+Fri May 28 22:20:03 1999 Anthony Green <green@cygnus.com>
+
+ * java/lang/fdlibm.h: Don't use __uint32_t. Include mprec.h.
+ * java/lang/e_log.c: Don't use __uint32_t.
+
+1999-05-27 Eric Christopher <echristo@cygnus.com>
+
+ * configure: Rebuilt
+ * configure.in: Fixed ISO C9X and namespace collision with __uint32_t
+ * acconfig.h: Rebuilt
+ * include/config.h.in: Rebuilt
+
+ * java/lang/mprec.h, java/lang/e_acos.c, java/lang/e_asin.c,
+ java/lang/e_atan2.c, java/lang/e_exp.c, java/lang/e_fmod.c,
+ e_log.c, java/lang/e_pow.c, java/lang/e_rem_pio2.c,
+ java/lang/e_remainder.c, java/lang/e_sqrt.c, java/lang/fdlibm.h,
+ k_tan.c, java/lang/mprec.h, java/lang/s_atan.c,
+ java/lang/s_ceil.c, java/lang/s_copysign.c, java/lang/s_fabs.c,
+ s_floor.c, java/lang/s_rint.c, java/lang/sf_rint.c: Fixed ISO C9X
+ and namespace collision with __uint32_t
+
1999-06-23 Tom Tromey <tromey@cygnus.com>
* java/util/zip/InflaterInputStream.java (read): Throw
/* Define if you have sleep. */
#undef HAVE_SLEEP
-/* Define if you have __int32_t and __uint32_t. */
+/* Define if you have int32_t and uint32_t. */
#undef HAVE_INT32_DEFINED
+/* Define if you have u_int32_t */
+#undef HAVE_BSD_INT32_DEFINED
+
/* Define if you're running eCos. */
#undef ECOS
cat > conftest.$ac_ext <<EOF
#line 2709 "configure"
#include "confdefs.h"
-#include <sys/types.h>
+#include <stdint.h>
EOF
if (eval "$ac_cpp conftest.$ac_ext") 2>&5 |
- egrep "__uint32_t" >/dev/null 2>&1; then
+ egrep "uint32_t" >/dev/null 2>&1; then
rm -rf conftest*
cat >> confdefs.h <<\EOF
#define HAVE_INT32_DEFINED 1
cat > conftest.$ac_ext <<EOF
#line 2724 "configure"
#include "confdefs.h"
-#include <sys/config.h>
+#include <inttypes.h>
EOF
if (eval "$ac_cpp conftest.$ac_ext") 2>&5 |
- egrep "__uint32_t" >/dev/null 2>&1; then
+ egrep "uint32_t" >/dev/null 2>&1; then
rm -rf conftest*
cat >> confdefs.h <<\EOF
#define HAVE_INT32_DEFINED 1
fi
rm -f conftest*
+cat > conftest.$ac_ext <<EOF
+#line 2739 "configure"
+#include "confdefs.h"
+#include <sys/types.h>
+EOF
+if (eval "$ac_cpp conftest.$ac_ext") 2>&5 |
+ egrep "u_int32_t" >/dev/null 2>&1; then
+ rm -rf conftest*
+ cat >> confdefs.h <<\EOF
+#define HAVE_BSD_INT32_DEFINED 1
+EOF
+
+fi
+rm -f conftest*
+
+cat > conftest.$ac_ext <<EOF
+#line 2754 "configure"
+#include "confdefs.h"
+#include <sys/config.h>
+EOF
+if (eval "$ac_cpp conftest.$ac_ext") 2>&5 |
+ egrep "u_int32_t" >/dev/null 2>&1; then
+ rm -rf conftest*
+ cat >> confdefs.h <<\EOF
+#define HAVE_BSD_INT32_DEFINED 1
+EOF
+
+fi
+rm -f conftest*
+
+
cat > conftest.$ac_ext <<EOF
-#line 2740 "configure"
+#line 2771 "configure"
#include "confdefs.h"
#include <time.h>
EOF
rm -f conftest*
cat > conftest.$ac_ext <<EOF
-#line 2755 "configure"
+#line 2786 "configure"
#include "confdefs.h"
#include <time.h>
EOF
libsubdir=.libs
echo $ac_n "checking for garbage collector to use""... $ac_c" 1>&6
-echo "configure:2793: checking for garbage collector to use" >&5
+echo "configure:2824: checking for garbage collector to use" >&5
# Check whether --enable-java-gc or --disable-java-gc was given.
if test "${enable_java_gc+set}" = set; then
enableval="$enable_java_gc"
echo $ac_n "checking for threads package to use""... $ac_c" 1>&6
-echo "configure:2843: checking for threads package to use" >&5
+echo "configure:2874: checking for threads package to use" >&5
# Check whether --enable-threads or --disable-threads was given.
if test "${enable_threads+set}" = set; then
enableval="$enable_threads"
for ac_func in strerror ioctl select open fsync sleep
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3035: checking for $ac_func" >&5
+echo "configure:3066: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3040 "configure"
+#line 3071 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3063: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3094: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
for ac_func in ctime_r ctime
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3090: checking for $ac_func" >&5
+echo "configure:3121: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3095 "configure"
+#line 3126 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3118: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3149: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
for ac_func in gmtime_r localtime_r readdir_r getpwuid_r
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3145: checking for $ac_func" >&5
+echo "configure:3176: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3150 "configure"
+#line 3181 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3173: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3204: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
for ac_func in access stat mkdir rename rmdir unlink realpath
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3200: checking for $ac_func" >&5
+echo "configure:3231: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3205 "configure"
+#line 3236 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3228: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3259: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
for ac_func in inet_aton inet_addr
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3255: checking for $ac_func" >&5
+echo "configure:3286: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3260 "configure"
+#line 3291 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3283: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3314: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
for ac_func in inet_pton uname
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3310: checking for $ac_func" >&5
+echo "configure:3341: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3315 "configure"
+#line 3346 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3338: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3369: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
for ac_func in gethostbyname_r
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3366: checking for $ac_func" >&5
+echo "configure:3397: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3371 "configure"
+#line 3402 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3394: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3425: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
# We look for the one that returns `int'.
# Hopefully this check is robust enough.
cat > conftest.$ac_ext <<EOF
-#line 3421 "configure"
+#line 3452 "configure"
#include "confdefs.h"
#include <netdb.h>
EOF
for ac_func in gethostbyaddr_r
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3445: checking for $ac_func" >&5
+echo "configure:3476: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3450 "configure"
+#line 3481 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3473: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3504: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
# We look for the one that returns `int'.
# Hopefully this check is robust enough.
cat > conftest.$ac_ext <<EOF
-#line 3500 "configure"
+#line 3531 "configure"
#include "confdefs.h"
#include <netdb.h>
EOF
for ac_func in gethostname
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3524: checking for $ac_func" >&5
+echo "configure:3555: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3529 "configure"
+#line 3560 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3552: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3583: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
EOF
cat > conftest.$ac_ext <<EOF
-#line 3576 "configure"
+#line 3607 "configure"
#include "confdefs.h"
#include <unistd.h>
EOF
for ac_func in pthread_mutexattr_settype pthread_mutexattr_setkind_np sched_yield
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3603: checking for $ac_func" >&5
+echo "configure:3634: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3608 "configure"
+#line 3639 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3631: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3662: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
for ac_func in sched_yield
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3659: checking for $ac_func" >&5
+echo "configure:3690: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3664 "configure"
+#line 3695 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3687: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3718: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
else
echo "$ac_t""no" 1>&6
echo $ac_n "checking for sched_yield in -lposix4""... $ac_c" 1>&6
-echo "configure:3709: checking for sched_yield in -lposix4" >&5
+echo "configure:3740: checking for sched_yield in -lposix4" >&5
ac_lib_var=`echo posix4'_'sched_yield | sed 'y%./+-%__p_%'`
if eval "test \"`echo '$''{'ac_cv_lib_$ac_lib_var'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
ac_save_LIBS="$LIBS"
LIBS="-lposix4 $LIBS"
cat > conftest.$ac_ext <<EOF
-#line 3717 "configure"
+#line 3748 "configure"
#include "confdefs.h"
/* Override any gcc2 internal prototype to avoid an error. */
/* We use char because int might match the return type of a gcc2
sched_yield()
; return 0; }
EOF
-if { (eval echo configure:3728: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3759: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_lib_$ac_lib_var=yes"
else
for ac_func in gettimeofday time ftime
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3763: checking for $ac_func" >&5
+echo "configure:3794: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3768 "configure"
+#line 3799 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3791: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3822: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
for ac_func in memmove
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3824: checking for $ac_func" >&5
+echo "configure:3855: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3829 "configure"
+#line 3860 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3852: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3883: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
for ac_func in memcpy
do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:3885: checking for $ac_func" >&5
+echo "configure:3916: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3890 "configure"
+#line 3921 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:3913: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:3944: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
#--------------------------------------------------------------------
echo $ac_n "checking for socket libraries""... $ac_c" 1>&6
-echo "configure:3961: checking for socket libraries" >&5
+echo "configure:3992: checking for socket libraries" >&5
if eval "test \"`echo '$''{'gcj_cv_lib_sockets'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
gcj_checkBoth=0
unset ac_cv_func_connect
echo $ac_n "checking for connect""... $ac_c" 1>&6
-echo "configure:3969: checking for connect" >&5
+echo "configure:4000: checking for connect" >&5
if eval "test \"`echo '$''{'ac_cv_func_connect'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 3974 "configure"
+#line 4005 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char connect(); below. */
; return 0; }
EOF
-if { (eval echo configure:3997: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4028: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_connect=yes"
else
if test "$gcj_checkSocket" = 1; then
unset ac_cv_func_connect
echo $ac_n "checking for main in -lsocket""... $ac_c" 1>&6
-echo "configure:4020: checking for main in -lsocket" >&5
+echo "configure:4051: checking for main in -lsocket" >&5
ac_lib_var=`echo socket'_'main | sed 'y%./+-%__p_%'`
if eval "test \"`echo '$''{'ac_cv_lib_$ac_lib_var'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
ac_save_LIBS="$LIBS"
LIBS="-lsocket $LIBS"
cat > conftest.$ac_ext <<EOF
-#line 4028 "configure"
+#line 4059 "configure"
#include "confdefs.h"
int main() {
main()
; return 0; }
EOF
-if { (eval echo configure:4035: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4066: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_lib_$ac_lib_var=yes"
else
LIBS="$LIBS -lsocket -lnsl"
unset ac_cv_func_accept
echo $ac_n "checking for accept""... $ac_c" 1>&6
-echo "configure:4062: checking for accept" >&5
+echo "configure:4093: checking for accept" >&5
if eval "test \"`echo '$''{'ac_cv_func_accept'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 4067 "configure"
+#line 4098 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char accept(); below. */
; return 0; }
EOF
-if { (eval echo configure:4090: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4121: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_accept=yes"
else
gcj_oldLibs=$LIBS
LIBS="$LIBS $gcj_cv_lib_sockets"
echo $ac_n "checking for gethostbyname""... $ac_c" 1>&6
-echo "configure:4117: checking for gethostbyname" >&5
+echo "configure:4148: checking for gethostbyname" >&5
if eval "test \"`echo '$''{'ac_cv_func_gethostbyname'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 4122 "configure"
+#line 4153 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char gethostbyname(); below. */
; return 0; }
EOF
-if { (eval echo configure:4145: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4176: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_gethostbyname=yes"
else
else
echo "$ac_t""no" 1>&6
echo $ac_n "checking for main in -lnsl""... $ac_c" 1>&6
-echo "configure:4163: checking for main in -lnsl" >&5
+echo "configure:4194: checking for main in -lnsl" >&5
ac_lib_var=`echo nsl'_'main | sed 'y%./+-%__p_%'`
if eval "test \"`echo '$''{'ac_cv_lib_$ac_lib_var'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
ac_save_LIBS="$LIBS"
LIBS="-lnsl $LIBS"
cat > conftest.$ac_ext <<EOF
-#line 4171 "configure"
+#line 4202 "configure"
#include "confdefs.h"
int main() {
main()
; return 0; }
EOF
-if { (eval echo configure:4178: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4209: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_lib_$ac_lib_var=yes"
else
if test "$with_system_zlib" = yes; then
echo $ac_n "checking for deflate in -lz""... $ac_c" 1>&6
-echo "configure:4210: checking for deflate in -lz" >&5
+echo "configure:4241: checking for deflate in -lz" >&5
ac_lib_var=`echo z'_'deflate | sed 'y%./+-%__p_%'`
if eval "test \"`echo '$''{'ac_cv_lib_$ac_lib_var'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
ac_save_LIBS="$LIBS"
LIBS="-lz $LIBS"
cat > conftest.$ac_ext <<EOF
-#line 4218 "configure"
+#line 4249 "configure"
#include "confdefs.h"
/* Override any gcc2 internal prototype to avoid an error. */
/* We use char because int might match the return type of a gcc2
deflate()
; return 0; }
EOF
-if { (eval echo configure:4229: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4260: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_lib_$ac_lib_var=yes"
else
# requires -ldl.
if test "$GC" = boehm; then
echo $ac_n "checking for main in -ldl""... $ac_c" 1>&6
-echo "configure:4258: checking for main in -ldl" >&5
+echo "configure:4289: checking for main in -ldl" >&5
ac_lib_var=`echo dl'_'main | sed 'y%./+-%__p_%'`
if eval "test \"`echo '$''{'ac_cv_lib_$ac_lib_var'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
ac_save_LIBS="$LIBS"
LIBS="-ldl $LIBS"
cat > conftest.$ac_ext <<EOF
-#line 4266 "configure"
+#line 4297 "configure"
#include "confdefs.h"
int main() {
main()
; return 0; }
EOF
-if { (eval echo configure:4273: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4304: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_lib_$ac_lib_var=yes"
else
-for ac_hdr in unistd.h sys/time.h sys/types.h fcntl.h sys/ioctl.h sys/filio.h sys/stat.h sys/select.h sys/socket.h netinet/in.h arpa/inet.h netdb.h pwd.h
+for ac_hdr in unistd.h sys/time.h sys/types.h fcntl.h sys/ioctl.h sys/filio.h sys/stat.h sys/select.h sys/socket.h netinet/in.h arpa/inet.h netdb.h pwd.h sys/config.h inttypes.h stdint.h
do
ac_safe=`echo "$ac_hdr" | sed 'y%./+-%__p_%'`
echo $ac_n "checking for $ac_hdr""... $ac_c" 1>&6
-echo "configure:4382: checking for $ac_hdr" >&5
+echo "configure:4413: checking for $ac_hdr" >&5
if eval "test \"`echo '$''{'ac_cv_header_$ac_safe'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 4387 "configure"
+#line 4418 "configure"
#include "confdefs.h"
#include <$ac_hdr>
EOF
ac_try="$ac_cpp conftest.$ac_ext >/dev/null 2>conftest.out"
-{ (eval echo configure:4392: \"$ac_try\") 1>&5; (eval $ac_try) 2>&5; }
+{ (eval echo configure:4423: \"$ac_try\") 1>&5; (eval $ac_try) 2>&5; }
ac_err=`grep -v '^ *+' conftest.out | grep -v "^conftest.${ac_ext}\$"`
if test -z "$ac_err"; then
rm -rf conftest*
do
ac_safe=`echo "$ac_hdr" | sed 'y%./+-%__p_%'`
echo $ac_n "checking for $ac_hdr""... $ac_c" 1>&6
-echo "configure:4422: checking for $ac_hdr" >&5
+echo "configure:4453: checking for $ac_hdr" >&5
if eval "test \"`echo '$''{'ac_cv_header_$ac_safe'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 4427 "configure"
+#line 4458 "configure"
#include "confdefs.h"
#include <$ac_hdr>
EOF
ac_try="$ac_cpp conftest.$ac_ext >/dev/null 2>conftest.out"
-{ (eval echo configure:4432: \"$ac_try\") 1>&5; (eval $ac_try) 2>&5; }
+{ (eval echo configure:4463: \"$ac_try\") 1>&5; (eval $ac_try) 2>&5; }
ac_err=`grep -v '^ *+' conftest.out | grep -v "^conftest.${ac_ext}\$"`
if test -z "$ac_err"; then
rm -rf conftest*
echo $ac_n "checking whether struct sockaddr_in6 is in netinet/in.h""... $ac_c" 1>&6
-echo "configure:4460: checking whether struct sockaddr_in6 is in netinet/in.h" >&5
+echo "configure:4491: checking whether struct sockaddr_in6 is in netinet/in.h" >&5
cat > conftest.$ac_ext <<EOF
-#line 4462 "configure"
+#line 4493 "configure"
#include "confdefs.h"
#include <netinet/in.h>
int main() {
struct sockaddr_in6 addr6;
; return 0; }
EOF
-if { (eval echo configure:4469: \"$ac_compile\") 1>&5; (eval $ac_compile) 2>&5; }; then
+if { (eval echo configure:4500: \"$ac_compile\") 1>&5; (eval $ac_compile) 2>&5; }; then
rm -rf conftest*
cat >> confdefs.h <<\EOF
#define HAVE_INET6 1
rm -f conftest*
echo $ac_n "checking for socklen_t in sys/socket.h""... $ac_c" 1>&6
-echo "configure:4485: checking for socklen_t in sys/socket.h" >&5
+echo "configure:4516: checking for socklen_t in sys/socket.h" >&5
cat > conftest.$ac_ext <<EOF
-#line 4487 "configure"
+#line 4518 "configure"
#include "confdefs.h"
#include <sys/socket.h>
int main() {
socklen_t x = 5;
; return 0; }
EOF
-if { (eval echo configure:4494: \"$ac_compile\") 1>&5; (eval $ac_compile) 2>&5; }; then
+if { (eval echo configure:4525: \"$ac_compile\") 1>&5; (eval $ac_compile) 2>&5; }; then
rm -rf conftest*
cat >> confdefs.h <<\EOF
#define HAVE_SOCKLEN_T 1
rm -f conftest*
echo $ac_n "checking for tm_gmtoff in struct tm""... $ac_c" 1>&6
-echo "configure:4510: checking for tm_gmtoff in struct tm" >&5
+echo "configure:4541: checking for tm_gmtoff in struct tm" >&5
cat > conftest.$ac_ext <<EOF
-#line 4512 "configure"
+#line 4543 "configure"
#include "confdefs.h"
#include <time.h>
int main() {
struct tm tim; tim.tm_gmtoff = 0;
; return 0; }
EOF
-if { (eval echo configure:4519: \"$ac_compile\") 1>&5; (eval $ac_compile) 2>&5; }; then
+if { (eval echo configure:4550: \"$ac_compile\") 1>&5; (eval $ac_compile) 2>&5; }; then
rm -rf conftest*
cat >> confdefs.h <<\EOF
#define STRUCT_TM_HAS_GMTOFF 1
rm -rf conftest*
echo "$ac_t""no" 1>&6
echo $ac_n "checking for global timezone variable""... $ac_c" 1>&6
-echo "configure:4532: checking for global timezone variable" >&5
+echo "configure:4563: checking for global timezone variable" >&5
cat > conftest.$ac_ext <<EOF
-#line 4534 "configure"
+#line 4565 "configure"
#include "confdefs.h"
#include <time.h>
int main() {
long z2 = timezone;
; return 0; }
EOF
-if { (eval echo configure:4541: \"$ac_compile\") 1>&5; (eval $ac_compile) 2>&5; }; then
+if { (eval echo configure:4572: \"$ac_compile\") 1>&5; (eval $ac_compile) 2>&5; }; then
rm -rf conftest*
cat >> confdefs.h <<\EOF
#define HAVE_TIMEZONE 1
# The Ultrix 4.2 mips builtin alloca declared by alloca.h only works
# for constant arguments. Useless!
echo $ac_n "checking for working alloca.h""... $ac_c" 1>&6
-echo "configure:4561: checking for working alloca.h" >&5
+echo "configure:4592: checking for working alloca.h" >&5
if eval "test \"`echo '$''{'ac_cv_header_alloca_h'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 4566 "configure"
+#line 4597 "configure"
#include "confdefs.h"
#include <alloca.h>
int main() {
char *p = alloca(2 * sizeof(int));
; return 0; }
EOF
-if { (eval echo configure:4573: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4604: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
ac_cv_header_alloca_h=yes
else
fi
echo $ac_n "checking for alloca""... $ac_c" 1>&6
-echo "configure:4594: checking for alloca" >&5
+echo "configure:4625: checking for alloca" >&5
if eval "test \"`echo '$''{'ac_cv_func_alloca_works'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 4599 "configure"
+#line 4630 "configure"
#include "confdefs.h"
#ifdef __GNUC__
char *p = (char *) alloca(1);
; return 0; }
EOF
-if { (eval echo configure:4627: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4658: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
ac_cv_func_alloca_works=yes
else
echo $ac_n "checking whether alloca needs Cray hooks""... $ac_c" 1>&6
-echo "configure:4659: checking whether alloca needs Cray hooks" >&5
+echo "configure:4690: checking whether alloca needs Cray hooks" >&5
if eval "test \"`echo '$''{'ac_cv_os_cray'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 4664 "configure"
+#line 4695 "configure"
#include "confdefs.h"
#if defined(CRAY) && ! defined(CRAY2)
webecray
if test $ac_cv_os_cray = yes; then
for ac_func in _getb67 GETB67 getb67; do
echo $ac_n "checking for $ac_func""... $ac_c" 1>&6
-echo "configure:4689: checking for $ac_func" >&5
+echo "configure:4720: checking for $ac_func" >&5
if eval "test \"`echo '$''{'ac_cv_func_$ac_func'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
cat > conftest.$ac_ext <<EOF
-#line 4694 "configure"
+#line 4725 "configure"
#include "confdefs.h"
/* System header to define __stub macros and hopefully few prototypes,
which can conflict with char $ac_func(); below. */
; return 0; }
EOF
-if { (eval echo configure:4717: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
+if { (eval echo configure:4748: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext}; then
rm -rf conftest*
eval "ac_cv_func_$ac_func=yes"
else
fi
echo $ac_n "checking stack direction for C alloca""... $ac_c" 1>&6
-echo "configure:4744: checking stack direction for C alloca" >&5
+echo "configure:4775: checking stack direction for C alloca" >&5
if eval "test \"`echo '$''{'ac_cv_c_stack_direction'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
ac_cv_c_stack_direction=0
else
cat > conftest.$ac_ext <<EOF
-#line 4752 "configure"
+#line 4783 "configure"
#include "confdefs.h"
find_stack_direction ()
{
exit (find_stack_direction() < 0);
}
EOF
-if { (eval echo configure:4771: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext} && (./conftest; exit) 2>/dev/null
+if { (eval echo configure:4802: \"$ac_link\") 1>&5; (eval $ac_link) 2>&5; } && test -s conftest${ac_exeext} && (./conftest; exit) 2>/dev/null
then
ac_cv_c_stack_direction=1
else
# Extract the first word of "$ac_prog", so it can be a program name with args.
set dummy $ac_prog; ac_word=$2
echo $ac_n "checking for $ac_word""... $ac_c" 1>&6
-echo "configure:4798: checking for $ac_word" >&5
+echo "configure:4829: checking for $ac_word" >&5
if eval "test \"`echo '$''{'ac_cv_prog_PERL'+set}'`\" = set"; then
echo $ac_n "(cached) $ac_c" 1>&6
else
dnl Process this with autoconf to create configure
AC_INIT(java/lang/System.java)
-dnl Can't be done in LIBGCJ_CONFIGURE because that confuses automake.
+dnl Can't be done in LIBGCJ_CONFIGURE because that confuses automake.
AC_CONFIG_AUX_DIR(..)
AC_CANONICAL_SYSTEM
;;
esac
-AC_EGREP_HEADER(__uint32_t, sys/types.h, AC_DEFINE(HAVE_INT32_DEFINED))
-AC_EGREP_HEADER(__uint32_t, sys/config.h, AC_DEFINE(HAVE_INT32_DEFINED))
+AC_EGREP_HEADER(uint32_t, stdint.h, AC_DEFINE(HAVE_INT32_DEFINED))
+AC_EGREP_HEADER(uint32_t, inttypes.h, AC_DEFINE(HAVE_INT32_DEFINED))
+AC_EGREP_HEADER(u_int32_t, sys/types.h, AC_DEFINE(HAVE_BSD_INT32_DEFINED))
+AC_EGREP_HEADER(u_int32_t, sys/config.h, AC_DEFINE(HAVE_BSD_INT32_DEFINED))
+
dnl These may not be defined in a non-ANS conformant embedded system.
dnl FIXME: Should these case a runtime exception in that case?
dnl We check for sys/filio.h because Solaris 2.5 defines FIONREAD there.
dnl On that system, sys/ioctl.h will not include sys/filio.h unless
dnl BSD_COMP is defined; just including sys/filio.h is simpler.
-AC_CHECK_HEADERS(unistd.h sys/time.h sys/types.h fcntl.h sys/ioctl.h sys/filio.h sys/stat.h sys/select.h sys/socket.h netinet/in.h arpa/inet.h netdb.h pwd.h)
+AC_CHECK_HEADERS(unistd.h sys/time.h sys/types.h fcntl.h sys/ioctl.h sys/filio.h sys/stat.h sys/select.h sys/socket.h netinet/in.h arpa/inet.h netdb.h pwd.h sys/config.h inttypes.h stdint.h)
dnl We avoid AC_HEADER_DIRENT since we really only care about dirent.h
dnl for now. If you change this, you also must update natFile.cc.
AC_CHECK_HEADERS(dirent.h)
/* Define if you have strerror. */
#undef HAVE_STRERROR
-/* Define if you have __int32_t and __uint32_t. */
+/* Define if you have int32_t and uint32_t. */
#undef HAVE_INT32_DEFINED
+/* Define if you have u_int32_t */
+#undef HAVE_BSD_INT32_DEFINED
+
/* Define if you're running eCos. */
#undef ECOS
/* Define if you have the <fcntl.h> header file. */
#undef HAVE_FCNTL_H
+/* Define if you have the <inttypes.h> header file. */
+#undef HAVE_INTTYPES_H
+
/* Define if you have the <netdb.h> header file. */
#undef HAVE_NETDB_H
/* Define if you have the <pwd.h> header file. */
#undef HAVE_PWD_H
+/* Define if you have the <stdint.h> header file. */
+#undef HAVE_STDINT_H
+
+/* Define if you have the <sys/config.h> header file. */
+#undef HAVE_SYS_CONFIG_H
+
/* Define if you have the <sys/filio.h> header file. */
#undef HAVE_SYS_FILIO_H
-/****************************************************************
- *
- * The author of this software is David M. Gay.
- *
- * Copyright (c) 1991 by AT&T.
- *
- * Permission to use, copy, modify, and distribute this software for any
- * purpose without fee is hereby granted, provided that this entire notice
- * is included in all copies of any software which is or includes a copy
- * or modification of this software and in all copies of the supporting
- * documentation for such software.
- *
- * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
- * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
- * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
- * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
- *
- ***************************************************************/
-
-/* Please send bug reports to
- David M. Gay
- AT&T Bell Laboratories, Room 2C-463
- 600 Mountain Avenue
- Murray Hill, NJ 07974-2070
- U.S.A.
- dmg@research.att.com or research!dmg
- */
-
-#include "mprec.h"
-
-static int
-_DEFUN (quorem,
- (b, S),
- _Jv_Bigint * b _AND _Jv_Bigint * S)
-{
- int n;
- long borrow, y;
- unsigned long carry, q, ys;
- unsigned long *bx, *bxe, *sx, *sxe;
-#ifdef Pack_32
- long z;
- unsigned long si, zs;
-#endif
-
- n = S->_wds;
-#ifdef DEBUG
- /*debug*/ if (b->_wds > n)
- /*debug*/ Bug ("oversize b in quorem");
-#endif
- if (b->_wds < n)
- return 0;
- sx = S->_x;
- sxe = sx + --n;
- bx = b->_x;
- bxe = bx + n;
- q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
-#ifdef DEBUG
- /*debug*/ if (q > 9)
- /*debug*/ Bug ("oversized quotient in quorem");
-#endif
- if (q)
- {
- borrow = 0;
- carry = 0;
- do
- {
-#ifdef Pack_32
- si = *sx++;
- ys = (si & 0xffff) * q + carry;
- zs = (si >> 16) * q + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend (borrow, y);
- z = (*bx >> 16) - (zs & 0xffff) + borrow;
- borrow = z >> 16;
- Sign_Extend (borrow, z);
- Storeinc (bx, z, y);
-#else
- ys = *sx++ * q + carry;
- carry = ys >> 16;
- y = *bx - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend (borrow, y);
- *bx++ = y & 0xffff;
-#endif
- }
- while (sx <= sxe);
- if (!*bxe)
- {
- bx = b->_x;
- while (--bxe > bx && !*bxe)
- --n;
- b->_wds = n;
- }
- }
- if (cmp (b, S) >= 0)
- {
- q++;
- borrow = 0;
- carry = 0;
- bx = b->_x;
- sx = S->_x;
- do
- {
-#ifdef Pack_32
- si = *sx++;
- ys = (si & 0xffff) + carry;
- zs = (si >> 16) + (ys >> 16);
- carry = zs >> 16;
- y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend (borrow, y);
- z = (*bx >> 16) - (zs & 0xffff) + borrow;
- borrow = z >> 16;
- Sign_Extend (borrow, z);
- Storeinc (bx, z, y);
-#else
- ys = *sx++ + carry;
- carry = ys >> 16;
- y = *bx - (ys & 0xffff) + borrow;
- borrow = y >> 16;
- Sign_Extend (borrow, y);
- *bx++ = y & 0xffff;
-#endif
- }
- while (sx <= sxe);
- bx = b->_x;
- bxe = bx + n;
- if (!*bxe)
- {
- while (--bxe > bx && !*bxe)
- --n;
- b->_wds = n;
- }
- }
- return q;
-}
-
-#ifdef DEBUG
-#include <stdio.h>
-
-void
-print (_Jv_Bigint * b)
-{
- int i, wds;
- unsigned long *x, y;
- wds = b->_wds;
- x = b->_x+wds;
- i = 0;
- do
- {
- x--;
- fprintf (stderr, "%08x", *x);
- }
- while (++i < wds);
- fprintf (stderr, "\n");
-}
-#endif
-
-/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
- *
- * Inspired by "How to Print Floating-Point Numbers Accurately" by
- * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
- *
- * Modifications:
- * 1. Rather than iterating, we use a simple numeric overestimate
- * to determine k = floor(log10(d)). We scale relevant
- * quantities using O(log2(k)) rather than O(k) multiplications.
- * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
- * try to generate digits strictly left to right. Instead, we
- * compute with fewer bits and propagate the carry if necessary
- * when rounding the final digit up. This is often faster.
- * 3. Under the assumption that input will be rounded nearest,
- * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
- * That is, we allow equality in stopping tests when the
- * round-nearest rule will give the same floating-point value
- * as would satisfaction of the stopping test with strict
- * inequality.
- * 4. We remove common factors of powers of 2 from relevant
- * quantities.
- * 5. When converting floating-point integers less than 1e16,
- * we use floating-point arithmetic rather than resorting
- * to multiple-precision integers.
- * 6. When asked to produce fewer than 15 digits, we first try
- * to get by with floating-point arithmetic; we resort to
- * multiple-precision integer arithmetic only if we cannot
- * guarantee that the floating-point calculation has given
- * the correctly rounded result. For k requested digits and
- * "uniformly" distributed input, the probability is
- * something like 10^(k-15) that we must resort to the long
- * calculation.
- */
-
-
-char *
-_DEFUN (_dtoa_r,
- (ptr, _d, mode, ndigits, decpt, sign, rve, float_type),
- struct _Jv_reent *ptr _AND
- double _d _AND
- int mode _AND
- int ndigits _AND
- int *decpt _AND
- int *sign _AND
- char **rve _AND
- int float_type)
-{
- /*
- float_type == 0 for double precision, 1 for float.
-
- Arguments ndigits, decpt, sign are similar to those
- of ecvt and fcvt; trailing zeros are suppressed from
- the returned string. If not null, *rve is set to point
- to the end of the return value. If d is +-Infinity or NaN,
- then *decpt is set to 9999.
-
- mode:
- 0 ==> shortest string that yields d when read in
- and rounded to nearest.
- 1 ==> like 0, but with Steele & White stopping rule;
- e.g. with IEEE P754 arithmetic , mode 0 gives
- 1e23 whereas mode 1 gives 9.999999999999999e22.
- 2 ==> max(1,ndigits) significant digits. This gives a
- return value similar to that of ecvt, except
- that trailing zeros are suppressed.
- 3 ==> through ndigits past the decimal point. This
- gives a return value similar to that from fcvt,
- except that trailing zeros are suppressed, and
- ndigits can be negative.
- 4-9 should give the same return values as 2-3, i.e.,
- 4 <= mode <= 9 ==> same return as mode
- 2 + (mode & 1). These modes are mainly for
- debugging; often they run slower but sometimes
- faster than modes 2-3.
- 4,5,8,9 ==> left-to-right digit generation.
- 6-9 ==> don't try fast floating-point estimate
- (if applicable).
-
- > 16 ==> Floating-point arg is treated as single precision.
-
- Values of mode other than 0-9 are treated as mode 0.
-
- Sufficient space is allocated to the return value
- to hold the suppressed trailing zeros.
- */
-
- int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, j, j1, k, k0,
- k_check, leftright, m2, m5, s2, s5, spec_case, try_quick;
- union double_union d, d2, eps;
- long L;
-#ifndef Sudden_Underflow
- int denorm;
- unsigned long x;
-#endif
- _Jv_Bigint *b, *b1, *delta, *mlo, *mhi, *S;
- double ds;
- char *s, *s0;
-
- d.d = _d;
-
- if (ptr->_result)
- {
- ptr->_result->_k = ptr->_result_k;
- ptr->_result->_maxwds = 1 << ptr->_result_k;
- Bfree (ptr, ptr->_result);
- ptr->_result = 0;
- }
-
- if (word0 (d) & Sign_bit)
- {
- /* set sign for everything, including 0's and NaNs */
- *sign = 1;
- word0 (d) &= ~Sign_bit; /* clear sign bit */
- }
- else
- *sign = 0;
-
-#if defined(IEEE_Arith) + defined(VAX)
-#ifdef IEEE_Arith
- if ((word0 (d) & Exp_mask) == Exp_mask)
-#else
- if (word0 (d) == 0x8000)
-#endif
- {
- /* Infinity or NaN */
- *decpt = 9999;
- s =
-#ifdef IEEE_Arith
- !word1 (d) && !(word0 (d) & 0xfffff) ? "Infinity" :
-#endif
- "NaN";
- if (rve)
- *rve =
-#ifdef IEEE_Arith
- s[3] ? s + 8 :
-#endif
- s + 3;
- return s;
- }
-#endif
-#ifdef IBM
- d.d += 0; /* normalize */
-#endif
- if (!d.d)
- {
- *decpt = 1;
- s = "0";
- if (rve)
- *rve = s + 1;
- return s;
- }
-
- b = d2b (ptr, d.d, &be, &bbits);
-#ifdef Sudden_Underflow
- i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1));
-#else
- if ((i = (int) (word0 (d) >> Exp_shift1 & (Exp_mask >> Exp_shift1))))
- {
-#endif
- d2.d = d.d;
- word0 (d2) &= Frac_mask1;
- word0 (d2) |= Exp_11;
-#ifdef IBM
- if (j = 11 - hi0bits (word0 (d2) & Frac_mask))
- d2.d /= 1 << j;
-#endif
-
- /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
- * log10(x) = log(x) / log(10)
- * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
- * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
- *
- * This suggests computing an approximation k to log10(d) by
- *
- * k = (i - Bias)*0.301029995663981
- * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
- *
- * We want k to be too large rather than too small.
- * The error in the first-order Taylor series approximation
- * is in our favor, so we just round up the constant enough
- * to compensate for any error in the multiplication of
- * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
- * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
- * adding 1e-13 to the constant term more than suffices.
- * Hence we adjust the constant term to 0.1760912590558.
- * (We could get a more accurate k by invoking log10,
- * but this is probably not worthwhile.)
- */
-
- i -= Bias;
-#ifdef IBM
- i <<= 2;
- i += j;
-#endif
-#ifndef Sudden_Underflow
- denorm = 0;
- }
- else
- {
- /* d is denormalized */
-
- i = bbits + be + (Bias + (P - 1) - 1);
- x = i > 32 ? word0 (d) << (64 - i) | word1 (d) >> (i - 32)
- : word1 (d) << (32 - i);
- d2.d = x;
- word0 (d2) -= 31 * Exp_msk1; /* adjust exponent */
- i -= (Bias + (P - 1) - 1) + 1;
- denorm = 1;
- }
-#endif
- ds = (d2.d - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
- k = (int) ds;
- if (ds < 0. && ds != k)
- k--; /* want k = floor(ds) */
- k_check = 1;
- if (k >= 0 && k <= Ten_pmax)
- {
- if (d.d < tens[k])
- k--;
- k_check = 0;
- }
- j = bbits - i - 1;
- if (j >= 0)
- {
- b2 = 0;
- s2 = j;
- }
- else
- {
- b2 = -j;
- s2 = 0;
- }
- if (k >= 0)
- {
- b5 = 0;
- s5 = k;
- s2 += k;
- }
- else
- {
- b2 -= k;
- b5 = -k;
- s5 = 0;
- }
- if (mode < 0 || mode > 9)
- mode = 0;
- try_quick = 1;
- if (mode > 5)
- {
- mode -= 4;
- try_quick = 0;
- }
- leftright = 1;
- switch (mode)
- {
- case 0:
- case 1:
- ilim = ilim1 = -1;
- i = 18;
- ndigits = 0;
- break;
- case 2:
- leftright = 0;
- /* no break */
- case 4:
- if (ndigits <= 0)
- ndigits = 1;
- ilim = ilim1 = i = ndigits;
- break;
- case 3:
- leftright = 0;
- /* no break */
- case 5:
- i = ndigits + k + 1;
- ilim = i;
- ilim1 = i - 1;
- if (i <= 0)
- i = 1;
- }
- j = sizeof (unsigned long);
- for (ptr->_result_k = 0; (int) (sizeof (_Jv_Bigint) - sizeof (unsigned long)) + j <= i;
- j <<= 1)
- ptr->_result_k++;
- ptr->_result = Balloc (ptr, ptr->_result_k);
- s = s0 = (char *) ptr->_result;
-
- if (ilim >= 0 && ilim <= Quick_max && try_quick)
- {
- /* Try to get by with floating-point arithmetic. */
-
- i = 0;
- d2.d = d.d;
- k0 = k;
- ilim0 = ilim;
- ieps = 2; /* conservative */
- if (k > 0)
- {
- ds = tens[k & 0xf];
- j = k >> 4;
- if (j & Bletch)
- {
- /* prevent overflows */
- j &= Bletch - 1;
- d.d /= bigtens[n_bigtens - 1];
- ieps++;
- }
- for (; j; j >>= 1, i++)
- if (j & 1)
- {
- ieps++;
- ds *= bigtens[i];
- }
- d.d /= ds;
- }
- else if ((j1 = -k))
- {
- d.d *= tens[j1 & 0xf];
- for (j = j1 >> 4; j; j >>= 1, i++)
- if (j & 1)
- {
- ieps++;
- d.d *= bigtens[i];
- }
- }
- if (k_check && d.d < 1. && ilim > 0)
- {
- if (ilim1 <= 0)
- goto fast_failed;
- ilim = ilim1;
- k--;
- d.d *= 10.;
- ieps++;
- }
- eps.d = ieps * d.d + 7.;
- word0 (eps) -= (P - 1) * Exp_msk1;
- if (ilim == 0)
- {
- S = mhi = 0;
- d.d -= 5.;
- if (d.d > eps.d)
- goto one_digit;
- if (d.d < -eps.d)
- goto no_digits;
- goto fast_failed;
- }
-#ifndef No_leftright
- if (leftright)
- {
- /* Use Steele & White method of only
- * generating digits needed.
- */
- eps.d = 0.5 / tens[ilim - 1] - eps.d;
- for (i = 0;;)
- {
- L = d.d;
- d.d -= L;
- *s++ = '0' + (int) L;
- if (d.d < eps.d)
- goto ret1;
- if (1. - d.d < eps.d)
- goto bump_up;
- if (++i >= ilim)
- break;
- eps.d *= 10.;
- d.d *= 10.;
- }
- }
- else
- {
-#endif
- /* Generate ilim digits, then fix them up. */
- eps.d *= tens[ilim - 1];
- for (i = 1;; i++, d.d *= 10.)
- {
- L = d.d;
- d.d -= L;
- *s++ = '0' + (int) L;
- if (i == ilim)
- {
- if (d.d > 0.5 + eps.d)
- goto bump_up;
- else if (d.d < 0.5 - eps.d)
- {
- while (*--s == '0');
- s++;
- goto ret1;
- }
- break;
- }
- }
-#ifndef No_leftright
- }
-#endif
- fast_failed:
- s = s0;
- d.d = d2.d;
- k = k0;
- ilim = ilim0;
- }
-
- /* Do we have a "small" integer? */
-
- if (be >= 0 && k <= Int_max)
- {
- /* Yes. */
- ds = tens[k];
- if (ndigits < 0 && ilim <= 0)
- {
- S = mhi = 0;
- if (ilim < 0 || d.d <= 5 * ds)
- goto no_digits;
- goto one_digit;
- }
- for (i = 1;; i++)
- {
- L = d.d / ds;
- d.d -= L * ds;
-#ifdef Check_FLT_ROUNDS
- /* If FLT_ROUNDS == 2, L will usually be high by 1 */
- if (d.d < 0)
- {
- L--;
- d.d += ds;
- }
-#endif
- *s++ = '0' + (int) L;
- if (i == ilim)
- {
- d.d += d.d;
- if (d.d > ds || (d.d == ds && L & 1))
- {
- bump_up:
- while (*--s == '9')
- if (s == s0)
- {
- k++;
- *s = '0';
- break;
- }
- ++*s++;
- }
- break;
- }
- if (!(d.d *= 10.))
- break;
- }
- goto ret1;
- }
-
- m2 = b2;
- m5 = b5;
- mhi = mlo = 0;
- if (leftright)
- {
- if (mode < 2)
- {
- i =
-#ifndef Sudden_Underflow
- denorm ? be + (Bias + (P - 1) - 1 + 1) :
-#endif
-#ifdef IBM
- 1 + 4 * P - 3 - bbits + ((bbits + be - 1) & 3);
-#else
- 1 + P - bbits;
-#endif
- }
- else
- {
- j = ilim - 1;
- if (m5 >= j)
- m5 -= j;
- else
- {
- s5 += j -= m5;
- b5 += j;
- m5 = 0;
- }
- if ((i = ilim) < 0)
- {
- m2 -= i;
- i = 0;
- }
- }
- b2 += i;
- s2 += i;
- mhi = i2b (ptr, 1);
- }
- if (m2 > 0 && s2 > 0)
- {
- i = m2 < s2 ? m2 : s2;
- b2 -= i;
- m2 -= i;
- s2 -= i;
- }
- if (b5 > 0)
- {
- if (leftright)
- {
- if (m5 > 0)
- {
- mhi = pow5mult (ptr, mhi, m5);
- b1 = mult (ptr, mhi, b);
- Bfree (ptr, b);
- b = b1;
- }
- if ((j = b5 - m5))
- b = pow5mult (ptr, b, j);
- }
- else
- b = pow5mult (ptr, b, b5);
- }
- S = i2b (ptr, 1);
- if (s5 > 0)
- S = pow5mult (ptr, S, s5);
-
- /* Check for special case that d is a normalized power of 2. */
-
- if (mode < 2)
- {
- if (!word1 (d) && !(word0 (d) & Bndry_mask)
-#ifndef Sudden_Underflow
- && word0 (d) & Exp_mask
-#endif
- )
- {
- /* The special case */
- b2 += Log2P;
- s2 += Log2P;
- spec_case = 1;
- }
- else
- spec_case = 0;
- }
-
- /* Arrange for convenient computation of quotients:
- * shift left if necessary so divisor has 4 leading 0 bits.
- *
- * Perhaps we should just compute leading 28 bits of S once
- * and for all and pass them and a shift to quorem, so it
- * can do shifts and ors to compute the numerator for q.
- */
-
-#ifdef Pack_32
- if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0x1f))
- i = 32 - i;
-#else
- if ((i = ((s5 ? 32 - hi0bits (S->_x[S->_wds - 1]) : 1) + s2) & 0xf))
- i = 16 - i;
-#endif
- if (i > 4)
- {
- i -= 4;
- b2 += i;
- m2 += i;
- s2 += i;
- }
- else if (i < 4)
- {
- i += 28;
- b2 += i;
- m2 += i;
- s2 += i;
- }
- if (b2 > 0)
- b = lshift (ptr, b, b2);
- if (s2 > 0)
- S = lshift (ptr, S, s2);
- if (k_check)
- {
- if (cmp (b, S) < 0)
- {
- k--;
- b = multadd (ptr, b, 10, 0); /* we botched the k estimate */
- if (leftright)
- mhi = multadd (ptr, mhi, 10, 0);
- ilim = ilim1;
- }
- }
- if (ilim <= 0 && mode > 2)
- {
- if (ilim < 0 || cmp (b, S = multadd (ptr, S, 5, 0)) <= 0)
- {
- /* no digits, fcvt style */
- no_digits:
- k = -1 - ndigits;
- goto ret;
- }
- one_digit:
- *s++ = '1';
- k++;
- goto ret;
- }
- if (leftright)
- {
- if (m2 > 0)
- mhi = lshift (ptr, mhi, m2);
-
- /* Single precision case, */
- if (float_type)
- mhi = lshift (ptr, mhi, 29);
-
- /* Compute mlo -- check for special case
- * that d is a normalized power of 2.
- */
-
- mlo = mhi;
- if (spec_case)
- {
- mhi = Balloc (ptr, mhi->_k);
- Bcopy (mhi, mlo);
- mhi = lshift (ptr, mhi, Log2P);
- }
-
- for (i = 1;; i++)
- {
- dig = quorem (b, S) + '0';
- /* Do we yet have the shortest decimal string
- * that will round to d?
- */
- j = cmp (b, mlo);
- delta = diff (ptr, S, mhi);
- j1 = delta->_sign ? 1 : cmp (b, delta);
- Bfree (ptr, delta);
-#ifndef ROUND_BIASED
- if (j1 == 0 && !mode && !(word1 (d) & 1))
- {
- if (dig == '9')
- goto round_9_up;
- if (j > 0)
- dig++;
- *s++ = dig;
- goto ret;
- }
-#endif
- if (j < 0 || (j == 0 && !mode
-#ifndef ROUND_BIASED
- && !(word1 (d) & 1)
-#endif
- ))
- {
- if (j1 > 0)
- {
- b = lshift (ptr, b, 1);
- j1 = cmp (b, S);
- if ((j1 > 0 || (j1 == 0 && dig & 1))
- && dig++ == '9')
- goto round_9_up;
- }
- *s++ = dig;
- goto ret;
- }
- if (j1 > 0)
- {
- if (dig == '9')
- { /* possible if i == 1 */
- round_9_up:
- *s++ = '9';
- goto roundoff;
- }
- *s++ = dig + 1;
- goto ret;
- }
- *s++ = dig;
- if (i == ilim)
- break;
- b = multadd (ptr, b, 10, 0);
- if (mlo == mhi)
- mlo = mhi = multadd (ptr, mhi, 10, 0);
- else
- {
- mlo = multadd (ptr, mlo, 10, 0);
- mhi = multadd (ptr, mhi, 10, 0);
- }
- }
- }
- else
- for (i = 1;; i++)
- {
- *s++ = dig = quorem (b, S) + '0';
- if (i >= ilim)
- break;
- b = multadd (ptr, b, 10, 0);
- }
-
- /* Round off last digit */
-
- b = lshift (ptr, b, 1);
- j = cmp (b, S);
- if (j > 0 || (j == 0 && dig & 1))
- {
- roundoff:
- while (*--s == '9')
- if (s == s0)
- {
- k++;
- *s++ = '1';
- goto ret;
- }
- ++*s++;
- }
- else
- {
- while (*--s == '0');
- s++;
- }
-ret:
- Bfree (ptr, S);
- if (mhi)
- {
- if (mlo && mlo != mhi)
- Bfree (ptr, mlo);
- Bfree (ptr, mhi);
- }
-ret1:
- Bfree (ptr, b);
- *s = 0;
- *decpt = k + 1;
- if (rve)
- *rve = s;
- return s0;
-}
-
-
-_VOID
-_DEFUN (_dtoa,
- (_d, mode, ndigits, decpt, sign, rve, buf, float_type),
- double _d _AND
- int mode _AND
- int ndigits _AND
- int *decpt _AND
- int *sign _AND
- char **rve _AND
- char *buf _AND
- int float_type)
-{
- struct _Jv_reent reent;
- char *p;
- memset (&reent, 0, sizeof reent);
-
- p = _dtoa_r (&reent, _d, mode, ndigits, decpt, sign, rve, float_type);
- strcpy (buf, p);
-
- return;
-}
-
-
+ /*
+ && word0(d) & Exp_mask
+ struct _Jv_reent reent;
-
-/* @(#)e_acos.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __ieee754_acos(x)
- * Method :
- * acos(x) = pi/2 - asin(x)
- * acos(-x) = pi/2 + 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(sqrt((1-x)/2)))
- * = 2asin(sqrt((1-x)/2))
- * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=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 ~ sqrt(z).
- * For x<-0.5
- * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
- * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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;
- __int32_t hx,ix;
- GET_HIGH_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x3ff00000) { /* |x| >= 1 */
- __uint32_t lx;
- GET_LOW_WORD(lx,x);
- if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
- if(hx>0) return 0.0; /* acos(1) = 0 */
- else return pi+2.0*pio2_lo; /* acos(-1)= pi */
- }
- return (x-x)/(x-x); /* 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 = __ieee754_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 = __ieee754_sqrt(z);
- df = s;
- SET_LOW_WORD(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);
- }
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ * software is freely granted, provided that this notice
+ * Method :
+ * = 2asin(sqrt((1-x)/2))
+static const double
+static double
+ int32_t hx,ix;
+ uint32_t lx;
-
-/* @(#)e_atan2.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- *
- */
-
-/* __ieee754_atan2(y,x)
- * Method :
- * 1. Reduce y to positive by atan2(y,x)=-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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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;
- __int32_t k,m,hx,hy,ix,iy;
- __uint32_t lx,ly;
-
- EXTRACT_WORDS(hx,lx,x);
- ix = hx&0x7fffffff;
- EXTRACT_WORDS(hy,ly,y);
- iy = hy&0x7fffffff;
- 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 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; /* atan(+-0,+anything)=+-0 */
- case 2: return pi+tiny;/* atan(+0,-anything) = pi */
- case 3: return -pi-tiny;/* 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;/* atan(+INF,+INF) */
- case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
- case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
- case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
- }
- } else {
- switch(m) {
- case 0: return zero ; /* atan(+...,+INF) */
- case 1: return -zero ; /* atan(-...,+INF) */
- case 2: return pi+tiny ; /* atan(+...,-INF) */
- case 3: return -pi-tiny ; /* 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=atan(fabs(y/x)); /* safe to do y/x */
- switch (m) {
- case 0: return z ; /* atan(+,+) */
- case 1: {
- __uint32_t zh;
- GET_HIGH_WORD(zh,z);
- SET_HIGH_WORD(z,zh ^ 0x80000000);
- }
- return z ; /* atan(-,+) */
- case 2: return pi-(z-pi_lo);/* atan(+,-) */
- default: /* case 3 */
- return (z-pi_lo)-pi;/* atan(-,-) */
- }
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ * software is freely granted, provided that this notice
+ * 2. Reduce x to positive by (if x and y are unexceptional):
+ * 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
+static const double
+static double
+{
+ int32_t k,m,hx,hy,ix,iy;
+ uint32_t lx,ly;
+ case 0:
+
+ uint32_t zh;
-
-/* @(#)e_exp.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __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 exp(r) by a special rational function on
- * the interval [0,0.34658]:
- * Write
- * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
- * We use a special Reme 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 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 exp(x):
- * From step 1, we have
- * exp(x) = 2^k * exp(r)
- *
- * Special cases:
- * exp(INF) is INF, exp(NaN) is NaN;
- * exp(-INF) is 0, and
- * for finite argument, only 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 exp(x) overflow
- * if x < -7.45133219101941108420e+02 then 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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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;
- __int32_t k,xsb;
- __uint32_t hx;
-
- GET_HIGH_WORD(hx,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) {
- __uint32_t lx;
- GET_LOW_WORD(lx,x);
- if(((hx&0xfffff)|lx)!=0)
- return x+x; /* NaN */
- else return (xsb==0)? x:0.0; /* 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 = 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) {
- __uint32_t hy;
- GET_HIGH_WORD(hy,y);
- SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */
- return y;
- } else {
- __uint32_t hy;
- GET_HIGH_WORD(hy,y);
- SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */
- return y*twom1000;
+ * software is freely granted, provided that this notice
+ * x = k*ln2 + r, |r| <= 0.5*ln2.
+ * Here r will be represented as r = hi-lo for better
+ * We use a special Reme algorithm on [0,0.34658] to generate
+ * a polynomial of degree 5 to approximate R. The maximum error
+ * | 2.0+P1*z+...+P5*z - R(z) | <= 2
+ * r*R1(r)
+ *
+ * For IEEE double
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ int32_t k,xsb;
+ uint32_t hx;
+ uint32_t lx;
+ if(((hx&0xfffff)|lx)!=0)
+ if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
}
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ if(k==0) return one-((x*c)/(c-2.0)-x);
+ uint32_t hy;
+ uint32_t hy;
-
-/* @(#)e_fmod.c 5.1 93/09/24 */
+ * software is freely granted, provided that this notice
/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
- * __ieee754_fmod(x,y)
- * Return x mod y in exact arithmetic
- * Method: shift and subtract
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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
-{
- __int32_t n,hx,hy,hz,ix,iy,sx,i;
- __uint32_t lx,ly,lz;
-
- EXTRACT_WORDS(hx,lx,x);
- EXTRACT_WORDS(hy,ly,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<hy)||(lx<ly)) return x; /* |x|<|y| return x */
- if(lx==ly)
- return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0*/
- }
-
- /* determine ix = 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 = 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<<n)|(lx>>(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<<n)|(ly>>(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<ly) hz -= 1;
- if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
- else {
- if((hz|lz)==0) /* return sign(x)*0 */
- return Zero[(__uint32_t)sx>>31];
- hx = hz+hz+(lz>>31); lx = lz+lz;
- }
- }
- hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
- if(hz>=0) {hx=hz;lx=lz;}
-
- /* convert back to floating value and restore the sign */
- if((hx|lx)==0) /* return sign(x)*0 */
- return Zero[(__uint32_t)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));
- INSERT_WORDS(x,hx|sx,lx);
- } else { /* subnormal output */
- n = -1022 - iy;
- if(n<=20) {
- lx = (lx>>n)|((__uint32_t)hx<<(32-n));
- hx >>= n;
- } else if (n<=31) {
- lx = (hx<<(32-n))|(lx>>n); hx = sx;
- } else {
- lx = hx>>(n-32); hx = sx;
- }
- INSERT_WORDS(x,hx|sx,lx);
- x *= one; /* create necessary signal */
- }
- return x; /* exact output */
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ int32_t n,hx,hy,hz,ix,iy,sx,i;
+ uint32_t lx,ly,lz;
+ if(lx==ly)
+ return Zero[(uint32_t)sx>>31]; /* |x|=|y| return x*0*/
+ if(ix >= -1022)
+ if(iy >= -1022)
+ return Zero[(uint32_t)sx>>31];
+ return Zero[(uint32_t)sx>>31];
+ lx = (lx>>n)|((uint32_t)hx<<(32-n));
-
-/* @(#)e_log.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * software is freely granted, provided that this notice
+ * Method :
+ * 1. Argument Reduction: find k and f such that
+ * x = 2^k * (1+f),
+ * We use a special Reme algorithm on [0,0.1716] to generate
+ * a polynomial of degree 14 to approximate R The maximum error
+ * | Lg1*s +...+Lg7*s - R(z) | <= 2
*
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __ieee754_log(x)
- * Return the logrithm of x
- *
- * Method :
- * 1. Argument Reduction: find k and f such that
- * x = 2^k * (1+f),
- * where sqrt(2)/2 < 1+f < sqrt(2) .
- *
- * 2. Approximation of log(1+f).
- * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - 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, log(x) = k*ln2 + 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; 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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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 */
-
-#ifdef __STDC__
-static const double zero = 0.0;
-#else
-static double zero = 0.0;
-#endif
-
-#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;
- __int32_t k,hx,i,j;
- __uint32_t lx;
-
- EXTRACT_WORDS(hx,lx,x);
-
- k=0;
- if (hx < 0x00100000) { /* x < 2**-1022 */
- if (((hx&0x7fffffff)|lx)==0)
- return -two54/zero; /* log(+-0)=-inf */
- if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
- k -= 54; x *= two54; /* subnormal number, scale up x */
- GET_HIGH_WORD(hx,x);
- }
- if (hx >= 0x7ff00000) return x+x;
- k += (hx>>20)-1023;
- hx &= 0x000fffff;
- i = (hx+0x95f64)&0x100000;
- SET_HIGH_WORD(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);
+ * 3. Finally, log(x) = k*ln2 + log(1+f).
+ * Here ln2 is split into two floating point number:
+ * log(x) is NaN with signal if x < 0 (including -INF) ;
+ * 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
+ int32_t k,hx,i,j;
+ uint32_t lx;
+ if (((hx&0x7fffffff)|lx)==0)
}
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ s = f/(2.0+f);
+ t1= w*(Lg2+w*(Lg4+w*Lg6));
+ t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
-
-/* @(#)e_pow.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __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*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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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)*(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;
- __int32_t i,j,k,yisint,n;
- __int32_t hx,hy,ix,iy;
- __uint32_t lx,ly;
-
- EXTRACT_WORDS(hx,lx,x);
- EXTRACT_WORDS(hy,ly,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((__uint32_t)(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 __ieee754_sqrt(x);
- }
- }
-
- ax = 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;
+ * software is freely granted, provided that this notice
+ * 2. Perform y*log2(x) = n+y' by simulating muti-precision
+ * always returns the correct integer provided it is
+ * 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
+static const double
+static double
+ int32_t i,j,k,yisint,n;
+ int32_t hx,hy,ix,iy;
+ uint32_t lx,ly;
+ if((iy|ly)==0) return one;
+ iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
+ return x+y;
+ if(hx<0) {
+ if((uint32_t)(j<<(52-k))==ly) yisint = 2-(j&1);
}
}
-
- /* (x<0)**(non-int) is NaN */
- /* CYGNUS LOCAL: This used to be
- if((((hx>>31)+1)|yisint)==0) return (x-x)/(x-x);
- but ANSI C says a right shift of a signed negative quantity is
- implementation defined. */
- if(((((__uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
-
- /* |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;
+ if(ly==0) {
}
- /* over/underflow if x is not close to one */
- if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
- if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
- /* now |1-x| is tiny <= 2**-20, suffice to compute
- log(x) by x-x^2/2+x^3/3-x^4/4 */
- t = x-1; /* 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;
- SET_LOW_WORD(t1,0);
- t2 = v-(t1-u);
- } else {
- double s2,s_h,s_l,t_h,t_l;
- n = 0;
- /* take care subnormal number */
- if(ix<0x00100000)
- {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
- n += ((ix)>>20)-0x3ff;
- j = ix&0x000fffff;
- /* determine interval */
- ix = j|0x3ff00000; /* normalize ix */
- if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
- else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
- else {k=0;n+=1;ix -= 0x00100000;}
- SET_HIGH_WORD(ax,ix);
+ return __ieee754_sqrt(x);
+ } else if(yisint==1)
- /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
- u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
- v = one/(ax+bp[k]);
- s = u*v;
- s_h = s;
- SET_LOW_WORD(s_h,0);
- /* t_h=ax+bp[k] High */
- t_h = zero;
- SET_HIGH_WORD(t_h,((ix>>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 log(ax) */
- s2 = s*s;
- r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
- r += s_l*(s_h+s);
- s2 = s_h*s_h;
- t_h = 3.0+s2+r;
- SET_LOW_WORD(t_h,0);
- t_l = r-((t_h-3.0)-s2);
- /* u+v = s*(1+...) */
- u = s_h*t_h;
- v = s_l*t_h+t_l*s;
- /* 2/(3log2)*(s+...) */
- p_h = u+v;
- SET_LOW_WORD(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) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
- t = (double)n;
- t1 = (((z_h+z_l)+dp_h[k])+t);
- SET_LOW_WORD(t1,0);
- t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+ if(((((uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
+ /* now |1-x| is tiny <= 2**-20, suffice to compute
+ if(((((uint32_t)hx>>31)-1)|(yisint-1))==0)
}
-
- s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
- if(((((__uint32_t)hx>>31)-1)|(yisint-1))==0)
- s = -one;/* (-ve)**(odd int) */
-
- /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
- y1 = y;
- SET_LOW_WORD(y1,0);
- p_l = (y-y1)*t1+y*t2;
- p_h = y1*t1;
- z = p_l+p_h;
- EXTRACT_WORDS(j,i,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;
- SET_HIGH_WORD(t,n&~(0x000fffff>>k));
- n = ((n&0x000fffff)|0x00100000)>>(20-k);
- if(j<0) n = -n;
- p_h -= t;
- }
- t = p_l+p_h;
- SET_LOW_WORD(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);
- GET_HIGH_WORD(j,z);
- j += (n<<20);
- if((j>>20)<=0) z = scalbn(z,(int)n); /* subnormal output */
- else SET_HIGH_WORD(z,j);
- return s*z;
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
-
-/* @(#)e_rem_pio2.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * software is freely granted, provided that this notice
*
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- *
- */
-
-/* __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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-/*
- * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
- */
-#ifdef __STDC__
-static const __int32_t two_over_pi[] = {
-#else
-static __int32_t two_over_pi[] = {
-#endif
-0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
-0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
-0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
-0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
-0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
-0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
-0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
-0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
-0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
-0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
-0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
-};
-
-#ifdef __STDC__
-static const __int32_t npio2_hw[] = {
-#else
-static __int32_t npio2_hw[] = {
-#endif
-0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
-0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
-0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
-0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
-0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
-0x404858EB, 0x404921FB,
-};
-
-/*
- * invpio2: 53 bits of 2/pi
- * pio2_1: first 33 bit of pi/2
- * pio2_1t: pi/2 - pio2_1
- * pio2_2: second 33 bit of pi/2
- * pio2_2t: pi/2 - (pio2_1+pio2_2)
- * pio2_3: third 33 bit of pi/2
- * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
- */
-
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
-half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
-two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
-invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
-pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
-pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
-pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
-pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
-pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
-pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
-
-#ifdef __STDC__
- __int32_t __ieee754_rem_pio2(double x, double *y)
-#else
- __int32_t __ieee754_rem_pio2(x,y)
- double x,y[];
-#endif
-{
- double z,w,t,r,fn;
- double tx[3];
- __int32_t i,j,n,ix,hx;
- int e0,nx;
- __uint32_t low;
-
- GET_HIGH_WORD(hx,x); /* high word of x */
- ix = hx&0x7fffffff;
- if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
- {y[0] = x; y[1] = 0; return 0;}
- if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
- if(hx>0) {
- z = x - pio2_1;
- if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
- y[0] = z - pio2_1t;
- y[1] = (z-y[0])-pio2_1t;
- } else { /* near pi/2, use 33+33+53 bit pi */
- z -= pio2_2;
- y[0] = z - pio2_2t;
- y[1] = (z-y[0])-pio2_2t;
- }
- return 1;
- } else { /* negative x */
- z = x + pio2_1;
- if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
- y[0] = z + pio2_1t;
- y[1] = (z-y[0])+pio2_1t;
- } else { /* near pi/2, use 33+33+53 bit pi */
- z += pio2_2;
- y[0] = z + pio2_2t;
- y[1] = (z-y[0])+pio2_2t;
- }
- return -1;
- }
- }
- if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
- t = fabs(x);
- n = (__int32_t) (t*invpio2+half);
- fn = (double)n;
- r = t-fn*pio2_1;
- w = fn*pio2_1t; /* 1st round good to 85 bit */
- if(n<32&&ix!=npio2_hw[n-1]) {
- y[0] = r-w; /* quick check no cancellation */
- } else {
- __uint32_t high;
- j = ix>>20;
- y[0] = r-w;
- GET_HIGH_WORD(high,y[0]);
- i = j-((high>>20)&0x7ff);
- if(i>16) { /* 2nd iteration needed, good to 118 */
- t = r;
- w = fn*pio2_2;
- r = t-w;
- w = fn*pio2_2t-((t-r)-w);
- y[0] = r-w;
- GET_HIGH_WORD(high,y[0]);
- i = j-((high>>20)&0x7ff);
- if(i>49) { /* 3rd iteration need, 151 bits acc */
- t = r; /* will cover all possible cases */
- w = fn*pio2_3;
- r = t-w;
- w = fn*pio2_3t-((t-r)-w);
- y[0] = r-w;
- }
- }
- }
- y[1] = (r-y[0])-w;
- if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
- else return n;
- }
- /*
- * all other (large) arguments
- */
- if(ix>=0x7ff00000) { /* x is inf or NaN */
- y[0]=y[1]=x-x; return 0;
- }
- /* set z = scalbn(|x|,ilogb(x)-23) */
- GET_LOW_WORD(low,x);
- SET_LOW_WORD(z,low);
- e0 = (int)((ix>>20)-1046); /* e0 = ilogb(z)-23; */
- SET_HIGH_WORD(z, ix - ((__int32_t)e0<<20));
- for(i=0;i<2;i++) {
- tx[i] = (double)((__int32_t)(z));
- z = (z-tx[i])*two24;
- }
- tx[2] = z;
- nx = 3;
- while(tx[nx-1]==zero) nx--; /* skip zero term */
- n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
- if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
- return n;
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ * return the remainder of x rem pi/2 in y[0]+y[1]
+ * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
+static const int32_t two_over_pi[] = {
+static int32_t two_over_pi[] = {
+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,
+static const int32_t npio2_hw[] = {
+static int32_t npio2_hw[] = {
+static const double
+static double
+ int32_t __ieee754_rem_pio2(double x, double *y)
+ int32_t __ieee754_rem_pio2(x,y)
+ int32_t i,j,n,ix,hx;
+ uint32_t low;
+ if(hx>0) {
+ n = (int32_t) (t*invpio2+half);
+ if(n<32&&ix!=npio2_hw[n-1]) {
+ uint32_t high;
+ y[0] = r-w;
+ w = fn*pio2_2;
+ w = fn*pio2_2t-((t-r)-w);
+ w = fn*pio2_3;
+ w = fn*pio2_3t-((t-r)-w);
+ /*
+ SET_HIGH_WORD(z, ix - ((int32_t)e0<<20));
+ tx[i] = (double)((int32_t)(z));
-
-/* @(#)e_remainder.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __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 fmod() return x-[x/p]chopped*p exactlp.
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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
-{
- __int32_t hx,hp;
- __uint32_t sx,lx,lp;
- double p_half;
-
- EXTRACT_WORDS(hx,lx,x);
- EXTRACT_WORDS(hp,lp,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 = fabs(x);
- p = 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;
- }
- }
- GET_HIGH_WORD(hx,x);
- SET_HIGH_WORD(x,hx^sx);
- return x;
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ * software is freely granted, provided that this notice
+ * Return :
+ * returns x REM p = x - [x/p]*p as if in infinite
+ * precise arithmetic, where [x/p] is the (infinite bit)
+ * Method :
+ int32_t hx,hp;
+ uint32_t sx,lx,lp;
-
-/* @(#)e_sqrt.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __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 * sqrt(y)
- * 2. Bit by bit computation
- * Let q = 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
+ * software is freely granted, provided that this notice
+ * Method:
+ * Bit by bit method using integer arithmetic. (Slow, but portable)
+ * Scale x to y in [1,4) with even powers of 2:
*
- * The advantage of (3) is that s and y can be computed by
- * i i
- * the following recurrence formula:
- * if (3) is false
+ * To compute q from q , one checks whether
+ * i+1 i
+ * that (2) is equivalent to
+ * The advantage of (3) is that s and y can be computed by
*
- * s = s , y = y ; (4)
- * i+1 i i+1 i
+ * One may easily use induction to prove (4) and (5).
+ * it does not necessary to do a full (53-bit) comparison
*
- * 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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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;
- __int32_t sign = (int)0x80000000;
- __uint32_t r,t1,s1,ix1,q1;
- __int32_t ix0,s0,q,m,t,i;
-
- EXTRACT_WORDS(ix0,ix1,x);
-
- /* take care of Inf and NaN */
- if((ix0&0x7ff00000)==0x7ff00000) {
- return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
- sqrt(-inf)=sNaN */
- }
- /* take care of zero */
- if(ix0<=0) {
- if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
- else if(ix0<0)
- return (x-x)/(x-x); /* 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 sqrt(x) bit by bit */
- ix0 += ix0 + ((ix1&sign)>>31);
- ix1 += ix1;
- q = q1 = s0 = s1 = 0; /* [q,q1] = 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<ix0)||((t==ix0)&&(t1<=ix1))) {
- s1 = t1+r;
- if(((t1&sign)==(__uint32_t)sign)&&(s1&sign)==0) s0 += 1;
+ int32_t sign = (int)0x80000000;
+ uint32_t r,t1,s1,ix1,q1;
+ int32_t ix0,s0,q,m,t,i;
+ if((ix0&0x7ff00000)==0x7ff00000) {
+ }
+ t = s0+r;
+ if(t<=ix0) {
+ s0 = t+r;
ix0 -= t;
- if (ix1 < t1) ix0 -= 1;
- ix1 -= t1;
- q1 += r;
- }
- ix0 += ix0 + ((ix1&sign)>>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==(__uint32_t)0xffffffff) { q1=0; q += 1;}
- else if (z>one) {
- if (q1==(__uint32_t)0xfffffffe) q+=1;
- q1+=2;
- } else
- q1 += (q1&1);
+ q += r;
}
- }
- ix0 = (q>>1)+0x3fe00000;
- ix1 = q1>>1;
- if ((q&1)==1) ix1 |= sign;
- ix0 += (m <<20);
- INSERT_WORDS(z,ix0,ix1);
- return z;
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
-
-/*
-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 sqrt(x)
- (IEEE double precision arithmetic) in software.
- Both supply 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. 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 sqrt(x) as
- follows.
-
- k := (x0>>1) + 0x1ff80000;
- y0 := k - T1[31&(k>>15)]. ... y ~ 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 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*sqrt(x)
- y := y - 0x00100006 ... almost 18 sig. bits to 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 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 sqrt(x):=y.
- } else {
- z := z - ulp; ... special rounding
- }
- }
- i := TRUE; ... 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 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. sqrt(x) by Reciproot Iteration
-
- (1) Initial approximation
-
- Let x0 and x1 be the leading and the trailing 32-bit words of
+ t1 = s1+r;
+ if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
+ if(((t1&sign)==(uint32_t)sign)&&(s1&sign)==0) s0 += 1;
+ if (q1==(uint32_t)0xffffffff) { q1=0; q += 1;}
+ if (q1==(uint32_t)0xfffffffe) q+=1;
+ q1+=2;
+
+(This is a copy of a drafted paper by Prof W. Kahan
+ Two algorithms are given here to implement sqrt(x)
+ to chop results of arithmetic operations instead of round them,
+ is executed exactly with no roundoff error, all part of the
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/sqrt(x) as follows.
-
- k := 0x5fe80000 - (x0>>1);
- y0:= k - T2[63&(k>>14)]. ... y ~ 1/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/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 sqrt(x)
- to about 1 ulp. To be exact, we will have
- -1ulp < 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/sqrt(x)
- y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
- ... special arrangement for better accuracy
- z := x*y ... 29 bits to sqrt(x), with z*y<1
- z := z + 0.5*z*(1-z*y) ... about 1 ulp to 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 < sqrt(x) - z < 1.0625 ulp
- instead of |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 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*z ... rounded up) z = z - ulp; else
- 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 = 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 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
+ Apply Heron's rule three times to y, we have y approximates
+ is slow. If division is very slow, then one should use the
+ By twiddling y's last bit it is possible to force y to be
- Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
- or even of logb(x) have the following relations:
+ Here k is a 32-bit integer and T2[] is an integer array
+ to about 1 ulp. To be exact, we will have
- -------------------------------------------------
- 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
- -------------------------------------------------
+ (a) the term z*y in the final iteration is always less than 1;
+ By twiddling y's last bit it is possible to force y to be
+ k := z1 >> 26; ... get z's 25-th and 26-th
+ If multiplication is cheaper then the foregoing red tape, the
+ Note that z*z can overwrite I; this value must be sensed if it is
+ z1: | f2 |
+ (4) Special cases (see (4) of Section A).
- (4) Special cases (see (4) of Section A).
-
- */
-
-/* @(#)k_cos.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * software is freely granted, provided that this notice
+ * Input y is the tail of x.
*
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
- * __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 cos(-x) = 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. 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
- * |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
- * cos(x) = 1 - x*x/2 + r
- * since cos(x+y) ~ cos(x) - sin(x)*y
- * ~ cos(x) - x*y,
- * a correction term is necessary in 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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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;
- __int32_t ix;
- GET_HIGH_WORD(ix,x);
- ix &= 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 {
- INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */
- }
- hz = 0.5*z-qx;
- a = one-qx;
- return a - (hz - (z*r-x*y));
- }
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ * 4 6 8 10 12 14
+ * since cos(x+y) ~ cos(x) - sin(x)*y
+static const double
+static double
+ int32_t ix;
+ if(ix < 0x3FD33333) /* if |x| < 0.3 */
-
-/* @(#)k_rem_pio2.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
- * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
- * double x[],y[]; int e0,nx,prec; int ipio2[];
- *
- * __kernel_rem_pio2 return the last three digits of N with
- * y = x - N*pi/2
- * so that |y| < pi/2.
- *
- * The method is to compute the integer (mod 8) and fraction parts of
- * (2/pi)*x without doing the full multiplication. In general we
- * skip the part of the product that are known to be a huge integer (
- * more accurately, = 0 mod 8 ). Thus the number of operations are
- * independent of the exponent of the input.
- *
- * (2/pi) is represented by an array of 24-bit integers in ipio2[].
- *
- * Input parameters:
- * x[] The input value (must be positive) is broken into nx
- * pieces of 24-bit integers in double precision format.
- * x[i] will be the i-th 24 bit of x. The scaled exponent
- * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
- * match x's up to 24 bits.
- *
- * Example of breaking a double positive z into x[0]+x[1]+x[2]:
- * e0 = ilogb(z)-23
- * z = scalbn(z,-e0)
- * for i = 0,1,2
- * x[i] = floor(z)
- * z = (z-x[i])*2**24
- *
- *
- * y[] ouput result in an array of double precision numbers.
- * The dimension of y[] is:
- * 24-bit precision 1
- * 53-bit precision 2
- * 64-bit precision 2
- * 113-bit precision 3
- * The actual value is the sum of them. Thus for 113-bit
- * 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 scalbn(), floor();
- *
- *
- * Here is the description of some local variables:
- *
- * jk jk+1 is the initial number of terms of ipio2[] needed
- * in the computation. The recommended value is 2,3,4,
- * 6 for single, double, extended,and quad.
- *
- * jz local integer variable indicating the number of
- * terms of ipio2[] used.
- *
- * jx nx - 1
- *
- * jv index for pointing to the suitable ipio2[] for the
- * computation. In general, we want
- * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
- * is an integer. Thus
- * e0-3-24*jv >= 0 or (e0-3)/24 >= jv
- * Hence jv = max(0,(e0-3)/24).
- *
- * jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
- *
- * q[] double array with integral value, representing the
- * 24-bits chunk of the product of x and 2/pi.
- *
- * q0 the corresponding exponent of q[0]. Note that the
- * exponent for q[i] would be q0-24*i.
- *
- * PIo2[] double precision array, obtained by cutting pi/2
- * into 24 bits chunks.
- *
- * f[] ipio2[] in floating point
- *
- * iq[] integer array by breaking up q[] in 24-bits chunk.
- *
- * fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
- *
- * ih integer. If >0 it indicates q[] is >= 0.5, hence
- * it also indicates the *sign* of the result.
- *
- */
-
-
-/*
- * Constants:
- * The hexadecimal values are the intended ones for the following
- * constants. The decimal values may be used, provided that the
- * compiler will convert from decimal to binary accurately enough
- * to produce the hexadecimal values shown.
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
-static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
-#else
-static int init_jk[] = {2,3,4,6};
-#endif
-
-#ifdef __STDC__
-static const double PIo2[] = {
-#else
-static double PIo2[] = {
-#endif
- 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
- 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
- 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
- 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
- 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
- 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
- 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
- 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
-};
-
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-zero = 0.0,
-one = 1.0,
-two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
-twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
-
-#ifdef __STDC__
- int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const __int32_t *ipio2)
-#else
- int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
- double x[], y[]; int e0,nx,prec; __int32_t ipio2[];
-#endif
-{
- __int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
- double z,fw,f[20],fq[20],q[20];
-
- /* initialize jk*/
- jk = init_jk[prec];
- jp = jk;
-
- /* determine jx,jv,q0, note that 3>q0 */
- jx = nx-1;
- jv = (e0-3)/24; if(jv<0) jv=0;
- q0 = e0-24*(jv+1);
-
- /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
- j = jv-jx; m = jx+jk;
- for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
-
- /* compute q[0],q[1],...q[jk] */
- for (i=0;i<=jk;i++) {
- for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
- }
-
- jz = jk;
-recompute:
- /* distill q[] into iq[] reversingly */
- for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
- fw = (double)((__int32_t)(twon24* z));
- iq[i] = (__int32_t)(z-two24*fw);
- z = q[j-1]+fw;
- }
-
- /* compute n */
- z = scalbn(z,(int)q0); /* actual value of z */
- z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
- n = (__int32_t) z;
- z -= (double)n;
- ih = 0;
- if(q0>0) { /* need iq[jz-1] to determine n */
- i = (iq[jz-1]>>(24-q0)); n += i;
- iq[jz-1] -= i<<(24-q0);
- ih = iq[jz-1]>>(23-q0);
- }
- else if(q0==0) ih = iq[jz-1]>>23;
- else if(z>=0.5) ih=2;
-
- if(ih>0) { /* q > 0.5 */
- n += 1; carry = 0;
- for(i=0;i<jz ;i++) { /* compute 1-q */
- j = iq[i];
- if(carry==0) {
- if(j!=0) {
- carry = 1; iq[i] = 0x1000000- j;
- }
- } else iq[i] = 0xffffff - j;
- }
- if(q0>0) { /* rare case: chance is 1 in 12 */
- switch(q0) {
- case 1:
- iq[jz-1] &= 0x7fffff; break;
- case 2:
- iq[jz-1] &= 0x3fffff; break;
- }
- }
- if(ih==2) {
- z = one - z;
- if(carry!=0) z -= scalbn(one,(int)q0);
- }
- }
-
- /* check if recomputation is needed */
- if(z==zero) {
- j = 0;
- for (i=jz-1;i>=jk;i--) j |= iq[i];
- if(j==0) { /* need recomputation */
- for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
-
- for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
- f[jx+i] = (double) ipio2[jv+i];
- for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
- q[i] = fw;
- }
- jz += k;
- goto recompute;
- }
- }
-
- /* chop off zero terms */
- if(z==0.0) {
- jz -= 1; q0 -= 24;
- while(iq[jz]==0) { jz--; q0-=24;}
- } else { /* break z into 24-bit if necessary */
- z = scalbn(z,-(int)q0);
- if(z>=two24) {
- fw = (double)((__int32_t)(twon24*z));
- iq[jz] = (__int32_t)(z-two24*fw);
- jz += 1; q0 += 24;
- iq[jz] = (__int32_t) fw;
- } else iq[jz] = (__int32_t) z ;
- }
-
- /* convert integer "bit" chunk to floating-point value */
- fw = scalbn(one,(int)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;
+ * software is freely granted, provided that this notice
+ *
+ * __kernel_rem_pio2 return the last three digits of N with
+ * The method is to compute the integer (mod 8) and fraction parts of
+ * x[] The input value (must be positive) is broken into nx
+ * 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
+ * integer array, contains the (24*i)-th to (24*i+23)-th
+ * bit of 2/pi after binary point. The corresponding
+ * jz local integer variable indicating the number of
+ * terms of ipio2[] used.
+ * into 24 bits chunks.
+ * f[] ipio2[] in floating point
+ * 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
+static int init_jk[] = {2,3,4,6};
+static const double
+static double
+ int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)
+ int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
+ double x[], y[]; int e0,nx,prec; int32_t ipio2[];
+ int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
+ fw = (double)((int32_t)(twon24* z));
+ iq[i] = (int32_t)(z-two24*fw);
+ n = (int32_t) z;
+ }
+ if(z>=two24) {
+ fw = (double)((int32_t)(twon24*z));
+ iq[jz] = (int32_t)(z-two24*fw);
+ iq[jz] = (int32_t) fw;
+ } else iq[jz] = (int32_t) z ;
+ y[0] = (ih==0)? fw: -fw;
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;
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ y[0] = (ih==0)? fw: -fw;
+ y[1] = (ih==0)? fw: -fw;
+ fw = fq[i-1]+fq[i];
+ fw = fq[i-1]+fq[i];
+ for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
-
-/* @(#)k_sin.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * software is freely granted, provided that this notice
+ * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
+ * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
*
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __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).
+ * | x |
*
- * Algorithm
- * 1. Since sin(-x) = -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. sin(x) is approximated by a polynomial of degree 13 on
- * [0,pi/4]
- * 3 13
- * sin(x) ~ x + S1*x + ... + S6*x
- * where
- *
- * |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. sin(x+y) = sin(x) + sin'(x')*y
- * ~ 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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#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;
- __int32_t ix;
- GET_HIGH_WORD(ix,x);
- ix &= 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);
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ * For better accuracy, let
+static const double
+static double
+ int32_t ix;
-
-/* @(#)k_tan.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * software is freely granted, provided that this notice
+ * Input k indicates whether tan (if k=1) or
+ * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
*
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* __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 tan (if k=1) or
- * -1/tan (if k= -1) is returned.
+ * | x |
*
- * Algorithm
- * 1. Since tan(-x) = -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. 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
- *
- * |tan(x) 2 4 26 | -59.2
- * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
- * | x |
- *
- * Note: tan(x+y) = tan(x) + tan'(x)*y
- * ~ tan(x) + (1+x*x)*y
- * Therefore, for better accuracy in computing 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) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
- * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
-pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
-pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
-T[] = {
- 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
- 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
- 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
- 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
- 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
- 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
- 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
- 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
- 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
- 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
- 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
- -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
- 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
-};
-
-#ifdef __STDC__
- double __kernel_tan(double x, double y, int iy)
-#else
- double __kernel_tan(x, y, iy)
- double x,y; int iy;
-#endif
-{
- double z,r,v,w,s;
- __int32_t ix,hx;
- GET_HIGH_WORD(hx,x);
- ix = hx&0x7fffffff; /* high word of |x| */
- if(ix<0x3e300000) /* x < 2**-28 */
- {if((int)x==0) { /* generate inexact */
- __uint32_t low;
- GET_LOW_WORD(low,x);
- if(((ix|low)|(iy+1))==0) return one/fabs(x);
- else return (iy==1)? x: -one/x;
- }
- }
- 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;
- SET_LOW_WORD(z,0);
- v = r-(z - x); /* z+v = r+x */
- t = a = -1.0/w; /* a = -1.0/w */
- SET_LOW_WORD(t,0);
- s = 1.0+t*z;
- return t+a*(s+t*v);
- }
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ * Therefore, for better accuracy in computing tan(x+y), let
+static const double
+static double
+ int32_t ix,hx;
+ uint32_t low;
+ else { /* if allow error up to 2 ulp,
-/****************************************************************
- *
- * The author of this software is David M. Gay.
- *
- * Copyright (c) 1991 by AT&T.
- *
- * Permission to use, copy, modify, and distribute this software for any
- * purpose without fee is hereby granted, provided that this entire notice
- * is included in all copies of any software which is or includes a copy
- * or modification of this software and in all copies of the supporting
- * documentation for such software.
- *
- * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
- * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
- * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
- * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
- *
- ***************************************************************/
-
-/* Please send bug reports to
- David M. Gay
- AT&T Bell Laboratories, Room 2C-463
- 600 Mountain Avenue
- Murray Hill, NJ 07974-2070
- U.S.A.
- dmg@research.att.com or research!dmg
- */
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-#include <config.h>
-#include "ieeefp.h"
-
-#include <math.h>
-// #include <float.h>
-// #include <errno.h>
-
-/* These typedefs are true for the targets running Java. */
-
-#ifndef HAVE_INT32_DEFINED
-typedef int __int32_t;
-typedef unsigned int __uint32_t;
-#endif
-
-#ifdef __IEEE_LITTLE_ENDIAN
-#define IEEE_8087
-#endif
-
-#ifdef __IEEE_BIG_ENDIAN
-#define IEEE_MC68k
-#endif
-
-#ifdef __Z8000__
-#define Just_16
-#endif
-
-#ifdef DEBUG
-#include "stdio.h"
-#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
-#endif
-
-
-#ifdef Unsigned_Shifts
-#define Sign_Extend(a,b) if (b < 0) a |= (__uint32_t)0xffff0000;
-#else
-#define Sign_Extend(a,b) /*no-op*/
-#endif
-
-#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
-Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
-#endif
-
-/* If we are going to examine or modify specific bits in a double using
- the word0 and/or word1 macros, then we must wrap the double inside
- a union. This is necessary to avoid undefined behavior according to
- the ANSI C spec. */
-union double_union
-{
- double d;
- // FIXME: This should be some well-defined 32 bit type.
- __uint32_t i[2];
-};
-
-#ifdef IEEE_8087
-#define word0(x) (x.i[1])
-#define word1(x) (x.i[0])
-#else
-#define word0(x) (x.i[0])
-#define word1(x) (x.i[1])
-#endif
-
-/* The following definition of Storeinc is appropriate for MIPS processors.
- * An alternative that might be better on some machines is
- * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
- */
-#if defined(IEEE_8087) + defined(VAX)
-#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
-((unsigned short *)a)[0] = (unsigned short)c, a++)
-#else
-#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
-((unsigned short *)a)[1] = (unsigned short)c, a++)
-#endif
-
-/* #define P DBL_MANT_DIG */
-/* Ten_pmax = floor(P*log(2)/log(5)) */
-/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
-/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
-/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
-
-#if defined(IEEE_8087) + defined(IEEE_MC68k)
-#if defined (_DOUBLE_IS_32BITS)
-#define Exp_shift 23
-#define Exp_shift1 23
-#define Exp_msk1 ((__uint32_t)0x00800000L)
-#define Exp_msk11 ((__uint32_t)0x00800000L)
-#define Exp_mask ((__uint32_t)0x7f800000L)
-#define P 24
-#define Bias 127
-#if 0
-#define IEEE_Arith /* it is, but the code doesn't handle IEEE singles yet */
-#endif
-#define Emin (-126)
-#define Exp_1 ((__uint32_t)0x3f800000L)
-#define Exp_11 ((__uint32_t)0x3f800000L)
-#define Ebits 8
-#define Frac_mask ((__uint32_t)0x007fffffL)
-#define Frac_mask1 ((__uint32_t)0x007fffffL)
-#define Ten_pmax 10
-#define Sign_bit ((__uint32_t)0x80000000L)
-#define Ten_pmax 10
-#define Bletch 2
-#define Bndry_mask ((__uint32_t)0x007fffffL)
-#define Bndry_mask1 ((__uint32_t)0x007fffffL)
-#define LSB 1
-#define Sign_bit ((__uint32_t)0x80000000L)
-#define Log2P 1
-#define Tiny0 0
-#define Tiny1 1
-#define Quick_max 5
-#define Int_max 6
-#define Infinite(x) (word0(x) == ((__uint32_t)0x7f800000L))
-#undef word0
-#undef word1
-
-#define word0(x) (x.i[0])
-#define word1(x) 0
-#else
-
-#define Exp_shift 20
-#define Exp_shift1 20
-#define Exp_msk1 ((__uint32_t)0x100000L)
-#define Exp_msk11 ((__uint32_t)0x100000L)
-#define Exp_mask ((__uint32_t)0x7ff00000L)
-#define P 53
-#define Bias 1023
-#define IEEE_Arith
-#define Emin (-1022)
-#define Exp_1 ((__uint32_t)0x3ff00000L)
-#define Exp_11 ((__uint32_t)0x3ff00000L)
-#define Ebits 11
-#define Frac_mask ((__uint32_t)0xfffffL)
-#define Frac_mask1 ((__uint32_t)0xfffffL)
-#define Ten_pmax 22
-#define Bletch 0x10
-#define Bndry_mask ((__uint32_t)0xfffffL)
-#define Bndry_mask1 ((__uint32_t)0xfffffL)
-#define LSB 1
-#define Sign_bit ((__uint32_t)0x80000000L)
-#define Log2P 1
-#define Tiny0 0
-#define Tiny1 1
-#define Quick_max 14
-#define Int_max 14
-#define Infinite(x) (word0(x) == ((__uint32_t)0x7ff00000L)) /* sufficient test for here */
-#endif
-
-#else
-#undef Sudden_Underflow
-#define Sudden_Underflow
-#ifdef IBM
-#define Exp_shift 24
-#define Exp_shift1 24
-#define Exp_msk1 ((__uint32_t)0x1000000L)
-#define Exp_msk11 ((__uint32_t)0x1000000L)
-#define Exp_mask ((__uint32_t)0x7f000000L)
-#define P 14
-#define Bias 65
-#define Exp_1 ((__uint32_t)0x41000000L)
-#define Exp_11 ((__uint32_t)0x41000000L)
-#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
-#define Frac_mask ((__uint32_t)0xffffffL)
-#define Frac_mask1 ((__uint32_t)0xffffffL)
-#define Bletch 4
-#define Ten_pmax 22
-#define Bndry_mask ((__uint32_t)0xefffffL)
-#define Bndry_mask1 ((__uint32_t)0xffffffL)
-#define LSB 1
-#define Sign_bit ((__uint32_t)0x80000000L)
-#define Log2P 4
-#define Tiny0 ((__uint32_t)0x100000L)
-#define Tiny1 0
-#define Quick_max 14
-#define Int_max 15
-#else /* VAX */
-#define Exp_shift 23
-#define Exp_shift1 7
-#define Exp_msk1 0x80
-#define Exp_msk11 ((__uint32_t)0x800000L)
-#define Exp_mask ((__uint32_t)0x7f80L)
-#define P 56
-#define Bias 129
-#define Exp_1 ((__uint32_t)0x40800000L)
-#define Exp_11 ((__uint32_t)0x4080L)
-#define Ebits 8
-#define Frac_mask ((__uint32_t)0x7fffffL)
-#define Frac_mask1 ((__uint32_t)0xffff007fL)
-#define Ten_pmax 24
-#define Bletch 2
-#define Bndry_mask ((__uint32_t)0xffff007fL)
-#define Bndry_mask1 ((__uint32_t)0xffff007fL)
-#define LSB ((__uint32_t)0x10000L)
-#define Sign_bit ((__uint32_t)0x8000L)
-#define Log2P 1
-#define Tiny0 0x80
-#define Tiny1 0
-#define Quick_max 15
-#define Int_max 15
-#endif
-#endif
-
-#ifndef IEEE_Arith
-#define ROUND_BIASED
-#endif
-
-#ifdef RND_PRODQUOT
-#define rounded_product(a,b) a = rnd_prod(a, b)
-#define rounded_quotient(a,b) a = rnd_quot(a, b)
-#ifdef KR_headers
-extern double rnd_prod(), rnd_quot();
-#else
-extern double rnd_prod(double, double), rnd_quot(double, double);
-#endif
-#else
-#define rounded_product(a,b) a *= b
-#define rounded_quotient(a,b) a /= b
-#endif
-
-#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
-#define Big1 ((__uint32_t)0xffffffffL)
-
-#ifndef Just_16
-/* When Pack_32 is not defined, we store 16 bits per 32-bit long.
- * This makes some inner loops simpler and sometimes saves work
- * during multiplications, but it often seems to make things slightly
- * slower. Hence the default is now to store 32 bits per long.
- */
-
-#ifndef Pack_32
-#define Pack_32
-#endif
-#endif
-
-
-#define MAX_BIGNUMS 16
-#define MAX_BIGNUM_WDS 32
-
-struct _Jv_Bigint
-{
- struct _Jv_Bigint *_next;
- int _k, _maxwds, _sign, _wds;
- unsigned long _x[MAX_BIGNUM_WDS];
-};
-
-
-#define _PTR void *
-#define _AND ,
-#define _NOARGS void
-#define _CONST const
-#define _VOLATILE volatile
-#define _SIGNED signed
-#define _DOTS , ...
-#define _VOID void
-#define _EXFUN(name, proto) name proto
-#define _DEFUN(name, arglist, args) name(args)
-#define _DEFUN_VOID(name) name(_NOARGS)
-#define _CAST_VOID (void)
-
-
-struct _Jv_reent
-{
- /* local copy of errno */
- int _errno;
-
- /* used by mprec routines */
- struct _Jv_Bigint *_result;
- int _result_k;
- struct _Jv_Bigint *_p5s;
-
- struct _Jv_Bigint _freelist[MAX_BIGNUMS];
- int _allocation_map;
-
- int num;
-};
-
-
-typedef struct _Jv_Bigint _Jv_Bigint;
-
-#define Balloc _Jv_Balloc
-#define Bfree _Jv_Bfree
-#define multadd _Jv_multadd
-#define s2b _Jv_s2b
-#define lo0bits _Jv_lo0bits
-#define hi0bits _Jv_hi0bits
-#define i2b _Jv_i2b
-#define mult _Jv_mult
-#define pow5mult _Jv_pow5mult
-#define lshift _Jv_lshift
-#define cmp _Jv__mcmp
-#define diff _Jv__mdiff
-#define ulp _Jv_ulp
-#define b2d _Jv_b2d
-#define d2b _Jv_d2b
-#define ratio _Jv_ratio
-
-#define tens _Jv__mprec_tens
-#define bigtens _Jv__mprec_bigtens
-#define tinytens _Jv__mprec_tinytens
-
-#define _dtoa _Jv_dtoa
-#define _dtoa_r _Jv_dtoa_r
-#define _strtod_r _Jv_strtod_r
-
-extern double _EXFUN(_strtod_r, (struct _Jv_reent *ptr, const char *s00, char **se));
-extern char* _EXFUN(_dtoa_r, (struct _Jv_reent *ptr, double d,
- int mode, int ndigits, int *decpt, int *sign,
- char **rve, int float_type));
-void _EXFUN(_dtoa, (double d, int mode, int ndigits, int *decpt, int *sign,
- char **rve, char *buf, int float_type));
-
-double _EXFUN(ulp,(double x));
-double _EXFUN(b2d,(_Jv_Bigint *a , int *e));
-_Jv_Bigint * _EXFUN(Balloc,(struct _Jv_reent *p, int k));
-void _EXFUN(Bfree,(struct _Jv_reent *p, _Jv_Bigint *v));
-_Jv_Bigint * _EXFUN(multadd,(struct _Jv_reent *p, _Jv_Bigint *, int, int));
-_Jv_Bigint * _EXFUN(s2b,(struct _Jv_reent *, const char*, int, int, unsigned long));
-_Jv_Bigint * _EXFUN(i2b,(struct _Jv_reent *,int));
-_Jv_Bigint * _EXFUN(mult, (struct _Jv_reent *, _Jv_Bigint *, _Jv_Bigint *));
-_Jv_Bigint * _EXFUN(pow5mult, (struct _Jv_reent *, _Jv_Bigint *, int k));
-int _EXFUN(hi0bits,(unsigned long));
-int _EXFUN(lo0bits,(unsigned long *));
-_Jv_Bigint * _EXFUN(d2b,(struct _Jv_reent *p, double d, int *e, int *bits));
-_Jv_Bigint * _EXFUN(lshift,(struct _Jv_reent *p, _Jv_Bigint *b, int k));
-_Jv_Bigint * _EXFUN(diff,(struct _Jv_reent *p, _Jv_Bigint *a, _Jv_Bigint *b));
-int _EXFUN(cmp,(_Jv_Bigint *a, _Jv_Bigint *b));
-
-double _EXFUN(ratio,(_Jv_Bigint *a, _Jv_Bigint *b));
-#define Bcopy(x,y) memcpy((char *)&x->_sign, (char *)&y->_sign, y->_wds*sizeof(long) + 2*sizeof(int))
-
-#if defined(_DOUBLE_IS_32BITS) && defined(__v800)
-#define n_bigtens 2
-#else
-#define n_bigtens 5
-#endif
-
-extern _CONST double tinytens[];
-extern _CONST double bigtens[];
-extern _CONST double tens[];
-
-#ifdef __cplusplus
-}
-#endif
-
+#if defined HAVE_STDINT_H
+#include <stdint.h>
+#elif defined HAVE_INTTYPES_H
+#include <inttypes.h>
+#endif
+
+#if defined HAVE_SYS_TYPES_H
+#include <sys/types.h>
+#endif
+#if defined HAVE_SYS_CONFIG_H
+#include <sys/config.h>
+
+/* ISO C9X int type declarations */
+
+#if !defined HAVE_INT32_DEFINED && defined HAVE_BSD_INT32_DEFINED
+typedef u_int32_t uint32_t;
+#endif
+
+#if !defined HAVE_BSD_INT32_DEFINED && !defined HAVE_INT32_DEFINED
+// FIXME -- this could have problems with systems that don't define SI to be 4
+typedef int int32_t __attribute__((mode(SI)));
+typedef unsigned int uint32_t __attribute__((mode(SI)));
+#endif
+
+ /* These typedefs are true for the targets running Java. */
+
+#define Sign_Extend(a,b) if (b < 0) a |= (uint32_t)0xffff0000;
+ uint32_t i[2];
+#if defined (_DOUBLE_IS_32BITS)
+#define Exp_msk1 ((uint32_t)0x00800000L)
+#define Exp_msk11 ((uint32_t)0x00800000L)
+#define Exp_mask ((uint32_t)0x7f800000L)
+#define Exp_1 ((uint32_t)0x3f800000L)
+#define Exp_11 ((uint32_t)0x3f800000L)
+#define Frac_mask ((uint32_t)0x007fffffL)
+#define Frac_mask1 ((uint32_t)0x007fffffL)
+#define Sign_bit ((uint32_t)0x80000000L)
+#define Bndry_mask ((uint32_t)0x007fffffL)
+#define Bndry_mask1 ((uint32_t)0x007fffffL)
+#define Sign_bit ((uint32_t)0x80000000L)
+#define Infinite(x) (word0(x) == ((uint32_t)0x7f800000L))
+#define Exp_msk1 ((uint32_t)0x100000L)
+#define Exp_msk11 ((uint32_t)0x100000L)
+#define Exp_mask ((uint32_t)0x7ff00000L)
+#define Exp_1 ((uint32_t)0x3ff00000L)
+#define Exp_11 ((uint32_t)0x3ff00000L)
+#define Frac_mask ((uint32_t)0xfffffL)
+#define Frac_mask1 ((uint32_t)0xfffffL)
+#define Bndry_mask ((uint32_t)0xfffffL)
+#define Bndry_mask1 ((uint32_t)0xfffffL)
+#define Sign_bit ((uint32_t)0x80000000L)
+#define Infinite(x) (word0(x) == ((uint32_t)0x7ff00000L)) /* sufficient test for here */
+#define Exp_msk1 ((uint32_t)0x1000000L)
+#define Exp_msk11 ((uint32_t)0x1000000L)
+#define Exp_mask ((uint32_t)0x7f000000L)
+#define Exp_1 ((uint32_t)0x41000000L)
+#define Exp_11 ((uint32_t)0x41000000L)
+#define Frac_mask ((uint32_t)0xffffffL)
+#define Frac_mask1 ((uint32_t)0xffffffL)
+#define Bndry_mask ((uint32_t)0xefffffL)
+#define Bndry_mask1 ((uint32_t)0xffffffL)
+#define Sign_bit ((uint32_t)0x80000000L)
+#define Tiny0 ((uint32_t)0x100000L)
+#define Exp_msk11 ((uint32_t)0x800000L)
+#define Exp_mask ((uint32_t)0x7f80L)
+#define Exp_1 ((uint32_t)0x40800000L)
+#define Exp_11 ((uint32_t)0x4080L)
+#define Frac_mask ((uint32_t)0x7fffffL)
+#define Frac_mask1 ((uint32_t)0xffff007fL)
+#define Bndry_mask ((uint32_t)0xffff007fL)
+#define Bndry_mask1 ((uint32_t)0xffff007fL)
+#define LSB ((uint32_t)0x10000L)
+#define Sign_bit ((uint32_t)0x8000L)
+#define Big1 ((uint32_t)0xffffffffL)
+struct _Jv_Bigint
+extern char* _EXFUN(_dtoa_r, (struct _Jv_reent *ptr, double d,
+ int mode, int ndigits, int *decpt, int *sign,
+void _EXFUN(_dtoa, (double d, int mode, int ndigits, int *decpt, int *sign,
-
-/* @(#)s_atan.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- *
- */
-
-/*
-FUNCTION
- <<atan>>, <<atanf>>---arc tangent
-
-INDEX
- atan
-INDEX
- atanf
-
-ANSI_SYNOPSIS
- #include <math.h>
- double atan(double <[x]>);
- float atanf(float <[x]>);
-
-TRAD_SYNOPSIS
- #include <math.h>
- double atan(<[x]>);
- double <[x]>;
-
- float atanf(<[x]>);
- float <[x]>;
-
-DESCRIPTION
-
-<<atan>> computes the inverse tangent (arc tangent) of the input value.
-
-<<atanf>> is identical to <<atan>>, save that it operates on <<floats>>.
-
-RETURNS
-@ifinfo
-<<atan>> returns a value in radians, in the range of -pi/2 to pi/2.
-@end ifinfo
-@tex
-<<atan>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$.
-@end tex
-
-PORTABILITY
-<<atan>> is ANSI C. <<atanf>> is an extension.
-
-*/
-
-/* atan(x)
- * Method
- * 1. Reduce x to positive by atan(x) = -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] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
- * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
- * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
- * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
- * [39/16,INF] atan(x) = atan(INF) + 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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
-static const double atanhi[] = {
-#else
-static double atanhi[] = {
-#endif
- 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
- 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
- 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
- 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
-};
-
-#ifdef __STDC__
-static const double atanlo[] = {
-#else
-static double atanlo[] = {
-#endif
- 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
- 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
- 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
- 6.12323399573676603587e-17, /* 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 atan(double x)
-#else
- double atan(x)
- double x;
-#endif
-{
- double w,s1,s2,z;
- __int32_t ix,hx,id;
-
- GET_HIGH_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix>=0x44100000) { /* if |x| >= 2^66 */
- __uint32_t low;
- GET_LOW_WORD(low,x);
- if(ix>0x7ff00000||
- (ix==0x7ff00000&&(low!=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 = 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;
- }
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * software is freely granted, provided that this notice
+ * 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
+ static const double
+ static double
+ int32_t ix,hx,id;
+ uint32_t low;
+ id = 0; x = (2.0*x-one)/(2.0+x);
+ id = 1; x = (x-one)/(x+one);
-
-/* @(#)s_ceil.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
- * ceil(x)
- * Return x rounded toward -inf to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to ceil(x).
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
-static const double huge = 1.0e300;
-#else
-static double huge = 1.0e300;
-#endif
-
-#ifdef __STDC__
- double ceil(double x)
-#else
- double ceil(x)
- double x;
-#endif
-{
- __int32_t i0,i1,j0;
- __uint32_t i,j;
- EXTRACT_WORDS(i0,i1,x);
- j0 = ((i0>>20)&0x7ff)-0x3ff;
- if(j0<20) {
- if(j0<0) { /* raise inexact if x != 0 */
- if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
- if(i0<0) {i0=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 = ((__uint32_t)(0xffffffff))>>(j0-20);
- if((i1&i)==0) return x; /* x is integral */
- if(huge+x>0.0) { /* raise inexact flag */
- if(i0>0) {
- if(j0==20) i0+=1;
- else {
- j = i1 + (1<<(52-j0));
- if(j<(__uint32_t)i1) i0+=1; /* got a carry */
- i1 = j;
- }
- }
- i1 &= (~i);
- }
- }
- INSERT_WORDS(x,i0,i1);
- return x;
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * software is freely granted, provided that this notice
+ int32_t i0,i1,j0;
+ uint32_t i,j;
+ if(i0<0) {i0=0x80000000;i1=0;}
+ i = ((uint32_t)(0xffffffff))>>(j0-20);
+ if(j0==20) i0+=1;
+ if(j<(uint32_t)i1) i0+=1; /* got a carry */
-
-/* @(#)s_copysign.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
-FUNCTION
-<<copysign>>, <<copysignf>>---sign of <[y]>, magnitude of <[x]>
-
-INDEX
- copysign
-INDEX
- copysignf
-
-ANSI_SYNOPSIS
- #include <math.h>
- double copysign (double <[x]>, double <[y]>);
- float copysignf (float <[x]>, float <[y]>);
-
-TRAD_SYNOPSIS
- #include <math.h>
- double copysign (<[x]>, <[y]>)
- double <[x]>;
- double <[y]>;
-
- float copysignf (<[x]>, <[y]>)
- float <[x]>;
- float <[y]>;
-
-DESCRIPTION
-<<copysign>> constructs a number with the magnitude (absolute value)
-of its first argument, <[x]>, and the sign of its second argument,
-<[y]>.
-
-<<copysignf>> does the same thing; the two functions differ only in
-the type of their arguments and result.
-
-RETURNS
-<<copysign>> returns a <<double>> with the magnitude of
-<[x]> and the sign of <[y]>.
-<<copysignf>> returns a <<float>> with the magnitude of
-<[x]> and the sign of <[y]>.
-
-PORTABILITY
-<<copysign>> is not required by either ANSI C or the System V Interface
-Definition (Issue 2).
-
-*/
-
-/*
- * copysign(double x, double y)
- * copysign(x,y) returns a value with the magnitude of x and
- * with the sign bit of y.
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
- double copysign(double x, double y)
-#else
- double copysign(x,y)
- double x,y;
-#endif
-{
- __uint32_t hx,hy;
- GET_HIGH_WORD(hx,x);
- GET_HIGH_WORD(hy,y);
- SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000));
- return x;
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * software is freely granted, provided that this notice
+ uint32_t hx,hy;
-
-/* @(#)s_cos.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/* cos(x)
- * Return cosine function of x.
- *
- * kernel function:
- * __kernel_sin ... sine function on [-pi/4,pi/4]
- * __kernel_cos ... cosine 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 sin(x) cos(x) 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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
- double cos(double x)
-#else
- double cos(x)
- double x;
-#endif
-{
- double y[2],z=0.0;
- __int32_t n,ix;
-
- /* High word of x. */
- GET_HIGH_WORD(ix,x);
-
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
-
- /* cos(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_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);
- }
- }
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * software is freely granted, provided that this notice
+ * 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
+ * TRIG(x) returns trig(x) nearly rounded
+ int32_t n,ix;
-
-/* @(#)s_fabs.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
-FUNCTION
- <<fabs>>, <<fabsf>>---absolute value (magnitude)
-INDEX
- fabs
-INDEX
- fabsf
-
-ANSI_SYNOPSIS
- #include <math.h>
- double fabs(double <[x]>);
- float fabsf(float <[x]>);
-
-TRAD_SYNOPSIS
- #include <math.h>
- double fabs(<[x]>)
- double <[x]>;
-
- float fabsf(<[x]>)
- float <[x]>;
-
-DESCRIPTION
-<<fabs>> and <<fabsf>> calculate
-@tex
-$|x|$,
-@end tex
-the absolute value (magnitude) of the argument <[x]>, by direct
-manipulation of the bit representation of <[x]>.
-
-RETURNS
-The calculated value is returned. No errors are detected.
-
-PORTABILITY
-<<fabs>> is ANSI.
-<<fabsf>> is an extension.
-
-*/
-
-/*
- * fabs(x) returns the absolute value of x.
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
- double fabs(double x)
-#else
- double fabs(x)
- double x;
-#endif
-{
- __uint32_t high;
- GET_HIGH_WORD(high,x);
- SET_HIGH_WORD(x,high&0x7fffffff);
- return x;
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * software is freely granted, provided that this notice
+ double fabs(<[x]>)
+<<fabs>> and <<fabsf>> calculate
+$|x|$,
+ uint32_t high;
-
-/* @(#)s_floor.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
-FUNCTION
-<<floor>>, <<floorf>>, <<ceil>>, <<ceilf>>---floor and ceiling
-INDEX
- floor
-INDEX
- floorf
-INDEX
- ceil
-INDEX
- ceilf
-
-ANSI_SYNOPSIS
- #include <math.h>
- double floor(double <[x]>);
- float floorf(float <[x]>);
- double ceil(double <[x]>);
- float ceilf(float <[x]>);
-
-TRAD_SYNOPSIS
- #include <math.h>
- double floor(<[x]>)
- double <[x]>;
- float floorf(<[x]>)
- float <[x]>;
- double ceil(<[x]>)
- double <[x]>;
- float ceilf(<[x]>)
- float <[x]>;
-
-DESCRIPTION
-<<floor>> and <<floorf>> find
-@tex
-$\lfloor x \rfloor$,
-@end tex
-the nearest integer less than or equal to <[x]>.
-<<ceil>> and <<ceilf>> find
-@tex
-$\lceil x\rceil$,
-@end tex
-the nearest integer greater than or equal to <[x]>.
-
-RETURNS
-<<floor>> and <<ceil>> return the integer result as a double.
-<<floorf>> and <<ceilf>> return the integer result as a float.
-
-PORTABILITY
-<<floor>> and <<ceil>> are ANSI.
-<<floorf>> and <<ceilf>> are extensions.
-
-
-*/
-
-/*
- * floor(x)
- * Return x rounded toward -inf to integral value
- * Method:
- * Bit twiddling.
- * Exception:
- * Inexact flag raised if x not equal to floor(x).
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
-static const double huge = 1.0e300;
-#else
-static double huge = 1.0e300;
-#endif
-
-#ifdef __STDC__
- double floor(double x)
-#else
- double floor(x)
- double x;
-#endif
-{
- __int32_t i0,i1,j0;
- __uint32_t i,j;
- EXTRACT_WORDS(i0,i1,x);
- j0 = ((i0>>20)&0x7ff)-0x3ff;
- if(j0<20) {
- if(j0<0) { /* raise inexact if x != 0 */
- if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
- if(i0>=0) {i0=i1=0;}
- else if(((i0&0x7fffffff)|i1)!=0)
- { i0=0xbff00000;i1=0;}
- }
- } else {
- i = (0x000fffff)>>j0;
- if(((i0&i)|i1)==0) return x; /* x is integral */
- if(huge+x>0.0) { /* raise inexact flag */
- if(i0<0) i0 += (0x00100000)>>j0;
- i0 &= (~i); i1=0;
- }
- }
- } else if (j0>51) {
- if(j0==0x400) return x+x; /* inf or NaN */
- else return x; /* x is integral */
- } else {
- i = ((__uint32_t)(0xffffffff))>>(j0-20);
- if((i1&i)==0) return x; /* x is integral */
- if(huge+x>0.0) { /* raise inexact flag */
- if(i0<0) {
- if(j0==20) i0+=1;
- else {
- j = i1+(1<<(52-j0));
- if(j<(__uint32_t)i1) i0 +=1 ; /* got a carry */
- i1=j;
- }
- }
- i1 &= (~i);
- }
- }
- INSERT_WORDS(x,i0,i1);
- return x;
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * software is freely granted, provided that this notice
+ float floorf(<[x]>)
+ double ceil(<[x]>)
+ float ceilf(<[x]>)
+<<floor>> and <<floorf>> find
+$\lfloor x \rfloor$,
+<<ceil>> and <<ceilf>> find
+ int32_t i0,i1,j0;
+ uint32_t i,j;
+ if(i0>=0) {i0=i1=0;}
+ i = ((uint32_t)(0xffffffff))>>(j0-20);
+ if(j0==20) i0+=1;
+ if(j<(uint32_t)i1) i0 +=1 ; /* got a carry */
-
-/* @(#)s_rint.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
- * 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 rint(x).
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-TWO52[2]={
- 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
- -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
-};
-
-#ifdef __STDC__
- double rint(double x)
-#else
- double rint(x)
- double x;
-#endif
-{
- __int32_t i0,j0,sx;
- __uint32_t i,i1;
- double t;
- volatile double w;
- EXTRACT_WORDS(i0,i1,x);
- sx = (i0>>31)&1;
- 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;
- SET_HIGH_WORD(x,i0);
- w = TWO52[sx]+x;
- t = w-TWO52[sx];
- GET_HIGH_WORD(i0,t);
- SET_HIGH_WORD(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 = ((__uint32_t)(0xffffffff))>>(j0-20);
- if((i1&i)==0) return x; /* x is integral */
- i>>=1;
- if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20));
- }
- INSERT_WORDS(x,i0,i1);
- w = TWO52[sx]+x;
- return w-TWO52[sx];
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * software is freely granted, provided that this notice
+static double
+ int32_t i0,j0,sx;
+ uint32_t i,i1;
+ if(j0<0) {
+ i = ((uint32_t)(0xffffffff))>>(j0-20);
-
-/* @(#)s_scalbn.c 5.1 93/09/24 */
+ * software is freely granted, provided that this notice
/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
-FUNCTION
-<<scalbn>>, <<scalbnf>>---scale by integer
-INDEX
- scalbn
-INDEX
- scalbnf
-
-ANSI_SYNOPSIS
- #include <math.h>
- double scalbn(double <[x]>, int <[y]>);
- float scalbnf(float <[x]>, int <[y]>);
-
-TRAD_SYNOPSIS
- #include <math.h>
- double scalbn(<[x]>,<[y]>)
- double <[x]>;
- int <[y]>;
- float scalbnf(<[x]>,<[y]>)
- float <[x]>;
- int <[y]>;
-
-DESCRIPTION
-<<scalbn>> and <<scalbnf>> scale <[x]> by <[n]>, returning <[x]> times
-2 to the power <[n]>. The result is computed by manipulating the
-exponent, rather than by actually performing an exponentiation or
-multiplication.
-
-RETURNS
-<[x]> times 2 to the power <[n]>.
-
-PORTABILITY
-Neither <<scalbn>> nor <<scalbnf>> is required by ANSI C or by the System V
-Interface Definition (Issue 2).
-
-*/
-
-/*
- * scalbn (double x, int n)
- * scalbn(x,n) returns x* 2**n computed by exponent
- * manipulation rather than by actually performing an
- * exponentiation or a multiplication.
- */
-
-#include "fdlibm.h"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
-static const double
-#else
-static double
-#endif
-two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
-twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
-huge = 1.0e+300,
-tiny = 1.0e-300;
-
-#ifdef __STDC__
- double scalbn (double x, int n)
-#else
- double scalbn (x,n)
- double x; int n;
-#endif
-{
- __int32_t k,hx,lx;
- EXTRACT_WORDS(hx,lx,x);
- k = (hx&0x7ff00000)>>20; /* extract exponent */
- if (k==0) { /* 0 or subnormal x */
- if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
- x *= two54;
- GET_HIGH_WORD(hx,x);
- k = ((hx&0x7ff00000)>>20) - 54;
- if (n< -50000) return tiny*x; /*underflow*/
- }
- if (k==0x7ff) return x+x; /* NaN or Inf */
- k = k+n;
- if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
- if (k > 0) /* normal result */
- {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;}
- if (k <= -54) {
- if (n > 50000) /* in case integer overflow in n+k */
- return huge*copysign(huge,x); /*overflow*/
- else return tiny*copysign(tiny,x); /*underflow*/
- }
- k += 54; /* subnormal result */
- SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20));
- return x*twom54;
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * scalbn(x,n) returns x* 2**n computed by exponent
+ * manipulation rather than by actually performing an
+ int32_t k,hx,lx;
+ x *= two54;
+ k = ((hx&0x7ff00000)>>20) - 54;
+ k = k+n;
-
-/* @(#)s_sin.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-/*
-FUNCTION
- <<sin>>, <<sinf>>, <<cos>>, <<cosf>>---sine or cosine
-INDEX
-sin
-INDEX
-sinf
-INDEX
-cos
-INDEX
-cosf
-ANSI_SYNOPSIS
- #include <math.h>
- double sin(double <[x]>);
- float sinf(float <[x]>);
- double cos(double <[x]>);
- float cosf(float <[x]>);
-
-TRAD_SYNOPSIS
- #include <math.h>
- double sin(<[x]>)
- double <[x]>;
- float sinf(<[x]>)
- float <[x]>;
-
- double cos(<[x]>)
- double <[x]>;
- float cosf(<[x]>)
- float <[x]>;
-
-DESCRIPTION
- <<sin>> and <<cos>> compute (respectively) the sine and cosine
- of the argument <[x]>. Angles are specified in radians.
-
- <<sinf>> and <<cosf>> are identical, save that they take and
- return <<float>> values.
-
-
-RETURNS
- The sine or cosine of <[x]> is returned.
-
-PORTABILITY
- <<sin>> and <<cos>> are ANSI C.
- <<sinf>> and <<cosf>> are extensions.
-
-QUICKREF
- sin ansi pure
- sinf - pure
-*/
-
-/* 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 sin(x) cos(x) 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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
- double sin(double x)
-#else
- double sin(x)
- double x;
-#endif
-{
- double y[2],z=0.0;
- __int32_t n,ix;
-
- /* High word of x. */
- GET_HIGH_WORD(ix,x);
-
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
-
- /* 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]);
- }
- }
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * software is freely granted, provided that this notice
+ of the argument <[x]>. Angles are specified in radians.
+ return <<float>> values.
+ <<sin>> and <<cos>> are ANSI C.
+ * 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
+ * TRIG(x) returns trig(x) nearly rounded
+ int32_t n,ix;
-
-/* @(#)s_tan.c 5.1 93/09/24 */
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-
-/*
-
-FUNCTION
- <<tan>>, <<tanf>>---tangent
-
-INDEX
-tan
-INDEX
-tanf
-
-ANSI_SYNOPSIS
- #include <math.h>
- double tan(double <[x]>);
- float tanf(float <[x]>);
-
-TRAD_SYNOPSIS
- #include <math.h>
- double tan(<[x]>)
- double <[x]>;
-
- float tanf(<[x]>)
- float <[x]>;
-
-
-DESCRIPTION
-<<tan>> computes the tangent of the argument <[x]>.
-Angles are specified in radians.
-
-<<tanf>> is identical, save that it takes and returns <<float>> values.
-
-RETURNS
-The tangent of <[x]> is returned.
-
-PORTABILITY
-<<tan>> is ANSI. <<tanf>> is an extension.
-*/
-
-/* 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 sin(x) cos(x) 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"
-
-#ifndef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
- double tan(double x)
-#else
- double tan(x)
- double x;
-#endif
-{
- double y[2],z=0.0;
- __int32_t n,ix;
-
- /* High word of x. */
- GET_HIGH_WORD(ix,x);
-
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
-
- /* 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 */
- }
-}
-
-#endif /* _DOUBLE_IS_32BITS */
+ * software is freely granted, provided that this notice
+<<tan>> computes the tangent of the argument <[x]>.
+Angles are specified in radians.
+The tangent of <[x]> is returned.
+ * 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
+ * TRIG(x) returns trig(x) nearly rounded
+ int32_t n,ix;
-/* sf_rint.c -- float version of s_rint.c.
- * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
- */
-
-/*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
- *
- * Developed at SunPro, a Sun Microsystems, Inc. business.
- * Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
- * is preserved.
- * ====================================================
- */
-
-#include "fdlibm.h"
-
-#ifdef __STDC__
-static const float
-#else
-static float
-#endif
-TWO23[2]={
- 8.3886080000e+06, /* 0x4b000000 */
- -8.3886080000e+06, /* 0xcb000000 */
-};
-
-#ifdef __STDC__
- float rintf(float x)
-#else
- float rintf(x)
- float x;
-#endif
-{
- __int32_t i0,j0,sx;
- __uint32_t i,i1;
- float w,t;
- GET_FLOAT_WORD(i0,x);
- sx = (i0>>31)&1;
- j0 = ((i0>>23)&0xff)-0x7f;
- if(j0<23) {
- if(j0<0) {
- if((i0&0x7fffffff)==0) return x;
- i1 = (i0&0x07fffff);
- i0 &= 0xfff00000;
- i0 |= ((i1|-i1)>>9)&0x400000;
- SET_FLOAT_WORD(x,i0);
- w = TWO23[sx]+x;
- t = w-TWO23[sx];
- GET_FLOAT_WORD(i0,t);
- SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31));
- return t;
- } else {
- i = (0x007fffff)>>j0;
- if((i0&i)==0) return x; /* x is integral */
- i>>=1;
- if((i0&i)!=0) i0 = (i0&(~i))|((0x100000)>>j0);
- }
- } else {
- if(j0==0x80) return x+x; /* inf or NaN */
- else return x; /* x is integral */
- }
- SET_FLOAT_WORD(x,i0);
- w = TWO23[sx]+x;
- return w-TWO23[sx];
-}
-
-#ifdef _DOUBLE_IS_32BITS
-
-#ifdef __STDC__
- double rint(double x)
-#else
- double rint(x)
- double x;
-#endif
-{
- return (double) rintf((float) x);
-}
-
-#endif /* defined(_DOUBLE_IS_32BITS) */
+ * software is freely granted, provided that this notice
+static float
+ int32_t i0,j0,sx;
+ uint32_t i,i1;
+ if(j0<0) {
projects / thirdparty / gcc.git / commitdiff
