glibc/sysdeps/libm-ieee754/e_exp.c
Ulrich Drepper 3f62b69af3 Update.
1998-07-27 17:42  Ulrich Drepper  <drepper@cygnus.com>

	* nss/nss_files/files-parse.c (INT_FIELD): Use strtoul instead of
	strtol.
	(INT_FIELD_MAYBE_NULL): Likewise.

	* posix/globtest.c: Rewrite for extended test suite.
	* posix/globtest.sh: More tests.
	Patch by Brian Wellington <bwelling@anomaly.munge.com>.

	* stdlib/strtol.c: Don't redefine LONG_MAX, LONG_MIN, and ULONG_MAX.
	Use new macro.

	* sysdeps/generic/readv.c: Correct return type.
	* sysdeps/generic/writev.c: Likewise.

1998-07-24  Gordon Matzigkeit  <gord@fig.org>

	* argp/argp-help.c (_GNU_SOURCE): Define, to suck in
	program_invocation_name when compiling outside of glibc.

1998-07-26  Philip Blundell  <philb@gnu.org>

	* sysdeps/unix/sysv/linux/arm/siglist.c: New file; ARM tools don't
	like `@' in .type directives.

	* sysdeps/libm-ieee754/e_expf.c (__ieee754_expf): Check whether
	FE_TONEAREST exists for this platform before using it.
	* sysdeps/libm-ieee754/e_exp.c (__ieee754_exp): Likewise.

	* sysdeps/arm/dl-machine.h (elf_machine_rel): Delete redundant
	debugging code.  Correct handling of PC24 relocs.

	* elf/Makefile (ld-map): Only define if versioning is in use.

	* sysdeps/arm/fpu_control.h: Move to ...
	* sysdeps/arm/fpu/fpu_control.h: ... here.
	* sysdeps/generic/fpu_control.h: Made usable as a dummy
	implementation.

	* sysdeps/unix/sysv/linux/arm/brk.c: New file.

	* sysdeps/arm/machine-gmon.h: Improved profiling for ARM.
	* sysdeps/arm/sysdep.h (CALL_MCOUNT): Replace stub with real
	implementation.
	* sysdeps/unix/sysv/linux/arm/clone.S: Likewise.
	Based on patch from Scott Bambrough and Pat Beirne.

	* shlib-versions: Add appropriate definitions for ARM machines.

	* README.template: Mention that Linux/ARM with ELF works now.

1998-07-18  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* Makerules: Generate compilation rules for all object suffixes,
	not only those currently selected, for sources in the current or
	object directory.

1998-07-24  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* posix/fnmatch.c (fnmatch): Allow `/' in character class.  Don't
	match `/' in filename by a character class if requested.
	* posix/testfnm.c: Rewritten.
	* posix/testfnm.args: Removed.

1998-07-25  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* posix/annexc.c (limits_syms): Add missing symbols.
	(stdarg_syms): Move va_list to `maybe' list.
	(stdio_syms): Add FOPEN_MAX.
1998-07-27 17:55:05 +00:00

163 lines
4.9 KiB
C

/* Double-precision floating point e^x.
Copyright (C) 1997, 1998 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
The GNU C Library 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
/* How this works:
The basic design here is from
Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical
Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft.,
17 (1), March 1991, pp. 26-45.
The input value, x, is written as
x = n * ln(2)_0 + t/512 + delta[t] + x + n * ln(2)_1
where:
- n is an integer, 1024 >= n >= -1075;
- ln(2)_0 is the first 43 bits of ln(2), and ln(2)_1 is the remainder, so
that |ln(2)_1| < 2^-32;
- t is an integer, 177 >= t >= -177
- delta is based on a table entry, delta[t] < 2^-28
- x is whatever is left, |x| < 2^-10
Then e^x is approximated as
e^x = 2^n_1 ( 2^n_0 e^(t/512 + delta[t])
+ ( 2^n_0 e^(t/512 + delta[t])
* ( p(x + n * ln(2)_1)
- n*ln(2)_1
- n*ln(2)_1 * p(x + n * ln(2)_1) ) ) )
where
- p(x) is a polynomial approximating e(x)-1;
- e^(t/512 + delta[t]) is obtained from a table;
- n_1 + n_0 = n, so that |n_0| < DBL_MIN_EXP-1.
If it happens that n_1 == 0 (this is the usual case), that multiplication
is omitted.
*/
#ifndef _GNU_SOURCE
#define _GNU_SOURCE
#endif
#include <float.h>
#include <ieee754.h>
#include <math.h>
#include <fenv.h>
#include <inttypes.h>
#include <math_private.h>
extern const float __exp_deltatable[178];
extern const double __exp_atable[355] /* __attribute__((mode(DF))) */;
static const volatile double TWO1023 = 8.988465674311579539e+307;
static const volatile double TWOM1000 = 9.3326361850321887899e-302;
double
__ieee754_exp (double x)
{
static const double himark = 709.7827128933840868;
static const double lomark = -745.1332191019412221;
/* Check for usual case. */
if (isless (x, himark) && isgreater (x, lomark))
{
static const double THREEp42 = 13194139533312.0;
static const double THREEp51 = 6755399441055744.0;
/* 1/ln(2). */
static const double M_1_LN2 = 1.442695040888963387;
/* ln(2), part 1 */
static const double M_LN2_0 = .6931471805598903302;
/* ln(2), part 2 */
static const double M_LN2_1 = 5.497923018708371155e-14;
int tval, unsafe, n_i;
double x22, n, t, dely, result;
union ieee754_double ex2_u, scale_u;
fenv_t oldenv;
feholdexcept (&oldenv);
#ifdef FE_TONEAREST
fesetround (FE_TONEAREST);
#endif
/* Calculate n. */
n = x * M_1_LN2 + THREEp51;
n -= THREEp51;
x = x - n*M_LN2_0;
/* Calculate t/512. */
t = x + THREEp42;
t -= THREEp42;
x -= t;
/* Compute tval = t. */
tval = (int) (t * 512.0);
if (t >= 0)
x -= __exp_deltatable[tval];
else
x += __exp_deltatable[-tval];
/* Now, the variable x contains x + n*ln(2)_1. */
dely = n*M_LN2_1;
/* Compute ex2 = 2^n_0 e^(t/512+delta[t]). */
ex2_u.d = __exp_atable[tval+177];
n_i = (int)n;
/* 'unsafe' is 1 iff n_1 != 0. */
unsafe = abs(n_i) >= -DBL_MIN_EXP - 1;
ex2_u.ieee.exponent += n_i >> unsafe;
/* Compute scale = 2^n_1. */
scale_u.d = 1.0;
scale_u.ieee.exponent += n_i - (n_i >> unsafe);
/* Approximate e^x2 - 1, using a fourth-degree polynomial,
with maximum error in [-2^-10-2^-28,2^-10+2^-28]
less than 4.9e-19. */
x22 = (((0.04166666898464281565
* x + 0.1666666766008501610)
* x + 0.499999999999990008)
* x + 0.9999999999999976685) * x;
/* Allow for impact of dely. */
x22 -= dely + dely*x22;
/* Return result. */
fesetenv (&oldenv);
result = x22 * ex2_u.d + ex2_u.d;
if (!unsafe)
return result;
else
return result * scale_u.d;
}
/* Exceptional cases: */
else if (isless (x, himark))
{
if (__isinf (x))
/* e^-inf == 0, with no error. */
return 0;
else
/* Underflow */
return TWOM1000 * TWOM1000;
}
else
/* Return x, if x is a NaN or Inf; or overflow, otherwise. */
return TWO1023*x;
}