG2_INVERSE 1.44269504088896340735992468100189213743 + +/* Best possible approximation of log(2)/256 as a 'double'. */ +#define LOG2_BY_256 0.00270760617406228636491106297444600221904 + +/* Best possible approximation of 256/log(2) as a 'double'. */ +#define LOG2_BY_256_INVERSE 369.329930467574632284140718336484387181 + +/* The upper 32 bits of log(2)/256. */ +#define LOG2_BY_256_HI_PART 0.0027076061733168899081647396087646484375 +/* log(2)/256 - LOG2_HI_PART. */ +#define LOG2_BY_256_LO_PART \ + 0.000000000000745396456746323365681353781544922399845 + +double +expm1 (double x) +{ + if (isnand (x)) + return x; + + if (x >= (double) DBL_MAX_EXP * LOG2_PLUS_EPSILON) + /* x > DBL_MAX_EXP * log(2) + hence exp(x) > 2^DBL_MAX_EXP, overflows to Infinity. */ + return HUGE_VAL; + + if (x <= (double) (- DBL_MANT_DIG) * LOG2_PLUS_EPSILON) + /* x < (- DBL_MANT_DIG) * log(2) + hence 0 < exp(x) < 2^-DBL_MANT_DIG, + hence -1 < exp(x)-1 < -1 + 2^-DBL_MANT_DIG + rounds to -1. */ + return -1.0; + + if (x <= - LOG2_PLUS_EPSILON) + /* 0 < exp(x) < 1/2. + Just compute exp(x), then subtract 1. */ + return exp (x) - 1.0; + + if (x == 0.0) + /* Return a zero with the same sign as x. */ + return x; + + /* Decompose x into + x = n * log(2) + m * log(2)/256 + y + where + n is an integer, n >= -1, + m is an integer, -128 <= m <= 128, + y is a number, |y| <= log(2)/512 + epsilon = 0.00135... + Then + exp(x) = 2^n * exp(m * log(2)/256) * exp(y) + Compute each factor minus one, then combine them through the + formula (1+a)*(1+b) = 1 + (a+b*(1+a)), + that is (1+a)*(1+b) - 1 = a + b*(1+a). + The first factor is an ldexpl() call. + The second factor is a table lookup. + The third factor minus one is computed + - either as sinh(y) + sinh(y)^2 / (cosh(y) + 1) + where sinh(y) is computed through the power series: + sinh(y) = y + y^3/3! + y^5/5! + ... + and cosh(y) is computed as hypot(1, sinh(y)), + - or as exp(2*z) - 1 = 2 * tanh(z) / (1 - tanh(z)) + where z = y/2 + and tanh(z) is computed through its power series: + tanh(z) = z + - 1/3 * z^3 + + 2/15 * z^5 + - 17/315 * z^7 + + 62/2835 * z^9 + - 1382/155925 * z^11 + + 21844/6081075 * z^13 + - 929569/638512875 * z^15 + + ... + Since |z| <= log(2)/1024 < 0.0007, the relative error of the z^7 term + is < 0.0007^6 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we can truncate + the series after the z^5 term. + + Given the usual bounds DBL_MAX_EXP <= 16384, DBL_MANT_DIG <= 120, we + can estimate x: -84 <= x <= 11357. + This means, when dividing x by log(2), where we want x mod log(2) + to be precise to DBL_MANT_DIG bits, we have to use an approximation + to log(2) that has 14+DBL_MANT_DIG bits. */ + + { + double nm = round (x * LOG2_BY_256_INVERSE); /* = 256 * n + m */ + /* n has at most 15 bits, nm therefore has at most 23 bits, therefore + n * LOG2_HI_PART is computed exactly, and n * LOG2_LO_PART is computed + with an absolute error < 2^15 * 2e-10 * 2^-DBL_MANT_DIG. */ + double y_tmp = x - nm * LOG2_BY_256_HI_PART; + double y = y_tmp - nm * LOG2_BY_256_LO_PART; + double z = 0.5L * y; + +/* Coefficients of the power series for tanh(z). */ +#define TANH_COEFF_1 1.0 +#define TANH_COEFF_3 -0.333333333333333333333333333333333333334 +#define TANH_COEFF_5 0.133333333333333333333333333333333333334 +#define TANH_COEFF_7 -0.053968253968253968253968253968253968254 +#define TANH_COEFF_9 0.0218694885361552028218694885361552028218 +#define TANH_COEFF_11 -0.00886323552990219656886323552990219656886 +#define TANH_COEFF_13 0.00359212803657248101692546136990581435026 +#define TANH_COEFF_15 -0.00145583438705131826824948518070211191904 + + double z2 = z * z; + double tanh_z = + ((TANH_COEFF_5 + * z2 + TANH_COEFF_3) + * z2 + TANH_COEFF_1) + * z; + + double exp_y_minus_1 = 2.0 * tanh_z / (1.0 - tanh_z); + + int n = (int) round (nm * (1.0 / 256.0)); + int m = (int) nm - 256 * n; + + /* expm1_table[i] = exp((i - 128) * log(2)/256) - 1. + Computed in GNU clisp through + (setf (long-float-digits) 128) + (setq a 0L0) + (setf (long-float-digits) 256) + (dotimes (i 257) + (format t " ~D,~%" + (float (- (exp (* (/ (- i 128) 256) (log 2L0))) 1) a))) */ + static const double expm1_table[257] = + { + -0.292893218813452475599155637895150960716, + -0.290976057839792401079436677742323809165, + -0.289053698915417220095325702647879950038, + -0.287126127947252846596498423285616993819, + -0.285193330804014994382467110862430046956, + -0.283255293316105578740250215722626632811, + -0.281312001275508837198386957752147486471, + -0.279363440435687168635744042695052413926, + 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0.2152473599804688781165202513387984576236, + 0.218542229827408361758207148117394510722, + 0.221846032972757516903891841911570785834, + 0.225158793637145437709464594384845353705, + 0.2284805361068700056940089577927818403626, + 0.231811284734075935884556653212794816605, + 0.235151063936933305692912507415415760296, + 0.238499898199816567833368865859612431546, + 0.241857812073484048593677468726595605511, + 0.245224830175257932775204967486152674173, + 0.248600977189204736621766097302495545187, + 0.251986277866316270060206031789203597321, + 0.255380757024691089579390657442301194598, + 0.258784439549716443077860441815162618762, + 0.262197350394250708014010258518416459672, + 0.265619514578806324196273999873453036297, + 0.269050957191733222554419081032338004715, + 0.272491703389402751236692044184602176772, + 0.27594177839639210038120243475928938891, + 0.279401207505669226913587970027852545961, + 0.282870016078778280726669781021514051111, + 0.286348229546025533601482208069738348358, + 0.289835873406665812232747295491552189677, + 0.293332973229089436725559789048704304684, + 0.296839554651009665933754117792451159835, + 0.300355643379650651014140567070917791291, + 0.303881265191935898574523648951997368331, + 0.30741644593467724479715157747196172848, + 0.310961211524764341922991786330755849366, + 0.314515587949354658485983613383997794966, + 0.318079601266063994690185647066116617661, + 0.321653277603157514326511812330609226158, + 0.325236643159741294629537095498721674113, + 0.32882972420595439547865089632866510792, + 0.33243254708316144935164337949073577407, + 0.336045138204145773442627904371869759286, + 0.339667524053303005360030669724352576023, + 0.343299731186835263824217146181630875424, + 0.346941786232945835788173713229537282073, + 0.350593715892034391408522196060133960038, + 0.354255546936892728298014740140702804344, + 0.357927306212901046494536695671766697444, + 0.361609020638224755585535938831941474643, + 0.365300717204011815430698360337542855432, + 0.369002422974590611929601132982192832168, + 0.372714165087668369284997857144717215791, + 0.376435970754530100216322805518686960261, + 0.380167867260238095581945274358283464698, + 0.383909881963831954872659527265192818003, + 0.387662042298529159042861017950775988895, + 0.391424375771926187149835529566243446678, + 0.395196909966200178275574599249220994717, + 0.398979672538311140209528136715194969206, + 0.402772691220204706374713524333378817108, + 0.40657599381901544248361973255451684411, + 0.410389608217270704414375128268675481146, + 0.414213562373095048801688724209698078569 + }; + + double t = expm1_table[128 + m]; + + /* (1+t) * (1+exp_y_minus_1) - 1 = t + (1+t)*exp_y_minus_1 */ + double p_minus_1 = t + (1.0 + t) * exp_y_minus_1; + + double s = ldexp (1.0, n) - 1.0; + + /* (1+s) * (1+p_minus_1) - 1 = s + (1+s)*p_minus_1 */ + return s + (1.0 + s) * p_minus_1; + } +}
--- a/lib/math.in.h +++ b/lib/math.in.h @@ -532,6 +532,21 @@ #endif +#if @GNULIB_EXPM1@ +# if !@HAVE_EXPM1@ +_GL_FUNCDECL_SYS (expm1, double, (double x)); +# endif +_GL_CXXALIAS_SYS (expm1, double, (double x)); +_GL_CXXALIASWARN (expm1); +#elif defined GNULIB_POSIXCHECK +# undef expm1 +# if HAVE_RAW_DECL_EXPM1 +_GL_WARN_ON_USE (expm1, "expm1 is unportable - " + "use gnulib module expm1 for portability"); +# endif +#endif + + #if @GNULIB_FABSF@ # if !@HAVE_FABSF@ # undef fabsf
new file mode 100644 --- /dev/null +++ b/m4/expm1.m4 @@ -0,0 +1,86 @@ +# expm1.m4 serial 1 +dnl Copyright (C) 2010-2012 Free Software Foundation, Inc. +dnl This file is free software; the Free Software Foundation +dnl gives unlimited permission to copy and/or distribute it, +dnl with or without modifications, as long as this notice is preserved. + +AC_DEFUN([gl_FUNC_EXPM1], +[ + AC_REQUIRE([gl_MATH_H_DEFAULTS]) + + dnl Persuade glibc <math.h> to declare expm1(). + AC_REQUIRE([gl_USE_SYSTEM_EXTENSIONS]) + + EXPM1_LIBM= + AC_CACHE_CHECK([whether expm1() can be used without linking with libm], + [gl_cv_func_expm1_no_libm], + [ + AC_LINK_IFELSE( + [AC_LANG_PROGRAM( + [[#ifndef __NO_MATH_INLINES + # define __NO_MATH_INLINES 1 /* for glibc */ + #endif + #include <math.h> + double (*funcptr) (double) = expm1; + double x;]], + [[return funcptr (x) > 0.5 + || expm1 (x) > 0.5;]])], + [gl_cv_func_expm1_no_libm=yes], + [gl_cv_func_expm1_no_libm=no]) + ]) + if test $gl_cv_func_expm1_no_libm = no; then + AC_CACHE_CHECK([whether expm1() can be used with libm], + [gl_cv_func_expm1_in_libm], + [ + save_LIBS="$LIBS" + LIBS="$LIBS -lm" + AC_LINK_IFELSE( + [AC_LANG_PROGRAM( + [[#ifndef __NO_MATH_INLINES + # define __NO_MATH_INLINES 1 /* for glibc */ + #endif + #include <math.h> + double (*funcptr) (double) = expm1; + double x;]], + [[return funcptr (x) > 0.5 + || expm1 (x) > 0.5;]])], + [gl_cv_func_expm1_in_libm=yes], + [gl_cv_func_expm1_in_libm=no]) + LIBS="$save_LIBS" + ]) + if test $gl_cv_func_expm1_in_libm = yes; then + EXPM1_LIBM=-lm + fi + fi + if test $gl_cv_func_expm1_no_libm = no \ + && test $gl_cv_func_expm1_in_libm = no; then + HAVE_EXPM1=0 + dnl Find libraries needed to link lib/expm1.c. + AC_REQUIRE([gl_FUNC_ISNAND]) + AC_REQUIRE([gl_FUNC_EXP]) + AC_REQUIRE([gl_FUNC_ROUND]) + AC_REQUIRE([gl_FUNC_LDEXP]) + EXPM1_LIBM= + dnl Append $ISNAND_LIBM to EXPM1_LIBM, avoiding gratuitous duplicates. + case " $EXPM1_LIBM " in + *" $ISNAND_LIBM "*) ;; + *) EXPM1_LIBM="$EXPM1_LIBM $ISNAND_LIBM" ;; + esac + dnl Append $EXP_LIBM to EXPM1_LIBM, avoiding gratuitous duplicates. + case " $EXPM1_LIBM " in + *" $EXP_LIBM "*) ;; + *) EXPM1_LIBM="$EXPM1_LIBM $EXP_LIBM" ;; + esac + dnl Append $ROUND_LIBM to EXPM1_LIBM, avoiding gratuitous duplicates. + case " $EXPM1_LIBM " in + *" $ROUND_LIBM "*) ;; + *) EXPM1_LIBM="$EXPM1_LIBM $ROUND_LIBM" ;; + esac + dnl Append $LDEXP_LIBM to EXPM1_LIBM, avoiding gratuitous duplicates. + case " $EXPM1_LIBM " in + *" $LDEXP_LIBM "*) ;; + *) EXPM1_LIBM="$EXPM1_LIBM $LDEXP_LIBM" ;; + esac + fi + AC_SUBST([EXPM1_LIBM]) +])
--- a/m4/math_h.m4 +++ b/m4/math_h.m4 @@ -1,4 +1,4 @@ -# math_h.m4 serial 79 +# math_h.m4 serial 80 dnl Copyright (C) 2007-2012 Free Software Foundation, Inc. dnl This file is free software; the Free Software Foundation dnl gives unlimited permission to copy and/or distribute it, @@ -41,7 +41,7 @@ gl_WARN_ON_USE_PREPARE([[#include <math.h>]], [acosf acosl asinf asinl atanf atanl cbrt cbrtf cbrtl ceilf ceill copysign copysignf copysignl cosf cosl coshf - expf expl fabsf fabsl floorf floorl fma fmaf fmal + expf expl expm1 fabsf fabsl floorf floorl fma fmaf fmal fmod fmodf fmodl frexpf frexpl hypotf hypotl ldexpf ldexpl logb logf logl log10f log10l modf modff modfl powf remainder remainderf remainderl @@ -81,6 +81,7 @@ GNULIB_COSHF=0; AC_SUBST([GNULIB_COSHF]) GNULIB_EXPF=0; AC_SUBST([GNULIB_EXPF]) GNULIB_EXPL=0; AC_SUBST([GNULIB_EXPL]) + GNULIB_EXPM1=0; AC_SUBST([GNULIB_EXPM1]) GNULIB_FABSF=0; AC_SUBST([GNULIB_FABSF]) GNULIB_FABSL=0; AC_SUBST([GNULIB_FABSL]) GNULIB_FLOOR=0; AC_SUBST([GNULIB_FLOOR]) @@ -155,6 +156,7 @@ HAVE_COSHF=1; AC_SUBST([HAVE_COSHF]) HAVE_EXPF=1; AC_SUBST([HAVE_EXPF]) HAVE_EXPL=1; AC_SUBST([HAVE_EXPL]) + HAVE_EXPM1=1; AC_SUBST([HAVE_EXPM1]) HAVE_FABSF=1; AC_SUBST([HAVE_FABSF]) HAVE_FABSL=1; AC_SUBST([HAVE_FABSL]) HAVE_FMA=1; AC_SUBST([HAVE_FMA])
new file mode 100644 --- /dev/null +++ b/modules/expm1 @@ -0,0 +1,36 @@ +Description: +expm1() function: exponential function minus one. + +Files: +lib/expm1.c +m4/expm1.m4 +m4/mathfunc.m4 + +Depends-on: +math +extensions +isnand [test $HAVE_EXPM1 = 0] +exp [test $HAVE_EXPM1 = 0] +round [test $HAVE_EXPM1 = 0] +ldexp [test $HAVE_EXPM1 = 0] + +configure.ac: +gl_FUNC_EXPM1 +if test $HAVE_EXPM1 = 0; then + AC_LIBOBJ([expm1]) +fi +gl_MATH_MODULE_INDICATOR([expm1]) + +Makefile.am: + +Include: +<math.h> + +Link: +$(EXPM1_LIBM) + +License: +LGPL + +Maintainer: +Bruno Haible
--- a/modules/math +++ b/modules/math @@ -49,6 +49,7 @@ -e 's/@''GNULIB_COSHF''@/$(GNULIB_COSHF)/g' \ -e 's/@''GNULIB_EXPF''@/$(GNULIB_EXPF)/g' \ -e 's/@''GNULIB_EXPL''@/$(GNULIB_EXPL)/g' \ + -e 's/@''GNULIB_EXPM1''@/$(GNULIB_EXPM1)/g' \ -e 's/@''GNULIB_FABSF''@/$(GNULIB_FABSF)/g' \ -e 's/@''GNULIB_FABSL''@/$(GNULIB_FABSL)/g' \ -e 's/@''GNULIB_FLOOR''@/$(GNULIB_FLOOR)/g' \ @@ -123,6 +124,7 @@ -e 's|@''HAVE_COSHF''@|$(HAVE_COSHF)|g' \ -e 's|@''HAVE_EXPF''@|$(HAVE_EXPF)|g' \ -e 's|@''HAVE_EXPL''@|$(HAVE_EXPL)|g' \ + -e 's|@''HAVE_EXPM1''@|$(HAVE_EXPM1)|g' \ -e 's|@''HAVE_FABSF''@|$(HAVE_FABSF)|g' \ -e 's|@''HAVE_FABSL''@|$(HAVE_FABSL)|g' \ -e 's|@''HAVE_FMA''@|$(HAVE_FMA)|g' \
--- a/tests/test-math-c++.cc +++ b/tests/test-math-c++.cc @@ -124,6 +124,10 @@ SIGNATURE_CHECK (GNULIB_NAMESPACE::expl, long double, (long double)); #endif +#if GNULIB_TEST_EXPM1 +SIGNATURE_CHECK (GNULIB_NAMESPACE::expm1, double, (double)); +#endif + #if GNULIB_TEST_FABSF SIGNATURE_CHECK (GNULIB_NAMESPACE::fabsf, float, (float)); #endif