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Commit 0058967b by Richard Guenther Committed by Richard Biener
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Makefile.def (target_modules): Add libgcc-math target module. 

2006-01-31  Richard Guenther  <rguenther@suse.de>
	Paolo Bonzini  <bonzini@gnu.org>

	* Makefile.def (target_modules): Add libgcc-math target module.
	* configure.in (target_libraries): Add libgcc-math target library.
	(--enable-libgcc-math): New configure switch.
	* Makefile.in: Re-generate.
	* configure: Re-generate.
	* libgcc-math: New toplevel directory.

	* doc/install.texi (--disable-libgcc-math): Document.

	libgcc-math/
	* configure.ac: New file.
	* Makefile.am: Likewise.
	* configure: New generated file.
	* Makefile.in: Likewise.
	* aclocal.m4: Likewise.
	* libtool-version: New file.
	* include/ieee754.h: New file.
	* include/libc-symbols.h: Likewise.
	* include/math_private.h: Likewise.
	* i386/Makefile.am: New file.
	* i386/Makefile.in: New generated file.
	* i386/sse2.h: New file.
	* i386/endian.h: Likewise.
	* i386/sse2.map: Linker script for SSE2 ABI math intrinsics.
	* flt-32/: Import from glibc.
	* dbl-64/: Likewise.

Co-Authored-By: Paolo Bonzini <bonzini@gnu.org>

From-SVN: r110434
parent 84217346
Showing with 4827 additions and 0 deletions
ChangeLog
2006-01-31 Richard Guenther <rguenther@suse.de>
Paolo Bonzini <bonzini@gnu.org>
* Makefile.def (target_modules): Add libgcc-math target module.
* configure.in (target_libraries): Add libgcc-math target library.
(--enable-libgcc-math): New configure switch.
* Makefile.in: Re-generate.
* configure: Re-generate.
* libgcc-math: New toplevel directory.
2006-01-26 Paolo Bonzini <bonzini@gnu.org> 2006-01-26 Paolo Bonzini <bonzini@gnu.org>
* configure.in: Set with_gnu_as, with_gnu_ld, with_newlib earlier. * configure.in: Set with_gnu_as, with_gnu_ld, with_newlib earlier.
......
Makefile.def
...@@ -117,6 +117,7 @@ host_modules= { module= gnattools; }; ...@@ -117,6 +117,7 @@ host_modules= { module= gnattools; };
target_modules = { module= libstdc++-v3; lib_path=.libs; raw_cxx=true; }; target_modules = { module= libstdc++-v3; lib_path=.libs; raw_cxx=true; };
target_modules = { module= libmudflap; lib_path=.libs; }; target_modules = { module= libmudflap; lib_path=.libs; };
target_modules = { module= libssp; lib_path=.libs; }; target_modules = { module= libssp; lib_path=.libs; };
target_modules = { module= libgcc-math; lib_path=.libs; };
target_modules = { module= newlib; }; target_modules = { module= newlib; };
target_modules = { module= libgfortran; }; target_modules = { module= libgfortran; };
target_modules = { module= libobjc; }; target_modules = { module= libobjc; };
......
configure.in
...@@ -148,6 +148,7 @@ target_libraries="target-libiberty \ ...@@ -148,6 +148,7 @@ target_libraries="target-libiberty \
target-libstdc++-v3 \ target-libstdc++-v3 \
target-libmudflap \ target-libmudflap \
target-libssp \ target-libssp \
target-libgcc-math \
target-libgfortran \ target-libgfortran \
${libgcj} \ ${libgcj} \
target-libobjc \ target-libobjc \
...@@ -316,6 +317,21 @@ if test "${ENABLE_LIBSSP}" != "yes" ; then ...@@ -316,6 +317,21 @@ if test "${ENABLE_LIBSSP}" != "yes" ; then
noconfigdirs="$noconfigdirs target-libssp" noconfigdirs="$noconfigdirs target-libssp"
fi fi
# Set the default so we build libgcc-math for ix86 and x86_64
AC_ARG_ENABLE(libgcc-math,
[ --enable-libgcc-math Builds libgcc-math directory],,
[
case "${target}" in
i?86-* | x86_64-* )
enable_libgcc_math=yes ;;
*)
enable_libgcc_math=no ;;
esac
])
if test "${enable_libgcc_math}" != "yes"; then
noconfigdirs="$noconfigdirs target-libgcc-math"
fi
# Save it here so that, even in case of --enable-libgcj, if the Java # Save it here so that, even in case of --enable-libgcj, if the Java
# front-end isn't enabled, we still get libgcj disabled. # front-end isn't enabled, we still get libgcj disabled.
libgcj_saved=$libgcj libgcj_saved=$libgcj
......
gcc/ChangeLog
2006-01-31 Richard Guenther <rguenther@suse.de>
Paolo Bonzini <bonzini@gnu.org>
* doc/install.texi (--disable-libgcc-math): Document.
2006-01-30 Marcin Dalecki <martin@dalecki.de> 2006-01-30 Marcin Dalecki <martin@dalecki.de>
* expr.h (expand_normal): new inline function. * expr.h (expand_normal): new inline function.
......
gcc/doc/install.texi
...@@ -1086,6 +1086,10 @@ do a @samp{make -C gcc gnatlib_and_tools}. ...@@ -1086,6 +1086,10 @@ do a @samp{make -C gcc gnatlib_and_tools}.
Specify that the run-time libraries for stack smashing protection Specify that the run-time libraries for stack smashing protection
should not be built. should not be built.
@item --disable-libgcc-math
Specify that the run-time libraries for arch and gcc specific math
functions should not be built.
@item --with-dwarf2 @item --with-dwarf2
Specify that the compiler should Specify that the compiler should
use DWARF 2 debugging information as the default. use DWARF 2 debugging information as the default.
......
libgcc-math/ChangeLog 0 → 100644
2006-01-31 Richard Guenther <rguenther@suse.de>
Paolo Bonzini <bonzini@gnu.org>
* configure.ac: New file.
* Makefile.am: Likewise.
* configure: New generated file.
* Makefile.in: Likewise.
* aclocal.m4: Likewise.
* libtool-version: New file.
* include/ieee754.h: New file.
* include/libc-symbols.h: Likewise.
* include/math_private.h: Likewise.
* i386/Makefile.am: New file.
* i386/Makefile.in: New generated file.
* i386/sse2.h: New file.
* i386/endian.h: Likewise.
* i386/sse2.map: Linker script for SSE2 ABI math intrinsics.
* flt-32/: Import from glibc.
* dbl-64/: Likewise.
libgcc-math/Makefile.am 0 → 100644
## Makefile for the toplevel directory of the libgcc-math library.
##
## Copyright (C) 2005
## Free Software Foundation, Inc.
##
AUTOMAKE_OPTIONS = 1.9.5 foreign
ACLOCAL_AMFLAGS = -I .. -I ../config
MAINT_CHARSET = latin1
SUBDIRS = @arch_subdirs@
# May be used by various substitution variables.
gcc_version := $(shell cat $(top_srcdir)/../gcc/BASE-VER)
if LIBGCCM_USE_SYMVER
version_arg = -Wl,--version-script=gccm.map
version_dep = gccm.map
.PHONY: gccm.map
gccm.map:
rm -f gccm.map
for map in @arch_maps@; do \
cat $(srcdir)/$$map >> gccm.map; \
done
else
version_arg =
version_dep =
endif
if BUILD_LIBGCC_MATH
toolexeclib_LTLIBRARIES = libgcc-math.la
libgcc_math_la_SOURCES =
libgcc_math_la_LIBADD = @arch_libraries@
libgcc_math_la_DEPENDENCIES = $(libgcc_math_la_LIBADD) $(version_dep)
libgcc_math_la_LDFLAGS = -version-info `grep -v '^\#' $(srcdir)/libtool-version` \
$(version_arg) -lm
endif
# XXX hack alert
# From libffi/Makefile.am
# Work around what appears to be a GNU make bug handling MAKEFLAGS
# values defined in terms of make variables, as is the case for CC and
# friends when we are called from the top level Makefile.
AM_MAKEFLAGS = \
"AR_FLAGS=$(AR_FLAGS)" \
"CC_FOR_BUILD=$(CC_FOR_BUILD)" \
"CFLAGS=$(CFLAGS)" \
"CXXFLAGS=$(CXXFLAGS)" \
"CFLAGS_FOR_BUILD=$(CFLAGS_FOR_BUILD)" \
"CFLAGS_FOR_TARGET=$(CFLAGS_FOR_TARGET)" \
"INSTALL=$(INSTALL)" \
"INSTALL_DATA=$(INSTALL_DATA)" \
"INSTALL_PROGRAM=$(INSTALL_PROGRAM)" \
"INSTALL_SCRIPT=$(INSTALL_SCRIPT)" \
"JC1FLAGS=$(JC1FLAGS)" \
"LDFLAGS=$(LDFLAGS)" \
"LIBCFLAGS=$(LIBCFLAGS)" \
"LIBCFLAGS_FOR_TARGET=$(LIBCFLAGS_FOR_TARGET)" \
"MAKE=$(MAKE)" \
"MAKEINFO=$(MAKEINFO) $(MAKEINFOFLAGS)" \
"PICFLAG=$(PICFLAG)" \
"PICFLAG_FOR_TARGET=$(PICFLAG_FOR_TARGET)" \
"SHELL=$(SHELL)" \
"RUNTESTFLAGS=$(RUNTESTFLAGS)" \
"exec_prefix=$(exec_prefix)" \
"infodir=$(infodir)" \
"libdir=$(libdir)" \
"prefix=$(prefix)" \
"includedir=$(includedir)" \
"AR=$(AR)" \
"AS=$(AS)" \
"CC=$(CC)" \
"CXX=$(CXX)" \
"LD=$(LD)" \
"LIBCFLAGS=$(LIBCFLAGS)" \
"NM=$(NM)" \
"PICFLAG=$(PICFLAG)" \
"RANLIB=$(RANLIB)" \
"DESTDIR=$(DESTDIR)"
MAKEOVERRIDES=
## ################################################################
libgcc-math/configure 0 → 100755
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libgcc-math/configure.ac 0 → 100644
# Process this file with autoconf to produce a configure script, like so:
# aclocal && autoconf && autoheader && automake
AC_PREREQ(2.59)
AC_INIT(libgcc-math, 1.0)
AC_CONFIG_SRCDIR(configure.ac)
AC_CANONICAL_SYSTEM
AM_INIT_AUTOMAKE
AC_MSG_CHECKING([for --enable-version-specific-runtime-libs])
AC_ARG_ENABLE(version-specific-runtime-libs,
[ --enable-version-specific-runtime-libs Specify that runtime libraries should be installed in a compiler-specific directory ],
[case "$enableval" in
yes) version_specific_libs=yes ;;
no) version_specific_libs=no ;;
*) AC_MSG_ERROR([Unknown argument to enable/disable version-specific libs]);;
esac],
[version_specific_libs=no])
AC_MSG_RESULT($version_specific_libs)
AM_MAINTAINER_MODE
AC_EXEEXT
AM_ENABLE_MULTILIB(, ..)
target_alias=${target_alias-$host_alias}
AC_SUBST(target_alias)
AC_LANG_C
# The same as in boehm-gc and libstdc++. Have to borrow it from there.
# We must force CC to /not/ be precious variables; otherwise
# the wrong, non-multilib-adjusted value will be used in multilibs.
# As a side effect, we have to subst CFLAGS ourselves.
m4_rename([_AC_ARG_VAR_PRECIOUS],[real_PRECIOUS])
m4_define([_AC_ARG_VAR_PRECIOUS],[])
AC_PROG_CC
m4_rename([real_PRECIOUS],[_AC_ARG_VAR_PRECIOUS])
AC_SUBST(CFLAGS)
if test "x$GCC" != "xyes"; then
AC_MSG_ERROR([libgcc-math must be built with GCC])
fi
AC_PROG_CPP
AM_PROG_AS
AC_MSG_CHECKING([whether hidden visibility is supported])
AC_TRY_COMPILE([
void __attribute__((visibility ("hidden"))) bar (void) {}],,
[gccm_hidden=yes],[gccm_hidden=no])
AC_MSG_RESULT($gccm_hidden)
if test x$gccm_hidden = xyes; then
AC_DEFINE([HAVE_HIDDEN_VISIBILITY],[1],[__attribute__((visibility ("hidden"))) supported])
fi
AC_MSG_CHECKING([whether symbol versioning is supported])
cat > conftest.map <<EOF
FOO_1.0 {
global: *foo*; bar; local: *;
};
EOF
save_LDFLAGS="$LDFLAGS"
LDFLAGS="$LDFLAGS -fPIC -shared -Wl,--version-script,./conftest.map"
AC_TRY_LINK([int foo;],[],[gccm_use_symver=yes],[gccm_use_symver=no])
LDFLAGS="$save_LDFLAGS"
AC_MSG_RESULT($gccm_use_symver)
AM_CONDITIONAL(LIBGCCM_USE_SYMVER, [test "x$gccm_use_symver" = xyes])
AC_MSG_CHECKING([whether we are a 32bit target])
save_CFLAGS="$CFLAGS"
CFLAGS="-O2"
AC_TRY_LINK(,[
if (sizeof(int) == 4 && sizeof(long) == 4 && sizeof(void *) == 4)
;
else
undefined_function ();
],
target_ilp32=yes,
target_ilp32=no)
CFLAGS="$save_CFLAGS"
AM_CONDITIONAL(TARGET_ILP32, [test "x$target_ilp32" = xyes])
AM_PROG_LIBTOOL
AC_SUBST(enable_shared)
AC_SUBST(enable_static)
# Calculate toolexeclibdir
# Also toolexecdir, though it's only used in toolexeclibdir
case ${version_specific_libs} in
yes)
# Need the gcc compiler version to know where to install libraries
# and header files if --enable-version-specific-runtime-libs option
# is selected.
toolexecdir='$(libdir)/gcc/$(target_alias)'
toolexeclibdir='$(toolexecdir)/$(gcc_version)$(MULTISUBDIR)'
;;
no)
if test -n "$with_cross_host" &&
test x"$with_cross_host" != x"no"; then
# Install a library built with a cross compiler in tooldir, not libdir.
toolexecdir='$(exec_prefix)/$(target_alias)'
toolexeclibdir='$(toolexecdir)/lib'
else
toolexecdir='$(libdir)/gcc-lib/$(target_alias)'
toolexeclibdir='$(libdir)'
fi
multi_os_directory=`$CC -print-multi-os-directory`
case $multi_os_directory in
.) ;; # Avoid trailing /.
*) toolexeclibdir=$toolexeclibdir/$multi_os_directory ;;
esac
;;
esac
AC_SUBST(toolexecdir)
AC_SUBST(toolexeclibdir)
if test ${multilib} = yes; then
multilib_arg="--enable-multilib"
else
multilib_arg=
fi
# Now check which parts we include in the library.
arch_subdirs=
case "${target}" in
i?86-* | x86_64-* )
# Handle multilib cases
if test "x$target_ilp32" = xyes; then
arch_subdirs="i386"
arch_libraries="i386/libsse2.la"
arch_maps="i386/sse2.map"
fi ;;
*)
;;
esac
AC_SUBST(arch_subdirs)
AC_SUBST(arch_libraries)
AC_SUBST(arch_maps)
AM_CONDITIONAL(BUILD_LIBGCC_MATH, [test "x$arch_subdirs" != x])
AC_CONFIG_FILES([Makefile i386/Makefile])
AC_OUTPUT
libgcc-math/dbl-64/MathLib.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/********************************************************************/
/* Ultimate math functions. Each function computes the exact */
/* theoretical value of its argument rounded to nearest or even. */
/* */
/* Assumption: Machine arithmetic operations are performed in */
/* round nearest mode of IEEE 754 standard. */
/********************************************************************/
#ifndef UMATH_LIB
#define UMATH_LIB
/********************************************************************/
/* Function changes the precision mode to IEEE 754 double precision */
/* and the rounding mode to nearest or even. */
/* It returns the original status of these modes. */
/* See further explanations of usage in DPChange.h */
/********************************************************************/
unsigned short Init_Lib(void);
/********************************************************************/
/* Function that changes the precision and rounding modes to the */
/* specified by the argument received. See further explanations in */
/* DPChange.h */
/********************************************************************/
void Exit_Lib(unsigned short);
/* The asin() function calculates the arc sine of its argument. */
/* The function returns the arc sine in radians */
/* (between -PI/2 and PI/2). */
/* If the argument is greater than 1 or less than -1 it returns */
/* a NaN. */
double uasin(double );
/* The acos() function calculates the arc cosine of its argument. */
/* The function returns the arc cosine in radians */
/* (between -PI/2 and PI/2). */
/* If the argument is greater than 1 or less than -1 it returns */
/* a NaN. */
double uacos(double );
/* The atan() function calculates the arctanget of its argument. */
/* The function returns the arc tangent in radians */
/* (between -PI/2 and PI/2). */
double uatan(double );
/* The uatan2() function calculates the arc tangent of the two arguments x */
/* and y (x is the right argument and y is the left one).The signs of both */
/* arguments are used to determine the quadrant of the result. */
/* The function returns the result in radians, which is between -PI and PI */
double uatan2(double ,double );
/* Compute log(x). The base of log is e (natural logarithm) */
double ulog(double );
/* Compute e raised to the power of argument x. */
double uexp(double );
/* Compute sin(x). The argument x is assumed to be given in radians.*/
double usin(double );
/* Compute cos(x). The argument x is assumed to be given in radians.*/
double ucos(double );
/* Compute tan(x). The argument x is assumed to be given in radians.*/
double utan(double );
/* Compute the square root of non-negative argument x. */
/* If x is negative the returned value is NaN. */
double usqrt(double );
/* Compute x raised to the power of y, where x is the left argument */
/* and y is the right argument. The function returns a NaN if x<0. */
/* If x equals zero it returns -inf */
double upow(double , double );
/* Computing x mod y, where x is the left argument and y is the */
/* right one. */
double uremainder(double , double );
#endif
libgcc-math/dbl-64/asincos.tbl 0 → 100644
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libgcc-math/dbl-64/atnat.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/************************************************************************/
/* MODULE_NAME: atnat.h */
/* */
/* */
/* common data and variables definition for BIG or LITTLE ENDIAN */
/************************************************************************/
#ifndef ATNAT_H
#define ATNAT_H
#define M 4
#ifdef BIG_ENDI
static const number
/* polynomial I */
/**/ d3 = {{0xbfd55555, 0x55555555} }, /* -0.333... */
/**/ d5 = {{0x3fc99999, 0x999997fd} }, /* 0.199... */
/**/ d7 = {{0xbfc24924, 0x923f7603} }, /* -0.142... */
/**/ d9 = {{0x3fbc71c6, 0xe5129a3b} }, /* 0.111... */
/**/ d11 = {{0xbfb74580, 0x22b13c25} }, /* -0.090... */
/**/ d13 = {{0x3fb375f0, 0x8b31cbce} }, /* 0.076... */
/* polynomial II */
/**/ f3 = {{0xbfd55555, 0x55555555} }, /* -1/3 */
/**/ ff3 = {{0xbc755555, 0x55555555} }, /* -1/3-f3 */
/**/ f5 = {{0x3fc99999, 0x9999999a} }, /* 1/5 */
/**/ ff5 = {{0xbc699999, 0x9999999a} }, /* 1/5-f5 */
/**/ f7 = {{0xbfc24924, 0x92492492} }, /* -1/7 */
/**/ ff7 = {{0xbc624924, 0x92492492} }, /* -1/7-f7 */
/**/ f9 = {{0x3fbc71c7, 0x1c71c71c} }, /* 1/9 */
/**/ ff9 = {{0x3c5c71c7, 0x1c71c71c} }, /* 1/9-f9 */
/**/ f11 = {{0xbfb745d1, 0x745d1746} }, /* -1/11 */
/**/ f13 = {{0x3fb3b13b, 0x13b13b14} }, /* 1/13 */
/**/ f15 = {{0xbfb11111, 0x11111111} }, /* -1/15 */
/**/ f17 = {{0x3fae1e1e, 0x1e1e1e1e} }, /* 1/17 */
/**/ f19 = {{0xbfaaf286, 0xbca1af28} }, /* -1/19 */
/* constants */
/**/ zero = {{0x00000000, 0x00000000} }, /* 0 */
/**/ one = {{0x3ff00000, 0x00000000} }, /* 1 */
/**/ a = {{0x3e4bb67a, 0x00000000} }, /* 1.290e-8 */
/**/ b = {{0x3fb00000, 0x00000000} }, /* 1/16 */
/**/ c = {{0x3ff00000, 0x00000000} }, /* 1 */
/**/ d = {{0x40300000, 0x00000000} }, /* 16 */
/**/ e = {{0x43349ff2, 0x00000000} }, /* 5.805e15 */
/**/ hpi = {{0x3ff921fb, 0x54442d18} }, /* pi/2 */
/**/ mhpi = {{0xbff921fb, 0x54442d18} }, /* -pi/2 */
/**/ hpi1 = {{0x3c91a626, 0x33145c07} }, /* pi/2-hpi */
/**/ u1 = {{0x3c2d3382, 0x00000000} }, /* 7.915e-19 */
/**/ u21 = {{0x3c6dffc0, 0x00000000} }, /* 1.301e-17 */
/**/ u22 = {{0x3c527bd0, 0x00000000} }, /* 4.008e-18 */
/**/ u23 = {{0x3c3cd057, 0x00000000} }, /* 1.562e-18 */
/**/ u24 = {{0x3c329cdf, 0x00000000} }, /* 1.009e-18 */
/**/ u31 = {{0x3c3a1edf, 0x00000000} }, /* 1.416e-18 */
/**/ u32 = {{0x3c33f0e1, 0x00000000} }, /* 1.081e-18 */
/**/ u4 = {{0x3bf955e4, 0x00000000} }, /* 8.584e-20 */
/**/ u5 = {{0x3aaef2d1, 0x00000000} }, /* 5e-26 */
/**/ u6 = {{0x3a98c56d, 0x00000000} }, /* 2.001e-26 */
/**/ u7 = {{0x3a9375de, 0x00000000} }, /* 1.572e-26 */
/**/ u8 = {{0x3a6eeb36, 0x00000000} }, /* 3.122e-27 */
/**/ u9[M] ={{{0x38c1aa5b, 0x00000000} }, /* 2.658e-35 */
/**/ {{0x35c1aa4d, 0x00000000} }, /* 9.443e-50 */
/**/ {{0x32c1aa88, 0x00000000} }, /* 3.355e-64 */
/**/ {{0x11c1aa56, 0x00000000} }},/* 3.818e-223 */
/**/ two8 = {{0x40700000, 0x00000000} }, /* 2**8=256 */
/**/ two52 = {{0x43300000, 0x00000000} }; /* 2**52 */
#else
#ifdef LITTLE_ENDI
static const number
/* polynomial I */
/**/ d3 = {{0x55555555, 0xbfd55555} }, /* -0.333... */
/**/ d5 = {{0x999997fd, 0x3fc99999} }, /* 0.199... */
/**/ d7 = {{0x923f7603, 0xbfc24924} }, /* -0.142... */
/**/ d9 = {{0xe5129a3b, 0x3fbc71c6} }, /* 0.111... */
/**/ d11 = {{0x22b13c25, 0xbfb74580} }, /* -0.090... */
/**/ d13 = {{0x8b31cbce, 0x3fb375f0} }, /* 0.076... */
/* polynomial II */
/**/ f3 = {{0x55555555, 0xbfd55555} }, /* -1/3 */
/**/ ff3 = {{0x55555555, 0xbc755555} }, /* -1/3-f3 */
/**/ f5 = {{0x9999999a, 0x3fc99999} }, /* 1/5 */
/**/ ff5 = {{0x9999999a, 0xbc699999} }, /* 1/5-f5 */
/**/ f7 = {{0x92492492, 0xbfc24924} }, /* -1/7 */
/**/ ff7 = {{0x92492492, 0xbc624924} }, /* -1/7-f7 */
/**/ f9 = {{0x1c71c71c, 0x3fbc71c7} }, /* 1/9 */
/**/ ff9 = {{0x1c71c71c, 0x3c5c71c7} }, /* 1/9-f9 */
/**/ f11 = {{0x745d1746, 0xbfb745d1} }, /* -1/11 */
/**/ f13 = {{0x13b13b14, 0x3fb3b13b} }, /* 1/13 */
/**/ f15 = {{0x11111111, 0xbfb11111} }, /* -1/15 */
/**/ f17 = {{0x1e1e1e1e, 0x3fae1e1e} }, /* 1/17 */
/**/ f19 = {{0xbca1af28, 0xbfaaf286} }, /* -1/19 */
/* constants */
/**/ zero = {{0x00000000, 0x00000000} }, /* 0 */
/**/ one = {{0x00000000, 0x3ff00000} }, /* 1 */
/**/ a = {{0x00000000, 0x3e4bb67a} }, /* 1.290e-8 */
/**/ b = {{0x00000000, 0x3fb00000} }, /* 1/16 */
/**/ c = {{0x00000000, 0x3ff00000} }, /* 1 */
/**/ d = {{0x00000000, 0x40300000} }, /* 16 */
/**/ e = {{0x00000000, 0x43349ff2} }, /* 5.805e15 */
/**/ hpi = {{0x54442d18, 0x3ff921fb} }, /* pi/2 */
/**/ mhpi = {{0x54442d18, 0xbff921fb} }, /* -pi/2 */
/**/ hpi1 = {{0x33145c07, 0x3c91a626} }, /* pi/2-hpi */
/**/ u1 = {{0x00000000, 0x3c2d3382} }, /* 7.915e-19 */
/**/ u21 = {{0x00000000, 0x3c6dffc0} }, /* 1.301e-17 */
/**/ u22 = {{0x00000000, 0x3c527bd0} }, /* 4.008e-18 */
/**/ u23 = {{0x00000000, 0x3c3cd057} }, /* 1.562e-18 */
/**/ u24 = {{0x00000000, 0x3c329cdf} }, /* 1.009e-18 */
/**/ u31 = {{0x00000000, 0x3c3a1edf} }, /* 1.416e-18 */
/**/ u32 = {{0x00000000, 0x3c33f0e1} }, /* 1.081e-18 */
/**/ u4 = {{0x00000000, 0x3bf955e4} }, /* 8.584e-20 */
/**/ u5 = {{0x00000000, 0x3aaef2d1} }, /* 5e-26 */
/**/ u6 = {{0x00000000, 0x3a98c56d} }, /* 2.001e-26 */
/**/ u7 = {{0x00000000, 0x3a9375de} }, /* 1.572e-26 */
/**/ u8 = {{0x00000000, 0x3a6eeb36} }, /* 3.122e-27 */
/**/ u9[M] ={{{0x00000000, 0x38c1aa5b} }, /* 2.658e-35 */
/**/ {{0x00000000, 0x35c1aa4d} }, /* 9.443e-50 */
/**/ {{0x00000000, 0x32c1aa88} }, /* 3.355e-64 */
/**/ {{0x00000000, 0x11c1aa56} }},/* 3.818e-223 */
/**/ two8 = {{0x00000000, 0x40700000} }, /* 2**8=256 */
/**/ two52 = {{0x00000000, 0x43300000} }; /* 2**52 */
#endif
#endif
#define ZERO zero.d
#define ONE one.d
#define A a.d
#define B b.d
#define C c.d
#define D d.d
#define E e.d
#define HPI hpi.d
#define MHPI mhpi.d
#define HPI1 hpi1.d
#define U1 u1.d
#define U21 u21.d
#define U22 u22.d
#define U23 u23.d
#define U24 u24.d
#define U31 u31.d
#define U32 u32.d
#define U4 u4.d
#define U5 u5.d
#define U6 u6.d
#define U7 u7.d
#define U8 u8.d
#define TWO8 two8.d
#define TWO52 two52.d
#endif
libgcc-math/dbl-64/branred.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/*******************************************************************/
/* */
/* MODULE_NAME: branred.c */
/* */
/* FUNCTIONS: branred */
/* */
/* FILES NEEDED: branred.h mydefs.h endian.h mpa.h */
/* mha.c */
/* */
/* Routine branred() performs range reduction of a double number */
/* x into Double length number a+aa,such that */
/* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,.... */
/* Routine returns the integer (n mod 4) of the above description */
/* of x. */
/*******************************************************************/
#include "endian.h"
#include "mydefs.h"
#include "branred.h"
#include "math_private.h"
/*******************************************************************/
/* Routine branred() performs range reduction of a double number */
/* x into Double length number a+aa,such that */
/* x=n*pi/2+(a+aa), abs(a+aa)<pi/4, n=0,+-1,+-2,.... */
/* Routine return integer (n mod 4) */
/*******************************************************************/
int __branred(double x, double *a, double *aa)
{
int i,k;
#if 0
int n;
#endif
mynumber u,gor;
#if 0
mynumber v;
#endif
double r[6],s,t,sum,b,bb,sum1,sum2,b1,bb1,b2,bb2,x1,x2,t1,t2;
x*=tm600.x;
t=x*split; /* split x to two numbers */
x1=t-(t-x);
x2=x-x1;
sum=0;
u.x = x1;
k = (u.i[HIGH_HALF]>>20)&2047;
k = (k-450)/24;
if (k<0)
k=0;
gor.x = t576.x;
gor.i[HIGH_HALF] -= ((k*24)<<20);
for (i=0;i<6;i++)
{ r[i] = x1*toverp[k+i]*gor.x; gor.x *= tm24.x; }
for (i=0;i<3;i++) {
s=(r[i]+big.x)-big.x;
sum+=s;
r[i]-=s;
}
t=0;
for (i=0;i<6;i++)
t+=r[5-i];
bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5];
s=(t+big.x)-big.x;
sum+=s;
t-=s;
b=t+bb;
bb=(t-b)+bb;
s=(sum+big1.x)-big1.x;
sum-=s;
b1=b;
bb1=bb;
sum1=sum;
sum=0;
u.x = x2;
k = (u.i[HIGH_HALF]>>20)&2047;
k = (k-450)/24;
if (k<0)
k=0;
gor.x = t576.x;
gor.i[HIGH_HALF] -= ((k*24)<<20);
for (i=0;i<6;i++)
{ r[i] = x2*toverp[k+i]*gor.x; gor.x *= tm24.x; }
for (i=0;i<3;i++) {
s=(r[i]+big.x)-big.x;
sum+=s;
r[i]-=s;
}
t=0;
for (i=0;i<6;i++)
t+=r[5-i];
bb=(((((r[0]-t)+r[1])+r[2])+r[3])+r[4])+r[5];
s=(t+big.x)-big.x;
sum+=s;
t-=s;
b=t+bb;
bb=(t-b)+bb;
s=(sum+big1.x)-big1.x;
sum-=s;
b2=b;
bb2=bb;
sum2=sum;
sum=sum1+sum2;
b=b1+b2;
bb = (ABS(b1)>ABS(b2))? (b1-b)+b2 : (b2-b)+b1;
if (b > 0.5)
{b-=1.0; sum+=1.0;}
else if (b < -0.5)
{b+=1.0; sum-=1.0;}
s=b+(bb+bb1+bb2);
t=((b-s)+bb)+(bb1+bb2);
b=s*split;
t1=b-(b-s);
t2=s-t1;
b=s*hp0.x;
bb=(((t1*mp1.x-b)+t1*mp2.x)+t2*mp1.x)+(t2*mp2.x+s*hp1.x+t*hp0.x);
s=b+bb;
t=(b-s)+bb;
*a=s;
*aa=t;
return ((int) sum)&3; /* return quater of unit circle */
}
libgcc-math/dbl-64/branred.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/************************************************************************/
/* MODULE_NAME: branred.h */
/* */
/* */
/* common data and variables definition for BIG or LITTLE ENDIAN */
/************************************************************************/
#ifndef BRANRED_H
#define BRANRED_H
#ifdef BIG_ENDI
static const mynumber
/**/ t576 = {{0x63f00000, 0x00000000}}, /* 2 ^ 576 */
/**/ tm600 = {{0x1a700000, 0x00000000}}, /* 2 ^- 600 */
/**/ tm24 = {{0x3e700000, 0x00000000}}, /* 2 ^- 24 */
/**/ big = {{0x43380000, 0x00000000}}, /* 6755399441055744 */
/**/ big1 = {{0x43580000, 0x00000000}}, /* 27021597764222976 */
/**/ hp0 = {{0x3FF921FB, 0x54442D18}} ,/* 1.5707963267948966 */
/**/ hp1 = {{0x3C91A626, 0x33145C07}} ,/* 6.123233995736766e-17 */
/**/ mp1 = {{0x3FF921FB, 0x58000000}}, /* 1.5707963407039642 */
/**/ mp2 = {{0xBE4DDE97, 0x40000000}}; /*-1.3909067675399456e-08 */
#else
#ifdef LITTLE_ENDI
static const mynumber
/**/ t576 = {{0x00000000, 0x63f00000}}, /* 2 ^ 576 */
/**/ tm600 = {{0x00000000, 0x1a700000}}, /* 2 ^- 600 */
/**/ tm24 = {{0x00000000, 0x3e700000}}, /* 2 ^- 24 */
/**/ big = {{0x00000000, 0x43380000}}, /* 6755399441055744 */
/**/ big1 = {{0x00000000, 0x43580000}}, /* 27021597764222976 */
/**/ hp0 = {{0x54442D18, 0x3FF921FB}}, /* 1.5707963267948966 */
/**/ hp1 = {{0x33145C07, 0x3C91A626}}, /* 6.123233995736766e-17 */
/**/ mp1 = {{0x58000000, 0x3FF921FB}}, /* 1.5707963407039642 */
/**/ mp2 = {{0x40000000, 0xBE4DDE97}}; /*-1.3909067675399456e-08 */
#endif
#endif
static const double toverp[75] = { /* 2/ PI base 24*/
10680707.0, 7228996.0, 1387004.0, 2578385.0, 16069853.0,
12639074.0, 9804092.0, 4427841.0, 16666979.0, 11263675.0,
12935607.0, 2387514.0, 4345298.0, 14681673.0, 3074569.0,
13734428.0, 16653803.0, 1880361.0, 10960616.0, 8533493.0,
3062596.0, 8710556.0, 7349940.0, 6258241.0, 3772886.0,
3769171.0, 3798172.0, 8675211.0, 12450088.0, 3874808.0,
9961438.0, 366607.0, 15675153.0, 9132554.0, 7151469.0,
3571407.0, 2607881.0, 12013382.0, 4155038.0, 6285869.0,
7677882.0, 13102053.0, 15825725.0, 473591.0, 9065106.0,
15363067.0, 6271263.0, 9264392.0, 5636912.0, 4652155.0,
7056368.0, 13614112.0, 10155062.0, 1944035.0, 9527646.0,
15080200.0, 6658437.0, 6231200.0, 6832269.0, 16767104.0,
5075751.0, 3212806.0, 1398474.0, 7579849.0, 6349435.0,
12618859.0, 4703257.0, 12806093.0, 14477321.0, 2786137.0,
12875403.0, 9837734.0, 14528324.0, 13719321.0, 343717.0 };
static const double split = 134217729.0;
#endif
libgcc-math/dbl-64/dla.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/***********************************************************************/
/*MODULE_NAME: dla.h */
/* */
/* This file holds C language macros for 'Double Length Floating Point */
/* Arithmetic'. The macros are based on the paper: */
/* T.J.Dekker, "A floating-point Technique for extending the */
/* Available Precision", Number. Math. 18, 224-242 (1971). */
/* A Double-Length number is defined by a pair (r,s), of IEEE double */
/* precision floating point numbers that satisfy, */
/* */
/* abs(s) <= abs(r+s)*2**(-53)/(1+2**(-53)). */
/* */
/* The computer arithmetic assumed is IEEE double precision in */
/* round to nearest mode. All variables in the macros must be of type */
/* IEEE double. */
/***********************************************************************/
/* CN = 1+2**27 = '41a0000002000000' IEEE double format */
#define CN 134217729.0
/* Exact addition of two single-length floating point numbers, Dekker. */
/* The macro produces a double-length number (z,zz) that satisfies */
/* z+zz = x+y exactly. */
#define EADD(x,y,z,zz) \
z=(x)+(y); zz=(ABS(x)>ABS(y)) ? (((x)-(z))+(y)) : (((y)-(z))+(x));
/* Exact subtraction of two single-length floating point numbers, Dekker. */
/* The macro produces a double-length number (z,zz) that satisfies */
/* z+zz = x-y exactly. */
#define ESUB(x,y,z,zz) \
z=(x)-(y); zz=(ABS(x)>ABS(y)) ? (((x)-(z))-(y)) : ((x)-((y)+(z)));
/* Exact multiplication of two single-length floating point numbers, */
/* Veltkamp. The macro produces a double-length number (z,zz) that */
/* satisfies z+zz = x*y exactly. p,hx,tx,hy,ty are temporary */
/* storage variables of type double. */
#define EMULV(x,y,z,zz,p,hx,tx,hy,ty) \
p=CN*(x); hx=((x)-p)+p; tx=(x)-hx; \
p=CN*(y); hy=((y)-p)+p; ty=(y)-hy; \
z=(x)*(y); zz=(((hx*hy-z)+hx*ty)+tx*hy)+tx*ty;
/* Exact multiplication of two single-length floating point numbers, Dekker. */
/* The macro produces a nearly double-length number (z,zz) (see Dekker) */
/* that satisfies z+zz = x*y exactly. p,hx,tx,hy,ty,q are temporary */
/* storage variables of type double. */
#define MUL12(x,y,z,zz,p,hx,tx,hy,ty,q) \
p=CN*(x); hx=((x)-p)+p; tx=(x)-hx; \
p=CN*(y); hy=((y)-p)+p; ty=(y)-hy; \
p=hx*hy; q=hx*ty+tx*hy; z=p+q; zz=((p-z)+q)+tx*ty;
/* Double-length addition, Dekker. The macro produces a double-length */
/* number (z,zz) which satisfies approximately z+zz = x+xx + y+yy. */
/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy) */
/* are assumed to be double-length numbers. r,s are temporary */
/* storage variables of type double. */
#define ADD2(x,xx,y,yy,z,zz,r,s) \
r=(x)+(y); s=(ABS(x)>ABS(y)) ? \
(((((x)-r)+(y))+(yy))+(xx)) : \
(((((y)-r)+(x))+(xx))+(yy)); \
z=r+s; zz=(r-z)+s;
/* Double-length subtraction, Dekker. The macro produces a double-length */
/* number (z,zz) which satisfies approximately z+zz = x+xx - (y+yy). */
/* An error bound: (abs(x+xx)+abs(y+yy))*4.94e-32. (x,xx), (y,yy) */
/* are assumed to be double-length numbers. r,s are temporary */
/* storage variables of type double. */
#define SUB2(x,xx,y,yy,z,zz,r,s) \
r=(x)-(y); s=(ABS(x)>ABS(y)) ? \
(((((x)-r)-(y))-(yy))+(xx)) : \
((((x)-((y)+r))+(xx))-(yy)); \
z=r+s; zz=(r-z)+s;
/* Double-length multiplication, Dekker. The macro produces a double-length */
/* number (z,zz) which satisfies approximately z+zz = (x+xx)*(y+yy). */
/* An error bound: abs((x+xx)*(y+yy))*1.24e-31. (x,xx), (y,yy) */
/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc are */
/* temporary storage variables of type double. */
#define MUL2(x,xx,y,yy,z,zz,p,hx,tx,hy,ty,q,c,cc) \
MUL12(x,y,c,cc,p,hx,tx,hy,ty,q) \
cc=((x)*(yy)+(xx)*(y))+cc; z=c+cc; zz=(c-z)+cc;
/* Double-length division, Dekker. The macro produces a double-length */
/* number (z,zz) which satisfies approximately z+zz = (x+xx)/(y+yy). */
/* An error bound: abs((x+xx)/(y+yy))*1.50e-31. (x,xx), (y,yy) */
/* are assumed to be double-length numbers. p,hx,tx,hy,ty,q,c,cc,u,uu */
/* are temporary storage variables of type double. */
#define DIV2(x,xx,y,yy,z,zz,p,hx,tx,hy,ty,q,c,cc,u,uu) \
c=(x)/(y); MUL12(c,y,u,uu,p,hx,tx,hy,ty,q) \
cc=(((((x)-u)-uu)+(xx))-c*(yy))/(y); z=c+cc; zz=(c-z)+cc;
/* Double-length addition, slower but more accurate than ADD2. */
/* The macro produces a double-length */
/* number (z,zz) which satisfies approximately z+zz = (x+xx)+(y+yy). */
/* An error bound: abs(x+xx + y+yy)*1.50e-31. (x,xx), (y,yy) */
/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */
/* are temporary storage variables of type double. */
#define ADD2A(x,xx,y,yy,z,zz,r,rr,s,ss,u,uu,w) \
r=(x)+(y); \
if (ABS(x)>ABS(y)) { rr=((x)-r)+(y); s=(rr+(yy))+(xx); } \
else { rr=((y)-r)+(x); s=(rr+(xx))+(yy); } \
if (rr!=0.0) { \
z=r+s; zz=(r-z)+s; } \
else { \
ss=(ABS(xx)>ABS(yy)) ? (((xx)-s)+(yy)) : (((yy)-s)+(xx)); \
u=r+s; \
uu=(ABS(r)>ABS(s)) ? ((r-u)+s) : ((s-u)+r) ; \
w=uu+ss; z=u+w; \
zz=(ABS(u)>ABS(w)) ? ((u-z)+w) : ((w-z)+u) ; }
/* Double-length subtraction, slower but more accurate than SUB2. */
/* The macro produces a double-length */
/* number (z,zz) which satisfies approximately z+zz = (x+xx)-(y+yy). */
/* An error bound: abs(x+xx - (y+yy))*1.50e-31. (x,xx), (y,yy) */
/* are assumed to be double-length numbers. r,rr,s,ss,u,uu,w */
/* are temporary storage variables of type double. */
#define SUB2A(x,xx,y,yy,z,zz,r,rr,s,ss,u,uu,w) \
r=(x)-(y); \
if (ABS(x)>ABS(y)) { rr=((x)-r)-(y); s=(rr-(yy))+(xx); } \
else { rr=(x)-((y)+r); s=(rr+(xx))-(yy); } \
if (rr!=0.0) { \
z=r+s; zz=(r-z)+s; } \
else { \
ss=(ABS(xx)>ABS(yy)) ? (((xx)-s)-(yy)) : ((xx)-((yy)+s)); \
u=r+s; \
uu=(ABS(r)>ABS(s)) ? ((r-u)+s) : ((s-u)+r) ; \
w=uu+ss; z=u+w; \
zz=(ABS(u)>ABS(w)) ? ((u-z)+w) : ((w-z)+u) ; }
libgcc-math/dbl-64/doasin.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/**********************************************************************/
/* MODULE_NAME: doasin.c */
/* */
/* FUNCTION: doasin */
/* */
/* FILES NEEDED:endian.h mydefs.h dla.h doasin.h */
/* mpa.c */
/* */
/* Compute arcsin(x,dx,v) of double-length number (x+dx) the result */
/* stored in v where v= v[0]+v[1] =arcsin(x+dx) */
/**********************************************************************/
#include "endian.h"
#include "mydefs.h"
#include "dla.h"
#include "math_private.h"
/********************************************************************/
/* Compute arcsin(x,dx,v) of double-length number (x+dx) the result */
/* stored in v where v= v[0]+v[1] =arcsin(x+dx) */
/********************************************************************/
void __doasin(double x, double dx, double v[]) {
#include "doasin.h"
static const double
d5 = 0.22372159090911789889975459505194491E-01,
d6 = 0.17352764422456822913014975683014622E-01,
d7 = 0.13964843843786693521653681033981614E-01,
d8 = 0.11551791438485242609036067259086589E-01,
d9 = 0.97622386568166960207425666787248914E-02,
d10 = 0.83638737193775788576092749009744976E-02,
d11 = 0.79470250400727425881446981833568758E-02;
double xx,p,pp,u,uu,r,s;
double hx,tx,hy,ty,tp,tq,tc,tcc;
/* Taylor series for arcsin for Double-Length numbers */
xx = x*x+2.0*x*dx;
p = ((((((d11*xx+d10)*xx+d9)*xx+d8)*xx+d7)*xx+d6)*xx+d5)*xx;
pp = 0;
MUL2(x,dx,x,dx,u,uu,tp,hx,tx,hy,ty,tq,tc,tcc);
ADD2(p,pp,c4.x,cc4.x,p,pp,r,s);
MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
ADD2(p,pp,c3.x,cc3.x,p,pp,r,s);
MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
ADD2(p,pp,c2.x,cc2.x,p,pp,r,s);
MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
ADD2(p,pp,c1.x,cc1.x,p,pp,r,s);
MUL2(p,pp,u,uu,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
MUL2(p,pp,x,dx,p,pp,tp,hx,tx,hy,ty,tq,tc,tcc);
ADD2(p,pp,x,dx,p,pp,r,s);
v[0]=p;
v[1]=pp; /* arcsin(x+dx)=v[0]+v[1] */
}
libgcc-math/dbl-64/doasin.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/************************************************************************/
/* MODULE_NAME: doasin.h */
/* */
/* */
/* common data and variables definition for BIG or LITTLE ENDIAN */
/************************************************************************/
#ifndef DOASIN_H
#define DOASIN_H
#ifdef BIG_ENDI
static const mynumber
/**/ c1 = {{0x3FC55555, 0x55555555}}, /* 0.16666666666666666 */
/**/ cc1 = {{0x3C655555, 0x55775389}}, /* 9.2518585419753846e-18 */
/**/ c2 = {{0x3FB33333, 0x33333333}}, /* 0.074999999999999997 */
/**/ cc2 = {{0x3C499993, 0x63F1A115}}, /* 2.7755472886508899e-18 */
/**/ c3 = {{0x3FA6DB6D, 0xB6DB6DB7}}, /* 0.044642857142857144 */
/**/ cc3 = {{0xBC320FC0, 0x3D5CF0C5}}, /* -9.7911734574147224e-19 */
/**/ c4 = {{0x3F9F1C71, 0xC71C71C5}}, /* 0.030381944444444437 */
/**/ cc4 = {{0xBC02B240, 0xFF23ED1E}}; /* -1.2669108566898312e-19 */
#else
#ifdef LITTLE_ENDI
static const mynumber
/**/ c1 = {{0x55555555, 0x3FC55555}}, /* 0.16666666666666666 */
/**/ cc1 = {{0x55775389, 0x3C655555}}, /* 9.2518585419753846e-18 */
/**/ c2 = {{0x33333333, 0x3FB33333}}, /* 0.074999999999999997 */
/**/ cc2 = {{0x63F1A115, 0x3C499993}}, /* 2.7755472886508899e-18 */
/**/ c3 = {{0xB6DB6DB7, 0x3FA6DB6D}}, /* 0.044642857142857144 */
/**/ cc3 = {{0x3D5CF0C5, 0xBC320FC0}}, /* -9.7911734574147224e-19 */
/**/ c4 = {{0xC71C71C5, 0x3F9F1C71}}, /* 0.030381944444444437 */
/**/ cc4 = {{0xFF23ED1E, 0xBC02B240}}; /* -1.2669108566898312e-19 */
#endif
#endif
#endif
libgcc-math/dbl-64/dosincos.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/********************************************************************/
/* */
/* MODULE_NAME: dosincos.c */
/* */
/* */
/* FUNCTIONS: dubsin */
/* dubcos */
/* docos */
/* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h */
/* sincos.tbl */
/* */
/* Routines compute sin() and cos() as Double-Length numbers */
/********************************************************************/
#include "endian.h"
#include "mydefs.h"
#include "sincos.tbl"
#include "dla.h"
#include "dosincos.h"
#include "math_private.h"
/***********************************************************************/
/* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */
/* as Double-Length number and store it at array v .It computes it by */
/* arithmetic action on Double-Length numbers */
/*(x+dx) between 0 and PI/4 */
/***********************************************************************/
void __dubsin(double x, double dx, double v[]) {
double r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee,
sn,ssn,cs,ccs,ds,dss,dc,dcc;
#if 0
double xx,y,yy,z,zz;
#endif
mynumber u;
int4 k;
u.x=x+big.x;
k = u.i[LOW_HALF]<<2;
x=x-(u.x-big.x);
d=x+dx;
dd=(x-d)+dx;
/* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */
MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc);
sn=sincos.x[k]; /* */
ssn=sincos.x[k+1]; /* sin(Xi) and cos(Xi) */
cs=sincos.x[k+2]; /* */
ccs=sincos.x[k+3]; /* */
MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* Taylor */
ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* series */
ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc); /* for sin */
MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
ADD2(ds,dss,d,dd,ds,dss,r,s); /* ds=sin(t) */
MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc); ;/* Taylor */
ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* series */
ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* for cos */
ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc); /* dc=cos(t) */
MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
SUB2(e,ee,dc,dcc,e,ee,r,s);
ADD2(e,ee,sn,ssn,e,ee,r,s); /* e+ee=sin(x+dx) */
v[0]=e;
v[1]=ee;
}
/**********************************************************************/
/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
/* as Double-Length number and store it in array v .It computes it by */
/* arithmetic action on Double-Length numbers */
/*(x+dx) between 0 and PI/4 */
/**********************************************************************/
void __dubcos(double x, double dx, double v[]) {
double r,s,p,hx,tx,hy,ty,q,c,cc,d,dd,d2,dd2,e,ee,
sn,ssn,cs,ccs,ds,dss,dc,dcc;
#if 0
double xx,y,yy,z,zz;
#endif
mynumber u;
int4 k;
u.x=x+big.x;
k = u.i[LOW_HALF]<<2;
x=x-(u.x-big.x);
d=x+dx;
dd=(x-d)+dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
MUL2(d,dd,d,dd,d2,dd2,p,hx,tx,hy,ty,q,c,cc);
sn=sincos.x[k]; /* */
ssn=sincos.x[k+1]; /* sin(Xi) and cos(Xi) */
cs=sincos.x[k+2]; /* */
ccs=sincos.x[k+3]; /* */
MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);
ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
ADD2(ds,dss,d,dd,ds,dss,r,s);
MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
MUL2(cs,ccs,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
MUL2(dc,dcc,sn,ssn,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
MUL2(d2,dd2,s7.x,ss7.x,ds,dss,p,hx,tx,hy,ty,q,c,cc);
ADD2(ds,dss,s5.x,ss5.x,ds,dss,r,s);
MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
ADD2(ds,dss,s3.x,ss3.x,ds,dss,r,s);
MUL2(d2,dd2,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
MUL2(d,dd,ds,dss,ds,dss,p,hx,tx,hy,ty,q,c,cc);
ADD2(ds,dss,d,dd,ds,dss,r,s);
MUL2(d2,dd2,c8.x,cc8.x,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
ADD2(dc,dcc,c6.x,cc6.x,dc,dcc,r,s);
MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
ADD2(dc,dcc,c4.x,cc4.x,dc,dcc,r,s);
MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
ADD2(dc,dcc,c2.x,cc2.x,dc,dcc,r,s);
MUL2(d2,dd2,dc,dcc,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
MUL2(sn,ssn,ds,dss,e,ee,p,hx,tx,hy,ty,q,c,cc);
MUL2(dc,dcc,cs,ccs,dc,dcc,p,hx,tx,hy,ty,q,c,cc);
ADD2(e,ee,dc,dcc,e,ee,r,s);
SUB2(cs,ccs,e,ee,e,ee,r,s);
v[0]=e;
v[1]=ee;
}
/**********************************************************************/
/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
/* as Double-Length number and store it in array v */
/**********************************************************************/
void __docos(double x, double dx, double v[]) {
double y,yy,p,w[2];
if (x>0) {y=x; yy=dx;}
else {y=-x; yy=-dx;}
if (y<0.5*hp0.x) /* y< PI/4 */
{__dubcos(y,yy,w); v[0]=w[0]; v[1]=w[1];}
else if (y<1.5*hp0.x) { /* y< 3/4 * PI */
p=hp0.x-y; /* p = PI/2 - y */
yy=hp1.x-yy;
y=p+yy;
yy=(p-y)+yy;
if (y>0) {__dubsin(y,yy,w); v[0]=w[0]; v[1]=w[1];}
/* cos(x) = sin ( 90 - x ) */
else {__dubsin(-y,-yy,w); v[0]=-w[0]; v[1]=-w[1];
}
}
else { /* y>= 3/4 * PI */
p=2.0*hp0.x-y; /* p = PI- y */
yy=2.0*hp1.x-yy;
y=p+yy;
yy=(p-y)+yy;
__dubcos(y,yy,w);
v[0]=-w[0];
v[1]=-w[1];
}
}
libgcc-math/dbl-64/dosincos.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/************************************************************************/
/* MODULE_NAME: dosincos.h */
/* */
/* */
/* common data and variables definition for BIG or LITTLE ENDIAN */
/************************************************************************/
#ifndef DOSINCOS_H
#define DOSINCOS_H
#ifdef BIG_ENDI
static const mynumber
/**/ s3 = {{0xBFC55555, 0x55555555}},/* -0.16666666666666666 */
/**/ ss3 = {{0xBC6553AA, 0xE77EE482}},/* -9.2490366677784492e-18 */
/**/ s5 = {{0x3F811111, 0x11110F15}},/* 0.008333333333332452 */
/**/ ss5 = {{0xBC21AC06, 0xDA488820}},/* -4.7899996586987931e-19 */
/**/ s7 = {{0xBF2A019F, 0x5816C78D}},/* -0.00019841261022928957 */
/**/ ss7 = {{0x3BCDCEC9, 0x6A18BF2A}},/* 1.2624077757871259e-20 */
/**/ c2 = {{0x3FE00000, 0x00000000}},/* 0.5 */
/**/ cc2 = {{0xBA282FD8, 0x00000000}},/* -1.5264073330037701e-28 */
/**/ c4 = {{0xBFA55555, 0x55555555}},/* -0.041666666666666664 */
/**/ cc4 = {{0xBC4554BC, 0x2FFF257E}},/* -2.312711276085743e-18 */
/**/ c6 = {{0x3F56C16C, 0x16C16A96}},/* 0.0013888888888888055 */
/**/ cc6 = {{0xBBD2E846, 0xE6346F14}},/* -1.6015133010194884e-20 */
/**/ c8 = {{0xBEFA019F, 0x821D5987}},/* -2.480157866754367e-05 */
/**/ cc8 = {{0x3B7AB71E, 0x72FFE5CC}},/* 3.5357416224857556e-22 */
/**/ big = {{0x42c80000, 0x00000000}}, /* 52776558133248 */
/**/ hp0 = {{0x3FF921FB, 0x54442D18}}, /* PI / 2 */
/**/ hp1 = {{0x3C91A626, 0x33145C07}}; /* 6.123233995736766e-17 */
#else
#ifdef LITTLE_ENDI
static const mynumber
/**/ s3 = {{0x55555555, 0xBFC55555}},/* -0.16666666666666666 */
/**/ ss3 = {{0xE77EE482, 0xBC6553AA}},/* -9.2490366677784492e-18 */
/**/ s5 = {{0x11110F15, 0x3F811111}},/* 0.008333333333332452 */
/**/ ss5 = {{0xDA488820, 0xBC21AC06}},/* -4.7899996586987931e-19 */
/**/ s7 = {{0x5816C78D, 0xBF2A019F}},/* -0.00019841261022928957 */
/**/ ss7 = {{0x6A18BF2A, 0x3BCDCEC9}},/* 1.2624077757871259e-20 */
/**/ c2 = {{0x00000000, 0x3FE00000}},/* 0.5 */
/**/ cc2 = {{0x00000000, 0xBA282FD8}},/* -1.5264073330037701e-28 */
/**/ c4 = {{0x55555555, 0xBFA55555}},/* -0.041666666666666664 */
/**/ cc4 = {{0x2FFF257E, 0xBC4554BC}},/* -2.312711276085743e-18 */
/**/ c6 = {{0x16C16A96, 0x3F56C16C}},/* 0.0013888888888888055 */
/**/ cc6 = {{0xE6346F14, 0xBBD2E846}},/* -1.6015133010194884e-20 */
/**/ c8 = {{0x821D5987, 0xBEFA019F}},/* -2.480157866754367e-05 */
/**/ cc8 = {{0x72FFE5CC, 0x3B7AB71E}},/* 3.5357416224857556e-22 */
/**/ big = {{0x00000000, 0x42c80000}}, /* 52776558133248 */
/**/ hp0 = {{0x54442D18, 0x3FF921FB}}, /* PI / 2 */
/**/ hp1 = {{0x33145C07, 0x3C91A626}}; /* 6.123233995736766e-17 */
#endif
#endif
#endif
libgcc-math/dbl-64/e_exp.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/***************************************************************************/
/* MODULE_NAME:uexp.c */
/* */
/* FUNCTION:uexp */
/* exp1 */
/* */
/* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h */
/* mpa.c mpexp.x slowexp.c */
/* */
/* An ultimate exp routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of e^x */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/***************************************************************************/
#include "endian.h"
#include "uexp.h"
#include "mydefs.h"
#include "MathLib.h"
#include "uexp.tbl"
#include "math_private.h"
double __slowexp(double);
/***************************************************************************/
/* An ultimate exp routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of e^x */
/***************************************************************************/
double __ieee754_exp(double x) {
double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
mynumber junk1, junk2, binexp = {{0,0}};
#if 0
int4 k;
#endif
int4 i,j,m,n,ex;
junk1.x = x;
m = junk1.i[HIGH_HALF];
n = m&hugeint;
if (n > smallint && n < bigint) {
y = x*log2e.x + three51.x;
bexp = y - three51.x; /* multiply the result by 2**bexp */
junk1.x = y;
eps = bexp*ln_two2.x; /* x = bexp*ln(2) + t - eps */
t = x - bexp*ln_two1.x;
y = t + three33.x;
base = y - three33.x; /* t rounded to a multiple of 2**-18 */
junk2.x = y;
del = (t - base) - eps; /* x = bexp*ln(2) + base + del */
eps = del + del*del*(p3.x*del + p2.x);
binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+1023)<<20;
i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
j = (junk2.i[LOW_HALF]&511)<<1;
al = coar.x[i]*fine.x[j];
bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
rem=(bet + bet*eps)+al*eps;
res = al + rem;
cor = (al - res) + rem;
if (res == (res+cor*err_0)) return res*binexp.x;
else return __slowexp(x); /*if error is over bound */
}
if (n <= smallint) return 1.0;
if (n >= badint) {
if (n > infint) return(x+x); /* x is NaN */
if (n < infint) return ( (x>0) ? (hhuge*hhuge) : (tiny*tiny) );
/* x is finite, cause either overflow or underflow */
if (junk1.i[LOW_HALF] != 0) return (x+x); /* x is NaN */
return ((x>0)?inf.x:zero ); /* |x| = inf; return either inf or 0 */
}
y = x*log2e.x + three51.x;
bexp = y - three51.x;
junk1.x = y;
eps = bexp*ln_two2.x;
t = x - bexp*ln_two1.x;
y = t + three33.x;
base = y - three33.x;
junk2.x = y;
del = (t - base) - eps;
eps = del + del*del*(p3.x*del + p2.x);
i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
j = (junk2.i[LOW_HALF]&511)<<1;
al = coar.x[i]*fine.x[j];
bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
rem=(bet + bet*eps)+al*eps;
res = al + rem;
cor = (al - res) + rem;
if (m>>31) {
ex=junk1.i[LOW_HALF];
if (res < 1.0) {res+=res; cor+=cor; ex-=1;}
if (ex >=-1022) {
binexp.i[HIGH_HALF] = (1023+ex)<<20;
if (res == (res+cor*err_0)) return res*binexp.x;
else return __slowexp(x); /*if error is over bound */
}
ex = -(1022+ex);
binexp.i[HIGH_HALF] = (1023-ex)<<20;
res*=binexp.x;
cor*=binexp.x;
eps=1.0000000001+err_0*binexp.x;
t=1.0+res;
y = ((1.0-t)+res)+cor;
res=t+y;
cor = (t-res)+y;
if (res == (res + eps*cor))
{ binexp.i[HIGH_HALF] = 0x00100000;
return (res-1.0)*binexp.x;
}
else return __slowexp(x); /* if error is over bound */
}
else {
binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+767)<<20;
if (res == (res+cor*err_0)) return res*binexp.x*t256.x;
else return __slowexp(x);
}
}
/************************************************************************/
/* Compute e^(x+xx)(Double-Length number) .The routine also receive */
/* bound of error of previous calculation .If after computing exp */
/* error bigger than allows routine return non positive number */
/*else return e^(x + xx) (always positive ) */
/************************************************************************/
double __exp1(double x, double xx, double error) {
double bexp, t, eps, del, base, y, al, bet, res, rem, cor;
mynumber junk1, junk2, binexp = {{0,0}};
#if 0
int4 k;
#endif
int4 i,j,m,n,ex;
junk1.x = x;
m = junk1.i[HIGH_HALF];
n = m&hugeint; /* no sign */
if (n > smallint && n < bigint) {
y = x*log2e.x + three51.x;
bexp = y - three51.x; /* multiply the result by 2**bexp */
junk1.x = y;
eps = bexp*ln_two2.x; /* x = bexp*ln(2) + t - eps */
t = x - bexp*ln_two1.x;
y = t + three33.x;
base = y - three33.x; /* t rounded to a multiple of 2**-18 */
junk2.x = y;
del = (t - base) + (xx-eps); /* x = bexp*ln(2) + base + del */
eps = del + del*del*(p3.x*del + p2.x);
binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+1023)<<20;
i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
j = (junk2.i[LOW_HALF]&511)<<1;
al = coar.x[i]*fine.x[j];
bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
rem=(bet + bet*eps)+al*eps;
res = al + rem;
cor = (al - res) + rem;
if (res == (res+cor*(1.0+error+err_1))) return res*binexp.x;
else return -10.0;
}
if (n <= smallint) return 1.0; /* if x->0 e^x=1 */
if (n >= badint) {
if (n > infint) return(zero/zero); /* x is NaN, return invalid */
if (n < infint) return ( (x>0) ? (hhuge*hhuge) : (tiny*tiny) );
/* x is finite, cause either overflow or underflow */
if (junk1.i[LOW_HALF] != 0) return (zero/zero); /* x is NaN */
return ((x>0)?inf.x:zero ); /* |x| = inf; return either inf or 0 */
}
y = x*log2e.x + three51.x;
bexp = y - three51.x;
junk1.x = y;
eps = bexp*ln_two2.x;
t = x - bexp*ln_two1.x;
y = t + three33.x;
base = y - three33.x;
junk2.x = y;
del = (t - base) + (xx-eps);
eps = del + del*del*(p3.x*del + p2.x);
i = ((junk2.i[LOW_HALF]>>8)&0xfffffffe)+356;
j = (junk2.i[LOW_HALF]&511)<<1;
al = coar.x[i]*fine.x[j];
bet =(coar.x[i]*fine.x[j+1] + coar.x[i+1]*fine.x[j]) + coar.x[i+1]*fine.x[j+1];
rem=(bet + bet*eps)+al*eps;
res = al + rem;
cor = (al - res) + rem;
if (m>>31) {
ex=junk1.i[LOW_HALF];
if (res < 1.0) {res+=res; cor+=cor; ex-=1;}
if (ex >=-1022) {
binexp.i[HIGH_HALF] = (1023+ex)<<20;
if (res == (res+cor*(1.0+error+err_1))) return res*binexp.x;
else return -10.0;
}
ex = -(1022+ex);
binexp.i[HIGH_HALF] = (1023-ex)<<20;
res*=binexp.x;
cor*=binexp.x;
eps=1.00000000001+(error+err_1)*binexp.x;
t=1.0+res;
y = ((1.0-t)+res)+cor;
res=t+y;
cor = (t-res)+y;
if (res == (res + eps*cor))
{binexp.i[HIGH_HALF] = 0x00100000; return (res-1.0)*binexp.x;}
else return -10.0;
}
else {
binexp.i[HIGH_HALF] =(junk1.i[LOW_HALF]+767)<<20;
if (res == (res+cor*(1.0+error+err_1)))
return res*binexp.x*t256.x;
else return -10.0;
}
}
libgcc-math/dbl-64/e_log.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/*********************************************************************/
/* */
/* MODULE_NAME:ulog.c */
/* */
/* FUNCTION:ulog */
/* */
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h ulog.h */
/* mpexp.c mplog.c mpa.c */
/* ulog.tbl */
/* */
/* An ultimate log routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of log(x). */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/*********************************************************************/
#include "endian.h"
#include "dla.h"
#include "mpa.h"
#include "MathLib.h"
#include "math_private.h"
void __mplog(mp_no *, mp_no *, int);
/*********************************************************************/
/* An ultimate log routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of log(x). */
/*********************************************************************/
double __ieee754_log(double x) {
#define M 4
static const int pr[M]={8,10,18,32};
int i,j,n,ux,dx,p;
#if 0
int k;
#endif
double dbl_n,u,p0,q,r0,w,nln2a,luai,lubi,lvaj,lvbj,
sij,ssij,ttij,A,B,B0,y,y1,y2,polI,polII,sa,sb,
t1,t2,t3,t4,t5,t6,t7,t8,t,ra,rb,ww,
a0,aa0,s1,s2,ss2,s3,ss3,a1,aa1,a,aa,b,bb,c;
number num;
mp_no mpx,mpy,mpy1,mpy2,mperr;
#include "ulog.tbl"
#include "ulog.h"
/* Treating special values of x ( x<=0, x=INF, x=NaN etc.). */
num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
n=0;
if (ux < 0x00100000) {
if (((ux & 0x7fffffff) | dx) == 0) return MHALF/ZERO; /* return -INF */
if (ux < 0) return (x-x)/ZERO; /* return NaN */
n -= 54; x *= two54.d; /* scale x */
num.d = x;
}
if (ux >= 0x7ff00000) return x+x; /* INF or NaN */
/* Regular values of x */
w = x-ONE;
if (ABS(w) > U03) { goto case_03; }
/*--- Stage I, the case abs(x-1) < 0.03 */
t8 = MHALF*w;
EMULV(t8,w,a,aa,t1,t2,t3,t4,t5)
EADD(w,a,b,bb)
/* Evaluate polynomial II */
polII = (b0.d+w*(b1.d+w*(b2.d+w*(b3.d+w*(b4.d+
w*(b5.d+w*(b6.d+w*(b7.d+w*b8.d))))))))*w*w*w;
c = (aa+bb)+polII;
/* End stage I, case abs(x-1) < 0.03 */
if ((y=b+(c+b*E2)) == b+(c-b*E2)) return y;
/*--- Stage II, the case abs(x-1) < 0.03 */
a = d11.d+w*(d12.d+w*(d13.d+w*(d14.d+w*(d15.d+w*(d16.d+
w*(d17.d+w*(d18.d+w*(d19.d+w*d20.d))))))));
EMULV(w,a,s2,ss2,t1,t2,t3,t4,t5)
ADD2(d10.d,dd10.d,s2,ss2,s3,ss3,t1,t2)
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(d9.d,dd9.d,s2,ss2,s3,ss3,t1,t2)
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(d8.d,dd8.d,s2,ss2,s3,ss3,t1,t2)
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(d7.d,dd7.d,s2,ss2,s3,ss3,t1,t2)
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(d6.d,dd6.d,s2,ss2,s3,ss3,t1,t2)
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(d5.d,dd5.d,s2,ss2,s3,ss3,t1,t2)
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(d4.d,dd4.d,s2,ss2,s3,ss3,t1,t2)
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(d3.d,dd3.d,s2,ss2,s3,ss3,t1,t2)
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(d2.d,dd2.d,s2,ss2,s3,ss3,t1,t2)
MUL2(w,ZERO,s3,ss3,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(w,ZERO,s2,ss2,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(w,ZERO, s3,ss3, b, bb,t1,t2)
/* End stage II, case abs(x-1) < 0.03 */
if ((y=b+(bb+b*E4)) == b+(bb-b*E4)) return y;
goto stage_n;
/*--- Stage I, the case abs(x-1) > 0.03 */
case_03:
/* Find n,u such that x = u*2**n, 1/sqrt(2) < u < sqrt(2) */
n += (num.i[HIGH_HALF] >> 20) - 1023;
num.i[HIGH_HALF] = (num.i[HIGH_HALF] & 0x000fffff) | 0x3ff00000;
if (num.d > SQRT_2) { num.d *= HALF; n++; }
u = num.d; dbl_n = (double) n;
/* Find i such that ui=1+(i-75)/2**8 is closest to u (i= 0,1,2,...,181) */
num.d += h1.d;
i = (num.i[HIGH_HALF] & 0x000fffff) >> 12;
/* Find j such that vj=1+(j-180)/2**16 is closest to v=u/ui (j= 0,...,361) */
num.d = u*Iu[i].d + h2.d;
j = (num.i[HIGH_HALF] & 0x000fffff) >> 4;
/* Compute w=(u-ui*vj)/(ui*vj) */
p0=(ONE+(i-75)*DEL_U)*(ONE+(j-180)*DEL_V);
q=u-p0; r0=Iu[i].d*Iv[j].d; w=q*r0;
/* Evaluate polynomial I */
polI = w+(a2.d+a3.d*w)*w*w;
/* Add up everything */
nln2a = dbl_n*LN2A;
luai = Lu[i][0].d; lubi = Lu[i][1].d;
lvaj = Lv[j][0].d; lvbj = Lv[j][1].d;
EADD(luai,lvaj,sij,ssij)
EADD(nln2a,sij,A ,ttij)
B0 = (((lubi+lvbj)+ssij)+ttij)+dbl_n*LN2B;
B = polI+B0;
/* End stage I, case abs(x-1) >= 0.03 */
if ((y=A+(B+E1)) == A+(B-E1)) return y;
/*--- Stage II, the case abs(x-1) > 0.03 */
/* Improve the accuracy of r0 */
EMULV(p0,r0,sa,sb,t1,t2,t3,t4,t5)
t=r0*((ONE-sa)-sb);
EADD(r0,t,ra,rb)
/* Compute w */
MUL2(q,ZERO,ra,rb,w,ww,t1,t2,t3,t4,t5,t6,t7,t8)
EADD(A,B0,a0,aa0)
/* Evaluate polynomial III */
s1 = (c3.d+(c4.d+c5.d*w)*w)*w;
EADD(c2.d,s1,s2,ss2)
MUL2(s2,ss2,w,ww,s3,ss3,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(s3,ss3,w,ww,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(s2,ss2,w,ww,s3,ss3,t1,t2)
ADD2(s3,ss3,a0,aa0,a1,aa1,t1,t2)
/* End stage II, case abs(x-1) >= 0.03 */
if ((y=a1+(aa1+E3)) == a1+(aa1-E3)) return y;
/* Final stages. Use multi-precision arithmetic. */
stage_n:
for (i=0; i<M; i++) {
p = pr[i];
__dbl_mp(x,&mpx,p); __dbl_mp(y,&mpy,p);
__mplog(&mpx,&mpy,p);
__dbl_mp(e[i].d,&mperr,p);
__add(&mpy,&mperr,&mpy1,p); __sub(&mpy,&mperr,&mpy2,p);
__mp_dbl(&mpy1,&y1,p); __mp_dbl(&mpy2,&y2,p);
if (y1==y2) return y1;
}
return y1;
}
libgcc-math/dbl-64/e_log10.c 0 → 100644
/* @(#)e_log10.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: e_log10.c,v 1.9 1995/05/10 20:45:51 jtc Exp $";
#endif
/* __ieee754_log10(x)
* Return the base 10 logarithm of x
*
* Method :
* Let log10_2hi = leading 40 bits of log10(2) and
* log10_2lo = log10(2) - log10_2hi,
* ivln10 = 1/log(10) rounded.
* Then
* n = ilogb(x),
* if(n<0) n = n+1;
* x = scalbn(x,-n);
* log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
*
* Note 1:
* To guarantee log10(10**n)=n, where 10**n is normal, the rounding
* mode must set to Round-to-Nearest.
* Note 2:
* [1/log(10)] rounded to 53 bits has error .198 ulps;
* log10 is monotonic at all binary break points.
*
* Special cases:
* log10(x) is NaN with signal if x < 0;
* log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
* log10(NaN) is that NaN with no signal;
* log10(10**N) = N for N=0,1,...,22.
*
* 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
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
#ifdef __STDC__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif
#ifdef __STDC__
double __ieee754_log10(double x)
#else
double __ieee754_log10(x)
double x;
#endif
{
double y,z;
int32_t i,k,hx;
u_int32_t lx;
EXTRACT_WORDS(hx,lx,x);
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/(x-x); /* log(+-0)=-inf */
if (hx<0) return (x-x)/(x-x); /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
GET_HIGH_WORD(hx,x);
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
i = ((u_int32_t)k&0x80000000)>>31;
hx = (hx&0x000fffff)|((0x3ff-i)<<20);
y = (double)(k+i);
SET_HIGH_WORD(x,hx);
z = y*log10_2lo + ivln10*__ieee754_log(x);
return z+y*log10_2hi;
}
libgcc-math/dbl-64/e_rem_pio2.c 0 → 100644
/* @(#)e_rem_pio2.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: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
#endif
/* __ieee754_rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __kernel_rem_pio2()
*/
#include "math.h"
#include "math_private.h"
/*
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
*/
#ifdef __STDC__
static const int32_t two_over_pi[] = {
#else
static int32_t two_over_pi[] = {
#endif
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
};
#ifdef __STDC__
static const int32_t npio2_hw[] = {
#else
static int32_t npio2_hw[] = {
#endif
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
0x404858EB, 0x404921FB,
};
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 33 bit of pi/2
* pio2_1t: pi/2 - pio2_1
* pio2_2: second 33 bit of pi/2
* pio2_2t: pi/2 - (pio2_1+pio2_2)
* pio2_3: third 33 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
#ifdef __STDC__
static const double
#else
static double
#endif
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
#ifdef __STDC__
int32_t __ieee754_rem_pio2(double x, double *y)
#else
int32_t __ieee754_rem_pio2(x,y)
double x,y[];
#endif
{
double z,w,t,r,fn;
double tx[3];
int32_t e0,i,j,nx,n,ix,hx;
u_int32_t low;
GET_HIGH_WORD(hx,x); /* high word of x */
ix = hx&0x7fffffff;
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
{y[0] = x; y[1] = 0; return 0;}
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
if(hx>0) {
z = x - pio2_1;
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
y[0] = z - pio2_1t;
y[1] = (z-y[0])-pio2_1t;
} else { /* near pi/2, use 33+33+53 bit pi */
z -= pio2_2;
y[0] = z - pio2_2t;
y[1] = (z-y[0])-pio2_2t;
}
return 1;
} else { /* negative x */
z = x + pio2_1;
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
y[0] = z + pio2_1t;
y[1] = (z-y[0])+pio2_1t;
} else { /* near pi/2, use 33+33+53 bit pi */
z += pio2_2;
y[0] = z + pio2_2t;
y[1] = (z-y[0])+pio2_2t;
}
return -1;
}
}
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
t = fabs(x);
n = (int32_t) (t*invpio2+half);
fn = (double)n;
r = t-fn*pio2_1;
w = fn*pio2_1t; /* 1st round good to 85 bit */
if(n<32&&ix!=npio2_hw[n-1]) {
y[0] = r-w; /* quick check no cancellation */
} else {
u_int32_t high;
j = ix>>20;
y[0] = r-w;
GET_HIGH_WORD(high,y[0]);
i = j-((high>>20)&0x7ff);
if(i>16) { /* 2nd iteration needed, good to 118 */
t = r;
w = fn*pio2_2;
r = t-w;
w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
GET_HIGH_WORD(high,y[0]);
i = j-((high>>20)&0x7ff);
if(i>49) { /* 3rd iteration need, 151 bits acc */
t = r; /* will cover all possible cases */
w = fn*pio2_3;
r = t-w;
w = fn*pio2_3t-((t-r)-w);
y[0] = r-w;
}
}
}
y[1] = (r-y[0])-w;
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
else return n;
}
/*
* all other (large) arguments
*/
if(ix>=0x7ff00000) { /* x is inf or NaN */
y[0]=y[1]=x-x; return 0;
}
/* set z = scalbn(|x|,ilogb(x)-23) */
GET_LOW_WORD(low,x);
SET_LOW_WORD(z,low);
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
for(i=0;i<2;i++) {
tx[i] = (double)((int32_t)(z));
z = (z-tx[i])*two24;
}
tx[2] = z;
nx = 3;
while(tx[nx-1]==zero) nx--; /* skip zero term */
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
return n;
}
libgcc-math/dbl-64/e_sqrt.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/*********************************************************************/
/* MODULE_NAME: uroot.c */
/* */
/* FUNCTION: usqrt */
/* */
/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
/* uroot.tbl */
/* */
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/*********************************************************************/
#include "endian.h"
#include "mydefs.h"
#include "dla.h"
#include "MathLib.h"
#include "root.tbl"
#include "math_private.h"
/*********************************************************************/
/* An ultimate sqrt routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of square */
/* root of x. */
/*********************************************************************/
double __ieee754_sqrt(double x) {
#include "uroot.h"
static const double
rt0 = 9.99999999859990725855365213134618E-01,
rt1 = 4.99999999495955425917856814202739E-01,
rt2 = 3.75017500867345182581453026130850E-01,
rt3 = 3.12523626554518656309172508769531E-01;
static const double big = 134217728.0;
double y,t,del,res,res1,hy,z,zz,p,hx,tx,ty,s;
mynumber a,c={{0,0}};
int4 k;
a.x=x;
k=a.i[HIGH_HALF];
a.i[HIGH_HALF]=(k&0x001fffff)|0x3fe00000;
t=inroot[(k&0x001fffff)>>14];
s=a.x;
/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
if (k>0x000fffff && k<0x7ff00000) {
y=1.0-t*(t*s);
t=t*(rt0+y*(rt1+y*(rt2+y*rt3)));
c.i[HIGH_HALF]=0x20000000+((k&0x7fe00000)>>1);
y=t*s;
hy=(y+big)-big;
del=0.5*t*((s-hy*hy)-(y-hy)*(y+hy));
res=y+del;
if (res == (res+1.002*((y-res)+del))) return res*c.x;
else {
res1=res+1.5*((y-res)+del);
EMULV(res,res1,z,zz,p,hx,tx,hy,ty); /* (z+zz)=res*res1 */
return ((((z-s)+zz)<0)?max(res,res1):min(res,res1))*c.x;
}
}
else {
if ((k & 0x7ff00000) == 0x7ff00000)
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
if (x==0) return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */
if (k<0) return (x-x)/(x-x); /* sqrt(-ve)=sNaN */
return tm256.x*__ieee754_sqrt(x*t512.x);
}
}
libgcc-math/dbl-64/halfulp.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001, 2005 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/************************************************************************/
/* */
/* MODULE_NAME:halfulp.c */
/* */
/* FUNCTIONS:halfulp */
/* FILES NEEDED: mydefs.h dla.h endian.h */
/* uroot.c */
/* */
/*Routine halfulp(double x, double y) computes x^y where result does */
/*not need rounding. If the result is closer to 0 than can be */
/*represented it returns 0. */
/* In the following cases the function does not compute anything */
/*and returns a negative number: */
/*1. if the result needs rounding, */
/*2. if y is outside the interval [0, 2^20-1], */
/*3. if x can be represented by x=2**n for some integer n. */
/************************************************************************/
#include "endian.h"
#include "mydefs.h"
#include "dla.h"
#include "math_private.h"
double __ieee754_sqrt(double x);
static const int4 tab54[32] = {
262143, 11585, 1782, 511, 210, 107, 63, 42,
30, 22, 17, 14, 12, 10, 9, 7,
7, 6, 5, 5, 5, 4, 4, 4,
3, 3, 3, 3, 3, 3, 3, 3 };
double __halfulp(double x, double y)
{
mynumber v;
double z,u,uu,j1,j2,j3,j4,j5;
int4 k,l,m,n;
if (y <= 0) { /*if power is negative or zero */
v.x = y;
if (v.i[LOW_HALF] != 0) return -10.0;
v.x = x;
if (v.i[LOW_HALF] != 0) return -10.0;
if ((v.i[HIGH_HALF]&0x000fffff) != 0) return -10; /* if x =2 ^ n */
k = ((v.i[HIGH_HALF]&0x7fffffff)>>20)-1023; /* find this n */
z = (double) k;
return (z*y == -1075.0)?0: -10.0;
}
/* if y > 0 */
v.x = y;
if (v.i[LOW_HALF] != 0) return -10.0;
v.x=x;
/* case where x = 2**n for some integer n */
if (((v.i[HIGH_HALF]&0x000fffff)|v.i[LOW_HALF]) == 0) {
k=(v.i[HIGH_HALF]>>20)-1023;
return (((double) k)*y == -1075.0)?0:-10.0;
}
v.x = y;
k = v.i[HIGH_HALF];
m = k<<12;
l = 0;
while (m)
{m = m<<1; l++; }
n = (k&0x000fffff)|0x00100000;
n = n>>(20-l); /* n is the odd integer of y */
k = ((k>>20) -1023)-l; /* y = n*2**k */
if (k>5) return -10.0;
if (k>0) for (;k>0;k--) n *= 2;
if (n > 34) return -10.0;
k = -k;
if (k>5) return -10.0;
/* now treat x */
while (k>0) {
z = __ieee754_sqrt(x);
EMULV(z,z,u,uu,j1,j2,j3,j4,j5);
if (((u-x)+uu) != 0) break;
x = z;
k--;
}
if (k) return -10.0;
/* it is impossible that n == 2, so the mantissa of x must be short */
v.x = x;
if (v.i[LOW_HALF]) return -10.0;
k = v.i[HIGH_HALF];
m = k<<12;
l = 0;
while (m) {m = m<<1; l++; }
m = (k&0x000fffff)|0x00100000;
m = m>>(20-l); /* m is the odd integer of x */
/* now check whether the length of m**n is at most 54 bits */
if (m > tab54[n-3]) return -10.0;
/* yes, it is - now compute x**n by simple multiplications */
u = x;
for (k=1;k<n;k++) u = u*x;
return u;
}
libgcc-math/dbl-64/k_rem_pio2.c 0 → 100644
/* @(#)k_rem_pio2.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: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $";
#endif
/*
* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
* double x[],y[]; int e0,nx,prec; int ipio2[];
*
* __kernel_rem_pio2 return the last three digits of N with
* y = x - N*pi/2
* so that |y| < pi/2.
*
* The method is to compute the integer (mod 8) and fraction parts of
* (2/pi)*x without doing the full multiplication. In general we
* skip the part of the product that are known to be a huge integer (
* more accurately, = 0 mod 8 ). Thus the number of operations are
* independent of the exponent of the input.
*
* (2/pi) is represented by an array of 24-bit integers in ipio2[].
*
* Input parameters:
* x[] The input value (must be positive) is broken into nx
* pieces of 24-bit integers in double precision format.
* x[i] will be the i-th 24 bit of x. The scaled exponent
* of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
* match x's up to 24 bits.
*
* Example of breaking a double positive z into x[0]+x[1]+x[2]:
* e0 = ilogb(z)-23
* z = scalbn(z,-e0)
* for i = 0,1,2
* x[i] = floor(z)
* z = (z-x[i])*2**24
*
*
* y[] ouput result in an array of double precision numbers.
* The dimension of y[] is:
* 24-bit precision 1
* 53-bit precision 2
* 64-bit precision 2
* 113-bit precision 3
* The actual value is the sum of them. Thus for 113-bit
* precision, one may have to do something like:
*
* long double t,w,r_head, r_tail;
* t = (long double)y[2] + (long double)y[1];
* w = (long double)y[0];
* r_head = t+w;
* r_tail = w - (r_head - t);
*
* e0 The exponent of x[0]
*
* nx dimension of x[]
*
* prec an integer indicating the precision:
* 0 24 bits (single)
* 1 53 bits (double)
* 2 64 bits (extended)
* 3 113 bits (quad)
*
* ipio2[]
* integer array, contains the (24*i)-th to (24*i+23)-th
* bit of 2/pi after binary point. The corresponding
* floating value is
*
* ipio2[i] * 2^(-24(i+1)).
*
* External function:
* double scalbn(), floor();
*
*
* Here is the description of some local variables:
*
* jk jk+1 is the initial number of terms of ipio2[] needed
* in the computation. The recommended value is 2,3,4,
* 6 for single, double, extended,and quad.
*
* jz local integer variable indicating the number of
* terms of ipio2[] used.
*
* jx nx - 1
*
* jv index for pointing to the suitable ipio2[] for the
* computation. In general, we want
* ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
* is an integer. Thus
* e0-3-24*jv >= 0 or (e0-3)/24 >= jv
* Hence jv = max(0,(e0-3)/24).
*
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
*
* q[] double array with integral value, representing the
* 24-bits chunk of the product of x and 2/pi.
*
* q0 the corresponding exponent of q[0]. Note that the
* exponent for q[i] would be q0-24*i.
*
* PIo2[] double precision array, obtained by cutting pi/2
* into 24 bits chunks.
*
* f[] ipio2[] in floating point
*
* iq[] integer array by breaking up q[] in 24-bits chunk.
*
* fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
*
* ih integer. If >0 it indicates q[] is >= 0.5, hence
* it also indicates the *sign* of the result.
*
*/
/*
* 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 int init_jk[] = {2,3,4,6}; /* initial value for jk */
#else
static int init_jk[] = {2,3,4,6};
#endif
#ifdef __STDC__
static const double PIo2[] = {
#else
static double PIo2[] = {
#endif
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
};
#ifdef __STDC__
static const double
#else
static double
#endif
zero = 0.0,
one = 1.0,
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
#ifdef __STDC__
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)
#else
int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
double x[], y[]; int e0,nx,prec; int32_t ipio2[];
#endif
{
int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
double z,fw,f[20],fq[20],q[20];
/* initialize jk*/
jk = init_jk[prec];
jp = jk;
/* determine jx,jv,q0, note that 3>q0 */
jx = nx-1;
jv = (e0-3)/24; if(jv<0) jv=0;
q0 = e0-24*(jv+1);
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
j = jv-jx; m = jx+jk;
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
/* compute q[0],q[1],...q[jk] */
for (i=0;i<=jk;i++) {
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
}
jz = jk;
recompute:
/* distill q[] into iq[] reversingly */
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
fw = (double)((int32_t)(twon24* z));
iq[i] = (int32_t)(z-two24*fw);
z = q[j-1]+fw;
}
/* compute n */
z = __scalbn(z,q0); /* actual value of z */
z -= 8.0*__floor(z*0.125); /* trim off integer >= 8 */
n = (int32_t) z;
z -= (double)n;
ih = 0;
if(q0>0) { /* need iq[jz-1] to determine n */
i = (iq[jz-1]>>(24-q0)); n += i;
iq[jz-1] -= i<<(24-q0);
ih = iq[jz-1]>>(23-q0);
}
else if(q0==0) ih = iq[jz-1]>>23;
else if(z>=0.5) ih=2;
if(ih>0) { /* q > 0.5 */
n += 1; carry = 0;
for(i=0;i<jz ;i++) { /* compute 1-q */
j = iq[i];
if(carry==0) {
if(j!=0) {
carry = 1; iq[i] = 0x1000000- j;
}
} else iq[i] = 0xffffff - j;
}
if(q0>0) { /* rare case: chance is 1 in 12 */
switch(q0) {
case 1:
iq[jz-1] &= 0x7fffff; break;
case 2:
iq[jz-1] &= 0x3fffff; break;
}
}
if(ih==2) {
z = one - z;
if(carry!=0) z -= __scalbn(one,q0);
}
}
/* check if recomputation is needed */
if(z==zero) {
j = 0;
for (i=jz-1;i>=jk;i--) j |= iq[i];
if(j==0) { /* need recomputation */
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
f[jx+i] = (double) ipio2[jv+i];
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
q[i] = fw;
}
jz += k;
goto recompute;
}
}
/* chop off zero terms */
if(z==0.0) {
jz -= 1; q0 -= 24;
while(iq[jz]==0) { jz--; q0-=24;}
} else { /* break z into 24-bit if necessary */
z = __scalbn(z,-q0);
if(z>=two24) {
fw = (double)((int32_t)(twon24*z));
iq[jz] = (int32_t)(z-two24*fw);
jz += 1; q0 += 24;
iq[jz] = (int32_t) fw;
} else iq[jz] = (int32_t) z ;
}
/* convert integer "bit" chunk to floating-point value */
fw = __scalbn(one,q0);
for(i=jz;i>=0;i--) {
q[i] = fw*(double)iq[i]; fw*=twon24;
}
/* compute PIo2[0,...,jp]*q[jz,...,0] */
for(i=jz;i>=0;i--) {
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
fq[jz-i] = fw;
}
/* compress fq[] into y[] */
switch(prec) {
case 0:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
break;
case 1:
case 2:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
fw = fq[0]-fw;
for (i=1;i<=jz;i++) fw += fq[i];
y[1] = (ih==0)? fw: -fw;
break;
case 3: /* painful */
for (i=jz;i>0;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (i=jz;i>1;i--) {
fw = fq[i-1]+fq[i];
fq[i] += fq[i-1]-fw;
fq[i-1] = fw;
}
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
if(ih==0) {
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
} else {
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
}
}
return n&7;
}
libgcc-math/dbl-64/mpa.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/************************************************************************/
/* MODULE_NAME: mpa.h */
/* */
/* FUNCTIONS: */
/* mcr */
/* acr */
/* cr */
/* cpy */
/* cpymn */
/* mp_dbl */
/* dbl_mp */
/* add */
/* sub */
/* mul */
/* inv */
/* dvd */
/* */
/* Arithmetic functions for multiple precision numbers. */
/* Common types and definition */
/************************************************************************/
#ifndef MPA_H
#define MPA_H
typedef struct {/* This structure holds the details of a multi-precision */
int e; /* floating point number, x: d[0] holds its sign (-1,0 or 1) */
double d[40]; /* e holds its exponent (...,-2,-1,0,1,2,...) and */
} mp_no; /* d[1]...d[p] hold its mantissa digits. The value of x is, */
/* x = d[1]*r**(e-1) + d[2]*r**(e-2) + ... + d[p]*r**(e-p). */
/* Here r = 2**24, 0 <= d[i] < r and 1 <= p <= 32. */
/* p is a global variable. A multi-precision number is */
/* always normalized. Namely, d[1] > 0. An exception is */
/* a zero which is characterized by d[0] = 0. The terms */
/* d[p+1], d[p+2], ... of a none zero number have no */
/* significance and so are the terms e, d[1],d[2],... */
/* of a zero. */
typedef union { int i[2]; double d; } number;
#define X x->d
#define Y y->d
#define Z z->d
#define EX x->e
#define EY y->e
#define EZ z->e
#define ABS(x) ((x) < 0 ? -(x) : (x))
int __acr(const mp_no *, const mp_no *, int);
int __cr(const mp_no *, const mp_no *, int);
void __cpy(const mp_no *, mp_no *, int);
void __cpymn(const mp_no *, int, mp_no *, int);
void __mp_dbl(const mp_no *, double *, int);
void __dbl_mp(double, mp_no *, int);
void __add(const mp_no *, const mp_no *, mp_no *, int);
void __sub(const mp_no *, const mp_no *, mp_no *, int);
void __mul(const mp_no *, const mp_no *, mp_no *, int);
void __inv(const mp_no *, mp_no *, int);
void __dvd(const mp_no *, const mp_no *, mp_no *, int);
extern void __mpatan (mp_no *, mp_no *, int);
extern void __mpatan2 (mp_no *, mp_no *, mp_no *, int);
extern void __mpsqrt (mp_no *, mp_no *, int);
extern void __mpexp (mp_no *, mp_no *__y, int);
extern void __c32 (mp_no *, mp_no *, mp_no *, int);
extern int __mpranred (double, mp_no *, int);
#endif
libgcc-math/dbl-64/mpa2.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/**************************************************************************/
/* */
/* MODULE_NAME:mpa2.h */
/* */
/* */
/* variables prototype and definition according to type of processor */
/* types definition */
/**************************************************************************/
#ifndef MPA2_H
#define MPA2_H
#ifdef BIG_ENDI
static const number
/**/ radix = {{0x41700000, 0x00000000} }, /* 2**24 */
/**/ radixi = {{0x3e700000, 0x00000000} }, /* 2**-24 */
/**/ cutter = {{0x44b00000, 0x00000000} }, /* 2**76 */
/**/ zero = {{0x00000000, 0x00000000} }, /* 0 */
/**/ one = {{0x3ff00000, 0x00000000} }, /* 1 */
/**/ mone = {{0xbff00000, 0x00000000} }, /* -1 */
/**/ two = {{0x40000000, 0x00000000} }, /* 2 */
/**/ half = {{0x3fe00000, 0x00000000} }, /* 1/2 */
/**/ two5 = {{0x40400000, 0x00000000} }, /* 2**5 */
/**/ two10 = {{0x40900000, 0x00000000} }, /* 2**10 */
/**/ two18 = {{0x41100000, 0x00000000} }, /* 2**18 */
/**/ two19 = {{0x41200000, 0x00000000} }, /* 2**19 */
/**/ two23 = {{0x41600000, 0x00000000} }, /* 2**23 */
/**/ two52 = {{0x43300000, 0x00000000} }, /* 2**52 */
/**/ two57 = {{0x43800000, 0x00000000} }, /* 2**57 */
/**/ two71 = {{0x44600000, 0x00000000} }, /* 2**71 */
/**/ twom1032 = {{0x00000400, 0x00000000} }; /* 2**-1032 */
#else
#ifdef LITTLE_ENDI
static const number
/**/ radix = {{0x00000000, 0x41700000} }, /* 2**24 */
/**/ radixi = {{0x00000000, 0x3e700000} }, /* 2**-24 */
/**/ cutter = {{0x00000000, 0x44b00000} }, /* 2**76 */
/**/ zero = {{0x00000000, 0x00000000} }, /* 0 */
/**/ one = {{0x00000000, 0x3ff00000} }, /* 1 */
/**/ mone = {{0x00000000, 0xbff00000} }, /* -1 */
/**/ two = {{0x00000000, 0x40000000} }, /* 2 */
/**/ half = {{0x00000000, 0x3fe00000} }, /* 1/2 */
/**/ two5 = {{0x00000000, 0x40400000} }, /* 2**5 */
/**/ two10 = {{0x00000000, 0x40900000} }, /* 2**10 */
/**/ two18 = {{0x00000000, 0x41100000} }, /* 2**18 */
/**/ two19 = {{0x00000000, 0x41200000} }, /* 2**19 */
/**/ two23 = {{0x00000000, 0x41600000} }, /* 2**23 */
/**/ two52 = {{0x00000000, 0x43300000} }, /* 2**52 */
/**/ two57 = {{0x00000000, 0x43800000} }, /* 2**57 */
/**/ two71 = {{0x00000000, 0x44600000} }, /* 2**71 */
/**/ twom1032 = {{0x00000000, 0x00000400} }; /* 2**-1032 */
#endif
#endif
#define RADIX radix.d
#define RADIXI radixi.d
#define CUTTER cutter.d
#define ZERO zero.d
#define ONE one.d
#define MONE mone.d
#define TWO two.d
#define HALF half.d
#define TWO5 two5.d
#define TWO10 two10.d
#define TWO18 two18.d
#define TWO19 two19.d
#define TWO23 two23.d
#define TWO52 two52.d
#define TWO57 two57.d
#define TWO71 two71.d
#define TWOM1032 twom1032.d
#endif
libgcc-math/dbl-64/mpatan.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:mpatan.c */
/* */
/* FUNCTIONS:mpatan */
/* */
/* FILES NEEDED: mpa.h endian.h mpatan.h */
/* mpa.c */
/* */
/* Multi-Precision Atan function subroutine, for precision p >= 4.*/
/* The relative error of the result is bounded by 34.32*r**(1-p), */
/* where r=2**24. */
/******************************************************************/
#include "endian.h"
#include "mpa.h"
void __mpsqrt(mp_no *, mp_no *, int);
void __mpatan(mp_no *x, mp_no *y, int p) {
#include "mpatan.h"
int i,m,n;
double dx;
mp_no
mpone = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
mptwo = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
mptwoim1 = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mps,mpsm,mpt,mpt1,mpt2,mpt3;
/* Choose m and initiate mpone, mptwo & mptwoim1 */
if (EX>0) m=7;
else if (EX<0) m=0;
else {
__mp_dbl(x,&dx,p); dx=ABS(dx);
for (m=6; m>0; m--)
{if (dx>xm[m].d) break;}
}
mpone.e = mptwo.e = mptwoim1.e = 1;
mpone.d[0] = mpone.d[1] = mptwo.d[0] = mptwoim1.d[0] = ONE;
mptwo.d[1] = TWO;
/* Reduce x m times */
__mul(x,x,&mpsm,p);
if (m==0) __cpy(x,&mps,p);
else {
for (i=0; i<m; i++) {
__add(&mpone,&mpsm,&mpt1,p);
__mpsqrt(&mpt1,&mpt2,p);
__add(&mpt2,&mpt2,&mpt1,p);
__add(&mptwo,&mpsm,&mpt2,p);
__add(&mpt1,&mpt2,&mpt3,p);
__dvd(&mpsm,&mpt3,&mpt1,p);
__cpy(&mpt1,&mpsm,p);
}
__mpsqrt(&mpsm,&mps,p); mps.d[0] = X[0];
}
/* Evaluate a truncated power series for Atan(s) */
n=np[p]; mptwoim1.d[1] = twonm1[p].d;
__dvd(&mpsm,&mptwoim1,&mpt,p);
for (i=n-1; i>1; i--) {
mptwoim1.d[1] -= TWO;
__dvd(&mpsm,&mptwoim1,&mpt1,p);
__mul(&mpsm,&mpt,&mpt2,p);
__sub(&mpt1,&mpt2,&mpt,p);
}
__mul(&mps,&mpt,&mpt1,p);
__sub(&mps,&mpt1,&mpt,p);
/* Compute Atan(x) */
mptwoim1.d[1] = twom[m].d;
__mul(&mptwoim1,&mpt,y,p);
return;
}
libgcc-math/dbl-64/mpatan.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:mpatan.h */
/* */
/* common data and variables prototype and definition */
/******************************************************************/
#ifndef MPATAN_H
#define MPATAN_H
#ifdef BIG_ENDI
static const number
xm[8] = { /* x[m] */
/**/ {{0x00000000, 0x00000000} }, /* 0.0 */
/**/ {{0x3f8930be, 0x00000000} }, /* 0.0123 */
/**/ {{0x3f991687, 0x00000000} }, /* 0.0245 */
/**/ {{0x3fa923a2, 0x00000000} }, /* 0.0491 */
/**/ {{0x3fb930be, 0x00000000} }, /* 0.0984 */
/**/ {{0x3fc95810, 0x00000000} }, /* 0.198 */
/**/ {{0x3fda7ef9, 0x00000000} }, /* 0.414 */
/**/ {{0x3ff00000, 0x00000000} }, /* 1.0 */
};
static const number
twonm1[33] = { /* 2n-1 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x40260000, 0x00000000} }, /* 11 */
/**/ {{0x402e0000, 0x00000000} }, /* 15 */
/**/ {{0x40330000, 0x00000000} }, /* 19 */
/**/ {{0x40350000, 0x00000000} }, /* 21 */
/**/ {{0x40390000, 0x00000000} }, /* 25 */
/**/ {{0x403d0000, 0x00000000} }, /* 29 */
/**/ {{0x40408000, 0x00000000} }, /* 33 */
/**/ {{0x40428000, 0x00000000} }, /* 37 */
/**/ {{0x40448000, 0x00000000} }, /* 41 */
/**/ {{0x40468000, 0x00000000} }, /* 45 */
/**/ {{0x40488000, 0x00000000} }, /* 49 */
/**/ {{0x404a8000, 0x00000000} }, /* 53 */
/**/ {{0x404b8000, 0x00000000} }, /* 55 */
/**/ {{0x404d8000, 0x00000000} }, /* 59 */
/**/ {{0x404f8000, 0x00000000} }, /* 63 */
/**/ {{0x4050c000, 0x00000000} }, /* 67 */
/**/ {{0x4051c000, 0x00000000} }, /* 71 */
/**/ {{0x4052c000, 0x00000000} }, /* 75 */
/**/ {{0x4053c000, 0x00000000} }, /* 79 */
/**/ {{0x4054c000, 0x00000000} }, /* 83 */
/**/ {{0x40554000, 0x00000000} }, /* 85 */
/**/ {{0x40564000, 0x00000000} }, /* 89 */
/**/ {{0x40574000, 0x00000000} }, /* 93 */
/**/ {{0x40584000, 0x00000000} }, /* 97 */
/**/ {{0x40594000, 0x00000000} }, /* 101 */
/**/ {{0x405a4000, 0x00000000} }, /* 105 */
/**/ {{0x405b4000, 0x00000000} }, /* 109 */
/**/ {{0x405c4000, 0x00000000} }, /* 113 */
/**/ {{0x405d4000, 0x00000000} }, /* 117 */
};
static const number
twom[8] = { /* 2**m */
/**/ {{0x3ff00000, 0x00000000} }, /* 1.0 */
/**/ {{0x40000000, 0x00000000} }, /* 2.0 */
/**/ {{0x40100000, 0x00000000} }, /* 4.0 */
/**/ {{0x40200000, 0x00000000} }, /* 8.0 */
/**/ {{0x40300000, 0x00000000} }, /* 16.0 */
/**/ {{0x40400000, 0x00000000} }, /* 32.0 */
/**/ {{0x40500000, 0x00000000} }, /* 64.0 */
/**/ {{0x40600000, 0x00000000} }, /* 128.0 */
};
static const number
/**/ one = {{0x3ff00000, 0x00000000} }, /* 1 */
/**/ two = {{0x40000000, 0x00000000} }; /* 2 */
#else
#ifdef LITTLE_ENDI
static const number
xm[8] = { /* x[m] */
/**/ {{0x00000000, 0x00000000} }, /* 0.0 */
/**/ {{0x00000000, 0x3f8930be} }, /* 0.0123 */
/**/ {{0x00000000, 0x3f991687} }, /* 0.0245 */
/**/ {{0x00000000, 0x3fa923a2} }, /* 0.0491 */
/**/ {{0x00000000, 0x3fb930be} }, /* 0.0984 */
/**/ {{0x00000000, 0x3fc95810} }, /* 0.198 */
/**/ {{0x00000000, 0x3fda7ef9} }, /* 0.414 */
/**/ {{0x00000000, 0x3ff00000} }, /* 1.0 */
};
static const number
twonm1[33] = { /* 2n-1 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x40260000} }, /* 11 */
/**/ {{0x00000000, 0x402e0000} }, /* 15 */
/**/ {{0x00000000, 0x40330000} }, /* 19 */
/**/ {{0x00000000, 0x40350000} }, /* 21 */
/**/ {{0x00000000, 0x40390000} }, /* 25 */
/**/ {{0x00000000, 0x403d0000} }, /* 29 */
/**/ {{0x00000000, 0x40408000} }, /* 33 */
/**/ {{0x00000000, 0x40428000} }, /* 37 */
/**/ {{0x00000000, 0x40448000} }, /* 41 */
/**/ {{0x00000000, 0x40468000} }, /* 45 */
/**/ {{0x00000000, 0x40488000} }, /* 49 */
/**/ {{0x00000000, 0x404a8000} }, /* 53 */
/**/ {{0x00000000, 0x404b8000} }, /* 55 */
/**/ {{0x00000000, 0x404d8000} }, /* 59 */
/**/ {{0x00000000, 0x404f8000} }, /* 63 */
/**/ {{0x00000000, 0x4050c000} }, /* 67 */
/**/ {{0x00000000, 0x4051c000} }, /* 71 */
/**/ {{0x00000000, 0x4052c000} }, /* 75 */
/**/ {{0x00000000, 0x4053c000} }, /* 79 */
/**/ {{0x00000000, 0x4054c000} }, /* 83 */
/**/ {{0x00000000, 0x40554000} }, /* 85 */
/**/ {{0x00000000, 0x40564000} }, /* 89 */
/**/ {{0x00000000, 0x40574000} }, /* 93 */
/**/ {{0x00000000, 0x40584000} }, /* 97 */
/**/ {{0x00000000, 0x40594000} }, /* 101 */
/**/ {{0x00000000, 0x405a4000} }, /* 105 */
/**/ {{0x00000000, 0x405b4000} }, /* 109 */
/**/ {{0x00000000, 0x405c4000} }, /* 113 */
/**/ {{0x00000000, 0x405d4000} }, /* 117 */
};
static const number
twom[8] = { /* 2**m */
/**/ {{0x00000000, 0x3ff00000} }, /* 1.0 */
/**/ {{0x00000000, 0x40000000} }, /* 2.0 */
/**/ {{0x00000000, 0x40100000} }, /* 4.0 */
/**/ {{0x00000000, 0x40200000} }, /* 8.0 */
/**/ {{0x00000000, 0x40300000} }, /* 16.0 */
/**/ {{0x00000000, 0x40400000} }, /* 32.0 */
/**/ {{0x00000000, 0x40500000} }, /* 64.0 */
/**/ {{0x00000000, 0x40600000} }, /* 128.0 */
};
static const number
/**/ one = {{0x00000000, 0x3ff00000} }, /* 1 */
/**/ two = {{0x00000000, 0x40000000} }; /* 2 */
#endif
#endif
#define ONE one.d
#define TWO two.d
static const int
np[33] = { 0, 0, 0, 0, 6, 8,10,11,13,15,17,19,21,23,25,27,28,
30,32,34,36,38,40,42,43,45,47,49,51,53,55,57,59};
#endif
libgcc-math/dbl-64/mpatan2.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* MODULE_NAME: mpatan2.c */
/* */
/* FUNCTIONS:mpatan2 */
/* */
/* FILES NEEDED: mpa.h */
/* mpa.c mpatan.c mpsqrt.c */
/* */
/* Multi-Precision Atan2(y,x) function subroutine, */
/* for precision p >= 4. */
/* y=0 is not permitted if x<=0. No error messages are given. */
/* The relative error of the result is bounded by 44.84*r**(1-p) */
/* if x <= 0, y != 0 and by 37.33*r**(1-p) if x>0. here r=2**24. */
/* */
/******************************************************************/
#include "mpa.h"
void __mpsqrt(mp_no *, mp_no *, int);
void __mpatan(mp_no *, mp_no *, int);
/* Multi-Precision Atan2(y,x) function subroutine, for p >= 4. */
/* y=0 is not permitted if x<=0. No error messages are given. */
void __mpatan2(mp_no *y, mp_no *x, mp_no *z, int p) {
static const double Zero = 0.0, One = 1.0;
mp_no mpone = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mpt1,mpt2,mpt3;
if (X[0] <= Zero) {
mpone.e = 1; mpone.d[0] = mpone.d[1] = One;
__dvd(x,y,&mpt1,p); __mul(&mpt1,&mpt1,&mpt2,p);
if (mpt1.d[0] != Zero) mpt1.d[0] = One;
__add(&mpt2,&mpone,&mpt3,p); __mpsqrt(&mpt3,&mpt2,p);
__add(&mpt1,&mpt2,&mpt3,p); mpt3.d[0]=Y[0];
__mpatan(&mpt3,&mpt1,p); __add(&mpt1,&mpt1,z,p);
}
else
{ __dvd(y,x,&mpt1,p);
__mpatan(&mpt1,z,p);
}
return;
}
libgcc-math/dbl-64/mpexp.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/*************************************************************************/
/* MODULE_NAME:mpexp.c */
/* */
/* FUNCTIONS: mpexp */
/* */
/* FILES NEEDED: mpa.h endian.h mpexp.h */
/* mpa.c */
/* */
/* Multi-Precision exponential function subroutine */
/* ( for p >= 4, 2**(-55) <= abs(x) <= 1024 ). */
/*************************************************************************/
#include "endian.h"
#include "mpa.h"
#include "mpa2.h"
#include "mpexp.h"
/* Multi-Precision exponential function subroutine (for p >= 4, */
/* 2**(-55) <= abs(x) <= 1024). */
void __mpexp(mp_no *x, mp_no *y, int p) {
int i,j,k,m,m1,m2,n;
double a,b;
static const int np[33] = {0,0,0,0,3,3,4,4,5,4,4,5,5,5,6,6,6,6,6,6,
6,6,6,6,7,7,7,7,8,8,8,8,8};
static const int m1p[33]= {0,0,0,0,17,23,23,28,27,38,42,39,43,47,43,47,50,54,
57,60,64,67,71,74,68,71,74,77,70,73,76,78,81};
static const int m1np[7][18] = {
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0,36,48,60,72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0,24,32,40,48,56,64,72, 0, 0, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0,17,23,29,35,41,47,53,59,65, 0, 0, 0, 0, 0},
{ 0, 0, 0, 0, 0, 0,23,28,33,38,42,47,52,57,62,66, 0, 0},
{ 0, 0, 0, 0, 0, 0, 0, 0,27, 0, 0,39,43,47,51,55,59,63},
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,43,47,50,54}};
mp_no mpone = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mpk = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mps,mpak,mpt1,mpt2;
/* Choose m,n and compute a=2**(-m) */
n = np[p]; m1 = m1p[p]; a = twomm1[p].d;
for (i=0; i<EX; i++) a *= RADIXI;
for ( ; i>EX; i--) a *= RADIX;
b = X[1]*RADIXI; m2 = 24*EX;
for (; b<HALF; m2--) { a *= TWO; b *= TWO; }
if (b == HALF) {
for (i=2; i<=p; i++) { if (X[i]!=ZERO) break; }
if (i==p+1) { m2--; a *= TWO; }
}
if ((m=m1+m2) <= 0) {
m=0; a=ONE;
for (i=n-1; i>0; i--,n--) { if (m1np[i][p]+m2>0) break; }
}
/* Compute s=x*2**(-m). Put result in mps */
__dbl_mp(a,&mpt1,p);
__mul(x,&mpt1,&mps,p);
/* Evaluate the polynomial. Put result in mpt2 */
mpone.e=1; mpone.d[0]=ONE; mpone.d[1]=ONE;
mpk.e = 1; mpk.d[0] = ONE; mpk.d[1]=nn[n].d;
__dvd(&mps,&mpk,&mpt1,p);
__add(&mpone,&mpt1,&mpak,p);
for (k=n-1; k>1; k--) {
__mul(&mps,&mpak,&mpt1,p);
mpk.d[1]=nn[k].d;
__dvd(&mpt1,&mpk,&mpt2,p);
__add(&mpone,&mpt2,&mpak,p);
}
__mul(&mps,&mpak,&mpt1,p);
__add(&mpone,&mpt1,&mpt2,p);
/* Raise polynomial value to the power of 2**m. Put result in y */
for (k=0,j=0; k<m; ) {
__mul(&mpt2,&mpt2,&mpt1,p); k++;
if (k==m) { j=1; break; }
__mul(&mpt1,&mpt1,&mpt2,p); k++;
}
if (j) __cpy(&mpt1,y,p);
else __cpy(&mpt2,y,p);
return;
}
libgcc-math/dbl-64/mpexp.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:mpexp.h */
/* */
/* common data and variables prototype and definition */
/******************************************************************/
#ifndef MPEXP_H
#define MPEXP_H
#ifdef BIG_ENDI
static const number
twomm1[33] = { /* 2**-m1 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x3ee00000, 0x00000000} }, /* 2**-17 */
/**/ {{0x3e800000, 0x00000000} }, /* 2**-23 */
/**/ {{0x3e800000, 0x00000000} }, /* 2**-23 */
/**/ {{0x3e300000, 0x00000000} }, /* 2**-28 */
/**/ {{0x3e400000, 0x00000000} }, /* 2**-27 */
/**/ {{0x3d900000, 0x00000000} }, /* 2**-38 */
/**/ {{0x3d500000, 0x00000000} }, /* 2**-42 */
/**/ {{0x3d800000, 0x00000000} }, /* 2**-39 */
/**/ {{0x3d400000, 0x00000000} }, /* 2**-43 */
/**/ {{0x3d000000, 0x00000000} }, /* 2**-47 */
/**/ {{0x3d400000, 0x00000000} }, /* 2**-43 */
/**/ {{0x3d000000, 0x00000000} }, /* 2**-47 */
/**/ {{0x3cd00000, 0x00000000} }, /* 2**-50 */
/**/ {{0x3c900000, 0x00000000} }, /* 2**-54 */
/**/ {{0x3c600000, 0x00000000} }, /* 2**-57 */
/**/ {{0x3c300000, 0x00000000} }, /* 2**-60 */
/**/ {{0x3bf00000, 0x00000000} }, /* 2**-64 */
/**/ {{0x3bc00000, 0x00000000} }, /* 2**-67 */
/**/ {{0x3b800000, 0x00000000} }, /* 2**-71 */
/**/ {{0x3b500000, 0x00000000} }, /* 2**-74 */
/**/ {{0x3bb00000, 0x00000000} }, /* 2**-68 */
/**/ {{0x3b800000, 0x00000000} }, /* 2**-71 */
/**/ {{0x3b500000, 0x00000000} }, /* 2**-74 */
/**/ {{0x3b200000, 0x00000000} }, /* 2**-77 */
/**/ {{0x3b900000, 0x00000000} }, /* 2**-70 */
/**/ {{0x3b600000, 0x00000000} }, /* 2**-73 */
/**/ {{0x3b300000, 0x00000000} }, /* 2**-76 */
/**/ {{0x3b100000, 0x00000000} }, /* 2**-78 */
/**/ {{0x3ae00000, 0x00000000} }, /* 2**-81 */
};
static const number
nn[9]={ /* n */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x3ff00000, 0x00000000} }, /* 1 */
/**/ {{0x40000000, 0x00000000} }, /* 2 */
/**/ {{0x40080000, 0x00000000} }, /* 3 */
/**/ {{0x40100000, 0x00000000} }, /* 4 */
/**/ {{0x40140000, 0x00000000} }, /* 5 */
/**/ {{0x40180000, 0x00000000} }, /* 6 */
/**/ {{0x401c0000, 0x00000000} }, /* 7 */
/**/ {{0x40200000, 0x00000000} }, /* 8 */
};
#else
#ifdef LITTLE_ENDI
static const number
twomm1[33] = { /* 2**-m1 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x3ee00000} }, /* 2**-17 */
/**/ {{0x00000000, 0x3e800000} }, /* 2**-23 */
/**/ {{0x00000000, 0x3e800000} }, /* 2**-23 */
/**/ {{0x00000000, 0x3e300000} }, /* 2**-28 */
/**/ {{0x00000000, 0x3e400000} }, /* 2**-27 */
/**/ {{0x00000000, 0x3d900000} }, /* 2**-38 */
/**/ {{0x00000000, 0x3d500000} }, /* 2**-42 */
/**/ {{0x00000000, 0x3d800000} }, /* 2**-39 */
/**/ {{0x00000000, 0x3d400000} }, /* 2**-43 */
/**/ {{0x00000000, 0x3d000000} }, /* 2**-47 */
/**/ {{0x00000000, 0x3d400000} }, /* 2**-43 */
/**/ {{0x00000000, 0x3d000000} }, /* 2**-47 */
/**/ {{0x00000000, 0x3cd00000} }, /* 2**-50 */
/**/ {{0x00000000, 0x3c900000} }, /* 2**-54 */
/**/ {{0x00000000, 0x3c600000} }, /* 2**-57 */
/**/ {{0x00000000, 0x3c300000} }, /* 2**-60 */
/**/ {{0x00000000, 0x3bf00000} }, /* 2**-64 */
/**/ {{0x00000000, 0x3bc00000} }, /* 2**-67 */
/**/ {{0x00000000, 0x3b800000} }, /* 2**-71 */
/**/ {{0x00000000, 0x3b500000} }, /* 2**-74 */
/**/ {{0x00000000, 0x3bb00000} }, /* 2**-68 */
/**/ {{0x00000000, 0x3b800000} }, /* 2**-71 */
/**/ {{0x00000000, 0x3b500000} }, /* 2**-74 */
/**/ {{0x00000000, 0x3b200000} }, /* 2**-77 */
/**/ {{0x00000000, 0x3b900000} }, /* 2**-70 */
/**/ {{0x00000000, 0x3b600000} }, /* 2**-73 */
/**/ {{0x00000000, 0x3b300000} }, /* 2**-76 */
/**/ {{0x00000000, 0x3b100000} }, /* 2**-78 */
/**/ {{0x00000000, 0x3ae00000} }, /* 2**-81 */
};
static const number
nn[9]={ /* n */
/**/ {{0x00000000, 0x00000000} }, /* 0 */
/**/ {{0x00000000, 0x3ff00000} }, /* 1 */
/**/ {{0x00000000, 0x40000000} }, /* 2 */
/**/ {{0x00000000, 0x40080000} }, /* 3 */
/**/ {{0x00000000, 0x40100000} }, /* 4 */
/**/ {{0x00000000, 0x40140000} }, /* 5 */
/**/ {{0x00000000, 0x40180000} }, /* 6 */
/**/ {{0x00000000, 0x401c0000} }, /* 7 */
/**/ {{0x00000000, 0x40200000} }, /* 8 */
};
#endif
#endif
#endif
libgcc-math/dbl-64/mplog.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/************************************************************************/
/* */
/* MODULE_NAME:mplog.c */
/* */
/* FUNCTIONS: mplog */
/* */
/* FILES NEEDED: endian.h mpa.h mplog.h */
/* mpexp.c */
/* */
/* Multi-Precision logarithm function subroutine (for precision p >= 4, */
/* 2**(-1024) < x < 2**1024) and x is outside of the interval */
/* [1-2**(-54),1+2**(-54)]. Upon entry, x should be set to the */
/* multi-precision value of the input and y should be set into a multi- */
/* precision value of an approximation of log(x) with relative error */
/* bound of at most 2**(-52). The routine improves the accuracy of y. */
/* */
/************************************************************************/
#include "endian.h"
#include "mpa.h"
void __mpexp(mp_no *, mp_no *, int);
void __mplog(mp_no *x, mp_no *y, int p) {
#include "mplog.h"
int i,m;
#if 0
int j,k,m1,m2,n;
double a,b;
#endif
static const int mp[33] = {0,0,0,0,0,1,1,2,2,2,2,3,3,3,3,3,3,3,3,
4,4,4,4,4,4,4,4,4,4,4,4,4,4};
mp_no mpone = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mpt1,mpt2;
/* Choose m and initiate mpone */
m = mp[p]; mpone.e = 1; mpone.d[0]=mpone.d[1]=ONE;
/* Perform m newton iterations to solve for y: exp(y)-x=0. */
/* The iterations formula is: y(n+1)=y(n)+(x*exp(-y(n))-1). */
__cpy(y,&mpt1,p);
for (i=0; i<m; i++) {
mpt1.d[0]=-mpt1.d[0];
__mpexp(&mpt1,&mpt2,p);
__mul(x,&mpt2,&mpt1,p);
__sub(&mpt1,&mpone,&mpt2,p);
__add(y,&mpt2,&mpt1,p);
__cpy(&mpt1,y,p);
}
return;
}
libgcc-math/dbl-64/mplog.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:mplog.h */
/* */
/* common data and variables prototype and definition */
/******************************************************************/
#ifndef MPLOG_H
#define MPLOG_H
#ifdef BIG_ENDI
static const number
/**/ one = {{0x3ff00000, 0x00000000} }; /* 1 */
#else
#ifdef LITTLE_ENDI
static const number
/**/ one = {{0x00000000, 0x3ff00000} }; /* 1 */
#endif
#endif
#define ONE one.d
#endif
libgcc-math/dbl-64/mpsqrt.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/****************************************************************************/
/* MODULE_NAME:mpsqrt.c */
/* */
/* FUNCTION:mpsqrt */
/* fastiroot */
/* */
/* FILES NEEDED:endian.h mpa.h mpsqrt.h */
/* mpa.c */
/* Multi-Precision square root function subroutine for precision p >= 4. */
/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */
/* */
/****************************************************************************/
#include "endian.h"
#include "mpa.h"
/****************************************************************************/
/* Multi-Precision square root function subroutine for precision p >= 4. */
/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */
/* Routine receives two pointers to Multi Precision numbers: */
/* x (left argument) and y (next argument). Routine also receives precision */
/* p as integer. Routine computes sqrt(*x) and stores result in *y */
/****************************************************************************/
double fastiroot(double);
void __mpsqrt(mp_no *x, mp_no *y, int p) {
#include "mpsqrt.h"
int i,m,ex,ey;
double dx,dy;
mp_no
mphalf = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
mp3halfs = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
mp_no mpxn,mpz,mpu,mpt1,mpt2;
/* Prepare multi-precision 1/2 and 3/2 */
mphalf.e =0; mphalf.d[0] =ONE; mphalf.d[1] =HALFRAD;
mp3halfs.e=1; mp3halfs.d[0]=ONE; mp3halfs.d[1]=ONE; mp3halfs.d[2]=HALFRAD;
ex=EX; ey=EX/2; __cpy(x,&mpxn,p); mpxn.e -= (ey+ey);
__mp_dbl(&mpxn,&dx,p); dy=fastiroot(dx); __dbl_mp(dy,&mpu,p);
__mul(&mpxn,&mphalf,&mpz,p);
m=mp[p];
for (i=0; i<m; i++) {
__mul(&mpu,&mpu,&mpt1,p);
__mul(&mpt1,&mpz,&mpt2,p);
__sub(&mp3halfs,&mpt2,&mpt1,p);
__mul(&mpu,&mpt1,&mpt2,p);
__cpy(&mpt2,&mpu,p);
}
__mul(&mpxn,&mpu,y,p); EY += ey;
return;
}
/***********************************************************/
/* Compute a double precision approximation for 1/sqrt(x) */
/* with the relative error bounded by 2**-51. */
/***********************************************************/
double fastiroot(double x) {
union {int i[2]; double d;} p,q;
double y,z, t;
int n;
static const double c0 = 0.99674, c1 = -0.53380, c2 = 0.45472, c3 = -0.21553;
p.d = x;
p.i[HIGH_HALF] = (p.i[HIGH_HALF] & 0x3FFFFFFF ) | 0x3FE00000 ;
q.d = x;
y = p.d;
z = y -1.0;
n = (q.i[HIGH_HALF] - p.i[HIGH_HALF])>>1;
z = ((c3*z + c2)*z + c1)*z + c0; /* 2**-7 */
z = z*(1.5 - 0.5*y*z*z); /* 2**-14 */
p.d = z*(1.5 - 0.5*y*z*z); /* 2**-28 */
p.i[HIGH_HALF] -= n;
t = x*p.d;
return p.d*(1.5 - 0.5*p.d*t);
}
libgcc-math/dbl-64/mpsqrt.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:mpatan.h */
/* */
/* common data and variables prototype and definition */
/******************************************************************/
#ifndef MPSQRT_H
#define MPSQRT_H
#ifdef BIG_ENDI
static const number
/**/ one = {{0x3ff00000, 0x00000000} }, /* 1 */
/**/ halfrad = {{0x41600000, 0x00000000} }; /* 2**23 */
#else
#ifdef LITTLE_ENDI
static const number
/**/ one = {{0x00000000, 0x3ff00000} }, /* 1 */
/**/ halfrad = {{0x00000000, 0x41600000} }; /* 2**23 */
#endif
#endif
#define ONE one.d
#define HALFRAD halfrad.d
static const int mp[33] = {0,0,0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,
4,4,4,4,4,4,4,4,4};
#endif
libgcc-math/dbl-64/mptan.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/**********************************************************************/
/* MODULE_NAME:mptan.c */
/* */
/* FUNCTION: mptan */
/* */
/* FILES NEEDED: endian.h mpa.h */
/* mpa.c sincos32.c branred.c */
/* */
/* Multi-Precision tan() function subroutine, for p=32. It is based */
/* on the routines mpranred() and c32(). mpranred() performs range */
/* reduction of a double number x into a multiple precision number */
/* y, such that y=x-n*pi/2, abs(y)<pi/4, n=0,+-1,+-2,.... c32() */
/* computes both sin(y), cos(y). tan(x) is either sin(y)/cos(y) */
/* or -cos(y)/sin(y). The precision of the result is of about 559 */
/* significant bits. */
/* */
/**********************************************************************/
#include "endian.h"
#include "mpa.h"
int __mpranred(double, mp_no *, int);
void __c32(mp_no *, mp_no *, mp_no *, int);
void __mptan(double x, mp_no *mpy, int p) {
static const double Mone = -1.0;
int n;
mp_no mpw, mpc, mps;
n = __mpranred(x, &mpw, p) & 0x00000001; /* negative or positive result */
__c32(&mpw, &mpc, &mps, p); /* computing sin(x) and cos(x) */
if (n) /* second or fourth quarter of unit circle */
{ __dvd(&mpc,&mps,mpy,p);
mpy->d[0] *= Mone;
} /* tan is negative in this area */
else __dvd(&mps,&mpc,mpy,p);
return;
}
libgcc-math/dbl-64/mydefs.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:mydefs.h */
/* */
/* common data and definition */
/******************************************************************/
#ifndef MY_H
#define MY_H
typedef int int4;
typedef union {int4 i[2]; double x;} mynumber;
#define ABS(x) (((x)>0)?(x):-(x))
#define max(x,y) (((y)>(x))?(y):(x))
#define min(x,y) (((y)<(x))?(y):(x))
#endif
libgcc-math/dbl-64/powtwo.tbl 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/****************************************************************/
/* TABLES FOR THE upow() FUNCTION */
/****************************************************************/
static const double powtwo[] = { 1.0, 2.0, 4.0,
8.0, 16.0, 32.0, 64.0, 128.0,
256.0, 512.0, 1024.0, 2048.0, 4096.0,
8192.0, 16384.0, 32768.0, 65536.0, 131072.0,
262144.0, 524288.0, 1048576.0, 2097152.0, 4194304.0,
8388608.0, 16777216.0, 33554432.0, 67108864.0, 134217728.0 };
libgcc-math/dbl-64/root.tbl 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/****************************************************************/
/* TABLES FOR THE usqrt() FUNCTION */
/****************************************************************/
static const double inroot[128] = {
1.40872145012100, 1.39792649065766, 1.38737595123859, 1.37706074531819,
1.36697225234682, 1.35710228748795, 1.34744307370643, 1.33798721601135,
1.32872767765984, 1.31965775814772, 1.31077107283046, 1.30206153403386,
1.29352333352711, 1.28515092624400, 1.27693901514820, 1.26888253714903,
1.26097664998256, 1.25321671998073, 1.24559831065844, 1.23811717205462,
1.23076923076923, 1.22355058064300, 1.21645747403153, 1.20948631362953,
1.20263364480453, 1.19589614840310, 1.18927063399547, 1.18275403352732,
1.17634339535009, 1.17003587860341, 1.16382874792529, 1.15771936846787,
1.15170520119791, 1.14578379846309, 1.13995279980655, 1.13420992801334,
1.12855298537376, 1.12297985014975, 1.11748847323133, 1.11207687497107,
1.10674314218572, 1.10148542531442, 1.09630193572405, 1.09119094315276,
1.08615077328341, 1.08117980543918, 1.07627647039410, 1.07143924829188,
1.06666666666667, 1.06195729855996, 1.05730976072814, 1.05272271193563,
1.04819485132867, 1.04372491688551, 1.03931168393861, 1.03495396376504,
1.03065060224133, 1.02640047855933, 1.02220250399990, 1.01805562076124,
1.01395880083916, 1.00991104495649, 1.00591138153909, 1.00195886573624,
0.99611649018350, 0.98848330114434, 0.98102294317595, 0.97372899112030,
0.96659534932828, 0.95961623024651, 0.95278613468066, 0.94609983358253,
0.93955235122353, 0.93313894963169, 0.92685511418159, 0.92069654023750,
0.91465912076005, 0.90873893479530, 0.90293223677296, 0.89723544654727,
0.89164514012056, 0.88615804099474, 0.88077101210109, 0.87548104826333,
0.87028526915267, 0.86518091269740, 0.86016532891275, 0.85523597411976,
0.85039040552437, 0.84562627613070, 0.84094132996422, 0.83633339758291,
0.83180039185606, 0.82734030399203, 0.82295119979782, 0.81863121615464,
0.81437855769486, 0.81019149366693, 0.80606835497581, 0.80200753138734,
0.79800746888611, 0.79406666717674, 0.79018367731967, 0.78635709949278,
0.78258558087123, 0.77886781361798, 0.77520253297841, 0.77158851547266,
0.76802457717971, 0.76450957210799, 0.76104239064719, 0.75762195809661,
0.75424723326565, 0.75091720714229, 0.74763090162560, 0.74438736831878,
0.74118568737933, 0.73802496642311, 0.73490433947940, 0.73182296599416,
0.72878002987884, 0.72577473860242, 0.72280632232420, 0.71987403306536,
0.71697714391715, 0.71411494828392, 0.71128675915902, 0.70849190843208 };
libgcc-math/dbl-64/s_atan.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/************************************************************************/
/* MODULE_NAME: atnat.c */
/* */
/* FUNCTIONS: uatan */
/* atanMp */
/* signArctan */
/* */
/* */
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */
/* mpatan.c mpatan2.c mpsqrt.c */
/* uatan.tbl */
/* */
/* An ultimate atan() routine. Given an IEEE double machine number x */
/* it computes the correctly rounded (to nearest) value of atan(x). */
/* */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/************************************************************************/
#include "dla.h"
#include "mpa.h"
#include "MathLib.h"
#include "uatan.tbl"
#include "atnat.h"
#include "math.h"
void __mpatan(mp_no *,mp_no *,int); /* see definition in mpatan.c */
static double atanMp(double,const int[]);
double __signArctan(double,double);
/* An ultimate atan() routine. Given an IEEE double machine number x, */
/* routine computes the correctly rounded (to nearest) value of atan(x). */
double atan(double x) {
double cor,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,u,u2,u3,
v,vv,w,ww,y,yy,z,zz;
#if 0
double y1,y2;
#endif
int i,ux,dx;
#if 0
int p;
#endif
static const int pr[M]={6,8,10,32};
number num;
#if 0
mp_no mpt1,mpx,mpy,mpy1,mpy2,mperr;
#endif
num.d = x; ux = num.i[HIGH_HALF]; dx = num.i[LOW_HALF];
/* x=NaN */
if (((ux&0x7ff00000)==0x7ff00000) && (((ux&0x000fffff)|dx)!=0x00000000))
return x+x;
/* Regular values of x, including denormals +-0 and +-INF */
u = (x<ZERO) ? -x : x;
if (u<C) {
if (u<B) {
if (u<A) { /* u < A */
return x; }
else { /* A <= u < B */
v=x*x; yy=x*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
if ((y=x+(yy-U1*x)) == x+(yy+U1*x)) return y;
EMULV(x,x,v,vv,t1,t2,t3,t4,t5) /* v+vv=x^2 */
s1=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d))));
ADD2(f9.d,ff9.d,s1,ZERO,s2,ss2,t1,t2)
MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(f7.d,ff7.d,s1,ss1,s2,ss2,t1,t2)
MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(f5.d,ff5.d,s1,ss1,s2,ss2,t1,t2)
MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(f3.d,ff3.d,s1,ss1,s2,ss2,t1,t2)
MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(x,ZERO,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(x,ZERO,s2,ss2,s1,ss1,t1,t2)
if ((y=s1+(ss1-U5*s1)) == s1+(ss1+U5*s1)) return y;
return atanMp(x,pr);
} }
else { /* B <= u < C */
i=(TWO52+TWO8*u)-TWO52; i-=16;
z=u-cij[i][0].d;
yy=z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+
z*(cij[i][5].d+z* cij[i][6].d))));
t1=cij[i][1].d;
if (i<112) {
if (i<48) u2=U21; /* u < 1/4 */
else u2=U22; } /* 1/4 <= u < 1/2 */
else {
if (i<176) u2=U23; /* 1/2 <= u < 3/4 */
else u2=U24; } /* 3/4 <= u <= 1 */
if ((y=t1+(yy-u2*t1)) == t1+(yy+u2*t1)) return __signArctan(x,y);
z=u-hij[i][0].d;
s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+
z*(hij[i][14].d+z* hij[i][15].d))));
ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(hij[i][7].d,hij[i][8].d,s1,ss1,s2,ss2,t1,t2)
MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(hij[i][5].d,hij[i][6].d,s1,ss1,s2,ss2,t1,t2)
MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(hij[i][3].d,hij[i][4].d,s1,ss1,s2,ss2,t1,t2)
MUL2(z,ZERO,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(hij[i][1].d,hij[i][2].d,s1,ss1,s2,ss2,t1,t2)
if ((y=s2+(ss2-U6*s2)) == s2+(ss2+U6*s2)) return __signArctan(x,y);
return atanMp(x,pr);
}
}
else {
if (u<D) { /* C <= u < D */
w=ONE/u;
EMULV(w,u,t1,t2,t3,t4,t5,t6,t7)
ww=w*((ONE-t1)-t2);
i=(TWO52+TWO8*w)-TWO52; i-=16;
z=(w-cij[i][0].d)+ww;
yy=HPI1-z*(cij[i][2].d+z*(cij[i][3].d+z*(cij[i][4].d+
z*(cij[i][5].d+z* cij[i][6].d))));
t1=HPI-cij[i][1].d;
if (i<112) u3=U31; /* w < 1/2 */
else u3=U32; /* w >= 1/2 */
if ((y=t1+(yy-u3)) == t1+(yy+u3)) return __signArctan(x,y);
DIV2(ONE,ZERO,u,ZERO,w,ww,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
t1=w-hij[i][0].d;
EADD(t1,ww,z,zz)
s1=z*(hij[i][11].d+z*(hij[i][12].d+z*(hij[i][13].d+
z*(hij[i][14].d+z* hij[i][15].d))));
ADD2(hij[i][9].d,hij[i][10].d,s1,ZERO,s2,ss2,t1,t2)
MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(hij[i][7].d,hij[i][8].d,s1,ss1,s2,ss2,t1,t2)
MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(hij[i][5].d,hij[i][6].d,s1,ss1,s2,ss2,t1,t2)
MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(hij[i][3].d,hij[i][4].d,s1,ss1,s2,ss2,t1,t2)
MUL2(z,zz,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(hij[i][1].d,hij[i][2].d,s1,ss1,s2,ss2,t1,t2)
SUB2(HPI,HPI1,s2,ss2,s1,ss1,t1,t2)
if ((y=s1+(ss1-U7)) == s1+(ss1+U7)) return __signArctan(x,y);
return atanMp(x,pr);
}
else {
if (u<E) { /* D <= u < E */
w=ONE/u; v=w*w;
EMULV(w,u,t1,t2,t3,t4,t5,t6,t7)
yy=w*v*(d3.d+v*(d5.d+v*(d7.d+v*(d9.d+v*(d11.d+v*d13.d)))));
ww=w*((ONE-t1)-t2);
ESUB(HPI,w,t3,cor)
yy=((HPI1+cor)-ww)-yy;
if ((y=t3+(yy-U4)) == t3+(yy+U4)) return __signArctan(x,y);
DIV2(ONE,ZERO,u,ZERO,w,ww,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
MUL2(w,ww,w,ww,v,vv,t1,t2,t3,t4,t5,t6,t7,t8)
s1=v*(f11.d+v*(f13.d+v*(f15.d+v*(f17.d+v*f19.d))));
ADD2(f9.d,ff9.d,s1,ZERO,s2,ss2,t1,t2)
MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(f7.d,ff7.d,s1,ss1,s2,ss2,t1,t2)
MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(f5.d,ff5.d,s1,ss1,s2,ss2,t1,t2)
MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(f3.d,ff3.d,s1,ss1,s2,ss2,t1,t2)
MUL2(v,vv,s2,ss2,s1,ss1,t1,t2,t3,t4,t5,t6,t7,t8)
MUL2(w,ww,s1,ss1,s2,ss2,t1,t2,t3,t4,t5,t6,t7,t8)
ADD2(w,ww,s2,ss2,s1,ss1,t1,t2)
SUB2(HPI,HPI1,s1,ss1,s2,ss2,t1,t2)
if ((y=s2+(ss2-U8)) == s2+(ss2+U8)) return __signArctan(x,y);
return atanMp(x,pr);
}
else {
/* u >= E */
if (x>0) return HPI;
else return MHPI; }
}
}
}
/* Fix the sign of y and return */
double __signArctan(double x,double y){
if (x<ZERO) return -y;
else return y;
}
/* Final stages. Compute atan(x) by multiple precision arithmetic */
static double atanMp(double x,const int pr[]){
mp_no mpx,mpy,mpy2,mperr,mpt1,mpy1;
double y1,y2;
int i,p;
for (i=0; i<M; i++) {
p = pr[i];
__dbl_mp(x,&mpx,p); __mpatan(&mpx,&mpy,p);
__dbl_mp(u9[i].d,&mpt1,p); __mul(&mpy,&mpt1,&mperr,p);
__add(&mpy,&mperr,&mpy1,p); __sub(&mpy,&mperr,&mpy2,p);
__mp_dbl(&mpy1,&y1,p); __mp_dbl(&mpy2,&y2,p);
if (y1==y2) return y1;
}
return y1; /*if unpossible to do exact computing */
}
#ifdef NO_LONG_DOUBLE
weak_alias (atan, atanl)
#endif
libgcc-math/dbl-64/s_floor.c 0 → 100644
/* @(#)s_floor.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_floor.c,v 1.8 1995/05/10 20:47:20 jtc Exp $";
#endif
/*
* floor(x)
* Return x rounded toward -inf to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to floor(x).
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif
#ifdef __STDC__
double __floor(double x)
#else
double __floor(x)
double x;
#endif
{
int32_t i0,i1,j0;
u_int32_t i,j;
EXTRACT_WORDS(i0,i1,x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
if(i0>=0) {i0=i1=0;}
else if(((i0&0x7fffffff)|i1)!=0)
{ i0=0xbff00000;i1=0;}
}
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) i0 += (0x00100000)>>j0;
i0 &= (~i); i1=0;
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((u_int32_t)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) {
if(j0==20) i0+=1;
else {
j = i1+(1<<(52-j0));
if(j<i1) i0 +=1 ; /* got a carry */
i1=j;
}
}
i1 &= (~i);
}
}
INSERT_WORDS(x,i0,i1);
return x;
}
weak_alias (__floor, floor)
#ifdef NO_LONG_DOUBLE
strong_alias (__floor, __floorl)
weak_alias (__floor, floorl)
#endif
libgcc-math/dbl-64/s_isinf.c 0 → 100644
/*
* Written by J.T. Conklin <jtc@netbsd.org>.
* Changed to return -1 for -Inf by Ulrich Drepper <drepper@cygnus.com>.
* Public domain.
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_isinf.c,v 1.3 1995/05/11 23:20:14 jtc Exp $";
#endif
/*
* isinf(x) returns 1 is x is inf, -1 if x is -inf, else 0;
* no branching!
*/
#include "math.h"
#include "math_private.h"
int
__isinf (double x)
{
int32_t hx,lx;
EXTRACT_WORDS(hx,lx,x);
lx |= (hx & 0x7fffffff) ^ 0x7ff00000;
lx |= -lx;
return ~(lx >> 31) & (hx >> 30);
}
hidden_def (__isinf)
weak_alias (__isinf, isinf)
#ifdef NO_LONG_DOUBLE
strong_alias (__isinf, __isinfl)
weak_alias (__isinf, isinfl)
#endif
libgcc-math/dbl-64/s_scalbn.c 0 → 100644
/* @(#)s_scalbn.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_scalbn.c,v 1.8 1995/05/10 20:48:08 jtc Exp $";
#endif
/*
* scalbn (double x, int n)
* scalbn(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* exponentiation or a multiplication.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
huge = 1.0e+300,
tiny = 1.0e-300;
#ifdef __STDC__
double __scalbn (double x, int n)
#else
double __scalbn (x,n)
double x; int n;
#endif
{
int32_t k,hx,lx;
EXTRACT_WORDS(hx,lx,x);
k = (hx&0x7ff00000)>>20; /* extract exponent */
if (k==0) { /* 0 or subnormal x */
if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
x *= two54;
GET_HIGH_WORD(hx,x);
k = ((hx&0x7ff00000)>>20) - 54;
}
if (k==0x7ff) return x+x; /* NaN or Inf */
k = k+n;
if (n> 50000 || k > 0x7fe)
return huge*__builtin_copysign(huge,x); /* overflow */
if (n< -50000) return tiny*__builtin_copysign(tiny,x); /*underflow*/
if (k > 0) /* normal result */
{SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;}
if (k <= -54)
return tiny*__builtin_copysign(tiny,x); /*underflow*/
k += 54; /* subnormal result */
SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20));
return x*twom54;
}
weak_alias (__scalbn, scalbn)
#ifdef NO_LONG_DOUBLE
strong_alias (__scalbn, __scalbnl)
weak_alias (__scalbn, scalbnl)
#endif
libgcc-math/dbl-64/sincos32.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:sincos32.h */
/* */
/* common data and variables prototype and definition */
/******************************************************************/
#ifndef SINCOS32_H
#define SINCCOS32_H
#ifdef BIG_ENDI
static const number
/**/ hpinv = {{0x3FE45F30, 0x6DC9C883}}, /* 0.63661977236758138 */
/**/ toint = {{0x43380000, 0x00000000}}; /* 6755399441055744 */
#else
#ifdef LITTLE_ENDI
static const number
/**/ hpinv = {{0x6DC9C883, 0x3FE45F30}}, /* 0.63661977236758138 */
/**/ toint = {{0x00000000, 0x43380000}}; /* 6755399441055744 */
#endif
#endif
static const mp_no
oofac27 = {-3,{1.0,7.0,4631664.0,12006312.0,13118056.0,6538613.0,646354.0,
8508025.0,9131256.0,7548776.0,2529842.0,8864927.0,660489.0,15595125.0,12777885.0,
11618489.0,13348664.0,5486686.0,514518.0,11275535.0,4727621.0,3575562.0,
13579710.0,5829745.0,7531862.0,9507898.0,6915060.0,4079264.0,1907586.0,
6078398.0,13789314.0,5504104.0,14136.0}},
pi = {1,{1.0,3.0,
2375530.0,8947107.0,578323.0,1673774.0,225395.0,4498441.0,3678761.0,
10432976.0,536314.0,10021966.0,7113029.0,2630118.0,3723283.0,7847508.0,
6737716.0,15273068.0,12626985.0,12044668.0,5299519.0,8705461.0,11880201.0,
1544726.0,14014857.0,7994139.0,13709579.0,10918111.0,11906095.0,16610011.0,
13638367.0,12040417.0,11529578.0,2522774.0}},
hp = {1,{1.0, 1.0,
9576373.0,4473553.0,8677769.0,9225495.0,112697.0,10637828.0,
10227988.0,13605096.0,268157.0,5010983.0,3556514.0,9703667.0,
1861641.0,12312362.0,3368858.0,7636534.0,6313492.0,14410942.0,
2649759.0,12741338.0,14328708.0,9160971.0,7007428.0,12385677.0,
15243397.0,13847663.0,14341655.0,16693613.0,15207791.0,14408816.0,
14153397.0,1261387.0,6110792.0,2291862.0,4181138.0,5295267.0}};
static const double toverp[75] = {
10680707.0, 7228996.0, 1387004.0, 2578385.0, 16069853.0,
12639074.0, 9804092.0, 4427841.0, 16666979.0, 11263675.0,
12935607.0, 2387514.0, 4345298.0, 14681673.0, 3074569.0,
13734428.0, 16653803.0, 1880361.0, 10960616.0, 8533493.0,
3062596.0, 8710556.0, 7349940.0, 6258241.0, 3772886.0,
3769171.0, 3798172.0, 8675211.0, 12450088.0, 3874808.0,
9961438.0, 366607.0, 15675153.0, 9132554.0, 7151469.0,
3571407.0, 2607881.0, 12013382.0, 4155038.0, 6285869.0,
7677882.0, 13102053.0, 15825725.0, 473591.0, 9065106.0,
15363067.0, 6271263.0, 9264392.0, 5636912.0, 4652155.0,
7056368.0, 13614112.0, 10155062.0, 1944035.0, 9527646.0,
15080200.0, 6658437.0, 6231200.0, 6832269.0, 16767104.0,
5075751.0, 3212806.0, 1398474.0, 7579849.0, 6349435.0,
12618859.0, 4703257.0, 12806093.0, 14477321.0, 2786137.0,
12875403.0, 9837734.0, 14528324.0, 13719321.0, 343717.0 };
#endif
libgcc-math/dbl-64/slowexp.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/**************************************************************************/
/* MODULE_NAME:slowexp.c */
/* */
/* FUNCTION:slowexp */
/* */
/* FILES NEEDED:mpa.h */
/* mpa.c mpexp.c */
/* */
/*Converting from double precision to Multi-precision and calculating */
/* e^x */
/**************************************************************************/
#include "mpa.h"
#include "math_private.h"
void __mpexp(mp_no *x, mp_no *y, int p);
/*Converting from double precision to Multi-precision and calculating e^x */
double __slowexp(double x) {
double w,z,res,eps=3.0e-26;
#if 0
double y;
#endif
int p;
#if 0
int orig,i;
#endif
mp_no mpx, mpy, mpz,mpw,mpeps,mpcor;
p=6;
__dbl_mp(x,&mpx,p); /* Convert a double precision number x */
/* into a multiple precision number mpx with prec. p. */
__mpexp(&mpx, &mpy, p); /* Multi-Precision exponential function */
__dbl_mp(eps,&mpeps,p);
__mul(&mpeps,&mpy,&mpcor,p);
__add(&mpy,&mpcor,&mpw,p);
__sub(&mpy,&mpcor,&mpz,p);
__mp_dbl(&mpw, &w, p);
__mp_dbl(&mpz, &z, p);
if (w == z) return w;
else { /* if calculating is not exactly */
p = 32;
__dbl_mp(x,&mpx,p);
__mpexp(&mpx, &mpy, p);
__mp_dbl(&mpy, &res, p);
return res;
}
}
libgcc-math/dbl-64/slowpow.c 0 → 100644
/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/*************************************************************************/
/* MODULE_NAME:slowpow.c */
/* */
/* FUNCTION:slowpow */
/* */
/*FILES NEEDED:mpa.h */
/* mpa.c mpexp.c mplog.c halfulp.c */
/* */
/* Given two IEEE double machine numbers y,x , routine computes the */
/* correctly rounded (to nearest) value of x^y. Result calculated by */
/* multiplication (in halfulp.c) or if result isn't accurate enough */
/* then routine converts x and y into multi-precision doubles and */
/* calls to mpexp routine */
/*************************************************************************/
#include "mpa.h"
#include "math_private.h"
void __mpexp(mp_no *x, mp_no *y, int p);
void __mplog(mp_no *x, mp_no *y, int p);
double ulog(double);
double __halfulp(double x,double y);
double __slowpow(double x, double y, double z) {
double res,res1;
mp_no mpx, mpy, mpz,mpw,mpp,mpr,mpr1;
static const mp_no eps = {-3,{1.0,4.0}};
int p;
res = __halfulp(x,y); /* halfulp() returns -10 or x^y */
if (res >= 0) return res; /* if result was really computed by halfulp */
/* else, if result was not really computed by halfulp */
p = 10; /* p=precision */
__dbl_mp(x,&mpx,p);
__dbl_mp(y,&mpy,p);
__dbl_mp(z,&mpz,p);
__mplog(&mpx, &mpz, p); /* log(x) = z */
__mul(&mpy,&mpz,&mpw,p); /* y * z =w */
__mpexp(&mpw, &mpp, p); /* e^w =pp */
__add(&mpp,&eps,&mpr,p); /* pp+eps =r */
__mp_dbl(&mpr, &res, p);
__sub(&mpp,&eps,&mpr1,p); /* pp -eps =r1 */
__mp_dbl(&mpr1, &res1, p); /* converting into double precision */
if (res == res1) return res;
p = 32; /* if we get here result wasn't calculated exactly, continue */
__dbl_mp(x,&mpx,p); /* for more exact calculation */
__dbl_mp(y,&mpy,p);
__dbl_mp(z,&mpz,p);
__mplog(&mpx, &mpz, p); /* log(c)=z */
__mul(&mpy,&mpz,&mpw,p); /* y*z =w */
__mpexp(&mpw, &mpp, p); /* e^w=pp */
__mp_dbl(&mpp, &res, p); /* converting into double precision */
return res;
}
libgcc-math/dbl-64/uasncs.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:uasncs.h */
/* */
/* common data and variables prototype and definition */
/******************************************************************/
#ifndef UANSNCS_H
#define UANSNCS_H
#ifdef BIG_ENDI
static const mynumber
/**/ a1 = {{0x3FC55580, 0x00000000 }}, /* 0.1666717529296875 */
/**/ a2 = {{0xBED55555, 0x55552330 }}, /* -5.0862630208224597e-06 */
/**/ hp0 = {{0x3FF921FB, 0x54442D18 }}, /* 1.5707963267948966 */
/**/ hp1 = {{0x3C91A626, 0x33145C07 }}; /* 6.123233995736766e-17 */
#else
#ifdef LITTLE_ENDI
static const mynumber
/**/ a1 = {{0x00000000, 0x3FC55580 }}, /* 0.1666717529296875 */
/**/ a2 = {{0x55552330, 0xBED55555 }}, /* -5.0862630208224597e-06 */
/**/ hp0 = {{0x54442D18, 0x3FF921FB }}, /* 1.5707963267948966 */
/**/ hp1 = {{0x33145C07, 0x3C91A626 }}; /* 6.123233995736766e-17 */
#endif
#endif
static const double
f1 = 1.66666666666664110590506577996662E-01,
f2 = 7.50000000026122686814431784722623E-02,
f3 = 4.46428561421059750978517350006940E-02,
f4 = 3.03821268582119319911193410625235E-02,
f5 = 2.23551211026525610742786300334557E-02,
f6 = 1.81382903404565056280372531963613E-02;
static const double
c2 = 0.74999999999985410757087492918602258E-01,
c3 = 0.44642857150311968932423372477866076E-01,
c4 = 0.30381942574778615766200591683810471E-01,
c5 = 0.22372413472984868331447708777000650E-01,
c6 = 0.17333630246451830686009693735025490E-01,
c7 = 0.14710362893628210269950864741085777E-01;
static const double big = 103079215104.0, t24 = 16777216.0, t27 = 134217728.0;
static const double
rt0 = 9.99999999859990725855365213134618E-01,
rt1 = 4.99999999495955425917856814202739E-01,
rt2 = 3.75017500867345182581453026130850E-01,
rt3 = 3.12523626554518656309172508769531E-01;
#endif
libgcc-math/dbl-64/uatan.tbl 0 → 100644
This source diff could not be displayed because it is too large. You can view the blob instead.
libgcc-math/dbl-64/uexp.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:uexp.h */
/* */
/* common data and variables prototype and definition */
/******************************************************************/
#ifndef UEXP_H
#define UEXP_H
#include "mydefs.h"
const static double one = 1.0, zero = 0.0, hhuge = 1.0e300, tiny = 1.0e-300,
err_0 = 1.000014, err_1 = 0.000016;
const static int4 bigint = 0x40862002,
badint = 0x40876000,smallint = 0x3C8fffff;
const static int4 hugeint = 0x7FFFFFFF, infint = 0x7ff00000;
#ifdef BIG_ENDI
const static mynumber inf = {{0x7FF00000, 0}}; /* inf */
const static mynumber t256 = {{0x4ff00000, 0}}; /* 2^256 */
const static mynumber ln_two1 = {{0x3FE62E42, 0xFEFA3800}};/*0.69314718055989033 */
const static mynumber ln_two2 = {{0x3D2EF357, 0x93C76730}};/*5.4979230187083712e-14*/
const static mynumber log2e = {{0x3FF71547, 0x652B82FE}};/* 1.4426950408889634 */
const static mynumber p2 = {{0x3FE00000, 0x000004DC}};/* 0.50000000000013811 */
const static mynumber p3 = {{0x3FC55555, 0x55555A0F}};/* 0.16666666666670024 */
const static mynumber three33 = {{0x42180000, 0}}; /* 25769803776 */
const static mynumber three51 = {{0x43380000, 0}}; /* 6755399441055744 */
#else
#ifdef LITTLE_ENDI
const static mynumber inf = {{0, 0x7FF00000}}; /* inf */
const static mynumber t256 = {{0, 0x4ff00000}}; /* 2^256 */
const static mynumber ln_two1 = {{0xFEFA3800, 0x3FE62E42}};/*0.69314718055989033 */
const static mynumber ln_two2 = {{0x93C76730, 0x3D2EF357}};/*5.4979230187083712e-14*/
const static mynumber log2e = {{0x652B82FE, 0x3FF71547}};/* 1.4426950408889634 */
const static mynumber p2 = {{0x000004DC, 0x3FE00000}};/* 0.50000000000013811 */
const static mynumber p3 = {{0x55555A0F, 0x3FC55555}};/* 0.16666666666670024 */
const static mynumber three33 = {{0, 0x42180000}}; /* 25769803776 */
const static mynumber three51 = {{0, 0x43380000}}; /* 6755399441055744 */
#endif
#endif
#endif
libgcc-math/dbl-64/ulog.tbl 0 → 100644
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libgcc-math/dbl-64/upow.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001, 2002 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:upow.h */
/* */
/* common data and variables prototype and definition */
/******************************************************************/
#ifndef UPOW_H
#define UPOW_H
#include "mydefs.h"
#ifdef BIG_ENDI
const static mynumber
/**/ nZERO = {{0x80000000, 0}}, /* -0.0 */
/**/ INF = {{0x7ff00000, 0x00000000}}, /* INF */
/**/ nINF = {{0xfff00000, 0x00000000}}, /* -INF */
/**/ NaNQ = {{0x7ff80000, 0x00000000}}, /* NaNQ */
/**/ sqrt_2 = {{0x3ff6a09e, 0x667f3bcc}}, /* sqrt(2) */
/**/ ln2a = {{0x3fe62e42, 0xfefa3800}}, /* ln(2) 43 bits */
/**/ ln2b = {{0x3d2ef357, 0x93c76730}}, /* ln(2)-ln2a */
/**/ bigu = {{0x4297ffff, 0xfffffd2c}}, /* 1.5*2**42 -724*2**-10 */
/**/ bigv = {{0x4207ffff, 0xfff8016a}}, /* 1.5*2**33-1+362*2**-19 */
/**/ t52 = {{0x43300000, 0x00000000}}, /* 2**52 */
/**/ two52e = {{0x43300000, 0x000003ff}}; /* 2**52' */
#else
#ifdef LITTLE_ENDI
const static mynumber
/**/ nZERO = {{0, 0x80000000}}, /* -0.0 */
/**/ INF = {{0x00000000, 0x7ff00000}}, /* INF */
/**/ nINF = {{0x00000000, 0xfff00000}}, /* -INF */
/**/ NaNQ = {{0x00000000, 0x7ff80000}}, /* NaNQ */
/**/ sqrt_2 = {{0x667f3bcc, 0x3ff6a09e}}, /* sqrt(2) */
/**/ ln2a = {{0xfefa3800, 0x3fe62e42}}, /* ln(2) 43 bits */
/**/ ln2b = {{0x93c76730, 0x3d2ef357}}, /* ln(2)-ln2a */
/**/ bigu = {{0xfffffd2c, 0x4297ffff}}, /* 1.5*2**42 -724*2**-10 */
/**/ bigv = {{0xfff8016a, 0x4207ffff}}, /* 1.5*2**33-1+362*2**-19 */
/**/ t52 = {{0x00000000, 0x43300000}}, /* 2**52 */
/**/ two52e = {{0x000003ff, 0x43300000}}; /* 2**52' */
#endif
#endif
const static double p2=-0.5, p3 = 3.3333333333333333333e-1, p4 = -0.25,
q2 = -0.5, q3 = 3.3333333333331404e-01, q4 = -2.4999999999996436e-01,
q5 = 2.0000010500004459e-01, q6 = -1.6666678916688004e-01,
r3 = 3.33333333333333333372884096563030E-01,
r4 = -2.50000000000000000213574153875908E-01,
r5 = 1.99999999999683593814072199830603E-01,
r6 = -1.66666666666065494878165510225378E-01,
r7 = 1.42857517857114380606360005067609E-01,
r8 = -1.25000449999974370683775964001702E-01,
s3 = 0.333251953125000000e0,
ss3 = 8.138020833333333333e-05,
s4 = -2.500000000000000000e-01,
s5 = 1.999999999999960937e-01,
s6 = -1.666666666666592447e-01,
s7 = 1.428571845238194705e-01,
s8 = -1.250000500000149097e-01;
#endif
libgcc-math/dbl-64/upow.tbl 0 → 100644
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libgcc-math/dbl-64/urem.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/************************************************************************/
/* MODULE_NAME: urem.h */
/* */
/* */
/* common data and variables definition for BIG or LITTLE ENDIAN */
/************************************************************************/
#ifndef UREM_H
#define UREM_H
#ifdef BIG_ENDI
static const mynumber big = {{0x43380000, 0}}, /* 6755399441055744 */
t128 = {{0x47f00000, 0}}, /* 2^ 128 */
tm128 = {{0x37f00000, 0}}, /* 2^-128 */
ZERO = {{0, 0}}, /* 0.0 */
nZERO = {{0x80000000, 0}}, /* -0.0 */
NAN = {{0x7ff80000, 0}}, /* NaN */
nNAN = {{0xfff80000, 0}}; /* -NaN */
#else
#ifdef LITTLE_ENDI
static const mynumber big = {{0, 0x43380000}}, /* 6755399441055744 */
t128 = {{0, 0x47f00000}}, /* 2^ 128 */
tm128 = {{0, 0x37f00000}}, /* 2^-128 */
ZERO = {{0, 0}}, /* 0.0 */
nZERO = {{0, 0x80000000}}, /* -0.0 */
NAN = {{0, 0x7ff80000}}, /* NaN */
nNAN = {{0, 0xfff80000}}; /* -NaN */
#endif
#endif
#endif
libgcc-math/dbl-64/uroot.h 0 → 100644
/*
* IBM Accurate Mathematical Library
* Written by International Business Machines Corp.
* Copyright (C) 2001 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 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 Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
/******************************************************************/
/* */
/* MODULE_NAME:uroot.h */
/* */
/* common data and variables prototype and definition */
/******************************************************************/
#ifndef UROOT_H
#define UROOT_H
#ifdef BIG_ENDI
static const mynumber
/**/ t512 = {{0x5ff00000, 0x00000000 }}, /* 2^512 */
/**/ tm256 = {{0x2ff00000, 0x00000000 }}; /* 2^-256 */
#else
#ifdef LITTLE_ENDI
static const mynumber
/**/ t512 = {{0x00000000, 0x5ff00000 }}, /* 2^512 */
/**/ tm256 = {{0x00000000, 0x2ff00000 }}; /* 2^-256 */
#endif
#endif
#endif
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