From f177c949113889342d74aee8011a86bd4f589841 Mon Sep 17 00:00:00 2001 From: The Android Open Source Project Date: Tue, 3 Mar 2009 18:28:23 -0800 Subject: auto import from //depot/cupcake/@135843 --- Android.mk | 39 - MD5 | 102 -- MODULE_LICENSE_BSD_LIKE | 0 changes | 77 -- configure | 3309 ----------------------------------------------- configure.in | 14 - e_acos.c | 105 -- e_acosh.c | 65 - e_asin.c | 114 -- e_atan2.c | 123 -- e_atanh.c | 68 - e_cosh.c | 89 -- e_exp.c | 156 --- e_fmod.c | 140 -- e_gamma.c | 33 - e_gamma_r.c | 32 - e_hypot.c | 115 -- e_j0.c | 478 ------- e_j1.c | 477 ------- e_jn.c | 272 ---- e_lgamma.c | 33 - e_lgamma_r.c | 304 ----- e_log.c | 139 -- e_log10.c | 91 -- e_pow.c | 309 ----- e_rem_pio2.c | 175 --- e_remainder.c | 77 -- e_scalb.c | 51 - e_sinh.c | 82 -- e_sqrt.c | 450 ------- fdlibm.h | 216 ---- index | 168 --- index.html | 180 --- k_cos.c | 92 -- k_rem_pio2.c | 316 ----- k_sin.c | 74 -- k_standard.c | 733 ----------- k_tan.c | 148 --- makefile.in | 154 --- readme | 261 ---- s_asinh.c | 61 - s_atan.c | 134 -- s_cbrt.c | 87 -- s_ceil.c | 78 -- s_copysign.c | 31 - s_cos.c | 78 -- s_erf.c | 310 ----- s_expm1.c | 216 ---- s_fabs.c | 29 - s_finite.c | 31 - s_floor.c | 79 -- s_frexp.c | 56 - s_ilogb.c | 46 - s_isnan.c | 34 - s_ldexp.c | 28 - s_lib_version.c | 35 - s_log1p.c | 165 --- s_logb.c | 38 - s_matherr.c | 26 - s_modf.c | 80 -- s_nextafter.c | 78 -- s_rint.c | 84 -- s_scalbn.c | 63 - s_signgam.c | 2 - s_significand.c | 30 - s_sin.c | 78 -- s_tan.c | 72 -- s_tanh.c | 82 -- w_acos.c | 39 - w_acosh.c | 39 - w_asin.c | 41 - w_atan2.c | 40 - w_atanh.c | 42 - w_cosh.c | 38 - w_exp.c | 48 - w_fmod.c | 39 - w_gamma.c | 46 - w_gamma_r.c | 42 - w_hypot.c | 39 - w_j0.c | 65 - w_j1.c | 66 - w_jn.c | 88 -- w_lgamma.c | 46 - w_lgamma_r.c | 42 - w_log.c | 39 - w_log10.c | 42 - w_pow.c | 60 - w_remainder.c | 38 - w_scalb.c | 56 - w_sinh.c | 38 - w_sqrt.c | 38 - 91 files changed, 13063 deletions(-) delete mode 100644 Android.mk delete mode 100644 MD5 delete mode 100644 MODULE_LICENSE_BSD_LIKE delete mode 100644 changes delete mode 100644 configure delete mode 100644 configure.in delete mode 100644 e_acos.c delete mode 100644 e_acosh.c delete mode 100644 e_asin.c delete mode 100644 e_atan2.c delete mode 100644 e_atanh.c delete mode 100644 e_cosh.c delete mode 100644 e_exp.c delete mode 100644 e_fmod.c delete mode 100644 e_gamma.c delete mode 100644 e_gamma_r.c delete mode 100644 e_hypot.c delete mode 100644 e_j0.c delete mode 100644 e_j1.c delete mode 100644 e_jn.c delete mode 100644 e_lgamma.c delete mode 100644 e_lgamma_r.c delete mode 100644 e_log.c delete mode 100644 e_log10.c delete mode 100644 e_pow.c delete mode 100644 e_rem_pio2.c delete mode 100644 e_remainder.c delete mode 100644 e_scalb.c delete mode 100644 e_sinh.c delete mode 100644 e_sqrt.c delete mode 100644 fdlibm.h delete mode 100644 index delete mode 100644 index.html delete mode 100644 k_cos.c delete mode 100644 k_rem_pio2.c delete mode 100644 k_sin.c delete mode 100644 k_standard.c delete mode 100644 k_tan.c delete mode 100644 makefile.in delete mode 100644 readme delete mode 100644 s_asinh.c delete mode 100644 s_atan.c delete mode 100644 s_cbrt.c delete mode 100644 s_ceil.c delete mode 100644 s_copysign.c delete mode 100644 s_cos.c delete mode 100644 s_erf.c delete mode 100644 s_expm1.c delete mode 100644 s_fabs.c delete mode 100644 s_finite.c delete mode 100644 s_floor.c delete mode 100644 s_frexp.c delete mode 100644 s_ilogb.c delete mode 100644 s_isnan.c delete mode 100644 s_ldexp.c delete mode 100644 s_lib_version.c delete mode 100644 s_log1p.c delete mode 100644 s_logb.c delete mode 100644 s_matherr.c delete mode 100644 s_modf.c delete mode 100644 s_nextafter.c delete mode 100644 s_rint.c delete mode 100644 s_scalbn.c delete mode 100644 s_signgam.c delete mode 100644 s_significand.c delete mode 100644 s_sin.c delete mode 100644 s_tan.c delete mode 100644 s_tanh.c delete mode 100644 w_acos.c delete mode 100644 w_acosh.c delete mode 100644 w_asin.c delete mode 100644 w_atan2.c delete mode 100644 w_atanh.c delete mode 100644 w_cosh.c delete mode 100644 w_exp.c delete mode 100644 w_fmod.c delete mode 100644 w_gamma.c delete mode 100644 w_gamma_r.c delete mode 100644 w_hypot.c delete mode 100644 w_j0.c delete mode 100644 w_j1.c delete mode 100644 w_jn.c delete mode 100644 w_lgamma.c delete mode 100644 w_lgamma_r.c delete mode 100644 w_log.c delete mode 100644 w_log10.c delete mode 100644 w_pow.c delete mode 100644 w_remainder.c delete mode 100644 w_scalb.c delete mode 100644 w_sinh.c delete mode 100644 w_sqrt.c diff --git a/Android.mk b/Android.mk deleted file mode 100644 index ecf6708..0000000 --- a/Android.mk +++ /dev/null @@ -1,39 +0,0 @@ -LOCAL_PATH:= $(call my-dir) -include $(CLEAR_VARS) - -LOCAL_SRC_FILES:= \ - k_standard.c k_rem_pio2.c \ - k_cos.c k_sin.c k_tan.c \ - e_acos.c e_acosh.c e_asin.c e_atan2.c \ - e_atanh.c e_cosh.c e_exp.c e_fmod.c \ - e_gamma.c e_gamma_r.c e_hypot.c e_j0.c \ - e_j1.c e_jn.c e_lgamma.c e_lgamma_r.c \ - e_log.c e_log10.c e_pow.c e_rem_pio2.c e_remainder.c \ - e_scalb.c e_sinh.c e_sqrt.c \ - w_acos.c w_acosh.c w_asin.c w_atan2.c \ - w_atanh.c w_cosh.c w_exp.c w_fmod.c \ - w_gamma.c w_gamma_r.c w_hypot.c w_j0.c \ - w_j1.c w_jn.c w_lgamma.c w_lgamma_r.c \ - w_log.c w_log10.c w_pow.c w_remainder.c \ - w_scalb.c w_sinh.c w_sqrt.c \ - s_asinh.c s_atan.c s_cbrt.c s_ceil.c s_copysign.c \ - s_cos.c s_erf.c s_expm1.c s_fabs.c s_finite.c s_floor.c \ - s_frexp.c s_ilogb.c s_isnan.c s_ldexp.c s_lib_version.c \ - s_log1p.c s_logb.c s_matherr.c s_modf.c s_nextafter.c \ - s_rint.c s_scalbn.c s_signgam.c s_significand.c s_sin.c \ - s_tan.c s_tanh.c - -LOCAL_MODULE := libfdlibm - -LOCAL_SYSTEM_SHARED_LIBRARIES := - -# Necessary to guarantee that the FDLIBM functions are in "IEEE spirit", -# i.e. to guarantee that the IEEE 754 core functions are used -LOCAL_CFLAGS := "-D_IEEE_LIBM" - -ifneq ($(filter $(TARGET_ARCH),arm x86),) -# When __LITTLE_ENDIAN is set, the source will compile for little endian cpus. -LOCAL_CFLAGS += "-D__LITTLE_ENDIAN" -endif - -include $(BUILD_STATIC_LIBRARY) diff --git a/MD5 b/MD5 deleted file mode 100644 index 3eeca4f..0000000 --- a/MD5 +++ /dev/null @@ -1,102 +0,0 @@ ------BEGIN PGP SIGNED MESSAGE----- - -# netlib-bl master Mon May 17 03:35:14 EDT 2004 -# http://cm.bell-labs.com/netlib/crc/netlib-bl.html -xqdt0SfICJbYU285K5kg9g changes -vXBJ84aVdIHpqtTdjwinqQ configure -ydqnyJgYpziE8zrr/WU4/g configure.in -P2sEgHh/v3RHTsLuS1UeTw e_acos.c -SReAT7diAMhuAtChHm1nLQ e_acosh.c -xsqL2/A2cuTbG4ZabFtgQg e_asin.c -uXwtBvNUrnsWp2lWS/ZPzg e_atan2.c -7+Zmokqk6yU+4B/dPWLVnQ e_atanh.c -FFRFIVaqeYuPIbZDy+GPLQ e_cosh.c -lGljkqn5/mLxl0XkN4fWxQ e_exp.c -ladlzVeoGGhd+r/RvPJUsw e_fmod.c -WwWDDWUnqoeniw5c6ShWUQ e_gamma.c -+rYzLHXdv60VBR9GpEVA7Q e_gamma_r.c -BUemgwLOjQ2tpsWv8fQOWA e_hypot.c -um0j/BMMHd0mEzOIg/iTIw e_j0.c -023e/9GjB47rNsYlxW9/Ug e_j1.c -X2UtLCi/Hg5Xx0ZAiaUHXQ e_jn.c -bBStzzLdDSzNsVlhy/Isdw e_lgamma.c -pYie2c6jvQAObJMq2IhNGQ e_lgamma_r.c -mj6pKYX+E8euiAP6577R4A e_log.c -fEuDo4brNfU8HRqvM0syqQ e_log10.c -ryT3m0UgTGJarnV+NzNhNQ e_pow.c -L/2ye70MqZA7YqsCtgMQlQ e_rem_pio2.c -kdemnBPRKpa3661lnjEcyw e_remainder.c -DW4MDjGPgkJLg4PBGX5yGg e_scalb.c -LiW0gFPaN5JVIuQZW4XbVQ e_sinh.c -JPBrE86qzL59qF5PFCDA/Q e_sqrt.c -uHfh5HgtlKGibLxJYYBFCg fdlibm.h -G21yQjn+xOAex15TPeLfBQ index -sDIZFCqsPOqSl9ykcjky8w k_cos.c -1t3fuGir+TOYRAO0N8Chng k_rem_pio2.c -1Fi/fEeHcsIq50vVplKVzQ k_sin.c -1ufaWqW1PRP1cOuPtb7O7A k_standard.c -0axra6/ERRuXJJcCc5js/Q k_tan.c -wDXTC07GG4Bd+EnUjk/MVw makefile -0ffZi8Ey9JbRT9vCxp4LLg makefile.in -Tw07rtlUiXvlgwzbRb632Q readme -WDSYQ245qaKiYXtEn9qSdg s_asinh.c -ucf0ncFkne9OW4Uv+CxRrQ s_atan.c -w2/WG3x7j7+b9uydji3FZg s_cbrt.c -YqCYHnPBw1dDvbYwjWJNbw s_ceil.c -JX6gTEPMyjuTQclyjiLC2w s_copysign.c -91ARVh9L6LTc2i9VGu9DSg s_cos.c -0Jwhkbo/6ewEss7CW1PI9w s_erf.c -cpq+MFqK2Vi883y8LA/hxA s_expm1.c -K6LRiJVYLNzThuQaOyibVA s_fabs.c -uvNnsV4Fmj90jAbySXd54w s_finite.c -etEc6khe9K27aeE+6ZpW0A s_floor.c -5KDyugUMkjOsPsq6fygPjg s_frexp.c -UWvuamu8A+XGSwi9twc/vQ s_ilogb.c -/KmGbiWbhyiZCru0HbLUpw s_isnan.c -+OZ/WHEZ12FiA8mZ7hk4rA s_ldexp.c -g33PLRuQjT5HRX4ZozySGA s_lib_version.c -MHsSOIzpsdw4sVVtAu4GTQ s_log1p.c -qWJm/3AkemsNi7aF295SGA s_logb.c -QGkKHdTmho+2Xbd0rObCmA s_matherr.c -Tfmhq38TAJspcNpJT9Tcww s_modf.c -k+onjlepmLUH/9xA+Wdqaw s_nextafter.c -omWcOHAaAKLjMuuSirX8Lw s_rint.c -6w2X17eamkvE+pCZlPm8Xg s_scalbn.c -z93vZw0EQ1IQUSqJMRu/IA s_signgam.c -S3OtNFaARNk7TltgUoVs+Q s_significand.c -yYuvBWZCWR0Y/YT6pmIr0w s_sin.c -LhJVti8VVlaWbptWR88XGg s_tan.c -QfLTJ1iGqgC7RhZWHi0PTQ s_tanh.c -vR2IBXoLtHZh+GHCV+Iydg w_acos.c -ZbhbPlbMYiu8Z1NXaDiPDQ w_acosh.c -KsvLAMHSqu1b72p5kYkJyQ w_asin.c -ENaJir3y0hZ4yWWKzBs89w w_atan2.c -+jLlTCXpNVY6yuncPyfWyw w_atanh.c -84kcBUnnIU16mG+cChPbRA w_cosh.c -bjKr6q9UZYgun3LytNO+1A w_exp.c -WQG0A3Gk/MlFkjx4h3yw6Q w_fmod.c -MNIqntvhf0fvFvKfzcPR1g w_gamma.c -TnrF3OPpiAEUymzT0PZiDw w_gamma_r.c -OLFqJDwkIZmIF7vm6BQuGQ w_hypot.c -cvayKIzuZlCxTj6dLXe+qQ w_j0.c -PB3rNmFTtPoMICeJFkAMeg w_j1.c -7qCc7gGMiRIp1GY0UQ3gLg w_jn.c -8URUp8BmBP32s79GRllwdw w_lgamma.c -AJyN8jlYXVe1Dwx+w6qlEQ w_lgamma_r.c -8fmXSpy3xt0Mgd+9BkKHRg w_log.c -/+qteyYx+IKTmLuv1fxqPQ w_log10.c -+o/ImP/JfknQmSxM4TA1ag w_pow.c -BkF5AkqkRA4Py2Y1p0bQIA w_remainder.c -77arOaApwrSQngHv26UWrg w_scalb.c -SgGvz6WUAuHs90sDA/GDbA w_sinh.c -2aR8vbagrVvvMtXPktM6CQ w_sqrt.c - ------BEGIN PGP SIGNATURE----- -Version: 2.6.2 - -iQCVAwUBQKhrNb5pvxO9gjtZAQGFgAP9GkR1sBbpgy/sXcoyIj/LMfystMc5ljYC -WeqSep2+0gmE3l/aLWBaEL/ngyVY8fWNV7lll/DKGA4oJBTWtozHhWGl2g8+tb+L -afoMIwLTbSMMkB4bPGfZm1MevZmOn5g4WLOHQ3aTPlykkBw8QDgmLm+7cWZrbHao -SJ+0t7F/FWI= -=aGTu ------END PGP SIGNATURE----- diff --git a/MODULE_LICENSE_BSD_LIKE b/MODULE_LICENSE_BSD_LIKE deleted file mode 100644 index e69de29..0000000 diff --git a/changes b/changes deleted file mode 100644 index 0407ab4..0000000 --- a/changes +++ /dev/null @@ -1,77 +0,0 @@ -21 Oct 2002 -bug fix in e_pow.c from "David G Hough at validlab.com" . -credit for bug report goes to andrew_johnson@uk.ibm.com -test example: ------------------------------ -static int fail=0; - -trypow(x,y,z) -double x,y,z; -{ -extern double ieee_pow(); -double p ; - -p = ieee_pow(x,y); -if (p != z) { - printf(" pow failure x %e y %e computed %e correct %e \n",x,y,p,z); - fail++; - return; -} -if (1/p != 1/z) { - printf(" pow failure x %e y %e computed %e correct %e \n",x,y,p,z); - fail++; - return; -} -} - -main() -{ - -trypow( 1.0000000001, 1.0000000001E10, 2.7182820535066154); -trypow(-1.0000000001, 1.0000000001E10, -2.7182820535066154); -trypow(-0.001, 1.0000000001E10, -0.0); -trypow(-1000.0, 1.0000000001E10, -1.0/0.0); - -if (fail == 0) { - printf(" fdlibm e_pow.c seems to be current \n"); - exit(0); -} -else { - printf(" fdlibm e_pow.c seems to be out of date \n"); - exit(1); -} - -} ------------------------------ - - - -What's new in FDLIBM 5.3? - -CONFIGURE - To build FDLIBM, edit the supplied Makefile or create - a local Makefile by running "sh configure" - using the supplied configure script contributed by Nelson Beebe - -BUGS FIXED - - 1. e_pow.c incorrect results when - x is very close to -1.0 and y is very large, e.g. - ieee_pow(-1.0000000000000002e+00,4.5035996273704970e+15) = 0 - ieee_pow(-9.9999999999999978e-01,4.5035996273704970e+15) = 0 - Correct results are close to -e and -1/e. - - 2. k_tan.c error was > 1 ulp target for FDLIBM - 5.2: Worst error at least 1.45 ulp at - ieee_tan(1.7765241907548024E+269) = 1.7733884462610958E+16 - 5.3: Worst error 0.96 ulp - -NOT FIXED YET - - 3. Compiler failure on non-standard code - Statements like - *(1+(int*)&t1) = 0; - are not standard C and cause some optimizing compilers (e.g. GCC) - to generate bad code under optimization. These cases - are to be addressed in the next release. - diff --git a/configure b/configure deleted file mode 100644 index d40f54b..0000000 --- a/configure +++ /dev/null @@ -1,3309 +0,0 @@ -#! /bin/sh -# Guess values for system-dependent variables and create Makefiles. -# Generated by GNU Autoconf 2.59 for fdlibm 5.3. -# -# Report bugs to >. -# -# Copyright (C) 2003 Free Software Foundation, Inc. -# This configure script is free software; the Free Software Foundation -# gives unlimited permission to copy, distribute and modify it. -## --------------------- ## -## M4sh Initialization. ## -## --------------------- ## - -# Be Bourne compatible -if test -n "${ZSH_VERSION+set}" && (emulate sh) >/dev/null 2>&1; then - emulate sh - NULLCMD=: - # Zsh 3.x and 4.x performs word splitting on ${1+"$@"}, which - # is contrary to our usage. Disable this feature. - alias -g '${1+"$@"}'='"$@"' -elif test -n "${BASH_VERSION+set}" && (set -o posix) >/dev/null 2>&1; then - set -o posix -fi -DUALCASE=1; export DUALCASE # for MKS sh - -# Support unset when possible. -if ( (MAIL=60; unset MAIL) || exit) >/dev/null 2>&1; then - as_unset=unset -else - as_unset=false -fi - - -# Work around bugs in pre-3.0 UWIN ksh. -$as_unset ENV MAIL MAILPATH -PS1='$ ' -PS2='> ' -PS4='+ ' - -# NLS nuisances. -for as_var in \ - LANG LANGUAGE LC_ADDRESS LC_ALL LC_COLLATE LC_CTYPE LC_IDENTIFICATION \ - LC_MEASUREMENT LC_MESSAGES LC_MONETARY LC_NAME LC_NUMERIC LC_PAPER \ - LC_TELEPHONE LC_TIME -do - if (set +x; test -z "`(eval $as_var=C; export $as_var) 2>&1`"); then - eval $as_var=C; export $as_var - else - $as_unset $as_var - fi -done - -# Required to use basename. -if expr a : '\(a\)' >/dev/null 2>&1; then - as_expr=expr -else - as_expr=false -fi - -if (basename /) >/dev/null 2>&1 && test "X`basename / 2>&1`" = "X/"; then - as_basename=basename -else - as_basename=false -fi - - -# Name of the executable. -as_me=`$as_basename "$0" || -$as_expr X/"$0" : '.*/\([^/][^/]*\)/*$' \| \ - X"$0" : 'X\(//\)$' \| \ - X"$0" : 'X\(/\)$' \| \ - . : '\(.\)' 2>/dev/null || -echo X/"$0" | - sed '/^.*\/\([^/][^/]*\)\/*$/{ s//\1/; q; } - /^X\/\(\/\/\)$/{ s//\1/; q; } - /^X\/\(\/\).*/{ s//\1/; q; } - s/.*/./; q'` - - -# PATH needs CR, and LINENO needs CR and PATH. -# Avoid depending upon Character Ranges. -as_cr_letters='abcdefghijklmnopqrstuvwxyz' -as_cr_LETTERS='ABCDEFGHIJKLMNOPQRSTUVWXYZ' -as_cr_Letters=$as_cr_letters$as_cr_LETTERS -as_cr_digits='0123456789' -as_cr_alnum=$as_cr_Letters$as_cr_digits - -# The user is always right. -if test "${PATH_SEPARATOR+set}" != set; then - echo "#! /bin/sh" >conf$$.sh - echo "exit 0" >>conf$$.sh - chmod +x conf$$.sh - if (PATH="/nonexistent;."; conf$$.sh) >/dev/null 2>&1; then - PATH_SEPARATOR=';' - else - PATH_SEPARATOR=: - fi - rm -f conf$$.sh -fi - - - as_lineno_1=$LINENO - as_lineno_2=$LINENO - as_lineno_3=`(expr $as_lineno_1 + 1) 2>/dev/null` - test "x$as_lineno_1" != "x$as_lineno_2" && - test "x$as_lineno_3" = "x$as_lineno_2" || { - # Find who we are. 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" - fi - configure_input=$configure_input"Generated from `echo $ac_file_in | - sed 's,.*/,,'` by configure." - - # First look for the input files in the build tree, otherwise in the - # src tree. - ac_file_inputs=`IFS=: - for f in $ac_file_in; do - case $f in - -) echo $tmp/stdin ;; - [\\/$]*) - # Absolute (can't be DOS-style, as IFS=:) - test -f "$f" || { { echo "$as_me:$LINENO: error: cannot find input file: $f" >&5 -echo "$as_me: error: cannot find input file: $f" >&2;} - { (exit 1); exit 1; }; } - echo "$f";; - *) # Relative - if test -f "$f"; then - # Build tree - echo "$f" - elif test -f "$srcdir/$f"; then - # Source tree - echo "$srcdir/$f" - else - # /dev/null tree - { { echo "$as_me:$LINENO: error: cannot find input file: $f" >&5 -echo "$as_me: error: cannot find input file: $f" >&2;} - { (exit 1); exit 1; }; } - fi;; - esac - done` || { (exit 1); exit 1; } -_ACEOF -cat >>$CONFIG_STATUS <<_ACEOF - sed "$ac_vpsub -$extrasub -_ACEOF -cat >>$CONFIG_STATUS <<\_ACEOF -:t -/@[a-zA-Z_][a-zA-Z_0-9]*@/!b -s,@configure_input@,$configure_input,;t t -s,@srcdir@,$ac_srcdir,;t t -s,@abs_srcdir@,$ac_abs_srcdir,;t t -s,@top_srcdir@,$ac_top_srcdir,;t t -s,@abs_top_srcdir@,$ac_abs_top_srcdir,;t t -s,@builddir@,$ac_builddir,;t t -s,@abs_builddir@,$ac_abs_builddir,;t t -s,@top_builddir@,$ac_top_builddir,;t t -s,@abs_top_builddir@,$ac_abs_top_builddir,;t t -" $ac_file_inputs | (eval "$ac_sed_cmds") >$tmp/out - rm -f $tmp/stdin - if test x"$ac_file" != x-; then - mv $tmp/out $ac_file - else - cat $tmp/out - rm -f $tmp/out - fi - -done -_ACEOF - -cat >>$CONFIG_STATUS <<\_ACEOF - -{ (exit 0); exit 0; } -_ACEOF -chmod +x $CONFIG_STATUS -ac_clean_files=$ac_clean_files_save - - -# configure is writing to config.log, and then calls config.status. -# config.status does its own redirection, appending to config.log. -# Unfortunately, on DOS this fails, as config.log is still kept open -# by configure, so config.status won't be able to write to it; its -# output is simply discarded. So we exec the FD to /dev/null, -# effectively closing config.log, so it can be properly (re)opened and -# appended to by config.status. When coming back to configure, we -# need to make the FD available again. -if test "$no_create" != yes; then - ac_cs_success=: - ac_config_status_args= - test "$silent" = yes && - ac_config_status_args="$ac_config_status_args --quiet" - exec 5>/dev/null - $SHELL $CONFIG_STATUS $ac_config_status_args || ac_cs_success=false - exec 5>>config.log - # Use ||, not &&, to avoid exiting from the if with $? = 1, which - # would make configure fail if this is the last instruction. - $ac_cs_success || { (exit 1); exit 1; } -fi - diff --git a/configure.in b/configure.in deleted file mode 100644 index e4517ab..0000000 --- a/configure.in +++ /dev/null @@ -1,14 +0,0 @@ -dnl Process this file with autoconf to produce a configure script -AC_INIT(fdlibm,5.3,[FDLIBM COMMENTS ]) -AC_CONFIG_SRCDIR(e_acos.c) - -dnl Checks for programs -AC_PROG_CC - -AC_CHECK_PROGS(AR, ar) -AC_CHECK_PROGS(CHMOD, chmod) -AC_CHECK_PROGS(CP, cp) -AC_CHECK_PROGS(RANLIB, [ranlib echo]) -AC_PATH_PROGS(RM, [/bin/rm rm]) - -AC_OUTPUT(Makefile) diff --git a/e_acos.c b/e_acos.c deleted file mode 100644 index 1b63553..0000000 --- a/e_acos.c +++ /dev/null @@ -1,105 +0,0 @@ - -/* @(#)e_acos.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_acos(x) - * Method : - * acos(x) = pi/2 - ieee_asin(x) - * acos(-x) = pi/2 + ieee_asin(x) - * For |x|<=0.5 - * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) - * For x>0.5 - * acos(x) = pi/2 - (pi/2 - 2asin(ieee_sqrt((1-x)/2))) - * = 2asin(ieee_sqrt((1-x)/2)) - * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=ieee_sqrt(z) - * = 2f + (2c + 2s*z*R(z)) - * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term - * for f so that f+c ~ ieee_sqrt(z). - * For x<-0.5 - * acos(x) = pi - 2asin(ieee_sqrt((1-|x|)/2)) - * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=ieee_sqrt(z) - * - * Special cases: - * if x is NaN, return x itself; - * if |x|>1, return NaN with invalid signal. - * - * Function needed: sqrt - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ -pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ -pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ -pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ -pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ -pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ -pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ -pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ -qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ -qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ -qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ -qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ - -#ifdef __STDC__ - double __ieee754_acos(double x) -#else - double __ieee754_acos(x) - double x; -#endif -{ - double z,p,q,r,w,s,c,df; - int hx,ix; - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x3ff00000) { /* |x| >= 1 */ - if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */ - if(hx>0) return 0.0; /* ieee_acos(1) = 0 */ - else return pi+2.0*pio2_lo; /* ieee_acos(-1)= pi */ - } - return (x-x)/(x-x); /* ieee_acos(|x|>1) is NaN */ - } - if(ix<0x3fe00000) { /* |x| < 0.5 */ - if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ - z = x*x; - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); - r = p/q; - return pio2_hi - (x - (pio2_lo-x*r)); - } else if (hx<0) { /* x < -0.5 */ - z = (one+x)*0.5; - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); - s = ieee_sqrt(z); - r = p/q; - w = r*s-pio2_lo; - return pi - 2.0*(s+w); - } else { /* x > 0.5 */ - z = (one-x)*0.5; - s = ieee_sqrt(z); - df = s; - __LO(df) = 0; - c = (z-df*df)/(s+df); - p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); - q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); - r = p/q; - w = r*s+c; - return 2.0*(df+w); - } -} diff --git a/e_acosh.c b/e_acosh.c deleted file mode 100644 index d98e81a..0000000 --- a/e_acosh.c +++ /dev/null @@ -1,65 +0,0 @@ - -/* @(#)e_acosh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* __ieee754_acosh(x) - * Method : - * Based on - * acosh(x) = log [ x + ieee_sqrt(x*x-1) ] - * we have - * acosh(x) := ieee_log(x)+ln2, if x is large; else - * acosh(x) := ieee_log(2x-1/(ieee_sqrt(x*x-1)+x)) if x>2; else - * acosh(x) := ieee_log1p(t+ieee_sqrt(2.0*t+t*t)); where t=x-1. - * - * Special cases: - * acosh(x) is NaN with signal if x<1. - * acosh(NaN) is NaN without signal. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -one = 1.0, -ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ - -#ifdef __STDC__ - double __ieee754_acosh(double x) -#else - double __ieee754_acosh(x) - double x; -#endif -{ - double t; - int hx; - hx = __HI(x); - if(hx<0x3ff00000) { /* x < 1 */ - return (x-x)/(x-x); - } else if(hx >=0x41b00000) { /* x > 2**28 */ - if(hx >=0x7ff00000) { /* x is inf of NaN */ - return x+x; - } else - return __ieee754_log(x)+ln2; /* acosh(huge)=ieee_log(2x) */ - } else if(((hx-0x3ff00000)|__LO(x))==0) { - return 0.0; /* acosh(1) = 0 */ - } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ - t=x*x; - return __ieee754_log(2.0*x-one/(x+ieee_sqrt(t-one))); - } else { /* 10.98 - * asin(x) = pi/2 - 2*(s+s*z*R(z)) - * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) - * For x<=0.98, let pio4_hi = pio2_hi/2, then - * f = hi part of s; - * c = ieee_sqrt(z) - f = (z-f*f)/(s+f) ...f+c=ieee_sqrt(z) - * and - * asin(x) = pi/2 - 2*(s+s*z*R(z)) - * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) - * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) - * - * Special cases: - * if x is NaN, return x itself; - * if |x|>1, return NaN with invalid signal. - * - */ - - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -huge = 1.000e+300, -pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ -pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ - /* coefficient for R(x^2) */ -pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ -pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ -pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ -pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ -pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ -pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ -qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ -qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ -qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ -qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ - -#ifdef __STDC__ - double __ieee754_asin(double x) -#else - double __ieee754_asin(x) - double x; -#endif -{ - double t,w,p,q,c,r,s; - int hx,ix; - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>= 0x3ff00000) { /* |x|>= 1 */ - if(((ix-0x3ff00000)|__LO(x))==0) - /* ieee_asin(1)=+-pi/2 with inexact */ - return x*pio2_hi+x*pio2_lo; - return (x-x)/(x-x); /* ieee_asin(|x|>1) is NaN */ - } else if (ix<0x3fe00000) { /* |x|<0.5 */ - if(ix<0x3e400000) { /* if |x| < 2**-27 */ - if(huge+x>one) return x;/* return x with inexact if x!=0*/ - } else - t = x*x; - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); - w = p/q; - return x+x*w; - } - /* 1> |x|>= 0.5 */ - w = one-ieee_fabs(x); - t = w*0.5; - p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); - q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); - s = ieee_sqrt(t); - if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ - w = p/q; - t = pio2_hi-(2.0*(s+s*w)-pio2_lo); - } else { - w = s; - __LO(w) = 0; - c = (t-w*w)/(s+w); - r = p/q; - p = 2.0*s*r-(pio2_lo-2.0*c); - q = pio4_hi-2.0*w; - t = pio4_hi-(p-q); - } - if(hx>0) return t; else return -t; -} diff --git a/e_atan2.c b/e_atan2.c deleted file mode 100644 index 73c43dd..0000000 --- a/e_atan2.c +++ /dev/null @@ -1,123 +0,0 @@ - -/* @(#)e_atan2.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* __ieee754_atan2(y,x) - * Method : - * 1. Reduce y to positive by ieee_atan2(y,x)=-ieee_atan2(-y,x). - * 2. Reduce x to positive by (if x and y are unexceptional): - * ARG (x+iy) = arctan(y/x) ... if x > 0, - * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, - * - * Special cases: - * - * ATAN2((anything), NaN ) is NaN; - * ATAN2(NAN , (anything) ) is NaN; - * ATAN2(+-0, +(anything but NaN)) is +-0 ; - * ATAN2(+-0, -(anything but NaN)) is +-pi ; - * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; - * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; - * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; - * ATAN2(+-INF,+INF ) is +-pi/4 ; - * ATAN2(+-INF,-INF ) is +-3pi/4; - * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; - * - * 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 "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -tiny = 1.0e-300, -zero = 0.0, -pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ -pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ -pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ -pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ - -#ifdef __STDC__ - double __ieee754_atan2(double y, double x) -#else - double __ieee754_atan2(y,x) - double y,x; -#endif -{ - double z; - int k,m,hx,hy,ix,iy; - unsigned lx,ly; - - hx = __HI(x); ix = hx&0x7fffffff; - lx = __LO(x); - hy = __HI(y); iy = hy&0x7fffffff; - ly = __LO(y); - if(((ix|((lx|-lx)>>31))>0x7ff00000)|| - ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ - return x+y; - if((hx-0x3ff00000|lx)==0) return ieee_atan(y); /* x=1.0 */ - m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ - - /* when y = 0 */ - if((iy|ly)==0) { - switch(m) { - case 0: - case 1: return y; /* ieee_atan(+-0,+anything)=+-0 */ - case 2: return pi+tiny;/* ieee_atan(+0,-anything) = pi */ - case 3: return -pi-tiny;/* ieee_atan(-0,-anything) =-pi */ - } - } - /* when x = 0 */ - if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; - - /* when x is INF */ - if(ix==0x7ff00000) { - if(iy==0x7ff00000) { - switch(m) { - case 0: return pi_o_4+tiny;/* ieee_atan(+INF,+INF) */ - case 1: return -pi_o_4-tiny;/* ieee_atan(-INF,+INF) */ - case 2: return 3.0*pi_o_4+tiny;/*ieee_atan(+INF,-INF)*/ - case 3: return -3.0*pi_o_4-tiny;/*ieee_atan(-INF,-INF)*/ - } - } else { - switch(m) { - case 0: return zero ; /* ieee_atan(+...,+INF) */ - case 1: return -zero ; /* ieee_atan(-...,+INF) */ - case 2: return pi+tiny ; /* ieee_atan(+...,-INF) */ - case 3: return -pi-tiny ; /* ieee_atan(-...,-INF) */ - } - } - } - /* when y is INF */ - if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; - - /* compute y/x */ - k = (iy-ix)>>20; - if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ - else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ - else z=ieee_atan(ieee_fabs(y/x)); /* safe to do y/x */ - switch (m) { - case 0: return z ; /* ieee_atan(+,+) */ - case 1: __HI(z) ^= 0x80000000; - return z ; /* ieee_atan(-,+) */ - case 2: return pi-(z-pi_lo);/* ieee_atan(+,-) */ - default: /* case 3 */ - return (z-pi_lo)-pi;/* ieee_atan(-,-) */ - } -} diff --git a/e_atanh.c b/e_atanh.c deleted file mode 100644 index 4793e4a..0000000 --- a/e_atanh.c +++ /dev/null @@ -1,68 +0,0 @@ - -/* @(#)e_atanh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* __ieee754_atanh(x) - * Method : - * 1.Reduced x to positive by atanh(-x) = -atanh(x) - * 2.For x>=0.5 - * 1 2x x - * atanh(x) = --- * ieee_log(1 + -------) = 0.5 * ieee_log1p(2 * --------) - * 2 1 - x 1 - x - * - * For x<0.5 - * atanh(x) = 0.5*ieee_log1p(2x+2x*x/(1-x)) - * - * Special cases: - * atanh(x) is NaN if |x| > 1 with signal; - * atanh(NaN) is that NaN with no signal; - * atanh(+-1) is +-INF with signal. - * - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double one = 1.0, huge = 1e300; -#else -static double one = 1.0, huge = 1e300; -#endif - -static double zero = 0.0; - -#ifdef __STDC__ - double __ieee754_atanh(double x) -#else - double __ieee754_atanh(x) - double x; -#endif -{ - double t; - int hx,ix; - unsigned lx; - hx = __HI(x); /* high word */ - lx = __LO(x); /* low word */ - ix = hx&0x7fffffff; - if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ - return (x-x)/(x-x); - if(ix==0x3ff00000) - return x/zero; - if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ - __HI(x) = ix; /* x <- |x| */ - if(ix<0x3fe00000) { /* x < 0.5 */ - t = x+x; - t = 0.5*ieee_log1p(t+t*x/(one-x)); - } else - t = 0.5*ieee_log1p((x+x)/(one-x)); - if(hx>=0) return t; else return -t; -} diff --git a/e_cosh.c b/e_cosh.c deleted file mode 100644 index a5c5ae6..0000000 --- a/e_cosh.c +++ /dev/null @@ -1,89 +0,0 @@ - -/* @(#)e_cosh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_cosh(x) - * Method : - * mathematically ieee_cosh(x) if defined to be (ieee_exp(x)+ieee_exp(-x))/2 - * 1. Replace x by |x| (ieee_cosh(x) = ieee_cosh(-x)). - * 2. - * [ ieee_exp(x) - 1 ]^2 - * 0 <= x <= ln2/2 : ieee_cosh(x) := 1 + ------------------- - * 2*ieee_exp(x) - * - * ieee_exp(x) + 1/ieee_exp(x) - * ln2/2 <= x <= 22 : ieee_cosh(x) := ------------------- - * 2 - * 22 <= x <= lnovft : ieee_cosh(x) := ieee_exp(x)/2 - * lnovft <= x <= ln2ovft: ieee_cosh(x) := ieee_exp(x/2)/2 * ieee_exp(x/2) - * ln2ovft < x : ieee_cosh(x) := huge*huge (overflow) - * - * Special cases: - * cosh(x) is |x| if x is +INF, -INF, or NaN. - * only ieee_cosh(0)=1 is exact for finite x. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double one = 1.0, half=0.5, huge = 1.0e300; -#else -static double one = 1.0, half=0.5, huge = 1.0e300; -#endif - -#ifdef __STDC__ - double __ieee754_cosh(double x) -#else - double __ieee754_cosh(x) - double x; -#endif -{ - double t,w; - int ix; - unsigned lx; - - /* High word of |x|. */ - ix = __HI(x); - ix &= 0x7fffffff; - - /* x is INF or NaN */ - if(ix>=0x7ff00000) return x*x; - - /* |x| in [0,0.5*ln2], return 1+ieee_expm1(|x|)^2/(2*ieee_exp(|x|)) */ - if(ix<0x3fd62e43) { - t = ieee_expm1(ieee_fabs(x)); - w = one+t; - if (ix<0x3c800000) return w; /* ieee_cosh(tiny) = 1 */ - return one+(t*t)/(w+w); - } - - /* |x| in [0.5*ln2,22], return (ieee_exp(|x|)+1/ieee_exp(|x|)/2; */ - if (ix < 0x40360000) { - t = __ieee754_exp(ieee_fabs(x)); - return half*t+half/t; - } - - /* |x| in [22, ieee_log(maxdouble)] return half*ieee_exp(|x|) */ - if (ix < 0x40862E42) return half*__ieee754_exp(ieee_fabs(x)); - - /* |x| in [log(maxdouble), overflowthresold] */ - lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); - if (ix<0x408633CE || - (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) { - w = __ieee754_exp(half*ieee_fabs(x)); - t = half*w; - return t*w; - } - - /* |x| > overflowthresold, ieee_cosh(x) overflow */ - return huge*huge; -} diff --git a/e_exp.c b/e_exp.c deleted file mode 100644 index e7aaa23..0000000 --- a/e_exp.c +++ /dev/null @@ -1,156 +0,0 @@ - -/* @(#)e_exp.c 1.6 04/04/22 */ -/* - * ==================================================== - * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_exp(x) - * Returns the exponential of x. - * - * Method - * 1. Argument reduction: - * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. - * Given x, find r and integer k such that - * - * x = k*ln2 + r, |r| <= 0.5*ln2. - * - * Here r will be represented as r = hi-lo for better - * accuracy. - * - * 2. Approximation of ieee_exp(r) by a special rational function on - * the interval [0,0.34658]: - * Write - * R(r**2) = r*(ieee_exp(r)+1)/(ieee_exp(r)-1) = 2 + r*r/6 - r**4/360 + ... - * We use a special Remes algorithm on [0,0.34658] to generate - * a polynomial of degree 5 to approximate R. The maximum error - * of this polynomial approximation is bounded by 2**-59. In - * other words, - * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 - * (where z=r*r, and the values of P1 to P5 are listed below) - * and - * | 5 | -59 - * | 2.0+P1*z+...+P5*z - R(z) | <= 2 - * | | - * The computation of ieee_exp(r) thus becomes - * 2*r - * exp(r) = 1 + ------- - * R - r - * r*R1(r) - * = 1 + r + ----------- (for better accuracy) - * 2 - R1(r) - * where - * 2 4 10 - * R1(r) = r - (P1*r + P2*r + ... + P5*r ). - * - * 3. Scale back to obtain ieee_exp(x): - * From step 1, we have - * ieee_exp(x) = 2^k * ieee_exp(r) - * - * Special cases: - * exp(INF) is INF, ieee_exp(NaN) is NaN; - * exp(-INF) is 0, and - * for finite argument, only ieee_exp(0)=1 is exact. - * - * Accuracy: - * according to an error analysis, the error is always less than - * 1 ulp (unit in the last place). - * - * Misc. info. - * For IEEE double - * if x > 7.09782712893383973096e+02 then ieee_exp(x) overflow - * if x < -7.45133219101941108420e+02 then ieee_exp(x) underflow - * - * 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 "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -one = 1.0, -halF[2] = {0.5,-0.5,}, -huge = 1.0e+300, -twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ -o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ -u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ -ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ - -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ -ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ - -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ -invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ -P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ -P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ -P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ -P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ -P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ - - -#ifdef __STDC__ - double __ieee754_exp(double x) /* default IEEE double exp */ -#else - double __ieee754_exp(x) /* default IEEE double exp */ - double x; -#endif -{ - double y,hi,lo,c,t; - int k,xsb; - unsigned hx; - - hx = __HI(x); /* high word of x */ - xsb = (hx>>31)&1; /* sign bit of x */ - hx &= 0x7fffffff; /* high word of |x| */ - - /* filter out non-finite argument */ - if(hx >= 0x40862E42) { /* if |x|>=709.78... */ - if(hx>=0x7ff00000) { - if(((hx&0xfffff)|__LO(x))!=0) - return x+x; /* NaN */ - else return (xsb==0)? x:0.0; /* ieee_exp(+-inf)={inf,0} */ - } - if(x > o_threshold) return huge*huge; /* overflow */ - if(x < u_threshold) return twom1000*twom1000; /* underflow */ - } - - /* argument reduction */ - if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ - if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ - hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; - } else { - k = (int)(invln2*x+halF[xsb]); - t = k; - hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ - lo = t*ln2LO[0]; - } - x = hi - lo; - } - else if(hx < 0x3e300000) { /* when |x|<2**-28 */ - if(huge+x>one) return one+x;/* trigger inexact */ - } - else k = 0; - - /* x is now in primary range */ - t = x*x; - c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); - if(k==0) return one-((x*c)/(c-2.0)-x); - else y = one-((lo-(x*c)/(2.0-c))-hi); - if(k >= -1021) { - __HI(y) += (k<<20); /* add k to y's exponent */ - return y; - } else { - __HI(y) += ((k+1000)<<20);/* add k to y's exponent */ - return y*twom1000; - } -} diff --git a/e_fmod.c b/e_fmod.c deleted file mode 100644 index e4b413b..0000000 --- a/e_fmod.c +++ /dev/null @@ -1,140 +0,0 @@ - -/* @(#)e_fmod.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * __ieee754_fmod(x,y) - * Return x mod y in exact arithmetic - * Method: shift and subtract - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double one = 1.0, Zero[] = {0.0, -0.0,}; -#else -static double one = 1.0, Zero[] = {0.0, -0.0,}; -#endif - -#ifdef __STDC__ - double __ieee754_fmod(double x, double y) -#else - double __ieee754_fmod(x,y) - double x,y ; -#endif -{ - int n,hx,hy,hz,ix,iy,sx,i; - unsigned lx,ly,lz; - - hx = __HI(x); /* high word of x */ - lx = __LO(x); /* low word of x */ - hy = __HI(y); /* high word of y */ - ly = __LO(y); /* low word of y */ - sx = hx&0x80000000; /* sign of x */ - hx ^=sx; /* |x| */ - hy &= 0x7fffffff; /* |y| */ - - /* purge off exception values */ - if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ - ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ - return (x*y)/(x*y); - if(hx<=hy) { - if((hx>31]; /* |x|=|y| return x*0*/ - } - - /* determine ix = ieee_ilogb(x) */ - if(hx<0x00100000) { /* subnormal x */ - if(hx==0) { - for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; - } else { - for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; - } - } else ix = (hx>>20)-1023; - - /* determine iy = ieee_ilogb(y) */ - if(hy<0x00100000) { /* subnormal y */ - if(hy==0) { - for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; - } else { - for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; - } - } else iy = (hy>>20)-1023; - - /* set up {hx,lx}, {hy,ly} and align y to x */ - if(ix >= -1022) - hx = 0x00100000|(0x000fffff&hx); - else { /* subnormal x, shift x to normal */ - n = -1022-ix; - if(n<=31) { - hx = (hx<>(32-n)); - lx <<= n; - } else { - hx = lx<<(n-32); - lx = 0; - } - } - if(iy >= -1022) - hy = 0x00100000|(0x000fffff&hy); - else { /* subnormal y, shift y to normal */ - n = -1022-iy; - if(n<=31) { - hy = (hy<>(32-n)); - ly <<= n; - } else { - hy = ly<<(n-32); - ly = 0; - } - } - - /* fix point fmod */ - n = ix - iy; - while(n--) { - hz=hx-hy;lz=lx-ly; if(lx>31); lx = lx+lx;} - else { - if((hz|lz)==0) /* return sign(x)*0 */ - return Zero[(unsigned)sx>>31]; - hx = hz+hz+(lz>>31); lx = lz+lz; - } - } - hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} - - /* convert back to floating value and restore the sign */ - if((hx|lx)==0) /* return sign(x)*0 */ - return Zero[(unsigned)sx>>31]; - while(hx<0x00100000) { /* normalize x */ - hx = hx+hx+(lx>>31); lx = lx+lx; - iy -= 1; - } - if(iy>= -1022) { /* normalize output */ - hx = ((hx-0x00100000)|((iy+1023)<<20)); - __HI(x) = hx|sx; - __LO(x) = lx; - } else { /* subnormal output */ - n = -1022 - iy; - if(n<=20) { - lx = (lx>>n)|((unsigned)hx<<(32-n)); - hx >>= n; - } else if (n<=31) { - lx = (hx<<(32-n))|(lx>>n); hx = sx; - } else { - lx = hx>>(n-32); hx = sx; - } - __HI(x) = hx|sx; - __LO(x) = lx; - x *= one; /* create necessary signal */ - } - return x; /* exact output */ -} diff --git a/e_gamma.c b/e_gamma.c deleted file mode 100644 index f4bc1aa..0000000 --- a/e_gamma.c +++ /dev/null @@ -1,33 +0,0 @@ - -/* @(#)e_gamma.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* __ieee754_gamma(x) - * Return the logarithm of the Gamma function of x. - * - * Method: call __ieee754_gamma_r - */ - -#include "fdlibm.h" - -extern int signgam; - -#ifdef __STDC__ - double __ieee754_gamma(double x) -#else - double __ieee754_gamma(x) - double x; -#endif -{ - return __ieee754_gamma_r(x,&signgam); -} diff --git a/e_gamma_r.c b/e_gamma_r.c deleted file mode 100644 index e851083..0000000 --- a/e_gamma_r.c +++ /dev/null @@ -1,32 +0,0 @@ - -/* @(#)e_gamma_r.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* __ieee754_gamma_r(x, signgamp) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). - * - * Method: See __ieee754_lgamma_r - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double __ieee754_gamma_r(double x, int *signgamp) -#else - double __ieee754_gamma_r(x,signgamp) - double x; int *signgamp; -#endif -{ - return __ieee754_lgamma_r(x,signgamp); -} diff --git a/e_hypot.c b/e_hypot.c deleted file mode 100644 index e88701d..0000000 --- a/e_hypot.c +++ /dev/null @@ -1,115 +0,0 @@ - -/* @(#)e_hypot.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_hypot(x,y) - * - * Method : - * If (assume round-to-nearest) z=x*x+y*y - * has error less than ieee_sqrt(2)/2 ulp, than - * sqrt(z) has error less than 1 ulp (exercise). - * - * So, compute ieee_sqrt(x*x+y*y) with some care as - * follows to get the error below 1 ulp: - * - * Assume x>y>0; - * (if possible, set rounding to round-to-nearest) - * 1. if x > 2y use - * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y - * where x1 = x with lower 32 bits cleared, x2 = x-x1; else - * 2. if x <= 2y use - * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) - * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, - * y1= y with lower 32 bits chopped, y2 = y-y1. - * - * NOTE: scaling may be necessary if some argument is too - * large or too tiny - * - * Special cases: - * hypot(x,y) is INF if x or y is +INF or -INF; else - * hypot(x,y) is NAN if x or y is NAN. - * - * Accuracy: - * hypot(x,y) returns ieee_sqrt(x^2+y^2) with error less - * than 1 ulps (units in the last place) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double __ieee754_hypot(double x, double y) -#else - double __ieee754_hypot(x,y) - double x, y; -#endif -{ - double a=x,b=y,t1,t2,y1,y2,w; - int j,k,ha,hb; - - ha = __HI(x)&0x7fffffff; /* high word of x */ - hb = __HI(y)&0x7fffffff; /* high word of y */ - if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} - __HI(a) = ha; /* a <- |a| */ - __HI(b) = hb; /* b <- |b| */ - if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ - k=0; - if(ha > 0x5f300000) { /* a>2**500 */ - if(ha >= 0x7ff00000) { /* Inf or NaN */ - w = a+b; /* for sNaN */ - if(((ha&0xfffff)|__LO(a))==0) w = a; - if(((hb^0x7ff00000)|__LO(b))==0) w = b; - return w; - } - /* scale a and b by 2**-600 */ - ha -= 0x25800000; hb -= 0x25800000; k += 600; - __HI(a) = ha; - __HI(b) = hb; - } - if(hb < 0x20b00000) { /* b < 2**-500 */ - if(hb <= 0x000fffff) { /* subnormal b or 0 */ - if((hb|(__LO(b)))==0) return a; - t1=0; - __HI(t1) = 0x7fd00000; /* t1=2^1022 */ - b *= t1; - a *= t1; - k -= 1022; - } else { /* scale a and b by 2^600 */ - ha += 0x25800000; /* a *= 2^600 */ - hb += 0x25800000; /* b *= 2^600 */ - k -= 600; - __HI(a) = ha; - __HI(b) = hb; - } - } - /* medium size a and b */ - w = a-b; - if (w>b) { - t1 = 0; - __HI(t1) = ha; - t2 = a-t1; - w = ieee_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); - } else { - a = a+a; - y1 = 0; - __HI(y1) = hb; - y2 = b - y1; - t1 = 0; - __HI(t1) = ha+0x00100000; - t2 = a - t1; - w = ieee_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); - } - if(k!=0) { - t1 = 1.0; - __HI(t1) += (k<<20); - return t1*w; - } else return w; -} diff --git a/e_j0.c b/e_j0.c deleted file mode 100644 index 2d24c72..0000000 --- a/e_j0.c +++ /dev/null @@ -1,478 +0,0 @@ - -/* @(#)e_j0.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_j0(x), __ieee754_y0(x) - * Bessel function of the first and second kinds of order zero. - * Method -- ieee_j0(x): - * 1. For tiny x, we use ieee_j0(x) = 1 - x^2/4 + x^4/64 - ... - * 2. Reduce x to |x| since ieee_j0(x)=ieee_j0(-x), and - * for x in (0,2) - * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; - * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) - * for x in (2,inf) - * j0(x) = ieee_sqrt(2/(pi*x))*(p0(x)*ieee_cos(x0)-q0(x)*ieee_sin(x0)) - * where x0 = x-pi/4. It is better to compute ieee_sin(x0),cos(x0) - * as follow: - * cos(x0) = ieee_cos(x)cos(pi/4)+ieee_sin(x)sin(pi/4) - * = 1/ieee_sqrt(2) * (ieee_cos(x) + ieee_sin(x)) - * sin(x0) = ieee_sin(x)cos(pi/4)-ieee_cos(x)sin(pi/4) - * = 1/ieee_sqrt(2) * (ieee_sin(x) - ieee_cos(x)) - * (To avoid cancellation, use - * sin(x) +- ieee_cos(x) = -ieee_cos(2x)/(ieee_sin(x) -+ ieee_cos(x)) - * to compute the worse one.) - * - * 3 Special cases - * j0(nan)= nan - * j0(0) = 1 - * j0(inf) = 0 - * - * Method -- ieee_y0(x): - * 1. For x<2. - * Since - * y0(x) = 2/pi*(ieee_j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) - * therefore ieee_y0(x)-2/pi*ieee_j0(x)*ln(x) is an even function. - * We use the following function to approximate y0, - * y0(x) = U(z)/V(z) + (2/pi)*(ieee_j0(x)*ln(x)), z= x^2 - * where - * U(z) = u00 + u01*z + ... + u06*z^6 - * V(z) = 1 + v01*z + ... + v04*z^4 - * with absolute approximation error bounded by 2**-72. - * Note: For tiny x, U/V = u0 and ieee_j0(x)~1, hence - * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) - * 2. For x>=2. - * y0(x) = ieee_sqrt(2/(pi*x))*(p0(x)*ieee_cos(x0)+q0(x)*ieee_sin(x0)) - * where x0 = x-pi/4. It is better to compute ieee_sin(x0),cos(x0) - * by the method mentioned above. - * 3. Special cases: ieee_y0(0)=-inf, ieee_y0(x<0)=NaN, ieee_y0(inf)=0. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static double pzero(double), qzero(double); -#else -static double pzero(), qzero(); -#endif - -#ifdef __STDC__ -static const double -#else -static double -#endif -huge = 1e300, -one = 1.0, -invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - /* R0/S0 on [0, 2.00] */ -R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ -R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ -R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ -R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ -S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ -S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ -S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ -S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ - -static double zero = 0.0; - -#ifdef __STDC__ - double __ieee754_j0(double x) -#else - double __ieee754_j0(x) - double x; -#endif -{ - double z, s,c,ss,cc,r,u,v; - int hx,ix; - - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) return one/(x*x); - x = ieee_fabs(x); - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = ieee_sin(x); - c = ieee_cos(x); - ss = s-c; - cc = s+c; - if(ix<0x7fe00000) { /* make sure x+x not overflow */ - z = -ieee_cos(x+x); - if ((s*c)0x48000000) z = (invsqrtpi*cc)/ieee_sqrt(x); - else { - u = pzero(x); v = qzero(x); - z = invsqrtpi*(u*cc-v*ss)/ieee_sqrt(x); - } - return z; - } - if(ix<0x3f200000) { /* |x| < 2**-13 */ - if(huge+x>one) { /* raise inexact if x != 0 */ - if(ix<0x3e400000) return one; /* |x|<2**-27 */ - else return one - 0.25*x*x; - } - } - z = x*x; - r = z*(R02+z*(R03+z*(R04+z*R05))); - s = one+z*(S01+z*(S02+z*(S03+z*S04))); - if(ix < 0x3FF00000) { /* |x| < 1.00 */ - return one + z*(-0.25+(r/s)); - } else { - u = 0.5*x; - return((one+u)*(one-u)+z*(r/s)); - } -} - -#ifdef __STDC__ -static const double -#else -static double -#endif -u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ -u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ -u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ -u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ -u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ -u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ -u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ -v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ -v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ -v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ -v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ - -#ifdef __STDC__ - double __ieee754_y0(double x) -#else - double __ieee754_y0(x) - double x; -#endif -{ - double z, s,c,ss,cc,u,v; - int hx,ix,lx; - - hx = __HI(x); - ix = 0x7fffffff&hx; - lx = __LO(x); - /* Y0(NaN) is NaN, ieee_y0(-inf) is Nan, ieee_y0(inf) is 0 */ - if(ix>=0x7ff00000) return one/(x+x*x); - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - /* ieee_y0(x) = ieee_sqrt(2/(pi*x))*(p0(x)*ieee_sin(x0)+q0(x)*ieee_cos(x0)) - * where x0 = x-pi/4 - * Better formula: - * ieee_cos(x0) = ieee_cos(x)cos(pi/4)+ieee_sin(x)sin(pi/4) - * = 1/ieee_sqrt(2) * (ieee_sin(x) + ieee_cos(x)) - * ieee_sin(x0) = ieee_sin(x)cos(3pi/4)-ieee_cos(x)sin(3pi/4) - * = 1/ieee_sqrt(2) * (ieee_sin(x) - ieee_cos(x)) - * To avoid cancellation, use - * ieee_sin(x) +- ieee_cos(x) = -ieee_cos(2x)/(ieee_sin(x) -+ ieee_cos(x)) - * to compute the worse one. - */ - s = ieee_sin(x); - c = ieee_cos(x); - ss = s-c; - cc = s+c; - /* - * ieee_j0(x) = 1/ieee_sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / ieee_sqrt(x) - * ieee_y0(x) = 1/ieee_sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / ieee_sqrt(x) - */ - if(ix<0x7fe00000) { /* make sure x+x not overflow */ - z = -ieee_cos(x+x); - if ((s*c)0x48000000) z = (invsqrtpi*ss)/ieee_sqrt(x); - else { - u = pzero(x); v = qzero(x); - z = invsqrtpi*(u*ss+v*cc)/ieee_sqrt(x); - } - return z; - } - if(ix<=0x3e400000) { /* x < 2**-27 */ - return(u00 + tpi*__ieee754_log(x)); - } - z = x*x; - u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); - v = one+z*(v01+z*(v02+z*(v03+z*v04))); - return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); -} - -/* The asymptotic expansions of pzero is - * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. - * For x >= 2, We approximate pzero by - * pzero(x) = 1 + (R/S) - * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 - * S = 1 + pS0*s^2 + ... + pS4*s^10 - * and - * | pzero(x)-1-R/S | <= 2 ** ( -60.26) - */ -#ifdef __STDC__ -static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ - -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ - -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ - -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ - -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ -}; -#ifdef __STDC__ -static const double pS8[5] = { -#else -static double pS8[5] = { -#endif - 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ - 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ - 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ - 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ - 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ -}; - -#ifdef __STDC__ -static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ - -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ - -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ - -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ - -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ - -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ -}; -#ifdef __STDC__ -static const double pS5[5] = { -#else -static double pS5[5] = { -#endif - 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ - 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ - 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ - 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ - 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ -}; - -#ifdef __STDC__ -static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#else -static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ - -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ - -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ - -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ - -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ - -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ -}; -#ifdef __STDC__ -static const double pS3[5] = { -#else -static double pS3[5] = { -#endif - 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ - 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ - 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ - 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ - 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ -}; - -#ifdef __STDC__ -static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ - -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ - -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ - -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ - -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ - -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ -}; -#ifdef __STDC__ -static const double pS2[5] = { -#else -static double pS2[5] = { -#endif - 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ - 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ - 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ - 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ - 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ -}; - -#ifdef __STDC__ - static double pzero(double x) -#else - static double pzero(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p,*q; -#else - double *p,*q; -#endif - double z,r,s; - int ix; - ix = 0x7fffffff&__HI(x); - if(ix>=0x40200000) {p = pR8; q= pS8;} - else if(ix>=0x40122E8B){p = pR5; q= pS5;} - else if(ix>=0x4006DB6D){p = pR3; q= pS3;} - else if(ix>=0x40000000){p = pR2; q= pS2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return one+ r/s; -} - - -/* For x >= 8, the asymptotic expansions of qzero is - * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. - * We approximate pzero by - * qzero(x) = s*(-1.25 + (R/S)) - * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 - * S = 1 + qS0*s^2 + ... + qS5*s^12 - * and - * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) - */ -#ifdef __STDC__ -static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ - 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ - 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ - 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ - 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ -}; -#ifdef __STDC__ -static const double qS8[6] = { -#else -static double qS8[6] = { -#endif - 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ - 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ - 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ - 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ - 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ - -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ -}; - -#ifdef __STDC__ -static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ - 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ - 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ - 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ - 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ - 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ -}; -#ifdef __STDC__ -static const double qS5[6] = { -#else -static double qS5[6] = { -#endif - 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ - 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ - 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ - 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ - 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ - -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ -}; - -#ifdef __STDC__ -static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#else -static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ - 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ - 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ - 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ - 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ - 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ -}; -#ifdef __STDC__ -static const double qS3[6] = { -#else -static double qS3[6] = { -#endif - 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ - 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ - 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ - 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ - 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ - -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ -}; - -#ifdef __STDC__ -static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ - 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ - 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ - 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ - 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ - 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ -}; -#ifdef __STDC__ -static const double qS2[6] = { -#else -static double qS2[6] = { -#endif - 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ - 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ - 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ - 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ - 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ - -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ -}; - -#ifdef __STDC__ - static double qzero(double x) -#else - static double qzero(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p,*q; -#else - double *p,*q; -#endif - double s,r,z; - int ix; - ix = 0x7fffffff&__HI(x); - if(ix>=0x40200000) {p = qR8; q= qS8;} - else if(ix>=0x40122E8B){p = qR5; q= qS5;} - else if(ix>=0x4006DB6D){p = qR3; q= qS3;} - else if(ix>=0x40000000){p = qR2; q= qS2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (-.125 + r/s)/x; -} diff --git a/e_j1.c b/e_j1.c deleted file mode 100644 index f8ed85f..0000000 --- a/e_j1.c +++ /dev/null @@ -1,477 +0,0 @@ - -/* @(#)e_j1.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_j1(x), __ieee754_y1(x) - * Bessel function of the first and second kinds of order zero. - * Method -- ieee_j1(x): - * 1. For tiny x, we use ieee_j1(x) = x/2 - x^3/16 + x^5/384 - ... - * 2. Reduce x to |x| since ieee_j1(x)=-ieee_j1(-x), and - * for x in (0,2) - * j1(x) = x/2 + x*z*R0/S0, where z = x*x; - * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) - * for x in (2,inf) - * j1(x) = ieee_sqrt(2/(pi*x))*(p1(x)*ieee_cos(x1)-q1(x)*ieee_sin(x1)) - * y1(x) = ieee_sqrt(2/(pi*x))*(p1(x)*ieee_sin(x1)+q1(x)*ieee_cos(x1)) - * where x1 = x-3*pi/4. It is better to compute ieee_sin(x1),cos(x1) - * as follow: - * cos(x1) = ieee_cos(x)cos(3pi/4)+ieee_sin(x)sin(3pi/4) - * = 1/ieee_sqrt(2) * (ieee_sin(x) - ieee_cos(x)) - * sin(x1) = ieee_sin(x)cos(3pi/4)-ieee_cos(x)sin(3pi/4) - * = -1/ieee_sqrt(2) * (ieee_sin(x) + ieee_cos(x)) - * (To avoid cancellation, use - * sin(x) +- ieee_cos(x) = -ieee_cos(2x)/(ieee_sin(x) -+ ieee_cos(x)) - * to compute the worse one.) - * - * 3 Special cases - * j1(nan)= nan - * j1(0) = 0 - * j1(inf) = 0 - * - * Method -- ieee_y1(x): - * 1. screen out x<=0 cases: ieee_y1(0)=-inf, ieee_y1(x<0)=NaN - * 2. For x<2. - * Since - * y1(x) = 2/pi*(ieee_j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) - * therefore ieee_y1(x)-2/pi*ieee_j1(x)*ln(x)-1/x is an odd function. - * We use the following function to approximate y1, - * y1(x) = x*U(z)/V(z) + (2/pi)*(ieee_j1(x)*ln(x)-1/x), z= x^2 - * where for x in [0,2] (abs err less than 2**-65.89) - * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 - * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 - * Note: For tiny x, 1/x dominate y1 and hence - * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) - * 3. For x>=2. - * y1(x) = ieee_sqrt(2/(pi*x))*(p1(x)*ieee_sin(x1)+q1(x)*ieee_cos(x1)) - * where x1 = x-3*pi/4. It is better to compute ieee_sin(x1),cos(x1) - * by method mentioned above. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static double pone(double), qone(double); -#else -static double pone(), qone(); -#endif - -#ifdef __STDC__ -static const double -#else -static double -#endif -huge = 1e300, -one = 1.0, -invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - /* R0/S0 on [0,2] */ -r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ -r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ -r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ -r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ -s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ -s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ -s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ -s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ -s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ - -static double zero = 0.0; - -#ifdef __STDC__ - double __ieee754_j1(double x) -#else - double __ieee754_j1(x) - double x; -#endif -{ - double z, s,c,ss,cc,r,u,v,y; - int hx,ix; - - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) return one/x; - y = ieee_fabs(x); - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = ieee_sin(y); - c = ieee_cos(y); - ss = -s-c; - cc = s-c; - if(ix<0x7fe00000) { /* make sure y+y not overflow */ - z = ieee_cos(y+y); - if ((s*c)>zero) cc = z/ss; - else ss = z/cc; - } - /* - * ieee_j1(x) = 1/ieee_sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / ieee_sqrt(x) - * ieee_y1(x) = 1/ieee_sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / ieee_sqrt(x) - */ - if(ix>0x48000000) z = (invsqrtpi*cc)/ieee_sqrt(y); - else { - u = pone(y); v = qone(y); - z = invsqrtpi*(u*cc-v*ss)/ieee_sqrt(y); - } - if(hx<0) return -z; - else return z; - } - if(ix<0x3e400000) { /* |x|<2**-27 */ - if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ - } - z = x*x; - r = z*(r00+z*(r01+z*(r02+z*r03))); - s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); - r *= x; - return(x*0.5+r/s); -} - -#ifdef __STDC__ -static const double U0[5] = { -#else -static double U0[5] = { -#endif - -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ - 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ - -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ - 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ - -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ -}; -#ifdef __STDC__ -static const double V0[5] = { -#else -static double V0[5] = { -#endif - 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ - 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ - 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ - 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ - 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ -}; - -#ifdef __STDC__ - double __ieee754_y1(double x) -#else - double __ieee754_y1(x) - double x; -#endif -{ - double z, s,c,ss,cc,u,v; - int hx,ix,lx; - - hx = __HI(x); - ix = 0x7fffffff&hx; - lx = __LO(x); - /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ - if(ix>=0x7ff00000) return one/(x+x*x); - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = ieee_sin(x); - c = ieee_cos(x); - ss = -s-c; - cc = s-c; - if(ix<0x7fe00000) { /* make sure x+x not overflow */ - z = ieee_cos(x+x); - if ((s*c)>zero) cc = z/ss; - else ss = z/cc; - } - /* ieee_y1(x) = ieee_sqrt(2/(pi*x))*(p1(x)*ieee_sin(x0)+q1(x)*ieee_cos(x0)) - * where x0 = x-3pi/4 - * Better formula: - * ieee_cos(x0) = ieee_cos(x)cos(3pi/4)+ieee_sin(x)sin(3pi/4) - * = 1/ieee_sqrt(2) * (ieee_sin(x) - ieee_cos(x)) - * ieee_sin(x0) = ieee_sin(x)cos(3pi/4)-ieee_cos(x)sin(3pi/4) - * = -1/ieee_sqrt(2) * (ieee_cos(x) + ieee_sin(x)) - * To avoid cancellation, use - * ieee_sin(x) +- ieee_cos(x) = -ieee_cos(2x)/(ieee_sin(x) -+ ieee_cos(x)) - * to compute the worse one. - */ - if(ix>0x48000000) z = (invsqrtpi*ss)/ieee_sqrt(x); - else { - u = pone(x); v = qone(x); - z = invsqrtpi*(u*ss+v*cc)/ieee_sqrt(x); - } - return z; - } - if(ix<=0x3c900000) { /* x < 2**-54 */ - return(-tpi/x); - } - z = x*x; - u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); - v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); - return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); -} - -/* For x >= 8, the asymptotic expansions of pone is - * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. - * We approximate pone by - * pone(x) = 1 + (R/S) - * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 - * S = 1 + ps0*s^2 + ... + ps4*s^10 - * and - * | pone(x)-1-R/S | <= 2 ** ( -60.06) - */ - -#ifdef __STDC__ -static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ - 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ - 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ - 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ - 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ -}; -#ifdef __STDC__ -static const double ps8[5] = { -#else -static double ps8[5] = { -#endif - 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ - 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ - 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ - 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ - 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ -}; - -#ifdef __STDC__ -static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ - 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ - 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ - 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ - 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ - 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ -}; -#ifdef __STDC__ -static const double ps5[5] = { -#else -static double ps5[5] = { -#endif - 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ - 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ - 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ - 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ - 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ -}; - -#ifdef __STDC__ -static const double pr3[6] = { -#else -static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ - 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ - 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ - 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ - 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ - 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ -}; -#ifdef __STDC__ -static const double ps3[5] = { -#else -static double ps3[5] = { -#endif - 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ - 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ - 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ - 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ - 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ -}; - -#ifdef __STDC__ -static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ - 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ - 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ - 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ - 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ - 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ -}; -#ifdef __STDC__ -static const double ps2[5] = { -#else -static double ps2[5] = { -#endif - 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ - 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ - 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ - 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ - 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ -}; - -#ifdef __STDC__ - static double pone(double x) -#else - static double pone(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p,*q; -#else - double *p,*q; -#endif - double z,r,s; - int ix; - ix = 0x7fffffff&__HI(x); - if(ix>=0x40200000) {p = pr8; q= ps8;} - else if(ix>=0x40122E8B){p = pr5; q= ps5;} - else if(ix>=0x4006DB6D){p = pr3; q= ps3;} - else if(ix>=0x40000000){p = pr2; q= ps2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return one+ r/s; -} - - -/* For x >= 8, the asymptotic expansions of qone is - * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. - * We approximate pone by - * qone(x) = s*(0.375 + (R/S)) - * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 - * S = 1 + qs1*s^2 + ... + qs6*s^12 - * and - * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) - */ - -#ifdef __STDC__ -static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ - -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ - -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ - -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ - -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ -}; -#ifdef __STDC__ -static const double qs8[6] = { -#else -static double qs8[6] = { -#endif - 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ - 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ - 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ - 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ - 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ - -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ -}; - -#ifdef __STDC__ -static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ - -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ - -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ - -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ - -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ - -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ -}; -#ifdef __STDC__ -static const double qs5[6] = { -#else -static double qs5[6] = { -#endif - 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ - 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ - 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ - 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ - 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ - -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ -}; - -#ifdef __STDC__ -static const double qr3[6] = { -#else -static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ - -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ - -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ - -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ - -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ - -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ -}; -#ifdef __STDC__ -static const double qs3[6] = { -#else -static double qs3[6] = { -#endif - 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ - 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ - 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ - 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ - 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ - -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ -}; - -#ifdef __STDC__ -static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ - -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ - -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ - -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ - -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ - -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ -}; -#ifdef __STDC__ -static const double qs2[6] = { -#else -static double qs2[6] = { -#endif - 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ - 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ - 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ - 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ - 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ - -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ -}; - -#ifdef __STDC__ - static double qone(double x) -#else - static double qone(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p,*q; -#else - double *p,*q; -#endif - double s,r,z; - int ix; - ix = 0x7fffffff&__HI(x); - if(ix>=0x40200000) {p = qr8; q= qs8;} - else if(ix>=0x40122E8B){p = qr5; q= qs5;} - else if(ix>=0x4006DB6D){p = qr3; q= qs3;} - else if(ix>=0x40000000){p = qr2; q= qs2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (.375 + r/s)/x; -} diff --git a/e_jn.c b/e_jn.c deleted file mode 100644 index 782bda3..0000000 --- a/e_jn.c +++ /dev/null @@ -1,272 +0,0 @@ - -/* @(#)e_jn.c 1.4 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * __ieee754_jn(n, x), __ieee754_yn(n, x) - * floating point Bessel's function of the 1st and 2nd kind - * of order n - * - * Special cases: - * y0(0)=ieee_y1(0)=ieee_yn(n,0) = -inf with division by zero signal; - * y0(-ve)=ieee_y1(-ve)=ieee_yn(n,-ve) are NaN with invalid signal. - * Note 2. About ieee_jn(n,x), ieee_yn(n,x) - * For n=0, ieee_j0(x) is called, - * for n=1, ieee_j1(x) is called, - * for nx, a continued fraction approximation to - * j(n,x)/j(n-1,x) is evaluated and then backward - * recursion is used starting from a supposed value - * for j(n,x). The resulting value of j(0,x) is - * compared with the actual value to correct the - * supposed value of j(n,x). - * - * yn(n,x) is similar in all respects, except - * that forward recursion is used for all - * values of n>1. - * - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ -one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ - -static double zero = 0.00000000000000000000e+00; - -#ifdef __STDC__ - double __ieee754_jn(int n, double x) -#else - double __ieee754_jn(n,x) - int n; double x; -#endif -{ - int i,hx,ix,lx, sgn; - double a, b, temp, di; - double z, w; - - /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) - * Thus, J(-n,x) = J(n,-x) - */ - hx = __HI(x); - ix = 0x7fffffff&hx; - lx = __LO(x); - /* if J(n,NaN) is NaN */ - if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x; - if(n<0){ - n = -n; - x = -x; - hx ^= 0x80000000; - } - if(n==0) return(__ieee754_j0(x)); - if(n==1) return(__ieee754_j1(x)); - sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ - x = ieee_fabs(x); - if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ - b = zero; - else if((double)n<=x) { - /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ - if(ix>=0x52D00000) { /* x > 2**302 */ - /* (x >> n**2) - * Jn(x) = ieee_cos(x-(2n+1)*pi/4)*ieee_sqrt(2/x*pi) - * Yn(x) = ieee_sin(x-(2n+1)*pi/4)*ieee_sqrt(2/x*pi) - * Let s=ieee_sin(x), c=ieee_cos(x), - * xn=x-(2n+1)*pi/4, sqt2 = ieee_sqrt(2),then - * - * n sin(xn)*sqt2 cos(xn)*sqt2 - * ---------------------------------- - * 0 s-c c+s - * 1 -s-c -c+s - * 2 -s+c -c-s - * 3 s+c c-s - */ - switch(n&3) { - case 0: temp = ieee_cos(x)+ieee_sin(x); break; - case 1: temp = -ieee_cos(x)+ieee_sin(x); break; - case 2: temp = -ieee_cos(x)-ieee_sin(x); break; - case 3: temp = ieee_cos(x)-ieee_sin(x); break; - } - b = invsqrtpi*temp/ieee_sqrt(x); - } else { - a = __ieee754_j0(x); - b = __ieee754_j1(x); - for(i=1;i33) /* underflow */ - b = zero; - else { - temp = x*0.5; b = temp; - for (a=one,i=2;i<=n;i++) { - a *= (double)i; /* a = n! */ - b *= temp; /* b = (x/2)^n */ - } - b = b/a; - } - } else { - /* use backward recurrence */ - /* x x^2 x^2 - * J(n,x)/J(n-1,x) = ---- ------ ------ ..... - * 2n - 2(n+1) - 2(n+2) - * - * 1 1 1 - * (for large x) = ---- ------ ------ ..... - * 2n 2(n+1) 2(n+2) - * -- - ------ - ------ - - * x x x - * - * Let w = 2n/x and h=2/x, then the above quotient - * is equal to the continued fraction: - * 1 - * = ----------------------- - * 1 - * w - ----------------- - * 1 - * w+h - --------- - * w+2h - ... - * - * To determine how many terms needed, let - * Q(0) = w, Q(1) = w(w+h) - 1, - * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), - * When Q(k) > 1e4 good for single - * When Q(k) > 1e9 good for double - * When Q(k) > 1e17 good for quadruple - */ - /* determine k */ - double t,v; - double q0,q1,h,tmp; int k,m; - w = (n+n)/(double)x; h = 2.0/(double)x; - q0 = w; z = w+h; q1 = w*z - 1.0; k=1; - while(q1<1.0e9) { - k += 1; z += h; - tmp = z*q1 - q0; - q0 = q1; - q1 = tmp; - } - m = n+n; - for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); - a = t; - b = one; - /* estimate ieee_log((2/x)^n*n!) = n*ieee_log(2/x)+n*ln(n) - * Hence, if n*(ieee_log(2n/x)) > ... - * single 8.8722839355e+01 - * double 7.09782712893383973096e+02 - * long double 1.1356523406294143949491931077970765006170e+04 - * then recurrent value may overflow and the result is - * likely underflow to zero - */ - tmp = n; - v = two/x; - tmp = tmp*__ieee754_log(ieee_fabs(v*tmp)); - if(tmp<7.09782712893383973096e+02) { - for(i=n-1,di=(double)(i+i);i>0;i--){ - temp = b; - b *= di; - b = b/x - a; - a = temp; - di -= two; - } - } else { - for(i=n-1,di=(double)(i+i);i>0;i--){ - temp = b; - b *= di; - b = b/x - a; - a = temp; - di -= two; - /* scale b to avoid spurious overflow */ - if(b>1e100) { - a /= b; - t /= b; - b = one; - } - } - } - b = (t*__ieee754_j0(x)/b); - } - } - if(sgn==1) return -b; else return b; -} - -#ifdef __STDC__ - double __ieee754_yn(int n, double x) -#else - double __ieee754_yn(n,x) - int n; double x; -#endif -{ - int i,hx,ix,lx; - int sign; - double a, b, temp; - - hx = __HI(x); - ix = 0x7fffffff&hx; - lx = __LO(x); - /* if Y(n,NaN) is NaN */ - if((ix|((unsigned)(lx|-lx))>>31)>0x7ff00000) return x+x; - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; - sign = 1; - if(n<0){ - n = -n; - sign = 1 - ((n&1)<<1); - } - if(n==0) return(__ieee754_y0(x)); - if(n==1) return(sign*__ieee754_y1(x)); - if(ix==0x7ff00000) return zero; - if(ix>=0x52D00000) { /* x > 2**302 */ - /* (x >> n**2) - * Jn(x) = ieee_cos(x-(2n+1)*pi/4)*ieee_sqrt(2/x*pi) - * Yn(x) = ieee_sin(x-(2n+1)*pi/4)*ieee_sqrt(2/x*pi) - * Let s=ieee_sin(x), c=ieee_cos(x), - * xn=x-(2n+1)*pi/4, sqt2 = ieee_sqrt(2),then - * - * n sin(xn)*sqt2 cos(xn)*sqt2 - * ---------------------------------- - * 0 s-c c+s - * 1 -s-c -c+s - * 2 -s+c -c-s - * 3 s+c c-s - */ - switch(n&3) { - case 0: temp = ieee_sin(x)-ieee_cos(x); break; - case 1: temp = -ieee_sin(x)-ieee_cos(x); break; - case 2: temp = -ieee_sin(x)+ieee_cos(x); break; - case 3: temp = ieee_sin(x)+ieee_cos(x); break; - } - b = invsqrtpi*temp/ieee_sqrt(x); - } else { - a = __ieee754_y0(x); - b = __ieee754_y1(x); - /* quit if b is -inf */ - for(i=1;i0) return b; else return -b; -} diff --git a/e_lgamma.c b/e_lgamma.c deleted file mode 100644 index 91677d6..0000000 --- a/e_lgamma.c +++ /dev/null @@ -1,33 +0,0 @@ - -/* @(#)e_lgamma.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* __ieee754_lgamma(x) - * Return the logarithm of the Gamma function of x. - * - * Method: call __ieee754_lgamma_r - */ - -#include "fdlibm.h" - -extern int signgam; - -#ifdef __STDC__ - double __ieee754_lgamma(double x) -#else - double __ieee754_lgamma(x) - double x; -#endif -{ - return __ieee754_lgamma_r(x,&signgam); -} diff --git a/e_lgamma_r.c b/e_lgamma_r.c deleted file mode 100644 index 42c1ebb..0000000 --- a/e_lgamma_r.c +++ /dev/null @@ -1,304 +0,0 @@ - -/* @(#)e_lgamma_r.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* __ieee754_lgamma_r(x, signgamp) - * Reentrant version of the logarithm of the Gamma function - * with user provide pointer for the sign of Gamma(x). - * - * Method: - * 1. Argument Reduction for 0 < x <= 8 - * Since ieee_gamma(1+s)=s*ieee_gamma(s), for x in [0,8], we may - * reduce x to a number in [1.5,2.5] by - * lgamma(1+s) = ieee_log(s) + ieee_lgamma(s) - * for example, - * lgamma(7.3) = ieee_log(6.3) + ieee_lgamma(6.3) - * = ieee_log(6.3*5.3) + ieee_lgamma(5.3) - * = ieee_log(6.3*5.3*4.3*3.3*2.3) + ieee_lgamma(2.3) - * 2. Polynomial approximation of lgamma around its - * minimun ymin=1.461632144968362245 to maintain monotonicity. - * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use - * Let z = x-ymin; - * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) - * where - * poly(z) is a 14 degree polynomial. - * 2. Rational approximation in the primary interval [2,3] - * We use the following approximation: - * s = x-2.0; - * lgamma(x) = 0.5*s + s*P(s)/Q(s) - * with accuracy - * |P/Q - (ieee_lgamma(x)-0.5s)| < 2**-61.71 - * Our algorithms are based on the following observation - * - * zeta(2)-1 2 zeta(3)-1 3 - * ieee_lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... - * 2 3 - * - * where Euler = 0.5771... is the Euler constant, which is very - * close to 0.5. - * - * 3. For x>=8, we have - * lgamma(x)~(x-0.5)log(x)-x+0.5*ieee_log(2pi)+1/(12x)-1/(360x**3)+.... - * (better formula: - * ieee_lgamma(x)~(x-0.5)*(ieee_log(x)-1)-.5*(ieee_log(2pi)-1) + ...) - * Let z = 1/x, then we approximation - * f(z) = ieee_lgamma(x) - (x-0.5)(ieee_log(x)-1) - * by - * 3 5 11 - * w = w0 + w1*z + w2*z + w3*z + ... + w6*z - * where - * |w - f(z)| < 2**-58.74 - * - * 4. For negative x, since (G is gamma function) - * -x*G(-x)*G(x) = pi/ieee_sin(pi*x), - * we have - * G(x) = pi/(ieee_sin(pi*x)*(-x)*G(-x)) - * since G(-x) is positive, sign(G(x)) = sign(ieee_sin(pi*x)) for x<0 - * Hence, for x<0, signgam = sign(ieee_sin(pi*x)) and - * lgamma(x) = ieee_log(|Gamma(x)|) - * = ieee_log(pi/(|x*ieee_sin(pi*x)|)) - ieee_lgamma(-x); - * Note: one should avoid compute pi*(-x) directly in the - * computation of ieee_sin(pi*(-x)). - * - * 5. Special Cases - * lgamma(2+s) ~ s*(1-Euler) for tiny s - * lgamma(1)=ieee_lgamma(2)=0 - * lgamma(x) ~ -ieee_log(x) for tiny x - * lgamma(0) = ieee_lgamma(inf) = inf - * lgamma(-integer) = +-inf - * - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ -half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ -a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ -a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ -a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ -a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ -a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ -a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ -a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ -a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ -a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ -a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ -a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ -a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ -tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ -tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ -/* tt = -(tail of tf) */ -tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ -t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ -t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ -t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ -t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ -t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ -t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ -t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ -t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ -t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ -t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ -t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ -t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ -t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ -t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ -t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ -u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ -u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ -u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ -u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ -u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ -u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ -v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ -v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ -v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ -v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ -v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ -s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ -s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ -s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ -s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ -s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ -s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ -s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ -r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ -r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ -r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ -r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ -r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ -r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ -w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ -w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ -w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ -w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ -w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ -w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ -w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ - -static double zero= 0.00000000000000000000e+00; - -#ifdef __STDC__ - static double sin_pi(double x) -#else - static double sin_pi(x) - double x; -#endif -{ - double y,z; - int n,ix; - - ix = 0x7fffffff&__HI(x); - - if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); - y = -x; /* x is assume negative */ - - /* - * argument reduction, make sure inexact flag not raised if input - * is an integer - */ - z = ieee_floor(y); - if(z!=y) { /* inexact anyway */ - y *= 0.5; - y = 2.0*(y - ieee_floor(y)); /* y = |x| mod 2.0 */ - n = (int) (y*4.0); - } else { - if(ix>=0x43400000) { - y = zero; n = 0; /* y must be even */ - } else { - if(ix<0x43300000) z = y+two52; /* exact */ - n = __LO(z)&1; /* lower word of z */ - y = n; - n<<= 2; - } - } - switch (n) { - case 0: y = __kernel_sin(pi*y,zero,0); break; - case 1: - case 2: y = __kernel_cos(pi*(0.5-y),zero); break; - case 3: - case 4: y = __kernel_sin(pi*(one-y),zero,0); break; - case 5: - case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; - default: y = __kernel_sin(pi*(y-2.0),zero,0); break; - } - return -y; -} - - -#ifdef __STDC__ - double __ieee754_lgamma_r(double x, int *signgamp) -#else - double __ieee754_lgamma_r(x,signgamp) - double x; int *signgamp; -#endif -{ - double t,y,z,nadj,p,p1,p2,p3,q,r,w; - int i,hx,lx,ix; - - hx = __HI(x); - lx = __LO(x); - - /* purge off +-inf, NaN, +-0, and negative arguments */ - *signgamp = 1; - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) return x*x; - if((ix|lx)==0) return one/zero; - if(ix<0x3b900000) { /* |x|<2**-70, return -ieee_log(|x|) */ - if(hx<0) { - *signgamp = -1; - return -__ieee754_log(-x); - } else return -__ieee754_log(x); - } - if(hx<0) { - if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ - return one/zero; - t = sin_pi(x); - if(t==zero) return one/zero; /* -integer */ - nadj = __ieee754_log(pi/ieee_fabs(t*x)); - if(t=0x3FE76944) {y = one-x; i= 0;} - else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} - else {y = x; i=2;} - } else { - r = zero; - if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ - else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ - else {y=x-one;i=2;} - } - switch(i) { - case 0: - z = y*y; - p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); - p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); - p = y*p1+p2; - r += (p-0.5*y); break; - case 1: - z = y*y; - w = z*y; - p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ - p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); - p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); - p = z*p1-(tt-w*(p2+y*p3)); - r += (tf + p); break; - case 2: - p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); - p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); - r += (-0.5*y + p1/p2); - } - } - else if(ix<0x40200000) { /* x < 8.0 */ - i = (int)x; - t = zero; - y = x-(double)i; - p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); - q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); - r = half*y+p/q; - z = one; /* ieee_lgamma(1+s) = ieee_log(s) + ieee_lgamma(s) */ - switch(i) { - case 7: z *= (y+6.0); /* FALLTHRU */ - case 6: z *= (y+5.0); /* FALLTHRU */ - case 5: z *= (y+4.0); /* FALLTHRU */ - case 4: z *= (y+3.0); /* FALLTHRU */ - case 3: z *= (y+2.0); /* FALLTHRU */ - r += __ieee754_log(z); break; - } - /* 8.0 <= x < 2**58 */ - } else if (ix < 0x43900000) { - t = __ieee754_log(x); - z = one/x; - y = z*z; - w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); - r = (x-half)*(t-one)+w; - } else - /* 2**58 <= x <= inf */ - r = x*(__ieee754_log(x)-one); - if(hx<0) r = nadj - r; - return r; -} diff --git a/e_log.c b/e_log.c deleted file mode 100644 index 13c14c8..0000000 --- a/e_log.c +++ /dev/null @@ -1,139 +0,0 @@ - -/* @(#)e_log.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_log(x) - * Return the logrithm of x - * - * Method : - * 1. Argument Reduction: find k and f such that - * x = 2^k * (1+f), - * where ieee_sqrt(2)/2 < 1+f < ieee_sqrt(2) . - * - * 2. Approximation of ieee_log(1+f). - * Let s = f/(2+f) ; based on ieee_log(1+f) = ieee_log(1+s) - ieee_log(1-s) - * = 2s + 2/3 s**3 + 2/5 s**5 + ....., - * = 2s + s*R - * We use a special Reme algorithm on [0,0.1716] to generate - * a polynomial of degree 14 to approximate R The maximum error - * of this polynomial approximation is bounded by 2**-58.45. In - * other words, - * 2 4 6 8 10 12 14 - * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s - * (the values of Lg1 to Lg7 are listed in the program) - * and - * | 2 14 | -58.45 - * | Lg1*s +...+Lg7*s - R(z) | <= 2 - * | | - * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. - * In order to guarantee error in log below 1ulp, we compute log - * by - * log(1+f) = f - s*(f - R) (if f is not too large) - * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) - * - * 3. Finally, ieee_log(x) = k*ln2 + ieee_log(1+f). - * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) - * Here ln2 is split into two floating point number: - * ln2_hi + ln2_lo, - * where n*ln2_hi is always exact for |n| < 2000. - * - * Special cases: - * log(x) is NaN with signal if x < 0 (including -INF) ; - * log(+INF) is +INF; ieee_log(0) is -INF with signal; - * log(NaN) is that NaN with no signal. - * - * Accuracy: - * according to an error analysis, the error is always less than - * 1 ulp (unit in the last place). - * - * 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 "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ -ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ -two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ -Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ -Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ -Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ -Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ -Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ -Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ -Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ - -static double zero = 0.0; - -#ifdef __STDC__ - double __ieee754_log(double x) -#else - double __ieee754_log(x) - double x; -#endif -{ - double hfsq,f,s,z,R,w,t1,t2,dk; - int k,hx,i,j; - unsigned lx; - - hx = __HI(x); /* high word of x */ - lx = __LO(x); /* low word of x */ - - k=0; - if (hx < 0x00100000) { /* x < 2**-1022 */ - if (((hx&0x7fffffff)|lx)==0) - return -two54/zero; /* ieee_log(+-0)=-inf */ - if (hx<0) return (x-x)/zero; /* ieee_log(-#) = NaN */ - k -= 54; x *= two54; /* subnormal number, scale up x */ - hx = __HI(x); /* high word of x */ - } - if (hx >= 0x7ff00000) return x+x; - k += (hx>>20)-1023; - hx &= 0x000fffff; - i = (hx+0x95f64)&0x100000; - __HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */ - k += (i>>20); - f = x-1.0; - if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ - if(f==zero) if(k==0) return zero; else {dk=(double)k; - return dk*ln2_hi+dk*ln2_lo;} - R = f*f*(0.5-0.33333333333333333*f); - if(k==0) return f-R; else {dk=(double)k; - return dk*ln2_hi-((R-dk*ln2_lo)-f);} - } - s = f/(2.0+f); - dk = (double)k; - z = s*s; - i = hx-0x6147a; - w = z*z; - j = 0x6b851-hx; - t1= w*(Lg2+w*(Lg4+w*Lg6)); - t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); - i |= j; - R = t2+t1; - if(i>0) { - hfsq=0.5*f*f; - if(k==0) return f-(hfsq-s*(hfsq+R)); else - return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); - } else { - if(k==0) return f-s*(f-R); else - return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); - } -} diff --git a/e_log10.c b/e_log10.c deleted file mode 100644 index 1a705f2..0000000 --- a/e_log10.c +++ /dev/null @@ -1,91 +0,0 @@ - -/* @(#)e_log10.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_log10(x) - * Return the base 10 logarithm of x - * - * Method : - * Let log10_2hi = leading 40 bits of ieee_log10(2) and - * log10_2lo = ieee_log10(2) - log10_2hi, - * ivln10 = 1/ieee_log(10) rounded. - * Then - * n = ieee_ilogb(x), - * if(n<0) n = n+1; - * x = ieee_scalbn(x,-n); - * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*ieee_log(x)) - * - * Note 1: - * To guarantee ieee_log10(10**n)=n, where 10**n is normal, the rounding - * mode must set to Round-to-Nearest. - * Note 2: - * [1/ieee_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; ieee_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 "fdlibm.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 */ - -static double zero = 0.0; - -#ifdef __STDC__ - double __ieee754_log10(double x) -#else - double __ieee754_log10(x) - double x; -#endif -{ - double y,z; - int i,k,hx; - unsigned lx; - - hx = __HI(x); /* high word of x */ - lx = __LO(x); /* low word of x */ - - k=0; - if (hx < 0x00100000) { /* x < 2**-1022 */ - if (((hx&0x7fffffff)|lx)==0) - return -two54/zero; /* ieee_log(+-0)=-inf */ - if (hx<0) return (x-x)/zero; /* ieee_log(-#) = NaN */ - k -= 54; x *= two54; /* subnormal number, scale up x */ - hx = __HI(x); /* high word of x */ - } - if (hx >= 0x7ff00000) return x+x; - k += (hx>>20)-1023; - i = ((unsigned)k&0x80000000)>>31; - hx = (hx&0x000fffff)|((0x3ff-i)<<20); - y = (double)(k+i); - __HI(x) = hx; - z = y*log10_2lo + ivln10*__ieee754_log(x); - return z+y*log10_2hi; -} diff --git a/e_pow.c b/e_pow.c deleted file mode 100644 index 808d53f..0000000 --- a/e_pow.c +++ /dev/null @@ -1,309 +0,0 @@ - -#ifndef lint -static char sccsid[] = "@(#)e_pow.c 1.5 04/04/22 SMI"; -#endif - -/* - * ==================================================== - * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_pow(x,y) return x**y - * - * n - * Method: Let x = 2 * (1+f) - * 1. Compute and return log2(x) in two pieces: - * log2(x) = w1 + w2, - * where w1 has 53-24 = 29 bit trailing zeros. - * 2. Perform y*log2(x) = n+y' by simulating muti-precision - * arithmetic, where |y'|<=0.5. - * 3. Return x**y = 2**n*ieee_exp(y'*log2) - * - * Special cases: - * 1. (anything) ** 0 is 1 - * 2. (anything) ** 1 is itself - * 3. (anything) ** NAN is NAN - * 4. NAN ** (anything except 0) is NAN - * 5. +-(|x| > 1) ** +INF is +INF - * 6. +-(|x| > 1) ** -INF is +0 - * 7. +-(|x| < 1) ** +INF is +0 - * 8. +-(|x| < 1) ** -INF is +INF - * 9. +-1 ** +-INF is NAN - * 10. +0 ** (+anything except 0, NAN) is +0 - * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 - * 12. +0 ** (-anything except 0, NAN) is +INF - * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF - * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) - * 15. +INF ** (+anything except 0,NAN) is +INF - * 16. +INF ** (-anything except 0,NAN) is +0 - * 17. -INF ** (anything) = -0 ** (-anything) - * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) - * 19. (-anything except 0 and inf) ** (non-integer) is NAN - * - * Accuracy: - * pow(x,y) returns x**y nearly rounded. In particular - * pow(integer,integer) - * always returns the correct integer provided it is - * representable. - * - * 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 "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -bp[] = {1.0, 1.5,}, -dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ -dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ -zero = 0.0, -one = 1.0, -two = 2.0, -two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ -huge = 1.0e300, -tiny = 1.0e-300, - /* poly coefs for (3/2)*(ieee_log(x)-2s-2/3*s**3 */ -L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ -L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ -L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ -L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ -L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ -L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ -P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ -P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ -P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ -P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ -P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ -lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ -lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ -lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ -ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ -cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ -cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ -cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ -ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ -ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ -ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ - -#ifdef __STDC__ - double __ieee754_pow(double x, double y) -#else - double __ieee754_pow(x,y) - double x, y; -#endif -{ - double z,ax,z_h,z_l,p_h,p_l; - double y1,t1,t2,r,s,t,u,v,w; - int i0,i1,i,j,k,yisint,n; - int hx,hy,ix,iy; - unsigned lx,ly; - - i0 = ((*(int*)&one)>>29)^1; i1=1-i0; - hx = __HI(x); lx = __LO(x); - hy = __HI(y); ly = __LO(y); - ix = hx&0x7fffffff; iy = hy&0x7fffffff; - - /* y==zero: x**0 = 1 */ - if((iy|ly)==0) return one; - - /* +-NaN return x+y */ - if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || - iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) - return x+y; - - /* determine if y is an odd int when x < 0 - * yisint = 0 ... y is not an integer - * yisint = 1 ... y is an odd int - * yisint = 2 ... y is an even int - */ - yisint = 0; - if(hx<0) { - if(iy>=0x43400000) yisint = 2; /* even integer y */ - else if(iy>=0x3ff00000) { - k = (iy>>20)-0x3ff; /* exponent */ - if(k>20) { - j = ly>>(52-k); - if((j<<(52-k))==ly) yisint = 2-(j&1); - } else if(ly==0) { - j = iy>>(20-k); - if((j<<(20-k))==iy) yisint = 2-(j&1); - } - } - } - - /* special value of y */ - if(ly==0) { - if (iy==0x7ff00000) { /* y is +-inf */ - if(((ix-0x3ff00000)|lx)==0) - return y - y; /* inf**+-1 is NaN */ - else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ - return (hy>=0)? y: zero; - else /* (|x|<1)**-,+inf = inf,0 */ - return (hy<0)?-y: zero; - } - if(iy==0x3ff00000) { /* y is +-1 */ - if(hy<0) return one/x; else return x; - } - if(hy==0x40000000) return x*x; /* y is 2 */ - if(hy==0x3fe00000) { /* y is 0.5 */ - if(hx>=0) /* x >= +0 */ - return ieee_sqrt(x); - } - } - - ax = ieee_fabs(x); - /* special value of x */ - if(lx==0) { - if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ - z = ax; /*x is +-0,+-inf,+-1*/ - if(hy<0) z = one/z; /* z = (1/|x|) */ - if(hx<0) { - if(((ix-0x3ff00000)|yisint)==0) { - z = (z-z)/(z-z); /* (-1)**non-int is NaN */ - } else if(yisint==1) - z = -z; /* (x<0)**odd = -(|x|**odd) */ - } - return z; - } - } - - n = (hx>>31)+1; - - /* (x<0)**(non-int) is NaN */ - if((n|yisint)==0) return (x-x)/(x-x); - - s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ - if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ - - /* |y| is huge */ - if(iy>0x41e00000) { /* if |y| > 2**31 */ - if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ - if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; - if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; - } - /* over/underflow if x is not close to one */ - if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny; - if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny; - /* now |1-x| is tiny <= 2**-20, suffice to compute - ieee_log(x) by x-x^2/2+x^3/3-x^4/4 */ - t = ax-one; /* t has 20 trailing zeros */ - w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); - u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ - v = t*ivln2_l-w*ivln2; - t1 = u+v; - __LO(t1) = 0; - t2 = v-(t1-u); - } else { - double ss,s2,s_h,s_l,t_h,t_l; - n = 0; - /* take care subnormal number */ - if(ix<0x00100000) - {ax *= two53; n -= 53; ix = __HI(ax); } - n += ((ix)>>20)-0x3ff; - j = ix&0x000fffff; - /* determine interval */ - ix = j|0x3ff00000; /* normalize ix */ - if(j<=0x3988E) k=0; /* |x|>1)|0x20000000)+0x00080000+(k<<18); - t_l = ax - (t_h-bp[k]); - s_l = v*((u-s_h*t_h)-s_h*t_l); - /* compute ieee_log(ax) */ - s2 = ss*ss; - r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); - r += s_l*(s_h+ss); - s2 = s_h*s_h; - t_h = 3.0+s2+r; - __LO(t_h) = 0; - t_l = r-((t_h-3.0)-s2); - /* u+v = ss*(1+...) */ - u = s_h*t_h; - v = s_l*t_h+t_l*ss; - /* 2/(3log2)*(ss+...) */ - p_h = u+v; - __LO(p_h) = 0; - p_l = v-(p_h-u); - z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ - z_l = cp_l*p_h+p_l*cp+dp_l[k]; - /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ - t = (double)n; - t1 = (((z_h+z_l)+dp_h[k])+t); - __LO(t1) = 0; - t2 = z_l-(((t1-t)-dp_h[k])-z_h); - } - - /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ - y1 = y; - __LO(y1) = 0; - p_l = (y-y1)*t1+y*t2; - p_h = y1*t1; - z = p_l+p_h; - j = __HI(z); - i = __LO(z); - if (j>=0x40900000) { /* z >= 1024 */ - if(((j-0x40900000)|i)!=0) /* if z > 1024 */ - return s*huge*huge; /* overflow */ - else { - if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ - } - } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ - if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ - return s*tiny*tiny; /* underflow */ - else { - if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ - } - } - /* - * compute 2**(p_h+p_l) - */ - i = j&0x7fffffff; - k = (i>>20)-0x3ff; - n = 0; - if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ - n = j+(0x00100000>>(k+1)); - k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ - t = zero; - __HI(t) = (n&~(0x000fffff>>k)); - n = ((n&0x000fffff)|0x00100000)>>(20-k); - if(j<0) n = -n; - p_h -= t; - } - t = p_l+p_h; - __LO(t) = 0; - u = t*lg2_h; - v = (p_l-(t-p_h))*lg2+t*lg2_l; - z = u+v; - w = v-(z-u); - t = z*z; - t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); - r = (z*t1)/(t1-two)-(w+z*w); - z = one-(r-z); - j = __HI(z); - j += (n<<20); - if((j>>20)<=0) z = ieee_scalbn(z,n); /* subnormal output */ - else __HI(z) += (n<<20); - return s*z; -} diff --git a/e_rem_pio2.c b/e_rem_pio2.c deleted file mode 100644 index 42f14f8..0000000 --- a/e_rem_pio2.c +++ /dev/null @@ -1,175 +0,0 @@ - -/* @(#)e_rem_pio2.c 1.4 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* __ieee754_rem_pio2(x,y) - * - * return the remainder of x rem pi/2 in y[0]+y[1] - * use __kernel_rem_pio2() - */ - -#include "fdlibm.h" - -/* - * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi - */ -#ifdef __STDC__ -static const int two_over_pi[] = { -#else -static int 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 int npio2_hw[] = { -#else -static int 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__ - int __ieee754_rem_pio2(double x, double *y) -#else - int __ieee754_rem_pio2(x,y) - double x,y[]; -#endif -{ - double z,w,t,r,fn; - double tx[3]; - int e0,i,j,nx,n,ix,hx; - - hx = __HI(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 = ieee_fabs(x); - n = (int) (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 { - j = ix>>20; - y[0] = r-w; - i = j-(((__HI(y[0]))>>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; - i = j-(((__HI(y[0]))>>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 = ieee_scalbn(|x|,ilogb(x)-23) */ - __LO(z) = __LO(x); - e0 = (ix>>20)-1046; /* e0 = ieee_ilogb(z)-23; */ - __HI(z) = ix - (e0<<20); - for(i=0;i<2;i++) { - tx[i] = (double)((int)(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; -} diff --git a/e_remainder.c b/e_remainder.c deleted file mode 100644 index 6de2135..0000000 --- a/e_remainder.c +++ /dev/null @@ -1,77 +0,0 @@ - -/* @(#)e_remainder.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_remainder(x,p) - * Return : - * returns x REM p = x - [x/p]*p as if in infinite - * precise arithmetic, where [x/p] is the (infinite bit) - * integer nearest x/p (in half way case choose the even one). - * Method : - * Based on ieee_fmod() return x-[x/p]chopped*p exactlp. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double zero = 0.0; -#else -static double zero = 0.0; -#endif - - -#ifdef __STDC__ - double __ieee754_remainder(double x, double p) -#else - double __ieee754_remainder(x,p) - double x,p; -#endif -{ - int hx,hp; - unsigned sx,lx,lp; - double p_half; - - hx = __HI(x); /* high word of x */ - lx = __LO(x); /* low word of x */ - hp = __HI(p); /* high word of p */ - lp = __LO(p); /* low word of p */ - sx = hx&0x80000000; - hp &= 0x7fffffff; - hx &= 0x7fffffff; - - /* purge off exception values */ - if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ - if((hx>=0x7ff00000)|| /* x not finite */ - ((hp>=0x7ff00000)&& /* p is NaN */ - (((hp-0x7ff00000)|lp)!=0))) - return (x*p)/(x*p); - - - if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */ - if (((hx-hp)|(lx-lp))==0) return zero*x; - x = ieee_fabs(x); - p = ieee_fabs(p); - if (hp<0x00200000) { - if(x+x>p) { - x-=p; - if(x+x>=p) x -= p; - } - } else { - p_half = 0.5*p; - if(x>p_half) { - x-=p; - if(x>=p_half) x -= p; - } - } - __HI(x) ^= sx; - return x; -} diff --git a/e_scalb.c b/e_scalb.c deleted file mode 100644 index f7f77c2..0000000 --- a/e_scalb.c +++ /dev/null @@ -1,51 +0,0 @@ - -/* @(#)e_scalb.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * __ieee754_scalb(x, fn) is provide for - * passing various standard test suite. One - * should use ieee_scalbn() instead. - */ - -#include "fdlibm.h" - -#ifdef _SCALB_INT -#ifdef __STDC__ - double __ieee754_scalb(double x, int fn) -#else - double __ieee754_scalb(x,fn) - double x; int fn; -#endif -#else -#ifdef __STDC__ - double __ieee754_scalb(double x, double fn) -#else - double __ieee754_scalb(x,fn) - double x, fn; -#endif -#endif -{ -#ifdef _SCALB_INT - return ieee_scalbn(x,fn); -#else - if (ieee_isnan(x)||ieee_isnan(fn)) return x*fn; - if (!ieee_finite(fn)) { - if(fn>0.0) return x*fn; - else return x/(-fn); - } - if (ieee_rint(fn)!=fn) return (fn-fn)/(fn-fn); - if ( fn > 65000.0) return ieee_scalbn(x, 65000); - if (-fn > 65000.0) return ieee_scalbn(x,-65000); - return ieee_scalbn(x,(int)fn); -#endif -} diff --git a/e_sinh.c b/e_sinh.c deleted file mode 100644 index 0a807c7..0000000 --- a/e_sinh.c +++ /dev/null @@ -1,82 +0,0 @@ - -/* @(#)e_sinh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_sinh(x) - * Method : - * mathematically ieee_sinh(x) if defined to be (ieee_exp(x)-ieee_exp(-x))/2 - * 1. Replace x by |x| (ieee_sinh(-x) = -ieee_sinh(x)). - * 2. - * E + E/(E+1) - * 0 <= x <= 22 : ieee_sinh(x) := --------------, E=ieee_expm1(x) - * 2 - * - * 22 <= x <= lnovft : ieee_sinh(x) := ieee_exp(x)/2 - * lnovft <= x <= ln2ovft: ieee_sinh(x) := ieee_exp(x/2)/2 * ieee_exp(x/2) - * ln2ovft < x : ieee_sinh(x) := x*shuge (overflow) - * - * Special cases: - * sinh(x) is |x| if x is +INF, -INF, or NaN. - * only ieee_sinh(0)=0 is exact for finite x. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double one = 1.0, shuge = 1.0e307; -#else -static double one = 1.0, shuge = 1.0e307; -#endif - -#ifdef __STDC__ - double __ieee754_sinh(double x) -#else - double __ieee754_sinh(x) - double x; -#endif -{ - double t,w,h; - int ix,jx; - unsigned lx; - - /* High word of |x|. */ - jx = __HI(x); - ix = jx&0x7fffffff; - - /* x is INF or NaN */ - if(ix>=0x7ff00000) return x+x; - - h = 0.5; - if (jx<0) h = -h; - /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ - if (ix < 0x40360000) { /* |x|<22 */ - if (ix<0x3e300000) /* |x|<2**-28 */ - if(shuge+x>one) return x;/* ieee_sinh(tiny) = tiny with inexact */ - t = ieee_expm1(ieee_fabs(x)); - if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); - return h*(t+t/(t+one)); - } - - /* |x| in [22, ieee_log(maxdouble)] return 0.5*ieee_exp(|x|) */ - if (ix < 0x40862E42) return h*__ieee754_exp(ieee_fabs(x)); - - /* |x| in [log(maxdouble), overflowthresold] */ - lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x); - if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) { - w = __ieee754_exp(0.5*ieee_fabs(x)); - t = h*w; - return t*w; - } - - /* |x| > overflowthresold, ieee_sinh(x) overflow */ - return x*shuge; -} diff --git a/e_sqrt.c b/e_sqrt.c deleted file mode 100644 index 942cbc7..0000000 --- a/e_sqrt.c +++ /dev/null @@ -1,450 +0,0 @@ -/* @(#)e_sqrt.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __ieee754_sqrt(x) - * Return correctly rounded sqrt. - * ------------------------------------------ - * | Use the hardware sqrt if you have one | - * ------------------------------------------ - * Method: - * Bit by bit method using integer arithmetic. (Slow, but portable) - * 1. Normalization - * Scale x to y in [1,4) with even powers of 2: - * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then - * sqrt(x) = 2^k * ieee_sqrt(y) - * 2. Bit by bit computation - * Let q = ieee_sqrt(y) truncated to i bit after binary point (q = 1), - * i 0 - * i+1 2 - * s = 2*q , and y = 2 * ( y - q ). (1) - * i i i i - * - * To compute q from q , one checks whether - * i+1 i - * - * -(i+1) 2 - * (q + 2 ) <= y. (2) - * i - * -(i+1) - * If (2) is false, then q = q ; otherwise q = q + 2 . - * i+1 i i+1 i - * - * With some algebric manipulation, it is not difficult to see - * that (2) is equivalent to - * -(i+1) - * s + 2 <= y (3) - * i i - * - * The advantage of (3) is that s and y can be computed by - * i i - * the following recurrence formula: - * if (3) is false - * - * s = s , y = y ; (4) - * i+1 i i+1 i - * - * otherwise, - * -i -(i+1) - * s = s + 2 , y = y - s - 2 (5) - * i+1 i i+1 i i - * - * One may easily use induction to prove (4) and (5). - * Note. Since the left hand side of (3) contain only i+2 bits, - * it does not necessary to do a full (53-bit) comparison - * in (3). - * 3. Final rounding - * After generating the 53 bits result, we compute one more bit. - * Together with the remainder, we can decide whether the - * result is exact, bigger than 1/2ulp, or less than 1/2ulp - * (it will never equal to 1/2ulp). - * The rounding mode can be detected by checking whether - * huge + tiny is equal to huge, and whether huge - tiny is - * equal to huge for some floating point number "huge" and "tiny". - * - * Special cases: - * sqrt(+-0) = +-0 ... exact - * sqrt(inf) = inf - * sqrt(-ve) = NaN ... with invalid signal - * sqrt(NaN) = NaN ... with invalid signal for signaling NaN - * - * Other methods : see the appended file at the end of the program below. - *--------------- - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double one = 1.0, tiny=1.0e-300; -#else -static double one = 1.0, tiny=1.0e-300; -#endif - -#ifdef __STDC__ - double __ieee754_sqrt(double x) -#else - double __ieee754_sqrt(x) - double x; -#endif -{ - double z; - int sign = (int)0x80000000; - unsigned r,t1,s1,ix1,q1; - int ix0,s0,q,m,t,i; - - ix0 = __HI(x); /* high word of x */ - ix1 = __LO(x); /* low word of x */ - - /* take care of Inf and NaN */ - if((ix0&0x7ff00000)==0x7ff00000) { - return x*x+x; /* ieee_sqrt(NaN)=NaN, ieee_sqrt(+inf)=+inf - ieee_sqrt(-inf)=sNaN */ - } - /* take care of zero */ - if(ix0<=0) { - if(((ix0&(~sign))|ix1)==0) return x;/* ieee_sqrt(+-0) = +-0 */ - else if(ix0<0) - return (x-x)/(x-x); /* ieee_sqrt(-ve) = sNaN */ - } - /* normalize x */ - m = (ix0>>20); - if(m==0) { /* subnormal x */ - while(ix0==0) { - m -= 21; - ix0 |= (ix1>>11); ix1 <<= 21; - } - for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1; - m -= i-1; - ix0 |= (ix1>>(32-i)); - ix1 <<= i; - } - m -= 1023; /* unbias exponent */ - ix0 = (ix0&0x000fffff)|0x00100000; - if(m&1){ /* odd m, double x to make it even */ - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - } - m >>= 1; /* m = [m/2] */ - - /* generate ieee_sqrt(x) bit by bit */ - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - q = q1 = s0 = s1 = 0; /* [q,q1] = ieee_sqrt(x) */ - r = 0x00200000; /* r = moving bit from right to left */ - - while(r!=0) { - t = s0+r; - if(t<=ix0) { - s0 = t+r; - ix0 -= t; - q += r; - } - ix0 += ix0 + ((ix1&sign)>>31); - ix1 += ix1; - r>>=1; - } - - r = sign; - while(r!=0) { - t1 = s1+r; - t = s0; - if((t>31); - ix1 += ix1; - r>>=1; - } - - /* use floating add to find out rounding direction */ - if((ix0|ix1)!=0) { - z = one-tiny; /* trigger inexact flag */ - if (z>=one) { - z = one+tiny; - if (q1==(unsigned)0xffffffff) { q1=0; q += 1;} - else if (z>one) { - if (q1==(unsigned)0xfffffffe) q+=1; - q1+=2; - } else - q1 += (q1&1); - } - } - ix0 = (q>>1)+0x3fe00000; - ix1 = q1>>1; - if ((q&1)==1) ix1 |= sign; - ix0 += (m <<20); - __HI(z) = ix0; - __LO(z) = ix1; - return z; -} - -/* -Other methods (use floating-point arithmetic) -------------- -(This is a copy of a drafted paper by Prof W. Kahan -and K.C. Ng, written in May, 1986) - - Two algorithms are given here to implement ieee_sqrt(x) - (IEEE double precision arithmetic) in software. - Both supply ieee_sqrt(x) correctly rounded. The first algorithm (in - Section A) uses newton iterations and involves four divisions. - The second one uses reciproot iterations to avoid division, but - requires more multiplications. Both algorithms need the ability - to chop results of arithmetic operations instead of round them, - and the INEXACT flag to indicate when an arithmetic operation - is executed exactly with no roundoff error, all part of the - standard (IEEE 754-1985). The ability to perform shift, add, - subtract and logical AND operations upon 32-bit words is needed - too, though not part of the standard. - -A. ieee_sqrt(x) by Newton Iteration - - (1) Initial approximation - - Let x0 and x1 be the leading and the trailing 32-bit words of - a floating point number x (in IEEE double format) respectively - - 1 11 52 ...widths - ------------------------------------------------------ - x: |s| e | f | - ------------------------------------------------------ - msb lsb msb lsb ...order - - - ------------------------ ------------------------ - x0: |s| e | f1 | x1: | f2 | - ------------------------ ------------------------ - - By performing shifts and subtracts on x0 and x1 (both regarded - as integers), we obtain an 8-bit approximation of ieee_sqrt(x) as - follows. - - k := (x0>>1) + 0x1ff80000; - y0 := k - T1[31&(k>>15)]. ... y ~ ieee_sqrt(x) to 8 bits - Here k is a 32-bit integer and T1[] is an integer array containing - correction terms. Now magically the floating value of y (y's - leading 32-bit word is y0, the value of its trailing word is 0) - approximates ieee_sqrt(x) to almost 8-bit. - - Value of T1: - static int T1[32]= { - 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592, - 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, - 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, - 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,}; - - (2) Iterative refinement - - Apply Heron's rule three times to y, we have y approximates - sqrt(x) to within 1 ulp (Unit in the Last Place): - - y := (y+x/y)/2 ... almost 17 sig. bits - y := (y+x/y)/2 ... almost 35 sig. bits - y := y-(y-x/y)/2 ... within 1 ulp - - - Remark 1. - Another way to improve y to within 1 ulp is: - - y := (y+x/y) ... almost 17 sig. bits to 2*ieee_sqrt(x) - y := y - 0x00100006 ... almost 18 sig. bits to ieee_sqrt(x) - - 2 - (x-y )*y - y := y + 2* ---------- ...within 1 ulp - 2 - 3y + x - - - This formula has one division fewer than the one above; however, - it requires more multiplications and additions. Also x must be - scaled in advance to avoid spurious overflow in evaluating the - expression 3y*y+x. Hence it is not recommended uless division - is slow. If division is very slow, then one should use the - reciproot algorithm given in section B. - - (3) Final adjustment - - By twiddling y's last bit it is possible to force y to be - correctly rounded according to the prevailing rounding mode - as follows. Let r and i be copies of the rounding mode and - inexact flag before entering the square root program. Also we - use the expression y+-ulp for the next representable floating - numbers (up and down) of y. Note that y+-ulp = either fixed - point y+-1, or multiply y by ieee_nextafter(1,+-inf) in chopped - mode. - - I := FALSE; ... reset INEXACT flag I - R := RZ; ... set rounding mode to round-toward-zero - z := x/y; ... chopped quotient, possibly inexact - If(not I) then { ... if the quotient is exact - if(z=y) { - I := i; ... restore inexact flag - R := r; ... restore rounded mode - return ieee_sqrt(x):=y. - } else { - z := z - ulp; ... special rounding - } - } - i := TRUE; ... ieee_sqrt(x) is inexact - If (r=RN) then z=z+ulp ... rounded-to-nearest - If (r=RP) then { ... round-toward-+inf - y = y+ulp; z=z+ulp; - } - y := y+z; ... chopped sum - y0:=y0-0x00100000; ... y := y/2 is correctly rounded. - I := i; ... restore inexact flag - R := r; ... restore rounded mode - return ieee_sqrt(x):=y. - - (4) Special cases - - Square root of +inf, +-0, or NaN is itself; - Square root of a negative number is NaN with invalid signal. - - -B. ieee_sqrt(x) by Reciproot Iteration - - (1) Initial approximation - - Let x0 and x1 be the leading and the trailing 32-bit words of - a floating point number x (in IEEE double format) respectively - (see section A). By performing shifs and subtracts on x0 and y0, - we obtain a 7.8-bit approximation of 1/ieee_sqrt(x) as follows. - - k := 0x5fe80000 - (x0>>1); - y0:= k - T2[63&(k>>14)]. ... y ~ 1/ieee_sqrt(x) to 7.8 bits - - Here k is a 32-bit integer and T2[] is an integer array - containing correction terms. Now magically the floating - value of y (y's leading 32-bit word is y0, the value of - its trailing word y1 is set to zero) approximates 1/ieee_sqrt(x) - to almost 7.8-bit. - - Value of T2: - static int T2[64]= { - 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, - 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, - 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, - 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, - 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, - 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, - 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, - 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,}; - - (2) Iterative refinement - - Apply Reciproot iteration three times to y and multiply the - result by x to get an approximation z that matches ieee_sqrt(x) - to about 1 ulp. To be exact, we will have - -1ulp < ieee_sqrt(x)-z<1.0625ulp. - - ... set rounding mode to Round-to-nearest - y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/ieee_sqrt(x) - y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/ieee_sqrt(x) - ... special arrangement for better accuracy - z := x*y ... 29 bits to ieee_sqrt(x), with z*y<1 - z := z + 0.5*z*(1-z*y) ... about 1 ulp to ieee_sqrt(x) - - Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that - (a) the term z*y in the final iteration is always less than 1; - (b) the error in the final result is biased upward so that - -1 ulp < ieee_sqrt(x) - z < 1.0625 ulp - instead of |ieee_sqrt(x)-z|<1.03125ulp. - - (3) Final adjustment - - By twiddling y's last bit it is possible to force y to be - correctly rounded according to the prevailing rounding mode - as follows. Let r and i be copies of the rounding mode and - inexact flag before entering the square root program. Also we - use the expression y+-ulp for the next representable floating - numbers (up and down) of y. Note that y+-ulp = either fixed - point y+-1, or multiply y by ieee_nextafter(1,+-inf) in chopped - mode. - - R := RZ; ... set rounding mode to round-toward-zero - switch(r) { - case RN: ... round-to-nearest - if(x<= z*(z-ulp)...chopped) z = z - ulp; else - if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp; - break; - case RZ:case RM: ... round-to-zero or round-to--inf - R:=RP; ... reset rounding mod to round-to-+inf - if(x=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp; - break; - case RP: ... round-to-+inf - if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else - if(x>z*z ...chopped) z = z+ulp; - break; - } - - Remark 3. The above comparisons can be done in fixed point. For - example, to compare x and w=z*z chopped, it suffices to compare - x1 and w1 (the trailing parts of x and w), regarding them as - two's complement integers. - - ...Is z an exact square root? - To determine whether z is an exact square root of x, let z1 be the - trailing part of z, and also let x0 and x1 be the leading and - trailing parts of x. - - If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0 - I := 1; ... Raise Inexact flag: z is not exact - else { - j := 1 - [(x0>>20)&1] ... j = ieee_logb(x) mod 2 - k := z1 >> 26; ... get z's 25-th and 26-th - fraction bits - I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); - } - R:= r ... restore rounded mode - return ieee_sqrt(x):=z. - - If multiplication is cheaper then the foregoing red tape, the - Inexact flag can be evaluated by - - I := i; - I := (z*z!=x) or I. - - Note that z*z can overwrite I; this value must be sensed if it is - True. - - Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be - zero. - - -------------------- - z1: | f2 | - -------------------- - bit 31 bit 0 - - Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd - or even of ieee_logb(x) have the following relations: - - ------------------------------------------------- - bit 27,26 of z1 bit 1,0 of x1 logb(x) - ------------------------------------------------- - 00 00 odd and even - 01 01 even - 10 10 odd - 10 00 even - 11 01 even - ------------------------------------------------- - - (4) Special cases (see (4) of Section A). - - */ - diff --git a/fdlibm.h b/fdlibm.h deleted file mode 100644 index f90d5c9..0000000 --- a/fdlibm.h +++ /dev/null @@ -1,216 +0,0 @@ - -/* @(#)fdlibm.h 1.5 04/04/22 */ -/* - * ==================================================== - * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* Sometimes it's necessary to define __LITTLE_ENDIAN explicitly - but these catch some common cases. */ - -#if defined(i386) || defined(i486) || \ - defined(intel) || defined(x86) || defined(i86pc) || \ - defined(__alpha) || defined(__osf__) -#define __LITTLE_ENDIAN -#endif - -#ifdef __LITTLE_ENDIAN -#define __HI(x) *(1+(int*)&x) -#define __LO(x) *(int*)&x -#define __HIp(x) *(1+(int*)x) -#define __LOp(x) *(int*)x -#else -#define __HI(x) *(int*)&x -#define __LO(x) *(1+(int*)&x) -#define __HIp(x) *(int*)x -#define __LOp(x) *(1+(int*)x) -#endif - -#ifdef __STDC__ -#define __P(p) p -#else -#define __P(p) () -#endif - -/* - * ANSI/POSIX - */ - -extern int signgam; - -#define MAXFLOAT ((float)3.40282346638528860e+38) - -enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix}; - -#define _LIB_VERSION_TYPE enum fdversion -#define _LIB_VERSION _fdlib_version - -/* if global variable _LIB_VERSION is not desirable, one may - * change the following to be a constant by: - * #define _LIB_VERSION_TYPE const enum version - * In that case, after one initializes the value _LIB_VERSION (see - * s_lib_version.c) during compile time, it cannot be modified - * in the middle of a program - */ -extern _LIB_VERSION_TYPE _LIB_VERSION; - -#define _IEEE_ fdlibm_ieee -#define _SVID_ fdlibm_svid -#define _XOPEN_ fdlibm_xopen -#define _POSIX_ fdlibm_posix - -struct exception { - int type; - char *name; - double arg1; - double arg2; - double retval; -}; - -#define HUGE MAXFLOAT - -/* - * set X_TLOSS = pi*2**52, which is possibly defined in - * (one may replace the following line by "#include ") - */ - -#define X_TLOSS 1.41484755040568800000e+16 - -#define DOMAIN 1 -#define SING 2 -#define OVERFLOW 3 -#define UNDERFLOW 4 -#define TLOSS 5 -#define PLOSS 6 - -/* - * ANSI/POSIX - */ -extern double ieee_acos __P((double)); -extern double ieee_asin __P((double)); -extern double ieee_atan __P((double)); -extern double ieee_atan2 __P((double, double)); -extern double ieee_cos __P((double)); -extern double ieee_sin __P((double)); -extern double ieee_tan __P((double)); - -extern double ieee_cosh __P((double)); -extern double ieee_sinh __P((double)); -extern double ieee_tanh __P((double)); - -extern double ieee_exp __P((double)); -extern double ieee_frexp __P((double, int *)); -extern double ieee_ldexp __P((double, int)); -extern double ieee_log __P((double)); -extern double ieee_log10 __P((double)); -extern double ieee_modf __P((double, double *)); - -extern double ieee_pow __P((double, double)); -extern double ieee_sqrt __P((double)); - -extern double ieee_ceil __P((double)); -extern double ieee_fabs __P((double)); -extern double ieee_floor __P((double)); -extern double ieee_fmod __P((double, double)); - -extern double ieee_erf __P((double)); -extern double ieee_erfc __P((double)); -extern double ieee_gamma __P((double)); -extern double ieee_hypot __P((double, double)); -extern int ieee_isnan __P((double)); -extern int ieee_finite __P((double)); -extern double ieee_j0 __P((double)); -extern double ieee_j1 __P((double)); -extern double ieee_jn __P((int, double)); -extern double ieee_lgamma __P((double)); -extern double ieee_y0 __P((double)); -extern double ieee_y1 __P((double)); -extern double ieee_yn __P((int, double)); - -extern double acosh __P((double)); -extern double asinh __P((double)); -extern double atanh __P((double)); -extern double ieee_cbrt __P((double)); -extern double ieee_logb __P((double)); -extern double ieee_nextafter __P((double, double)); -extern double ieee_remainder __P((double, double)); -#ifdef _SCALB_INT -extern double ieee_scalb __P((double, int)); -#else -extern double ieee_scalb __P((double, double)); -#endif - -extern int ieee_matherr __P((struct exception *)); - -/* - * IEEE Test Vector - */ -extern double ieee_significand __P((double)); - -/* - * Functions callable from C, intended to support IEEE arithmetic. - */ -extern double ieee_copysign __P((double, double)); -extern int ieee_ilogb __P((double)); -extern double ieee_rint __P((double)); -extern double ieee_scalbn __P((double, int)); - -/* - * BSD math library entry points - */ -extern double ieee_expm1 __P((double)); -extern double ieee_log1p __P((double)); - -/* - * Reentrant version of gamma & lgamma; passes signgam back by reference - * as the second argument; user must allocate space for signgam. - */ -#ifdef _REENTRANT -extern double ieee_gamma_r __P((double, int *)); -extern double ieee_lgamma_r __P((double, int *)); -#endif /* _REENTRANT */ - -/* ieee style elementary functions */ -extern double __ieee754_sqrt __P((double)); -extern double __ieee754_acos __P((double)); -extern double __ieee754_acosh __P((double)); -extern double __ieee754_log __P((double)); -extern double __ieee754_atanh __P((double)); -extern double __ieee754_asin __P((double)); -extern double __ieee754_atan2 __P((double,double)); -extern double __ieee754_exp __P((double)); -extern double __ieee754_cosh __P((double)); -extern double __ieee754_fmod __P((double,double)); -extern double __ieee754_pow __P((double,double)); -extern double __ieee754_lgamma_r __P((double,int *)); -extern double __ieee754_gamma_r __P((double,int *)); -extern double __ieee754_lgamma __P((double)); -extern double __ieee754_gamma __P((double)); -extern double __ieee754_log10 __P((double)); -extern double __ieee754_sinh __P((double)); -extern double __ieee754_hypot __P((double,double)); -extern double __ieee754_j0 __P((double)); -extern double __ieee754_j1 __P((double)); -extern double __ieee754_y0 __P((double)); -extern double __ieee754_y1 __P((double)); -extern double __ieee754_jn __P((int,double)); -extern double __ieee754_yn __P((int,double)); -extern double __ieee754_remainder __P((double,double)); -extern int __ieee754_rem_pio2 __P((double,double*)); -#ifdef _SCALB_INT -extern double __ieee754_scalb __P((double,int)); -#else -extern double __ieee754_scalb __P((double,double)); -#endif - -/* fdlibm kernel function */ -extern double __kernel_standard __P((double,double,int)); -extern double __kernel_sin __P((double,double,int)); -extern double __kernel_cos __P((double,double)); -extern double __kernel_tan __P((double,double,int)); -extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*)); diff --git a/index b/index deleted file mode 100644 index de2de81..0000000 --- a/index +++ /dev/null @@ -1,168 +0,0 @@ -file fdlibm/fdlibm.h - -file fdlibm/index - -file fdlibm/e_acos.c - -file fdlibm/e_acosh.c - -file fdlibm/e_asin.c - -file fdlibm/e_atan2.c - -file fdlibm/e_atanh.c - -file fdlibm/e_cosh.c - -file fdlibm/e_exp.c - -file fdlibm/e_fmod.c - -file fdlibm/e_gamma.c - -file fdlibm/e_gamma_r.c - -file fdlibm/e_hypot.c - -file fdlibm/e_j0.c - -file fdlibm/e_j1.c - -file fdlibm/e_jn.c - -file fdlibm/e_lgamma.c - -file fdlibm/e_lgamma_r.c - -file fdlibm/e_log.c - -file fdlibm/e_log10.c - -file fdlibm/e_pow.c - -file fdlibm/e_rem_pio2.c - -file fdlibm/e_remainder.c - -file fdlibm/e_scalb.c - -file fdlibm/e_sinh.c - -file fdlibm/e_sqrt.c - -file fdlibm/k_cos.c - -file fdlibm/k_rem_pio2.c - -file fdlibm/k_sin.c - -file fdlibm/k_standard.c - -file fdlibm/k_tan.c - -file fdlibm/makefile - -file fdlibm/s_asinh.c - -file fdlibm/s_atan.c - -file fdlibm/s_cbrt.c - -file fdlibm/s_ceil.c - -file fdlibm/s_copysign.c - -file fdlibm/s_cos.c - -file fdlibm/s_erf.c - -file fdlibm/s_expm1.c - -file fdlibm/s_fabs.c - -file fdlibm/s_finite.c - -file fdlibm/s_floor.c - -file fdlibm/s_frexp.c - -file fdlibm/s_ilogb.c - -file fdlibm/s_isnan.c - -file fdlibm/s_ldexp.c - -file fdlibm/s_lib_version.c - -file fdlibm/s_log1p.c - -file fdlibm/s_logb.c - -file fdlibm/s_matherr.c - -file fdlibm/s_modf.c - -file fdlibm/s_nextafter.c - -file fdlibm/s_rint.c - -file fdlibm/s_scalbn.c - -file fdlibm/s_signgam.c - -file fdlibm/s_significand.c - -file fdlibm/s_sin.c - -file fdlibm/s_tan.c - -file fdlibm/s_tanh.c - -file fdlibm/w_acos.c - -file fdlibm/w_acosh.c - -file fdlibm/w_asin.c - -file fdlibm/w_atan2.c - -file fdlibm/w_atanh.c - -file fdlibm/w_cosh.c - -file fdlibm/w_exp.c - -file fdlibm/w_fmod.c - -file fdlibm/w_gamma.c - -file fdlibm/w_gamma_r.c - -file fdlibm/w_hypot.c - -file fdlibm/w_j0.c - -file fdlibm/w_j1.c - -file fdlibm/w_jn.c - -file fdlibm/w_lgamma.c - -file fdlibm/w_lgamma_r.c - -file fdlibm/w_log.c - -file fdlibm/w_log10.c - -file fdlibm/w_pow.c - -file fdlibm/w_remainder.c - -file fdlibm/w_scalb.c - -file fdlibm/w_sinh.c - -file fdlibm/w_sqrt.c - -file fdlibm/readme - diff --git a/index.html b/index.html deleted file mode 100644 index d84410e..0000000 --- a/index.html +++ /dev/null @@ -1,180 +0,0 @@ - -fdlibm - - -

fdlibm

-

-Click here to see the number of accesses to this library. -


-
-file	fdlibm.h
-
-file	index
-
-file	e_acos.c  e_acos.c plus dependencies
-
-file	e_acosh.c  e_acosh.c plus dependencies
-
-file	e_asin.c  e_asin.c plus dependencies
-
-file	e_atan2.c  e_atan2.c plus dependencies
-
-file	e_atanh.c  e_atanh.c plus dependencies
-
-file	e_cosh.c  e_cosh.c plus dependencies
-
-file	e_exp.c  e_exp.c plus dependencies
-
-file	e_fmod.c  e_fmod.c plus dependencies
-
-file	e_gamma.c  e_gamma.c plus dependencies
-
-file	e_gamma_r.c  e_gamma_r.c plus dependencies
-
-file	e_hypot.c  e_hypot.c plus dependencies
-
-file	e_j0.c  e_j0.c plus dependencies
-
-file	e_j1.c  e_j1.c plus dependencies
-
-file	e_jn.c  e_jn.c plus dependencies
-
-file	e_lgamma.c  e_lgamma.c plus dependencies
-
-file	e_lgamma_r.c  e_lgamma_r.c plus dependencies
-
-file	e_log.c  e_log.c plus dependencies
-
-file	e_log10.c  e_log10.c plus dependencies
-
-file	e_pow.c  e_pow.c plus dependencies
-
-file	e_rem_pio2.c  e_rem_pio2.c plus dependencies
-
-file	e_remainder.c  e_remainder.c plus dependencies
-
-file	e_scalb.c  e_scalb.c plus dependencies
-
-file	e_sinh.c  e_sinh.c plus dependencies
-
-file	e_sqrt.c  e_sqrt.c plus dependencies
-
-file	k_cos.c  k_cos.c plus dependencies
-
-file	k_rem_pio2.c  k_rem_pio2.c plus dependencies
-
-file	k_sin.c  k_sin.c plus dependencies
-
-file	k_standard.c  k_standard.c plus dependencies
-
-file	k_tan.c  k_tan.c plus dependencies
-
-file	makefile
-
-file	s_asinh.c  s_asinh.c plus dependencies
-
-file	s_atan.c  s_atan.c plus dependencies
-
-file	s_cbrt.c  s_cbrt.c plus dependencies
-
-file	s_ceil.c  s_ceil.c plus dependencies
-
-file	s_copysign.c  s_copysign.c plus dependencies
-
-file	s_cos.c  s_cos.c plus dependencies
-
-file	s_erf.c  s_erf.c plus dependencies
-
-file	s_expm1.c  s_expm1.c plus dependencies
-
-file	s_fabs.c  s_fabs.c plus dependencies
-
-file	s_finite.c  s_finite.c plus dependencies
-
-file	s_floor.c  s_floor.c plus dependencies
-
-file	s_frexp.c  s_frexp.c plus dependencies
-
-file	s_ilogb.c  s_ilogb.c plus dependencies
-
-file	s_isnan.c  s_isnan.c plus dependencies
-
-file	s_ldexp.c  s_ldexp.c plus dependencies
-
-file	s_lib_version.c  s_lib_version.c plus dependencies
-
-file	s_log1p.c  s_log1p.c plus dependencies
-
-file	s_logb.c  s_logb.c plus dependencies
-
-file	s_matherr.c  s_matherr.c plus dependencies
-
-file	s_modf.c  s_modf.c plus dependencies
-
-file	s_nextafter.c  s_nextafter.c plus dependencies
-
-file	s_rint.c  s_rint.c plus dependencies
-
-file	s_scalbn.c  s_scalbn.c plus dependencies
-
-file	s_signgam.c  s_signgam.c plus dependencies
-
-file	s_significand.c  s_significand.c plus dependencies
-
-file	s_sin.c  s_sin.c plus dependencies
-
-file	s_tan.c  s_tan.c plus dependencies
-
-file	s_tanh.c  s_tanh.c plus dependencies
-
-file	w_acos.c  w_acos.c plus dependencies
-
-file	w_acosh.c  w_acosh.c plus dependencies
-
-file	w_asin.c  w_asin.c plus dependencies
-
-file	w_atan2.c  w_atan2.c plus dependencies
-
-file	w_atanh.c  w_atanh.c plus dependencies
-
-file	w_cosh.c  w_cosh.c plus dependencies
-
-file	w_exp.c  w_exp.c plus dependencies
-
-file	w_fmod.c  w_fmod.c plus dependencies
-
-file	w_gamma.c  w_gamma.c plus dependencies
-
-file	w_gamma_r.c  w_gamma_r.c plus dependencies
-
-file	w_hypot.c  w_hypot.c plus dependencies
-
-file	w_j0.c  w_j0.c plus dependencies
-
-file	w_j1.c  w_j1.c plus dependencies
-
-file	w_jn.c  w_jn.c plus dependencies
-
-file	w_lgamma.c  w_lgamma.c plus dependencies
-
-file	w_lgamma_r.c  w_lgamma_r.c plus dependencies
-
-file	w_log.c  w_log.c plus dependencies
-
-file	w_log10.c  w_log10.c plus dependencies
-
-file	w_pow.c  w_pow.c plus dependencies
-
-file	w_remainder.c  w_remainder.c plus dependencies
-
-file	w_scalb.c  w_scalb.c plus dependencies
-
-file	w_sinh.c  w_sinh.c plus dependencies
-
-file	w_sqrt.c  w_sqrt.c plus dependencies
-
-file	readme
-
-
- - diff --git a/k_cos.c b/k_cos.c deleted file mode 100644 index 2e70850..0000000 --- a/k_cos.c +++ /dev/null @@ -1,92 +0,0 @@ - -/* @(#)k_cos.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * __kernel_cos( x, y ) - * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * - * Algorithm - * 1. Since ieee_cos(-x) = ieee_cos(x), we need only to consider positive x. - * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. - * 3. ieee_cos(x) is approximated by a polynomial of degree 14 on - * [0,pi/4] - * 4 14 - * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x - * where the remez error is - * - * | 2 4 6 8 10 12 14 | -58 - * |ieee_cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 - * | | - * - * 4 6 8 10 12 14 - * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then - * ieee_cos(x) = 1 - x*x/2 + r - * since ieee_cos(x+y) ~ ieee_cos(x) - ieee_sin(x)*y - * ~ ieee_cos(x) - x*y, - * a correction term is necessary in ieee_cos(x) and hence - * cos(x+y) = 1 - (x*x/2 - (r - x*y)) - * For better accuracy when x > 0.3, let qx = |x|/4 with - * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. - * Then - * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). - * Note that 1-qx and (x*x/2-qx) is EXACT here, and the - * magnitude of the latter is at least a quarter of x*x/2, - * thus, reducing the rounding error in the subtraction. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ -C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ -C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ -C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ -C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ -C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ - -#ifdef __STDC__ - double __kernel_cos(double x, double y) -#else - double __kernel_cos(x, y) - double x,y; -#endif -{ - double a,hz,z,r,qx; - int ix; - ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/ - if(ix<0x3e400000) { /* if x < 2**27 */ - if(((int)x)==0) return one; /* generate inexact */ - } - z = x*x; - r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); - if(ix < 0x3FD33333) /* if |x| < 0.3 */ - return one - (0.5*z - (z*r - x*y)); - else { - if(ix > 0x3fe90000) { /* x > 0.78125 */ - qx = 0.28125; - } else { - __HI(qx) = ix-0x00200000; /* x/4 */ - __LO(qx) = 0; - } - hz = 0.5*z-qx; - a = one-qx; - return a - (hz - (z*r-x*y)); - } -} diff --git a/k_rem_pio2.c b/k_rem_pio2.c deleted file mode 100644 index 3938005..0000000 --- a/k_rem_pio2.c +++ /dev/null @@ -1,316 +0,0 @@ - -/* @(#)k_rem_pio2.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * __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 = ieee_ilogb(z)-23 - * z = ieee_scalbn(z,-e0) - * for i = 0,1,2 - * x[i] = ieee_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 - * precison, 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 ieee_scalbn(), ieee_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 "fdlibm.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 int *ipio2) -#else - int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) - double x[], y[]; int e0,nx,prec; int ipio2[]; -#endif -{ - int 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)((int)(twon24* z)); - iq[i] = (int)(z-two24*fw); - z = q[j-1]+fw; - } - - /* compute n */ - z = ieee_scalbn(z,q0); /* actual value of z */ - z -= 8.0*ieee_floor(z*0.125); /* trim off integer >= 8 */ - n = (int) 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;i0) { /* 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 -= ieee_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 = ieee_scalbn(z,-q0); - if(z>=two24) { - fw = (double)((int)(twon24*z)); - iq[jz] = (int)(z-two24*fw); - jz += 1; q0 += 24; - iq[jz] = (int) fw; - } else iq[jz] = (int) z ; - } - - /* convert integer "bit" chunk to floating-point value */ - fw = ieee_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; -} diff --git a/k_sin.c b/k_sin.c deleted file mode 100644 index 3138e4f..0000000 --- a/k_sin.c +++ /dev/null @@ -1,74 +0,0 @@ - -/* @(#)k_sin.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __kernel_sin( x, y, iy) - * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). - * - * Algorithm - * 1. Since ieee_sin(-x) = -ieee_sin(x), we need only to consider positive x. - * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. - * 3. ieee_sin(x) is approximated by a polynomial of degree 13 on - * [0,pi/4] - * 3 13 - * sin(x) ~ x + S1*x + ... + S6*x - * where - * - * |ieee_sin(x) 2 4 6 8 10 12 | -58 - * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 - * | x | - * - * 4. ieee_sin(x+y) = ieee_sin(x) + sin'(x')*y - * ~ ieee_sin(x) + (1-x*x/2)*y - * For better accuracy, let - * 3 2 2 2 2 - * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) - * then 3 2 - * sin(x) = x + (S1*x + (x *(r-y/2)+y)) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ -S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ -S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ -S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ -S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ -S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ -S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ - -#ifdef __STDC__ - double __kernel_sin(double x, double y, int iy) -#else - double __kernel_sin(x, y, iy) - double x,y; int iy; /* iy=0 if y is zero */ -#endif -{ - double z,r,v; - int ix; - ix = __HI(x)&0x7fffffff; /* high word of x */ - if(ix<0x3e400000) /* |x| < 2**-27 */ - {if((int)x==0) return x;} /* generate inexact */ - z = x*x; - v = z*x; - r = S2+z*(S3+z*(S4+z*(S5+z*S6))); - if(iy==0) return x+v*(S1+z*r); - else return x-((z*(half*y-v*r)-y)-v*S1); -} diff --git a/k_standard.c b/k_standard.c deleted file mode 100644 index fb13464..0000000 --- a/k_standard.c +++ /dev/null @@ -1,733 +0,0 @@ - -/* @(#)k_standard.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -#include "fdlibm.h" -#include - -#ifndef _USE_WRITE -#include /* fputs(), stderr */ -#define WRITE2(u,v) fputs(u, stderr) -#else /* !defined(_USE_WRITE) */ -#include /* write */ -#define WRITE2(u,v) write(2, u, v) -#undef fflush -#endif /* !defined(_USE_WRITE) */ - -static double zero = 0.0; /* used as const */ - -/* - * Standard conformance (non-IEEE) on exception cases. - * Mapping: - * 1 -- ieee_acos(|x|>1) - * 2 -- ieee_asin(|x|>1) - * 3 -- ieee_atan2(+-0,+-0) - * 4 -- hypot overflow - * 5 -- cosh overflow - * 6 -- exp overflow - * 7 -- exp underflow - * 8 -- ieee_y0(0) - * 9 -- ieee_y0(-ve) - * 10-- ieee_y1(0) - * 11-- ieee_y1(-ve) - * 12-- ieee_yn(0) - * 13-- ieee_yn(-ve) - * 14-- ieee_lgamma(finite) overflow - * 15-- ieee_lgamma(-integer) - * 16-- ieee_log(0) - * 17-- ieee_log(x<0) - * 18-- ieee_log10(0) - * 19-- ieee_log10(x<0) - * 20-- ieee_pow(0.0,0.0) - * 21-- ieee_pow(x,y) overflow - * 22-- ieee_pow(x,y) underflow - * 23-- ieee_pow(0,negative) - * 24-- ieee_pow(neg,non-integral) - * 25-- ieee_sinh(finite) overflow - * 26-- ieee_sqrt(negative) - * 27-- ieee_fmod(x,0) - * 28-- ieee_remainder(x,0) - * 29-- acosh(x<1) - * 30-- atanh(|x|>1) - * 31-- atanh(|x|=1) - * 32-- scalb overflow - * 33-- scalb underflow - * 34-- ieee_j0(|x|>X_TLOSS) - * 35-- ieee_y0(x>X_TLOSS) - * 36-- ieee_j1(|x|>X_TLOSS) - * 37-- ieee_y1(x>X_TLOSS) - * 38-- ieee_jn(|x|>X_TLOSS, n) - * 39-- ieee_yn(x>X_TLOSS, n) - * 40-- ieee_gamma(finite) overflow - * 41-- ieee_gamma(-integer) - * 42-- ieee_pow(NaN,0.0) - */ - - -#ifdef __STDC__ - double __kernel_standard(double x, double y, int type) -#else - double __kernel_standard(x,y,type) - double x,y; int type; -#endif -{ - struct exception exc; -#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ -#define HUGE_VAL inf - double inf = 0.0; - - __HI(inf) = 0x7ff00000; /* set inf to infinite */ -#endif - -#ifdef _USE_WRITE - (void) fflush(stdout); -#endif - exc.arg1 = x; - exc.arg2 = y; - switch(type) { - case 1: - /* ieee_acos(|x|>1) */ - exc.type = DOMAIN; - exc.name = "acos"; - exc.retval = zero; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if(_LIB_VERSION == _SVID_) { - (void) WRITE2("acos: DOMAIN error\n", 19); - } - errno = EDOM; - } - break; - case 2: - /* ieee_asin(|x|>1) */ - exc.type = DOMAIN; - exc.name = "asin"; - exc.retval = zero; - if(_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if(_LIB_VERSION == _SVID_) { - (void) WRITE2("asin: DOMAIN error\n", 19); - } - errno = EDOM; - } - break; - case 3: - /* ieee_atan2(+-0,+-0) */ - exc.arg1 = y; - exc.arg2 = x; - exc.type = DOMAIN; - exc.name = "atan2"; - exc.retval = zero; - if(_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if(_LIB_VERSION == _SVID_) { - (void) WRITE2("atan2: DOMAIN error\n", 20); - } - errno = EDOM; - } - break; - case 4: - /* ieee_hypot(finite,finite) overflow */ - exc.type = OVERFLOW; - exc.name = "hypot"; - if (_LIB_VERSION == _SVID_) - exc.retval = HUGE; - else - exc.retval = HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - errno = ERANGE; - } - break; - case 5: - /* ieee_cosh(finite) overflow */ - exc.type = OVERFLOW; - exc.name = "cosh"; - if (_LIB_VERSION == _SVID_) - exc.retval = HUGE; - else - exc.retval = HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - errno = ERANGE; - } - break; - case 6: - /* ieee_exp(finite) overflow */ - exc.type = OVERFLOW; - exc.name = "exp"; - if (_LIB_VERSION == _SVID_) - exc.retval = HUGE; - else - exc.retval = HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - errno = ERANGE; - } - break; - case 7: - /* ieee_exp(finite) underflow */ - exc.type = UNDERFLOW; - exc.name = "exp"; - exc.retval = zero; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - errno = ERANGE; - } - break; - case 8: - /* ieee_y0(0) = -inf */ - exc.type = DOMAIN; /* should be SING for IEEE */ - exc.name = "y0"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("y0: DOMAIN error\n", 17); - } - errno = EDOM; - } - break; - case 9: - /* ieee_y0(x<0) = NaN */ - exc.type = DOMAIN; - exc.name = "y0"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("y0: DOMAIN error\n", 17); - } - errno = EDOM; - } - break; - case 10: - /* ieee_y1(0) = -inf */ - exc.type = DOMAIN; /* should be SING for IEEE */ - exc.name = "y1"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("y1: DOMAIN error\n", 17); - } - errno = EDOM; - } - break; - case 11: - /* ieee_y1(x<0) = NaN */ - exc.type = DOMAIN; - exc.name = "y1"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("y1: DOMAIN error\n", 17); - } - errno = EDOM; - } - break; - case 12: - /* ieee_yn(n,0) = -inf */ - exc.type = DOMAIN; /* should be SING for IEEE */ - exc.name = "yn"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("yn: DOMAIN error\n", 17); - } - errno = EDOM; - } - break; - case 13: - /* ieee_yn(x<0) = NaN */ - exc.type = DOMAIN; - exc.name = "yn"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("yn: DOMAIN error\n", 17); - } - errno = EDOM; - } - break; - case 14: - /* ieee_lgamma(finite) overflow */ - exc.type = OVERFLOW; - exc.name = "lgamma"; - if (_LIB_VERSION == _SVID_) - exc.retval = HUGE; - else - exc.retval = HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - errno = ERANGE; - } - break; - case 15: - /* ieee_lgamma(-integer) or ieee_lgamma(0) */ - exc.type = SING; - exc.name = "lgamma"; - if (_LIB_VERSION == _SVID_) - exc.retval = HUGE; - else - exc.retval = HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("lgamma: SING error\n", 19); - } - errno = EDOM; - } - break; - case 16: - /* ieee_log(0) */ - exc.type = SING; - exc.name = "log"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("log: SING error\n", 16); - } - errno = EDOM; - } - break; - case 17: - /* ieee_log(x<0) */ - exc.type = DOMAIN; - exc.name = "log"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("log: DOMAIN error\n", 18); - } - errno = EDOM; - } - break; - case 18: - /* ieee_log10(0) */ - exc.type = SING; - exc.name = "log10"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("log10: SING error\n", 18); - } - errno = EDOM; - } - break; - case 19: - /* ieee_log10(x<0) */ - exc.type = DOMAIN; - exc.name = "log10"; - if (_LIB_VERSION == _SVID_) - exc.retval = -HUGE; - else - exc.retval = -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("log10: DOMAIN error\n", 20); - } - errno = EDOM; - } - break; - case 20: - /* ieee_pow(0.0,0.0) */ - /* error only if _LIB_VERSION == _SVID_ */ - exc.type = DOMAIN; - exc.name = "pow"; - exc.retval = zero; - if (_LIB_VERSION != _SVID_) exc.retval = 1.0; - else if (!ieee_matherr(&exc)) { - (void) WRITE2("pow(0,0): DOMAIN error\n", 23); - errno = EDOM; - } - break; - case 21: - /* ieee_pow(x,y) overflow */ - exc.type = OVERFLOW; - exc.name = "pow"; - if (_LIB_VERSION == _SVID_) { - exc.retval = HUGE; - y *= 0.5; - if(xzero) ? HUGE : -HUGE); - else - exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL); - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - errno = ERANGE; - } - break; - case 26: - /* ieee_sqrt(x<0) */ - exc.type = DOMAIN; - exc.name = "sqrt"; - if (_LIB_VERSION == _SVID_) - exc.retval = zero; - else - exc.retval = zero/zero; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("sqrt: DOMAIN error\n", 19); - } - errno = EDOM; - } - break; - case 27: - /* ieee_fmod(x,0) */ - exc.type = DOMAIN; - exc.name = "fmod"; - if (_LIB_VERSION == _SVID_) - exc.retval = x; - else - exc.retval = zero/zero; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("fmod: DOMAIN error\n", 20); - } - errno = EDOM; - } - break; - case 28: - /* ieee_remainder(x,0) */ - exc.type = DOMAIN; - exc.name = "remainder"; - exc.retval = zero/zero; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("remainder: DOMAIN error\n", 24); - } - errno = EDOM; - } - break; - case 29: - /* acosh(x<1) */ - exc.type = DOMAIN; - exc.name = "acosh"; - exc.retval = zero/zero; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("acosh: DOMAIN error\n", 20); - } - errno = EDOM; - } - break; - case 30: - /* atanh(|x|>1) */ - exc.type = DOMAIN; - exc.name = "atanh"; - exc.retval = zero/zero; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("atanh: DOMAIN error\n", 20); - } - errno = EDOM; - } - break; - case 31: - /* atanh(|x|=1) */ - exc.type = SING; - exc.name = "atanh"; - exc.retval = x/zero; /* sign(x)*inf */ - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("atanh: SING error\n", 18); - } - errno = EDOM; - } - break; - case 32: - /* scalb overflow; SVID also returns +-HUGE_VAL */ - exc.type = OVERFLOW; - exc.name = "scalb"; - exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - errno = ERANGE; - } - break; - case 33: - /* scalb underflow */ - exc.type = UNDERFLOW; - exc.name = "scalb"; - exc.retval = ieee_copysign(zero,x); - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - errno = ERANGE; - } - break; - case 34: - /* ieee_j0(|x|>X_TLOSS) */ - exc.type = TLOSS; - exc.name = "j0"; - exc.retval = zero; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2(exc.name, 2); - (void) WRITE2(": TLOSS error\n", 14); - } - errno = ERANGE; - } - break; - case 35: - /* ieee_y0(x>X_TLOSS) */ - exc.type = TLOSS; - exc.name = "y0"; - exc.retval = zero; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2(exc.name, 2); - (void) WRITE2(": TLOSS error\n", 14); - } - errno = ERANGE; - } - break; - case 36: - /* ieee_j1(|x|>X_TLOSS) */ - exc.type = TLOSS; - exc.name = "j1"; - exc.retval = zero; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2(exc.name, 2); - (void) WRITE2(": TLOSS error\n", 14); - } - errno = ERANGE; - } - break; - case 37: - /* ieee_y1(x>X_TLOSS) */ - exc.type = TLOSS; - exc.name = "y1"; - exc.retval = zero; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2(exc.name, 2); - (void) WRITE2(": TLOSS error\n", 14); - } - errno = ERANGE; - } - break; - case 38: - /* ieee_jn(|x|>X_TLOSS) */ - exc.type = TLOSS; - exc.name = "jn"; - exc.retval = zero; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2(exc.name, 2); - (void) WRITE2(": TLOSS error\n", 14); - } - errno = ERANGE; - } - break; - case 39: - /* ieee_yn(x>X_TLOSS) */ - exc.type = TLOSS; - exc.name = "yn"; - exc.retval = zero; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2(exc.name, 2); - (void) WRITE2(": TLOSS error\n", 14); - } - errno = ERANGE; - } - break; - case 40: - /* ieee_gamma(finite) overflow */ - exc.type = OVERFLOW; - exc.name = "gamma"; - if (_LIB_VERSION == _SVID_) - exc.retval = HUGE; - else - exc.retval = HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = ERANGE; - else if (!ieee_matherr(&exc)) { - errno = ERANGE; - } - break; - case 41: - /* ieee_gamma(-integer) or ieee_gamma(0) */ - exc.type = SING; - exc.name = "gamma"; - if (_LIB_VERSION == _SVID_) - exc.retval = HUGE; - else - exc.retval = HUGE_VAL; - if (_LIB_VERSION == _POSIX_) - errno = EDOM; - else if (!ieee_matherr(&exc)) { - if (_LIB_VERSION == _SVID_) { - (void) WRITE2("gamma: SING error\n", 18); - } - errno = EDOM; - } - break; - case 42: - /* ieee_pow(NaN,0.0) */ - /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */ - exc.type = DOMAIN; - exc.name = "pow"; - exc.retval = x; - if (_LIB_VERSION == _IEEE_ || - _LIB_VERSION == _POSIX_) exc.retval = 1.0; - else if (!ieee_matherr(&exc)) { - errno = EDOM; - } - break; - } - return exc.retval; -} diff --git a/k_tan.c b/k_tan.c deleted file mode 100644 index d789a40..0000000 --- a/k_tan.c +++ /dev/null @@ -1,148 +0,0 @@ -#pragma ident "@(#)k_tan.c 1.5 04/04/22 SMI" - -/* - * ==================================================== - * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* INDENT OFF */ -/* __kernel_tan( x, y, k ) - * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * Input k indicates whether ieee_tan (if k = 1) or -1/tan (if k = -1) is returned. - * - * Algorithm - * 1. Since ieee_tan(-x) = -ieee_tan(x), we need only to consider positive x. - * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. - * 3. ieee_tan(x) is approximated by a odd polynomial of degree 27 on - * [0,0.67434] - * 3 27 - * tan(x) ~ x + T1*x + ... + T13*x - * where - * - * |ieee_tan(x) 2 4 26 | -59.2 - * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 - * | x | - * - * Note: ieee_tan(x+y) = ieee_tan(x) + tan'(x)*y - * ~ ieee_tan(x) + (1+x*x)*y - * Therefore, for better accuracy in computing ieee_tan(x+y), let - * 3 2 2 2 2 - * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) - * then - * 3 2 - * tan(x+y) = x + (T1*x + (x *(r+y)+y)) - * - * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then - * tan(x) = ieee_tan(pi/4-y) = (1-ieee_tan(y))/(1+ieee_tan(y)) - * = 1 - 2*(ieee_tan(y) - (ieee_tan(y)^2)/(1+ieee_tan(y))) - */ - -#include "fdlibm.h" - -static const double xxx[] = { - 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ - 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ - 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ - 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ - 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ - 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ - 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ - 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ - 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ - 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ - 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ - -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ - 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ -/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ -/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ -/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */ -}; -#define one xxx[13] -#define pio4 xxx[14] -#define pio4lo xxx[15] -#define T xxx -/* INDENT ON */ - -double -__kernel_tan(double x, double y, int iy) { - double z, r, v, w, s; - int ix, hx; - - hx = __HI(x); /* high word of x */ - ix = hx & 0x7fffffff; /* high word of |x| */ - if (ix < 0x3e300000) { /* x < 2**-28 */ - if ((int) x == 0) { /* generate inexact */ - if (((ix | __LO(x)) | (iy + 1)) == 0) - return one / ieee_fabs(x); - else { - if (iy == 1) - return x; - else { /* compute -1 / (x+y) carefully */ - double a, t; - - z = w = x + y; - __LO(z) = 0; - v = y - (z - x); - t = a = -one / w; - __LO(t) = 0; - s = one + t * z; - return t + a * (s + t * v); - } - } - } - } - if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ - if (hx < 0) { - x = -x; - y = -y; - } - z = pio4 - x; - w = pio4lo - y; - x = z + w; - y = 0.0; - } - z = x * x; - w = z * z; - /* - * Break x^5*(T[1]+x^2*T[2]+...) into - * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + - * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) - */ - r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + - w * T[11])))); - v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + - w * T[12]))))); - s = z * x; - r = y + z * (s * (r + v) + y); - r += T[0] * s; - w = x + r; - if (ix >= 0x3FE59428) { - v = (double) iy; - return (double) (1 - ((hx >> 30) & 2)) * - (v - 2.0 * (x - (w * w / (w + v) - r))); - } - if (iy == 1) - return w; - else { - /* - * if allow error up to 2 ulp, simply return - * -1.0 / (x+r) here - */ - /* compute -1.0 / (x+r) accurately */ - double a, t; - z = w; - __LO(z) = 0; - v = r - (z - x); /* z+v = r+x */ - t = a = -1.0 / w; /* a = -1.0/w */ - __LO(t) = 0; - s = 1.0 + t * z; - return t + a * (s + t * v); - } -} diff --git a/makefile.in b/makefile.in deleted file mode 100644 index b125beb..0000000 --- a/makefile.in +++ /dev/null @@ -1,154 +0,0 @@ -# -# @(#)Makefile 1.4 95/01/18 -# -# ==================================================== -# Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. -# -# Developed at SunSoft, a Sun Microsystems, Inc. business. -# Permission to use, copy, modify, and distribute this -# software is freely granted, provided that this notice -# is preserved. -# ==================================================== -# -# - -# -# There are two options in making libm at fdlibm compile time: -# _IEEE_LIBM --- IEEE libm; smaller, and somewhat faster -# _MULTI_LIBM --- Support multi-standard at runtime by -# imposing wrapper functions defined in -# fdlibm.h: -# _IEEE_MODE -- IEEE -# _XOPEN_MODE -- X/OPEN -# _POSIX_MODE -- POSIX/ANSI -# _SVID3_MODE -- SVID -# -# Here is how to set up CFLAGS to create the desired libm at -# compile time: -# -# CFLAGS = -D_IEEE_LIBM ... IEEE libm (recommended) -# CFLAGS = -D_SVID3_MODE ... Multi-standard supported -# libm with SVID as the -# default standard -# CFLAGS = -D_XOPEN_MODE ... Multi-standard supported -# libm with XOPEN as the -# default standard -# CFLAGS = -D_POSIX_MODE ... Multi-standard supported -# libm with POSIX as the -# default standard -# CFLAGS = ... Multi-standard supported -# libm with IEEE as the -# default standard -# -# NOTE: if scalb's second arguement is an int, then one must -# define _SCALB_INT in CFLAGS. The default prototype of scalb -# is double ieee_scalb(double, double) -# - -prefix = @prefix@ - -AR = @AR@ - -CC = @CC@ - -# -# Default IEEE libm -# -CFLAGS = @CFLAGS@ -D_IEEE_LIBM - -CHMOD = @CHMOD@ - -CP = @CP@ - -INCFILES = fdlibm.h - -LDFLAGS = @LDFLAGS@ - -LIB = libfdm.a - -LIBS = @LIBS@ - -RANLIB = @RANLIB@ - -RM = @RM@ -f - -.INIT: $(INCFILES) - -.KEEP_STATE: - -src = k_standard.c k_rem_pio2.c \ - k_cos.c k_sin.c k_tan.c \ - e_acos.c e_acosh.c e_asin.c e_atan2.c \ - e_atanh.c e_cosh.c e_exp.c e_fmod.c \ - e_gamma.c e_gamma_r.c e_hypot.c e_j0.c \ - e_j1.c e_jn.c e_lgamma.c e_lgamma_r.c \ - e_log.c e_log10.c e_pow.c e_rem_pio2.c e_remainder.c \ - e_scalb.c e_sinh.c e_sqrt.c \ - w_acos.c w_acosh.c w_asin.c w_atan2.c \ - w_atanh.c w_cosh.c w_exp.c w_fmod.c \ - w_gamma.c w_gamma_r.c w_hypot.c w_j0.c \ - w_j1.c w_jn.c w_lgamma.c w_lgamma_r.c \ - w_log.c w_log10.c w_pow.c w_remainder.c \ - w_scalb.c w_sinh.c w_sqrt.c \ - s_asinh.c s_atan.c s_cbrt.c s_ceil.c s_copysign.c \ - s_cos.c s_erf.c s_expm1.c s_fabs.c s_finite.c s_floor.c \ - s_frexp.c s_ilogb.c s_isnan.c s_ldexp.c s_lib_version.c \ - s_log1p.c s_logb.c s_matherr.c s_modf.c s_nextafter.c \ - s_rint.c s_scalbn.c s_signgam.c s_significand.c s_sin.c \ - s_tan.c s_tanh.c - -obj = k_standard.o k_rem_pio2.o \ - k_cos.o k_sin.o k_tan.o \ - e_acos.o e_acosh.o e_asin.o e_atan2.o \ - e_atanh.o e_cosh.o e_exp.o e_fmod.o \ - e_gamma.o e_gamma_r.o e_hypot.o e_j0.o \ - e_j1.o e_jn.o e_lgamma.o e_lgamma_r.o \ - e_log.o e_log10.o e_pow.o e_rem_pio2.o e_remainder.o \ - e_scalb.o e_sinh.o e_sqrt.o \ - w_acos.o w_acosh.o w_asin.o w_atan2.o \ - w_atanh.o w_cosh.o w_exp.o w_fmod.o \ - w_gamma.o w_gamma_r.o w_hypot.o w_j0.o \ - w_j1.o w_jn.o w_lgamma.o w_lgamma_r.o \ - w_log.o w_log10.o w_pow.o w_remainder.o \ - w_scalb.o w_sinh.o w_sqrt.o \ - s_asinh.o s_atan.o s_cbrt.o s_ceil.o s_copysign.o \ - s_cos.o s_erf.o s_expm1.o s_fabs.o s_finite.o s_floor.o \ - s_frexp.o s_ilogb.o s_isnan.o s_ldexp.o s_lib_version.o \ - s_log1p.o s_logb.o s_matherr.o s_modf.o s_nextafter.o \ - s_rint.o s_scalbn.o s_signgam.o s_significand.o s_sin.o \ - s_tan.o s_tanh.o - -all: $(LIB) - -check: - @echo This package does not have a validation suite. - -clean: - -$(RM) *~ #* core a.out - -distclean: mostlyclean - -$(RM) $(LIB) - -$(RM) -r autom4te.cache/ - -$(RM) config.cache config.log config.status Makefile - -install: $(LIB) uninstall - $(CP) $(LIB) $(prefix)/lib/$(LIB) - $(CHMOD) 664 $(prefix)/lib/$(LIB) - $(RANLIB) $(prefix)/lib/$(LIB) || true - -$(LIB) : $(obj) - $(AR) cru $(LIB) $(obj) - $(RANLIB) $(LIB) || true - -maintainer-clean: distclean - @echo "This command is intended for maintainers to use;" - @echo "it deletes files that may require special tools to rebuild." - -$(RM) configure - -mostlyclean: clean - -$(RM) $(obj) - -source: $(src) README - -uninstall: - -$(RM) $(prefix)/lib/$(LIB) diff --git a/readme b/readme deleted file mode 100644 index a0d5623..0000000 --- a/readme +++ /dev/null @@ -1,261 +0,0 @@ - - ********************************* - * Announcing FDLIBM Version 5.3 * - ********************************* -============================================================ - FDLIBM -============================================================ - developed at Sun Microsystems, Inc. - -What's new in FDLIBM 5.3? - -CONFIGURE - To build FDLIBM, edit the supplied Makefile or create - a local Makefile by running "sh configure" - using the supplied configure script contributed by Nelson Beebe - -BUGS FIXED - - 1. e_pow.c incorrect results when - x is very close to -1.0 and y is very large, e.g. - pow(-1.0000000000000002e+00,4.5035996273704970e+15) = 0 - pow(-9.9999999999999978e-01,4.5035996273704970e+15) = 0 - Correct results are close to -e and -1/e. - - 2. k_tan.c error was > 1 ulp target for FDLIBM - 5.2: Worst error at least 1.45 ulp at - tan(1.7765241907548024E+269) = 1.7733884462610958E+16 - 5.3: Worst error 0.96 ulp - -NOT FIXED YET - - 3. Compiler failure on non-standard code - Statements like - *(1+(int*)&t1) = 0; - are not standard C and cause some optimizing compilers (e.g. GCC) - to generate bad code under optimization. These cases - are to be addressed in the next release. - -FDLIBM (Freely Distributable LIBM) is a C math library -for machines that support IEEE 754 floating-point arithmetic. -In this release, only double precision is supported. - -FDLIBM is intended to provide a reasonably portable (see -assumptions below), reference quality (below one ulp for -major functions like sin,cos,exp,log) math library -(libm.a). For a copy of FDLIBM, please see - http://www.netlib.org/fdlibm/ -or - http://www.validlab.com/software/ - --------------- -1. ASSUMPTIONS --------------- -FDLIBM (double precision version) assumes: - a. IEEE 754 style (if not precise compliance) arithmetic; - b. 32 bit 2's complement integer arithmetic; - c. Each double precision floating-point number must be in IEEE 754 - double format, and that each number can be retrieved as two 32-bit - integers through the using of pointer bashing as in the example - below: - - Example: let y = 2.0 - double fp number y: 2.0 - IEEE double format: 0x4000000000000000 - - Referencing y as two integers: - *(int*)&y,*(1+(int*)&y) = {0x40000000,0x0} (on sparc) - {0x0,0x40000000} (on 386) - - Note: Four macros are defined in fdlibm.h to handle this kind of - retrieving: - - __HI(x) the high part of a double x - (sign,exponent,the first 21 significant bits) - __LO(x) the least 32 significant bits of x - __HIp(x) same as __HI except that the argument is a pointer - to a double - __LOp(x) same as __LO except that the argument is a pointer - to a double - - To ensure obtaining correct ordering, one must define __LITTLE_ENDIAN - during compilation for little endian machine (like 386,486). The - default is big endian. - - If the behavior of pointer bashing is undefined, one may hack on the - macro in fdlibm.h. - - d. IEEE exceptions may trigger "signals" as is common in Unix - implementations. - -------------------- -2. EXCEPTION CASES -------------------- -All exception cases in the FDLIBM functions will be mapped -to one of the following four exceptions: - - +-huge*huge, +-tiny*tiny, +-1.0/0.0, +-0.0/0.0 - (overflow) (underflow) (divided-by-zero) (invalid) - -For example, ieee_log(0) is a singularity and is thus mapped to - -1.0/0.0 = -infinity. -That is, FDLIBM's log will compute -one/zero and return the -computed value. On an IEEE machine, this will trigger the -divided-by-zero exception and a negative infinity is returned by -default. - -Similarly, ieee_exp(-huge) will be mapped to tiny*tiny to generate -an underflow signal. - - --------------------------------- -3. STANDARD CONFORMANCE WRAPPER --------------------------------- -The default FDLIBM functions (compiled with -D_IEEE_LIBM flag) -are in "IEEE spirit" (i.e., return the most reasonable result in -floating-point arithmetic). If one wants FDLIBM to comply with -standards like SVID, X/OPEN, or POSIX/ANSI, then one can -create a multi-standard compliant FDLIBM. In this case, each -function in FDLIBM is actually a standard compliant wrapper -function. - -File organization: - 1. For FDLIBM's kernel (internal) function, - File name Entry point - --------------------------- - k_sin.c __kernel_sin - k_tan.c __kernel_tan - --------------------------- - 2. For functions that have no standards conflict - File name Entry point - --------------------------- - s_sin.c sin - s_erf.c erf - --------------------------- - 3. Ieee754 core functions - File name Entry point - --------------------------- - e_exp.c __ieee754_exp - e_sinh.c __ieee754_sinh - --------------------------- - 4. Wrapper functions - File name Entry point - --------------------------- - w_exp.c exp - w_sinh.c sinh - --------------------------- - -Wrapper functions will twist the result of the ieee754 -function to comply to the standard specified by the value -of _LIB_VERSION - if _LIB_VERSION = _IEEE_, return the ieee754 result; - if _LIB_VERSION = _SVID_, return SVID result; - if _LIB_VERSION = _XOPEN_, return XOPEN result; - if _LIB_VERSION = _POSIX_, return POSIX/ANSI result. -(These are macros, see fdlibm.h for their definition.) - - --------------------------------- -4. HOW TO CREATE FDLIBM's libm.a --------------------------------- -There are two types of libm.a. One is IEEE only, and the other is -multi-standard compliant (supports IEEE,XOPEN,POSIX/ANSI,SVID). - -To create the IEEE only libm.a, use - make "CFLAGS = -D_IEEE_LIBM" -This will create an IEEE libm.a, which is smaller in size, and -somewhat faster. - -To create a multi-standard compliant libm, use - make "CFLAGS = -D_IEEE_MODE" --- multi-standard fdlibm: default - to IEEE - make "CFLAGS = -D_XOPEN_MODE" --- multi-standard fdlibm: default - to X/OPEN - make "CFLAGS = -D_POSIX_MODE" --- multi-standard fdlibm: default - to POSIX/ANSI - make "CFLAGS = -D_SVID3_MODE" --- multi-standard fdlibm: default - to SVID - - -Here is how one makes a SVID compliant libm. - Make the library by - make "CFLAGS = -D_SVID3_MODE". - The libm.a of FDLIBM will be multi-standard compliant and - _LIB_VERSION is initialized to the value _SVID_ . - - example1: - --------- - main() - { - double ieee_y0(); - printf("y0(1e300) = %1.20e\n",y0(1e300)); - exit(0); - } - - % cc example1.c libm.a - % a.out - y0: TLOSS error - ieee_y0(1e300) = 0.00000000000000000000e+00 - - -It is possible to change the default standard in multi-standard -fdlibm. Here is an example of how to do it: - example2: - --------- - #include "fdlibm.h" /* must include FDLIBM's fdlibm.h */ - main() - { - double ieee_y0(); - _LIB_VERSION = _IEEE_; - printf("IEEE: ieee_y0(1e300) = %1.20e\n",y0(1e300)); - _LIB_VERSION = _XOPEN_; - printf("XOPEN ieee_y0(1e300) = %1.20e\n",y0(1e300)); - _LIB_VERSION = _POSIX_; - printf("POSIX ieee_y0(1e300) = %1.20e\n",y0(1e300)); - _LIB_VERSION = _SVID_; - printf("SVID ieee_y0(1e300) = %1.20e\n",y0(1e300)); - exit(0); - } - - % cc example2.c libm.a - % a.out - IEEE: ieee_y0(1e300) = -1.36813604503424810557e-151 - XOPEN ieee_y0(1e300) = 0.00000000000000000000e+00 - POSIX ieee_y0(1e300) = 0.00000000000000000000e+00 - y0: TLOSS error - SVID ieee_y0(1e300) = 0.00000000000000000000e+00 - -Note: Here _LIB_VERSION is a global variable. If global variables - are forbidden, then one should modify fdlibm.h to change - _LIB_VERSION to be a global constant. In this case, one - may not change the value of _LIB_VERSION as in example2. - ---------------------------- -5. NOTES ON PORTING FDLIBM ---------------------------- - Care must be taken when installing FDLIBM over existing - libm.a. - All co-existing function prototypes must agree, otherwise - users will encounter mysterious failures. - - So far, the only known likely conflict is the declaration - of the IEEE recommended function scalb: - - double ieee_scalb(double,double) (1) SVID3 defined - double ieee_scalb(double,int) (2) IBM,DEC,... - - FDLIBM follows Sun definition and use (1) as default. - If one's existing libm.a uses (2), then one may raise - the flags _SCALB_INT during the compilation of FDLIBM - to get the correct function prototype. - (E.g., make "CFLAGS = -D_IEEE_LIBM -D_SCALB_INT".) - NOTE that if -D_SCALB_INT is raised, it won't be SVID3 - conformant. - --------------- -6. PROBLEMS ? --------------- -Please send comments and bug reports to the electronic mail address -suggested by: - fdlibm-comments AT sun.com - diff --git a/s_asinh.c b/s_asinh.c deleted file mode 100644 index c1d7bf1..0000000 --- a/s_asinh.c +++ /dev/null @@ -1,61 +0,0 @@ - -/* @(#)s_asinh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* asinh(x) - * Method : - * Based on - * asinh(x) = sign(x) * log [ |x| + ieee_sqrt(x*x+1) ] - * we have - * asinh(x) := x if 1+x*x=1, - * := sign(x)*(ieee_log(x)+ln2)) for large |x|, else - * := sign(x)*ieee_log(2|x|+1/(|x|+ieee_sqrt(x*x+1))) if|x|>2, else - * := sign(x)*ieee_log1p(|x| + x^2/(1 + ieee_sqrt(1+x^2))) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ -huge= 1.00000000000000000000e+300; - -#ifdef __STDC__ - double asinh(double x) -#else - double asinh(x) - double x; -#endif -{ - double t,w; - int hx,ix; - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ - if(ix< 0x3e300000) { /* |x|<2**-28 */ - if(huge+x>one) return x; /* return x inexact except 0 */ - } - if(ix>0x41b00000) { /* |x| > 2**28 */ - w = __ieee754_log(ieee_fabs(x))+ln2; - } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ - t = ieee_fabs(x); - w = __ieee754_log(2.0*t+one/(ieee_sqrt(x*x+one)+t)); - } else { /* 2.0 > |x| > 2**-28 */ - t = x*x; - w =ieee_log1p(ieee_fabs(x)+t/(one+ieee_sqrt(one+t))); - } - if(hx>0) return w; else return -w; -} diff --git a/s_atan.c b/s_atan.c deleted file mode 100644 index 2be1182..0000000 --- a/s_atan.c +++ /dev/null @@ -1,134 +0,0 @@ - -/* @(#)s_atan.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* ieee_atan(x) - * Method - * 1. Reduce x to positive by ieee_atan(x) = -ieee_atan(-x). - * 2. According to the integer k=4t+0.25 chopped, t=x, the argument - * is further reduced to one of the following intervals and the - * arctangent of t is evaluated by the corresponding formula: - * - * [0,7/16] ieee_atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) - * [7/16,11/16] ieee_atan(x) = ieee_atan(1/2) + ieee_atan( (t-0.5)/(1+t/2) ) - * [11/16.19/16] ieee_atan(x) = ieee_atan( 1 ) + ieee_atan( (t-1)/(1+t) ) - * [19/16,39/16] ieee_atan(x) = ieee_atan(3/2) + ieee_atan( (t-1.5)/(1+1.5t) ) - * [39/16,INF] ieee_atan(x) = ieee_atan(INF) + ieee_atan( -1/t ) - * - * 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 "fdlibm.h" - -#ifdef __STDC__ -static const double atanhi[] = { -#else -static double atanhi[] = { -#endif - 4.63647609000806093515e-01, /* ieee_atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ - 7.85398163397448278999e-01, /* ieee_atan(1.0)hi 0x3FE921FB, 0x54442D18 */ - 9.82793723247329054082e-01, /* ieee_atan(1.5)hi 0x3FEF730B, 0xD281F69B */ - 1.57079632679489655800e+00, /* ieee_atan(inf)hi 0x3FF921FB, 0x54442D18 */ -}; - -#ifdef __STDC__ -static const double atanlo[] = { -#else -static double atanlo[] = { -#endif - 2.26987774529616870924e-17, /* ieee_atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ - 3.06161699786838301793e-17, /* ieee_atan(1.0)lo 0x3C81A626, 0x33145C07 */ - 1.39033110312309984516e-17, /* ieee_atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ - 6.12323399573676603587e-17, /* ieee_atan(inf)lo 0x3C91A626, 0x33145C07 */ -}; - -#ifdef __STDC__ -static const double aT[] = { -#else -static double aT[] = { -#endif - 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ - -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ - 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ - -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ - 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ - -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ - 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ - -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ - 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ - -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ - 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ -}; - -#ifdef __STDC__ - static const double -#else - static double -#endif -one = 1.0, -huge = 1.0e300; - -#ifdef __STDC__ - double ieee_atan(double x) -#else - double ieee_atan(x) - double x; -#endif -{ - double w,s1,s2,z; - int ix,hx,id; - - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x44100000) { /* if |x| >= 2^66 */ - if(ix>0x7ff00000|| - (ix==0x7ff00000&&(__LO(x)!=0))) - return x+x; /* NaN */ - if(hx>0) return atanhi[3]+atanlo[3]; - else return -atanhi[3]-atanlo[3]; - } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ - if (ix < 0x3e200000) { /* |x| < 2^-29 */ - if(huge+x>one) return x; /* raise inexact */ - } - id = -1; - } else { - x = ieee_fabs(x); - if (ix < 0x3ff30000) { /* |x| < 1.1875 */ - if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ - id = 0; x = (2.0*x-one)/(2.0+x); - } else { /* 11/16<=|x|< 19/16 */ - id = 1; x = (x-one)/(x+one); - } - } else { - if (ix < 0x40038000) { /* |x| < 2.4375 */ - id = 2; x = (x-1.5)/(one+1.5*x); - } else { /* 2.4375 <= |x| < 2^66 */ - id = 3; x = -1.0/x; - } - }} - /* end of argument reduction */ - z = x*x; - w = z*z; - /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ - s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); - s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); - if (id<0) return x - x*(s1+s2); - else { - z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); - return (hx<0)? -z:z; - } -} diff --git a/s_cbrt.c b/s_cbrt.c deleted file mode 100644 index f8ce933..0000000 --- a/s_cbrt.c +++ /dev/null @@ -1,87 +0,0 @@ - -/* @(#)s_cbrt.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -#include "fdlibm.h" - -/* ieee_cbrt(x) - * Return cube root of x - */ -#ifdef __STDC__ -static const unsigned -#else -static unsigned -#endif - B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ - B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ - -#ifdef __STDC__ -static const double -#else -static double -#endif -C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ -D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ -E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ -F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ -G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ - -#ifdef __STDC__ - double ieee_cbrt(double x) -#else - double ieee_cbrt(x) - double x; -#endif -{ - int hx; - double r,s,t=0.0,w; - unsigned sign; - - - hx = __HI(x); /* high word of x */ - sign=hx&0x80000000; /* sign= sign(x) */ - hx ^=sign; - if(hx>=0x7ff00000) return(x+x); /* ieee_cbrt(NaN,INF) is itself */ - if((hx|__LO(x))==0) - return(x); /* ieee_cbrt(0) is itself */ - - __HI(x) = hx; /* x <- |x| */ - /* rough cbrt to 5 bits */ - if(hx<0x00100000) /* subnormal number */ - {__HI(t)=0x43500000; /* set t= 2**54 */ - t*=x; __HI(t)=__HI(t)/3+B2; - } - else - __HI(t)=hx/3+B1; - - - /* new cbrt to 23 bits, may be implemented in single precision */ - r=t*t/x; - s=C+r*t; - t*=G+F/(s+E+D/s); - - /* chopped to 20 bits and make it larger than ieee_cbrt(x) */ - __LO(t)=0; __HI(t)+=0x00000001; - - - /* one step newton iteration to 53 bits with error less than 0.667 ulps */ - s=t*t; /* t*t is exact */ - r=x/s; - w=t+t; - r=(r-t)/(w+r); /* r-s is exact */ - t=t+t*r; - - /* retore the sign bit */ - __HI(t) |= sign; - return(t); -} diff --git a/s_ceil.c b/s_ceil.c deleted file mode 100644 index cddb1d6..0000000 --- a/s_ceil.c +++ /dev/null @@ -1,78 +0,0 @@ - -/* @(#)s_ceil.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * ieee_ceil(x) - * Return x rounded toward -inf to integral value - * Method: - * Bit twiddling. - * Exception: - * Inexact flag raised if x not equal to ieee_ceil(x). - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double huge = 1.0e300; -#else -static double huge = 1.0e300; -#endif - -#ifdef __STDC__ - double ieee_ceil(double x) -#else - double ieee_ceil(x) - double x; -#endif -{ - int i0,i1,j0; - unsigned i,j; - i0 = __HI(x); - i1 = __LO(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=0x80000000;i1=0;} - else if((i0|i1)!=0) { i0=0x3ff00000;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 = ((unsigned)(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=0x7ff00000) return x-x; - - /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x,y); - switch(n&3) { - case 0: return __kernel_cos(y[0],y[1]); - case 1: return -__kernel_sin(y[0],y[1],1); - case 2: return -__kernel_cos(y[0],y[1]); - default: - return __kernel_sin(y[0],y[1],1); - } - } -} diff --git a/s_erf.c b/s_erf.c deleted file mode 100644 index f4e3856..0000000 --- a/s_erf.c +++ /dev/null @@ -1,310 +0,0 @@ - -/* @(#)s_erf.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* double ieee_erf(double x) - * double ieee_erfc(double x) - * x - * 2 |\ - * ieee_erf(x) = --------- | ieee_exp(-t*t)dt - * ieee_sqrt(pi) \| - * 0 - * - * ieee_erfc(x) = 1-ieee_erf(x) - * Note that - * erf(-x) = -ieee_erf(x) - * erfc(-x) = 2 - ieee_erfc(x) - * - * Method: - * 1. For |x| in [0, 0.84375] - * ieee_erf(x) = x + x*R(x^2) - * ieee_erfc(x) = 1 - ieee_erf(x) if x in [-.84375,0.25] - * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] - * where R = P/Q where P is an odd poly of degree 8 and - * Q is an odd poly of degree 10. - * -57.90 - * | R - (ieee_erf(x)-x)/x | <= 2 - * - * - * Remark. The formula is derived by noting - * ieee_erf(x) = (2/ieee_sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) - * and that - * 2/ieee_sqrt(pi) = 1.128379167095512573896158903121545171688 - * is close to one. The interval is chosen because the fix - * point of ieee_erf(x) is near 0.6174 (i.e., ieee_erf(x)=x when x is - * near 0.6174), and by some experiment, 0.84375 is chosen to - * guarantee the error is less than one ulp for erf. - * - * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and - * c = 0.84506291151 rounded to single (24 bits) - * erf(x) = sign(x) * (c + P1(s)/Q1(s)) - * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 - * 1+(c+P1(s)/Q1(s)) if x < 0 - * |P1/Q1 - (ieee_erf(|x|)-c)| <= 2**-59.06 - * Remark: here we use the taylor series expansion at x=1. - * erf(1+s) = ieee_erf(1) + s*Poly(s) - * = 0.845.. + P1(s)/Q1(s) - * That is, we use rational approximation to approximate - * erf(1+s) - (c = (single)0.84506291151) - * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] - * where - * P1(s) = degree 6 poly in s - * Q1(s) = degree 6 poly in s - * - * 3. For x in [1.25,1/0.35(~2.857143)], - * erfc(x) = (1/x)*ieee_exp(-x*x-0.5625+R1/S1) - * erf(x) = 1 - ieee_erfc(x) - * where - * R1(z) = degree 7 poly in z, (z=1/x^2) - * S1(z) = degree 8 poly in z - * - * 4. For x in [1/0.35,28] - * erfc(x) = (1/x)*ieee_exp(-x*x-0.5625+R2/S2) if x > 0 - * = 2.0 - (1/x)*ieee_exp(-x*x-0.5625+R2/S2) if -6 x >= 28 - * erf(x) = sign(x) *(1 - tiny) (raise inexact) - * erfc(x) = tiny*tiny (raise underflow) if x > 0 - * = 2 - tiny if x<0 - * - * 7. Special case: - * erf(0) = 0, ieee_erf(inf) = 1, ieee_erf(-inf) = -1, - * erfc(0) = 1, ieee_erfc(inf) = 0, ieee_erfc(-inf) = 2, - * erfc/ieee_erf(NaN) is NaN - */ - - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -tiny = 1e-300, -half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ - /* c = (float)0.84506291151 */ -erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ -/* - * Coefficients for approximation to erf on [0,0.84375] - */ -efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ -efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ -pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ -pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ -pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ -pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ -pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ -qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ -qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ -qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ -qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ -qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ -/* - * Coefficients for approximation to erf in [0.84375,1.25] - */ -pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ -pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ -pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ -pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ -pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ -pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ -pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ -qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ -qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ -qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ -qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ -qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ -qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ -/* - * Coefficients for approximation to erfc in [1.25,1/0.35] - */ -ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ -ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ -ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ -ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ -ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ -ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ -ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ -ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ -sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ -sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ -sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ -sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ -sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ -sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ -sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ -sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ -/* - * Coefficients for approximation to erfc in [1/.35,28] - */ -rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ -rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ -rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ -rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ -rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ -rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ -rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ -sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ -sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ -sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ -sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ -sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ -sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ -sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ - -#ifdef __STDC__ - double ieee_erf(double x) -#else - double ieee_erf(x) - double x; -#endif -{ - int hx,ix,i; - double R,S,P,Q,s,y,z,r; - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) { /* ieee_erf(nan)=nan */ - i = ((unsigned)hx>>31)<<1; - return (double)(1-i)+one/x; /* ieee_erf(+-inf)=+-1 */ - } - - if(ix < 0x3feb0000) { /* |x|<0.84375 */ - if(ix < 0x3e300000) { /* |x|<2**-28 */ - if (ix < 0x00800000) - return 0.125*(8.0*x+efx8*x); /*avoid underflow */ - return x + efx*x; - } - z = x*x; - r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); - s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); - y = r/s; - return x + x*y; - } - if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ - s = ieee_fabs(x)-one; - P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); - Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); - if(hx>=0) return erx + P/Q; else return -erx - P/Q; - } - if (ix >= 0x40180000) { /* inf>|x|>=6 */ - if(hx>=0) return one-tiny; else return tiny-one; - } - x = ieee_fabs(x); - s = one/(x*x); - if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */ - R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( - ra5+s*(ra6+s*ra7)))))); - S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( - sa5+s*(sa6+s*(sa7+s*sa8))))))); - } else { /* |x| >= 1/0.35 */ - R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( - rb5+s*rb6))))); - S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( - sb5+s*(sb6+s*sb7)))))); - } - z = x; - __LO(z) = 0; - r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S); - if(hx>=0) return one-r/x; else return r/x-one; -} - -#ifdef __STDC__ - double ieee_erfc(double x) -#else - double ieee_erfc(x) - double x; -#endif -{ - int hx,ix; - double R,S,P,Q,s,y,z,r; - hx = __HI(x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) { /* ieee_erfc(nan)=nan */ - /* ieee_erfc(+-inf)=0,2 */ - return (double)(((unsigned)hx>>31)<<1)+one/x; - } - - if(ix < 0x3feb0000) { /* |x|<0.84375 */ - if(ix < 0x3c700000) /* |x|<2**-56 */ - return one-x; - z = x*x; - r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); - s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); - y = r/s; - if(hx < 0x3fd00000) { /* x<1/4 */ - return one-(x+x*y); - } else { - r = x*y; - r += (x-half); - return half - r ; - } - } - if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ - s = ieee_fabs(x)-one; - P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); - Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); - if(hx>=0) { - z = one-erx; return z - P/Q; - } else { - z = erx+P/Q; return one+z; - } - } - if (ix < 0x403c0000) { /* |x|<28 */ - x = ieee_fabs(x); - s = one/(x*x); - if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/ - R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( - ra5+s*(ra6+s*ra7)))))); - S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( - sa5+s*(sa6+s*(sa7+s*sa8))))))); - } else { /* |x| >= 1/.35 ~ 2.857143 */ - if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */ - R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( - rb5+s*rb6))))); - S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( - sb5+s*(sb6+s*sb7)))))); - } - z = x; - __LO(z) = 0; - r = __ieee754_exp(-z*z-0.5625)* - __ieee754_exp((z-x)*(z+x)+R/S); - if(hx>0) return r/x; else return two-r/x; - } else { - if(hx>0) return tiny*tiny; else return two-tiny; - } -} diff --git a/s_expm1.c b/s_expm1.c deleted file mode 100644 index f1f01af..0000000 --- a/s_expm1.c +++ /dev/null @@ -1,216 +0,0 @@ - -/* @(#)s_expm1.c 1.5 04/04/22 */ -/* - * ==================================================== - * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* ieee_expm1(x) - * Returns ieee_exp(x)-1, the exponential of x minus 1. - * - * Method - * 1. Argument reduction: - * Given x, find r and integer k such that - * - * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 - * - * Here a correction term c will be computed to compensate - * the error in r when rounded to a floating-point number. - * - * 2. Approximating ieee_expm1(r) by a special rational function on - * the interval [0,0.34658]: - * Since - * r*(ieee_exp(r)+1)/(ieee_exp(r)-1) = 2+ r^2/6 - r^4/360 + ... - * we define R1(r*r) by - * r*(ieee_exp(r)+1)/(ieee_exp(r)-1) = 2+ r^2/6 * R1(r*r) - * That is, - * R1(r**2) = 6/r *((ieee_exp(r)+1)/(ieee_exp(r)-1) - 2/r) - * = 6/r * ( 1 + 2.0*(1/(ieee_exp(r)-1) - 1/r)) - * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... - * We use a special Remes algorithm on [0,0.347] to generate - * a polynomial of degree 5 in r*r to approximate R1. The - * maximum error of this polynomial approximation is bounded - * by 2**-61. In other words, - * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 - * where Q1 = -1.6666666666666567384E-2, - * Q2 = 3.9682539681370365873E-4, - * Q3 = -9.9206344733435987357E-6, - * Q4 = 2.5051361420808517002E-7, - * Q5 = -6.2843505682382617102E-9; - * (where z=r*r, and the values of Q1 to Q5 are listed below) - * with error bounded by - * | 5 | -61 - * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 - * | | - * - * expm1(r) = ieee_exp(r)-1 is then computed by the following - * specific way which minimize the accumulation rounding error: - * 2 3 - * r r [ 3 - (R1 + R1*r/2) ] - * ieee_expm1(r) = r + --- + --- * [--------------------] - * 2 2 [ 6 - r*(3 - R1*r/2) ] - * - * To compensate the error in the argument reduction, we use - * expm1(r+c) = ieee_expm1(r) + c + ieee_expm1(r)*c - * ~ ieee_expm1(r) + c + r*c - * Thus c+r*c will be added in as the correction terms for - * expm1(r+c). Now rearrange the term to avoid optimization - * screw up: - * ( 2 2 ) - * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) - * ieee_expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) - * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) - * ( ) - * - * = r - E - * 3. Scale back to obtain ieee_expm1(x): - * From step 1, we have - * ieee_expm1(x) = either 2^k*[expm1(r)+1] - 1 - * = or 2^k*[expm1(r) + (1-2^-k)] - * 4. Implementation notes: - * (A). To save one multiplication, we scale the coefficient Qi - * to Qi*2^i, and replace z by (x^2)/2. - * (B). To achieve maximum accuracy, we compute ieee_expm1(x) by - * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) - * (ii) if k=0, return r-E - * (iii) if k=-1, return 0.5*(r-E)-0.5 - * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) - * else return 1.0+2.0*(r-E); - * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or ieee_exp(x)-1) - * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else - * (vii) return 2^k(1-((E+2^-k)-r)) - * - * Special cases: - * expm1(INF) is INF, ieee_expm1(NaN) is NaN; - * expm1(-INF) is -1, and - * for finite argument, only ieee_expm1(0)=0 is exact. - * - * Accuracy: - * according to an error analysis, the error is always less than - * 1 ulp (unit in the last place). - * - * Misc. info. - * For IEEE double - * if x > 7.09782712893383973096e+02 then ieee_expm1(x) overflow - * - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -one = 1.0, -huge = 1.0e+300, -tiny = 1.0e-300, -o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ -ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ -ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ -invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */ - /* scaled coefficients related to expm1 */ -Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ -Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ -Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ -Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ -Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ - -#ifdef __STDC__ - double ieee_expm1(double x) -#else - double ieee_expm1(x) - double x; -#endif -{ - double y,hi,lo,c,t,e,hxs,hfx,r1; - int k,xsb; - unsigned hx; - - hx = __HI(x); /* high word of x */ - xsb = hx&0x80000000; /* sign bit of x */ - if(xsb==0) y=x; else y= -x; /* y = |x| */ - hx &= 0x7fffffff; /* high word of |x| */ - - /* filter out huge and non-finite argument */ - if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ - if(hx >= 0x40862E42) { /* if |x|>=709.78... */ - if(hx>=0x7ff00000) { - if(((hx&0xfffff)|__LO(x))!=0) - return x+x; /* NaN */ - else return (xsb==0)? x:-1.0;/* ieee_exp(+-inf)={inf,-1} */ - } - if(x > o_threshold) return huge*huge; /* overflow */ - } - if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ - if(x+tiny<0.0) /* raise inexact */ - return tiny-one; /* return -1 */ - } - } - - /* argument reduction */ - if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ - if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ - if(xsb==0) - {hi = x - ln2_hi; lo = ln2_lo; k = 1;} - else - {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} - } else { - k = invln2*x+((xsb==0)?0.5:-0.5); - t = k; - hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ - lo = t*ln2_lo; - } - x = hi - lo; - c = (hi-x)-lo; - } - else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ - // t = huge+x; /* return x with inexact flags when x!=0 */ - // return x - (t-(huge+x)); - return x; // inexact flag is not set, but Java ignors this flag anyway - } - else k = 0; - - /* x is now in primary range */ - hfx = 0.5*x; - hxs = x*hfx; - r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); - t = 3.0-r1*hfx; - e = hxs*((r1-t)/(6.0 - x*t)); - if(k==0) return x - (x*e-hxs); /* c is 0 */ - else { - e = (x*(e-c)-c); - e -= hxs; - if(k== -1) return 0.5*(x-e)-0.5; - if(k==1) - if(x < -0.25) return -2.0*(e-(x+0.5)); - else return one+2.0*(x-e); - if (k <= -2 || k>56) { /* suffice to return ieee_exp(x)-1 */ - y = one-(e-x); - __HI(y) += (k<<20); /* add k to y's exponent */ - return y-one; - } - t = one; - if(k<20) { - __HI(t) = 0x3ff00000 - (0x200000>>k); /* t=1-2^-k */ - y = t-(e-x); - __HI(y) += (k<<20); /* add k to y's exponent */ - } else { - __HI(t) = ((0x3ff-k)<<20); /* 2^-k */ - y = x-(e+t); - y += one; - __HI(y) += (k<<20); /* add k to y's exponent */ - } - } - return y; -} diff --git a/s_fabs.c b/s_fabs.c deleted file mode 100644 index 498b51f..0000000 --- a/s_fabs.c +++ /dev/null @@ -1,29 +0,0 @@ - -/* @(#)s_fabs.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * ieee_fabs(x) returns the absolute value of x. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_fabs(double x) -#else - double ieee_fabs(x) - double x; -#endif -{ - __HI(x) &= 0x7fffffff; - return x; -} diff --git a/s_finite.c b/s_finite.c deleted file mode 100644 index 41a4b17..0000000 --- a/s_finite.c +++ /dev/null @@ -1,31 +0,0 @@ - -/* @(#)s_finite.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * ieee_finite(x) returns 1 is x is finite, else 0; - * no branching! - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - int ieee_finite(double x) -#else - int ieee_finite(x) - double x; -#endif -{ - int hx; - hx = __HI(x); - return (unsigned)((hx&0x7fffffff)-0x7ff00000)>>31; -} diff --git a/s_floor.c b/s_floor.c deleted file mode 100644 index c55e0b7..0000000 --- a/s_floor.c +++ /dev/null @@ -1,79 +0,0 @@ - -/* @(#)s_floor.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * ieee_floor(x) - * Return x rounded toward -inf to integral value - * Method: - * Bit twiddling. - * Exception: - * Inexact flag raised if x not equal to ieee_floor(x). - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double huge = 1.0e300; -#else -static double huge = 1.0e300; -#endif - -#ifdef __STDC__ - double ieee_floor(double x) -#else - double ieee_floor(x) - double x; -#endif -{ - int i0,i1,j0; - unsigned i,j; - i0 = __HI(x); - i1 = __LO(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 = ((unsigned)(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=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */ - if (ix<0x00100000) { /* subnormal */ - x *= two54; - hx = __HI(x); - ix = hx&0x7fffffff; - *eptr = -54; - } - *eptr += (ix>>20)-1022; - hx = (hx&0x800fffff)|0x3fe00000; - __HI(x) = hx; - return x; -} diff --git a/s_ilogb.c b/s_ilogb.c deleted file mode 100644 index 240f9bf..0000000 --- a/s_ilogb.c +++ /dev/null @@ -1,46 +0,0 @@ - -/* @(#)s_ilogb.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* ieee_ilogb(double x) - * return the binary exponent of non-zero x - * ieee_ilogb(0) = 0x80000001 - * ieee_ilogb(inf/NaN) = 0x7fffffff (no signal is raised) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - int ieee_ilogb(double x) -#else - int ieee_ilogb(x) - double x; -#endif -{ - int hx,lx,ix; - - hx = (__HI(x))&0x7fffffff; /* high word of x */ - if(hx<0x00100000) { - lx = __LO(x); - if((hx|lx)==0) - return 0x80000001; /* ieee_ilogb(0) = 0x80000001 */ - else /* subnormal x */ - if(hx==0) { - for (ix = -1043; lx>0; lx<<=1) ix -=1; - } else { - for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1; - } - return ix; - } - else if (hx<0x7ff00000) return (hx>>20)-1023; - else return 0x7fffffff; -} diff --git a/s_isnan.c b/s_isnan.c deleted file mode 100644 index 0500c32..0000000 --- a/s_isnan.c +++ /dev/null @@ -1,34 +0,0 @@ - -/* @(#)s_isnan.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * ieee_isnan(x) returns 1 is x is nan, else 0; - * no branching! - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - int ieee_isnan(double x) -#else - int ieee_isnan(x) - double x; -#endif -{ - int hx,lx; - hx = (__HI(x)&0x7fffffff); - lx = __LO(x); - hx |= (unsigned)(lx|(-lx))>>31; - hx = 0x7ff00000 - hx; - return ((unsigned)(hx))>>31; -} diff --git a/s_ldexp.c b/s_ldexp.c deleted file mode 100644 index ce29da1..0000000 --- a/s_ldexp.c +++ /dev/null @@ -1,28 +0,0 @@ - -/* @(#)s_ldexp.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "fdlibm.h" -#include - -#ifdef __STDC__ - double ieee_ldexp(double value, int exp) -#else - double ieee_ldexp(value, exp) - double value; int exp; -#endif -{ - if(!ieee_finite(value)||value==0.0) return value; - value = ieee_scalbn(value,exp); - if(!ieee_finite(value)||value==0.0) errno = ERANGE; - return value; -} diff --git a/s_lib_version.c b/s_lib_version.c deleted file mode 100644 index 40f065e..0000000 --- a/s_lib_version.c +++ /dev/null @@ -1,35 +0,0 @@ - -/* @(#)s_lib_version.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * MACRO for standards - */ - -#include "fdlibm.h" - -/* - * define and initialize _LIB_VERSION - */ -#ifdef _POSIX_MODE -_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_; -#else -#ifdef _XOPEN_MODE -_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_; -#else -#ifdef _SVID3_MODE -_LIB_VERSION_TYPE _LIB_VERSION = _SVID_; -#else /* default _IEEE_MODE */ -_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_; -#endif -#endif -#endif diff --git a/s_log1p.c b/s_log1p.c deleted file mode 100644 index 5b92347..0000000 --- a/s_log1p.c +++ /dev/null @@ -1,165 +0,0 @@ - -/* @(#)s_log1p.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* double ieee_log1p(double x) - * - * Method : - * 1. Argument Reduction: find k and f such that - * 1+x = 2^k * (1+f), - * where ieee_sqrt(2)/2 < 1+f < ieee_sqrt(2) . - * - * Note. If k=0, then f=x is exact. However, if k!=0, then f - * may not be representable exactly. In that case, a correction - * term is need. Let u=1+x rounded. Let c = (1+x)-u, then - * log(1+x) - ieee_log(u) ~ c/u. Thus, we proceed to compute ieee_log(u), - * and add back the correction term c/u. - * (Note: when x > 2**53, one can simply return ieee_log(x)) - * - * 2. Approximation of ieee_log1p(f). - * Let s = f/(2+f) ; based on ieee_log(1+f) = ieee_log(1+s) - ieee_log(1-s) - * = 2s + 2/3 s**3 + 2/5 s**5 + ....., - * = 2s + s*R - * We use a special Reme algorithm on [0,0.1716] to generate - * a polynomial of degree 14 to approximate R The maximum error - * of this polynomial approximation is bounded by 2**-58.45. In - * other words, - * 2 4 6 8 10 12 14 - * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s - * (the values of Lp1 to Lp7 are listed in the program) - * and - * | 2 14 | -58.45 - * | Lp1*s +...+Lp7*s - R(z) | <= 2 - * | | - * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. - * In order to guarantee error in log below 1ulp, we compute log - * by - * log1p(f) = f - (hfsq - s*(hfsq+R)). - * - * 3. Finally, ieee_log1p(x) = k*ln2 + ieee_log1p(f). - * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) - * Here ln2 is split into two floating point number: - * ln2_hi + ln2_lo, - * where n*ln2_hi is always exact for |n| < 2000. - * - * Special cases: - * log1p(x) is NaN with signal if x < -1 (including -INF) ; - * log1p(+INF) is +INF; ieee_log1p(-1) is -INF with signal; - * log1p(NaN) is that NaN with no signal. - * - * Accuracy: - * according to an error analysis, the error is always less than - * 1 ulp (unit in the last place). - * - * 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. - * - * Note: Assuming ieee_log() return accurate answer, the following - * algorithm can be used to compute ieee_log1p(x) to within a few ULP: - * - * u = 1+x; - * if(u==1.0) return x ; else - * return ieee_log(u)*(x/(u-1.0)); - * - * See HP-15C Advanced Functions Handbook, p.193. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ -ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ -two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ -Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ -Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ -Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ -Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ -Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ -Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ -Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ - -static double zero = 0.0; - -#ifdef __STDC__ - double ieee_log1p(double x) -#else - double ieee_log1p(x) - double x; -#endif -{ - double hfsq,f,c,s,z,R,u; - int k,hx,hu,ax; - - hx = __HI(x); /* high word of x */ - ax = hx&0x7fffffff; - - k = 1; - if (hx < 0x3FDA827A) { /* x < 0.41422 */ - if(ax>=0x3ff00000) { /* x <= -1.0 */ - if(x==-1.0) return -two54/zero; /* ieee_log1p(-1)=+inf */ - else return (x-x)/(x-x); /* ieee_log1p(x<-1)=NaN */ - } - if(ax<0x3e200000) { /* |x| < 2**-29 */ - if(two54+x>zero /* raise inexact */ - &&ax<0x3c900000) /* |x| < 2**-54 */ - return x; - else - return x - x*x*0.5; - } - if(hx>0||hx<=((int)0xbfd2bec3)) { - k=0;f=x;hu=1;} /* -0.2929= 0x7ff00000) return x+x; - if(k!=0) { - if(hx<0x43400000) { - u = 1.0+x; - hu = __HI(u); /* high word of u */ - k = (hu>>20)-1023; - c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ - c /= u; - } else { - u = x; - hu = __HI(u); /* high word of u */ - k = (hu>>20)-1023; - c = 0; - } - hu &= 0x000fffff; - if(hu<0x6a09e) { - __HI(u) = hu|0x3ff00000; /* normalize u */ - } else { - k += 1; - __HI(u) = hu|0x3fe00000; /* normalize u/2 */ - hu = (0x00100000-hu)>>2; - } - f = u-1.0; - } - hfsq=0.5*f*f; - if(hu==0) { /* |f| < 2**-20 */ - if(f==zero) if(k==0) return zero; - else {c += k*ln2_lo; return k*ln2_hi+c;} - R = hfsq*(1.0-0.66666666666666666*f); - if(k==0) return f-R; else - return k*ln2_hi-((R-(k*ln2_lo+c))-f); - } - s = f/(2.0+f); - z = s*s; - R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); - if(k==0) return f-(hfsq-s*(hfsq+R)); else - return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); -} diff --git a/s_logb.c b/s_logb.c deleted file mode 100644 index a9b1bb8..0000000 --- a/s_logb.c +++ /dev/null @@ -1,38 +0,0 @@ - -/* @(#)s_logb.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * double ieee_logb(x) - * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. - * Use ilogb instead. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_logb(double x) -#else - double ieee_logb(x) - double x; -#endif -{ - int lx,ix; - ix = (__HI(x))&0x7fffffff; /* high |x| */ - lx = __LO(x); /* low x */ - if((ix|lx)==0) return -1.0/ieee_fabs(x); - if(ix>=0x7ff00000) return x*x; - if((ix>>=20)==0) /* IEEE 754 logb */ - return -1022.0; - else - return (double) (ix-1023); -} diff --git a/s_matherr.c b/s_matherr.c deleted file mode 100644 index ece2d23..0000000 --- a/s_matherr.c +++ /dev/null @@ -1,26 +0,0 @@ - -/* @(#)s_matherr.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - int ieee_matherr(struct exception *x) -#else - int ieee_matherr(x) - struct exception *x; -#endif -{ - int n=0; - if(x->arg1!=x->arg1) return 0; - return n; -} diff --git a/s_modf.c b/s_modf.c deleted file mode 100644 index 0d7faa4..0000000 --- a/s_modf.c +++ /dev/null @@ -1,80 +0,0 @@ - -/* @(#)s_modf.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * ieee_modf(double x, double *iptr) - * return fraction part of x, and return x's integral part in *iptr. - * Method: - * Bit twiddling. - * - * Exception: - * No exception. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double one = 1.0; -#else -static double one = 1.0; -#endif - -#ifdef __STDC__ - double ieee_modf(double x, double *iptr) -#else - double ieee_modf(x, iptr) - double x,*iptr; -#endif -{ - int i0,i1,j0; - unsigned i; - i0 = __HI(x); /* high x */ - i1 = __LO(x); /* low x */ - j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent of x */ - if(j0<20) { /* integer part in high x */ - if(j0<0) { /* |x|<1 */ - __HIp(iptr) = i0&0x80000000; - __LOp(iptr) = 0; /* *iptr = +-0 */ - return x; - } else { - i = (0x000fffff)>>j0; - if(((i0&i)|i1)==0) { /* x is integral */ - *iptr = x; - __HI(x) &= 0x80000000; - __LO(x) = 0; /* return +-0 */ - return x; - } else { - __HIp(iptr) = i0&(~i); - __LOp(iptr) = 0; - return x - *iptr; - } - } - } else if (j0>51) { /* no fraction part */ - *iptr = x*one; - __HI(x) &= 0x80000000; - __LO(x) = 0; /* return +-0 */ - return x; - } else { /* fraction part in low x */ - i = ((unsigned)(0xffffffff))>>(j0-20); - if((i1&i)==0) { /* x is integral */ - *iptr = x; - __HI(x) &= 0x80000000; - __LO(x) = 0; /* return +-0 */ - return x; - } else { - __HIp(iptr) = i0; - __LOp(iptr) = i1&(~i); - return x - *iptr; - } - } -} diff --git a/s_nextafter.c b/s_nextafter.c deleted file mode 100644 index 0e6db32..0000000 --- a/s_nextafter.c +++ /dev/null @@ -1,78 +0,0 @@ - -/* @(#)s_nextafter.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* IEEE functions - * nextafter(x,y) - * return the next machine floating-point number of x in the - * direction toward y. - * Special cases: - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_nextafter(double x, double y) -#else - double ieee_nextafter(x,y) - double x,y; -#endif -{ - int hx,hy,ix,iy; - unsigned lx,ly; - - hx = __HI(x); /* high word of x */ - lx = __LO(x); /* low word of x */ - hy = __HI(y); /* high word of y */ - ly = __LO(y); /* low word of y */ - ix = hx&0x7fffffff; /* |x| */ - iy = hy&0x7fffffff; /* |y| */ - - if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ - ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */ - return x+y; - if(x==y) return x; /* x=y, return x */ - if((ix|lx)==0) { /* x == 0 */ - __HI(x) = hy&0x80000000; /* return +-minsubnormal */ - __LO(x) = 1; - y = x*x; - if(y==x) return y; else return x; /* raise underflow flag */ - } - if(hx>=0) { /* x > 0 */ - if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ - if(lx==0) hx -= 1; - lx -= 1; - } else { /* x < y, x += ulp */ - lx += 1; - if(lx==0) hx += 1; - } - } else { /* x < 0 */ - if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */ - if(lx==0) hx -= 1; - lx -= 1; - } else { /* x > y, x += ulp */ - lx += 1; - if(lx==0) hx += 1; - } - } - hy = hx&0x7ff00000; - if(hy>=0x7ff00000) return x+x; /* overflow */ - if(hy<0x00100000) { /* underflow */ - y = x*x; - if(y!=x) { /* raise underflow flag */ - __HI(y) = hx; __LO(y) = lx; - return y; - } - } - __HI(x) = hx; __LO(x) = lx; - return x; -} diff --git a/s_rint.c b/s_rint.c deleted file mode 100644 index fbbd0fd..0000000 --- a/s_rint.c +++ /dev/null @@ -1,84 +0,0 @@ - -/* @(#)s_rint.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * ieee_rint(x) - * Return x rounded to integral value according to the prevailing - * rounding mode. - * Method: - * Using floating addition. - * Exception: - * Inexact flag raised if x not equal to ieee_rint(x). - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -TWO52[2]={ - 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ - -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ -}; - -#ifdef __STDC__ - double ieee_rint(double x) -#else - double ieee_rint(x) - double x; -#endif -{ - int i0,j0,sx; - unsigned i,i1; - double w,t; - i0 = __HI(x); - sx = (i0>>31)&1; - i1 = __LO(x); - j0 = ((i0>>20)&0x7ff)-0x3ff; - if(j0<20) { - if(j0<0) { - if(((i0&0x7fffffff)|i1)==0) return x; - i1 |= (i0&0x0fffff); - i0 &= 0xfffe0000; - i0 |= ((i1|-i1)>>12)&0x80000; - __HI(x)=i0; - w = TWO52[sx]+x; - t = w-TWO52[sx]; - i0 = __HI(t); - __HI(t) = (i0&0x7fffffff)|(sx<<31); - return t; - } else { - i = (0x000fffff)>>j0; - if(((i0&i)|i1)==0) return x; /* x is integral */ - i>>=1; - if(((i0&i)|i1)!=0) { - if(j0==19) i1 = 0x40000000; else - i0 = (i0&(~i))|((0x20000)>>j0); - } - } - } else if (j0>51) { - if(j0==0x400) return x+x; /* inf or NaN */ - else return x; /* x is integral */ - } else { - i = ((unsigned)(0xffffffff))>>(j0-20); - if((i1&i)==0) return x; /* x is integral */ - i>>=1; - if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20)); - } - __HI(x) = i0; - __LO(x) = i1; - w = TWO52[sx]+x; - return w-TWO52[sx]; -} diff --git a/s_scalbn.c b/s_scalbn.c deleted file mode 100644 index 0edb815..0000000 --- a/s_scalbn.c +++ /dev/null @@ -1,63 +0,0 @@ - -/* @(#)s_scalbn.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * ieee_scalbn (double x, int n) - * ieee_scalbn(x,n) returns x* 2**n computed by exponent - * manipulation rather than by actually performing an - * exponentiation or a multiplication. - */ - -#include "fdlibm.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 ieee_scalbn (double x, int n) -#else - double ieee_scalbn (x,n) - double x; int n; -#endif -{ - int k,hx,lx; - hx = __HI(x); - lx = __LO(x); - k = (hx&0x7ff00000)>>20; /* extract exponent */ - if (k==0) { /* 0 or subnormal x */ - if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ - x *= two54; - hx = __HI(x); - k = ((hx&0x7ff00000)>>20) - 54; - if (n< -50000) return tiny*x; /*underflow*/ - } - if (k==0x7ff) return x+x; /* NaN or Inf */ - k = k+n; - if (k > 0x7fe) return huge*ieee_copysign(huge,x); /* overflow */ - if (k > 0) /* normal result */ - {__HI(x) = (hx&0x800fffff)|(k<<20); return x;} - if (k <= -54) - if (n > 50000) /* in case integer overflow in n+k */ - return huge*ieee_copysign(huge,x); /*overflow*/ - else return tiny*ieee_copysign(tiny,x); /*underflow*/ - k += 54; /* subnormal result */ - __HI(x) = (hx&0x800fffff)|(k<<20); - return x*twom54; -} diff --git a/s_signgam.c b/s_signgam.c deleted file mode 100644 index 8ed291a..0000000 --- a/s_signgam.c +++ /dev/null @@ -1,2 +0,0 @@ -#include "fdlibm.h" -int signgam = 0; diff --git a/s_significand.c b/s_significand.c deleted file mode 100644 index 7048563..0000000 --- a/s_significand.c +++ /dev/null @@ -1,30 +0,0 @@ - -/* @(#)s_significand.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * ieee_significand(x) computes just - * scalb(x, (double) -ieee_ilogb(x)), - * for exercising the fraction-part(F) IEEE 754-1985 test vector. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_significand(double x) -#else - double ieee_significand(x) - double x; -#endif -{ - return __ieee754_scalb(x,(double) -ieee_ilogb(x)); -} diff --git a/s_sin.c b/s_sin.c deleted file mode 100644 index eb6bd3f..0000000 --- a/s_sin.c +++ /dev/null @@ -1,78 +0,0 @@ - -/* @(#)s_sin.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* ieee_sin(x) - * Return sine function of x. - * - * kernel function: - * __kernel_sin ... sine function on [-pi/4,pi/4] - * __kernel_cos ... cose function on [-pi/4,pi/4] - * __ieee754_rem_pio2 ... argument reduction routine - * - * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 - * in [-pi/4 , +pi/4], and let n = k mod 4. - * We have - * - * n ieee_sin(x) ieee_cos(x) ieee_tan(x) - * ---------------------------------------------------------- - * 0 S C T - * 1 C -S -1/T - * 2 -S -C T - * 3 -C S -1/T - * ---------------------------------------------------------- - * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; - * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_sin(double x) -#else - double ieee_sin(x) - double x; -#endif -{ - double y[2],z=0.0; - int n, ix; - - /* High word of x. */ - ix = __HI(x); - - /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); - - /* ieee_sin(Inf or NaN) is NaN */ - else if (ix>=0x7ff00000) return x-x; - - /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x,y); - switch(n&3) { - case 0: return __kernel_sin(y[0],y[1],1); - case 1: return __kernel_cos(y[0],y[1]); - case 2: return -__kernel_sin(y[0],y[1],1); - default: - return -__kernel_cos(y[0],y[1]); - } - } -} diff --git a/s_tan.c b/s_tan.c deleted file mode 100644 index 1c0b297..0000000 --- a/s_tan.c +++ /dev/null @@ -1,72 +0,0 @@ - -/* @(#)s_tan.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* ieee_tan(x) - * Return tangent function of x. - * - * kernel function: - * __kernel_tan ... tangent function on [-pi/4,pi/4] - * __ieee754_rem_pio2 ... argument reduction routine - * - * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 - * in [-pi/4 , +pi/4], and let n = k mod 4. - * We have - * - * n ieee_sin(x) ieee_cos(x) ieee_tan(x) - * ---------------------------------------------------------- - * 0 S C T - * 1 C -S -1/T - * 2 -S -C T - * 3 -C S -1/T - * ---------------------------------------------------------- - * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; - * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_tan(double x) -#else - double ieee_tan(x) - double x; -#endif -{ - double y[2],z=0.0; - int n, ix; - - /* High word of x. */ - ix = __HI(x); - - /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); - - /* ieee_tan(Inf or NaN) is NaN */ - else if (ix>=0x7ff00000) return x-x; /* NaN */ - - /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x,y); - return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even - -1 -- n odd */ - } -} diff --git a/s_tanh.c b/s_tanh.c deleted file mode 100644 index d232629..0000000 --- a/s_tanh.c +++ /dev/null @@ -1,82 +0,0 @@ - -/* @(#)s_tanh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* Tanh(x) - * Return the Hyperbolic Tangent of x - * - * Method : - * x -x - * e - e - * 0. ieee_tanh(x) is defined to be ----------- - * x -x - * e + e - * 1. reduce x to non-negative by ieee_tanh(-x) = -ieee_tanh(x). - * 2. 0 <= x <= 2**-55 : ieee_tanh(x) := x*(one+x) - * -t - * 2**-55 < x <= 1 : ieee_tanh(x) := -----; t = ieee_expm1(-2x) - * t + 2 - * 2 - * 1 <= x <= 22.0 : ieee_tanh(x) := 1- ----- ; t=ieee_expm1(2x) - * t + 2 - * 22.0 < x <= INF : ieee_tanh(x) := 1. - * - * Special cases: - * tanh(NaN) is NaN; - * only ieee_tanh(0)=0 is exact for finite argument. - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double one=1.0, two=2.0, tiny = 1.0e-300; -#else -static double one=1.0, two=2.0, tiny = 1.0e-300; -#endif - -#ifdef __STDC__ - double ieee_tanh(double x) -#else - double ieee_tanh(x) - double x; -#endif -{ - double t,z; - int jx,ix; - - /* High word of |x|. */ - jx = __HI(x); - ix = jx&0x7fffffff; - - /* x is INF or NaN */ - if(ix>=0x7ff00000) { - if (jx>=0) return one/x+one; /* ieee_tanh(+-inf)=+-1 */ - else return one/x-one; /* ieee_tanh(NaN) = NaN */ - } - - /* |x| < 22 */ - if (ix < 0x40360000) { /* |x|<22 */ - if (ix<0x3c800000) /* |x|<2**-55 */ - return x*(one+x); /* ieee_tanh(small) = small */ - if (ix>=0x3ff00000) { /* |x|>=1 */ - t = ieee_expm1(two*ieee_fabs(x)); - z = one - two/(t+two); - } else { - t = ieee_expm1(-two*ieee_fabs(x)); - z= -t/(t+two); - } - /* |x| > 22, return +-1 */ - } else { - z = one - tiny; /* raised inexact flag */ - } - return (jx>=0)? z: -z; -} diff --git a/w_acos.c b/w_acos.c deleted file mode 100644 index 1233f9d..0000000 --- a/w_acos.c +++ /dev/null @@ -1,39 +0,0 @@ - -/* @(#)w_acos.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrap_acos(x) - */ - -#include "fdlibm.h" - - -#ifdef __STDC__ - double ieee_acos(double x) /* wrapper acos */ -#else - double ieee_acos(x) /* wrapper acos */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_acos(x); -#else - double z; - z = __ieee754_acos(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x)) return z; - if(ieee_fabs(x)>1.0) { - return __kernel_standard(x,x,1); /* ieee_acos(|x|>1) */ - } else - return z; -#endif -} diff --git a/w_acosh.c b/w_acosh.c deleted file mode 100644 index 650d461..0000000 --- a/w_acosh.c +++ /dev/null @@ -1,39 +0,0 @@ - -/* @(#)w_acosh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* - * wrapper acosh(x) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double acosh(double x) /* wrapper acosh */ -#else - double acosh(x) /* wrapper acosh */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_acosh(x); -#else - double z; - z = __ieee754_acosh(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x)) return z; - if(x<1.0) { - return __kernel_standard(x,x,29); /* acosh(x<1) */ - } else - return z; -#endif -} diff --git a/w_asin.c b/w_asin.c deleted file mode 100644 index 46000e5..0000000 --- a/w_asin.c +++ /dev/null @@ -1,41 +0,0 @@ - -/* @(#)w_asin.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* - * wrapper ieee_asin(x) - */ - - -#include "fdlibm.h" - - -#ifdef __STDC__ - double ieee_asin(double x) /* wrapper asin */ -#else - double ieee_asin(x) /* wrapper asin */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_asin(x); -#else - double z; - z = __ieee754_asin(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x)) return z; - if(ieee_fabs(x)>1.0) { - return __kernel_standard(x,x,2); /* ieee_asin(|x|>1) */ - } else - return z; -#endif -} diff --git a/w_atan2.c b/w_atan2.c deleted file mode 100644 index f4cc0eb..0000000 --- a/w_atan2.c +++ /dev/null @@ -1,40 +0,0 @@ - -/* @(#)w_atan2.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* - * wrapper ieee_atan2(y,x) - */ - -#include "fdlibm.h" - - -#ifdef __STDC__ - double ieee_atan2(double y, double x) /* wrapper atan2 */ -#else - double ieee_atan2(y,x) /* wrapper atan2 */ - double y,x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_atan2(y,x); -#else - double z; - z = __ieee754_atan2(y,x); - if(_LIB_VERSION == _IEEE_||ieee_isnan(x)||ieee_isnan(y)) return z; - if(x==0.0&&y==0.0) { - return __kernel_standard(y,x,3); /* ieee_atan2(+-0,+-0) */ - } else - return z; -#endif -} diff --git a/w_atanh.c b/w_atanh.c deleted file mode 100644 index 436f5db..0000000 --- a/w_atanh.c +++ /dev/null @@ -1,42 +0,0 @@ - -/* @(#)w_atanh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ -/* - * wrapper atanh(x) - */ - -#include "fdlibm.h" - - -#ifdef __STDC__ - double atanh(double x) /* wrapper atanh */ -#else - double atanh(x) /* wrapper atanh */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_atanh(x); -#else - double z,y; - z = __ieee754_atanh(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x)) return z; - y = ieee_fabs(x); - if(y>=1.0) { - if(y>1.0) - return __kernel_standard(x,x,30); /* atanh(|x|>1) */ - else - return __kernel_standard(x,x,31); /* atanh(|x|==1) */ - } else - return z; -#endif -} diff --git a/w_cosh.c b/w_cosh.c deleted file mode 100644 index 81fc900..0000000 --- a/w_cosh.c +++ /dev/null @@ -1,38 +0,0 @@ - -/* @(#)w_cosh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_cosh(x) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_cosh(double x) /* wrapper cosh */ -#else - double ieee_cosh(x) /* wrapper cosh */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_cosh(x); -#else - double z; - z = __ieee754_cosh(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x)) return z; - if(ieee_fabs(x)>7.10475860073943863426e+02) { - return __kernel_standard(x,x,5); /* cosh overflow */ - } else - return z; -#endif -} diff --git a/w_exp.c b/w_exp.c deleted file mode 100644 index 1eefd83..0000000 --- a/w_exp.c +++ /dev/null @@ -1,48 +0,0 @@ - -/* @(#)w_exp.c 1.4 04/04/22 */ -/* - * ==================================================== - * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_exp(x) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif -o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ -u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */ - -#ifdef __STDC__ - double ieee_exp(double x) /* wrapper exp */ -#else - double ieee_exp(x) /* wrapper exp */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_exp(x); -#else - double z; - z = __ieee754_exp(x); - if(_LIB_VERSION == _IEEE_) return z; - if(ieee_finite(x)) { - if(x>o_threshold) - return __kernel_standard(x,x,6); /* exp overflow */ - else if(xX_TLOSS) { - return __kernel_standard(x,x,34); /* ieee_j0(|x|>X_TLOSS) */ - } else - return z; -#endif -} - -#ifdef __STDC__ - double ieee_y0(double x) /* wrapper y0 */ -#else - double ieee_y0(x) /* wrapper y0 */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_y0(x); -#else - double z; - z = __ieee754_y0(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x) ) return z; - if(x <= 0.0){ - if(x==0.0) - /* d= -one/(x-x); */ - return __kernel_standard(x,x,8); - else - /* d = zero/(x-x); */ - return __kernel_standard(x,x,9); - } - if(x>X_TLOSS) { - return __kernel_standard(x,x,35); /* ieee_y0(x>X_TLOSS) */ - } else - return z; -#endif -} diff --git a/w_j1.c b/w_j1.c deleted file mode 100644 index 8d27040..0000000 --- a/w_j1.c +++ /dev/null @@ -1,66 +0,0 @@ - -/* @(#)w_j1.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper of j1,y1 - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_j1(double x) /* wrapper j1 */ -#else - double ieee_j1(x) /* wrapper j1 */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_j1(x); -#else - double z; - z = __ieee754_j1(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x) ) return z; - if(ieee_fabs(x)>X_TLOSS) { - return __kernel_standard(x,x,36); /* ieee_j1(|x|>X_TLOSS) */ - } else - return z; -#endif -} - -#ifdef __STDC__ - double ieee_y1(double x) /* wrapper y1 */ -#else - double ieee_y1(x) /* wrapper y1 */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_y1(x); -#else - double z; - z = __ieee754_y1(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x) ) return z; - if(x <= 0.0){ - if(x==0.0) - /* d= -one/(x-x); */ - return __kernel_standard(x,x,10); - else - /* d = zero/(x-x); */ - return __kernel_standard(x,x,11); - } - if(x>X_TLOSS) { - return __kernel_standard(x,x,37); /* ieee_y1(x>X_TLOSS) */ - } else - return z; -#endif -} diff --git a/w_jn.c b/w_jn.c deleted file mode 100644 index 3b5ab45..0000000 --- a/w_jn.c +++ /dev/null @@ -1,88 +0,0 @@ - -/* @(#)w_jn.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_jn(int n, double x), ieee_yn(int n, double x) - * floating point Bessel's function of the 1st and 2nd kind - * of order n - * - * Special cases: - * y0(0)=ieee_y1(0)=ieee_yn(n,0) = -inf with division by zero signal; - * y0(-ve)=ieee_y1(-ve)=ieee_yn(n,-ve) are NaN with invalid signal. - * Note 2. About ieee_jn(n,x), ieee_yn(n,x) - * For n=0, ieee_j0(x) is called, - * for n=1, ieee_j1(x) is called, - * for nx, a continued fraction approximation to - * j(n,x)/j(n-1,x) is evaluated and then backward - * recursion is used starting from a supposed value - * for j(n,x). The resulting value of j(0,x) is - * compared with the actual value to correct the - * supposed value of j(n,x). - * - * yn(n,x) is similar in all respects, except - * that forward recursion is used for all - * values of n>1. - * - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_jn(int n, double x) /* wrapper jn */ -#else - double ieee_jn(n,x) /* wrapper jn */ - double x; int n; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_jn(n,x); -#else - double z; - z = __ieee754_jn(n,x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x) ) return z; - if(ieee_fabs(x)>X_TLOSS) { - return __kernel_standard((double)n,x,38); /* ieee_jn(|x|>X_TLOSS,n) */ - } else - return z; -#endif -} - -#ifdef __STDC__ - double ieee_yn(int n, double x) /* wrapper yn */ -#else - double ieee_yn(n,x) /* wrapper yn */ - double x; int n; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_yn(n,x); -#else - double z; - z = __ieee754_yn(n,x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x) ) return z; - if(x <= 0.0){ - if(x==0.0) - /* d= -one/(x-x); */ - return __kernel_standard((double)n,x,12); - else - /* d = zero/(x-x); */ - return __kernel_standard((double)n,x,13); - } - if(x>X_TLOSS) { - return __kernel_standard((double)n,x,39); /* ieee_yn(x>X_TLOSS,n) */ - } else - return z; -#endif -} diff --git a/w_lgamma.c b/w_lgamma.c deleted file mode 100644 index 6c09dd4..0000000 --- a/w_lgamma.c +++ /dev/null @@ -1,46 +0,0 @@ - -/* @(#)w_lgamma.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - * - */ - -/* double ieee_lgamma(double x) - * Return the logarithm of the Gamma function of x. - * - * Method: call __ieee754_lgamma_r - */ - -#include "fdlibm.h" - -extern int signgam; - -#ifdef __STDC__ - double ieee_lgamma(double x) -#else - double ieee_lgamma(x) - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_lgamma_r(x,&signgam); -#else - double y; - y = __ieee754_lgamma_r(x,&signgam); - if(_LIB_VERSION == _IEEE_) return y; - if(!ieee_finite(y)&&ieee_finite(x)) { - if(ieee_floor(x)==x&&x<=0.0) - return __kernel_standard(x,x,15); /* lgamma pole */ - else - return __kernel_standard(x,x,14); /* lgamma overflow */ - } else - return y; -#endif -} diff --git a/w_lgamma_r.c b/w_lgamma_r.c deleted file mode 100644 index c59e1d6..0000000 --- a/w_lgamma_r.c +++ /dev/null @@ -1,42 +0,0 @@ - -/* @(#)w_lgamma_r.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper double ieee_lgamma_r(double x, int *signgamp) - */ - -#include "fdlibm.h" - - -#ifdef __STDC__ - double ieee_lgamma_r(double x, int *signgamp) /* wrapper lgamma_r */ -#else - double ieee_lgamma_r(x,signgamp) /* wrapper lgamma_r */ - double x; int *signgamp; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_lgamma_r(x,signgamp); -#else - double y; - y = __ieee754_lgamma_r(x,signgamp); - if(_LIB_VERSION == _IEEE_) return y; - if(!ieee_finite(y)&&ieee_finite(x)) { - if(ieee_floor(x)==x&&x<=0.0) - return __kernel_standard(x,x,15); /* lgamma pole */ - else - return __kernel_standard(x,x,14); /* lgamma overflow */ - } else - return y; -#endif -} diff --git a/w_log.c b/w_log.c deleted file mode 100644 index b73cc6d..0000000 --- a/w_log.c +++ /dev/null @@ -1,39 +0,0 @@ - -/* @(#)w_log.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_log(x) - */ - -#include "fdlibm.h" - - -#ifdef __STDC__ - double ieee_log(double x) /* wrapper log */ -#else - double ieee_log(x) /* wrapper log */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_log(x); -#else - double z; - z = __ieee754_log(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x) || x > 0.0) return z; - if(x==0.0) - return __kernel_standard(x,x,16); /* ieee_log(0) */ - else - return __kernel_standard(x,x,17); /* ieee_log(x<0) */ -#endif -} diff --git a/w_log10.c b/w_log10.c deleted file mode 100644 index e429d6c..0000000 --- a/w_log10.c +++ /dev/null @@ -1,42 +0,0 @@ - -/* @(#)w_log10.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_log10(X) - */ - -#include "fdlibm.h" - - -#ifdef __STDC__ - double ieee_log10(double x) /* wrapper log10 */ -#else - double ieee_log10(x) /* wrapper log10 */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_log10(x); -#else - double z; - z = __ieee754_log10(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x)) return z; - if(x<=0.0) { - if(x==0.0) - return __kernel_standard(x,x,18); /* ieee_log10(0) */ - else - return __kernel_standard(x,x,19); /* ieee_log10(x<0) */ - } else - return z; -#endif -} diff --git a/w_pow.c b/w_pow.c deleted file mode 100644 index 100e04c..0000000 --- a/w_pow.c +++ /dev/null @@ -1,60 +0,0 @@ - - -/* @(#)w_pow.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_pow(x,y) return x**y - */ - -#include "fdlibm.h" - - -#ifdef __STDC__ - double ieee_pow(double x, double y) /* wrapper pow */ -#else - double ieee_pow(x,y) /* wrapper pow */ - double x,y; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_pow(x,y); -#else - double z; - z=__ieee754_pow(x,y); - if(_LIB_VERSION == _IEEE_|| ieee_isnan(y)) return z; - if(ieee_isnan(x)) { - if(y==0.0) - return __kernel_standard(x,y,42); /* ieee_pow(NaN,0.0) */ - else - return z; - } - if(x==0.0){ - if(y==0.0) - return __kernel_standard(x,y,20); /* ieee_pow(0.0,0.0) */ - if(ieee_finite(y)&&y<0.0) - return __kernel_standard(x,y,23); /* ieee_pow(0.0,negative) */ - return z; - } - if(!ieee_finite(z)) { - if(ieee_finite(x)&&ieee_finite(y)) { - if(ieee_isnan(z)) - return __kernel_standard(x,y,24); /* pow neg**non-int */ - else - return __kernel_standard(x,y,21); /* pow overflow */ - } - } - if(z==0.0&&ieee_finite(x)&&ieee_finite(y)) - return __kernel_standard(x,y,22); /* pow underflow */ - return z; -#endif -} diff --git a/w_remainder.c b/w_remainder.c deleted file mode 100644 index f38065d..0000000 --- a/w_remainder.c +++ /dev/null @@ -1,38 +0,0 @@ - -/* @(#)w_remainder.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_remainder(x,p) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_remainder(double x, double y) /* wrapper remainder */ -#else - double ieee_remainder(x,y) /* wrapper remainder */ - double x,y; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_remainder(x,y); -#else - double z; - z = __ieee754_remainder(x,y); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(y)) return z; - if(y==0.0) - return __kernel_standard(x,y,28); /* ieee_remainder(x,0) */ - else - return z; -#endif -} diff --git a/w_scalb.c b/w_scalb.c deleted file mode 100644 index 7130993..0000000 --- a/w_scalb.c +++ /dev/null @@ -1,56 +0,0 @@ - -/* @(#)w_scalb.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_scalb(double x, double fn) is provide for - * passing various standard test suite. One - * should use ieee_scalbn() instead. - */ - -#include "fdlibm.h" - -#include - -#ifdef __STDC__ -#ifdef _SCALB_INT - double ieee_scalb(double x, int fn) /* wrapper scalb */ -#else - double ieee_scalb(double x, double fn) /* wrapper scalb */ -#endif -#else - double ieee_scalb(x,fn) /* wrapper scalb */ -#ifdef _SCALB_INT - double x; int fn; -#else - double x,fn; -#endif -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_scalb(x,fn); -#else - double z; - z = __ieee754_scalb(x,fn); - if(_LIB_VERSION == _IEEE_) return z; - if(!(ieee_finite(z)||ieee_isnan(z))&&ieee_finite(x)) { - return __kernel_standard(x,(double)fn,32); /* scalb overflow */ - } - if(z==0.0&&z!=x) { - return __kernel_standard(x,(double)fn,33); /* scalb underflow */ - } -#ifndef _SCALB_INT - if(!ieee_finite(fn)) errno = ERANGE; -#endif - return z; -#endif -} diff --git a/w_sinh.c b/w_sinh.c deleted file mode 100644 index a9b0cb3..0000000 --- a/w_sinh.c +++ /dev/null @@ -1,38 +0,0 @@ - -/* @(#)w_sinh.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_sinh(x) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_sinh(double x) /* wrapper sinh */ -#else - double ieee_sinh(x) /* wrapper sinh */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_sinh(x); -#else - double z; - z = __ieee754_sinh(x); - if(_LIB_VERSION == _IEEE_) return z; - if(!ieee_finite(z)&&ieee_finite(x)) { - return __kernel_standard(x,x,25); /* sinh overflow */ - } else - return z; -#endif -} diff --git a/w_sqrt.c b/w_sqrt.c deleted file mode 100644 index ab8a793..0000000 --- a/w_sqrt.c +++ /dev/null @@ -1,38 +0,0 @@ - -/* @(#)w_sqrt.c 1.3 95/01/18 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunSoft, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* - * wrapper ieee_sqrt(x) - */ - -#include "fdlibm.h" - -#ifdef __STDC__ - double ieee_sqrt(double x) /* wrapper sqrt */ -#else - double ieee_sqrt(x) /* wrapper sqrt */ - double x; -#endif -{ -#ifdef _IEEE_LIBM - return __ieee754_sqrt(x); -#else - double z; - z = __ieee754_sqrt(x); - if(_LIB_VERSION == _IEEE_ || ieee_isnan(x)) return z; - if(x<0.0) { - return __kernel_standard(x,x,26); /* ieee_sqrt(negative) */ - } else - return z; -#endif -} -- cgit v1.2.3