glibc/sysdeps/libm-ieee754/s_expm1.c
Ulrich Drepper cccda09fd7 update from main archive 961005
Sun Oct  6 02:05:52 1996  Ulrich Drepper  <drepper@cygnus.com>

	* posix/getopt.c: Add casts to prevent warnings.
	* posix/regex.c: Likewise.

	* math/Makefile (long-m-routines, long-m-yes): Define to correct
	values to make `long double' functions available.
	(distribute): Add $(long-m-yes:=.c).

	* sysdeps/libm-i387/s_ceill.S: Correct loading of return value.
	Use long double instruction.

	* sysdeps/libm-ieee754/e_atanhl.c (huge): Correct constant.
	* sysdeps/libm-ieee754/e_asinhl.c: Likewise.
	* sysdeps/libm-ieee754/s_tanhl.c: Likewise.

	* sysdeps/libm-ieee754/e_coshl.c: New file.

	* sysdeps/libm-ieee754/s_asinh.c [!NO_LONG_DOUBLE]: Define names
	for `long double' version as alias.
	* sysdeps/libm-ieee754/s_atan.c: Likewise.
	* sysdeps/libm-ieee754/s_cbrt.c: Likewise.
	* sysdeps/libm-ieee754/s_ceil.c: Likewise.
	* sysdeps/libm-ieee754/s_copysign.c: Likewise.
	* sysdeps/libm-ieee754/s_cos.c: Likewise.
	* sysdeps/libm-ieee754/s_erf.c: Likewise.
	* sysdeps/libm-ieee754/s_expm1.c: Likewise.
	* sysdeps/libm-ieee754/s_fabs.c: Likewise.
	* sysdeps/libm-ieee754/s_finite.c: Likewise.
	* sysdeps/libm-ieee754/s_floor.c: Likewise.
	* sysdeps/libm-ieee754/s_frexp.c: Likewise.
	* sysdeps/libm-ieee754/s_ilogb.c: Likewise.
	* sysdeps/libm-ieee754/s_ldexp.c: Likewise.
	* sysdeps/libm-ieee754/s_log1p.c: Likewise.
	* sysdeps/libm-ieee754/s_logb.c: Likewise.
	* sysdeps/libm-ieee754/s_modf.c: Likewise.
	* sysdeps/libm-ieee754/s_nextafter.c: Likewise.
	* sysdeps/libm-ieee754/s_rint.c: Likewise.
	* sysdeps/libm-ieee754/s_scalbn.c: Likewise.
	* sysdeps/libm-ieee754/s_significand.c: Likewise.
	* sysdeps/libm-ieee754/s_sin.c: Likewise.
	* sysdeps/libm-ieee754/s_tan.c: Likewise.
	* sysdeps/libm-ieee754/s_tanh.c: Likewise.
	* sysdeps/libm-ieee754/w_acos.c: Likewise.
	* sysdeps/libm-ieee754/w_acosh.c: Likewise.
	* sysdeps/libm-ieee754/w_sin.c: Likewise.
	* sysdeps/libm-ieee754/w_atan2.c: Likewise.
	* sysdeps/libm-ieee754/w_atanh.c: Likewise.
	* sysdeps/libm-ieee754/w_cabs.c: Likewise.
	* sysdeps/libm-ieee754/w_cosh.c: Likewise.
	* sysdeps/libm-ieee754/w_drem.c: Likewise.
	* sysdeps/libm-ieee754/w_exp.c: Likewise.
	* sysdeps/libm-ieee754/w_fmod.c: Likewise.
	* sysdeps/libm-ieee754/w_gamma.c: Likewise.
	* sysdeps/libm-ieee754/w_gamma_r.c: Likewise.
	* sysdeps/libm-ieee754/w_hypot.c: Likewise.
	* sysdeps/libm-ieee754/w_j0.c: Likewise.
	* sysdeps/libm-ieee754/w_j1.c: Likewise.
	* sysdeps/libm-ieee754/w_jn.c: Likewise.
	* sysdeps/libm-ieee754/w_lgamma.c: Likewise.
	* sysdeps/libm-ieee754/w_lgamma_r.c: Likewise.
	* sysdeps/libm-ieee754/w_log.c: Likewise.
	* sysdeps/libm-ieee754/w_log10.c: Likewise.
	* sysdeps/libm-ieee754/w_pow.c: Likewise.
	* sysdeps/libm-ieee754/w_remainder.c: Likewise.
	* sysdeps/libm-ieee754/w_scalb.c: Likewise.
	* sysdeps/libm-ieee754/w_sinh.c: Likewise.
	* sysdeps/libm-ieee754/w_sqrt.c: Likewise.

	Stub files for missing long double math functions.
	* sysdeps/stub/e_acoshl.c: New file.
	* sysdeps/stub/e_hypotl.c: New file.
	* sysdeps/stub/e_j0l.c: New file.
	* sysdeps/stub/e_j1l.c: New file.
	* sysdeps/stub/e_jnl.c: New file.
	* sysdeps/stub/e_lgammal_r.c: New file.
	* sysdeps/stub/e_powl.c: New file.
	* sysdeps/stub/e_rem_pio2l.c: New file.
	* sysdeps/stub/e_sinhl.c: New file.
	* sysdeps/stub/k_cosl.c: New file.
	* sysdeps/stub/k_rem_pio2l.c: New file.
	* sysdeps/stub/k_sinl.c: New file.
	* sysdeps/stub/k_tanl.c: New file.
	* sysdeps/stub/s_erfl.c: New file.
	* sysdeps/stub/s_expm1l.c: New file.

	* sysdeps/i386/__longjmp.S: Use PSEUDO_END macro to provide
	.size directive.
	* sysdeps/i386/bsd-_setjmp.S: Likewise.
	* sysdeps/i386/bsd-setjmp.S: Likewise.
	* sysdeps/i386/memchr.S: Likewise.
	* sysdeps/i386/memcmp.S: Likewise.
	* sysdeps/i386/setjmp.S: Likewise.
	* sysdeps/i386/stpcpy.S: Likewise.
	* sysdeps/i386/stpncpy.S: Likewise.
	* sysdeps/i386/strchr.S: Likewise.
	* sysdeps/i386/strcspn.S: Likewise.
	* sysdeps/i386/strpbrk.S: Likewise.
	* sysdeps/i386/strrchr.S: Likewise.
	* sysdeps/i386/strspn.S: Likewise.
	* sysdeps/i386/strtok.S: Likewise.
	* sysdeps/i386/i486/strcat.S: Likewise.
	* sysdeps/i386/i486/strlen.S: Likewise.
	* sysdeps/i386/i586/memset.S: Likewise.
	* sysdeps/i386/i586/strchr.S: Likewise.
	* sysdeps/i386/i586/strlen.S: Likewise.
	* sysdeps/libm-i387/e_acos.S: Likewise.
	* sysdeps/libm-i387/e_acosl.S: Likewise.
	* sysdeps/libm-i387/e_asin.S: Likewise.
	* sysdeps/libm-i387/e_asinl.S: Likewise.
	* sysdeps/libm-i387/e_atan2.S: Likewise.
	* sysdeps/libm-i387/e_atan2l.S: Likewise.
	* sysdeps/libm-i387/e_exp.S: Likewise.
	* sysdeps/libm-i387/e_expl.S: Likewise.
	* sysdeps/libm-i387/e_fmod.S: Likewise.
	* sysdeps/libm-i387/e_fmodl.S: Likewise.
	* sysdeps/libm-i387/e_log.S: Likewise.
	* sysdeps/libm-i387/e_log10.S: Likewise.
	* sysdeps/libm-i387/e_log10l.S: Likewise.
	* sysdeps/libm-i387/e_logl.S: Likewise.
	* sysdeps/libm-i387/e_remainder.S: Likewise.
	* sysdeps/libm-i387/e_remainderf.S: Likewise.
	* sysdeps/libm-i387/e_remainderl.S: Likewise.
	* sysdeps/libm-i387/e_scalb.S: Likewise.
	* sysdeps/libm-i387/e_scalbl.S: Likewise.
	* sysdeps/libm-i387/e_sqrt.S: Likewise.
	* sysdeps/libm-i387/e_sqrtf.S: Likewise.
	* sysdeps/libm-i387/e_sqrtl.S: Likewise.
	* sysdeps/libm-i387/s_atan.S: Likewise.
	* sysdeps/libm-i387/s_atanf.S: Likewise.
	* sysdeps/libm-i387/s_atanl.S: Likewise.
	* sysdeps/libm-i387/s_ceil.S: Likewise.
	* sysdeps/libm-i387/s_ceilf.S: Likewise.
	* sysdeps/libm-i387/s_ceill.S: Likewise.
	* sysdeps/libm-i387/s_copysign.S: Likewise.
	* sysdeps/libm-i387/s_copysignf.S: Likewise.
	* sysdeps/libm-i387/s_copysignl.S: Likewise.
	* sysdeps/libm-i387/s_cos.S: Likewise.
	* sysdeps/libm-i387/s_cosf.S: Likewise.
	* sysdeps/libm-i387/s_cosl.S: Likewise.
	* sysdeps/libm-i387/s_finite.S: Likewise.
	* sysdeps/libm-i387/s_finitef.S: Likewise.
	* sysdeps/libm-i387/s_finitel.S: Likewise.
	* sysdeps/libm-i387/s_floor.S: Likewise.
	* sysdeps/libm-i387/s_floorf.S: Likewise.
	* sysdeps/libm-i387/s_floorl.S: Likewise.
	* sysdeps/libm-i387/s_ilogb.S: Likewise.
	* sysdeps/libm-i387/s_ilogbf.S: Likewise.
	* sysdeps/libm-i387/s_ilogbl.S: Likewise.
	* sysdeps/libm-i387/s_log1p.S: Likewise.
	* sysdeps/libm-i387/s_log1pf.S: Likewise.
	* sysdeps/libm-i387/s_log1pl.S: Likewise.
	* sysdeps/libm-i387/s_logb.S: Likewise.
	* sysdeps/libm-i387/s_logbf.S: Likewise.
	* sysdeps/libm-i387/s_logbl.S: Likewise.
	* sysdeps/libm-i387/s_rint.S: Likewise.
	* sysdeps/libm-i387/s_rintf.S: Likewise.
	* sysdeps/libm-i387/s_rintl.S: Likewise.
	* sysdeps/libm-i387/s_scalbn.S: Likewise.
	* sysdeps/libm-i387/s_scalbnf.S: Likewise.
	* sysdeps/libm-i387/s_scalbnl.S: Likewise.
	* sysdeps/libm-i387/s_significand.S: Likewise.
	* sysdeps/libm-i387/s_significandf.S: Likewise.
	* sysdeps/libm-i387/s_significandl.S: Likewise.
	* sysdeps/libm-i387/s_sin.S: Likewise.
	* sysdeps/libm-i387/s_sinf.S: Likewise.
	* sysdeps/libm-i387/s_sinl.S: Likewise.
	* sysdeps/libm-i387/s_tan.S: Likewise.
	* sysdeps/libm-i387/s_tanf.S: Likewise.
	* sysdeps/libm-i387/s_tanl.S: Likewise.

	* sysdeps/unix/sysv/linux/i386/clone.S: Add .size directive.
	* sysdeps/unix/sysv/linux/i386/mmap.S. Likewise.
	* sysdeps/unix/sysv/linux/i386/socket.S. Likewise.
	* sysdeps/unix/sysv/linux/i386/sysdep.S. More compact .size line.

	* sysdeps/i386/sysdep.h (ASM_SIZE_DIRECTIVE): New macro.  Used
	to provide .size directive on ELF systems.

	* sysdeps/unix/sysv/linux/i386/profil-counter.h: Include
	<sigcontext.h> and rename parameter type to sigcontext.
	* sysdeps/unix/sysv/linux/i386/sigcontext.h New file.

	* sysdeps/unix/sysv/linux/i386/syscall.S: From Linux 2.1 on
	negative values might occur as positive results.  Test against
	-125 to decide for error or not.
	* sysdeps/unix/sysv/linux/i386/sysdep.h: Likewise for system calls.

Thu Oct  3 21:07:58 1996  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* elf/dl-open.c: Use _DYNAMIC instead of _dl_start to decide
	whether this is a statically linked program.  The latter is now
	always defined.

Fri Oct  4 02:08:10 1996  Bang Jun-Young  <bangjy@nownuri.nowcom.co.kr>

	* po/ko.po: Update.

Fri Oct  4 02:07:46 1996  Michel Robitaille  <robitail@IRO.UMontreal.CA>

	* po/fr.po: New file.

Fri Oct  4 05:04:52 1996  Ulrich Drepper  <drepper@cygnus.com>

	* sysdeps/unix/sysv/linux/i386/sigcontext.h: New file.

	Add support for MD5 crypt replacement.
	* Makefile (subdirs): Add crypt.
	* shlib-versions: Add entry for libcrypt.
	* crypt/md5-crypt.c: New file.
	* crypt/md5.c: New file.
	* crypt/md5.h: New file.
	* sysdeps/generic/crypt-entry.c: New file.
	* sysdeps/generic/crypt.h: New file.

Thu Oct  3 20:53:23 1996  Andreas Jaeger  <aj@arthur.pfalz.de>

	* dirent/tst-seekdir.c: Provide correct prototypes.
	* io/test-utime.c: Likewise.
	* malloc/mallocbug.c: Likewise.
	* posix/testfnm.c: Likewise.
	* stdio-common/xbug.c: Likewise.
	* sysdeps/posix/cuserid.c: Likewise.

Wed Oct  2 13:33:48 1996  Richard Henderson  <rth@tamu.edu>

	Provide optimized string functions for Alpha processors.
	* sysdeps/alpha/bzero.S: New file.
	* sysdeps/alpha/memset.S: New file.
	* sysdeps/alpha/stpcpy.S: New file.
	* sysdeps/alpha/stpncpy.S: New file.
	* sysdeps/alpha/strcat.S: New file.
	* sysdeps/alpha/strchr.S: New file.
	* sysdeps/alpha/strcpy.S: New file.
	* sysdeps/alpha/strncat.S: New file.
	* sysdeps/alpha/strncpy.S: New file.
	* sysdeps/alpha/strrchr.S: New file.
	* sysdeps/alpha/stxcpy.S: New file.
	* sysdeps/alpha/stxncpy.S: New file.

	* sysdeps/alpha/Makefile [$(sudir)==string]: Add stxcpy and
	stxncpy to sysdep_routines.
	Minor correction.

Wed Oct  2 13:41:48 1996  Ulrich Drepper  <drepper@cygnus.com>

	* sysdeps/generic/strtok.c: Don't set stored pointer to NULL when
 	notheing is found.  This guarantees all subsequent calls behave
 	the same.
	* sysdeps/generic/strtok_r.c: Likewise.

Mon Sep 30 22:27:36 1996  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* sysdeps/posix/tempname.c (__stdio_gen_tempname): Don't declare
	`i' as const.

Mon Sep 30 22:38:29 1996  Richard Henderson  <rth@tamu.edu>

	* sysdeps/generic/strtok.c: When we hit EOS, don't set olds to
	NULL immediately; we're going to get called one more time.
	* sysdeps/generic/strtok_r.c: Likewise.

Tue Oct  1 09:12:21 1996  Ulrich Drepper  <drepper@cygnus.com>

	* locale/programs/ld-time.c: Always write some bytes at the end of
 	the file even if no `era's are specified.

	* stdio-common/tmpname.c (tmpbuf): Don't define as array of
 	pointers.

Tue Oct  1 01:43:11 1996  Ulrich Drepper  <drepper@cygnus.com>

	* libio/iofclose.c: Move unlocking to right position.

Mon Sep 30 03:08:34 1996  Richard Henderson  <rth@tamu.edu>

	* misc/Makefile: Kill force-wrapper.
	* misc/force-wrapper.c: Delete.

	* elf/eval.c: Add <string.h>.

	* gmon/sys/gmon_out.h: Nonsense like `char foo[sizeof(char*)]'
	followed by `bcopy(&ptr, &foo, sizeof(foo))' helps portability
	and binary compatibility not at all.  Better to do `char *foo'
	followed by `foo = ptr' as it is much cleaner.
	(struct gmon_hdr): Fix version.
	(struct gmon_hist_hdr): Fix low_pc, high_pc, hist_size, prof_rate.
	(struct gmon_cg_arc_record): Fix from_pc, self_pc, count.
	* gmon/gmon.c: De-ansidecl-ify.
	(write_hist): De-bcopy-fy.
	(write_call_graph): Likewise.

	* gmon/mcount.c: Assume _MCOUNT_DECL does the entire declaration.
	* sysdeps/alpha/machine-gmon.h: Update _MCOUNT_DECL.
	* sysdeps/generic/machine-gmon.h: Likewise.

	* resolv/netdb.h: Add __set_h_errno to mimic __set_errno.
	* nss/getXXent_r.c: Use __set_h_errno to set h_errno in all funcs.
	* nss/nss_dns/dns-network.c: Likewise.
	* resolv/getunamaddr.c: Likewise.  Also use __set_errno where needed.
	* resolv/getnetnamadr.c: Likewise.
	* resolv/res_debug.c: Likewise.
	* resolv/res_mkquery.c: Likewise.
	* resolv/res_query.c: Likewise.

	* libio/clearerr_u.c: It's not necessary to define __ protected
	function so don't do it.
	* libio/feof_u.c, libio/ferror_u.c, libio/fputc_u.c,
	  libio/getc_u.c, libio/getchar_u.c, libio/iofflush_u.c: Likewise.

	* libio/fgetc.c: Avoid a warning by casting _IO_funlockfile for
	the cleanup registrar.
	* libio/fputc.c, libio/freopen.c, libio/fseek.c, libio/getc.c,
	  libio/getchar.c, libio/iofclose.c, libio/iofflush.c,
	  libio/iofgetpos.c, libio/iofgets.c, libio/iofputs.c,
	  libio/iofread.c, libio/iofsetpos.c, libio/ioftell.c,
	  libio/iofwrite.c, libio/iogetdelim.c, libio/iogets.c,
	  libio/ioputs.c, libio/iosetbuffer.c, libio/iosetvbuf.c,
	  libio/ioungetc.c, libio/putc.c, libio/putchar.c, libio/rewind.c:
	Likewise.

	* locale/programs/ld-ctype.c: Include <alloca.h>.

	* login/login_tty.c: Get login_tty prototype from <utmp.h>.

	* posix/sys/types.h: Change #defines to typedefs.  This is looking
	forward to more comprehensive namespace cleanups for C++.
	* posix/unistd.h: Likewise for ssize_t.

	* pwd/getpw.c: Prototype and rename getpw -> __getpw and add a
	weak alias.

	* resolv/base64.c: Don't do `for (NULL; ...)' as it causes
	`statement with no effect' warnings.
	* resolv/inet_neta.c: Include <string.h> for strlen.

	* stdio-common/getline.c: Undef ssize_t before libio redefinition.
	* stdio-common/tstgetln.c: Same.  De-ansidecl-ify.
	* stdio-common/vfprintf.c: Same for va_list.
	* stdio-common/vfscanf.c: Same.
	* stdio-common/reg-printf.c: Prototype the __ function.
	* stdio-common/scanf.c [USE_IN_LIBIO]: Include <libioP.h> for
	_IO_vscanf declaration.

	* string/tester.c: Tsk, tsk.  Don't cast pointers to int,
	but to unsigned long for the health of 64-bit systems.

	* sunrpc/svc_udp.c: Define MAX only if we don't have it yet.
	Many system's <sys/param.h> pulls this in.

	* sysdeps/generic/dl-cache.c: Kill the bottom half of the
	patch doubled file.

	* sysdeps/generic/pty.c (forkpty): Get login_tty decl from <utmp.h>
	instead of defining it locally.

	* sysdeps/posix/sigvec.c: Prototype wrapper_handler and convert_mask.
	* sysdeps/stub/chflags.c: Prototype chflags.
	* sysdeps/stub/fchflags.c: Prototype fchflags.
	* sysdeps/stub/sstk.c: Prototype sstk.

	* sysdeps/unix/alpha/sysdep.S:  Add strong alias from errno
	variable to __errno.  Update __syscall_error to store to both
	the global and per-thread variables.

	* sysdeps/unix/sysv/linux/init-first.c: Change include of
	init-first.h from "" to <> as "" does not search the include path.
	Prototype _dl_start.

Sun Sep 29 14:41:17 1996  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* sysdeps/unix/Makefile ($(common-objpfx)s-proto.d): Make it a
	pattern rule to get the right stem.

Sat Sep 28 01:30:06 1996  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* Makefile ($(objpfx)version-info.h): Fix typo in previous change.

Sat Sep 28 00:44:38 1996  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* sysdeps/posix/euidaccess.c (__set_errno): Fix typo.

Sat Sep 28 00:40:38 1996  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* malloc/free.c (_free_internal): Don't call free recursively, use
	the internal functions instead.

Sat Sep 28 00:23:20 1996  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* sysdeps/posix/tempname.c (__stdio_gen_tempname) [USE_IN_LIBIO &&
	_IO_MTSAFE_IO]: Allocate and initialize the file lock.

Fri Sep 27 23:58:17 1996  Andreas Schwab  <schwab@issan.informatik.uni-dortmund.de>

	* catgets/gencat.c (main): Print version information on stdout,
	not stderr.
	* db/makedb.c: Likewise.
	* locale/programs/locale.c: Likewise.
	* locale/programs/localedef.c: Likewise.

Mon Sep 30 00:14:26 1996  Ulrich Drepper  <drepper@cygnus.com>

	Add implementation of netgroup.
	* inet/Makefile (distributes): Add netgroup.h.
	(routines): Add getnetgrent.c and getnetgrent_r.c.
	* inet/getnetgrent.c: New file.
	* inet/getnetgrent_r.c: New file.
	* inet/netgroup.h: New file.
	* netgroup.h: New file.
	* nsswitch.h: New file.
	* nss/Makefile (databases): Add getgrp.
	* nss/databases.def: Add netgroup.
	* nss/db-Makefile: Add rules for netgroup.
	* nss/netgrp-lookup.c: New file.
	* nss/nss.h: Add new status value NSS_STATUS_RETURN which will
	always return without a check of the transition table.
	* nss/nsswitch.h (struct service_user): Extend actions array to
	five elements.
	* nss/nsswitch.c (__nss_next): Allow NSS_STATUS_RETURN as legal
	status value.
	(nss_parse_service_list): Initialize action for NSS_STATUS_RETURN
	to NSS_ACTION_RETURN.
	* nss/nss_db/db-netgrp.c: New file.
	* nss/nss_files/files-netgrp.c: New file.
	* nss/nsswitch.conf: Add entry for netgroup.
	* resolv/netdb.h: Add prototypes for netgroup functions.

	* nss/nss_db/db-XXX.c: Use `enum nss_status' type when status
	value is used.

Sun Sep 29 12:55:58 1996  Ulrich Drepper  <drepper@cygnus.com>

	* sysdeps/unix/sysv/linux/syscalls.list: Change funciton name for
 	_llseek to _llseek (not llseek).
	Reported by Matthias Urlichs <smurf@smurf.noris.de>.

Sun Sep 29 05:34:32 1996  Ulrich Drepper  <drepper@cygnus.com>

	* inet/rcmd.c: Remove definition of MIN.

Sat Sep 28 14:22:51 1996  Ulrich Drepper  <drepper@cygnus.com>

	* dirent/readdir_r.c: Removed.  We indeed need a real implementation.
	* sysdeps/unix/readdir_r.c: New file.
	* sysdeps/unix/readdir.c: Remove check for correct parameter
	values.  Let them simply die.
	* manual/filesys.texi: Document readdir_r.

	* sysdeps/gnu/errlist.awk: Define _sys_errlist as `const char* const'.
	Proposed by Per Abrahamsen <abraham@dina.kvl.dk>.
1996-10-06 02:05:11 +00:00

234 lines
7.6 KiB
C

/* @(#)s_expm1.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_expm1.c,v 1.8 1995/05/10 20:47:09 jtc Exp $";
#endif
/* expm1(x)
* Returns exp(x)-1, the exponential of x minus 1.
*
* Method
* 1. Argument reduction:
* Given x, find r and integer k such that
*
* x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
*
* Here a correction term c will be computed to compensate
* the error in r when rounded to a floating-point number.
*
* 2. Approximating expm1(r) by a special rational function on
* the interval [0,0.34658]:
* Since
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
* we define R1(r*r) by
* r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
* That is,
* R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
* = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
* = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
* We use a special Reme algorithm on [0,0.347] to generate
* a polynomial of degree 5 in r*r to approximate R1. The
* maximum error of this polynomial approximation is bounded
* by 2**-61. In other words,
* R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
* where Q1 = -1.6666666666666567384E-2,
* Q2 = 3.9682539681370365873E-4,
* Q3 = -9.9206344733435987357E-6,
* Q4 = 2.5051361420808517002E-7,
* Q5 = -6.2843505682382617102E-9;
* (where z=r*r, and the values of Q1 to Q5 are listed below)
* with error bounded by
* | 5 | -61
* | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
* | |
*
* expm1(r) = exp(r)-1 is then computed by the following
* specific way which minimize the accumulation rounding error:
* 2 3
* r r [ 3 - (R1 + R1*r/2) ]
* expm1(r) = r + --- + --- * [--------------------]
* 2 2 [ 6 - r*(3 - R1*r/2) ]
*
* To compensate the error in the argument reduction, we use
* expm1(r+c) = expm1(r) + c + expm1(r)*c
* ~ expm1(r) + c + r*c
* Thus c+r*c will be added in as the correction terms for
* expm1(r+c). Now rearrange the term to avoid optimization
* screw up:
* ( 2 2 )
* ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
* expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
* ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
* ( )
*
* = r - E
* 3. Scale back to obtain expm1(x):
* From step 1, we have
* expm1(x) = either 2^k*[expm1(r)+1] - 1
* = or 2^k*[expm1(r) + (1-2^-k)]
* 4. Implementation notes:
* (A). To save one multiplication, we scale the coefficient Qi
* to Qi*2^i, and replace z by (x^2)/2.
* (B). To achieve maximum accuracy, we compute expm1(x) by
* (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
* (ii) if k=0, return r-E
* (iii) if k=-1, return 0.5*(r-E)-0.5
* (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
* else return 1.0+2.0*(r-E);
* (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
* (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
* (vii) return 2^k(1-((E+2^-k)-r))
*
* Special cases:
* expm1(INF) is INF, expm1(NaN) is NaN;
* expm1(-INF) is -1, and
* for finite argument, only expm1(0)=0 is exact.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* Misc. info.
* For IEEE double
* if x > 7.09782712893383973096e+02 then expm1(x) overflow
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
huge = 1.0e+300,
tiny = 1.0e-300,
o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
/* scaled coefficients related to expm1 */
Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
#ifdef __STDC__
double __expm1(double x)
#else
double __expm1(x)
double x;
#endif
{
double y,hi,lo,c,t,e,hxs,hfx,r1;
int32_t k,xsb;
u_int32_t hx;
GET_HIGH_WORD(hx,x);
xsb = hx&0x80000000; /* sign bit of x */
if(xsb==0) y=x; else y= -x; /* y = |x| */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out huge and non-finite argument */
if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
if(hx>=0x7ff00000) {
u_int32_t low;
GET_LOW_WORD(low,x);
if(((hx&0xfffff)|low)!=0)
return x+x; /* NaN */
else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
}
if(x > o_threshold) return huge*huge; /* overflow */
}
if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
if(x+tiny<0.0) /* raise inexact */
return tiny-one; /* return -1 */
}
}
/* argument reduction */
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
if(xsb==0)
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
else
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
} else {
k = invln2*x+((xsb==0)?0.5:-0.5);
t = k;
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
lo = t*ln2_lo;
}
x = hi - lo;
c = (hi-x)-lo;
}
else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
t = huge+x; /* return x with inexact flags when x!=0 */
return x - (t-(huge+x));
}
else k = 0;
/* x is now in primary range */
hfx = 0.5*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
t = 3.0-r1*hfx;
e = hxs*((r1-t)/(6.0 - x*t));
if(k==0) return x - (x*e-hxs); /* c is 0 */
else {
e = (x*(e-c)-c);
e -= hxs;
if(k== -1) return 0.5*(x-e)-0.5;
if(k==1)
if(x < -0.25) return -2.0*(e-(x+0.5));
else return one+2.0*(x-e);
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
u_int32_t high;
y = one-(e-x);
GET_HIGH_WORD(high,y);
SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
return y-one;
}
t = one;
if(k<20) {
u_int32_t high;
SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */
y = t-(e-x);
GET_HIGH_WORD(high,y);
SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
} else {
u_int32_t high;
SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */
y = x-(e+t);
y += one;
GET_HIGH_WORD(high,y);
SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
}
}
return y;
}
weak_alias (__expm1, expm1)
#ifdef NO_LONG_DOUBLE
strong_alias (__expm1, __expm1l)
weak_alias (__expm1, expm1l)
#endif