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author | cvs2svn <> | 2001-04-22 20:19:29 +0400 |
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committer | cvs2svn <> | 2001-04-22 20:19:29 +0400 |
commit | 4a39e41e48923241b90cb82881c60758d4f2ee87 (patch) | |
tree | 19ceb5f761a720481d76610443a8fca59347de66 /newlib/libm/mathfp/e_j1.c | |
parent | 96dc5dd7e594df1a835f3303e9fee5f5a8c78206 (diff) |
This commit was manufactured by cvs2svn to create branch 'cygwin-1-3-1'.cygwin-1-3-1
Sprout from master 2001-04-22 16:19:27 UTC Christopher Faylor <me@cgf.cx> '* shortcut.c (check_shortcut): Close input file handle before returning.'
Delete:
COPYING
COPYING.LIB
COPYING.NEWLIB
ChangeLog
MAINTAINERS
Makefile.in
README
README-maintainer-mode
config-ml.in
config.guess
config.if
config.sub
config/ChangeLog
config/acinclude.m4
config/mh-a68bsd
config/mh-aix386
config/mh-apollo68
config/mh-armpic
config/mh-cxux
config/mh-cygwin
config/mh-decstation
config/mh-delta88
config/mh-dgux
config/mh-dgux386
config/mh-djgpp
config/mh-elfalphapic
config/mh-hp300
config/mh-hpux
config/mh-hpux8
config/mh-i370pic
config/mh-ia64pic
config/mh-interix
config/mh-irix4
config/mh-irix5
config/mh-irix6
config/mh-lynxos
config/mh-lynxrs6k
config/mh-m68kpic
config/mh-mingw32
config/mh-ncr3000
config/mh-ncrsvr43
config/mh-necv4
config/mh-openedition
config/mh-papic
config/mh-ppcpic
config/mh-riscos
config/mh-s390pic
config/mh-sco
config/mh-solaris
config/mh-sparcpic
config/mh-sun3
config/mh-sysv
config/mh-sysv4
config/mh-sysv5
config/mh-vaxult2
config/mh-x86pic
config/mpw-mh-mpw
config/mpw/ChangeLog
config/mpw/MoveIfChange
config/mpw/README
config/mpw/forward-include
config/mpw/g-mpw-make.sed
config/mpw/mpw-touch
config/mpw/mpw-true
config/mpw/null-command
config/mpw/open-brace
config/mpw/tr-7to8-src
config/mpw/true
config/mt-aix43
config/mt-armpic
config/mt-d30v
config/mt-elfalphapic
config/mt-i370pic
config/mt-ia64pic
config/mt-linux
config/mt-m68kpic
config/mt-netware
config/mt-ospace
config/mt-papic
config/mt-ppcpic
config/mt-s390pic
config/mt-sparcpic
config/mt-v810
config/mt-wince
config/mt-x86pic
configure
configure.in
djunpack.bat
etc/ChangeLog
etc/Makefile.in
etc/add-log.el
etc/add-log.vi
etc/configbuild.ein
etc/configbuild.fig
etc/configbuild.jin
etc/configbuild.tin
etc/configdev.ein
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etc/configdev.jin
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etc/configure
etc/configure.in
etc/configure.texi
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etc/standards.texi
etc/texi2pod.pl
gettext.m4
include/COPYING
include/ChangeLog
include/MAINTAINERS
include/alloca-conf.h
include/ansidecl.h
include/aout/ChangeLog
include/aout/adobe.h
include/aout/aout64.h
include/aout/ar.h
include/aout/dynix3.h
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include/aout/host.h
include/aout/hp.h
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include/aout/ranlib.h
include/aout/reloc.h
include/aout/stab.def
include/aout/stab_gnu.h
include/aout/sun4.h
include/bfdlink.h
include/bin-bugs.h
include/bout.h
include/callback.h
include/coff/ChangeLog
include/coff/a29k.h
include/coff/alpha.h
include/coff/apollo.h
include/coff/arm.h
include/coff/aux-coff.h
include/coff/ecoff.h
include/coff/external.h
include/coff/go32exe.h
include/coff/h8300.h
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include/coff/powerpc.h
include/coff/rs6000.h
include/coff/rs6k64.h
include/coff/sh.h
include/coff/sparc.h
include/coff/sym.h
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include/coff/ti.h
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include/coff/w65.h
include/coff/we32k.h
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include/demangle.h
include/dis-asm.h
include/dyn-string.h
include/elf/ChangeLog
include/elf/alpha.h
include/elf/arc.h
include/elf/arm.h
include/elf/avr.h
include/elf/common.h
include/elf/cris.h
include/elf/d10v.h
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include/elf/external.h
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include/elf/hppa.h
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include/elf/i386.h
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include/elf/i960.h
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include/elf/internal.h
include/elf/m32r.h
include/elf/m68hc11.h
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include/elf/mcore.h
include/elf/mips.h
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include/elf/pj.h
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include/elf/reloc-macros.h
include/elf/s390.h
include/elf/sh.h
include/elf/sparc.h
include/elf/v850.h
include/elf/x86-64.h
include/filenames.h
include/floatformat.h
include/fnmatch.h
include/fopen-bin.h
include/fopen-same.h
include/fopen-vms.h
include/gdbm.h
include/getopt.h
include/hashtab.h
include/hp-symtab.h
include/ieee.h
include/libiberty.h
include/md5.h
include/mpw/ChangeLog
include/mpw/README
include/mpw/dir.h
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include/nlm/ChangeLog
include/nlm/alpha-ext.h
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include/nlm/external.h
include/nlm/i386-ext.h
include/nlm/internal.h
include/nlm/ppc-ext.h
include/nlm/sparc32-ext.h
include/oasys.h
include/objalloc.h
include/obstack.h
include/opcode/ChangeLog
include/opcode/a29k.h
include/opcode/alpha.h
include/opcode/arc.h
include/opcode/arm.h
include/opcode/avr.h
include/opcode/cgen.h
include/opcode/convex.h
include/opcode/cris.h
include/opcode/d10v.h
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include/opcode/h8300.h
include/opcode/hppa.h
include/opcode/i370.h
include/opcode/i386.h
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include/opcode/ia64.h
include/opcode/m68hc11.h
include/opcode/m68k.h
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include/opcode/mips.h
include/opcode/mn10200.h
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include/opcode/np1.h
include/opcode/ns32k.h
include/opcode/pdp11.h
include/opcode/pj.h
include/opcode/pn.h
include/opcode/ppc.h
include/opcode/pyr.h
include/opcode/s390.h
include/opcode/sparc.h
include/opcode/tahoe.h
include/opcode/tic30.h
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include/opcode/tic80.h
include/opcode/v850.h
include/opcode/vax.h
include/os9k.h
include/partition.h
include/progress.h
include/regs/ChangeLog
include/remote-sim.h
include/safe-ctype.h
include/sim-d10v.h
include/sort.h
include/splay-tree.h
include/symcat.h
include/ternary.h
install-sh
libgloss/ChangeLog
libgloss/Makefile.in
libgloss/README
libgloss/close.c
libgloss/config/default.mh
libgloss/config/default.mt
libgloss/config/dos.mh
libgloss/config/mips.mt
libgloss/config/mn10200.mt
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libgloss/config/ppc.mh
libgloss/configure
libgloss/configure.in
libgloss/d30v/Makefile.in
libgloss/d30v/configure
libgloss/d30v/configure.in
libgloss/d30v/crt0.S
libgloss/d30v/inbyte.c
libgloss/d30v/outbyte.c
libgloss/d30v/syscalls.c
libgloss/debug.c
libgloss/debug.h
libgloss/doc/Makefile.in
libgloss/doc/configure
libgloss/doc/configure.in
libgloss/doc/porting.texi
libgloss/fr30/Makefile.in
libgloss/fr30/configure
libgloss/fr30/configure.in
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libgloss/fr30/syscalls.c
libgloss/fstat.c
libgloss/getpid.c
libgloss/glue.h
libgloss/hp74x/Makefile.in
libgloss/hp74x/README
libgloss/hp74x/checksum.c
libgloss/hp74x/configure
libgloss/hp74x/configure.in
libgloss/hp74x/crt0.s
libgloss/hp74x/debugger.h
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libgloss/hp74x/diagnose.h
libgloss/hp74x/hppa-defs.h
libgloss/hp74x/hppa.ld
libgloss/hp74x/io.c
libgloss/hp74x/iva_table.h
libgloss/hp74x/iva_table.s
libgloss/hp74x/pa_stub.c
libgloss/hp74x/test.c
libgloss/i386/Makefile.in
libgloss/i386/configure
libgloss/i386/configure.in
libgloss/i386/cygmon-crt0.S
libgloss/i386/cygmon-gmon.c
libgloss/i386/cygmon-gmon.h
libgloss/i386/cygmon-salib.c
libgloss/i386/cygmon-syscall.h
libgloss/i386/cygmon.ld
libgloss/i960/Makefile.in
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libgloss/i960/configure
libgloss/i960/configure.in
libgloss/i960/crt0.c
libgloss/i960/mon-read.c
libgloss/i960/mon-syscalls.S
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libgloss/isatty.c
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libgloss/libnosys/Makefile.in
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libgloss/libnosys/close.c
libgloss/libnosys/config.h.in
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libgloss/libnosys/environ.c
libgloss/libnosys/execve.c
libgloss/libnosys/fork.c
libgloss/libnosys/fstat.c
libgloss/libnosys/getpid.c
libgloss/libnosys/gettod.c
libgloss/libnosys/isatty.c
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libgloss/libnosys/warning.h
libgloss/libnosys/write.c
libgloss/lseek.c
libgloss/m32r/Makefile.in
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libgloss/m32r/close.c
libgloss/m32r/configure
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libgloss/m68k/Makefile.in
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libgloss/m68k/asm.h
libgloss/m68k/bcc.ld
libgloss/m68k/configure
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libgloss/m68k/cpu32bug.S
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libgloss/m68k/crt0.S
libgloss/m68k/dbug-exit.S
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libgloss/m68k/dtor.C
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libgloss/m68k/idp-outbyte.c
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libgloss/m68k/mc68681reg.h
libgloss/m68k/mc68ec.c
libgloss/m68k/mvme-stub.c
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libgloss/m68k/sim-abort.c
libgloss/m68k/sim-crt0.S
libgloss/m68k/sim-errno.c
libgloss/m68k/sim-funcs.c
libgloss/m68k/sim-inbyte.c
libgloss/m68k/sim-print.c
libgloss/m68k/sim-sbrk.c
libgloss/m68k/sim.ld
libgloss/m68k/simulator.S
libgloss/m68k/test.c
libgloss/mcore/Makefile.in
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libgloss/mcore/cmb-exit.c
libgloss/mcore/cmb-inbyte.c
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libgloss/mcore/configure
libgloss/mcore/configure.in
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libgloss/mcore/getpid.c
libgloss/mcore/kill.c
libgloss/mcore/lseek.c
libgloss/mcore/open.c
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libgloss/mcore/print.c
libgloss/mcore/putnum.c
libgloss/mcore/raise.c
libgloss/mcore/read.c
libgloss/mcore/sbrk.c
libgloss/mcore/stat.c
libgloss/mcore/syscalls.S
libgloss/mcore/unlink.c
libgloss/mcore/write.c
libgloss/mips/Makefile.in
libgloss/mips/array-io.c
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libgloss/mips/cma101.c
libgloss/mips/configure
libgloss/mips/configure.in
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libgloss/mips/ddb.ld
libgloss/mips/dtor.C
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libgloss/mips/dvemon.c
libgloss/mips/entry.S
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libgloss/mips/lsi33k-stub.c
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libgloss/mips/lsipmon.S
libgloss/mips/nullmon.c
libgloss/mips/nullmon.ld
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libgloss/mips/syscalls.c
libgloss/mips/test.c
libgloss/mips/vr4300.S
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libgloss/mn10200/Makefile.in
libgloss/mn10200/_exit.c
libgloss/mn10200/access.c
libgloss/mn10200/chmod.c
libgloss/mn10200/chown.c
libgloss/mn10200/close.c
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libgloss/mn10200/read.c
libgloss/mn10200/sbrk.c
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libgloss/mn10200/time.c
libgloss/mn10200/times.c
libgloss/mn10200/trap.S
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libgloss/mn10200/unlink.c
libgloss/mn10200/utime.c
libgloss/mn10200/wait.c
libgloss/mn10200/write.c
libgloss/mn10300/Makefile.in
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libgloss/mn10300/chown.c
libgloss/mn10300/close.c
libgloss/mn10300/configure
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libgloss/mn10300/getpid.c
libgloss/mn10300/gettime.c
libgloss/mn10300/isatty.c
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libgloss/mn10300/lseek.c
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libgloss/mn10300/read.c
libgloss/mn10300/sbrk.c
libgloss/mn10300/sim.ld
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libgloss/mn10300/test.c
libgloss/mn10300/time.c
libgloss/mn10300/times.c
libgloss/mn10300/trap.S
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libgloss/mn10300/unlink.c
libgloss/mn10300/utime.c
libgloss/mn10300/wait.c
libgloss/mn10300/write.c
libgloss/open.c
libgloss/pa/Makefile.in
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libgloss/pa/configure
libgloss/pa/configure.in
libgloss/pa/crt0.S
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libgloss/pa/op50n-io.S
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libgloss/pa/w89k-io.c
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libgloss/print.c
libgloss/putnum.c
libgloss/read.c
libgloss/rs6000/Makefile.in
libgloss/rs6000/ads-exit.S
libgloss/rs6000/ads-io.c
libgloss/rs6000/ads.ld
libgloss/rs6000/configure
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libgloss/rs6000/mbx-exit.c
libgloss/rs6000/mbx-inbyte.c
libgloss/rs6000/mbx-outbyte.c
libgloss/rs6000/mbx-print.c
libgloss/rs6000/mbx.ld
libgloss/rs6000/mbx.specs
libgloss/rs6000/mcount.S
libgloss/rs6000/mvme-errno.c
libgloss/rs6000/mvme-exit.S
libgloss/rs6000/mvme-inbyte.S
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libgloss/rs6000/mvme-print.c
libgloss/rs6000/mvme-read.c
libgloss/rs6000/sim-abort.c
libgloss/rs6000/sim-crt0.S
libgloss/rs6000/sim-errno.c
libgloss/rs6000/sim-inbyte.c
libgloss/rs6000/sim-print.c
libgloss/rs6000/sim-sbrk.c
libgloss/rs6000/simulator.S
libgloss/rs6000/sol-cfuncs.c
libgloss/rs6000/sol-syscall.S
libgloss/rs6000/test.c
libgloss/rs6000/yellowknife.ld
libgloss/sbrk.c
libgloss/sh/sh1lcevb.ld
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libgloss/sparc/Makefile.in
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libgloss/sparc/cache.c
libgloss/sparc/configure
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libgloss/sparc/cygmon-salib.c
libgloss/sparc/cygmon-sparc64-ld.src
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libgloss/sparc/dtor.C
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libgloss/sparc/erc32-crt0.S
libgloss/sparc/erc32-io.c
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winsup/utils/cygcheck.cc
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winsup/utils/getfacl.c
winsup/utils/kill.cc
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winsup/utils/mkpasswd.c
winsup/utils/module_info.cc
winsup/utils/mount.cc
winsup/utils/parse_pe.cc
winsup/utils/passwd.c
winsup/utils/ps.cc
winsup/utils/regtool.cc
winsup/utils/setfacl.c
winsup/utils/ssp.c
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winsup/utils/strace.cc
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winsup/utils/utils.sgml
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winsup/w32api/include/nb30.h
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winsup/w32api/include/ole2ver.h
winsup/w32api/include/oleauto.h
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winsup/w32api/include/ras.h
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winsup/w32api/include/rassapi.h
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winsup/w32api/include/richedit.h
winsup/w32api/include/richole.h
winsup/w32api/include/rpc.h
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winsup/w32api/include/rpcndr.h
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winsup/w32api/include/scrnsave.h
winsup/w32api/include/shellapi.h
winsup/w32api/include/shlguid.h
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winsup/w32api/include/sqltypes.h
winsup/w32api/include/sqlucode.h
winsup/w32api/include/subauth.h
winsup/w32api/include/tlhelp32.h
winsup/w32api/include/unknwn.h
winsup/w32api/include/userenv.h
winsup/w32api/include/w32api.h
winsup/w32api/include/winbase.h
winsup/w32api/include/wincon.h
winsup/w32api/include/wincrypt.h
winsup/w32api/include/windef.h
winsup/w32api/include/windows.h
winsup/w32api/include/windowsx.h
winsup/w32api/include/winerror.h
winsup/w32api/include/wingdi.h
winsup/w32api/include/wininet.h
winsup/w32api/include/winioctl.h
winsup/w32api/include/winnetwk.h
winsup/w32api/include/winnls.h
winsup/w32api/include/winnt.h
winsup/w32api/include/winperf.h
winsup/w32api/include/winreg.h
winsup/w32api/include/winresrc.h
winsup/w32api/include/winsock.h
winsup/w32api/include/winsock2.h
winsup/w32api/include/winspool.h
winsup/w32api/include/winsvc.h
winsup/w32api/include/winuser.h
winsup/w32api/include/winver.h
winsup/w32api/include/ws2tcpip.h
winsup/w32api/include/wtypes.h
winsup/w32api/include/zmouse.h
winsup/w32api/install-sh
winsup/w32api/lib/Makefile.in
winsup/w32api/lib/advapi32.def
winsup/w32api/lib/cap.def
winsup/w32api/lib/comctl32.def
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winsup/w32api/lib/d3drm.def
winsup/w32api/lib/d3dxof.def
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winsup/w32api/lib/dinput.c
winsup/w32api/lib/dinput.def
winsup/w32api/lib/dlcapi.def
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winsup/w32api/lib/dsound.def
winsup/w32api/lib/dxguid.c
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winsup/w32api/lib/shell32.c
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winsup/w32api/lib/th32.def
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winsup/w32api/lib/url.def
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winsup/w32api/lib/uuid.c
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winsup/w32api/lib/vfw32.def
winsup/w32api/lib/win32spl.def
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winsup/w32api/lib/winspool.def
winsup/w32api/lib/winstrm.def
winsup/w32api/lib/wow32.def
winsup/w32api/lib/ws2_32.def
winsup/w32api/lib/wsock32.def
winsup/w32api/lib/wst.def
ylwrap
Diffstat (limited to 'newlib/libm/mathfp/e_j1.c')
-rw-r--r-- | newlib/libm/mathfp/e_j1.c | 486 |
1 files changed, 0 insertions, 486 deletions
diff --git a/newlib/libm/mathfp/e_j1.c b/newlib/libm/mathfp/e_j1.c deleted file mode 100644 index 274adfdc8..000000000 --- a/newlib/libm/mathfp/e_j1.c +++ /dev/null @@ -1,486 +0,0 @@ - -/* @(#)e_j1.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. - * ==================================================== - */ - -/* j1(x), y1(x) - * Bessel function of the first and second kinds of order zero. - * Method -- j1(x): - * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... - * 2. Reduce x to |x| since j1(x)=-j1(-x), and - * for x in (0,2) - * j1(x) = x/2 + x*z*R0/S0, where z = x*x; - * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) - * for x in (2,inf) - * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) - * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) - * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) - * as follow: - * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) - * = 1/sqrt(2) * (sin(x) - cos(x)) - * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) - * = -1/sqrt(2) * (sin(x) + cos(x)) - * (To avoid cancellation, use - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one.) - * - * 3 Special cases - * j1(nan)= nan - * j1(0) = 0 - * j1(inf) = 0 - * - * Method -- y1(x): - * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN - * 2. For x<2. - * Since - * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) - * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. - * We use the following function to approximate y1, - * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 - * where for x in [0,2] (abs err less than 2**-65.89) - * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 - * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 - * Note: For tiny x, 1/x dominate y1 and hence - * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) - * 3. For x>=2. - * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) - * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) - * by method mentioned above. - */ - -#include "fdlibm.h" - -#ifndef _DOUBLE_IS_32BITS - -#ifdef __STDC__ -static double pone(double), qone(double); -#else -static double pone(), qone(); -#endif - -#ifdef __STDC__ -static const double -#else -static double -#endif -huge = 1e300, -one = 1.0, -invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ -tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - /* R0/S0 on [0,2] */ -r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ -r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ -r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ -r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ -s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ -s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ -s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ -s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ -s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ - -#ifdef __STDC__ -static const double zero = 0.0; -#else -static double zero = 0.0; -#endif - -#ifdef __STDC__ - double j1(double x) -#else - double j1(x) - double x; -#endif -{ - double z, s,c,ss,cc,r,u,v,y; - __int32_t hx,ix; - - GET_HIGH_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix>=0x7ff00000) return one/x; - y = fabs(x); - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = sin(y); - c = cos(y); - ss = -s-c; - cc = s-c; - if(ix<0x7fe00000) { /* make sure y+y not overflow */ - z = cos(y+y); - if ((s*c)>zero) cc = z/ss; - else ss = z/cc; - } - /* - * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) - * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) - */ - if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); - else { - u = pone(y); v = qone(y); - z = invsqrtpi*(u*cc-v*ss)/sqrt(y); - } - if(hx<0) return -z; - else return z; - } - if(ix<0x3e400000) { /* |x|<2**-27 */ - if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ - } - z = x*x; - r = z*(r00+z*(r01+z*(r02+z*r03))); - s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); - r *= x; - return(x*0.5+r/s); -} - -#ifdef __STDC__ -static const double U0[5] = { -#else -static double U0[5] = { -#endif - -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ - 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ - -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ - 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ - -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ -}; -#ifdef __STDC__ -static const double V0[5] = { -#else -static double V0[5] = { -#endif - 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ - 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ - 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ - 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ - 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ -}; - -#ifdef __STDC__ - double y1(double x) -#else - double y1(x) - double x; -#endif -{ - double z, s,c,ss,cc,u,v; - __int32_t hx,ix,lx; - - EXTRACT_WORDS(hx,lx,x); - ix = 0x7fffffff&hx; - /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ - if(ix>=0x7ff00000) return one/(x+x*x); - if((ix|lx)==0) return -one/zero; - if(hx<0) return zero/zero; - if(ix >= 0x40000000) { /* |x| >= 2.0 */ - s = sin(x); - c = cos(x); - ss = -s-c; - cc = s-c; - if(ix<0x7fe00000) { /* make sure x+x not overflow */ - z = cos(x+x); - if ((s*c)>zero) cc = z/ss; - else ss = z/cc; - } - /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) - * where x0 = x-3pi/4 - * Better formula: - * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) - * = 1/sqrt(2) * (sin(x) - cos(x)) - * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) - * = -1/sqrt(2) * (cos(x) + sin(x)) - * To avoid cancellation, use - * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) - * to compute the worse one. - */ - if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); - else { - u = pone(x); v = qone(x); - z = invsqrtpi*(u*ss+v*cc)/sqrt(x); - } - return z; - } - if(ix<=0x3c900000) { /* x < 2**-54 */ - return(-tpi/x); - } - z = x*x; - u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); - v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); - return(x*(u/v) + tpi*(j1(x)*log(x)-one/x)); -} - -/* For x >= 8, the asymptotic expansions of pone is - * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. - * We approximate pone by - * pone(x) = 1 + (R/S) - * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 - * S = 1 + ps0*s^2 + ... + ps4*s^10 - * and - * | pone(x)-1-R/S | <= 2 ** ( -60.06) - */ - -#ifdef __STDC__ -static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ - 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ - 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ - 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ - 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ -}; -#ifdef __STDC__ -static const double ps8[5] = { -#else -static double ps8[5] = { -#endif - 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ - 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ - 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ - 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ - 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ -}; - -#ifdef __STDC__ -static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ - 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ - 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ - 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ - 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ - 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ -}; -#ifdef __STDC__ -static const double ps5[5] = { -#else -static double ps5[5] = { -#endif - 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ - 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ - 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ - 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ - 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ -}; - -#ifdef __STDC__ -static const double pr3[6] = { -#else -static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ - 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ - 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ - 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ - 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ - 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ -}; -#ifdef __STDC__ -static const double ps3[5] = { -#else -static double ps3[5] = { -#endif - 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ - 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ - 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ - 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ - 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ -}; - -#ifdef __STDC__ -static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ - 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ - 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ - 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ - 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ - 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ -}; -#ifdef __STDC__ -static const double ps2[5] = { -#else -static double ps2[5] = { -#endif - 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ - 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ - 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ - 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ - 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ -}; - -#ifdef __STDC__ - static double pone(double x) -#else - static double pone(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p,*q; -#else - double *p,*q; -#endif - double z,r,s; - __int32_t ix; - GET_HIGH_WORD(ix,x); - ix &= 0x7fffffff; - if(ix>=0x40200000) {p = pr8; q= ps8;} - else if(ix>=0x40122E8B){p = pr5; q= ps5;} - else if(ix>=0x4006DB6D){p = pr3; q= ps3;} - else {p = pr2; q= ps2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); - return one+ r/s; -} - - -/* For x >= 8, the asymptotic expansions of qone is - * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. - * We approximate qone by - * qone(x) = s*(0.375 + (R/S)) - * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 - * S = 1 + qs1*s^2 + ... + qs6*s^12 - * and - * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) - */ - -#ifdef __STDC__ -static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#else -static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ -#endif - 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ - -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ - -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ - -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ - -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ -}; -#ifdef __STDC__ -static const double qs8[6] = { -#else -static double qs8[6] = { -#endif - 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ - 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ - 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ - 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ - 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ - -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ -}; - -#ifdef __STDC__ -static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#else -static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -#endif - -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ - -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ - -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ - -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ - -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ - -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ -}; -#ifdef __STDC__ -static const double qs5[6] = { -#else -static double qs5[6] = { -#endif - 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ - 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ - 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ - 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ - 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ - -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ -}; - -#ifdef __STDC__ -static const double qr3[6] = { -#else -static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -#endif - -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ - -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ - -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ - -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ - -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ - -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ -}; -#ifdef __STDC__ -static const double qs3[6] = { -#else -static double qs3[6] = { -#endif - 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ - 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ - 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ - 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ - 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ - -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ -}; - -#ifdef __STDC__ -static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#else -static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -#endif - -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ - -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ - -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ - -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ - -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ - -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ -}; -#ifdef __STDC__ -static const double qs2[6] = { -#else -static double qs2[6] = { -#endif - 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ - 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ - 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ - 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ - 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ - -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ -}; - -#ifdef __STDC__ - static double qone(double x) -#else - static double qone(x) - double x; -#endif -{ -#ifdef __STDC__ - const double *p,*q; -#else - double *p,*q; -#endif - double s,r,z; - __int32_t ix; - GET_HIGH_WORD(ix,x); - ix &= 0x7fffffff; - if(ix>=0x40200000) {p = qr8; q= qs8;} - else if(ix>=0x40122E8B){p = qr5; q= qs5;} - else if(ix>=0x4006DB6D){p = qr3; q= qs3;} - else {p = qr2; q= qs2;} - z = one/(x*x); - r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); - s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); - return (.375 + r/s)/x; -} - -#endif /* defined(_DOUBLE_IS_32BITS) */ |