view lib/expl.c @ 16366:bb182ee4a09d

maint: replace FSF snail-mail addresses with URLs * config/argz.mk, lib/accept4.c, lib/alignof.h, lib/alloca.in.h: * lib/alphasort.c, lib/arcfour.c, lib/arcfour.h, lib/arctwo.c: * lib/arctwo.h, lib/argz.c, lib/arpa_inet.in.h, lib/asnprintf.c: * lib/asprintf.c, lib/assert.in.h, lib/base32.c, lib/base32.h: * lib/base64.c, lib/base64.h, lib/c-ctype.c, lib/c-ctype.h: * lib/c-strcase.h, lib/c-strcasecmp.c, lib/c-strncasecmp.c: * lib/check-version.c, lib/check-version.h, lib/config.charset: * lib/ctype.in.h, lib/des.c, lib/des.h, lib/dup3.c, lib/errno.in.h: * lib/float+.h, lib/fnmatch.c, lib/fnmatch.in.h, lib/fnmatch_loop.c: * lib/fseeko.c, lib/gai_strerror.c, lib/gc-gnulib.c: * lib/gc-libgcrypt.c, lib/gc-pbkdf2-sha1.c, lib/gc.h: * lib/getaddrinfo.c, lib/getdelim.c, lib/getfilecon.c, lib/getline.c: * lib/getlogin_r.c, lib/getpass.c, lib/getpass.h, lib/gettext.h: * lib/gettimeofday.c, lib/glob.in.h, lib/glthread/cond.c: * lib/glthread/cond.h, lib/glthread/lock.c, lib/glthread/lock.h: * lib/glthread/thread.c, lib/glthread/thread.h: * lib/glthread/threadlib.c, lib/glthread/yield.h, lib/hmac-md5.c: * lib/hmac-sha1.c, lib/hmac.h, lib/iconv.c, lib/iconv.in.h: * lib/iconv_close.c, lib/iconv_open.c, lib/inet_ntop.c, lib/isfinite.c: * lib/isinf.c, lib/iswblank.c, lib/langinfo.in.h, lib/link.c: * lib/localcharset.c, lib/localcharset.h, lib/lseek.c, lib/malloc.c: * lib/malloca.c, lib/malloca.h, lib/md2.c, lib/md2.h, lib/md4.c: * lib/md4.h, lib/md5.c, lib/md5.h, lib/memmem.c, lib/mempcpy.c: * lib/memset.c, lib/memxor.c, lib/memxor.h, lib/minmax.h, lib/mktime.c: * lib/msvc-inval.c, lib/msvc-inval.h, lib/msvc-nothrow.c: * lib/msvc-nothrow.h, lib/netdb.in.h, lib/netinet_in.in.h, lib/nproc.c: * lib/nproc.h, lib/obstack_printf.c, lib/pathmax.h, lib/pipe.c: * lib/pipe2.c, lib/poll.c, lib/poll.in.h, lib/printf-args.c: * lib/printf-args.h, lib/printf-parse.c, lib/printf-parse.h: * lib/pselect.c, lib/pthread.in.h, lib/pty-private.h, lib/pty.in.h: * lib/read-file.c, lib/read-file.h, lib/ref-add.sin, lib/ref-del.sin: * lib/regcomp.c, lib/regex.c, lib/regex.h, lib/regex_internal.c: * lib/regex_internal.h, lib/regexec.c, lib/rijndael-alg-fst.c: * lib/rijndael-alg-fst.h, lib/rijndael-api-fst.c: * lib/rijndael-api-fst.h, lib/rint.c, lib/rintf.c, lib/rintl.c: * lib/round.c, lib/roundf.c, lib/roundl.c, lib/scandir.c, lib/select.c: * lib/sha1.c, lib/sha1.h, lib/size_max.h, lib/snprintf.c: * lib/stdalign.in.h, lib/stdarg.in.h, lib/stdbool.in.h: * lib/stddef.in.h, lib/stdint.in.h, lib/stdio.in.h, lib/str-kmp.h: * lib/str-two-way.h, lib/strcasecmp.c, lib/strcasestr.c, lib/strdup.c: * lib/striconv.c, lib/striconv.h, lib/string.in.h, lib/strings.in.h: * lib/strncasecmp.c, lib/strndup.c, lib/strnlen.c, lib/strpbrk.c: * lib/strptime.c, lib/strsep.c, lib/strstr.c, lib/strverscmp.c: * lib/sys_file.in.h, lib/sys_ioctl.in.h, lib/sys_select.in.h: * lib/sys_socket.in.h, lib/sys_stat.in.h, lib/sys_time.in.h: * lib/sys_times.in.h, lib/sys_types.in.h, lib/sys_uio.in.h: * lib/sys_utsname.in.h, lib/sys_wait.in.h, lib/tcgetsid.c: * lib/termios.in.h, lib/time.in.h, lib/time_r.c, lib/timegm.c: * lib/times.c, lib/unictype/3level.h, lib/unictype/3levelbit.h: * lib/unistd.in.h, lib/vasnprintf.c, lib/vasnprintf.h, lib/vasprintf.c: * lib/vsnprintf.c, lib/waitpid.c, lib/wchar.in.h, lib/wctype.in.h: * lib/xsize.h, tests/test-closein.c, tests/test-des.c: * tests/test-fclose.c, tests/test-fgetc.c, tests/test-filevercmp.c: * tests/test-fputc.c, tests/test-fread.c, tests/test-fwrite.c: * tests/test-gc-arcfour.c, tests/test-gc-arctwo.c, tests/test-gc-des.c: * tests/test-gc-hmac-md5.c, tests/test-gc-hmac-sha1.c: * tests/test-gc-md2.c, tests/test-gc-md4.c, tests/test-gc-md5.c: * tests/test-gc-pbkdf2-sha1.c, tests/test-gc-rijndael.c: * tests/test-gc-sha1.c, tests/test-gc.c, tests/test-getdelim.c: * tests/test-getline.c, tests/test-getndelim2.c, tests/test-md2.c: * tests/test-md4.c, tests/test-parse-datetime.c, tests/test-perror.c: * tests/test-perror2.c, tests/test-pipe.c, tests/test-pipe2.c: * tests/test-poll.c, tests/test-quotearg-simple.c: * tests/test-quotearg.c, tests/test-quotearg.h: * tests/test-round-ieee.c, tests/test-round1.c: * tests/test-roundf-ieee.c, tests/test-roundf1.c: * tests/test-roundl-ieee.c, tests/test-roundl.c: * tests/test-safe-alloc.c, tests/test-sigpipe.c: * tests/test-spawn-pipe-child.c, tests/test-spawn-pipe-main.c: * tests/test-strerror.c, tests/test-strerror_r.c: * tests/test-strsignal.c, tests/test-strverscmp.c: * tests/test-xmemdup0.c: Replace FSF snail mail addresses with URLs, as per GNU coding standards. See glibc bug <http://sourceware.org/bugzilla/show_bug.cgi?id=13673>.
author Paul Eggert <eggert@cs.ucla.edu>
date Thu, 09 Feb 2012 21:39:05 -0800 (2012-02-10)
parents a712776b11ce
children 2074f2bf7216
line wrap: on
line source
/* Emulation for expl.
   Contributed by Paolo Bonzini

   Copyright 2002-2003, 2007, 2009-2012 Free Software Foundation, Inc.

   This file is part of gnulib.

   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>

#if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE

long double
expl (long double x)
{
  return exp (x);
}

#else

# include <float.h>

static const long double C[] = {
/* Chebyshev polynomial coefficients for (exp(x)-1)/x */
# define P1 C[0]
# define P2 C[1]
# define P3 C[2]
# define P4 C[3]
# define P5 C[4]
# define P6 C[5]
 0.5L,
 1.66666666666666666666666666666666683E-01L,
 4.16666666666666666666654902320001674E-02L,
 8.33333333333333333333314659767198461E-03L,
 1.38888888889899438565058018857254025E-03L,
 1.98412698413981650382436541785404286E-04L,

/* Smallest integer x for which e^x overflows.  */
# define himark C[6]
 11356.523406294143949491931077970765L,

/* Largest integer x for which e^x underflows.  */
# define lomark C[7]
-11433.4627433362978788372438434526231L,

/* very small number */
# define TINY C[8]
 1.0e-4900L,

/* 2^16383 */
# define TWO16383 C[9]
 5.94865747678615882542879663314003565E+4931L};

long double
expl (long double x)
{
  /* Check for usual case.  */
  if (x < himark && x > lomark)
    {
      int exponent;
      long double t, x22;
      int k = 1;
      long double result = 1.0;

      /* Compute an integer power of e with a granularity of 0.125.  */
      exponent = (int) floorl (x * 8.0L);
      x -= exponent / 8.0L;

      if (x > 0.0625)
        {
          exponent++;
          x -= 0.125L;
        }

      if (exponent < 0)
        {
          t = 0.8824969025845954028648921432290507362220L; /* e^-0.25 */
          exponent = -exponent;
        }
      else
        t = 1.1331484530668263168290072278117938725655L; /* e^0.25 */

      while (exponent)
        {
          if (exponent & k)
            {
              result *= t;
              exponent ^= k;
            }
          t *= t;
          k <<= 1;
        }

      /* Approximate (e^x - 1)/x, using a seventh-degree polynomial,
         with maximum error in [-2^-16-2^-53,2^-16+2^-53]
         less than 4.8e-39.  */
      x22 = x + x*x*(P1+x*(P2+x*(P3+x*(P4+x*(P5+x*P6)))));

      return result + result * x22;
    }
  /* Exceptional cases:  */
  else if (x < himark)
    {
      if (x + x == x)
        /* e^-inf == 0, with no error.  */
        return 0;
      else
        /* Underflow */
        return TINY * TINY;
    }
  else
    /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
    return TWO16383*x;
}

#endif

#if 0
int
main (void)
{
  printf ("%.16Lg\n", expl (1.0L));
  printf ("%.16Lg\n", expl (-1.0L));
  printf ("%.16Lg\n", expl (2.0L));
  printf ("%.16Lg\n", expl (4.0L));
  printf ("%.16Lg\n", expl (-2.0L));
  printf ("%.16Lg\n", expl (-4.0L));
  printf ("%.16Lg\n", expl (0.0625L));
  printf ("%.16Lg\n", expl (0.3L));
  printf ("%.16Lg\n", expl (0.6L));
}
#endif