diff options
Diffstat (limited to 'newlib/libm/math')
137 files changed, 17666 insertions, 0 deletions
diff --git a/newlib/libm/math/Makefile.am b/newlib/libm/math/Makefile.am new file mode 100644 index 00000000000..9e16155bf5b --- /dev/null +++ b/newlib/libm/math/Makefile.am @@ -0,0 +1,173 @@ +## Process this file with automake to generate Makefile.in + +AUTOMAKE_OPTIONS = cygnus + +INCLUDES = -I$(srcdir)/../common $(NEWLIB_CFLAGS) $(CROSS_CFLAGS) $(TARGET_CFLAGS) + +noinst_LIBRARIES = lib.a + +src = k_standard.c k_rem_pio2.c \ + k_cos.c k_sin.c k_tan.c \ + e_acos.c e_acosh.c e_asin.c e_atan2.c \ + e_atanh.c e_cosh.c e_exp.c e_fmod.c \ + er_gamma.c e_hypot.c e_j0.c \ + e_j1.c e_jn.c er_lgamma.c \ + e_log.c e_log10.c e_pow.c e_rem_pio2.c e_remainder.c \ + e_scalb.c e_sinh.c e_sqrt.c \ + w_acos.c w_acosh.c w_asin.c w_atan2.c \ + w_atanh.c w_cosh.c w_exp.c w_fmod.c \ + w_gamma.c wr_gamma.c w_hypot.c w_j0.c \ + w_j1.c w_jn.c w_lgamma.c wr_lgamma.c \ + w_log.c w_log10.c w_pow.c w_remainder.c \ + w_scalb.c w_sinh.c w_sqrt.c \ + w_cabs.c w_drem.c \ + s_asinh.c s_atan.c s_ceil.c \ + s_cos.c s_erf.c s_fabs.c s_floor.c \ + s_frexp.c s_isnan.c s_ldexp.c \ + s_signif.c s_sin.c \ + s_tan.c s_tanh.c \ + s_isinf.c s_infconst.c + +fsrc = kf_rem_pio2.c \ + kf_cos.c kf_sin.c kf_tan.c \ + ef_acos.c ef_acosh.c ef_asin.c ef_atan2.c \ + ef_atanh.c ef_cosh.c ef_exp.c ef_fmod.c \ + erf_gamma.c ef_hypot.c ef_j0.c \ + ef_j1.c ef_jn.c erf_lgamma.c \ + ef_log.c ef_log10.c ef_pow.c ef_rem_pio2.c ef_remainder.c \ + ef_scalb.c ef_sinh.c ef_sqrt.c \ + wf_acos.c wf_acosh.c wf_asin.c wf_atan2.c \ + wf_atanh.c wf_cosh.c wf_exp.c wf_fmod.c \ + wf_gamma.c wrf_gamma.c wf_hypot.c wf_j0.c \ + wf_j1.c wf_jn.c wf_lgamma.c wrf_lgamma.c \ + wf_log.c wf_log10.c wf_pow.c wf_remainder.c \ + wf_scalb.c wf_sinh.c wf_sqrt.c \ + wf_cabs.c wf_drem.c \ + sf_asinh.c sf_atan.c sf_ceil.c \ + sf_cos.c sf_erf.c sf_fabs.c sf_floor.c \ + sf_frexp.c sf_isnan.c sf_ldexp.c \ + sf_signif.c sf_sin.c \ + sf_tan.c sf_tanh.c \ + sf_isinf.c + +lib_a_SOURCES = $(src) $(fsrc) + +chobj = wacos.def wacosh.def wasin.def sasinh.def \ + satan.def watan2.def watanh.def wj0.def \ + wcosh.def serf.def wexp.def \ + sfabs.def sfloor.def wfmod.def sfrexp.def \ + wgamma.def whypot.def sldexp.def wlog.def \ + wlog10.def \ + wpow.def wremainder.def ssin.def wsinh.def \ + wsqrt.def stan.def stanh.def \ + sisnan.def + +SUFFIXES = .def + +CHEW = ../../doc/makedoc -f $(srcdir)/../../doc/doc.str + +.c.def: + $(CHEW) < $< > $*.def 2> $*.ref + touch stmp-def + +TARGETDOC = ../tmp.texi + +doc: $(chobj) + cat $(srcdir)/math.tex >> $(TARGETDOC) + +CLEANFILES = $(chobj) *.ref + +# Texinfo does not appear to support underscores in file names, so we +# name the .def files without underscores. + +wacos.def: w_acos.c + $(CHEW) < $(srcdir)/w_acos.c >$@ 2>/dev/null + touch stmp-def +wacosh.def: w_acosh.c + $(CHEW) < $(srcdir)/w_acosh.c >$@ 2>/dev/null + touch stmp-def +wasin.def: w_asin.c + $(CHEW) < $(srcdir)/w_asin.c >$@ 2>/dev/null + touch stmp-def +sasinh.def: s_asinh.c + $(CHEW) < $(srcdir)/s_asinh.c >$@ 2>/dev/null + touch stmp-def +satan.def: s_atan.c + $(CHEW) < $(srcdir)/s_atan.c >$@ 2>/dev/null + touch stmp-def +watan2.def: w_atan2.c + $(CHEW) < $(srcdir)/w_atan2.c >$@ 2>/dev/null + touch stmp-def +watanh.def: w_atanh.c + $(CHEW) < $(srcdir)/w_atanh.c >$@ 2>/dev/null + touch stmp-def +wj0.def: w_j0.c + $(CHEW) < $(srcdir)/w_j0.c >$@ 2>/dev/null + touch stmp-def +scopysign.def: s_copysign.c + $(CHEW) < $(srcdir)/../common/s_copysign.c >$@ 2>/dev/null + touch stmp-def +wcosh.def: w_cosh.c + $(CHEW) < $(srcdir)/w_cosh.c >$@ 2>/dev/null + touch stmp-def +serf.def: s_erf.c + $(CHEW) < $(srcdir)/s_erf.c >$@ 2>/dev/null + touch stmp-def +wexp.def: w_exp.c + $(CHEW) < $(srcdir)/w_exp.c >$@ 2>/dev/null + touch stmp-def +sfabs.def: s_fabs.c + $(CHEW) < $(srcdir)/s_fabs.c >$@ 2>/dev/null + touch stmp-def +sfloor.def: s_floor.c + $(CHEW) < $(srcdir)/s_floor.c >$@ 2>/dev/null + touch stmp-def +wfmod.def: w_fmod.c + $(CHEW) < $(srcdir)/w_fmod.c >$@ 2>/dev/null + touch stmp-def +sfrexp.def: s_frexp.c + $(CHEW) < $(srcdir)/s_frexp.c >$@ 2>/dev/null + touch stmp-def +wgamma.def: w_gamma.c + $(CHEW) < $(srcdir)/w_gamma.c >$@ 2>/dev/null + touch stmp-def +whypot.def: w_hypot.c + $(CHEW) < $(srcdir)/w_hypot.c >$@ 2>/dev/null + touch stmp-def +sldexp.def: s_ldexp.c + $(CHEW) < $(srcdir)/s_ldexp.c >$@ 2>/dev/null + touch stmp-def +wlog.def: w_log.c + $(CHEW) < $(srcdir)/w_log.c >$@ 2>/dev/null + touch stmp-def +wlog10.def: w_log10.c + $(CHEW) < $(srcdir)/w_log10.c >$@ 2>/dev/null + touch stmp-def +wpow.def: w_pow.c + $(CHEW) < $(srcdir)/w_pow.c >$@ 2>/dev/null + touch stmp-def +wremainder.def: w_remainder.c + $(CHEW) < $(srcdir)/w_remainder.c >$@ 2>/dev/null + touch stmp-def +ssin.def: s_sin.c + $(CHEW) < $(srcdir)/s_sin.c >$@ 2>/dev/null + touch stmp-def +wsinh.def: w_sinh.c + $(CHEW) < $(srcdir)/w_sinh.c >$@ 2>/dev/null + touch stmp-def +wsqrt.def: w_sqrt.c + $(CHEW) < $(srcdir)/w_sqrt.c >$@ 2>/dev/null + touch stmp-def +stan.def: s_tan.c + $(CHEW) < $(srcdir)/s_tan.c >$@ 2>/dev/null + touch stmp-def +stanh.def: s_tanh.c + $(CHEW) < $(srcdir)/s_tanh.c >$@ 2>/dev/null + touch stmp-def +sisnan.def: s_isnan.c + $(CHEW) < $(srcdir)/s_isnan.c >$@ 2>/dev/null + touch stmp-def + +# A partial dependency list. + +$(lib_a_OBJECTS): $(srcdir)/../../libc/include/math.h $(srcdir)/../common/fdlibm.h diff --git a/newlib/libm/math/Makefile.in b/newlib/libm/math/Makefile.in new file mode 100644 index 00000000000..b80f8fb5596 --- /dev/null +++ b/newlib/libm/math/Makefile.in @@ -0,0 +1,431 @@ +# Makefile.in generated automatically by automake 1.3b from Makefile.am + +# Copyright (C) 1994, 1995, 1996, 1997, 1998 Free Software Foundation, Inc. +# This Makefile.in is free software; the Free Software Foundation +# gives unlimited permission to copy and/or distribute it, +# with or without modifications, as long as this notice is preserved. + +# This program is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY, to the extent permitted by law; without +# even the implied warranty of MERCHANTABILITY or FITNESS FOR A +# PARTICULAR PURPOSE. + + +SHELL = @SHELL@ + +srcdir = @srcdir@ +top_srcdir = @top_srcdir@ +VPATH = @srcdir@ +prefix = @prefix@ +exec_prefix = @exec_prefix@ + +bindir = @bindir@ +sbindir = @sbindir@ +libexecdir = @libexecdir@ +datadir = @datadir@ +sysconfdir = @sysconfdir@ +sharedstatedir = @sharedstatedir@ +localstatedir = @localstatedir@ +libdir = @libdir@ +infodir = @infodir@ +mandir = @mandir@ +includedir = @includedir@ +oldincludedir = /usr/include + +DESTDIR = + +pkgdatadir = $(datadir)/@PACKAGE@ +pkglibdir = $(libdir)/@PACKAGE@ +pkgincludedir = $(includedir)/@PACKAGE@ + +top_builddir = .. + +ACLOCAL = @ACLOCAL@ +AUTOCONF = @AUTOCONF@ +AUTOMAKE = @AUTOMAKE@ +AUTOHEADER = @AUTOHEADER@ + +INSTALL = @INSTALL@ +INSTALL_PROGRAM = @INSTALL_PROGRAM@ +INSTALL_DATA = @INSTALL_DATA@ +INSTALL_SCRIPT = @INSTALL_SCRIPT@ +transform = @program_transform_name@ + +NORMAL_INSTALL = : +PRE_INSTALL = : +POST_INSTALL = : +NORMAL_UNINSTALL = : +PRE_UNINSTALL = : +POST_UNINSTALL = : +host_alias = @host_alias@ +host_triplet = @host@ +AR = @AR@ +AS = @AS@ +CC = @CC@ +CPP = @CPP@ +EXEEXT = @EXEEXT@ +MAINT = @MAINT@ +MAKEINFO = @MAKEINFO@ +NEWLIB_CFLAGS = @NEWLIB_CFLAGS@ +PACKAGE = @PACKAGE@ +RANLIB = @RANLIB@ +VERSION = @VERSION@ +machine_dir = @machine_dir@ +newlib_basedir = @newlib_basedir@ +sys_dir = @sys_dir@ + +AUTOMAKE_OPTIONS = cygnus + +INCLUDES = -I$(srcdir)/../common $(NEWLIB_CFLAGS) $(CROSS_CFLAGS) $(TARGET_CFLAGS) + +noinst_LIBRARIES = lib.a + +src = k_standard.c k_rem_pio2.c \ + k_cos.c k_sin.c k_tan.c \ + e_acos.c e_acosh.c e_asin.c e_atan2.c \ + e_atanh.c e_cosh.c e_exp.c e_fmod.c \ + er_gamma.c e_hypot.c e_j0.c \ + e_j1.c e_jn.c er_lgamma.c \ + e_log.c e_log10.c e_pow.c e_rem_pio2.c e_remainder.c \ + e_scalb.c e_sinh.c e_sqrt.c \ + w_acos.c w_acosh.c w_asin.c w_atan2.c \ + w_atanh.c w_cosh.c w_exp.c w_fmod.c \ + w_gamma.c wr_gamma.c w_hypot.c w_j0.c \ + w_j1.c w_jn.c w_lgamma.c wr_lgamma.c \ + w_log.c w_log10.c w_pow.c w_remainder.c \ + w_scalb.c w_sinh.c w_sqrt.c \ + w_cabs.c w_drem.c \ + s_asinh.c s_atan.c s_ceil.c \ + s_cos.c s_erf.c s_fabs.c s_floor.c \ + s_frexp.c s_isnan.c s_ldexp.c \ + s_signif.c s_sin.c \ + s_tan.c s_tanh.c \ + s_isinf.c s_infconst.c + +fsrc = kf_rem_pio2.c \ + kf_cos.c kf_sin.c kf_tan.c \ + ef_acos.c ef_acosh.c ef_asin.c ef_atan2.c \ + ef_atanh.c ef_cosh.c ef_exp.c ef_fmod.c \ + erf_gamma.c ef_hypot.c ef_j0.c \ + ef_j1.c ef_jn.c erf_lgamma.c \ + ef_log.c ef_log10.c ef_pow.c ef_rem_pio2.c ef_remainder.c \ + ef_scalb.c ef_sinh.c ef_sqrt.c \ + wf_acos.c wf_acosh.c wf_asin.c wf_atan2.c \ + wf_atanh.c wf_cosh.c wf_exp.c wf_fmod.c \ + wf_gamma.c wrf_gamma.c wf_hypot.c wf_j0.c \ + wf_j1.c wf_jn.c wf_lgamma.c wrf_lgamma.c \ + wf_log.c wf_log10.c wf_pow.c wf_remainder.c \ + wf_scalb.c wf_sinh.c wf_sqrt.c \ + wf_cabs.c wf_drem.c \ + sf_asinh.c sf_atan.c sf_ceil.c \ + sf_cos.c sf_erf.c sf_fabs.c sf_floor.c \ + sf_frexp.c sf_isnan.c sf_ldexp.c \ + sf_signif.c sf_sin.c \ + sf_tan.c sf_tanh.c \ + sf_isinf.c + +lib_a_SOURCES = $(src) $(fsrc) + +chobj = wacos.def wacosh.def wasin.def sasinh.def \ + satan.def watan2.def watanh.def wj0.def \ + wcosh.def serf.def wexp.def \ + sfabs.def sfloor.def wfmod.def sfrexp.def \ + wgamma.def whypot.def sldexp.def wlog.def \ + wlog10.def \ + wpow.def wremainder.def ssin.def wsinh.def \ + wsqrt.def stan.def stanh.def \ + sisnan.def + +SUFFIXES = .def + +CHEW = ../../doc/makedoc -f $(srcdir)/../../doc/doc.str + +TARGETDOC = ../tmp.texi + +CLEANFILES = $(chobj) *.ref +mkinstalldirs = $(SHELL) $(top_srcdir)/../../mkinstalldirs +CONFIG_CLEAN_FILES = +LIBRARIES = $(noinst_LIBRARIES) + + +DEFS = @DEFS@ -I. -I$(srcdir) +CPPFLAGS = @CPPFLAGS@ +LDFLAGS = @LDFLAGS@ +LIBS = @LIBS@ +lib_a_LIBADD = +lib_a_OBJECTS = k_standard.o k_rem_pio2.o k_cos.o k_sin.o k_tan.o \ +e_acos.o e_acosh.o e_asin.o e_atan2.o e_atanh.o e_cosh.o e_exp.o \ +e_fmod.o er_gamma.o e_hypot.o e_j0.o e_j1.o e_jn.o er_lgamma.o e_log.o \ +e_log10.o e_pow.o e_rem_pio2.o e_remainder.o e_scalb.o e_sinh.o \ +e_sqrt.o w_acos.o w_acosh.o w_asin.o w_atan2.o w_atanh.o w_cosh.o \ +w_exp.o w_fmod.o w_gamma.o wr_gamma.o w_hypot.o w_j0.o w_j1.o w_jn.o \ +w_lgamma.o wr_lgamma.o w_log.o w_log10.o w_pow.o w_remainder.o \ +w_scalb.o w_sinh.o w_sqrt.o w_cabs.o w_drem.o s_asinh.o s_atan.o \ +s_ceil.o s_cos.o s_erf.o s_fabs.o s_floor.o s_frexp.o s_isnan.o \ +s_ldexp.o s_signif.o s_sin.o s_tan.o s_tanh.o s_isinf.o s_infconst.o \ +kf_rem_pio2.o kf_cos.o kf_sin.o kf_tan.o ef_acos.o ef_acosh.o ef_asin.o \ +ef_atan2.o ef_atanh.o ef_cosh.o ef_exp.o ef_fmod.o erf_gamma.o \ +ef_hypot.o ef_j0.o ef_j1.o ef_jn.o erf_lgamma.o ef_log.o ef_log10.o \ +ef_pow.o ef_rem_pio2.o ef_remainder.o ef_scalb.o ef_sinh.o ef_sqrt.o \ +wf_acos.o wf_acosh.o wf_asin.o wf_atan2.o wf_atanh.o wf_cosh.o wf_exp.o \ +wf_fmod.o wf_gamma.o wrf_gamma.o wf_hypot.o wf_j0.o wf_j1.o wf_jn.o \ +wf_lgamma.o wrf_lgamma.o wf_log.o wf_log10.o wf_pow.o wf_remainder.o \ +wf_scalb.o wf_sinh.o wf_sqrt.o wf_cabs.o wf_drem.o sf_asinh.o sf_atan.o \ +sf_ceil.o sf_cos.o sf_erf.o sf_fabs.o sf_floor.o sf_frexp.o sf_isnan.o \ +sf_ldexp.o sf_signif.o sf_sin.o sf_tan.o sf_tanh.o sf_isinf.o +CFLAGS = @CFLAGS@ +COMPILE = $(CC) $(DEFS) $(INCLUDES) $(AM_CPPFLAGS) $(CPPFLAGS) $(AM_CFLAGS) $(CFLAGS) +LINK = $(CC) $(AM_CFLAGS) $(CFLAGS) $(LDFLAGS) -o $@ +DIST_COMMON = Makefile.am Makefile.in + + +DISTFILES = $(DIST_COMMON) $(SOURCES) $(HEADERS) $(TEXINFOS) $(EXTRA_DIST) + +TAR = tar +GZIP = --best +SOURCES = $(lib_a_SOURCES) +OBJECTS = $(lib_a_OBJECTS) + +all: Makefile $(LIBRARIES) + +.SUFFIXES: +.SUFFIXES: .S .c .def .o .s +$(srcdir)/Makefile.in: @MAINT@ Makefile.am $(top_srcdir)/configure.in $(ACLOCAL_M4) + cd $(top_srcdir) && $(AUTOMAKE) --cygnus math/Makefile + +Makefile: $(srcdir)/Makefile.in $(top_builddir)/config.status + cd $(top_builddir) \ + && CONFIG_FILES=$(subdir)/$@ CONFIG_HEADERS= $(SHELL) ./config.status + + +mostlyclean-noinstLIBRARIES: + +clean-noinstLIBRARIES: + -test -z "$(noinst_LIBRARIES)" || rm -f $(noinst_LIBRARIES) + +distclean-noinstLIBRARIES: + +maintainer-clean-noinstLIBRARIES: + +.c.o: + $(COMPILE) -c $< + +.s.o: + $(COMPILE) -c $< + +.S.o: + $(COMPILE) -c $< + +mostlyclean-compile: + -rm -f *.o core *.core + +clean-compile: + +distclean-compile: + -rm -f *.tab.c + +maintainer-clean-compile: + +lib.a: $(lib_a_OBJECTS) $(lib_a_DEPENDENCIES) + -rm -f lib.a + $(AR) cru lib.a $(lib_a_OBJECTS) $(lib_a_LIBADD) + $(RANLIB) lib.a + +tags: TAGS + +ID: $(HEADERS) $(SOURCES) $(LISP) + here=`pwd` && cd $(srcdir) \ + && mkid -f$$here/ID $(SOURCES) $(HEADERS) $(LISP) + +TAGS: $(HEADERS) $(SOURCES) $(TAGS_DEPENDENCIES) $(LISP) + tags=; \ + here=`pwd`; \ + list='$(SOURCES) $(HEADERS)'; \ + unique=`for i in $$list; do echo $$i; done | \ + awk ' { files[$$0] = 1; } \ + END { for (i in files) print i; }'`; \ + test -z "$(ETAGS_ARGS)$$unique$(LISP)$$tags" \ + || (cd $(srcdir) && etags $(ETAGS_ARGS) $$tags $$unique $(LISP) -o $$here/TAGS) + +mostlyclean-tags: + +clean-tags: + +distclean-tags: + -rm -f TAGS ID + +maintainer-clean-tags: + +distdir = $(top_builddir)/$(PACKAGE)-$(VERSION)/$(subdir) + +subdir = math + +distdir: $(DISTFILES) + @for file in $(DISTFILES); do \ + if test -f $$file; then d=.; else d=$(srcdir); fi; \ + test -f $(distdir)/$$file \ + || ln $$d/$$file $(distdir)/$$file 2> /dev/null \ + || cp -p $$d/$$file $(distdir)/$$file; \ + done +info: +dvi: +check: +installcheck: +install-info: +install-exec: + @$(NORMAL_INSTALL) + +install-data: + @$(NORMAL_INSTALL) + +install: install-exec install-data all + @: + +uninstall: + +install-strip: + $(MAKE) $(AM_MAKEFLAGS) INSTALL_PROGRAM='$(INSTALL_PROGRAM) -s' INSTALL_SCRIPT='$(INSTALL_PROGRAM)' install +installdirs: + + +mostlyclean-generic: + +clean-generic: + -test -z "$(CLEANFILES)" || rm -f $(CLEANFILES) + +distclean-generic: + -rm -f Makefile $(CONFIG_CLEAN_FILES) + -rm -f config.cache config.log stamp-h stamp-h[0-9]* + +maintainer-clean-generic: +mostlyclean: mostlyclean-noinstLIBRARIES mostlyclean-compile \ + mostlyclean-tags mostlyclean-generic + +clean: clean-noinstLIBRARIES clean-compile clean-tags clean-generic \ + mostlyclean + +distclean: distclean-noinstLIBRARIES distclean-compile distclean-tags \ + distclean-generic clean + -rm -f config.status + +maintainer-clean: maintainer-clean-noinstLIBRARIES \ + maintainer-clean-compile maintainer-clean-tags \ + maintainer-clean-generic distclean + @echo "This command is intended for maintainers to use;" + @echo "it deletes files that may require special tools to rebuild." + +.PHONY: mostlyclean-noinstLIBRARIES distclean-noinstLIBRARIES \ +clean-noinstLIBRARIES maintainer-clean-noinstLIBRARIES \ +mostlyclean-compile distclean-compile clean-compile \ +maintainer-clean-compile tags mostlyclean-tags distclean-tags \ +clean-tags maintainer-clean-tags distdir info dvi installcheck \ +install-info install-exec install-data install uninstall all \ +installdirs mostlyclean-generic distclean-generic clean-generic \ +maintainer-clean-generic clean mostlyclean distclean maintainer-clean + + +.c.def: + $(CHEW) < $< > $*.def 2> $*.ref + touch stmp-def + +doc: $(chobj) + cat $(srcdir)/math.tex >> $(TARGETDOC) + +# Texinfo does not appear to support underscores in file names, so we +# name the .def files without underscores. + +wacos.def: w_acos.c + $(CHEW) < $(srcdir)/w_acos.c >$@ 2>/dev/null + touch stmp-def +wacosh.def: w_acosh.c + $(CHEW) < $(srcdir)/w_acosh.c >$@ 2>/dev/null + touch stmp-def +wasin.def: w_asin.c + $(CHEW) < $(srcdir)/w_asin.c >$@ 2>/dev/null + touch stmp-def +sasinh.def: s_asinh.c + $(CHEW) < $(srcdir)/s_asinh.c >$@ 2>/dev/null + touch stmp-def +satan.def: s_atan.c + $(CHEW) < $(srcdir)/s_atan.c >$@ 2>/dev/null + touch stmp-def +watan2.def: w_atan2.c + $(CHEW) < $(srcdir)/w_atan2.c >$@ 2>/dev/null + touch stmp-def +watanh.def: w_atanh.c + $(CHEW) < $(srcdir)/w_atanh.c >$@ 2>/dev/null + touch stmp-def +wj0.def: w_j0.c + $(CHEW) < $(srcdir)/w_j0.c >$@ 2>/dev/null + touch stmp-def +scopysign.def: s_copysign.c + $(CHEW) < $(srcdir)/../common/s_copysign.c >$@ 2>/dev/null + touch stmp-def +wcosh.def: w_cosh.c + $(CHEW) < $(srcdir)/w_cosh.c >$@ 2>/dev/null + touch stmp-def +serf.def: s_erf.c + $(CHEW) < $(srcdir)/s_erf.c >$@ 2>/dev/null + touch stmp-def +wexp.def: w_exp.c + $(CHEW) < $(srcdir)/w_exp.c >$@ 2>/dev/null + touch stmp-def +sfabs.def: s_fabs.c + $(CHEW) < $(srcdir)/s_fabs.c >$@ 2>/dev/null + touch stmp-def +sfloor.def: s_floor.c + $(CHEW) < $(srcdir)/s_floor.c >$@ 2>/dev/null + touch stmp-def +wfmod.def: w_fmod.c + $(CHEW) < $(srcdir)/w_fmod.c >$@ 2>/dev/null + touch stmp-def +sfrexp.def: s_frexp.c + $(CHEW) < $(srcdir)/s_frexp.c >$@ 2>/dev/null + touch stmp-def +wgamma.def: w_gamma.c + $(CHEW) < $(srcdir)/w_gamma.c >$@ 2>/dev/null + touch stmp-def +whypot.def: w_hypot.c + $(CHEW) < $(srcdir)/w_hypot.c >$@ 2>/dev/null + touch stmp-def +sldexp.def: s_ldexp.c + $(CHEW) < $(srcdir)/s_ldexp.c >$@ 2>/dev/null + touch stmp-def +wlog.def: w_log.c + $(CHEW) < $(srcdir)/w_log.c >$@ 2>/dev/null + touch stmp-def +wlog10.def: w_log10.c + $(CHEW) < $(srcdir)/w_log10.c >$@ 2>/dev/null + touch stmp-def +wpow.def: w_pow.c + $(CHEW) < $(srcdir)/w_pow.c >$@ 2>/dev/null + touch stmp-def +wremainder.def: w_remainder.c + $(CHEW) < $(srcdir)/w_remainder.c >$@ 2>/dev/null + touch stmp-def +ssin.def: s_sin.c + $(CHEW) < $(srcdir)/s_sin.c >$@ 2>/dev/null + touch stmp-def +wsinh.def: w_sinh.c + $(CHEW) < $(srcdir)/w_sinh.c >$@ 2>/dev/null + touch stmp-def +wsqrt.def: w_sqrt.c + $(CHEW) < $(srcdir)/w_sqrt.c >$@ 2>/dev/null + touch stmp-def +stan.def: s_tan.c + $(CHEW) < $(srcdir)/s_tan.c >$@ 2>/dev/null + touch stmp-def +stanh.def: s_tanh.c + $(CHEW) < $(srcdir)/s_tanh.c >$@ 2>/dev/null + touch stmp-def +sisnan.def: s_isnan.c + $(CHEW) < $(srcdir)/s_isnan.c >$@ 2>/dev/null + touch stmp-def + +# A partial dependency list. + +$(lib_a_OBJECTS): $(srcdir)/../../libc/include/math.h $(srcdir)/../common/fdlibm.h + +# Tell versions [3.59,3.63) of GNU make to not export all variables. +# Otherwise a system limit (for SysV at least) may be exceeded. +.NOEXPORT: diff --git a/newlib/libm/math/e_acos.c b/newlib/libm/math/e_acos.c new file mode 100644 index 00000000000..319b1d56fa0 --- /dev/null +++ b/newlib/libm/math/e_acos.c @@ -0,0 +1,111 @@ + +/* @(#)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) */ diff --git a/newlib/libm/math/e_acosh.c b/newlib/libm/math/e_acosh.c new file mode 100644 index 00000000000..27984eb23ef --- /dev/null +++ b/newlib/libm/math/e_acosh.c @@ -0,0 +1,70 @@ + +/* @(#)e_acosh.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_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +#ifdef __STDC__ + double __ieee754_acosh(double x) +#else + double __ieee754_acosh(x) + double x; +#endif +{ + double t; + __int32_t hx; + __uint32_t lx; + EXTRACT_WORDS(hx,lx,x); + if(hx<0x3ff00000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x41b00000) { /* x > 2**28 */ + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return log1p(t+__ieee754_sqrt(2.0*t+t*t)); + } +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_asin.c b/newlib/libm/math/e_asin.c new file mode 100644 index 00000000000..559f2884a26 --- /dev/null +++ b/newlib/libm/math/e_asin.c @@ -0,0 +1,120 @@ + +/* @(#)e_asin.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_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * where + * R(x^2) is a rational approximation of (asin(x)-x)/x^3 + * and its remez error is bounded by + * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) + * + * For x in [0.5,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +huge = 1.000e+300, +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ + /* coefficient for R(x^2) */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +#ifdef __STDC__ + double __ieee754_asin(double x) +#else + double __ieee754_asin(x) + double x; +#endif +{ + double t,w,p,q,c,r,s; + __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) + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3fe00000) { /* |x|<0.5 */ + if(ix<0x3e400000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabs(x); + t = w*0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = __ieee754_sqrt(t); + if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + w = s; + SET_LOW_WORD(w,0); + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_atan2.c b/newlib/libm/math/e_atan2.c new file mode 100644 index 00000000000..268be64a9ff --- /dev/null +++ b/newlib/libm/math/e_atan2.c @@ -0,0 +1,131 @@ + +/* @(#)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) */ diff --git a/newlib/libm/math/e_atanh.c b/newlib/libm/math/e_atanh.c new file mode 100644 index 00000000000..58ad325f9ad --- /dev/null +++ b/newlib/libm/math/e_atanh.c @@ -0,0 +1,75 @@ + +/* @(#)e_atanh.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_atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double one = 1.0, huge = 1e300; +#else +static double one = 1.0, huge = 1e300; +#endif + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_atanh(double x) +#else + double __ieee754_atanh(x) + double x; +#endif +{ + double t; + __int32_t hx,ix; + __uint32_t lx; + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3ff00000) + return x/zero; + if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_HIGH_WORD(x,ix); + if(ix<0x3fe00000) { /* x < 0.5 */ + t = x+x; + t = 0.5*log1p(t+t*x/(one-x)); + } else + t = 0.5*log1p((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_cosh.c b/newlib/libm/math/e_cosh.c new file mode 100644 index 00000000000..54ca1fb95de --- /dev/null +++ b/newlib/libm/math/e_cosh.c @@ -0,0 +1,93 @@ + +/* @(#)e_cosh.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_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double one = 1.0, half=0.5, huge = 1.0e300; +#else +static double one = 1.0, half=0.5, huge = 1.0e300; +#endif + +#ifdef __STDC__ + double __ieee754_cosh(double x) +#else + double __ieee754_cosh(x) + double x; +#endif +{ + double t,w; + __int32_t ix; + __uint32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e43) { + t = expm1(fabs(x)); + w = one+t; + if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x40360000) { + t = __ieee754_exp(fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633CE || + (ix==0x408633ce)&&(lx<=(__uint32_t)0x8fb9f87d)) { + w = __ieee754_exp(half*fabs(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_exp.c b/newlib/libm/math/e_exp.c new file mode 100644 index 00000000000..ce093c61065 --- /dev/null +++ b/newlib/libm/math/e_exp.c @@ -0,0 +1,167 @@ + +/* @(#)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; + } +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_fmod.c b/newlib/libm/math/e_fmod.c new file mode 100644 index 00000000000..f9739eec25d --- /dev/null +++ b/newlib/libm/math/e_fmod.c @@ -0,0 +1,140 @@ + +/* @(#)e_fmod.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_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) */ diff --git a/newlib/libm/math/e_hypot.c b/newlib/libm/math/e_hypot.c new file mode 100644 index 00000000000..03f7f51e5f7 --- /dev/null +++ b/newlib/libm/math/e_hypot.c @@ -0,0 +1,128 @@ + +/* @(#)e_hypot.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_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double __ieee754_hypot(double x, double y) +#else + double __ieee754_hypot(x,y) + double x, y; +#endif +{ + double a=x,b=y,t1,t2,y1,y2,w; + __int32_t j,k,ha,hb; + + GET_HIGH_WORD(ha,x); + ha &= 0x7fffffff; + GET_HIGH_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_HIGH_WORD(a,ha); /* a <- |a| */ + SET_HIGH_WORD(b,hb); /* b <- |b| */ + if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ + k=0; + if(ha > 0x5f300000) { /* a>2**500 */ + if(ha >= 0x7ff00000) { /* Inf or NaN */ + __uint32_t low; + w = a+b; /* for sNaN */ + GET_LOW_WORD(low,a); + if(((ha&0xfffff)|low)==0) w = a; + GET_LOW_WORD(low,b); + if(((hb^0x7ff00000)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + if(hb < 0x20b00000) { /* b < 2**-500 */ + if(hb <= 0x000fffff) { /* subnormal b or 0 */ + __uint32_t low; + GET_LOW_WORD(low,b); + if((hb|low)==0) return a; + t1=0; + SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + } else { /* scale a and b by 2^600 */ + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_HIGH_WORD(t1,ha); + t2 = a-t1; + w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + y1 = 0; + SET_HIGH_WORD(y1,hb); + y2 = b - y1; + t1 = 0; + SET_HIGH_WORD(t1,ha+0x00100000); + t2 = a - t1; + w = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + __uint32_t high; + t1 = 1.0; + GET_HIGH_WORD(high,t1); + SET_HIGH_WORD(t1,high+(k<<20)); + return t1*w; + } else return w; +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_j0.c b/newlib/libm/math/e_j0.c new file mode 100644 index 00000000000..43ea389825f --- /dev/null +++ b/newlib/libm/math/e_j0.c @@ -0,0 +1,487 @@ + +/* @(#)e_j0.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_j0(x), __ieee754_y0(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; + * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/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 + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * where + * U(z) = u00 + u01*z + ... + u06*z^6 + * V(z) = 1 + v01*z + ... + v04*z^4 + * with absolute approximation error bounded by 2**-72. + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static double pzero(double), qzero(double); +#else +static double pzero(), qzero(); +#endif + +#ifdef __STDC__ +static const double +#else +static double +#endif +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ +R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ +R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ +R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ +S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ +S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ +S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ +S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_j0(double x) +#else + double __ieee754_j0(x) + double x; +#endif +{ + double z, s,c,ss,cc,r,u,v; + __int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/(x*x); + x = fabs(x); + 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; + } + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(x); + } + return z; + } + if(ix<0x3f200000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x3e400000) return one; /* |x|<2**-27 */ + else return one - 0.25*x*x; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3FF00000) { /* |x| < 1.00 */ + return one + z*(-0.25+(r/s)); + } else { + u = 0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +#ifdef __STDC__ +static const double +#else +static double +#endif +u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ +u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ +u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ +u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ +u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ +u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ +u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ +v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ +v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ +v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ +v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ + +#ifdef __STDC__ + double __ieee754_y0(double x) +#else + double __ieee754_y0(x) + double x; +#endif +{ + double z, s,c,ss,cc,u,v; + __int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = 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. + */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x); + } + return z; + } + if(ix<=0x3e400000) { /* x < 2**-27 */ + return(u00 + tpi*__ieee754_log(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +#ifdef __STDC__ +static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ + -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ + -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ + -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ + -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ +}; +#ifdef __STDC__ +static const double pS8[5] = { +#else +static double pS8[5] = { +#endif + 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ + 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ + 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ + 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ + 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ +}; + +#ifdef __STDC__ +static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ + -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ + -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ + -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ + -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ + -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ +}; +#ifdef __STDC__ +static const double pS5[5] = { +#else +static double pS5[5] = { +#endif + 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ + 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ + 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ + 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ + 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ +}; + +#ifdef __STDC__ +static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ + -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ + -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ + -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ + -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ + -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ +}; +#ifdef __STDC__ +static const double pS3[5] = { +#else +static double pS3[5] = { +#endif + 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ + 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ + 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ + 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ + 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ +}; + +#ifdef __STDC__ +static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ + -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ + -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ + -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ + -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ + -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ +}; +#ifdef __STDC__ +static const double pS2[5] = { +#else +static double pS2[5] = { +#endif + 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ + 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ + 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ + 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ + 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ +}; + +#ifdef __STDC__ + static double pzero(double x) +#else + static double pzero(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p,*q; +#else + double *p,*q; +#endif + double z,r,s; + __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 if(ix>=0x40000000){p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +#ifdef __STDC__ +static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ + 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ + 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ + 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ + 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ +}; +#ifdef __STDC__ +static const double qS8[6] = { +#else +static double qS8[6] = { +#endif + 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ + 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ + 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ + 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ + 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ + -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ +}; + +#ifdef __STDC__ +static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ + 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ + 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ + 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ + 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ + 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ +}; +#ifdef __STDC__ +static const double qS5[6] = { +#else +static double qS5[6] = { +#endif + 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ + 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ + 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ + 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ + 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ + -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ +}; + +#ifdef __STDC__ +static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ + 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ + 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ + 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ + 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ + 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ +}; +#ifdef __STDC__ +static const double qS3[6] = { +#else +static double qS3[6] = { +#endif + 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ + 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ + 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ + 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ + 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ + -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ +}; + +#ifdef __STDC__ +static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ + 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ + 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ + 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ + 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ + 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ +}; +#ifdef __STDC__ +static const double qS2[6] = { +#else +static double qS2[6] = { +#endif + 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ + 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ + 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ + 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ + 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ + -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ +}; + +#ifdef __STDC__ + static double qzero(double x) +#else + static double qzero(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p,*q; +#else + double *p,*q; +#endif + double s,r,z; + __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 if(ix>=0x40000000){p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-.125 + r/s)/x; +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_j1.c b/newlib/libm/math/e_j1.c new file mode 100644 index 00000000000..feaa732debf --- /dev/null +++ b/newlib/libm/math/e_j1.c @@ -0,0 +1,486 @@ + +/* @(#)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. + * ==================================================== + */ + +/* __ieee754_j1(x), __ieee754_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 __ieee754_j1(double x) +#else + double __ieee754_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/__ieee754_sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / __ieee754_sqrt(x) + * y1(x) = 1/__ieee754_sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / __ieee754_sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y); + else { + u = pone(y); v = qone(y); + z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x3e400000) { /* |x|<2**-27 */ + if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*0.5+r/s); +} + +#ifdef __STDC__ +static const double U0[5] = { +#else +static double U0[5] = { +#endif + -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ + 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ + -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ + 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ + -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ +}; +#ifdef __STDC__ +static const double V0[5] = { +#else +static double V0[5] = { +#endif + 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ + 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ + 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ + 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ + 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ +}; + +#ifdef __STDC__ + double __ieee754_y1(double x) +#else + double __ieee754_y1(x) + double x; +#endif +{ + double z, s,c,ss,cc,u,v; + __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)/__ieee754_sqrt(x); + else { + u = pone(x); v = qone(x); + z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x); + } + return z; + } + if(ix<=0x3c900000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +#ifdef __STDC__ +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ + 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ + 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ + 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ + 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ +}; +#ifdef __STDC__ +static const double ps8[5] = { +#else +static double ps8[5] = { +#endif + 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ + 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ + 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ + 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ + 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ +}; + +#ifdef __STDC__ +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ + 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ + 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ + 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ + 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ + 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ +}; +#ifdef __STDC__ +static const double ps5[5] = { +#else +static double ps5[5] = { +#endif + 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ + 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ + 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ + 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ + 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ +}; + +#ifdef __STDC__ +static const double pr3[6] = { +#else +static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ + 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ + 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ + 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ + 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ + 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ +}; +#ifdef __STDC__ +static const double ps3[5] = { +#else +static double ps3[5] = { +#endif + 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ + 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ + 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ + 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ + 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ +}; + +#ifdef __STDC__ +static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ + 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ + 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ + 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ + 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ + 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ +}; +#ifdef __STDC__ +static const double ps2[5] = { +#else +static double ps2[5] = { +#endif + 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ + 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ + 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ + 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ + 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ +}; + +#ifdef __STDC__ + static double pone(double x) +#else + static double pone(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p,*q; +#else + double *p,*q; +#endif + double z,r,s; + __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 if(ix>=0x40000000){p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +#ifdef __STDC__ +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ + -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ + -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ + -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ + -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ +}; +#ifdef __STDC__ +static const double qs8[6] = { +#else +static double qs8[6] = { +#endif + 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ + 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ + 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ + 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ + 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ + -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ +}; + +#ifdef __STDC__ +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ + -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ + -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ + -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ + -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ + -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ +}; +#ifdef __STDC__ +static const double qs5[6] = { +#else +static double qs5[6] = { +#endif + 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ + 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ + 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ + 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ + 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ + -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ +}; + +#ifdef __STDC__ +static const double qr3[6] = { +#else +static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ + -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ + -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ + -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ + -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ + -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ +}; +#ifdef __STDC__ +static const double qs3[6] = { +#else +static double qs3[6] = { +#endif + 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ + 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ + 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ + 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ + 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ + -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ +}; + +#ifdef __STDC__ +static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ + -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ + -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ + -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ + -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ + -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ +}; +#ifdef __STDC__ +static const double qs2[6] = { +#else +static double qs2[6] = { +#endif + 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ + 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ + 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ + 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ + 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ + -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ +}; + +#ifdef __STDC__ + static double qone(double x) +#else + static double qone(x) + double x; +#endif +{ +#ifdef __STDC__ + const double *p,*q; +#else + double *p,*q; +#endif + double s,r,z; + __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 if(ix>=0x40000000){p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (.375 + r/s)/x; +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_jn.c b/newlib/libm/math/e_jn.c new file mode 100644 index 00000000000..1eea27be038 --- /dev/null +++ b/newlib/libm/math/e_jn.c @@ -0,0 +1,281 @@ + +/* @(#)e_jn.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_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for n<x, forward recursion us used starting + * from values of j0(x) and j1(x). + * for n>x, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ +one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ + +#ifdef __STDC__ +static const double zero = 0.00000000000000000000e+00; +#else +static double zero = 0.00000000000000000000e+00; +#endif + +#ifdef __STDC__ + double __ieee754_jn(int n, double x) +#else + double __ieee754_jn(n,x) + int n; double x; +#endif +{ + __int32_t i,hx,ix,lx, sgn; + double a, b, temp, di; + double z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if((ix|((__uint32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0(x)); + if(n==1) return(__ieee754_j1(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabs(x); + if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ + b = zero; + else if((double)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = cos(x)+sin(x); break; + case 1: temp = -cos(x)+sin(x); break; + case 2: temp = -cos(x)-sin(x); break; + case 3: temp = cos(x)-sin(x); break; + } + b = invsqrtpi*temp/__ieee754_sqrt(x); + } else { + a = __ieee754_j0(x); + b = __ieee754_j1(x); + for(i=1;i<n;i++){ + temp = b; + b = b*((double)(i+i)/x) - a; /* avoid underflow */ + a = temp; + } + } + } else { + if(ix<0x3e100000) { /* x < 2**-29 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if(n>33) /* underflow */ + b = zero; + else { + temp = x*0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (double)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + double t,v; + double q0,q1,h,tmp; __int32_t k,m; + w = (n+n)/(double)x; h = 2.0/(double)x; + q0 = w; z = w+h; q1 = w*z - 1.0; k=1; + while(q1<1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_log(fabs(v*tmp)); + if(tmp<7.09782712893383973096e+02) { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>1e100) { + a /= b; + t /= b; + b = one; + } + } + } + b = (t*__ieee754_j0(x)/b); + } + } + if(sgn==1) return -b; else return b; +} + +#ifdef __STDC__ + double __ieee754_yn(int n, double x) +#else + double __ieee754_yn(n,x) + int n; double x; +#endif +{ + __int32_t i,hx,ix,lx; + __int32_t sign; + double a, b, temp; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if((ix|((__uint32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0(x)); + if(n==1) return(sign*__ieee754_y1(x)); + if(ix==0x7ff00000) return zero; + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = sin(x)-cos(x); break; + case 1: temp = -sin(x)-cos(x); break; + case 2: temp = -sin(x)+cos(x); break; + case 3: temp = sin(x)+cos(x); break; + } + b = invsqrtpi*temp/__ieee754_sqrt(x); + } else { + __uint32_t high; + a = __ieee754_y0(x); + b = __ieee754_y1(x); + /* quit if b is -inf */ + GET_HIGH_WORD(high,b); + for(i=1;i<n&&high!=0xfff00000;i++){ + temp = b; + b = ((double)(i+i)/x)*b - a; + GET_HIGH_WORD(high,b); + a = temp; + } + } + if(sign>0) return b; else return -b; +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_log.c b/newlib/libm/math/e_log.c new file mode 100644 index 00000000000..774ca389f74 --- /dev/null +++ b/newlib/libm/math/e_log.c @@ -0,0 +1,146 @@ + +/* @(#)e_log.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_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); + } +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_log10.c b/newlib/libm/math/e_log10.c new file mode 100644 index 00000000000..f7daaa1b264 --- /dev/null +++ b/newlib/libm/math/e_log10.c @@ -0,0 +1,98 @@ + +/* @(#)e_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ +log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ +log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +#ifdef __STDC__ +static const double zero = 0.0; +#else +static double zero = 0.0; +#endif + +#ifdef __STDC__ + double __ieee754_log10(double x) +#else + double __ieee754_log10(x) + double x; +#endif +{ + double y,z; + __int32_t i,k,hx; + __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; + i = ((__uint32_t)k&0x80000000)>>31; + hx = (hx&0x000fffff)|((0x3ff-i)<<20); + y = (double)(k+i); + SET_HIGH_WORD(x,hx); + z = y*log10_2lo + ivln10*__ieee754_log(x); + return z+y*log10_2hi; +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_pow.c b/newlib/libm/math/e_pow.c new file mode 100644 index 00000000000..9312085d4a6 --- /dev/null +++ b/newlib/libm/math/e_pow.c @@ -0,0 +1,312 @@ + +/* @(#)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((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; + } + } + + /* (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; + } + /* 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); + + /* 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); + } + + 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) */ diff --git a/newlib/libm/math/e_rem_pio2.c b/newlib/libm/math/e_rem_pio2.c new file mode 100644 index 00000000000..3e5d0f7a227 --- /dev/null +++ b/newlib/libm/math/e_rem_pio2.c @@ -0,0 +1,185 @@ + +/* @(#)e_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* __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) */ diff --git a/newlib/libm/math/e_remainder.c b/newlib/libm/math/e_remainder.c new file mode 100644 index 00000000000..ae7ce649ad5 --- /dev/null +++ b/newlib/libm/math/e_remainder.c @@ -0,0 +1,80 @@ + +/* @(#)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) */ diff --git a/newlib/libm/math/e_scalb.c b/newlib/libm/math/e_scalb.c new file mode 100644 index 00000000000..0bb924b43ee --- /dev/null +++ b/newlib/libm/math/e_scalb.c @@ -0,0 +1,55 @@ + +/* @(#)e_scalb.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_scalb(x, fn) is provide for + * passing various standard test suite. One + * should use scalbn() instead. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef _SCALB_INT +#ifdef __STDC__ + double __ieee754_scalb(double x, int fn) +#else + double __ieee754_scalb(x,fn) + double x; int fn; +#endif +#else +#ifdef __STDC__ + double __ieee754_scalb(double x, double fn) +#else + double __ieee754_scalb(x,fn) + double x, fn; +#endif +#endif +{ +#ifdef _SCALB_INT + return scalbn(x,fn); +#else + if (isnan(x)||isnan(fn)) return x*fn; + if (!finite(fn)) { + if(fn>0.0) return x*fn; + else return x/(-fn); + } + if (rint(fn)!=fn) return (fn-fn)/(fn-fn); + if ( fn > 65000.0) return scalbn(x, 65000); + if (-fn > 65000.0) return scalbn(x,-65000); + return scalbn(x,(int)fn); +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_sinh.c b/newlib/libm/math/e_sinh.c new file mode 100644 index 00000000000..fd953ddaaed --- /dev/null +++ b/newlib/libm/math/e_sinh.c @@ -0,0 +1,86 @@ + +/* @(#)e_sinh.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_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double one = 1.0, shuge = 1.0e307; +#else +static double one = 1.0, shuge = 1.0e307; +#endif + +#ifdef __STDC__ + double __ieee754_sinh(double x) +#else + double __ieee754_sinh(x) + double x; +#endif +{ + double t,w,h; + __int32_t ix,jx; + __uint32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3e300000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1(fabs(x)); + if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633CE || (ix==0x408633ce)&&(lx<=(__uint32_t)0x8fb9f87d)) { + w = __ieee754_exp(0.5*fabs(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/e_sqrt.c b/newlib/libm/math/e_sqrt.c new file mode 100644 index 00000000000..460125a8fda --- /dev/null +++ b/newlib/libm/math/e_sqrt.c @@ -0,0 +1,452 @@ + +/* @(#)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 + * + * The advantage of (3) is that s and y can be computed by + * i i + * the following recurrence formula: + * if (3) is false + * + * s = s , y = y ; (4) + * i+1 i i+1 i + * + * otherwise, + * -i -(i+1) + * s = s + 2 , y = y - s - 2 (5) + * i+1 i i+1 i i + * + * One may easily use induction to prove (4) and (5). + * Note. Since the left hand side of (3) contain only i+2 bits, + * it does not necessary to do a full (53-bit) comparison + * in (3). + * 3. Final rounding + * After generating the 53 bits result, we compute one more bit. + * Together with the remainder, we can decide whether the + * result is exact, bigger than 1/2ulp, or less than 1/2ulp + * (it will never equal to 1/2ulp). + * The rounding mode can be detected by checking whether + * huge + tiny is equal to huge, and whether huge - tiny is + * equal to huge for some floating point number "huge" and "tiny". + * + * Special cases: + * sqrt(+-0) = +-0 ... exact + * sqrt(inf) = inf + * sqrt(-ve) = NaN ... with invalid signal + * sqrt(NaN) = NaN ... with invalid signal for signaling NaN + * + * Other methods : see the appended file at the end of the program below. + *--------------- + */ + +#include "fdlibm.h" + +#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)==sign)&&(s1&sign)==0) s0 += 1; + 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); + } + } + 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 + 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 + + 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: + + ------------------------------------------------- + bit 27,26 of z1 bit 1,0 of x1 logb(x) + ------------------------------------------------- + 00 00 odd and even + 01 01 even + 10 10 odd + 10 00 even + 11 01 even + ------------------------------------------------- + + (4) Special cases (see (4) of Section A). + + */ diff --git a/newlib/libm/math/ef_acos.c b/newlib/libm/math/ef_acos.c new file mode 100644 index 00000000000..f73f97de75a --- /dev/null +++ b/newlib/libm/math/ef_acos.c @@ -0,0 +1,84 @@ +/* ef_acos.c -- float version of e_acos.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 +one = 1.0000000000e+00, /* 0x3F800000 */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +#ifdef __STDC__ + float __ieee754_acosf(float x) +#else + float __ieee754_acosf(x) + float x; +#endif +{ + float z,p,q,r,w,s,c,df; + __int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ + } else if(ix>0x3f800000) { /* |x| >= 1 */ + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3f000000) { /* |x| < 0.5 */ + if(ix<=0x23000000) 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)*(float)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_sqrtf(z); + r = p/q; + w = r*s-pio2_lo; + return pi - (float)2.0*(s+w); + } else { /* x > 0.5 */ + __int32_t idf; + z = (one-x)*(float)0.5; + s = __ieee754_sqrtf(z); + df = s; + GET_FLOAT_WORD(idf,df); + SET_FLOAT_WORD(df,idf&0xfffff000); + 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 (float)2.0*(df+w); + } +} diff --git a/newlib/libm/math/ef_acosh.c b/newlib/libm/math/ef_acosh.c new file mode 100644 index 00000000000..37c788576ef --- /dev/null +++ b/newlib/libm/math/ef_acosh.c @@ -0,0 +1,53 @@ +/* ef_acosh.c -- float version of e_acosh.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 +one = 1.0, +ln2 = 6.9314718246e-01; /* 0x3f317218 */ + +#ifdef __STDC__ + float __ieee754_acoshf(float x) +#else + float __ieee754_acoshf(x) + float x; +#endif +{ + float t; + __int32_t hx; + GET_FLOAT_WORD(hx,x); + if(hx<0x3f800000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4d800000) { /* x > 2**28 */ + if(hx >=0x7f800000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */ + } else if (hx==0x3f800000) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one))); + } else { /* 1<x<2 */ + t = x-one; + return log1pf(t+__ieee754_sqrtf((float)2.0*t+t*t)); + } +} diff --git a/newlib/libm/math/ef_asin.c b/newlib/libm/math/ef_asin.c new file mode 100644 index 00000000000..bbe210b7cbd --- /dev/null +++ b/newlib/libm/math/ef_asin.c @@ -0,0 +1,87 @@ +/* ef_asin.c -- float version of e_asin.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 +one = 1.0000000000e+00, /* 0x3F800000 */ +huge = 1.000e+30, +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */ + /* coefficient for R(x^2) */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +#ifdef __STDC__ + float __ieee754_asinf(float x) +#else + float __ieee754_asinf(x) + float x; +#endif +{ + float t,w,p,q,c,r,s; + __int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + } else if(ix> 0x3f800000) { /* |x|>= 1 */ + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3f000000) { /* |x|<0.5 */ + if(ix<0x32000000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabsf(x); + t = w*(float)0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = __ieee754_sqrtf(t); + if(ix>=0x3F79999A) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo); + } else { + __int32_t iw; + w = s; + GET_FLOAT_WORD(iw,w); + SET_FLOAT_WORD(w,iw&0xfffff000); + c = (t-w*w)/(s+w); + r = p/q; + p = (float)2.0*s*r-(pio2_lo-(float)2.0*c); + q = pio4_hi-(float)2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff --git a/newlib/libm/math/ef_atan2.c b/newlib/libm/math/ef_atan2.c new file mode 100644 index 00000000000..25e86b3746c --- /dev/null +++ b/newlib/libm/math/ef_atan2.c @@ -0,0 +1,101 @@ +/* ef_atan2.c -- float version of e_atan2.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 +tiny = 1.0e-30, +zero = 0.0, +pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */ +pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pi_lo = 1.5099578832e-07; /* 0x34222168 */ + +#ifdef __STDC__ + float __ieee754_atan2f(float y, float x) +#else + float __ieee754_atan2f(y,x) + float y,x; +#endif +{ + float z; + __int32_t k,m,hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + GET_FLOAT_WORD(hy,y); + iy = hy&0x7fffffff; + if((ix>0x7f800000)|| + (iy>0x7f800000)) /* x or y is NaN */ + return x+y; + if(hx==0x3f800000) return atanf(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if(iy==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==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7f800000) { + if(iy==0x7f800000) { + 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 (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return (float)-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==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>23; + if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=atanf(fabsf(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + __uint32_t zh; + GET_FLOAT_WORD(zh,z); + SET_FLOAT_WORD(z,zh ^ 0x80000000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/newlib/libm/math/ef_atanh.c b/newlib/libm/math/ef_atanh.c new file mode 100644 index 00000000000..74b3d3d6a04 --- /dev/null +++ b/newlib/libm/math/ef_atanh.c @@ -0,0 +1,54 @@ +/* ef_atanh.c -- float version of e_atanh.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 one = 1.0, huge = 1e30; +#else +static float one = 1.0, huge = 1e30; +#endif + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_atanhf(float x) +#else + float __ieee754_atanhf(x) + float x; +#endif +{ + float t; + __int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if (ix>0x3f800000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3f800000) + return x/zero; + if(ix<0x31800000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_FLOAT_WORD(x,ix); + if(ix<0x3f000000) { /* x < 0.5 */ + t = x+x; + t = (float)0.5*log1pf(t+t*x/(one-x)); + } else + t = (float)0.5*log1pf((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff --git a/newlib/libm/math/ef_cosh.c b/newlib/libm/math/ef_cosh.c new file mode 100644 index 00000000000..68e59f88694 --- /dev/null +++ b/newlib/libm/math/ef_cosh.c @@ -0,0 +1,70 @@ +/* ef_cosh.c -- float version of e_cosh.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 __v810__ +#define const +#endif + +#ifdef __STDC__ +static const float one = 1.0, half=0.5, huge = 1.0e30; +#else +static float one = 1.0, half=0.5, huge = 1.0e30; +#endif + +#ifdef __STDC__ + float __ieee754_coshf(float x) +#else + float __ieee754_coshf(x) + float x; +#endif +{ + float t,w; + __int32_t ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3eb17218) { + t = expm1f(fabsf(x)); + w = one+t; + if (ix<0x24000000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x41b00000) { + t = __ieee754_expf(fabsf(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x42b17180) return half*__ieee754_expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = __ieee754_expf(half*fabsf(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/newlib/libm/math/ef_exp.c b/newlib/libm/math/ef_exp.c new file mode 100644 index 00000000000..04331a52a60 --- /dev/null +++ b/newlib/libm/math/ef_exp.c @@ -0,0 +1,102 @@ +/* ef_exp.c -- float version of e_exp.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 __v810__ +#define const +#endif + +#ifdef __STDC__ +static const float +#else +static float +#endif +one = 1.0, +halF[2] = {0.5,-0.5,}, +huge = 1.0e+30, +twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ +o_threshold= 8.8721679688e+01, /* 0x42b17180 */ +u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ +ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */ + -6.9313812256e-01,}, /* 0xbf317180 */ +ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */ + -9.0580006145e-06,}, /* 0xb717f7d1 */ +invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08; /* 0x3331bb4c */ + +#ifdef __STDC__ + float __ieee754_expf(float x) /* default IEEE double exp */ +#else + float __ieee754_expf(x) /* default IEEE double exp */ + float x; +#endif +{ + float y,hi,lo,c,t; + __int32_t k,xsb; + __uint32_t hx; + + GET_FLOAT_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom100*twom100; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* 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 < 0x31800000) { /* 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-(float)2.0)-x); + else y = one-((lo-(x*c)/((float)2.0-c))-hi); + if(k >= -125) { + __uint32_t hy; + GET_FLOAT_WORD(hy,y); + SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ + return y; + } else { + __uint32_t hy; + GET_FLOAT_WORD(hy,y); + SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ + return y*twom100; + } +} diff --git a/newlib/libm/math/ef_fmod.c b/newlib/libm/math/ef_fmod.c new file mode 100644 index 00000000000..d5d28e08ea7 --- /dev/null +++ b/newlib/libm/math/ef_fmod.c @@ -0,0 +1,108 @@ +/* ef_fmod.c -- float version of e_fmod.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. + * ==================================================== + */ + +/* + * __ieee754_fmodf(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const float one = 1.0, Zero[] = {0.0, -0.0,}; +#else +static float one = 1.0, Zero[] = {0.0, -0.0,}; +#endif + +#ifdef __STDC__ + float __ieee754_fmodf(float x, float y) +#else + float __ieee754_fmodf(x,y) + float x,y ; +#endif +{ + __int32_t n,hx,hy,hz,ix,iy,sx,i; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */ + (hy>0x7f800000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<hy) return x; /* |x|<|y| return x */ + if(hx==hy) + return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0*/ + + /* determine ix = ilogb(x) */ + if(hx<0x00800000) { /* subnormal x */ + for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; + } else ix = (hx>>23)-127; + + /* determine iy = ilogb(y) */ + if(hy<0x00800000) { /* subnormal y */ + for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1; + } else iy = (hy>>23)-127; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -126) + hx = 0x00800000|(0x007fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -126-ix; + hx = hx<<n; + } + if(iy >= -126) + hy = 0x00800000|(0x007fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -126-iy; + hy = hy<<n; + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy; + if(hz<0){hx = hx+hx;} + else { + if(hz==0) /* return sign(x)*0 */ + return Zero[(__uint32_t)sx>>31]; + hx = hz+hz; + } + } + hz=hx-hy; + if(hz>=0) {hx=hz;} + + /* convert back to floating value and restore the sign */ + if(hx==0) /* return sign(x)*0 */ + return Zero[(__uint32_t)sx>>31]; + while(hx<0x00800000) { /* normalize x */ + hx = hx+hx; + iy -= 1; + } + if(iy>= -126) { /* normalize output */ + hx = ((hx-0x00800000)|((iy+127)<<23)); + SET_FLOAT_WORD(x,hx|sx); + } else { /* subnormal output */ + n = -126 - iy; + hx >>= n; + SET_FLOAT_WORD(x,hx|sx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/newlib/libm/math/ef_hypot.c b/newlib/libm/math/ef_hypot.c new file mode 100644 index 00000000000..a87fa489ea7 --- /dev/null +++ b/newlib/libm/math/ef_hypot.c @@ -0,0 +1,82 @@ +/* ef_hypot.c -- float version of e_hypot.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__ + float __ieee754_hypotf(float x, float y) +#else + float __ieee754_hypotf(x,y) + float x, y; +#endif +{ + float a=x,b=y,t1,t2,y1,y2,w; + __int32_t j,k,ha,hb; + + GET_FLOAT_WORD(ha,x); + ha &= 0x7fffffffL; + GET_FLOAT_WORD(hb,y); + hb &= 0x7fffffffL; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_FLOAT_WORD(a,ha); /* a <- |a| */ + SET_FLOAT_WORD(b,hb); /* b <- |b| */ + if((ha-hb)>0xf000000L) {return a+b;} /* x/y > 2**30 */ + k=0; + if(ha > 0x58800000L) { /* a>2**50 */ + if(ha >= 0x7f800000L) { /* Inf or NaN */ + w = a+b; /* for sNaN */ + if(ha == 0x7f800000L) w = a; + if(hb == 0x7f800000L) w = b; + return w; + } + /* scale a and b by 2**-60 */ + ha -= 0x5d800000L; hb -= 0x5d800000L; k += 60; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + if(hb < 0x26800000L) { /* b < 2**-50 */ + if(hb <= 0x007fffffL) { /* subnormal b or 0 */ + if(hb==0) return a; + SET_FLOAT_WORD(t1,0x3f000000L); /* t1=2^126 */ + b *= t1; + a *= t1; + k -= 126; + } else { /* scale a and b by 2^60 */ + ha += 0x5d800000; /* a *= 2^60 */ + hb += 0x5d800000; /* b *= 2^60 */ + k -= 60; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + SET_FLOAT_WORD(t1,ha&0xfffff000L); + t2 = a-t1; + w = __ieee754_sqrtf(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + SET_FLOAT_WORD(y1,hb&0xfffff000L); + y2 = b - y1; + SET_FLOAT_WORD(t1,ha+0x00800000L); + t2 = a - t1; + w = __ieee754_sqrtf(t1*y1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + SET_FLOAT_WORD(t1,0x3f800000L+(k<<23)); + return t1*w; + } else return w; +} diff --git a/newlib/libm/math/ef_j0.c b/newlib/libm/math/ef_j0.c new file mode 100644 index 00000000000..5ae6f308f3a --- /dev/null +++ b/newlib/libm/math/ef_j0.c @@ -0,0 +1,439 @@ +/* ef_j0.c -- float version of e_j0.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 float pzerof(float), qzerof(float); +#else +static float pzerof(), qzerof(); +#endif + +#ifdef __STDC__ +static const float +#else +static float +#endif +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.5625000000e-02, /* 0x3c800000 */ +R03 = -1.8997929874e-04, /* 0xb947352e */ +R04 = 1.8295404516e-06, /* 0x35f58e88 */ +R05 = -4.6183270541e-09, /* 0xb19eaf3c */ +S01 = 1.5619102865e-02, /* 0x3c7fe744 */ +S02 = 1.1692678527e-04, /* 0x38f53697 */ +S03 = 5.1354652442e-07, /* 0x3509daa6 */ +S04 = 1.1661400734e-09; /* 0x30a045e8 */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_j0f(float x) +#else + float __ieee754_j0f(x) + float x; +#endif +{ + float z, s,c,ss,cc,r,u,v; + __int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/(x*x); + x = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(x); + c = cosf(x); + ss = s-c; + cc = s+c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -cosf(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix>0x80000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(x); + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(x); + } + return z; + } + if(ix<0x39000000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x32000000) return one; /* |x|<2**-27 */ + else return one - (float)0.25*x*x; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3F800000) { /* |x| < 1.00 */ + return one + z*((float)-0.25+(r/s)); + } else { + u = (float)0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +#ifdef __STDC__ +static const float +#else +static float +#endif +u00 = -7.3804296553e-02, /* 0xbd9726b5 */ +u01 = 1.7666645348e-01, /* 0x3e34e80d */ +u02 = -1.3818567619e-02, /* 0xbc626746 */ +u03 = 3.4745343146e-04, /* 0x39b62a69 */ +u04 = -3.8140706238e-06, /* 0xb67ff53c */ +u05 = 1.9559013964e-08, /* 0x32a802ba */ +u06 = -3.9820518410e-11, /* 0xae2f21eb */ +v01 = 1.2730483897e-02, /* 0x3c509385 */ +v02 = 7.6006865129e-05, /* 0x389f65e0 */ +v03 = 2.5915085189e-07, /* 0x348b216c */ +v04 = 4.4111031494e-10; /* 0x2ff280c2 */ + +#ifdef __STDC__ + float __ieee754_y0f(float x) +#else + float __ieee754_y0f(x) + float x; +#endif +{ + float z, s,c,ss,cc,u,v; + __int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = 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. + */ + s = sinf(x); + c = cosf(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -cosf(x+x); + if ((s*c)<zero) cc = z/ss; + else ss = z/cc; + } + if(ix>0x80000000) z = (invsqrtpi*ss)/__ieee754_sqrtf(x); + else { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x); + } + return z; + } + if(ix<=0x32000000) { /* x < 2**-27 */ + return(u00 + tpi*__ieee754_logf(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +#ifdef __STDC__ +static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.0000000000e+00, /* 0x00000000 */ + -7.0312500000e-02, /* 0xbd900000 */ + -8.0816707611e+00, /* 0xc1014e86 */ + -2.5706311035e+02, /* 0xc3808814 */ + -2.4852163086e+03, /* 0xc51b5376 */ + -5.2530439453e+03, /* 0xc5a4285a */ +}; +#ifdef __STDC__ +static const float pS8[5] = { +#else +static float pS8[5] = { +#endif + 1.1653436279e+02, /* 0x42e91198 */ + 3.8337448730e+03, /* 0x456f9beb */ + 4.0597855469e+04, /* 0x471e95db */ + 1.1675296875e+05, /* 0x47e4087c */ + 4.7627726562e+04, /* 0x473a0bba */ +}; +#ifdef __STDC__ +static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -1.1412546255e-11, /* 0xad48c58a */ + -7.0312492549e-02, /* 0xbd8fffff */ + -4.1596107483e+00, /* 0xc0851b88 */ + -6.7674766541e+01, /* 0xc287597b */ + -3.3123129272e+02, /* 0xc3a59d9b */ + -3.4643338013e+02, /* 0xc3ad3779 */ +}; +#ifdef __STDC__ +static const float pS5[5] = { +#else +static float pS5[5] = { +#endif + 6.0753936768e+01, /* 0x42730408 */ + 1.0512523193e+03, /* 0x44836813 */ + 5.9789707031e+03, /* 0x45bad7c4 */ + 9.6254453125e+03, /* 0x461665c8 */ + 2.4060581055e+03, /* 0x451660ee */ +}; + +#ifdef __STDC__ +static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -2.5470459075e-09, /* 0xb12f081b */ + -7.0311963558e-02, /* 0xbd8fffb8 */ + -2.4090321064e+00, /* 0xc01a2d95 */ + -2.1965976715e+01, /* 0xc1afba52 */ + -5.8079170227e+01, /* 0xc2685112 */ + -3.1447946548e+01, /* 0xc1fb9565 */ +}; +#ifdef __STDC__ +static const float pS3[5] = { +#else +static float pS3[5] = { +#endif + 3.5856033325e+01, /* 0x420f6c94 */ + 3.6151397705e+02, /* 0x43b4c1ca */ + 1.1936077881e+03, /* 0x44953373 */ + 1.1279968262e+03, /* 0x448cffe6 */ + 1.7358093262e+02, /* 0x432d94b8 */ +}; + +#ifdef __STDC__ +static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -8.8753431271e-08, /* 0xb3be98b7 */ + -7.0303097367e-02, /* 0xbd8ffb12 */ + -1.4507384300e+00, /* 0xbfb9b1cc */ + -7.6356959343e+00, /* 0xc0f4579f */ + -1.1193166733e+01, /* 0xc1331736 */ + -3.2336456776e+00, /* 0xc04ef40d */ +}; +#ifdef __STDC__ +static const float pS2[5] = { +#else +static float pS2[5] = { +#endif + 2.2220300674e+01, /* 0x41b1c32d */ + 1.3620678711e+02, /* 0x430834f0 */ + 2.7047027588e+02, /* 0x43873c32 */ + 1.5387539673e+02, /* 0x4319e01a */ + 1.4657617569e+01, /* 0x416a859a */ +}; + +#ifdef __STDC__ + static float pzerof(float x) +#else + static float pzerof(x) + float x; +#endif +{ +#ifdef __STDC__ + const float *p,*q; +#else + float *p,*q; +#endif + float z,r,s; + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pR8; q= pS8;} + else if(ix>=0x40f71c58){p = pR5; q= pS5;} + else if(ix>=0x4036db68){p = pR3; q= pS3;} + else if(ix>=0x40000000){p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +#ifdef __STDC__ +static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.0000000000e+00, /* 0x00000000 */ + 7.3242187500e-02, /* 0x3d960000 */ + 1.1768206596e+01, /* 0x413c4a93 */ + 5.5767340088e+02, /* 0x440b6b19 */ + 8.8591972656e+03, /* 0x460a6cca */ + 3.7014625000e+04, /* 0x471096a0 */ +}; +#ifdef __STDC__ +static const float qS8[6] = { +#else +static float qS8[6] = { +#endif + 1.6377603149e+02, /* 0x4323c6aa */ + 8.0983447266e+03, /* 0x45fd12c2 */ + 1.4253829688e+05, /* 0x480b3293 */ + 8.0330925000e+05, /* 0x49441ed4 */ + 8.4050156250e+05, /* 0x494d3359 */ + -3.4389928125e+05, /* 0xc8a7eb69 */ +}; + +#ifdef __STDC__ +static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.8408595828e-11, /* 0x2da1ec79 */ + 7.3242180049e-02, /* 0x3d95ffff */ + 5.8356351852e+00, /* 0x40babd86 */ + 1.3511157227e+02, /* 0x43071c90 */ + 1.0272437744e+03, /* 0x448067cd */ + 1.9899779053e+03, /* 0x44f8bf4b */ +}; +#ifdef __STDC__ +static const float qS5[6] = { +#else +static float qS5[6] = { +#endif + 8.2776611328e+01, /* 0x42a58da0 */ + 2.0778142090e+03, /* 0x4501dd07 */ + 1.8847289062e+04, /* 0x46933e94 */ + 5.6751113281e+04, /* 0x475daf1d */ + 3.5976753906e+04, /* 0x470c88c1 */ + -5.3543427734e+03, /* 0xc5a752be */ +}; + +#ifdef __STDC__ +static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#else +static float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 4.3774099900e-09, /* 0x3196681b */ + 7.3241114616e-02, /* 0x3d95ff70 */ + 3.3442313671e+00, /* 0x405607e3 */ + 4.2621845245e+01, /* 0x422a7cc5 */ + 1.7080809021e+02, /* 0x432acedf */ + 1.6673394775e+02, /* 0x4326bbe4 */ +}; +#ifdef __STDC__ +static const float qS3[6] = { +#else +static float qS3[6] = { +#endif + 4.8758872986e+01, /* 0x42430916 */ + 7.0968920898e+02, /* 0x44316c1c */ + 3.7041481934e+03, /* 0x4567825f */ + 6.4604252930e+03, /* 0x45c9e367 */ + 2.5163337402e+03, /* 0x451d4557 */ + -1.4924745178e+02, /* 0xc3153f59 */ +}; + +#ifdef __STDC__ +static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.5044444979e-07, /* 0x342189db */ + 7.3223426938e-02, /* 0x3d95f62a */ + 1.9981917143e+00, /* 0x3fffc4bf */ + 1.4495602608e+01, /* 0x4167edfd */ + 3.1666231155e+01, /* 0x41fd5471 */ + 1.6252708435e+01, /* 0x4182058c */ +}; +#ifdef __STDC__ +static const float qS2[6] = { +#else +static float qS2[6] = { +#endif + 3.0365585327e+01, /* 0x41f2ecb8 */ + 2.6934811401e+02, /* 0x4386ac8f */ + 8.4478375244e+02, /* 0x44533229 */ + 8.8293585205e+02, /* 0x445cbbe5 */ + 2.1266638184e+02, /* 0x4354aa98 */ + -5.3109550476e+00, /* 0xc0a9f358 */ +}; + +#ifdef __STDC__ + static float qzerof(float x) +#else + static float qzerof(x) + float x; +#endif +{ +#ifdef __STDC__ + const float *p,*q; +#else + float *p,*q; +#endif + float s,r,z; + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = qR8; q= qS8;} + else if(ix>=0x40f71c58){p = qR5; q= qS5;} + else if(ix>=0x4036db68){p = qR3; q= qS3;} + else if(ix>=0x40000000){p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-(float).125 + r/s)/x; +} diff --git a/newlib/libm/math/ef_j1.c b/newlib/libm/math/ef_j1.c new file mode 100644 index 00000000000..a3e75f6515d --- /dev/null +++ b/newlib/libm/math/ef_j1.c @@ -0,0 +1,439 @@ +/* ef_j1.c -- float version of e_j1.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 float ponef(float), qonef(float); +#else +static float ponef(), qonef(); +#endif + +#ifdef __STDC__ +static const float +#else +static float +#endif +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0,2] */ +r00 = -6.2500000000e-02, /* 0xbd800000 */ +r01 = 1.4070566976e-03, /* 0x3ab86cfd */ +r02 = -1.5995563444e-05, /* 0xb7862e36 */ +r03 = 4.9672799207e-08, /* 0x335557d2 */ +s01 = 1.9153760746e-02, /* 0x3c9ce859 */ +s02 = 1.8594678841e-04, /* 0x3942fab6 */ +s03 = 1.1771846857e-06, /* 0x359dffc2 */ +s04 = 5.0463624390e-09, /* 0x31ad6446 */ +s05 = 1.2354227016e-11; /* 0x2d59567e */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_j1f(float x) +#else + float __ieee754_j1f(x) + float x; +#endif +{ + float z, s,c,ss,cc,r,u,v,y; + __int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/x; + y = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(y); + c = cosf(y); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure y+y not overflow */ + z = cosf(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>0x80000000) z = (invsqrtpi*cc)/__ieee754_sqrtf(y); + else { + u = ponef(y); v = qonef(y); + z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrtf(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x32000000) { /* |x|<2**-27 */ + if(huge+x>one) return (float)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*(float)0.5+r/s); +} + +#ifdef __STDC__ +static const float U0[5] = { +#else +static float U0[5] = { +#endif + -1.9605709612e-01, /* 0xbe48c331 */ + 5.0443872809e-02, /* 0x3d4e9e3c */ + -1.9125689287e-03, /* 0xbafaaf2a */ + 2.3525259166e-05, /* 0x37c5581c */ + -9.1909917899e-08, /* 0xb3c56003 */ +}; +#ifdef __STDC__ +static const float V0[5] = { +#else +static float V0[5] = { +#endif + 1.9916731864e-02, /* 0x3ca3286a */ + 2.0255257550e-04, /* 0x3954644b */ + 1.3560879779e-06, /* 0x35b602d4 */ + 6.2274145840e-09, /* 0x31d5f8eb */ + 1.6655924903e-11, /* 0x2d9281cf */ +}; + +#ifdef __STDC__ + float __ieee754_y1f(float x) +#else + float __ieee754_y1f(x) + float x; +#endif +{ + float z, s,c,ss,cc,u,v; + __int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(x); + c = cosf(x); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = cosf(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)/__ieee754_sqrtf(x); + else { + u = ponef(x); v = qonef(x); + z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrtf(x); + } + return z; + } + if(ix<=0x24800000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(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 float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.0000000000e+00, /* 0x00000000 */ + 1.1718750000e-01, /* 0x3df00000 */ + 1.3239480972e+01, /* 0x4153d4ea */ + 4.1205184937e+02, /* 0x43ce06a3 */ + 3.8747453613e+03, /* 0x45722bed */ + 7.9144794922e+03, /* 0x45f753d6 */ +}; +#ifdef __STDC__ +static const float ps8[5] = { +#else +static float ps8[5] = { +#endif + 1.1420736694e+02, /* 0x42e46a2c */ + 3.6509309082e+03, /* 0x45642ee5 */ + 3.6956207031e+04, /* 0x47105c35 */ + 9.7602796875e+04, /* 0x47bea166 */ + 3.0804271484e+04, /* 0x46f0a88b */ +}; + +#ifdef __STDC__ +static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + 1.3199052094e-11, /* 0x2d68333f */ + 1.1718749255e-01, /* 0x3defffff */ + 6.8027510643e+00, /* 0x40d9b023 */ + 1.0830818176e+02, /* 0x42d89dca */ + 5.1763616943e+02, /* 0x440168b7 */ + 5.2871520996e+02, /* 0x44042dc6 */ +}; +#ifdef __STDC__ +static const float ps5[5] = { +#else +static float ps5[5] = { +#endif + 5.9280597687e+01, /* 0x426d1f55 */ + 9.9140142822e+02, /* 0x4477d9b1 */ + 5.3532670898e+03, /* 0x45a74a23 */ + 7.8446904297e+03, /* 0x45f52586 */ + 1.5040468750e+03, /* 0x44bc0180 */ +}; + +#ifdef __STDC__ +static const float pr3[6] = { +#else +static float pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + 3.0250391081e-09, /* 0x314fe10d */ + 1.1718686670e-01, /* 0x3defffab */ + 3.9329774380e+00, /* 0x407bb5e7 */ + 3.5119403839e+01, /* 0x420c7a45 */ + 9.1055007935e+01, /* 0x42b61c2a */ + 4.8559066772e+01, /* 0x42423c7c */ +}; +#ifdef __STDC__ +static const float ps3[5] = { +#else +static float ps3[5] = { +#endif + 3.4791309357e+01, /* 0x420b2a4d */ + 3.3676245117e+02, /* 0x43a86198 */ + 1.0468714600e+03, /* 0x4482dbe3 */ + 8.9081134033e+02, /* 0x445eb3ed */ + 1.0378793335e+02, /* 0x42cf936c */ +}; + +#ifdef __STDC__ +static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + 1.0771083225e-07, /* 0x33e74ea8 */ + 1.1717621982e-01, /* 0x3deffa16 */ + 2.3685150146e+00, /* 0x401795c0 */ + 1.2242610931e+01, /* 0x4143e1bc */ + 1.7693971634e+01, /* 0x418d8d41 */ + 5.0735230446e+00, /* 0x40a25a4d */ +}; +#ifdef __STDC__ +static const float ps2[5] = { +#else +static float ps2[5] = { +#endif + 2.1436485291e+01, /* 0x41ab7dec */ + 1.2529022980e+02, /* 0x42fa9499 */ + 2.3227647400e+02, /* 0x436846c7 */ + 1.1767937469e+02, /* 0x42eb5bd7 */ + 8.3646392822e+00, /* 0x4105d590 */ +}; + +#ifdef __STDC__ + static float ponef(float x) +#else + static float ponef(x) + float x; +#endif +{ +#ifdef __STDC__ + const float *p,*q; +#else + float *p,*q; +#endif + float z,r,s; + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pr8; q= ps8;} + else if(ix>=0x40f71c58){p = pr5; q= ps5;} + else if(ix>=0x4036db68){p = pr3; q= ps3;} + else if(ix>=0x40000000){p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +#ifdef __STDC__ +static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#else +static float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ +#endif + 0.0000000000e+00, /* 0x00000000 */ + -1.0253906250e-01, /* 0xbdd20000 */ + -1.6271753311e+01, /* 0xc1822c8d */ + -7.5960174561e+02, /* 0xc43de683 */ + -1.1849806641e+04, /* 0xc639273a */ + -4.8438511719e+04, /* 0xc73d3683 */ +}; +#ifdef __STDC__ +static const float qs8[6] = { +#else +static float qs8[6] = { +#endif + 1.6139537048e+02, /* 0x43216537 */ + 7.8253862305e+03, /* 0x45f48b17 */ + 1.3387534375e+05, /* 0x4802bcd6 */ + 7.1965775000e+05, /* 0x492fb29c */ + 6.6660125000e+05, /* 0x4922be94 */ + -2.9449025000e+05, /* 0xc88fcb48 */ +}; + +#ifdef __STDC__ +static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#else +static float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ +#endif + -2.0897993405e-11, /* 0xadb7d219 */ + -1.0253904760e-01, /* 0xbdd1fffe */ + -8.0564479828e+00, /* 0xc100e736 */ + -1.8366960144e+02, /* 0xc337ab6b */ + -1.3731937256e+03, /* 0xc4aba633 */ + -2.6124443359e+03, /* 0xc523471c */ +}; +#ifdef __STDC__ +static const float qs5[6] = { +#else +static float qs5[6] = { +#endif + 8.1276550293e+01, /* 0x42a28d98 */ + 1.9917987061e+03, /* 0x44f8f98f */ + 1.7468484375e+04, /* 0x468878f8 */ + 4.9851425781e+04, /* 0x4742bb6d */ + 2.7948074219e+04, /* 0x46da5826 */ + -4.7191835938e+03, /* 0xc5937978 */ +}; + +#ifdef __STDC__ +static const float qr3[6] = { +#else +static float qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ +#endif + -5.0783124372e-09, /* 0xb1ae7d4f */ + -1.0253783315e-01, /* 0xbdd1ff5b */ + -4.6101160049e+00, /* 0xc0938612 */ + -5.7847221375e+01, /* 0xc267638e */ + -2.2824453735e+02, /* 0xc3643e9a */ + -2.1921012878e+02, /* 0xc35b35cb */ +}; +#ifdef __STDC__ +static const float qs3[6] = { +#else +static float qs3[6] = { +#endif + 4.7665153503e+01, /* 0x423ea91e */ + 6.7386511230e+02, /* 0x4428775e */ + 3.3801528320e+03, /* 0x45534272 */ + 5.5477290039e+03, /* 0x45ad5dd5 */ + 1.9031191406e+03, /* 0x44ede3d0 */ + -1.3520118713e+02, /* 0xc3073381 */ +}; + +#ifdef __STDC__ +static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#else +static float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ +#endif + -1.7838172539e-07, /* 0xb43f8932 */ + -1.0251704603e-01, /* 0xbdd1f475 */ + -2.7522056103e+00, /* 0xc0302423 */ + -1.9663616180e+01, /* 0xc19d4f16 */ + -4.2325313568e+01, /* 0xc2294d1f */ + -2.1371921539e+01, /* 0xc1aaf9b2 */ +}; +#ifdef __STDC__ +static const float qs2[6] = { +#else +static float qs2[6] = { +#endif + 2.9533363342e+01, /* 0x41ec4454 */ + 2.5298155212e+02, /* 0x437cfb47 */ + 7.5750280762e+02, /* 0x443d602e */ + 7.3939318848e+02, /* 0x4438d92a */ + 1.5594900513e+02, /* 0x431bf2f2 */ + -4.9594988823e+00, /* 0xc09eb437 */ +}; + +#ifdef __STDC__ + static float qonef(float x) +#else + static float qonef(x) + float x; +#endif +{ +#ifdef __STDC__ + const float *p,*q; +#else + float *p,*q; +#endif + float s,r,z; + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qr8; q= qs8;} + else if(ix>=0x40f71c58){p = qr5; q= qs5;} + else if(ix>=0x4036db68){p = qr3; q= qs3;} + else if(ix>=0x40000000){p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return ((float).375 + r/s)/x; +} diff --git a/newlib/libm/math/ef_jn.c b/newlib/libm/math/ef_jn.c new file mode 100644 index 00000000000..04a93b685ed --- /dev/null +++ b/newlib/libm/math/ef_jn.c @@ -0,0 +1,207 @@ +/* ef_jn.c -- float version of e_jn.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 +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +two = 2.0000000000e+00, /* 0x40000000 */ +one = 1.0000000000e+00; /* 0x3F800000 */ + +#ifdef __STDC__ +static const float zero = 0.0000000000e+00; +#else +static float zero = 0.0000000000e+00; +#endif + +#ifdef __STDC__ + float __ieee754_jnf(int n, float x) +#else + float __ieee754_jnf(n,x) + int n; float x; +#endif +{ + __int32_t i,hx,ix, sgn; + float a, b, temp, di; + float z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0f(x)); + if(n==1) return(__ieee754_j1f(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabsf(x); + if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */ + b = zero; + else if((float)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + a = __ieee754_j0f(x); + b = __ieee754_j1f(x); + for(i=1;i<n;i++){ + temp = b; + b = b*((float)(i+i)/x) - a; /* avoid underflow */ + a = temp; + } + } else { + if(ix<0x30800000) { /* x < 2**-29 */ + /* x is tiny, return the first Taylor expansion of J(n,x) + * J(n,x) = 1/n!*(x/2)^n - ... + */ + if(n>33) /* underflow */ + b = zero; + else { + temp = x*(float)0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (float)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + float t,v; + float q0,q1,h,tmp; __int32_t k,m; + w = (n+n)/(float)x; h = (float)2.0/(float)x; + q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1; + while(q1<(float)1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_logf(fabsf(v*tmp)); + if(tmp<(float)8.8721679688e+01) { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>(float)1e10) { + a /= b; + t /= b; + b = one; + } + } + } + b = (t*__ieee754_j0f(x)/b); + } + } + if(sgn==1) return -b; else return b; +} + +#ifdef __STDC__ + float __ieee754_ynf(int n, float x) +#else + float __ieee754_ynf(n,x) + int n; float x; +#endif +{ + __int32_t i,hx,ix,ib; + __int32_t sign; + float a, b, temp; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0f(x)); + if(n==1) return(sign*__ieee754_y1f(x)); + if(ix==0x7f800000) return zero; + + a = __ieee754_y0f(x); + b = __ieee754_y1f(x); + /* quit if b is -inf */ + GET_FLOAT_WORD(ib,b); + for(i=1;i<n&&ib!=0xff800000;i++){ + temp = b; + b = ((float)(i+i)/x)*b - a; + GET_FLOAT_WORD(ib,b); + a = temp; + } + if(sign>0) return b; else return -b; +} diff --git a/newlib/libm/math/ef_log.c b/newlib/libm/math/ef_log.c new file mode 100644 index 00000000000..93f072c56bc --- /dev/null +++ b/newlib/libm/math/ef_log.c @@ -0,0 +1,92 @@ +/* ef_log.c -- float version of e_log.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 +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lg3 = 2.8571429849e-01, /* 3E924925 */ +Lg4 = 2.2222198546e-01, /* 3E638E29 */ +Lg5 = 1.8183572590e-01, /* 3E3A3325 */ +Lg6 = 1.5313838422e-01, /* 3E1CD04F */ +Lg7 = 1.4798198640e-01; /* 3E178897 */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_logf(float x) +#else + float __ieee754_logf(x) + float x; +#endif +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + __int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if ((ix&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (ix >= 0x7f800000) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + f = x-(float)1.0; + if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ + if(f==zero) if(k==0) return zero; else {dk=(float)k; + return dk*ln2_hi+dk*ln2_lo;} + R = f*f*((float)0.5-(float)0.33333333333333333*f); + if(k==0) return f-R; else {dk=(float)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/((float)2.0+f); + dk = (float)k; + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + 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=(float)0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/newlib/libm/math/ef_log10.c b/newlib/libm/math/ef_log10.c new file mode 100644 index 00000000000..63fee9b9d42 --- /dev/null +++ b/newlib/libm/math/ef_log10.c @@ -0,0 +1,62 @@ +/* ef_log10.c -- float version of e_log10.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 +two25 = 3.3554432000e+07, /* 0x4c000000 */ +ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */ +log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */ +log10_2lo = 7.9034151668e-07; /* 0x355427db */ + +#ifdef __STDC__ +static const float zero = 0.0; +#else +static float zero = 0.0; +#endif + +#ifdef __STDC__ + float __ieee754_log10f(float x) +#else + float __ieee754_log10f(x) + float x; +#endif +{ + float y,z; + __int32_t i,k,hx; + + GET_FLOAT_WORD(hx,x); + + k=0; + if (hx < 0x00800000) { /* x < 2**-126 */ + if ((hx&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(hx,x); + } + if (hx >= 0x7f800000) return x+x; + k += (hx>>23)-127; + i = ((__uint32_t)k&0x80000000)>>31; + hx = (hx&0x007fffff)|((0x7f-i)<<23); + y = (float)(k+i); + SET_FLOAT_WORD(x,hx); + z = y*log10_2lo + ivln10*__ieee754_logf(x); + return z+y*log10_2hi; +} diff --git a/newlib/libm/math/ef_pow.c b/newlib/libm/math/ef_pow.c new file mode 100644 index 00000000000..40b679d6e80 --- /dev/null +++ b/newlib/libm/math/ef_pow.c @@ -0,0 +1,252 @@ +/* ef_pow.c -- float version of e_pow.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 __v810__ +#define const +#endif + +#ifdef __STDC__ +static const float +#else +static float +#endif +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ +dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ +zero = 0.0, +one = 1.0, +two = 2.0, +two24 = 16777216.0, /* 0x4b800000 */ +huge = 1.0e30, +tiny = 1.0e-30, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 6.0000002384e-01, /* 0x3f19999a */ +L2 = 4.2857143283e-01, /* 0x3edb6db7 */ +L3 = 3.3333334327e-01, /* 0x3eaaaaab */ +L4 = 2.7272811532e-01, /* 0x3e8ba305 */ +L5 = 2.3066075146e-01, /* 0x3e6c3255 */ +L6 = 2.0697501302e-01, /* 0x3e53f142 */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08, /* 0x3331bb4c */ +lg2 = 6.9314718246e-01, /* 0x3f317218 */ +lg2_h = 6.93145752e-01, /* 0x3f317200 */ +lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ +ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ +cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ +cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */ +cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */ +ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ +ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ +ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ + +#ifdef __STDC__ + float __ieee754_powf(float x, float y) +#else + float __ieee754_powf(x,y) + float x, y; +#endif +{ + float z,ax,z_h,z_l,p_h,p_l; + float y1,t1,t2,r,s,t,u,v,w; + __int32_t i,j,k,yisint,n; + __int32_t hx,hy,ix,iy,is; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if(iy==0) return one; + + /* +-NaN return x+y */ + if(ix > 0x7f800000 || + iy > 0x7f800000) + 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>=0x4b800000) yisint = 2; /* even integer y */ + else if(iy>=0x3f800000) { + k = (iy>>23)-0x7f; /* exponent */ + j = iy>>(23-k); + if((j<<(23-k))==iy) yisint = 2-(j&1); + } + } + + /* special value of y */ + if (iy==0x7f800000) { /* y is +-inf */ + if (ix==0x3f800000) + return y - y; /* inf**+-1 is NaN */ + else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3f800000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3f000000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return __ieee754_sqrtf(x); + } + + ax = fabsf(x); + /* special value of x */ + if(ix==0x7f800000||ix==0||ix==0x3f800000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3f800000)|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; + } + + /* (x<0)**(non-int) is NaN */ + if(((((__uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); + + /* |y| is huge */ + if(iy>0x4d000000) { /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny; + if(ix>0x3f800007) 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)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); + u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = v-(t1-u); + } else { + float s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00800000) + {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); } + n += ((ix)>>23)-0x7f; + j = ix&0x007fffff; + /* determine interval */ + ix = j|0x3f800000; /* normalize ix */ + if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */ + else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */ + else {k=0;n+=1;ix -= 0x00800000;} + SET_FLOAT_WORD(ax,ix); + + /* 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; + GET_FLOAT_WORD(is,s_h); + SET_FLOAT_WORD(s_h,is&0xfffff000); + /* t_h=ax+bp[k] High */ + SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21)); + 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 = (float)3.0+s2+r; + GET_FLOAT_WORD(is,t_h); + SET_FLOAT_WORD(t_h,is&0xfffff000); + t_l = r-((t_h-(float)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; + GET_FLOAT_WORD(is,p_h); + SET_FLOAT_WORD(p_h,is&0xfffff000); + 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 = (float)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + 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) */ + GET_FLOAT_WORD(is,y); + SET_FLOAT_WORD(y1,is&0xfffff000); + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + GET_FLOAT_WORD(j,z); + if (j>0x43000000) /* if z > 128 */ + return s*huge*huge; /* overflow */ + else if (j==0x43000000) { /* if z == 128 */ + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */ + return s*tiny*tiny; /* underflow */ + else if (j==0xc3160000){ /* z == -150 */ + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>23)-0x7f; + n = 0; + if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00800000>>(k+1)); + k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ + SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); + n = ((n&0x007fffff)|0x00800000)>>(23-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + GET_FLOAT_WORD(is,t); + SET_FLOAT_WORD(t,is&0xfffff000); + 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_FLOAT_WORD(j,z); + j += (n<<23); + if((j>>23)<=0) z = scalbnf(z,(int)n); /* subnormal output */ + else SET_FLOAT_WORD(z,j); + return s*z; +} diff --git a/newlib/libm/math/ef_rem_pio2.c b/newlib/libm/math/ef_rem_pio2.c new file mode 100644 index 00000000000..e91aa47f370 --- /dev/null +++ b/newlib/libm/math/ef_rem_pio2.c @@ -0,0 +1,193 @@ +/* ef_rem_pio2.c -- float version of e_rem_pio2.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. + * ==================================================== + * + */ + +/* __ieee754_rem_pio2f(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2f() + */ + +#include "fdlibm.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +#ifdef __STDC__ +static const __int32_t two_over_pi[] = { +#else +static __int32_t two_over_pi[] = { +#endif +0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, +0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, +0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, +0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, +0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, +0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, +0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, +0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, +0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, +0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, +0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, +0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, +0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, +0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, +0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, +0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, +0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, +0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, +0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, +0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, +0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, +0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, +}; + +/* This array is like the one in e_rem_pio2.c, but the numbers are + single precision and the last 8 bits are forced to 0. */ +#ifdef __STDC__ +static const __int32_t npio2_hw[] = { +#else +static __int32_t npio2_hw[] = { +#endif +0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, +0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, +0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, +0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, +0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, +0x4242c700, 0x42490f00 +}; + +/* + * invpio2: 24 bits of 2/pi + * pio2_1: first 17 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 17 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 17 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +#ifdef __STDC__ +static const float +#else +static float +#endif +zero = 0.0000000000e+00, /* 0x00000000 */ +half = 5.0000000000e-01, /* 0x3f000000 */ +two8 = 2.5600000000e+02, /* 0x43800000 */ +invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ +pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ +pio2_1t = 1.0804334124e-05, /* 0x37354443 */ +pio2_2 = 1.0804273188e-05, /* 0x37354400 */ +pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ +pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ +pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ + +#ifdef __STDC__ + __int32_t __ieee754_rem_pio2f(float x, float *y) +#else + __int32_t __ieee754_rem_pio2f(x,y) + float x,y[]; +#endif +{ + float z,w,t,r,fn; + float tx[3]; + __int32_t i,j,n,ix,hx; + int e0,nx; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 24+24+24 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&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ + t = fabsf(x); + n = (__int32_t) (t*invpio2+half); + fn = (float)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 40 bit */ + if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + __uint32_t high; + j = ix>>23; + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>8) { /* 2nd iteration needed, good to 57 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>25) { /* 3rd iteration need, 74 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>=0x7f800000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-7) */ + e0 = (int)((ix>>23)-134); /* e0 = ilogb(z)-7; */ + SET_FLOAT_WORD(z, ix - ((__int32_t)e0<<23)); + for(i=0;i<2;i++) { + tx[i] = (float)((__int32_t)(z)); + z = (z-tx[i])*two8; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff --git a/newlib/libm/math/ef_remainder.c b/newlib/libm/math/ef_remainder.c new file mode 100644 index 00000000000..8ce7fac9972 --- /dev/null +++ b/newlib/libm/math/ef_remainder.c @@ -0,0 +1,68 @@ +/* ef_remainder.c -- float version of e_remainder.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 zero = 0.0; +#else +static float zero = 0.0; +#endif + + +#ifdef __STDC__ + float __ieee754_remainderf(float x, float p) +#else + float __ieee754_remainderf(x,p) + float x,p; +#endif +{ + __int32_t hx,hp; + __uint32_t sx; + float p_half; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if(hp==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7f800000)|| /* x not finite */ + ((hp>0x7f800000))) /* p is NaN */ + return (x*p)/(x*p); + + + if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p); /* now x < 2p */ + if ((hx-hp)==0) return zero*x; + x = fabsf(x); + p = fabsf(p); + if (hp<0x01000000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = (float)0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_FLOAT_WORD(hx,x); + SET_FLOAT_WORD(x,hx^sx); + return x; +} diff --git a/newlib/libm/math/ef_scalb.c b/newlib/libm/math/ef_scalb.c new file mode 100644 index 00000000000..3677a3b1fda --- /dev/null +++ b/newlib/libm/math/ef_scalb.c @@ -0,0 +1,53 @@ +/* ef_scalb.c -- float version of e_scalb.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" +#include <limits.h> + +#ifdef _SCALB_INT +#ifdef __STDC__ + float __ieee754_scalbf(float x, int fn) +#else + float __ieee754_scalbf(x,fn) + float x; int fn; +#endif +#else +#ifdef __STDC__ + float __ieee754_scalbf(float x, float fn) +#else + float __ieee754_scalbf(x,fn) + float x, fn; +#endif +#endif +{ +#ifdef _SCALB_INT + return scalbnf(x,fn); +#else + if (isnanf(x)||isnanf(fn)) return x*fn; + if (!finitef(fn)) { + if(fn>(float)0.0) return x*fn; + else return x/(-fn); + } + if (rintf(fn)!=fn) return (fn-fn)/(fn-fn); +#if INT_MAX > 65000 + if ( fn > (float)65000.0) return scalbnf(x, 65000); + if (-fn > (float)65000.0) return scalbnf(x,-65000); +#else + if ( fn > (float)32000.0) return scalbnf(x, 32000); + if (-fn > (float)32000.0) return scalbnf(x,-32000); +#endif + return scalbnf(x,(int)fn); +#endif +} diff --git a/newlib/libm/math/ef_sinh.c b/newlib/libm/math/ef_sinh.c new file mode 100644 index 00000000000..37519834473 --- /dev/null +++ b/newlib/libm/math/ef_sinh.c @@ -0,0 +1,63 @@ +/* ef_sinh.c -- float version of e_sinh.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 one = 1.0, shuge = 1.0e37; +#else +static float one = 1.0, shuge = 1.0e37; +#endif + +#ifdef __STDC__ + float __ieee754_sinhf(float x) +#else + float __ieee754_sinhf(x) + float x; +#endif +{ + float t,w,h; + __int32_t ix,jx; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (ix<0x31800000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1f(fabsf(x)); + if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x42b17180) return h*__ieee754_expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = __ieee754_expf((float)0.5*fabsf(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff --git a/newlib/libm/math/ef_sqrt.c b/newlib/libm/math/ef_sqrt.c new file mode 100644 index 00000000000..aabbc51cea8 --- /dev/null +++ b/newlib/libm/math/ef_sqrt.c @@ -0,0 +1,92 @@ +/* ef_sqrtf.c -- float version of e_sqrt.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 one = 1.0, tiny=1.0e-30; +#else +static float one = 1.0, tiny=1.0e-30; +#endif + +#ifdef __STDC__ + float __ieee754_sqrtf(float x) +#else + float __ieee754_sqrtf(x) + float x; +#endif +{ + float z; + __int32_t sign = (__int32_t)0x80000000; + __uint32_t r; + __int32_t ix,s,q,m,t,i; + + GET_FLOAT_WORD(ix,x); + + /* take care of Inf and NaN */ + if((ix&0x7f800000L)==0x7f800000L) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix<=0) { + if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix>>23); + if(m==0) { /* subnormal x */ + for(i=0;(ix&0x00800000L)==0;i++) ix<<=1; + m -= i-1; + } + m -= 127; /* unbias exponent */ + ix = (ix&0x007fffffL)|0x00800000L; + if(m&1) /* odd m, double x to make it even */ + ix += ix; + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix += ix; + q = s = 0; /* q = sqrt(x) */ + r = 0x01000000L; /* r = moving bit from right to left */ + + while(r!=0) { + t = s+r; + if(t<=ix) { + s = t+r; + ix -= t; + q += r; + } + ix += ix; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if(ix!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (z>one) + q += 2; + else + q += (q&1); + } + } + ix = (q>>1)+0x3f000000L; + ix += (m <<23); + SET_FLOAT_WORD(z,ix); + return z; +} diff --git a/newlib/libm/math/er_gamma.c b/newlib/libm/math/er_gamma.c new file mode 100644 index 00000000000..a7183c50f81 --- /dev/null +++ b/newlib/libm/math/er_gamma.c @@ -0,0 +1,32 @@ + +/* @(#)er_gamma.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_gamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: See __ieee754_lgamma_r + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + double __ieee754_gamma_r(double x, int *signgamp) +#else + double __ieee754_gamma_r(x,signgamp) + double x; int *signgamp; +#endif +{ + return __ieee754_lgamma_r(x,signgamp); +} diff --git a/newlib/libm/math/er_lgamma.c b/newlib/libm/math/er_lgamma.c new file mode 100644 index 00000000000..7c9a153ed1b --- /dev/null +++ b/newlib/libm/math/er_lgamma.c @@ -0,0 +1,309 @@ + +/* @(#)er_lgamma.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_lgamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * where + * poly(z) is a 14 degree polynomial. + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * with accuracy + * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * where + * |w - f(z)| < 2**-58.74 + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ +a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ +a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ +a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ +a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ +a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ +a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ +a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ +a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ +a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ +a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ +a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ +tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ +tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ +/* tt = -(tail of tf) */ +tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ +t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ +t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ +t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ +t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ +t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ +t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ +t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ +t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ +t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ +t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ +t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ +t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ +t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ +t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ +t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ +u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ +u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ +u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ +u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ +u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ +v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ +v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ +v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ +v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ +v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ +s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ +s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ +s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ +s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ +s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ +s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ +r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ +r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ +r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ +r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ +r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ +r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ +w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ +w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ +w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ +w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ +w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ +w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ +w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ + +#ifdef __STDC__ +static const double zero= 0.00000000000000000000e+00; +#else +static double zero= 0.00000000000000000000e+00; +#endif + +#ifdef __STDC__ + static double sin_pi(double x) +#else + static double sin_pi(x) + double x; +#endif +{ + double y,z; + __int32_t n,ix; + + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floor(y); + if(z!=y) { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */ + n = (__int32_t) (y*4.0); + } else { + if(ix>=0x43400000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x43300000) z = y+two52; /* exact */ + GET_LOW_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sin(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cos(pi*(0.5-y),zero); break; + case 3: + case 4: y = __kernel_sin(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; + default: y = __kernel_sin(pi*(y-2.0),zero,0); break; + } + return -y; +} + + +#ifdef __STDC__ + double __ieee754_lgamma_r(double x, int *signgamp) +#else + double __ieee754_lgamma_r(x,signgamp) + double x; int *signgamp; +#endif +{ + double t,y,z,nadj,p,p1,p2,p3,q,r,w; + __int32_t i,hx,lx,ix; + + EXTRACT_WORDS(hx,lx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x*x; + if((ix|lx)==0) return one/zero; + if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_log(-x); + } else return -__ieee754_log(x); + } + if(hx<0) { + if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ + return one/zero; + t = sin_pi(x); + if(t==zero) return one/zero; /* -integer */ + nadj = __ieee754_log(pi/fabs(t*x)); + if(t<zero) *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0; + /* for x < 2.0 */ + else if(ix<0x40000000) { + if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -__ieee754_log(x); + if(ix>=0x3FE76944) {y = one-x; i= 0;} + else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-0.5*y + p1/p2); + } + } + else if(ix<0x40200000) { /* x < 8.0 */ + i = (__int32_t)x; + t = zero; + y = x-(double)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6.0); /* FALLTHRU */ + case 6: z *= (y+5.0); /* FALLTHRU */ + case 5: z *= (y+4.0); /* FALLTHRU */ + case 4: z *= (y+3.0); /* FALLTHRU */ + case 3: z *= (y+2.0); /* FALLTHRU */ + r += __ieee754_log(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x43900000) { + t = __ieee754_log(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(__ieee754_log(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/newlib/libm/math/erf_gamma.c b/newlib/libm/math/erf_gamma.c new file mode 100644 index 00000000000..c619dfb2c6b --- /dev/null +++ b/newlib/libm/math/erf_gamma.c @@ -0,0 +1,34 @@ +/* erf_gamma.c -- float version of er_gamma.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. + * ==================================================== + * + */ + +/* __ieee754_gammaf_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: See __ieee754_lgammaf_r + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + float __ieee754_gammaf_r(float x, int *signgamp) +#else + float __ieee754_gammaf_r(x,signgamp) + float x; int *signgamp; +#endif +{ + return __ieee754_lgammaf_r(x,signgamp); +} diff --git a/newlib/libm/math/erf_lgamma.c b/newlib/libm/math/erf_lgamma.c new file mode 100644 index 00000000000..90cc5425de9 --- /dev/null +++ b/newlib/libm/math/erf_lgamma.c @@ -0,0 +1,244 @@ +/* erf_lgamma.c -- float version of er_lgamma.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= 8.3886080000e+06, /* 0x4b000000 */ +half= 5.0000000000e-01, /* 0x3f000000 */ +one = 1.0000000000e+00, /* 0x3f800000 */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +a0 = 7.7215664089e-02, /* 0x3d9e233f */ +a1 = 3.2246702909e-01, /* 0x3ea51a66 */ +a2 = 6.7352302372e-02, /* 0x3d89f001 */ +a3 = 2.0580807701e-02, /* 0x3ca89915 */ +a4 = 7.3855509982e-03, /* 0x3bf2027e */ +a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ +a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ +a7 = 5.1006977446e-04, /* 0x3a05b634 */ +a8 = 2.2086278477e-04, /* 0x39679767 */ +a9 = 1.0801156895e-04, /* 0x38e28445 */ +a10 = 2.5214456400e-05, /* 0x37d383a2 */ +a11 = 4.4864096708e-05, /* 0x383c2c75 */ +tc = 1.4616321325e+00, /* 0x3fbb16c3 */ +tf = -1.2148628384e-01, /* 0xbdf8cdcd */ +/* tt = -(tail of tf) */ +tt = 6.6971006518e-09, /* 0x31e61c52 */ +t0 = 4.8383611441e-01, /* 0x3ef7b95e */ +t1 = -1.4758771658e-01, /* 0xbe17213c */ +t2 = 6.4624942839e-02, /* 0x3d845a15 */ +t3 = -3.2788541168e-02, /* 0xbd064d47 */ +t4 = 1.7970675603e-02, /* 0x3c93373d */ +t5 = -1.0314224288e-02, /* 0xbc28fcfe */ +t6 = 6.1005386524e-03, /* 0x3bc7e707 */ +t7 = -3.6845202558e-03, /* 0xbb7177fe */ +t8 = 2.2596477065e-03, /* 0x3b141699 */ +t9 = -1.4034647029e-03, /* 0xbab7f476 */ +t10 = 8.8108185446e-04, /* 0x3a66f867 */ +t11 = -5.3859531181e-04, /* 0xba0d3085 */ +t12 = 3.1563205994e-04, /* 0x39a57b6b */ +t13 = -3.1275415677e-04, /* 0xb9a3f927 */ +t14 = 3.3552918467e-04, /* 0x39afe9f7 */ +u0 = -7.7215664089e-02, /* 0xbd9e233f */ +u1 = 6.3282704353e-01, /* 0x3f2200f4 */ +u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ +u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ +u4 = 2.2896373272e-01, /* 0x3e6a7578 */ +u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ +v1 = 2.4559779167e+00, /* 0x401d2ebe */ +v2 = 2.1284897327e+00, /* 0x4008392d */ +v3 = 7.6928514242e-01, /* 0x3f44efdf */ +v4 = 1.0422264785e-01, /* 0x3dd572af */ +v5 = 3.2170924824e-03, /* 0x3b52d5db */ +s0 = -7.7215664089e-02, /* 0xbd9e233f */ +s1 = 2.1498242021e-01, /* 0x3e5c245a */ +s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ +s3 = 1.4635047317e-01, /* 0x3e15dce6 */ +s4 = 2.6642270386e-02, /* 0x3cda40e4 */ +s5 = 1.8402845599e-03, /* 0x3af135b4 */ +s6 = 3.1947532989e-05, /* 0x3805ff67 */ +r1 = 1.3920053244e+00, /* 0x3fb22d3b */ +r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ +r3 = 1.7193385959e-01, /* 0x3e300f6e */ +r4 = 1.8645919859e-02, /* 0x3c98bf54 */ +r5 = 7.7794247773e-04, /* 0x3a4beed6 */ +r6 = 7.3266842264e-06, /* 0x36f5d7bd */ +w0 = 4.1893854737e-01, /* 0x3ed67f1d */ +w1 = 8.3333335817e-02, /* 0x3daaaaab */ +w2 = -2.7777778450e-03, /* 0xbb360b61 */ +w3 = 7.9365057172e-04, /* 0x3a500cfd */ +w4 = -5.9518753551e-04, /* 0xba1c065c */ +w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ +w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ + +#ifdef __STDC__ +static const float zero= 0.0000000000e+00; +#else +static float zero= 0.0000000000e+00; +#endif + +#ifdef __STDC__ + static float sin_pif(float x) +#else + static float sin_pif(x) + float x; +#endif +{ + float y,z; + __int32_t n,ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floorf(y); + if(z!=y) { /* inexact anyway */ + y *= (float)0.5; + y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ + n = (__int32_t) (y*(float)4.0); + } else { + if(ix>=0x4b800000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x4b000000) z = y+two23; /* exact */ + GET_FLOAT_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sinf(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; + case 3: + case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; + default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; + } + return -y; +} + + +#ifdef __STDC__ + float __ieee754_lgammaf_r(float x, int *signgamp) +#else + float __ieee754_lgammaf_r(x,signgamp) + float x; int *signgamp; +#endif +{ + float t,y,z,nadj,p,p1,p2,p3,q,r,w; + __int32_t i,hx,ix; + + GET_FLOAT_WORD(hx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x*x; + if(ix==0) return one/zero; + if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_logf(-x); + } else return -__ieee754_logf(x); + } + if(hx<0) { + if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ + return one/zero; + t = sin_pif(x); + if(t==zero) return one/zero; /* -integer */ + nadj = __ieee754_logf(pi/fabsf(t*x)); + if(t<zero) *signgamp = -1; + x = -x; + } + + /* purge off 1 and 2 */ + if (ix==0x3f800000||ix==0x40000000) r = 0; + /* for x < 2.0 */ + else if(ix<0x40000000) { + if(ix<=0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ + r = -__ieee754_logf(x); + if(ix>=0x3f3b4a20) {y = one-x; i= 0;} + else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-(float)0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-(float)0.5*y + p1/p2); + } + } + else if(ix<0x41000000) { /* x < 8.0 */ + i = (__int32_t)x; + t = zero; + y = x-(float)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+(float)6.0); /* FALLTHRU */ + case 6: z *= (y+(float)5.0); /* FALLTHRU */ + case 5: z *= (y+(float)4.0); /* FALLTHRU */ + case 4: z *= (y+(float)3.0); /* FALLTHRU */ + case 3: z *= (y+(float)2.0); /* FALLTHRU */ + r += __ieee754_logf(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x5c800000) { + t = __ieee754_logf(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(__ieee754_logf(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/newlib/libm/math/k_cos.c b/newlib/libm/math/k_cos.c new file mode 100644 index 00000000000..6c60c243856 --- /dev/null +++ b/newlib/libm/math/k_cos.c @@ -0,0 +1,96 @@ + +/* @(#)k_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. + * ==================================================== + */ + +/* + * __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) */ diff --git a/newlib/libm/math/k_rem_pio2.c b/newlib/libm/math/k_rem_pio2.c new file mode 100644 index 00000000000..8569256686c --- /dev/null +++ b/newlib/libm/math/k_rem_pio2.c @@ -0,0 +1,320 @@ + +/* @(#)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; + 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) */ diff --git a/newlib/libm/math/k_sin.c b/newlib/libm/math/k_sin.c new file mode 100644 index 00000000000..f119916dfbc --- /dev/null +++ b/newlib/libm/math/k_sin.c @@ -0,0 +1,79 @@ + +/* @(#)k_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. + * ==================================================== + */ + +/* __kernel_sin( x, y, iy) + * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since 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) */ diff --git a/newlib/libm/math/k_standard.c b/newlib/libm/math/k_standard.c new file mode 100644 index 00000000000..0d72f1a530d --- /dev/null +++ b/newlib/libm/math/k_standard.c @@ -0,0 +1,784 @@ + +/* @(#)k_standard.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. + * ==================================================== + * + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _USE_WRITE +#include <stdio.h> /* fputs(), stderr */ +#define WRITE2(u,v) fputs(u, stderr) +#else /* !defined(_USE_WRITE) */ +#include <unistd.h> /* write */ +#define WRITE2(u,v) write(2, u, v) +#undef fflush +#endif /* !defined(_USE_WRITE) */ + +#ifdef __STDC__ +static const double zero = 0.0; /* used as const */ +#else +static double zero = 0.0; /* used as const */ +#endif + +/* + * Standard conformance (non-IEEE) on exception cases. + * Mapping: + * 1 -- acos(|x|>1) + * 2 -- asin(|x|>1) + * 3 -- atan2(+-0,+-0) + * 4 -- hypot overflow + * 5 -- cosh overflow + * 6 -- exp overflow + * 7 -- exp underflow + * 8 -- y0(0) + * 9 -- y0(-ve) + * 10-- y1(0) + * 11-- y1(-ve) + * 12-- yn(0) + * 13-- yn(-ve) + * 14-- lgamma(finite) overflow + * 15-- lgamma(-integer) + * 16-- log(0) + * 17-- log(x<0) + * 18-- log10(0) + * 19-- log10(x<0) + * 20-- pow(0.0,0.0) + * 21-- pow(x,y) overflow + * 22-- pow(x,y) underflow + * 23-- pow(0,negative) + * 24-- pow(neg,non-integral) + * 25-- sinh(finite) overflow + * 26-- sqrt(negative) + * 27-- fmod(x,0) + * 28-- remainder(x,0) + * 29-- acosh(x<1) + * 30-- atanh(|x|>1) + * 31-- atanh(|x|=1) + * 32-- scalb overflow + * 33-- scalb underflow + * 34-- j0(|x|>X_TLOSS) + * 35-- y0(x>X_TLOSS) + * 36-- j1(|x|>X_TLOSS) + * 37-- y1(x>X_TLOSS) + * 38-- jn(|x|>X_TLOSS, n) + * 39-- yn(x>X_TLOSS, n) + * 40-- gamma(finite) overflow + * 41-- gamma(-integer) + * 42-- pow(NaN,0.0) + */ + + +#ifdef __STDC__ + double __kernel_standard(double x, double y, int type) +#else + double __kernel_standard(x,y,type) + double x,y; int type; +#endif +{ + struct exception exc; +#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + +#ifdef _USE_WRITE + /* (void) fflush(_stdout_r(p)); */ +#endif + exc.arg1 = x; + exc.arg2 = y; + exc.err = 0; + switch(type) { + case 1: + case 101: + /* acos(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "acos" : "acosf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if(_LIB_VERSION == _SVID_) { + (void) WRITE2("acos: DOMAIN error\n", 19); + } */ + errno = EDOM; + } + break; + case 2: + case 102: + /* asin(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "asin" : "asinf"; + exc.retval = zero; + if(_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if(_LIB_VERSION == _SVID_) { + (void) WRITE2("asin: DOMAIN error\n", 19); + } */ + errno = EDOM; + } + break; + case 3: + case 103: + /* atan2(+-0,+-0) */ + exc.arg1 = y; + exc.arg2 = x; + exc.type = DOMAIN; + exc.name = type < 100 ? "atan2" : "atan2f"; + exc.retval = zero; + if(_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if(_LIB_VERSION == _SVID_) { + (void) WRITE2("atan2: DOMAIN error\n", 20); + } */ + errno = EDOM; + } + break; + case 4: + case 104: + /* hypot(finite,finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "hypot" : "hypotf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 5: + case 105: + /* cosh(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "cosh" : "coshf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 6: + case 106: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "exp" : "expf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 7: + case 107: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "exp" : "expf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 8: + case 108: + /* y0(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "y0" : "y0f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } */ + errno = EDOM; + } + break; + case 9: + case 109: + /* y0(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "y0" : "y0f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /*if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } */ + errno = EDOM; + } + break; + case 10: + case 110: + /* y1(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "y1" : "y1f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } */ + errno = EDOM; + } + break; + case 11: + case 111: + /* y1(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "y1" : "y1f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } */ + errno = EDOM; + } + break; + case 12: + case 112: + /* yn(n,0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "yn" : "ynf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } */ + errno = EDOM; + } + break; + case 13: + case 113: + /* yn(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "yn" : "ynf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } */ + errno = EDOM; + } + break; + case 14: + case 114: + /* lgamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "lgamma" : "lgammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 15: + case 115: + /* lgamma(-integer) or lgamma(0) */ + exc.type = SING; + exc.name = type < 100 ? "lgamma" : "lgammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("lgamma: SING error\n", 19); + } */ + errno = EDOM; + } + break; + case 16: + case 116: + /* log(0) */ + exc.type = SING; + exc.name = type < 100 ? "log" : "logf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: SING error\n", 16); + } */ + errno = EDOM; + } + break; + case 17: + case 117: + /* log(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "log" : "logf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: DOMAIN error\n", 18); + } */ + errno = EDOM; + } + break; + case 18: + case 118: + /* log10(0) */ + exc.type = SING; + exc.name = type < 100 ? "log10" : "log10f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: SING error\n", 18); + } */ + errno = EDOM; + } + break; + case 19: + case 119: + /* log10(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "log10" : "log10f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: DOMAIN error\n", 20); + } */ + errno = EDOM; + } + break; + case 20: + case 120: + /* pow(0.0,0.0) */ + /* error only if _LIB_VERSION == _SVID_ */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : "powf"; + exc.retval = zero; + if (_LIB_VERSION != _SVID_) exc.retval = 1.0; + else if (!matherr(&exc)) { + /* (void) WRITE2("pow(0,0): DOMAIN error\n", 23); */ + errno = EDOM; + } + break; + case 21: + case 121: + /* pow(x,y) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "pow" : "powf"; + if (_LIB_VERSION == _SVID_) { + exc.retval = HUGE; + y *= 0.5; + if(x<zero&&rint(y)!=y) exc.retval = -HUGE; + } else { + exc.retval = HUGE_VAL; + y *= 0.5; + if(x<zero&&rint(y)!=y) exc.retval = -HUGE_VAL; + } + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 22: + case 122: + /* pow(x,y) underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "pow" : "powf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 23: + case 123: + /* 0**neg */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : "powf"; + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("pow(0,neg): DOMAIN error\n", 25); + } */ + errno = EDOM; + } + break; + case 24: + case 124: + /* neg**non-integral */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : "powf"; + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = zero/zero; /* X/Open allow NaN */ + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("neg**non-integral: DOMAIN error\n", 32); + } */ + errno = EDOM; + } + break; + case 25: + case 125: + /* sinh(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "sinh" : "sinhf"; + if (_LIB_VERSION == _SVID_) + exc.retval = ( (x>zero) ? HUGE : -HUGE); + else + exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 26: + case 126: + /* sqrt(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "sqrt" : "sqrtf"; + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("sqrt: DOMAIN error\n", 19); + } */ + errno = EDOM; + } + break; + case 27: + case 127: + /* fmod(x,0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "fmod" : "fmodf"; + if (_LIB_VERSION == _SVID_) + exc.retval = x; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("fmod: DOMAIN error\n", 20); + } */ + errno = EDOM; + } + break; + case 28: + case 128: + /* remainder(x,0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "remainder" : "remainderf"; + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("remainder: DOMAIN error\n", 24); + } */ + errno = EDOM; + } + break; + case 29: + case 129: + /* acosh(x<1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "acosh" : "acoshf"; + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("acosh: DOMAIN error\n", 20); + } */ + errno = EDOM; + } + break; + case 30: + case 130: + /* atanh(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "atanh" : "atanhf"; + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: DOMAIN error\n", 20); + } */ + errno = EDOM; + } + break; + case 31: + case 131: + /* atanh(|x|=1) */ + exc.type = SING; + exc.name = type < 100 ? "atanh" : "atanhf"; + exc.retval = x/zero; /* sign(x)*inf */ + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: SING error\n", 18); + } */ + errno = EDOM; + } + break; + case 32: + case 132: + /* scalb overflow; SVID also returns +-HUGE_VAL */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "scalb" : "scalbf"; + exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 33: + case 133: + /* scalb underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "scalb" : "scalbf"; + exc.retval = copysign(zero,x); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 34: + case 134: + /* j0(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "j0" : "j0f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } */ + errno = ERANGE; + } + break; + case 35: + case 135: + /* y0(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "y0" : "y0f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } */ + errno = ERANGE; + } + break; + case 36: + case 136: + /* j1(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "j1" : "j1f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } */ + errno = ERANGE; + } + break; + case 37: + case 137: + /* y1(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "y1" : "y1f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } */ + errno = ERANGE; + } + break; + case 38: + case 138: + /* jn(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "jn" : "jnf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } */ + errno = ERANGE; + } + break; + case 39: + case 139: + /* yn(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "yn" : "ynf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } */ + errno = ERANGE; + } + break; + case 40: + case 140: + /* gamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "gamma" : "gammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 41: + case 141: + /* gamma(-integer) or gamma(0) */ + exc.type = SING; + exc.name = type < 100 ? "gamma" : "gammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + /* if (_LIB_VERSION == _SVID_) { + (void) WRITE2("gamma: SING error\n", 18); + } */ + errno = EDOM; + } + break; + case 42: + case 142: + /* pow(NaN,0.0) */ + /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : "powf"; + exc.retval = x; + if (_LIB_VERSION == _IEEE_ || + _LIB_VERSION == _POSIX_) exc.retval = 1.0; + else if (!matherr(&exc)) { + errno = EDOM; + } + break; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; +} + + diff --git a/newlib/libm/math/k_tan.c b/newlib/libm/math/k_tan.c new file mode 100644 index 00000000000..9f5b307600c --- /dev/null +++ b/newlib/libm/math/k_tan.c @@ -0,0 +1,132 @@ + +/* @(#)k_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. + * ==================================================== + */ + +/* __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. + * + * 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) */ diff --git a/newlib/libm/math/kf_cos.c b/newlib/libm/math/kf_cos.c new file mode 100644 index 00000000000..4f71af237bf --- /dev/null +++ b/newlib/libm/math/kf_cos.c @@ -0,0 +1,59 @@ +/* kf_cos.c -- float version of k_cos.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 +one = 1.0000000000e+00, /* 0x3f800000 */ +C1 = 4.1666667908e-02, /* 0x3d2aaaab */ +C2 = -1.3888889225e-03, /* 0xbab60b61 */ +C3 = 2.4801587642e-05, /* 0x37d00d01 */ +C4 = -2.7557314297e-07, /* 0xb493f27c */ +C5 = 2.0875723372e-09, /* 0x310f74f6 */ +C6 = -1.1359647598e-11; /* 0xad47d74e */ + +#ifdef __STDC__ + float __kernel_cosf(float x, float y) +#else + float __kernel_cosf(x, y) + float x,y; +#endif +{ + float a,hz,z,r,qx; + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x32000000) { /* 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 < 0x3e99999a) /* if |x| < 0.3 */ + return one - ((float)0.5*z - (z*r - x*y)); + else { + if(ix > 0x3f480000) { /* x > 0.78125 */ + qx = (float)0.28125; + } else { + SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */ + } + hz = (float)0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/newlib/libm/math/kf_rem_pio2.c b/newlib/libm/math/kf_rem_pio2.c new file mode 100644 index 00000000000..261c4812965 --- /dev/null +++ b/newlib/libm/math/kf_rem_pio2.c @@ -0,0 +1,208 @@ +/* kf_rem_pio2.c -- float version of k_rem_pio2.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" + +/* In the float version, the input parameter x contains 8 bit + integers, not 24 bit integers. 113 bit precision is not supported. */ + +#ifdef __STDC__ +static const int init_jk[] = {4,7,9}; /* initial value for jk */ +#else +static int init_jk[] = {4,7,9}; +#endif + +#ifdef __STDC__ +static const float PIo2[] = { +#else +static float PIo2[] = { +#endif + 1.5703125000e+00, /* 0x3fc90000 */ + 4.5776367188e-04, /* 0x39f00000 */ + 2.5987625122e-05, /* 0x37da0000 */ + 7.5437128544e-08, /* 0x33a20000 */ + 6.0026650317e-11, /* 0x2e840000 */ + 7.3896444519e-13, /* 0x2b500000 */ + 5.3845816694e-15, /* 0x27c20000 */ + 5.6378512969e-18, /* 0x22d00000 */ + 8.3009228831e-20, /* 0x1fc40000 */ + 3.2756352257e-22, /* 0x1bc60000 */ + 6.3331015649e-25, /* 0x17440000 */ +}; + +#ifdef __STDC__ +static const float +#else +static float +#endif +zero = 0.0, +one = 1.0, +two8 = 2.5600000000e+02, /* 0x43800000 */ +twon8 = 3.9062500000e-03; /* 0x3b800000 */ + +#ifdef __STDC__ + int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2) +#else + int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) + float 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; + float 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)/8; if(jv<0) jv=0; + q0 = e0-8*(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 : (float) 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 = (float)((__int32_t)(twon8* z)); + iq[i] = (__int32_t)(z-two8*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbnf(z,(int)q0); /* actual value of z */ + z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ + n = (__int32_t) z; + z -= (float)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(8-q0)); n += i; + iq[jz-1] -= i<<(8-q0); + ih = iq[jz-1]>>(7-q0); + } + else if(q0==0) ih = iq[jz-1]>>8; + else if(z>=(float)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] = 0x100- j; + } + } else iq[i] = 0xff - j; + } + if(q0>0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7f; break; + case 2: + iq[jz-1] &= 0x3f; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbnf(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] = (float) 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==(float)0.0) { + jz -= 1; q0 -= 8; + while(iq[jz]==0) { jz--; q0-=8;} + } else { /* break z into 8-bit if necessary */ + z = scalbnf(z,-(int)q0); + if(z>=two8) { + fw = (float)((__int32_t)(twon8*z)); + iq[jz] = (__int32_t)(z-two8*fw); + jz += 1; q0 += 8; + iq[jz] = (__int32_t) fw; + } else iq[jz] = (__int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbnf(one,(int)q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(float)iq[i]; fw*=twon8; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/newlib/libm/math/kf_sin.c b/newlib/libm/math/kf_sin.c new file mode 100644 index 00000000000..e81fa0bd81b --- /dev/null +++ b/newlib/libm/math/kf_sin.c @@ -0,0 +1,49 @@ +/* kf_sin.c -- float version of k_sin.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 +half = 5.0000000000e-01,/* 0x3f000000 */ +S1 = -1.6666667163e-01, /* 0xbe2aaaab */ +S2 = 8.3333337680e-03, /* 0x3c088889 */ +S3 = -1.9841270114e-04, /* 0xb9500d01 */ +S4 = 2.7557314297e-06, /* 0x3638ef1b */ +S5 = -2.5050759689e-08, /* 0xb2d72f34 */ +S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */ + +#ifdef __STDC__ + float __kernel_sinf(float x, float y, int iy) +#else + float __kernel_sinf(x, y, iy) + float x,y; int iy; /* iy=0 if y is zero */ +#endif +{ + float z,r,v; + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x32000000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/newlib/libm/math/kf_tan.c b/newlib/libm/math/kf_tan.c new file mode 100644 index 00000000000..285d7f647d8 --- /dev/null +++ b/newlib/libm/math/kf_tan.c @@ -0,0 +1,96 @@ +/* kf_tan.c -- float version of k_tan.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 +one = 1.0000000000e+00, /* 0x3f800000 */ +pio4 = 7.8539812565e-01, /* 0x3f490fda */ +pio4lo= 3.7748947079e-08, /* 0x33222168 */ +T[] = { + 3.3333334327e-01, /* 0x3eaaaaab */ + 1.3333334029e-01, /* 0x3e088889 */ + 5.3968254477e-02, /* 0x3d5d0dd1 */ + 2.1869488060e-02, /* 0x3cb327a4 */ + 8.8632395491e-03, /* 0x3c11371f */ + 3.5920790397e-03, /* 0x3b6b6916 */ + 1.4562094584e-03, /* 0x3abede48 */ + 5.8804126456e-04, /* 0x3a1a26c8 */ + 2.4646313977e-04, /* 0x398137b9 */ + 7.8179444245e-05, /* 0x38a3f445 */ + 7.1407252108e-05, /* 0x3895c07a */ + -1.8558637748e-05, /* 0xb79bae5f */ + 2.5907305826e-05, /* 0x37d95384 */ +}; + +#ifdef __STDC__ + float __kernel_tanf(float x, float y, int iy) +#else + float __kernel_tanf(x, y, iy) + float x,y; int iy; +#endif +{ + float z,r,v,w,s; + __int32_t ix,hx; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; /* high word of |x| */ + if(ix<0x31800000) /* x < 2**-28 */ + {if((int)x==0) { /* generate inexact */ + if((ix|(iy+1))==0) return one/fabsf(x); + else return (iy==1)? x: -one/x; + } + } + if(ix>=0x3f2ca140) { /* |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>=0x3f2ca140) { + v = (float)iy; + return (float)(1-((hx>>30)&2))*(v-(float)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 */ + float a,t; + __int32_t i; + z = w; + GET_FLOAT_WORD(i,z); + SET_FLOAT_WORD(z,i&0xfffff000); + v = r-(z - x); /* z+v = r+x */ + t = a = -(float)1.0/w; /* a = -1.0/w */ + GET_FLOAT_WORD(i,t); + SET_FLOAT_WORD(t,i&0xfffff000); + s = (float)1.0+t*z; + return t+a*(s+t*v); + } +} diff --git a/newlib/libm/math/math.tex b/newlib/libm/math/math.tex new file mode 100644 index 00000000000..c6035deae27 --- /dev/null +++ b/newlib/libm/math/math.tex @@ -0,0 +1,199 @@ +@node Math +@chapter Mathematical Functions (@file{math.h}) + +This chapter groups a wide variety of mathematical functions. The +corresponding definitions and declarations are in @file{math.h}. +Two definitions from @file{math.h} are of particular interest. + +@enumerate +@item +The representation of infinity as a @code{double} is defined as +@code{HUGE_VAL}; this number is returned on overflow by many functions. + +@item +The structure @code{exception} is used when you write customized error +handlers for the mathematical functions. You can customize error +handling for most of these functions by defining your own version of +@code{matherr}; see the section on @code{matherr} for details. +@end enumerate + +@cindex system calls +@cindex support subroutines +@cindex stubs +@cindex OS stubs +Since the error handling code calls @code{fputs}, the mathematical +subroutines require stubs or minimal implementations for the same list +of OS subroutines as @code{fputs}: @code{close}, @code{fstat}, +@code{isatty}, @code{lseek}, @code{read}, @code{sbrk}, @code{write}. +@xref{syscalls,,System Calls, libc.info, The Cygnus C Support Library}, +for a discussion and for sample minimal implementations of these support +subroutines. + +Alternative declarations of the mathematical functions, which exploit +specific machine capabilities to operate faster---but generally have +less error checking and may reflect additional limitations on some +machines---are available when you include @file{fastmath.h} instead of +@file{math.h}. + +@menu +* version:: Version of library +* acos:: Arccosine +* acosh:: Inverse hyperbolic cosine +* asin:: Arcsine +* asinh:: Inverse hyperbolic sine +* atan:: Arctangent +* atan2:: Arctangent of y/x +* atanh:: Inverse hyperbolic tangent +* jN:: Bessel functions (jN, yN) +* cbrt:: Cube root +* copysign:: Sign of Y, magnitude of X +* cosh:: Hyperbolic cosine +* erf:: Error function (erf, erfc) +* exp:: Exponential +* expm1:: Exponential of x, - 1 +* fabs:: Absolute value (magnitude) +* floor:: Floor and ceiling (floor, ceil) +* fmod:: Floating-point remainder (modulo) +* frexp:: Split floating-point number +* gamma:: Logarithmic gamma function +* hypot:: Distance from origin +* ilogb:: Get exponent +* infinity:: Floating infinity +* isnan:: Check type of number +* ldexp:: Load exponent +* log:: Natural logarithms +* log10:: Base 10 logarithms +* log1p:: Log of 1 + X +* matherr:: Modifiable math error handler +* modf:: Split fractional and integer parts +* nan:: Floating Not a Number +* nextafter:: Get next representable number +* pow:: X to the power Y +* remainder:: remainder of X divided by Y +* scalbn:: scalbn +* sin:: Sine or cosine (sin, cos) +* sinh:: Hyperbolic sine +* sqrt:: Positive square root +* tan:: Tangent +* tanh:: Hyperbolic tangent +@end menu + +@page +@node version +@section Version of library + +There are four different versions of the math library routines: IEEE, +POSIX, X/Open, or SVID. The version may be selected at runtime by +setting the global variable @code{_LIB_VERSION}, defined in +@file{math.h}. It may be set to one of the following constants defined +in @file{math.h}: @code{_IEEE_}, @code{_POSIX_}, @code{_XOPEN_}, or +@code{_SVID_}. The @code{_LIB_VERSION} variable is not specific to any +thread, and changing it will affect all threads. + +The versions of the library differ only in how errors are handled. + +In IEEE mode, the @code{matherr} function is never called, no warning +messages are printed, and @code{errno} is never set. + +In POSIX mode, @code{errno} is set correctly, but the @code{matherr} +function is never called and no warning messages are printed. + +In X/Open mode, @code{errno} is set correctly, and @code{matherr} is +called, but warning message are not printed. + +In SVID mode, functions which overflow return 3.40282346638528860e+38, +the maximum single precision floating point value, rather than infinity. +Also, @code{errno} is set correctly, @code{matherr} is called, and, if +@code{matherr} returns 0, warning messages are printed for some errors. +For example, by default @samp{log(-1.0)} writes this message on standard +error output: + +@example +log: DOMAIN error +@end example + +The library is set to X/Open mode by default. + +@page +@include math/wacos.def + +@page +@include math/wacosh.def + +@page +@include math/wasin.def + +@page +@include math/sasinh.def + +@page +@include math/satan.def + +@page +@include math/watan2.def + +@page +@include math/watanh.def + +@page +@include math/wj0.def + +@page +@include math/wcosh.def + +@page +@include math/serf.def + +@page +@include math/wexp.def + +@page +@include math/sfabs.def + +@page +@include math/sfloor.def + +@page +@include math/wfmod.def + +@page +@include math/sfrexp.def + +@page +@include math/wgamma.def + +@page +@include math/whypot.def + +@page +@include math/sisnan.def + +@page +@include math/sldexp.def + +@page +@include math/wlog.def + +@page +@include math/wlog10.def + +@page +@include math/wpow.def + +@page +@include math/wremainder.def + +@page +@include math/wsqrt.def + +@page +@include math/ssin.def + +@page +@include math/wsinh.def + +@page +@include math/stan.def + +@page +@include math/stanh.def diff --git a/newlib/libm/math/s_asinh.c b/newlib/libm/math/s_asinh.c new file mode 100644 index 00000000000..958b71f820a --- /dev/null +++ b/newlib/libm/math/s_asinh.c @@ -0,0 +1,107 @@ + +/* @(#)s_asinh.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 + <<asinh>>, <<asinhf>>---inverse hyperbolic sine + +INDEX + asinh +INDEX + asinhf + +ANSI_SYNOPSIS + #include <math.h> + double asinh(double <[x]>); + float asinhf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double asinh(<[x]>) + double <[x]>; + + float asinhf(<[x]>) + float <[x]>; + +DESCRIPTION +<<asinh>> calculates the inverse hyperbolic sine of <[x]>. +<<asinh>> is defined as +@ifinfo +. sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>)) +@end ifinfo +@tex +$$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$ +@end tex + +<<asinhf>> is identical, other than taking and returning floats. + +RETURNS +<<asinh>> and <<asinhf>> return the calculated value. + +PORTABILITY +Neither <<asinh>> nor <<asinhf>> are ANSI C. + +*/ + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +huge= 1.00000000000000000000e+300; + +#ifdef __STDC__ + double asinh(double x) +#else + double asinh(x) + double x; +#endif +{ + double t,w; + __int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = __ieee754_log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); + w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); + } + if(hx>0) return w; else return -w; +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/s_atan.c b/newlib/libm/math/s_atan.c new file mode 100644 index 00000000000..b1410ecca55 --- /dev/null +++ b/newlib/libm/math/s_atan.c @@ -0,0 +1,181 @@ + +/* @(#)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 */ diff --git a/newlib/libm/math/s_ceil.c b/newlib/libm/math/s_ceil.c new file mode 100644 index 00000000000..24d69169c35 --- /dev/null +++ b/newlib/libm/math/s_ceil.c @@ -0,0 +1,80 @@ + +/* @(#)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<i1) i0+=1; /* got a carry */ + i1 = j; + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/s_cos.c b/newlib/libm/math/s_cos.c new file mode 100644 index 00000000000..c4712330137 --- /dev/null +++ b/newlib/libm/math/s_cos.c @@ -0,0 +1,82 @@ + +/* @(#)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 */ diff --git a/newlib/libm/math/s_erf.c b/newlib/libm/math/s_erf.c new file mode 100644 index 00000000000..825309dee84 --- /dev/null +++ b/newlib/libm/math/s_erf.c @@ -0,0 +1,373 @@ + +/* @(#)s_erf.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 + <<erf>>, <<erff>>, <<erfc>>, <<erfcf>>---error function +INDEX + erf +INDEX + erff +INDEX + erfc +INDEX + erfcf + +ANSI_SYNOPSIS + #include <math.h> + double erf(double <[x]>); + float erff(float <[x]>); + double erfc(double <[x]>); + float erfcf(float <[x]>); +TRAD_SYNOPSIS + #include <math.h> + + double erf(<[x]>) + double <[x]>; + + float erff(<[x]>) + float <[x]>; + + double erfc(<[x]>) + double <[x]>; + + float erfcf(<[x]>) + float <[x]>; + +DESCRIPTION + <<erf>> calculates an approximation to the ``error function'', + which estimates the probability that an observation will fall within + <[x]> standard deviations of the mean (assuming a normal + distribution). + @tex + The error function is defined as + $${2\over\sqrt\pi}\times\int_0^x e^{-t^2}dt$$ + @end tex + + <<erfc>> calculates the complementary probability; that is, + <<erfc(<[x]>)>> is <<1 - erf(<[x]>)>>. <<erfc>> is computed directly, + so that you can use it to avoid the loss of precision that would + result from subtracting large probabilities (on large <[x]>) from 1. + + <<erff>> and <<erfcf>> differ from <<erf>> and <<erfc>> only in the + argument and result types. + +RETURNS + For positive arguments, <<erf>> and all its variants return a + probability---a number between 0 and 1. + +PORTABILITY + None of the variants of <<erf>> are ANSI C. +*/ + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * where R = P/Q where P is an odd poly of degree 8 and + * Q is an odd poly of degree 10. + * -57.90 + * | R - (erf(x)-x)/x | <= 2 + * + * + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * That is, we use rational approximation to approximate + * erf(1+s) - (c = (single)0.84506291151) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * where + * P1(s) = degree 6 poly in s + * Q1(s) = degree 6 poly in s + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) + * erf(x) = 1 - erfc(x) + * where + * R1(z) = degree 7 poly in z, (z=1/x^2) + * S1(z) = degree 8 poly in z + * + * 4. For x in [1/0.35,28] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6<x<0 + * = 2.0 - tiny (if x <= -6) + * erf(x) = sign(x)*(1.0 - erfc(x)) if x < 6, else + * erf(x) = sign(x)*(1.0 - tiny) + * where + * R2(z) = degree 6 poly in z, (z=1/x^2) + * S2(z) = degree 7 poly in z + * + * Note1: + * To compute exp(-x*x-0.5625+R/S), let s be a single + * precision number and s := x; then + * -x*x = -s*s + (s-x)*(s+x) + * exp(-x*x-0.5626+R/S) = + * exp(-s*s-0.5625)*exp((s-x)*(s+x)+R/S); + * Note2: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ) + * x*sqrt(pi) + * We use rational approximation to approximate + * g(s)=f(1/x^2) = log(erfc(x)*x) - x*x + 0.5625 + * Here is the error bound for R1/S1 and R2/S2 + * |R1/S1 - f(x)| < 2**(-62.57) + * |R2/S2 - f(x)| < 2**(-61.52) + * + * 5. For inf > x >= 28 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +tiny = 1e-300, +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ + /* c = (float)0.84506291151 */ +erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ +efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ +pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ +pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ +pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ +pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ +pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ +qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ +qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ +qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ +qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ +qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ +pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ +pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ +pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ +pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ +pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ +pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ +qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ +qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ +qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ +qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ +qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ +qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ +ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ +ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ +ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ +ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ +ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ +ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ +ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ +sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ +sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ +sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ +sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ +sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ +sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ +sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ +sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ +rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ +rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ +rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ +rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ +rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ +rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ +sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ +sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ +sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ +sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ +sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ +sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ +sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ + +#ifdef __STDC__ + double erf(double x) +#else + double erf(x) + double x; +#endif +{ + __int32_t hx,ix,i; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erf(nan)=nan */ + i = ((__uint32_t)hx>>31)<<1; + return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3e300000) { /* |x|<2**-28 */ + if (ix < 0x00800000) + return 0.125*(8.0*x+efx8*x); /*avoid underflow */ + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40180000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} + +#ifdef __STDC__ + double erfc(double x) +#else + double erfc(x) + double x; +#endif +{ + __int32_t hx,ix; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (double)(((__uint32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3c700000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3fd00000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x403c0000) { /* |x|<28 */ + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)* + __ieee754_exp((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/s_fabs.c b/newlib/libm/math/s_fabs.c new file mode 100644 index 00000000000..95b871ca53a --- /dev/null +++ b/newlib/libm/math/s_fabs.c @@ -0,0 +1,73 @@ + +/* @(#)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 */ diff --git a/newlib/libm/math/s_floor.c b/newlib/libm/math/s_floor.c new file mode 100644 index 00000000000..65e234ed299 --- /dev/null +++ b/newlib/libm/math/s_floor.c @@ -0,0 +1,134 @@ + +/* @(#)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<i1) i0 +=1 ; /* got a carry */ + i1=j; + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/s_frexp.c b/newlib/libm/math/s_frexp.c new file mode 100644 index 00000000000..aaa36068ad7 --- /dev/null +++ b/newlib/libm/math/s_frexp.c @@ -0,0 +1,114 @@ + +/* @(#)s_frexp.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 + <<frexp>>, <<frexpf>>---split floating-point number +INDEX + frexp +INDEX + frexpf + +ANSI_SYNOPSIS + #include <math.h> + double frexp(double <[val]>, int *<[exp]>); + float frexpf(float <[val]>, int *<[exp]>); + +TRAD_SYNOPSIS + #include <math.h> + double frexp(<[val]>, <[exp]>) + double <[val]>; + int *<[exp]>; + + float frexpf(<[val]>, <[exp]>) + float <[val]>; + int *<[exp]>; + + +DESCRIPTION + All non zero, normal numbers can be described as <[m]> * 2**<[p]>. + <<frexp>> represents the double <[val]> as a mantissa <[m]> + and a power of two <[p]>. The resulting mantissa will always + be greater than or equal to <<0.5>>, and less than <<1.0>> (as + long as <[val]> is nonzero). The power of two will be stored + in <<*>><[exp]>. + +@ifinfo +<[m]> and <[p]> are calculated so that +<[val]> is <[m]> times <<2>> to the power <[p]>. +@end ifinfo +@tex +<[m]> and <[p]> are calculated so that +$ val = m \times 2^p $. +@end tex + +<<frexpf>> is identical, other than taking and returning +floats rather than doubles. + +RETURNS +<<frexp>> returns the mantissa <[m]>. If <[val]> is <<0>>, infinity, +or Nan, <<frexp>> will set <<*>><[exp]> to <<0>> and return <[val]>. + +PORTABILITY +<<frexp>> is ANSI. +<<frexpf>> is an extension. + + +*/ + +/* + * for non-zero x + * x = frexp(arg,&exp); + * return a double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */ + +#ifdef __STDC__ + double frexp(double x, int *eptr) +#else + double frexp(x, eptr) + double x; int *eptr; +#endif +{ + __int32_t hx, ix, lx; + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */ + if (ix<0x00100000) { /* subnormal */ + x *= two54; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -54; + } + *eptr += (ix>>20)-1022; + hx = (hx&0x800fffff)|0x3fe00000; + SET_HIGH_WORD(x,hx); + return x; +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/s_infconst.c b/newlib/libm/math/s_infconst.c new file mode 100644 index 00000000000..85b3b689c9d --- /dev/null +++ b/newlib/libm/math/s_infconst.c @@ -0,0 +1,15 @@ +/* Infinity as a constant value. This is used for HUGE_VAL. + * Added by Cygnus Support. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS +#ifdef __IEEE_BIG_ENDIAN +const union __dmath __infinity = { 0x7ff00000, 0 }; +#else +const union __dmath __infinity = { 0, 0x7ff00000 }; +#endif +#else /* defined (_DOUBLE_IS_32BITS) */ +const union __dmath __infinity = { 0x7f800000, 0 }; +#endif /* defined (_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/s_isinf.c b/newlib/libm/math/s_isinf.c new file mode 100644 index 00000000000..87f099566b6 --- /dev/null +++ b/newlib/libm/math/s_isinf.c @@ -0,0 +1,26 @@ +/* + * isinf(x) returns 1 if x is infinity, else 0; + * no branching! + * Added by Cygnus Support. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + int isinf(double x) +#else + int isinf(x) + double x; +#endif +{ + __int32_t hx,lx; + EXTRACT_WORDS(hx,lx,x); + hx &= 0x7fffffff; + hx |= (__uint32_t)(lx|(-lx))>>31; + hx = 0x7ff00000 - hx; + return 1 - (int)((__uint32_t)(hx|(-hx))>>31); +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/s_isnan.c b/newlib/libm/math/s_isnan.c new file mode 100644 index 00000000000..5d83fc04326 --- /dev/null +++ b/newlib/libm/math/s_isnan.c @@ -0,0 +1,122 @@ + +/* @(#)s_isnan.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 + <<isnan>>,<<isnanf>>,<<isinf>>,<<isinff>>,<<finite>>,<<finitef>>---test for exceptional numbers + +INDEX + isnan +INDEX + isinf +INDEX + finite + +INDEX + isnanf +INDEX + isinff +INDEX + finitef + +ANSI_SYNOPSIS + #include <ieeefp.h> + int isnan(double <[arg]>); + int isinf(double <[arg]>); + int finite(double <[arg]>); + int isnanf(float <[arg]>); + int isinff(float <[arg]>); + int finitef(float <[arg]>); + +TRAD_SYNOPSIS + #include <ieeefp.h> + int isnan(<[arg]>) + double <[arg]>; + int isinf(<[arg]>) + double <[arg]>; + int finite(<[arg]>); + double <[arg]>; + int isnanf(<[arg]>); + float <[arg]>; + int isinff(<[arg]>); + float <[arg]>; + int finitef(<[arg]>); + float <[arg]>; + + +DESCRIPTION + These functions provide information on the floating point + argument supplied. + + There are five major number formats - + o+ + o zero + a number which contains all zero bits. + o subnormal + Is used to represent number with a zero exponent, but a non zero fraction. + o normal + A number with an exponent, and a fraction + o infinity + A number with an all 1's exponent and a zero fraction. + o NAN + A number with an all 1's exponent and a non zero fraction. + + o- + + <<isnan>> returns 1 if the argument is a nan. <<isinf>> + returns 1 if the argument is infinity. <<finite>> returns 1 if the + argument is zero, subnormal or normal. + + The <<isnanf>>, <<isinff>> and <<finitef>> perform the same + operations as their <<isnan>>, <<isinf>> and <<finite>> + counterparts, but on single precision floating point numbers. + +QUICKREF + isnan - pure +QUICKREF + isinf - pure +QUICKREF + finite - pure +QUICKREF + isnan - pure +QUICKREF + isinf - pure +QUICKREF + finite - pure +*/ + +/* + * isnan(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + int isnan(double x) +#else + int isnan(x) + double x; +#endif +{ + __int32_t hx,lx; + EXTRACT_WORDS(hx,lx,x); + hx &= 0x7fffffff; + hx |= (__uint32_t)(lx|(-lx))>>31; + hx = 0x7ff00000 - hx; + return (int)(((__uint32_t)(hx))>>31); +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/s_ldexp.c b/newlib/libm/math/s_ldexp.c new file mode 100644 index 00000000000..ccf7171b18a --- /dev/null +++ b/newlib/libm/math/s_ldexp.c @@ -0,0 +1,81 @@ + +/* @(#)s_ldexp.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 + <<ldexp>>, <<ldexpf>>---load exponent + +INDEX + ldexp +INDEX + ldexpf + +ANSI_SYNOPSIS + #include <math.h> + double ldexp(double <[val]>, int <[exp]>); + float ldexpf(float <[val]>, int <[exp]>); + +TRAD_SYNOPSIS + #include <math.h> + + double ldexp(<[val]>, <[exp]>) + double <[val]>; + int <[exp]>; + + float ldexpf(<[val]>, <[exp]>) + float <[val]>; + int <[exp]>; + + +DESCRIPTION +<<ldexp>> calculates the value +@ifinfo +<[val]> times 2 to the power <[exp]>. +@end ifinfo +@tex +$val\times 2^{exp}$. +@end tex +<<ldexpf>> is identical, save that it takes and returns <<float>> +rather than <<double>> values. + +RETURNS +<<ldexp>> returns the calculated value. + +Underflow and overflow both set <<errno>> to <<ERANGE>>. +On underflow, <<ldexp>> and <<ldexpf>> return 0.0. +On overflow, <<ldexp>> returns plus or minus <<HUGE_VAL>>. + +PORTABILITY +<<ldexp>> is ANSI, <<ldexpf>> is an extension. + +*/ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double ldexp(double value, int exp) +#else + double ldexp(value, exp) + double value; int exp; +#endif +{ + if(!finite(value)||value==0.0) return value; + value = scalbn(value,exp); + if(!finite(value)||value==0.0) errno = ERANGE; + return value; +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/s_signif.c b/newlib/libm/math/s_signif.c new file mode 100644 index 00000000000..f68046bdc27 --- /dev/null +++ b/newlib/libm/math/s_signif.c @@ -0,0 +1,34 @@ + +/* @(#)s_signif.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. + * ==================================================== + */ + +/* + * significand(x) computes just + * scalb(x, (double) -ilogb(x)), + * for exercising the fraction-part(F) IEEE 754-1985 test vector. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double significand(double x) +#else + double significand(x) + double x; +#endif +{ + return __ieee754_scalb(x,(double) -ilogb(x)); +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/s_sin.c b/newlib/libm/math/s_sin.c new file mode 100644 index 00000000000..28259f378fe --- /dev/null +++ b/newlib/libm/math/s_sin.c @@ -0,0 +1,132 @@ + +/* @(#)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 */ diff --git a/newlib/libm/math/s_tan.c b/newlib/libm/math/s_tan.c new file mode 100644 index 00000000000..2959f416e83 --- /dev/null +++ b/newlib/libm/math/s_tan.c @@ -0,0 +1,114 @@ + +/* @(#)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 */ diff --git a/newlib/libm/math/s_tanh.c b/newlib/libm/math/s_tanh.c new file mode 100644 index 00000000000..b5541d02853 --- /dev/null +++ b/newlib/libm/math/s_tanh.c @@ -0,0 +1,128 @@ + +/* @(#)s_tanh.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 + <<tanh>>, <<tanhf>>---hyperbolic tangent + +INDEX +tanh +INDEX +tanhf + +ANSI_SYNOPSIS + #include <math.h> + double tanh(double <[x]>); + float tanhf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double tanh(<[x]>) + double <[x]>; + + float tanhf(<[x]>) + float <[x]>; + + +DESCRIPTION + +<<tanh>> computes the hyperbolic tangent of +the argument <[x]>. Angles are specified in radians. + +<<tanh(<[x]>)>> is defined as +. sinh(<[x]>)/cosh(<[x]>) + +<<tanhf>> is identical, save that it takes and returns <<float>> values. + +RETURNS +The hyperbolic tangent of <[x]> is returned. + +PORTABILITY +<<tanh>> is ANSI C. <<tanhf>> is an extension. + +*/ + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 22.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include "fdlibm.h" + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double one=1.0, two=2.0, tiny = 1.0e-300; +#else +static double one=1.0, two=2.0, tiny = 1.0e-300; +#endif + +#ifdef __STDC__ + double tanh(double x) +#else + double tanh(x) + double x; +#endif +{ + double t,z; + __int32_t jx,ix; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3c800000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3ff00000) { /* |x|>=1 */ + t = expm1(two*fabs(x)); + z = one - two/(t+two); + } else { + t = expm1(-two*fabs(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} + +#endif /* _DOUBLE_IS_32BITS */ diff --git a/newlib/libm/math/sf_asinh.c b/newlib/libm/math/sf_asinh.c new file mode 100644 index 00000000000..d5dfef81194 --- /dev/null +++ b/newlib/libm/math/sf_asinh.c @@ -0,0 +1,66 @@ +/* sf_asinh.c -- float version of s_asinh.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 +one = 1.0000000000e+00, /* 0x3F800000 */ +ln2 = 6.9314718246e-01, /* 0x3f317218 */ +huge= 1.0000000000e+30; + +#ifdef __STDC__ + float asinhf(float x) +#else + float asinhf(x) + float x; +#endif +{ + float t,w; + __int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x+x; /* x is inf or NaN */ + if(ix< 0x31800000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x4d800000) { /* |x| > 2**28 */ + w = __ieee754_logf(fabsf(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabsf(x); + w = __ieee754_logf((float)2.0*t+one/(__ieee754_sqrtf(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1pf(fabsf(x)+t/(one+__ieee754_sqrtf(one+t))); + } + if(hx>0) return w; else return -w; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double asinh(double x) +#else + double asinh(x) + double x; +#endif +{ + return (double) asinhf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_atan.c b/newlib/libm/math/sf_atan.c new file mode 100644 index 00000000000..7ea664f23af --- /dev/null +++ b/newlib/libm/math/sf_atan.c @@ -0,0 +1,129 @@ +/* sf_atan.c -- float version of s_atan.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 atanhi[] = { +#else +static float atanhi[] = { +#endif + 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ + 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ + 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ + 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ +}; + +#ifdef __STDC__ +static const float atanlo[] = { +#else +static float atanlo[] = { +#endif + 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ + 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ + 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ + 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ +}; + +#ifdef __STDC__ +static const float aT[] = { +#else +static float aT[] = { +#endif + 3.3333334327e-01, /* 0x3eaaaaaa */ + -2.0000000298e-01, /* 0xbe4ccccd */ + 1.4285714924e-01, /* 0x3e124925 */ + -1.1111110449e-01, /* 0xbde38e38 */ + 9.0908870101e-02, /* 0x3dba2e6e */ + -7.6918758452e-02, /* 0xbd9d8795 */ + 6.6610731184e-02, /* 0x3d886b35 */ + -5.8335702866e-02, /* 0xbd6ef16b */ + 4.9768779427e-02, /* 0x3d4bda59 */ + -3.6531571299e-02, /* 0xbd15a221 */ + 1.6285819933e-02, /* 0x3c8569d7 */ +}; + +#ifdef __STDC__ + static const float +#else + static float +#endif +one = 1.0, +huge = 1.0e30; + +#ifdef __STDC__ + float atanf(float x) +#else + float atanf(x) + float x; +#endif +{ + float w,s1,s2,z; + __int32_t ix,hx,id; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x50800000) { /* if |x| >= 2^34 */ + if(ix>0x7f800000) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ + if (ix < 0x31000000) { /* |x| < 2^-29 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabsf(x); + if (ix < 0x3f980000) { /* |x| < 1.1875 */ + if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = ((float)2.0*x-one)/((float)2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x401c0000) { /* |x| < 2.4375 */ + id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -(float)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; + } +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double atan(double x) +#else + double atan(x) + double x; +#endif +{ + return (double) atanf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_ceil.c b/newlib/libm/math/sf_ceil.c new file mode 100644 index 00000000000..85f0e971499 --- /dev/null +++ b/newlib/libm/math/sf_ceil.c @@ -0,0 +1,69 @@ +/* sf_ceil.c -- float version of s_ceil.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 huge = 1.0e30; +#else +static float huge = 1.0e30; +#endif + +#ifdef __STDC__ + float ceilf(float x) +#else + float ceilf(x) + float x; +#endif +{ + __int32_t i0,j0; + __uint32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;} + else if(i0!=0) { i0=0x3f800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double ceil(double x) +#else + double ceil(x) + double x; +#endif +{ + return (double) ceilf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_cos.c b/newlib/libm/math/sf_cos.c new file mode 100644 index 00000000000..8f3a8af01b6 --- /dev/null +++ b/newlib/libm/math/sf_cos.c @@ -0,0 +1,68 @@ +/* sf_cos.c -- float version of s_cos.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 one=1.0; +#else +static float one=1.0; +#endif + +#ifdef __STDC__ + float cosf(float x) +#else + float cosf(x) + float x; +#endif +{ + float y[2],z=0.0; + __int32_t n,ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_cosf(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_cosf(y[0],y[1]); + case 1: return -__kernel_sinf(y[0],y[1],1); + case 2: return -__kernel_cosf(y[0],y[1]); + default: + return __kernel_sinf(y[0],y[1],1); + } + } +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double cos(double x) +#else + double cos(x) + double x; +#endif +{ + return (double) cosf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_erf.c b/newlib/libm/math/sf_erf.c new file mode 100644 index 00000000000..1a9fa8d0126 --- /dev/null +++ b/newlib/libm/math/sf_erf.c @@ -0,0 +1,246 @@ +/* sf_erf.c -- float version of s_erf.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 __v810__ +#define const +#endif + +#ifdef __STDC__ +static const float +#else +static float +#endif +tiny = 1e-30, +half= 5.0000000000e-01, /* 0x3F000000 */ +one = 1.0000000000e+00, /* 0x3F800000 */ +two = 2.0000000000e+00, /* 0x40000000 */ + /* c = (subfloat)0.84506291151 */ +erx = 8.4506291151e-01, /* 0x3f58560b */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.2837916613e-01, /* 0x3e0375d4 */ +efx8= 1.0270333290e+00, /* 0x3f8375d4 */ +pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ +pp1 = -3.2504209876e-01, /* 0xbea66beb */ +pp2 = -2.8481749818e-02, /* 0xbce9528f */ +pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ +pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ +qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ +qq2 = 6.5022252500e-02, /* 0x3d852a63 */ +qq3 = 5.0813062117e-03, /* 0x3ba68116 */ +qq4 = 1.3249473704e-04, /* 0x390aee49 */ +qq5 = -3.9602282413e-06, /* 0xb684e21a */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ +pa1 = 4.1485610604e-01, /* 0x3ed46805 */ +pa2 = -3.7220788002e-01, /* 0xbebe9208 */ +pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ +pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ +pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ +pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ +qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ +qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ +qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ +qa4 = 1.2617121637e-01, /* 0x3e013307 */ +qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ +qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.8649440333e-03, /* 0xbc21a093 */ +ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ +ra2 = -1.0558626175e+01, /* 0xc128f022 */ +ra3 = -6.2375331879e+01, /* 0xc2798057 */ +ra4 = -1.6239666748e+02, /* 0xc322658c */ +ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ +ra6 = -8.1287437439e+01, /* 0xc2a2932b */ +ra7 = -9.8143291473e+00, /* 0xc11d077e */ +sa1 = 1.9651271820e+01, /* 0x419d35ce */ +sa2 = 1.3765776062e+02, /* 0x4309a863 */ +sa3 = 4.3456588745e+02, /* 0x43d9486f */ +sa4 = 6.4538726807e+02, /* 0x442158c9 */ +sa5 = 4.2900814819e+02, /* 0x43d6810b */ +sa6 = 1.0863500214e+02, /* 0x42d9451f */ +sa7 = 6.5702495575e+00, /* 0x40d23f7c */ +sa8 = -6.0424413532e-02, /* 0xbd777f97 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.8649431020e-03, /* 0xbc21a092 */ +rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ +rb2 = -1.7757955551e+01, /* 0xc18e104b */ +rb3 = -1.6063638306e+02, /* 0xc320a2ea */ +rb4 = -6.3756646729e+02, /* 0xc41f6441 */ +rb5 = -1.0250950928e+03, /* 0xc480230b */ +rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ +sb1 = 3.0338060379e+01, /* 0x41f2b459 */ +sb2 = 3.2579251099e+02, /* 0x43a2e571 */ +sb3 = 1.5367296143e+03, /* 0x44c01759 */ +sb4 = 3.1998581543e+03, /* 0x4547fdbb */ +sb5 = 2.5530502930e+03, /* 0x451f90ce */ +sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ +sb7 = -2.2440952301e+01; /* 0xc1b38712 */ + +#ifdef __STDC__ + float erff(float x) +#else + float erff(x) + float x; +#endif +{ + __int32_t hx,ix,i; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erf(nan)=nan */ + i = ((__uint32_t)hx>>31)<<1; + return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x31800000) { /* |x|<2**-28 */ + if (ix < 0x04000000) + /*avoid underflow */ + return (float)0.125*((float)8.0*x+efx8*x); + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40c00000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xfffff000); + r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} + +#ifdef __STDC__ + float erfcf(float x) +#else + float erfcf(x) + float x; +#endif +{ + __int32_t hx,ix; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (float)(((__uint32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x23800000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3e800000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x41e00000) { /* |x|<28 */ + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xfffff000); + r = __ieee754_expf(-z*z-(float)0.5625)* + __ieee754_expf((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double erf(double x) +#else + double erf(x) + double x; +#endif +{ + return (double) erff((float) x); +} + +#ifdef __STDC__ + double erfc(double x) +#else + double erfc(x) + double x; +#endif +{ + return (double) erfcf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_fabs.c b/newlib/libm/math/sf_fabs.c new file mode 100644 index 00000000000..2aaed326ab9 --- /dev/null +++ b/newlib/libm/math/sf_fabs.c @@ -0,0 +1,47 @@ +/* sf_fabs.c -- float version of s_fabs.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. + * ==================================================== + */ + +/* + * fabsf(x) returns the absolute value of x. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + float fabsf(float x) +#else + float fabsf(x) + float x; +#endif +{ + __uint32_t ix; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x7fffffff); + return x; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double fabs(double x) +#else + double fabs(x) + double x; +#endif +{ + return (double) fabsf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_floor.c b/newlib/libm/math/sf_floor.c new file mode 100644 index 00000000000..787f2fdf025 --- /dev/null +++ b/newlib/libm/math/sf_floor.c @@ -0,0 +1,79 @@ +/* sf_floor.c -- float version of s_floor.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. + * ==================================================== + */ + +/* + * floorf(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floorf(x). + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const float huge = 1.0e30; +#else +static float huge = 1.0e30; +#endif + +#ifdef __STDC__ + float floorf(float x) +#else + float floorf(x) + float x; +#endif +{ + __int32_t i0,j0; + __uint32_t i; + GET_FLOAT_WORD(i0,x); + j0 = ((i0>>23)&0xff)-0x7f; + if(j0<23) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffff)!=0) + { i0=0xbf800000;} + } + } else { + i = (0x007fffff)>>j0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00800000)>>j0; + i0 &= (~i); + } + } + } else { + if(j0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double floor(double x) +#else + double floor(x) + double x; +#endif +{ + return (double) floorf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_frexp.c b/newlib/libm/math/sf_frexp.c new file mode 100644 index 00000000000..271fb9dca68 --- /dev/null +++ b/newlib/libm/math/sf_frexp.c @@ -0,0 +1,61 @@ +/* sf_frexp.c -- float version of s_frexp.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 +two25 = 3.3554432000e+07; /* 0x4c000000 */ + +#ifdef __STDC__ + float frexpf(float x, int *eptr) +#else + float frexpf(x, eptr) + float x; int *eptr; +#endif +{ + __int32_t hx, ix; + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7f800000||(ix==0)) return x; /* 0,inf,nan */ + if (ix<0x00800000) { /* subnormal */ + x *= two25; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -25; + } + *eptr += (ix>>23)-126; + hx = (hx&0x807fffff)|0x3f000000; + SET_FLOAT_WORD(x,hx); + return x; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double frexp(double x, int *eptr) +#else + double frexp(x, eptr) + double x; int *eptr; +#endif +{ + return (double) frexpf((float) x, eptr); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_isinf.c b/newlib/libm/math/sf_isinf.c new file mode 100644 index 00000000000..1af4aab2abe --- /dev/null +++ b/newlib/libm/math/sf_isinf.c @@ -0,0 +1,35 @@ +/* + * isinff(x) returns 1 if x is infinity, else 0; + * no branching! + * Added by Cygnus Support. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + int isinff(float x) +#else + int isinff(x) + float x; +#endif +{ + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + ix = 0x7f800000 - ix; + return 1 - (int)((__uint32_t)(ix|(-ix))>>31); +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + int isinf(double x) +#else + int isinf(x) + double x; +#endif +{ + return isinff((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_isnan.c b/newlib/libm/math/sf_isnan.c new file mode 100644 index 00000000000..8fdb6adf251 --- /dev/null +++ b/newlib/libm/math/sf_isnan.c @@ -0,0 +1,49 @@ +/* sf_isnan.c -- float version of s_isnan.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. + * ==================================================== + */ + +/* + * isnanf(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + int isnanf(float x) +#else + int isnanf(x) + float x; +#endif +{ + __int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + ix = 0x7f800000 - ix; + return (int)(((__uint32_t)(ix))>>31); +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + int isnan(double x) +#else + int isnan(x) + double x; +#endif +{ + return isnanf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_ldexp.c b/newlib/libm/math/sf_ldexp.c new file mode 100644 index 00000000000..2781304825c --- /dev/null +++ b/newlib/libm/math/sf_ldexp.c @@ -0,0 +1,44 @@ +/* sf_ldexp.c -- float version of s_ldexp.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" +#include <errno.h> + +#ifdef __STDC__ + float ldexpf(float value, int exp) +#else + float ldexpf(value, exp) + float value; int exp; +#endif +{ + if(!finitef(value)||value==(float)0.0) return value; + value = scalbnf(value,exp); + if(!finitef(value)||value==(float)0.0) errno = ERANGE; + return value; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double ldexp(double value, int exp) +#else + double ldexp(value, exp) + double value; int exp; +#endif +{ + return (double) ldexpf((float) value, exp); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_signif.c b/newlib/libm/math/sf_signif.c new file mode 100644 index 00000000000..fd4a072479a --- /dev/null +++ b/newlib/libm/math/sf_signif.c @@ -0,0 +1,40 @@ +/* sf_signif.c -- float version of s_signif.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__ + float significandf(float x) +#else + float significandf(x) + float x; +#endif +{ + return __ieee754_scalbf(x,(float) -ilogbf(x)); +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double significand(double x) +#else + double significand(x) + double x; +#endif +{ + return (double) significandf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_sin.c b/newlib/libm/math/sf_sin.c new file mode 100644 index 00000000000..315d4b4ba1e --- /dev/null +++ b/newlib/libm/math/sf_sin.c @@ -0,0 +1,62 @@ +/* sf_sin.c -- float version of s_sin.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__ + float sinf(float x) +#else + float sinf(x) + float x; +#endif +{ + float y[2],z=0.0; + __int32_t n,ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_sinf(y[0],y[1],1); + case 1: return __kernel_cosf(y[0],y[1]); + case 2: return -__kernel_sinf(y[0],y[1],1); + default: + return -__kernel_cosf(y[0],y[1]); + } + } +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double sin(double x) +#else + double sin(x) + double x; +#endif +{ + return (double) sinf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_tan.c b/newlib/libm/math/sf_tan.c new file mode 100644 index 00000000000..ade1cb216e5 --- /dev/null +++ b/newlib/libm/math/sf_tan.c @@ -0,0 +1,57 @@ +/* sf_tan.c -- float version of s_tan.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__ + float tanf(float x) +#else + float tanf(x) + float x; +#endif +{ + float y[2],z=0.0; + __int32_t n,ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double tan(double x) +#else + double tan(x) + double x; +#endif +{ + return (double) tanf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/sf_tanh.c b/newlib/libm/math/sf_tanh.c new file mode 100644 index 00000000000..ba9edf5c0c5 --- /dev/null +++ b/newlib/libm/math/sf_tanh.c @@ -0,0 +1,73 @@ +/* sf_tanh.c -- float version of s_tanh.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 one=1.0, two=2.0, tiny = 1.0e-30; +#else +static float one=1.0, two=2.0, tiny = 1.0e-30; +#endif + +#ifdef __STDC__ + float tanhf(float x) +#else + float tanhf(x) + float x; +#endif +{ + float t,z; + __int32_t jx,ix; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (ix<0x24000000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3f800000) { /* |x|>=1 */ + t = expm1f(two*fabsf(x)); + z = one - two/(t+two); + } else { + t = expm1f(-two*fabsf(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double tanh(double x) +#else + double tanh(x) + double x; +#endif +{ + return (double) tanhf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_acos.c b/newlib/libm/math/w_acos.c new file mode 100644 index 00000000000..c9ca99c4041 --- /dev/null +++ b/newlib/libm/math/w_acos.c @@ -0,0 +1,118 @@ + +/* @(#)w_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. + * ==================================================== + */ + +/* +FUNCTION + <<acos>>, <<acosf>>---arc cosine + +INDEX + acos +INDEX + acosf + +ANSI_SYNOPSIS + #include <math.h> + double acos(double <[x]>); + float acosf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double acos(<[x]>) + double <[x]>; + + float acosf(<[x]>) + float <[x]>; + + + +DESCRIPTION + + <<acos>> computes the inverse cosine (arc cosine) of the input value. + Arguments to <<acos>> must be in the range @minus{}1 to 1. + + <<acosf>> is identical to <<acos>>, except that it performs + its calculations on <<floats>>. + +RETURNS + @ifinfo + <<acos>> and <<acosf>> return values in radians, in the range of 0 to pi. + @end ifinfo + @tex + <<acos>> and <<acosf>> return values in radians, in the range of <<0>> to $\pi$. + @end tex + + If <[x]> is not between @minus{}1 and 1, the returned value is NaN + (not a number) the global variable <<errno>> is set to <<EDOM>>, and a + <<DOMAIN error>> message is sent as standard error output. + + You can modify error handling for these functions using <<matherr>>. + + +QUICKREF ANSI SVID POSIX RENTRANT + acos y,y,y,m + acosf n,n,n,m + +MATHREF + acos, [-1,1], acos(arg),,, + acos, NAN, arg,DOMAIN,EDOM + +MATHREF + acosf, [-1,1], acosf(arg),,, + acosf, NAN, argf,DOMAIN,EDOM + +*/ + +/* + * wrap_acos(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double acos(double x) /* wrapper acos */ +#else + double acos(x) /* wrapper acos */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_acos(x); +#else + double z; + struct exception exc; + z = __ieee754_acos(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>1.0) { + /* acos(|x|>1) */ + exc.type = DOMAIN; + exc.name = "acos"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_acosh.c b/newlib/libm/math/w_acosh.c new file mode 100644 index 00000000000..4120d7b129b --- /dev/null +++ b/newlib/libm/math/w_acosh.c @@ -0,0 +1,122 @@ + +/* @(#)w_acosh.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 +<<acosh>>, <<acoshf>>---inverse hyperbolic cosine + +INDEX +acosh +INDEX +acoshf + +ANSI_SYNOPSIS + #include <math.h> + double acosh(double <[x]>); + float acoshf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double acosh(<[x]>) + double <[x]>; + + float acoshf(<[x]>) + float <[x]>; + +DESCRIPTION +<<acosh>> calculates the inverse hyperbolic cosine of <[x]>. +<<acosh>> is defined as +@ifinfo +. log(<[x]> + sqrt(<[x]>*<[x]>-1)) +@end ifinfo +@tex +$$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$ +@end tex + +<[x]> must be a number greater than or equal to 1. + +<<acoshf>> is identical, other than taking and returning floats. + +RETURNS +<<acosh>> and <<acoshf>> return the calculated value. If <[x]> +less than 1, the return value is NaN and <<errno>> is set to <<EDOM>>. + +You can change the error-handling behavior with the non-ANSI +<<matherr>> function. + +PORTABILITY +Neither <<acosh>> nor <<acoshf>> are ANSI C. They are not recommended +for portable programs. + + +QUICKREF ANSI SVID POSIX RENTRANT + acos n,n,n,m + acosf n,n,n,m + +MATHREF + acosh, NAN, arg,DOMAIN,EDOM + acosh, < 1.0, NAN,DOMAIN,EDOM + acosh, >=1.0, acosh(arg),,, + +MATHREF + acoshf, NAN, arg,DOMAIN,EDOM + acoshf, < 1.0, NAN,DOMAIN,EDOM + acoshf, >=1.0, acosh(arg),,, + +*/ + +/* + * wrapper acosh(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double acosh(double x) /* wrapper acosh */ +#else + double acosh(x) /* wrapper acosh */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_acosh(x); +#else + double z; + struct exception exc; + z = __ieee754_acosh(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<1.0) { + /* acosh(x<1) */ + exc.type = DOMAIN; + exc.name = "acosh"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_asin.c b/newlib/libm/math/w_asin.c new file mode 100644 index 00000000000..f6cb271d392 --- /dev/null +++ b/newlib/libm/math/w_asin.c @@ -0,0 +1,121 @@ + +/* @(#)w_asin.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 + <<asin>>, <<asinf>>---arc sine + +INDEX + asin +INDEX + asinf + +ANSI_SYNOPSIS + #include <math.h> + double asin(double <[x]>); + float asinf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double asin(<[x]>) + double <[x]>; + + float asinf(<[x]>) + float <[x]>; + + +DESCRIPTION + +<<asin>> computes the inverse sine (arc sine) of the argument <[x]>. +Arguments to <<asin>> must be in the range @minus{}1 to 1. + +<<asinf>> is identical to <<asin>>, other than taking and +returning floats. + +You can modify error handling for these routines using <<matherr>>. + +RETURNS +@ifinfo +<<asin>> returns values in radians, in the range of -pi/2 to pi/2. +@end ifinfo +@tex +<<asin>> returns values in radians, in the range of $-\pi/2$ to $\pi/2$. +@end tex + +If <[x]> is not in the range @minus{}1 to 1, <<asin>> and <<asinf>> +return NaN (not a number), set the global variable <<errno>> to +<<EDOM>>, and issue a <<DOMAIN error>> message. + +You can change this error treatment using <<matherr>>. + +QUICKREF ANSI SVID POSIX RENTRANT + asin y,y,y,m + asinf n,n,n,m + +MATHREF + asin, -1<=arg<=1, asin(arg),,, + asin, NAN, arg,EDOM, DOMAIN + +MATHREF + asinf, -1<=arg<=1, asin(arg),,, + asinf, NAN, arg,EDOM, DOMAIN + + +*/ + +/* + * wrapper asin(x) + */ + + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double asin(double x) /* wrapper asin */ +#else + double asin(x) /* wrapper asin */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_asin(x); +#else + double z; + struct exception exc; + z = __ieee754_asin(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>1.0) { + /* asin(|x|>1) */ + exc.type = DOMAIN; + exc.name = "asin"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = 0.0; + if(_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_atan2.c b/newlib/libm/math/w_atan2.c new file mode 100644 index 00000000000..91742c72b91 --- /dev/null +++ b/newlib/libm/math/w_atan2.c @@ -0,0 +1,117 @@ + +/* @(#)w_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. + * ==================================================== + * + */ + +/* +FUNCTION + <<atan2>>, <<atan2f>>---arc tangent of y/x + +INDEX + atan2 +INDEX + atan2f + +ANSI_SYNOPSIS + #include <math.h> + double atan2(double <[y]>,double <[x]>); + float atan2f(float <[y]>,float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double atan2(<[y]>,<[x]>); + double <[y]>; + double <[x]>; + + float atan2f(<[y]>,<[x]>); + float <[y]>; + float <[x]>; + +DESCRIPTION + +<<atan2>> computes the inverse tangent (arc tangent) of <[y]>/<[x]>. +<<atan2>> produces the correct result even for angles near +@ifinfo +pi/2 or -pi/2 +@end ifinfo +@tex +$\pi/2$ or $-\pi/2$ +@end tex +(that is, when <[x]> is near 0). + +<<atan2f>> is identical to <<atan2>>, save that it takes and returns +<<float>>. + +RETURNS +<<atan2>> and <<atan2f>> return a value in radians, in the range of +@ifinfo +-pi to pi. +@end ifinfo +@tex +$-\pi$ to $\pi$. +@end tex + +If both <[x]> and <[y]> are 0.0, <<atan2>> causes a <<DOMAIN>> error. + +You can modify error handling for these functions using <<matherr>>. + +PORTABILITY +<<atan2>> is ANSI C. <<atan2f>> is an extension. + + +*/ + +/* + * wrapper atan2(y,x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double atan2(double y, double x) /* wrapper atan2 */ +#else + double atan2(y,x) /* wrapper atan2 */ + double y,x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_atan2(y,x); +#else + double z; + struct exception exc; + z = __ieee754_atan2(y,x); + if(_LIB_VERSION == _IEEE_||isnan(x)||isnan(y)) return z; + if(x==0.0&&y==0.0) { + /* atan2(+-0,+-0) */ + exc.arg1 = y; + exc.arg2 = x; + exc.type = DOMAIN; + exc.name = "atan2"; + exc.err = 0; + exc.retval = 0.0; + if(_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_atanh.c b/newlib/libm/math/w_atanh.c new file mode 100644 index 00000000000..b89d4f02537 --- /dev/null +++ b/newlib/libm/math/w_atanh.c @@ -0,0 +1,140 @@ + +/* @(#)w_atanh.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 + <<atanh>>, <<atanhf>>---inverse hyperbolic tangent + +INDEX + atanh +INDEX + atanhf + +ANSI_SYNOPSIS + #include <math.h> + double atanh(double <[x]>); + float atanhf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double atanh(<[x]>) + double <[x]>; + + float atanhf(<[x]>) + float <[x]>; + +DESCRIPTION + <<atanh>> calculates the inverse hyperbolic tangent of <[x]>. + + <<atanhf>> is identical, other than taking and returning + <<float>> values. + +RETURNS + <<atanh>> and <<atanhf>> return the calculated value. + + If + @ifinfo + |<[x]>| + @end ifinfo + @tex + $|x|$ + @end tex + is greater than 1, the global <<errno>> is set to <<EDOM>> and + the result is a NaN. A <<DOMAIN error>> is reported. + + If + @ifinfo + |<[x]>| + @end ifinfo + @tex + $|x|$ + @end tex + is 1, the global <<errno>> is set to <<EDOM>>; and the result is + infinity with the same sign as <<x>>. A <<SING error>> is reported. + + You can modify the error handling for these routines using + <<matherr>>. + +PORTABILITY + Neither <<atanh>> nor <<atanhf>> are ANSI C. + +QUICKREF + atanh - pure + atanhf - pure + + +*/ + +/* + * wrapper atanh(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double atanh(double x) /* wrapper atanh */ +#else + double atanh(x) /* wrapper atanh */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_atanh(x); +#else + double z,y; + struct exception exc; + z = __ieee754_atanh(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + y = fabs(x); + if(y>=1.0) { + if(y>1.0) { + /* atanh(|x|>1) */ + exc.type = DOMAIN; + exc.name = "atanh"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* atanh(|x|=1) */ + exc.type = SING; + exc.name = "atanh"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = x/0.0; /* sign(x)*inf */ + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ + + + + diff --git a/newlib/libm/math/w_cabs.c b/newlib/libm/math/w_cabs.c new file mode 100644 index 00000000000..bef76680c06 --- /dev/null +++ b/newlib/libm/math/w_cabs.c @@ -0,0 +1,20 @@ +/* + * cabs() wrapper for hypot(). + * + * Written by J.T. Conklin, <jtc@wimsey.com> + * Placed into the Public Domain, 1994. + */ + +#include "fdlibm.h" + +struct complex { + double x; + double y; +}; + +double +cabs(z) + struct complex z; +{ + return hypot(z.x, z.y); +} diff --git a/newlib/libm/math/w_cosh.c b/newlib/libm/math/w_cosh.c new file mode 100644 index 00000000000..7b38dcb088f --- /dev/null +++ b/newlib/libm/math/w_cosh.c @@ -0,0 +1,116 @@ + +/* @(#)w_cosh.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 + <<cosh>>, <<coshf>>---hyperbolic cosine + +ANSI_SYNOPSIS + #include <math.h> + double cosh(double <[x]>); + float coshf(float <[x]>) + +TRAD_SYNOPSIS + #include <math.h> + double cosh(<[x]>) + double <[x]>; + + float coshf(<[x]>) + float <[x]>; + +DESCRIPTION + + <<cosh>> computes the hyperbolic cosine of the argument <[x]>. + <<cosh(<[x]>)>> is defined as + @ifinfo + . (exp(x) + exp(-x))/2 + @end ifinfo + @tex + $${(e^x + e^{-x})} \over 2$$ + @end tex + + Angles are specified in radians. + + <<coshf>> is identical, save that it takes and returns <<float>>. + +RETURNS + The computed value is returned. When the correct value would create + an overflow, <<cosh>> returns the value <<HUGE_VAL>> with the + appropriate sign, and the global value <<errno>> is set to <<ERANGE>>. + + You can modify error handling for these functions using the + function <<matherr>>. + +PORTABILITY + <<cosh>> is ANSI. + <<coshf>> is an extension. + +QUICKREF + cosh ansi pure + coshf - pure +*/ + +/* + * wrapper cosh(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double cosh(double x) /* wrapper cosh */ +#else + double cosh(x) /* wrapper cosh */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_cosh(x); +#else + double z; + struct exception exc; + z = __ieee754_cosh(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>7.10475860073943863426e+02) { + /* cosh(finite) overflow */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = OVERFLOW; + exc.name = "cosh"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_drem.c b/newlib/libm/math/w_drem.c new file mode 100644 index 00000000000..d289bdaac9e --- /dev/null +++ b/newlib/libm/math/w_drem.c @@ -0,0 +1,15 @@ +/* + * drem() wrapper for remainder(). + * + * Written by J.T. Conklin, <jtc@wimsey.com> + * Placed into the Public Domain, 1994. + */ + +#include "fdlibm.h" + +double +drem(x, y) + double x, y; +{ + return remainder(x, y); +} diff --git a/newlib/libm/math/w_exp.c b/newlib/libm/math/w_exp.c new file mode 100644 index 00000000000..ae792a84642 --- /dev/null +++ b/newlib/libm/math/w_exp.c @@ -0,0 +1,136 @@ + +/* @(#)w_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. + * ==================================================== + */ + +/* +FUNCTION + <<exp>>, <<expf>>---exponential +INDEX + exp +INDEX + expf + +ANSI_SYNOPSIS + #include <math.h> + double exp(double <[x]>); + float expf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double exp(<[x]>); + double <[x]>; + + float expf(<[x]>); + float <[x]>; + +DESCRIPTION + <<exp>> and <<expf>> calculate the exponential of <[x]>, that is, + @ifinfo + e raised to the power <[x]> (where e + @end ifinfo + @tex + $e^x$ (where $e$ + @end tex + is the base of the natural system of logarithms, approximately 2.71828). + + You can use the (non-ANSI) function <<matherr>> to specify + error handling for these functions. + +RETURNS + On success, <<exp>> and <<expf>> return the calculated value. + If the result underflows, the returned value is <<0>>. If the + result overflows, the returned value is <<HUGE_VAL>>. In + either case, <<errno>> is set to <<ERANGE>>. + +PORTABILITY + <<exp>> is ANSI C. <<expf>> is an extension. + +*/ + +/* + * wrapper exp(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +static const double +#else +static double +#endif +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */ + +#ifdef __STDC__ + double exp(double x) /* wrapper exp */ +#else + double exp(x) /* wrapper exp */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_exp(x); +#else + double z; + struct exception exc; + z = __ieee754_exp(x); + if(_LIB_VERSION == _IEEE_) return z; + if(finite(x)) { + if(x>o_threshold) { + /* exp(finite) overflow */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = OVERFLOW; + exc.name = "exp"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else if(x<u_threshold) { + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = "exp"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + } + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_fmod.c b/newlib/libm/math/w_fmod.c new file mode 100644 index 00000000000..b6b36cb76ab --- /dev/null +++ b/newlib/libm/math/w_fmod.c @@ -0,0 +1,107 @@ + +/* @(#)w_fmod.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 +<<fmod>>, <<fmodf>>---floating-point remainder (modulo) + +INDEX +fmod +INDEX +fmodf + +ANSI_SYNOPSIS +#include <math.h> +double fmod(double <[x]>, double <[y]>) +float fmodf(float <[x]>, float <[y]>) + +TRAD_SYNOPSIS +#include <math.h> +double fmod(<[x]>, <[y]>) +double (<[x]>, <[y]>); + +float fmodf(<[x]>, <[y]>) +float (<[x]>, <[y]>); + +DESCRIPTION +The <<fmod>> and <<fmodf>> functions compute the floating-point +remainder of <[x]>/<[y]> (<[x]> modulo <[y]>). + +RETURNS +The <<fmod>> function returns the value +@ifinfo +<[x]>-<[i]>*<[y]>, +@end ifinfo +@tex +$x-i\times y$, +@end tex +for the largest integer <[i]> such that, if <[y]> is nonzero, the +result has the same sign as <[x]> and magnitude less than the +magnitude of <[y]>. + +<<fmod(<[x]>,0)>> returns NaN, and sets <<errno>> to <<EDOM>>. + +You can modify error treatment for these functions using <<matherr>>. + +PORTABILITY +<<fmod>> is ANSI C. <<fmodf>> is an extension. +*/ + +/* + * wrapper fmod(x,y) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double fmod(double x, double y) /* wrapper fmod */ +#else + double fmod(x,y) /* wrapper fmod */ + double x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_fmod(x,y); +#else + double z; + struct exception exc; + z = __ieee754_fmod(x,y); + if(_LIB_VERSION == _IEEE_ ||isnan(y)||isnan(x)) return z; + if(y==0.0) { + /* fmod(x,0) */ + exc.type = DOMAIN; + exc.name = "fmod"; + exc.arg1 = x; + exc.arg2 = y; + exc.err = 0; + if (_LIB_VERSION == _SVID_) + exc.retval = x; + else + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_gamma.c b/newlib/libm/math/w_gamma.c new file mode 100644 index 00000000000..da0211555d2 --- /dev/null +++ b/newlib/libm/math/w_gamma.c @@ -0,0 +1,193 @@ + +/* @(#)w_gamma.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 + <<gamma>>, <<gammaf>>, <<lgamma>>, <<lgammaf>>, <<gamma_r>>, + <<gammaf_r>>, <<lgamma_r>>, <<lgammaf_r>>---logarithmic gamma + function +INDEX +gamma +INDEX +gammaf +INDEX +lgamma +INDEX +lgammaf +INDEX +gamma_r +INDEX +gammaf_r +INDEX +lgamma_r +INDEX +lgammaf_r + +ANSI_SYNOPSIS +#include <math.h> +double gamma(double <[x]>); +float gammaf(float <[x]>); +double lgamma(double <[x]>); +float lgammaf(float <[x]>); +double gamma_r(double <[x]>, int *<[signgamp]>); +float gammaf_r(float <[x]>, int *<[signgamp]>); +double lgamma_r(double <[x]>, int *<[signgamp]>); +float lgammaf_r(float <[x]>, int *<[signgamp]>); + +TRAD_SYNOPSIS +#include <math.h> +double gamma(<[x]>) +double <[x]>; +float gammaf(<[x]>) +float <[x]>; +double lgamma(<[x]>) +double <[x]>; +float lgammaf(<[x]>) +float <[x]>; +double gamma_r(<[x]>, <[signgamp]>) +double <[x]>; +int <[signgamp]>; +float gammaf_r(<[x]>, <[signgamp]>) +float <[x]>; +int <[signgamp]>; +double lgamma_r(<[x]>, <[signgamp]>) +double <[x]>; +int <[signgamp]>; +float lgammaf_r(<[x]>, <[signgamp]>) +float <[x]>; +int <[signgamp]>; + +DESCRIPTION +<<gamma>> calculates +@tex +$\mit ln\bigl(\Gamma(x)\bigr)$, +@end tex +the natural logarithm of the gamma function of <[x]>. The gamma function +(<<exp(gamma(<[x]>))>>) is a generalization of factorial, and retains +the property that +@ifinfo +<<exp(gamma(N))>> is equivalent to <<N*exp(gamma(N-1))>>. +@end ifinfo +@tex +$\mit \Gamma(N)\equiv N\times\Gamma(N-1)$. +@end tex +Accordingly, the results of the gamma function itself grow very +quickly. <<gamma>> is defined as +@tex +$\mit ln\bigl(\Gamma(x)\bigr)$ rather than simply $\mit \Gamma(x)$ +@end tex +@ifinfo +the natural log of the gamma function, rather than the gamma function +itself, +@end ifinfo +to extend the useful range of results representable. + +The sign of the result is returned in the global variable <<signgam>>, +which is declared in math.h. + +<<gammaf>> performs the same calculation as <<gamma>>, but uses and +returns <<float>> values. + +<<lgamma>> and <<lgammaf>> are alternate names for <<gamma>> and +<<gammaf>>. The use of <<lgamma>> instead of <<gamma>> is a reminder +that these functions compute the log of the gamma function, rather +than the gamma function itself. + +The functions <<gamma_r>>, <<gammaf_r>>, <<lgamma_r>>, and +<<lgammaf_r>> are just like <<gamma>>, <<gammaf>>, <<lgamma>>, and +<<lgammaf>>, respectively, but take an additional argument. This +additional argument is a pointer to an integer. This additional +argument is used to return the sign of the result, and the global +variable <<signgam>> is not used. These functions may be used for +reentrant calls (but they will still set the global variable <<errno>> +if an error occurs). + +RETURNS +Normally, the computed result is returned. + +When <[x]> is a nonpositive integer, <<gamma>> returns <<HUGE_VAL>> +and <<errno>> is set to <<EDOM>>. If the result overflows, <<gamma>> +returns <<HUGE_VAL>> and <<errno>> is set to <<ERANGE>>. + +You can modify this error treatment using <<matherr>>. + +PORTABILITY +Neither <<gamma>> nor <<gammaf>> is ANSI C. */ + +/* double gamma(double x) + * Return the logarithm of the Gamma function of x. + * + * Method: call gamma_r + */ + +#include "fdlibm.h" +#include <reent.h> +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double gamma(double x) +#else + double gamma(x) + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_gamma_r(x,&(_REENT->_new._reent._gamma_signgam)); +#else + double y; + struct exception exc; + y = __ieee754_gamma_r(x,&(_REENT->_new._reent._gamma_signgam)); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "gamma"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if(floor(x)==x&&x<=0.0) { + /* gamma(-integer) or gamma(0) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* gamma(finite) overflow */ + exc.type = OVERFLOW; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return y; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_hypot.c b/newlib/libm/math/w_hypot.c new file mode 100644 index 00000000000..318853d5616 --- /dev/null +++ b/newlib/libm/math/w_hypot.c @@ -0,0 +1,109 @@ + +/* @(#)w_hypot.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 + <<hypot>>, <<hypotf>>---distance from origin +INDEX + hypot +INDEX + hypotf + +ANSI_SYNOPSIS + #include <math.h> + double hypot(double <[x]>, double <[y]>); + float hypotf(float <[x]>, float <[y]>); + +TRAD_SYNOPSIS + double hypot(<[x]>, <[y]>) + double <[x]>, <[y]>; + + float hypotf(<[x]>, <[y]>) + float <[x]>, <[y]>; + +DESCRIPTION + <<hypot>> calculates the Euclidean distance + @tex + $\sqrt{x^2+y^2}$ + @end tex + @ifinfo + <<sqrt(<[x]>*<[x]> + <[y]>*<[y]>)>> + @end ifinfo + between the origin (0,0) and a point represented by the + Cartesian coordinates (<[x]>,<[y]>). <<hypotf>> differs only + in the type of its arguments and result. + +RETURNS + Normally, the distance value is returned. On overflow, + <<hypot>> returns <<HUGE_VAL>> and sets <<errno>> to + <<ERANGE>>. + + You can change the error treatment with <<matherr>>. + +PORTABILITY + <<hypot>> and <<hypotf>> are not ANSI C. */ + +/* + * wrapper hypot(x,y) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double hypot(double x, double y)/* wrapper hypot */ +#else + double hypot(x,y) /* wrapper hypot */ + double x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_hypot(x,y); +#else + double z; + struct exception exc; + z = __ieee754_hypot(x,y); + if(_LIB_VERSION == _IEEE_) return z; + if((!finite(z))&&finite(x)&&finite(y)) { + /* hypot(finite,finite) overflow */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = OVERFLOW; + exc.name = "hypot"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = y; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_j0.c b/newlib/libm/math/w_j0.c new file mode 100644 index 00000000000..4f07908422e --- /dev/null +++ b/newlib/libm/math/w_j0.c @@ -0,0 +1,229 @@ + +/* @(#)w_j0.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 +<<jN>>,<<jNf>>,<<yN>>,<<yNf>>---Bessel functions + +INDEX +j0 +INDEX +j0f +INDEX +j1 +INDEX +j1f +INDEX +jn +INDEX +jnf +INDEX +y0 +INDEX +y0f +INDEX +y1 +INDEX +y1f +INDEX +yn +INDEX +ynf + +ANSI_SYNOPSIS +#include <math.h> +double j0(double <[x]>); +float j0f(float <[x]>); +double j1(double <[x]>); +float j1f(float <[x]>); +double jn(int <[n]>, double <[x]>); +float jnf(int <[n]>, float <[x]>); +double y0(double <[x]>); +float y0f(float <[x]>); +double y1(double <[x]>); +float y1f(float <[x]>); +double yn(int <[n]>, double <[x]>); +float ynf(int <[n]>, float <[x]>); + +TRAD_SYNOPSIS +#include <math.h> + +double j0(<[x]>) +double <[x]>; +float j0f(<[x]>) +float <[x]>; +double j1(<[x]>) +double <[x]>; +float j1f(<[x]>) +float <[x]>; +double jn(<[n]>, <[x]>) +int <[n]>; +double <[x]>; +float jnf(<[n]>, <[x]>) +int <[n]>; +float <[x]>; + +double y0(<[x]>) +double <[x]>; +float y0f(<[x]>) +float <[x]>; +double y1(<[x]>) +double <[x]>; +float y1f(<[x]>) +float <[x]>; +double yn(<[n]>, <[x]>) +int <[n]>; +double <[x]>; +float ynf(<[n]>, <[x]>) +int <[n]>; +float <[x]>; + +DESCRIPTION +The Bessel functions are a family of functions that solve the +differential equation +@ifinfo +. 2 2 2 +. x y'' + xy' + (x - p )y = 0 +@end ifinfo +@tex +$$x^2{d^2y\over dx^2} + x{dy\over dx} + (x^2-p^2)y = 0$$ +@end tex +These functions have many applications in engineering and physics. + +<<jn>> calculates the Bessel function of the first kind of order +<[n]>. <<j0>> and <<j1>> are special cases for order 0 and order +1 respectively. + +Similarly, <<yn>> calculates the Bessel function of the second kind of +order <[n]>, and <<y0>> and <<y1>> are special cases for order 0 and +1. + +<<jnf>>, <<j0f>>, <<j1f>>, <<ynf>>, <<y0f>>, and <<y1f>> perform the +same calculations, but on <<float>> rather than <<double>> values. + +RETURNS +The value of each Bessel function at <[x]> is returned. + +PORTABILITY +None of the Bessel functions are in ANSI C. +*/ + +/* + * wrapper j0(double x), y0(double x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double j0(double x) /* wrapper j0 */ +#else + double j0(x) /* wrapper j0 */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_j0(x); +#else + struct exception exc; + double z = __ieee754_j0(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>X_TLOSS) { + /* j0(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "j0"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#ifdef __STDC__ + double y0(double x) /* wrapper y0 */ +#else + double y0(x) /* wrapper y0 */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_y0(x); +#else + double z; + struct exception exc; + z = __ieee754_y0(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(x <= 0.0){ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + /* y0(0) = -inf or y0(x<0) = NaN */ + exc.type = DOMAIN; /* should be SING for IEEE y0(0) */ + exc.name = "y0"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + if(x>X_TLOSS) { + /* y0(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "y0"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ + + + + + + + diff --git a/newlib/libm/math/w_j1.c b/newlib/libm/math/w_j1.c new file mode 100644 index 00000000000..ba7df15660f --- /dev/null +++ b/newlib/libm/math/w_j1.c @@ -0,0 +1,121 @@ + +/* @(#)w_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. + * ==================================================== + */ + +/* + * wrapper of j1,y1 + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double j1(double x) /* wrapper j1 */ +#else + double j1(x) /* wrapper j1 */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_j1(x); +#else + double z; + struct exception exc; + z = __ieee754_j1(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(fabs(x)>X_TLOSS) { + /* j1(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "j1"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#ifdef __STDC__ + double y1(double x) /* wrapper y1 */ +#else + double y1(x) /* wrapper y1 */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_y1(x); +#else + double z; + struct exception exc; + z = __ieee754_y1(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(x <= 0.0){ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + /* y1(0) = -inf or y1(x<0) = NaN */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = "y1"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + if(x>X_TLOSS) { + /* y1(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "y1"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ + + + + + diff --git a/newlib/libm/math/w_jn.c b/newlib/libm/math/w_jn.c new file mode 100644 index 00000000000..6cadc9a0104 --- /dev/null +++ b/newlib/libm/math/w_jn.c @@ -0,0 +1,141 @@ + +/* @(#)w_jn.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. + * ==================================================== + */ + +/* + * wrapper jn(int n, double x), yn(int n, double x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for n<x, forward recursion us used starting + * from values of j0(x) and j1(x). + * for n>x, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double jn(int n, double x) /* wrapper jn */ +#else + double jn(n,x) /* wrapper jn */ + double x; int n; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_jn(n,x); +#else + double z; + struct exception exc; + z = __ieee754_jn(n,x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(fabs(x)>X_TLOSS) { + /* jn(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "jn"; + exc.err = 0; + exc.arg1 = n; + exc.arg2 = x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#ifdef __STDC__ + double yn(int n, double x) /* wrapper yn */ +#else + double yn(n,x) /* wrapper yn */ + double x; int n; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_yn(n,x); +#else + double z; + struct exception exc; + z = __ieee754_yn(n,x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(x <= 0.0){ + /* yn(n,0) = -inf or yn(x<0) = NaN */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = "yn"; + exc.err = 0; + exc.arg1 = n; + exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + if(x>X_TLOSS) { + /* yn(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "yn"; + exc.err = 0; + exc.arg1 = n; + exc.arg2 = x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_lgamma.c b/newlib/libm/math/w_lgamma.c new file mode 100644 index 00000000000..1dc63994f54 --- /dev/null +++ b/newlib/libm/math/w_lgamma.c @@ -0,0 +1,89 @@ + +/* @(#)w_lgamma.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. + * ==================================================== + * + */ + +/* double lgamma(double x) + * Return the logarithm of the Gamma function of x. + * + * Method: call __ieee754_lgamma_r + */ + +#include "fdlibm.h" +#include <reent.h> +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double lgamma(double x) +#else + double lgamma(x) + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_lgamma_r(x,&(_REENT->_new._reent._gamma_signgam)); +#else + double y; + struct exception exc; + y = __ieee754_lgamma_r(x,&(_REENT->_new._reent._gamma_signgam)); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "lgamma"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if(floor(x)==x&&x<=0.0) { + /* lgamma(-integer) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + + } else { + /* lgamma(finite) overflow */ + exc.type = OVERFLOW; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return y; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ + + + + + + + diff --git a/newlib/libm/math/w_log.c b/newlib/libm/math/w_log.c new file mode 100644 index 00000000000..dcc8b9762ec --- /dev/null +++ b/newlib/libm/math/w_log.c @@ -0,0 +1,115 @@ + +/* @(#)w_log.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 + <<log>>, <<logf>>---natural logarithms + +INDEX + log +INDEX + logf + +ANSI_SYNOPSIS + #include <math.h> + double log(double <[x]>); + float logf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double log(<[x]>); + double <[x]>; + + float logf(<[x]>); + float <[x]>; + +DESCRIPTION +Return the natural logarithm of <[x]>, that is, its logarithm base e +(where e is the base of the natural system of logarithms, 2.71828@dots{}). +<<log>> and <<logf>> are identical save for the return and argument types. + +You can use the (non-ANSI) function <<matherr>> to specify error +handling for these functions. + +RETURNS +Normally, returns the calculated value. When <[x]> is zero, the +returned value is <<-HUGE_VAL>> and <<errno>> is set to <<ERANGE>>. +When <[x]> is negative, the returned value is <<-HUGE_VAL>> and +<<errno>> is set to <<EDOM>>. You can control the error behavior via +<<matherr>>. + +PORTABILITY +<<log>> is ANSI, <<logf>> is an extension. +*/ + +/* + * wrapper log(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double log(double x) /* wrapper log */ +#else + double log(x) /* wrapper log */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_log(x); +#else + double z; + struct exception exc; + z = __ieee754_log(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z; +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "log"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if(x==0.0) { + /* log(0) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* log(x<0) */ + exc.type = DOMAIN; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_log10.c b/newlib/libm/math/w_log10.c new file mode 100644 index 00000000000..f427b86ccd7 --- /dev/null +++ b/newlib/libm/math/w_log10.c @@ -0,0 +1,115 @@ + +/* @(#)w_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* +FUNCTION + <<log10>>, <<log10f>>---base 10 logarithms + +INDEX +log10 +INDEX +log10f + +ANSI_SYNOPSIS + #include <math.h> + double log10(double <[x]>); + float log10f(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double log10(<[x]>) + double <[x]>; + + float log10f(<[x]>) + float <[x]>; + +DESCRIPTION +<<log10>> returns the base 10 logarithm of <[x]>. +It is implemented as <<log(<[x]>) / log(10)>>. + +<<log10f>> is identical, save that it takes and returns <<float>> values. + +RETURNS +<<log10>> and <<log10f>> return the calculated value. + +See the description of <<log>> for information on errors. + +PORTABILITY +<<log10>> is ANSI C. <<log10f>> is an extension. + + */ + +/* + * wrapper log10(X) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double log10(double x) /* wrapper log10 */ +#else + double log10(x) /* wrapper log10 */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_log10(x); +#else + double z; + struct exception exc; + z = __ieee754_log10(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<=0.0) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "log10"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if(x==0.0) { + /* log10(0) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* log10(x<0) */ + exc.type = DOMAIN; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_pow.c b/newlib/libm/math/w_pow.c new file mode 100644 index 00000000000..3df099a1714 --- /dev/null +++ b/newlib/libm/math/w_pow.c @@ -0,0 +1,231 @@ + + +/* @(#)w_pow.c 5.2 93/10/01 */ +/* + * ==================================================== + * 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 + <<pow>>, <<powf>>---x to the power y +INDEX + pow +INDEX + powf + + +ANSI_SYNOPSIS + #include <math.h> + double pow(double <[x]>, double <[y]>); + float pow(float <[x]>, float <[y]>); + +TRAD_SYNOPSIS + #include <math.h> + double pow(<[x]>, <[y]>); + double <[x]>, <[y]>; + + float pow(<[x]>, <[y]>); + float <[x]>, <[y]>; + +DESCRIPTION + <<pow>> and <<powf>> calculate <[x]> raised to the exp1.0nt <[y]>. + @tex + (That is, $x^y$.) + @end tex + +RETURNS + On success, <<pow>> and <<powf>> return the value calculated. + + When the argument values would produce overflow, <<pow>> + returns <<HUGE_VAL>> and set <<errno>> to <<ERANGE>>. If the + argument <[x]> passed to <<pow>> or <<powf>> is a negative + noninteger, and <[y]> is also not an integer, then <<errno>> + is set to <<EDOM>>. If <[x]> and <[y]> are both 0, then + <<pow>> and <<powf>> return <<1>>. + + You can modify error handling for these functions using <<matherr>>. + +PORTABILITY + <<pow>> is ANSI C. <<powf>> is an extension. */ + +/* + * wrapper pow(x,y) return x**y + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double pow(double x, double y) /* wrapper pow */ +#else + double pow(x,y) /* wrapper pow */ + double x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_pow(x,y); +#else + double z; +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + struct exception exc; + z=__ieee754_pow(x,y); + if(_LIB_VERSION == _IEEE_|| isnan(y)) return z; + if(isnan(x)) { + if(y==0.0) { + /* pow(NaN,0.0) */ + /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */ + exc.type = DOMAIN; + exc.name = "pow"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = y; + exc.retval = x; + if (_LIB_VERSION == _IEEE_ || + _LIB_VERSION == _POSIX_) exc.retval = 1.0; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; + } + if(x==0.0){ + if(y==0.0) { + /* pow(0.0,0.0) */ + /* error only if _LIB_VERSION == _SVID_ */ + exc.type = DOMAIN; + exc.name = "pow"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = y; + exc.retval = 0.0; + if (_LIB_VERSION != _SVID_) exc.retval = 1.0; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + if(finite(y)&&y<0.0) { + /* 0**neg */ + exc.type = DOMAIN; + exc.name = "pow"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = y; + if (_LIB_VERSION == _SVID_) + exc.retval = 0.0; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + return z; + } + if(!finite(z)) { + if(finite(x)&&finite(y)) { + if(isnan(z)) { + /* neg**non-integral */ + exc.type = DOMAIN; + exc.name = "pow"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = y; + if (_LIB_VERSION == _SVID_) + exc.retval = 0.0; + else + exc.retval = 0.0/0.0; /* X/Open allow NaN */ + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else { + /* pow(x,y) overflow */ + exc.type = OVERFLOW; + exc.name = "pow"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = y; + if (_LIB_VERSION == _SVID_) { + exc.retval = HUGE; + y *= 0.5; + if(x<0.0&&rint(y)!=y) exc.retval = -HUGE; + } else { + exc.retval = HUGE_VAL; + y *= 0.5; + if(x<0.0&&rint(y)!=y) exc.retval = -HUGE_VAL; + } + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + } + } + if(z==0.0&&finite(x)&&finite(y)) { + /* pow(x,y) underflow */ + exc.type = UNDERFLOW; + exc.name = "pow"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = y; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ + + + + + + + + + + + + + + diff --git a/newlib/libm/math/w_remainder.c b/newlib/libm/math/w_remainder.c new file mode 100644 index 00000000000..e4c1967160c --- /dev/null +++ b/newlib/libm/math/w_remainder.c @@ -0,0 +1,108 @@ + +/* @(#)w_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. + * ==================================================== + */ + +/* +FUNCTION +<<remainder>>, <<remainderf>>---round and remainder +INDEX + remainder +INDEX + remainderf + +ANSI_SYNOPSIS + #include <math.h> + double remainder(double <[x]>, double <[y]>); + float remainderf(float <[x]>, float <[y]>); + +TRAD_SYNOPSIS + #include <math.h> + double remainder(<[x]>,<[y]>) + double <[x]>, <[y]>; + float remainderf(<[x]>,<[y]>) + float <[x]>, <[y]>; + +DESCRIPTION +<<remainder>> and <<remainderf>> find the remainder of +<[x]>/<[y]>; this value is in the range -<[y]>/2 .. +<[y]>/2. + +RETURNS +<<remainder>> returns the integer result as a double. + +PORTABILITY +<<remainder>> is a System V release 4. +<<remainderf>> is an extension. + +*/ + +/* + * wrapper remainder(x,p) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double remainder(double x, double y) /* wrapper remainder */ +#else + double remainder(x,y) /* wrapper remainder */ + double x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_remainder(x,y); +#else + double z; + struct exception exc; + z = __ieee754_remainder(x,y); + if(_LIB_VERSION == _IEEE_ || isnan(y)) return z; + if(y==0.0) { + /* remainder(x,0) */ + exc.type = DOMAIN; + exc.name = "remainder"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = y; + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ + + + + + + + + + + + + + + + + + diff --git a/newlib/libm/math/w_scalb.c b/newlib/libm/math/w_scalb.c new file mode 100644 index 00000000000..c3249689238 --- /dev/null +++ b/newlib/libm/math/w_scalb.c @@ -0,0 +1,94 @@ + +/* @(#)w_scalb.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. + * ==================================================== + */ + +/* + * wrapper scalb(double x, double fn) is provide for + * passing various standard test suite. One + * should use scalbn() instead. + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +#ifdef _SCALB_INT + double scalb(double x, int fn) /* wrapper scalb */ +#else + double scalb(double x, double fn) /* wrapper scalb */ +#endif +#else + double scalb(x,fn) /* wrapper scalb */ +#ifdef _SCALB_INT + double x; int fn; +#else + double x,fn; +#endif +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_scalb(x,fn); +#else + double z; +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + struct exception exc; + z = __ieee754_scalb(x,fn); + if(_LIB_VERSION == _IEEE_) return z; + if(!(finite(z)||isnan(z))&&finite(x)) { + /* scalb overflow; SVID also returns +-HUGE_VAL */ + exc.type = OVERFLOW; + exc.name = "scalb"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = fn; + exc.retval = x > 0.0 ? HUGE_VAL : -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + if(z==0.0&&z!=x) { + /* scalb underflow */ + exc.type = UNDERFLOW; + exc.name = "scalb"; + exc.err = 0; + exc.arg1 = x; + exc.arg2 = fn; + exc.retval = copysign(0.0,x); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } +#ifndef _SCALB_INT + if(!finite(fn)) errno = ERANGE; +#endif + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_sinh.c b/newlib/libm/math/w_sinh.c new file mode 100644 index 00000000000..02a388862b9 --- /dev/null +++ b/newlib/libm/math/w_sinh.c @@ -0,0 +1,120 @@ + +/* @(#)w_sinh.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 + <<sinh>>, <<sinhf>>---hyperbolic sine + +INDEX + sinh +INDEX + sinhf + +ANSI_SYNOPSIS + #include <math.h> + double sinh(double <[x]>); + float sinhf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double sinh(<[x]>) + double <[x]>; + + float sinhf(<[x]>) + float <[x]>; + +DESCRIPTION + <<sinh>> computes the hyperbolic sine of the argument <[x]>. + Angles are specified in radians. <<sinh>>(<[x]>) is defined as + @ifinfo + . (exp(<[x]>) - exp(-<[x]>))/2 + @end ifinfo + @tex + $${e^x - e^{-x}}\over 2$$ + @end tex + + <<sinhf>> is identical, save that it takes and returns <<float>> values. + +RETURNS + The hyperbolic sine of <[x]> is returned. + + When the correct result is too large to be representable (an + overflow), <<sinh>> returns <<HUGE_VAL>> with the + appropriate sign, and sets the global value <<errno>> to + <<ERANGE>>. + + You can modify error handling for these functions with <<matherr>>. + +PORTABILITY + <<sinh>> is ANSI C. + <<sinhf>> is an extension. + +QUICKREF + sinh ansi pure + sinhf - pure +*/ + +/* + * wrapper sinh(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double sinh(double x) /* wrapper sinh */ +#else + double sinh(x) /* wrapper sinh */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_sinh(x); +#else + double z; + struct exception exc; + z = __ieee754_sinh(x); + if(_LIB_VERSION == _IEEE_) return z; + if(!finite(z)&&finite(x)) { + /* sinh(finite) overflow */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = OVERFLOW; + exc.name = "sinh"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = ( (x>0.0) ? HUGE : -HUGE); + else + exc.retval = ( (x>0.0) ? HUGE_VAL : -HUGE_VAL); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/w_sqrt.c b/newlib/libm/math/w_sqrt.c new file mode 100644 index 00000000000..23a793ce74a --- /dev/null +++ b/newlib/libm/math/w_sqrt.c @@ -0,0 +1,93 @@ + +/* @(#)w_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. + * ==================================================== + */ + +/* +FUNCTION + <<sqrt>>, <<sqrtf>>---positive square root + +INDEX + sqrt +INDEX + sqrtf + +ANSI_SYNOPSIS + #include <math.h> + double sqrt(double <[x]>); + float sqrtf(float <[x]>); + +TRAD_SYNOPSIS + #include <math.h> + double sqrt(<[x]>); + float sqrtf(<[x]>); + +DESCRIPTION + <<sqrt>> computes the positive square root of the argument. + You can modify error handling for this function with + <<matherr>>. + +RETURNS + On success, the square root is returned. If <[x]> is real and + positive, then the result is positive. If <[x]> is real and + negative, the global value <<errno>> is set to <<EDOM>> (domain error). + + +PORTABILITY + <<sqrt>> is ANSI C. <<sqrtf>> is an extension. +*/ + +/* + * wrapper sqrt(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double sqrt(double x) /* wrapper sqrt */ +#else + double sqrt(x) /* wrapper sqrt */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_sqrt(x); +#else + struct exception exc; + double z; + z = __ieee754_sqrt(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<0.0) { + exc.type = DOMAIN; + exc.name = "sqrt"; + exc.err = 0; + exc.arg1 = exc.arg2 = x; + if (_LIB_VERSION == _SVID_) + exc.retval = 0.0; + else + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_acos.c b/newlib/libm/math/wf_acos.c new file mode 100644 index 00000000000..8a1037441b7 --- /dev/null +++ b/newlib/libm/math/wf_acos.c @@ -0,0 +1,69 @@ +/* wf_acos.c -- float version of w_acos.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. + * ==================================================== + */ + +/* + * wrap_acosf(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef _HAVE_STDC + float acosf(float x) /* wrapper acosf */ +#else + float acosf(x) /* wrapper acosf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_acosf(x); +#else + float z; + struct exception exc; + z = __ieee754_acosf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(fabsf(x)>(float)1.0) { + /* acosf(|x|>1) */ + exc.type = DOMAIN; + exc.name = "acosf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double acos(double x) +#else + double acos(x) + double x; +#endif +{ + return (double) acosf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_acosh.c b/newlib/libm/math/wf_acosh.c new file mode 100644 index 00000000000..19c2450e6f2 --- /dev/null +++ b/newlib/libm/math/wf_acosh.c @@ -0,0 +1,70 @@ +/* wf_acosh.c -- float version of w_acosh.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. + * ==================================================== + * + */ + +/* + * wrapper acoshf(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float acoshf(float x) /* wrapper acoshf */ +#else + float acoshf(x) /* wrapper acoshf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_acoshf(x); +#else + float z; + struct exception exc; + z = __ieee754_acoshf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(x<(float)1.0) { + /* acoshf(x<1) */ + exc.type = DOMAIN; + exc.name = "acoshf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double acosh(double x) +#else + double acosh(x) + double x; +#endif +{ + return (double) acoshf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_asin.c b/newlib/libm/math/wf_asin.c new file mode 100644 index 00000000000..a5225f2f44c --- /dev/null +++ b/newlib/libm/math/wf_asin.c @@ -0,0 +1,71 @@ +/* wf_asin.c -- float version of w_asin.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. + * ==================================================== + * + */ + +/* + * wrapper asinf(x) + */ + + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float asinf(float x) /* wrapper asinf */ +#else + float asinf(x) /* wrapper asinf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_asinf(x); +#else + float z; + struct exception exc; + z = __ieee754_asinf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(fabsf(x)>(float)1.0) { + /* asinf(|x|>1) */ + exc.type = DOMAIN; + exc.name = "asinf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = 0.0; + if(_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double asin(double x) +#else + double asin(x) + double x; +#endif +{ + return (double) asinf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_atan2.c b/newlib/libm/math/wf_atan2.c new file mode 100644 index 00000000000..069a7ca13ad --- /dev/null +++ b/newlib/libm/math/wf_atan2.c @@ -0,0 +1,71 @@ +/* wf_atan2.c -- float version of w_atan2.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. + * ==================================================== + * + */ + +/* + * wrapper atan2f(y,x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float atan2f(float y, float x) /* wrapper atan2f */ +#else + float atan2f(y,x) /* wrapper atan2 */ + float y,x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_atan2f(y,x); +#else + float z; + struct exception exc; + z = __ieee754_atan2f(y,x); + if(_LIB_VERSION == _IEEE_||isnanf(x)||isnanf(y)) return z; + if(x==(float)0.0&&y==(float)0.0) { + /* atan2f(+-0,+-0) */ + exc.arg1 = y; + exc.arg2 = x; + exc.err = 0; + exc.type = DOMAIN; + exc.name = "atan2f"; + exc.retval = 0.0; + if(_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double atan2(double y, double x) +#else + double atan2(y,x) + double y,x; +#endif +{ + return (double) atan2f((float) y, (float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_atanh.c b/newlib/libm/math/wf_atanh.c new file mode 100644 index 00000000000..457cdc6e2a3 --- /dev/null +++ b/newlib/libm/math/wf_atanh.c @@ -0,0 +1,83 @@ +/* wf_atanh.c -- float version of w_atanh.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. + * ==================================================== + */ +/* + * wrapper atanhf(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float atanhf(float x) /* wrapper atanhf */ +#else + float atanhf(x) /* wrapper atanhf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_atanhf(x); +#else + float z,y; + struct exception exc; + z = __ieee754_atanhf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + y = fabsf(x); + if(y>=(float)1.0) { + if(y>(float)1.0) { + /* atanhf(|x|>1) */ + exc.type = DOMAIN; + exc.name = "atanhf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* atanhf(|x|=1) */ + exc.type = SING; + exc.name = "atanhf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = x/0.0; /* sign(x)*inf */ + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double atanh(double x) +#else + double atanh(x) + double x; +#endif +{ + return (double) atanhf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_cabs.c b/newlib/libm/math/wf_cabs.c new file mode 100644 index 00000000000..c3ed0caa241 --- /dev/null +++ b/newlib/libm/math/wf_cabs.c @@ -0,0 +1,20 @@ +/* + * cabsf() wrapper for hypotf(). + * + * Written by J.T. Conklin, <jtc@wimsey.com> + * Placed into the Public Domain, 1994. + */ + +#include "fdlibm.h" + +struct complex { + float x; + float y; +}; + +float +cabsf(z) + struct complex z; +{ + return hypotf(z.x, z.y); +} diff --git a/newlib/libm/math/wf_cosh.c b/newlib/libm/math/wf_cosh.c new file mode 100644 index 00000000000..82b76f3c455 --- /dev/null +++ b/newlib/libm/math/wf_cosh.c @@ -0,0 +1,78 @@ +/* wf_cosh.c -- float version of w_cosh.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. + * ==================================================== + */ + +/* + * wrapper coshf(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float coshf(float x) /* wrapper coshf */ +#else + float coshf(x) /* wrapper coshf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_coshf(x); +#else + float z; + struct exception exc; + z = __ieee754_coshf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(fabsf(x)>(float)8.9415985107e+01) { + /* coshf(finite) overflow */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = OVERFLOW; + exc.name = "coshf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double cosh(double x) +#else + double cosh(x) + double x; +#endif +{ + return (double) coshf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_drem.c b/newlib/libm/math/wf_drem.c new file mode 100644 index 00000000000..7c3f7c58eca --- /dev/null +++ b/newlib/libm/math/wf_drem.c @@ -0,0 +1,19 @@ +/* + * dremf() wrapper for remainderf(). + * + * Written by J.T. Conklin, <jtc@wimsey.com> + * Placed into the Public Domain, 1994. + */ + +#include "fdlibm.h" + +float +#ifdef __STDC__ +dremf(float x, float y) +#else +dremf(x, y) + float x, y; +#endif +{ + return remainderf(x, y); +} diff --git a/newlib/libm/math/wf_exp.c b/newlib/libm/math/wf_exp.c new file mode 100644 index 00000000000..70f4459b4a8 --- /dev/null +++ b/newlib/libm/math/wf_exp.c @@ -0,0 +1,103 @@ +/* wf_exp.c -- float version of w_exp.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. + * ==================================================== + */ + +/* + * wrapper expf(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ +static const float +#else +static float +#endif +o_threshold= 8.8721679688e+01, /* 0x42b17180 */ +u_threshold= -1.0397208405e+02; /* 0xc2cff1b5 */ + +#ifdef __STDC__ + float expf(float x) /* wrapper expf */ +#else + float expf(x) /* wrapper expf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_expf(x); +#else + float z; + struct exception exc; + z = __ieee754_expf(x); + if(_LIB_VERSION == _IEEE_) return z; + if(finitef(x)) { + if(x>o_threshold) { + /* expf(finite) overflow */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = OVERFLOW; + exc.name = "expf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else if(x<u_threshold) { + /* expf(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = "expf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + } + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double exp(double x) +#else + double exp(x) + double x; +#endif +{ + return (double) expf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_fmod.c b/newlib/libm/math/wf_fmod.c new file mode 100644 index 00000000000..320daabde08 --- /dev/null +++ b/newlib/libm/math/wf_fmod.c @@ -0,0 +1,73 @@ +/* wf_fmod.c -- float version of w_fmod.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. + * ==================================================== + */ + +/* + * wrapper fmodf(x,y) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float fmodf(float x, float y) /* wrapper fmodf */ +#else + float fmodf(x,y) /* wrapper fmodf */ + float x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_fmodf(x,y); +#else + float z; + struct exception exc; + z = __ieee754_fmodf(x,y); + if(_LIB_VERSION == _IEEE_ ||isnanf(y)||isnanf(x)) return z; + if(y==(float)0.0) { + /* fmodf(x,0) */ + exc.type = DOMAIN; + exc.name = "fmodf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)y; + if (_LIB_VERSION == _SVID_) + exc.retval = x; + else + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double fmod(double x, double y) +#else + double fmod(x,y) + double x,y; +#endif +{ + return (double) fmodf((float) x, (float) y); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_gamma.c b/newlib/libm/math/wf_gamma.c new file mode 100644 index 00000000000..fbeb38af10e --- /dev/null +++ b/newlib/libm/math/wf_gamma.c @@ -0,0 +1,93 @@ +/* wf_gamma.c -- float version of w_gamma.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" +#include <reent.h> +#include <errno.h> + +#ifdef __STDC__ + float gammaf(float x) +#else + float gammaf(x) + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_gammaf_r(x,&(_REENT->_new._reent._gamma_signgam)); +#else + float y; + struct exception exc; + y = __ieee754_gammaf_r(x,&(_REENT->_new._reent._gamma_signgam)); + if(_LIB_VERSION == _IEEE_) return y; + if(!finitef(y)&&finitef(x)) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + if(floorf(x)==x&&x<=(float)0.0) { + /* gammaf(-integer) or gammaf(0) */ + exc.type = SING; + exc.name = "gammaf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* gammaf(finite) overflow */ + exc.type = OVERFLOW; + exc.name = "gammaf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return y; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double gamma(double x) +#else + double gamma(x) + double x; +#endif +{ + return (double) gammaf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_hypot.c b/newlib/libm/math/wf_hypot.c new file mode 100644 index 00000000000..c04ace1102c --- /dev/null +++ b/newlib/libm/math/wf_hypot.c @@ -0,0 +1,79 @@ +/* wf_hypot.c -- float version of w_hypot.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. + * ==================================================== + */ + +/* + * wrapper hypotf(x,y) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float hypotf(float x, float y) /* wrapper hypotf */ +#else + float hypotf(x,y) /* wrapper hypotf */ + float x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_hypotf(x,y); +#else + float z; + struct exception exc; + z = __ieee754_hypotf(x,y); + if(_LIB_VERSION == _IEEE_) return z; + if((!finitef(z))&&finitef(x)&&finitef(y)) { + /* hypotf(finite,finite) overflow */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = OVERFLOW; + exc.name = "hypotf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)y; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double hypot(double x, double y) +#else + double hypot(x,y) + double x,y; +#endif +{ + return (double) hypotf((float) x, (float) y); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_j0.c b/newlib/libm/math/wf_j0.c new file mode 100644 index 00000000000..0f3a7c1c67f --- /dev/null +++ b/newlib/libm/math/wf_j0.c @@ -0,0 +1,137 @@ +/* wf_j0.c -- float version of w_j0.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. + * ==================================================== + */ + +/* + * wrapper j0f(float x), y0f(float x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float j0f(float x) /* wrapper j0f */ +#else + float j0f(x) /* wrapper j0f */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_j0f(x); +#else + struct exception exc; + float z = __ieee754_j0f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(fabsf(x)>(float)X_TLOSS) { + /* j0f(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "j0f"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef __STDC__ + float y0f(float x) /* wrapper y0f */ +#else + float y0f(x) /* wrapper y0f */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_y0f(x); +#else + float z; + struct exception exc; + z = __ieee754_y0f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(x <= (float)0.0){ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + /* y0f(0) = -inf or y0f(x<0) = NaN */ + exc.type = DOMAIN; /* should be SING for IEEE y0f(0) */ + exc.name = "y0f"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } + if(x>(float)X_TLOSS) { + /* y0f(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "y0f"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double j0(double x) +#else + double j0(x) + double x; +#endif +{ + return (double) j0f((float) x); +} + +#ifdef __STDC__ + double y0(double x) +#else + double y0(x) + double x; +#endif +{ + return (double) y0f((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_j1.c b/newlib/libm/math/wf_j1.c new file mode 100644 index 00000000000..f9d3e0ed8ff --- /dev/null +++ b/newlib/libm/math/wf_j1.c @@ -0,0 +1,139 @@ +/* wf_j1.c -- float version of w_j1.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. + * ==================================================== + */ + +/* + * wrapper of j1f,y1f + */ + +#include "fdlibm.h" +#include <errno.h> + + +#ifdef __STDC__ + float j1f(float x) /* wrapper j1f */ +#else + float j1f(x) /* wrapper j1f */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_j1f(x); +#else + float z; + struct exception exc; + z = __ieee754_j1f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(fabsf(x)>(float)X_TLOSS) { + /* j1f(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "j1f"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#ifdef __STDC__ + float y1f(float x) /* wrapper y1f */ +#else + float y1f(x) /* wrapper y1f */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_y1f(x); +#else + float z; + struct exception exc; + z = __ieee754_y1f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(x <= (float)0.0){ + /* y1f(0) = -inf or y1f(x<0) = NaN */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = "y1f"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } + if(x>(float)X_TLOSS) { + /* y1f(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "y1f"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double j1(double x) +#else + double j1(x) + double x; +#endif +{ + return (double) j1f((float) x); +} + +#ifdef __STDC__ + double y1(double x) +#else + double y1(x) + double x; +#endif +{ + return (double) y1f((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_jn.c b/newlib/libm/math/wf_jn.c new file mode 100644 index 00000000000..c3a52630b43 --- /dev/null +++ b/newlib/libm/math/wf_jn.c @@ -0,0 +1,138 @@ +/* wf_jn.c -- float version of w_jn.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" +#include <errno.h> + + +#ifdef __STDC__ + float jnf(int n, float x) /* wrapper jnf */ +#else + float jnf(n,x) /* wrapper jnf */ + float x; int n; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_jnf(n,x); +#else + float z; + struct exception exc; + z = __ieee754_jnf(n,x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(fabsf(x)>(float)X_TLOSS) { + /* jnf(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "jnf"; + exc.err = 0; + exc.arg1 = (double)n; + exc.arg2 = (double)x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return z; +#endif +} + +#ifdef __STDC__ + float ynf(int n, float x) /* wrapper ynf */ +#else + float ynf(n,x) /* wrapper ynf */ + float x; int n; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_ynf(n,x); +#else + float z; + struct exception exc; + z = __ieee754_ynf(n,x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(x <= (float)0.0){ + /* ynf(n,0) = -inf or ynf(x<0) = NaN */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = "ynf"; + exc.err = 0; + exc.arg1 = (double)n; + exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } + if(x>(float)X_TLOSS) { + /* ynf(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "ynf"; + exc.err = 0; + exc.arg1 = (double)n; + exc.arg2 = (double)x; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double jn(int n, double x) +#else + double jn(n,x) + double x; int n; +#endif +{ + return (double) jnf(n, (float) x); +} + +#ifdef __STDC__ + double yn(int n, double x) +#else + double yn(n,x) + double x; int n; +#endif +{ + return (double) ynf(n, (float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_lgamma.c b/newlib/libm/math/wf_lgamma.c new file mode 100644 index 00000000000..e1765c4a0ad --- /dev/null +++ b/newlib/libm/math/wf_lgamma.c @@ -0,0 +1,87 @@ +/* wf_lgamma.c -- float version of w_lgamma.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" +#include <reent.h> +#include <errno.h> + +#ifdef __STDC__ + float lgammaf(float x) +#else + float lgammaf(x) + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_lgammaf_r(x,&(_REENT->_new._reent._gamma_signgam)); +#else + float y; + struct exception exc; + y = __ieee754_lgammaf_r(x,&(_REENT->_new._reent._gamma_signgam)); + if(_LIB_VERSION == _IEEE_) return y; + if(!finitef(y)&&finitef(x)) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "lgammaf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if(floorf(x)==x&&x<=(float)0.0) { + /* lgammaf(-integer) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + + } else { + /* lgammaf(finite) overflow */ + exc.type = OVERFLOW; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return y; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double lgamma(double x) +#else + double lgamma(x) + double x; +#endif +{ + return (double) lgammaf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_log.c b/newlib/libm/math/wf_log.c new file mode 100644 index 00000000000..cd373b402e5 --- /dev/null +++ b/newlib/libm/math/wf_log.c @@ -0,0 +1,85 @@ +/* wf_log.c -- float version of w_log.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. + * ==================================================== + */ + +/* + * wrapper logf(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float logf(float x) /* wrapper logf */ +#else + float logf(x) /* wrapper logf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_logf(x); +#else + float z; + struct exception exc; + z = __ieee754_logf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) || x > (float)0.0) return z; +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "logf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if(x==(float)0.0) { + /* logf(0) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* logf(x<0) */ + exc.type = DOMAIN; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double log(double x) +#else + double log(x) + double x; +#endif +{ + return (double) logf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_log10.c b/newlib/libm/math/wf_log10.c new file mode 100644 index 00000000000..15fa5d939b5 --- /dev/null +++ b/newlib/libm/math/wf_log10.c @@ -0,0 +1,88 @@ +/* wf_log10.c -- float version of w_log10.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. + * ==================================================== + */ + +/* + * wrapper log10f(X) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float log10f(float x) /* wrapper log10f */ +#else + float log10f(x) /* wrapper log10f */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_log10f(x); +#else + float z; + struct exception exc; + z = __ieee754_log10f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(x<=(float)0.0) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "log10f"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if(x==(float)0.0) { + /* log10f(0) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* log10f(x<0) */ + exc.type = DOMAIN; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double log10(double x) +#else + double log10(x) + double x; +#endif +{ + return (double) log10f((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_pow.c b/newlib/libm/math/wf_pow.c new file mode 100644 index 00000000000..42655da4a2a --- /dev/null +++ b/newlib/libm/math/wf_pow.c @@ -0,0 +1,179 @@ +/* wf_pow.c -- float version of w_pow.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. + * ==================================================== + */ + +/* + * wrapper powf(x,y) return x**y + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float powf(float x, float y) /* wrapper powf */ +#else + float powf(x,y) /* wrapper powf */ + float x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_powf(x,y); +#else + float z; + struct exception exc; + z=__ieee754_powf(x,y); + if(_LIB_VERSION == _IEEE_|| isnanf(y)) return z; + if(isnanf(x)) { + if(y==(float)0.0) { + /* powf(NaN,0.0) */ + /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */ + exc.type = DOMAIN; + exc.name = "powf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)y; + exc.retval = x; + if (_LIB_VERSION == _IEEE_ || + _LIB_VERSION == _POSIX_) exc.retval = 1.0; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; + } + if(x==(float)0.0){ + if(y==(float)0.0) { + /* powf(0.0,0.0) */ + /* error only if _LIB_VERSION == _SVID_ */ + exc.type = DOMAIN; + exc.name = "powf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)y; + exc.retval = 0.0; + if (_LIB_VERSION != _SVID_) exc.retval = 1.0; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } + if(finitef(y)&&y<(float)0.0) { + /* 0**neg */ + exc.type = DOMAIN; + exc.name = "powf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)y; + if (_LIB_VERSION == _SVID_) + exc.retval = 0.0; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } + return z; + } + if(!finitef(z)) { + if(finitef(x)&&finitef(y)) { + if(isnanf(z)) { + /* neg**non-integral */ + exc.type = DOMAIN; + exc.name = "powf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)y; + if (_LIB_VERSION == _SVID_) + exc.retval = 0.0; + else + exc.retval = 0.0/0.0; /* X/Open allow NaN */ + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else { + /* powf(x,y) overflow */ + exc.type = OVERFLOW; + exc.name = "powf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)y; + if (_LIB_VERSION == _SVID_) { + exc.retval = HUGE; + y *= 0.5; + if(x<0.0&&rint(y)!=y) exc.retval = -HUGE; + } else { + exc.retval = HUGE_VAL; + y *= 0.5; + if(x<0.0&&rint(y)!=y) exc.retval = -HUGE_VAL; + } + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } + } + } + if(z==(float)0.0&&finitef(x)&&finitef(y)) { + /* powf(x,y) underflow */ + exc.type = UNDERFLOW; + exc.name = "powf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)y; + exc.retval = 0.0; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double pow(double x, double y) +#else + double pow(x,y) + double x,y; +#endif +{ + return (double) powf((float) x, (float) y); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_remainder.c b/newlib/libm/math/wf_remainder.c new file mode 100644 index 00000000000..0071a977219 --- /dev/null +++ b/newlib/libm/math/wf_remainder.c @@ -0,0 +1,74 @@ +/* wf_remainder.c -- float version of w_remainder.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. + * ==================================================== + */ + +/* + * wrapper remainderf(x,p) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float remainderf(float x, float y) /* wrapper remainder */ +#else + float remainderf(x,y) /* wrapper remainder */ + float x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_remainderf(x,y); +#else + float z; + struct exception exc; + z = __ieee754_remainderf(x,y); + if(_LIB_VERSION == _IEEE_ || isnanf(y)) return z; + if(y==(float)0.0) { + /* remainderf(x,0) */ + exc.type = DOMAIN; + exc.name = "remainderf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)y; + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double remainder(double x, double y) +#else + double remainder(x,y) + double x,y; +#endif +{ + return (double) remainderf((float) x, (float) y); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ + + + + diff --git a/newlib/libm/math/wf_scalb.c b/newlib/libm/math/wf_scalb.c new file mode 100644 index 00000000000..bd2d9f8b426 --- /dev/null +++ b/newlib/libm/math/wf_scalb.c @@ -0,0 +1,118 @@ +/* wf_scalb.c -- float version of w_scalb.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. + * ==================================================== + */ + +/* + * wrapper scalbf(float x, float fn) is provide for + * passing various standard test suite. One + * should use scalbn() instead. + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ +#ifdef _SCALB_INT + float scalbf(float x, int fn) /* wrapper scalbf */ +#else + float scalbf(float x, float fn) /* wrapper scalbf */ +#endif +#else + float scalbf(x,fn) /* wrapper scalbf */ +#ifdef _SCALB_INT + float x; int fn; +#else + float x,fn; +#endif +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_scalbf(x,fn); +#else + float z; +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + struct exception exc; + z = __ieee754_scalbf(x,fn); + if(_LIB_VERSION == _IEEE_) return z; + if(!(finitef(z)||isnanf(z))&&finitef(x)) { + /* scalbf overflow; SVID also returns +-HUGE_VAL */ + exc.type = OVERFLOW; + exc.name = "scalbf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)fn; + exc.retval = x > 0.0 ? HUGE_VAL : -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } + if(z==(float)0.0&&z!=x) { + /* scalbf underflow */ + exc.type = UNDERFLOW; + exc.name = "scalbf"; + exc.err = 0; + exc.arg1 = (double)x; + exc.arg2 = (double)fn; + exc.retval = copysign(0.0,x); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } +#ifndef _SCALB_INT + if(!finitef(fn)) errno = ERANGE; +#endif + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ +#ifdef _SCALB_INT + double scalb(double x, int fn) +#else + double scalb(double x, double fn) +#endif +#else + double scalb(x, fn) +#ifdef _SCALB_INT + double x; int fn; +#else + double x,fn; +#endif +#endif +{ +#ifdef _SCALB_INT + return (double) scalbf((float) x, fn); +#else + return (double) scalbf((float) x, (float) fn); +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_sinh.c b/newlib/libm/math/wf_sinh.c new file mode 100644 index 00000000000..80c7a8e6e2f --- /dev/null +++ b/newlib/libm/math/wf_sinh.c @@ -0,0 +1,78 @@ +/* wf_sinh.c -- float version of w_sinh.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. + * ==================================================== + */ + +/* + * wrapper sinhf(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float sinhf(float x) /* wrapper sinhf */ +#else + float sinhf(x) /* wrapper sinhf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_sinhf(x); +#else + float z; + struct exception exc; + z = __ieee754_sinhf(x); + if(_LIB_VERSION == _IEEE_) return z; + if(!finitef(z)&&finitef(x)) { + /* sinhf(finite) overflow */ +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.type = OVERFLOW; + exc.name = "sinhf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = ( (x>0.0) ? HUGE : -HUGE); + else + exc.retval = ( (x>0.0) ? HUGE_VAL : -HUGE_VAL); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double sinh(double x) +#else + double sinh(x) + double x; +#endif +{ + return (double) sinhf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wf_sqrt.c b/newlib/libm/math/wf_sqrt.c new file mode 100644 index 00000000000..6e792c923dd --- /dev/null +++ b/newlib/libm/math/wf_sqrt.c @@ -0,0 +1,72 @@ +/* wf_sqrt.c -- float version of w_sqrt.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. + * ==================================================== + */ + +/* + * wrapper sqrtf(x) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float sqrtf(float x) /* wrapper sqrtf */ +#else + float sqrtf(x) /* wrapper sqrtf */ + float x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_sqrtf(x); +#else + float z; + struct exception exc; + z = __ieee754_sqrtf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(x<(float)0.0) { + /* sqrtf(negative) */ + exc.type = DOMAIN; + exc.name = "sqrtf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = 0.0; + else + exc.retval = 0.0/0.0; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return z; +#endif +} + +#ifdef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double sqrt(double x) +#else + double sqrt(x) + double x; +#endif +{ + return (double) sqrtf((float) x); +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wr_gamma.c b/newlib/libm/math/wr_gamma.c new file mode 100644 index 00000000000..0092ed02c77 --- /dev/null +++ b/newlib/libm/math/wr_gamma.c @@ -0,0 +1,76 @@ + +/* @(#)wr_gamma.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. + * ==================================================== + */ + +/* + * wrapper double gamma_r(double x, int *signgamp) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double gamma_r(double x, int *signgamp) /* wrapper lgamma_r */ +#else + double gamma_r(x,signgamp) /* wrapper lgamma_r */ + double x; int *signgamp; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_gamma_r(x,signgamp); +#else + double y; + struct exception exc; + y = __ieee754_gamma_r(x,signgamp); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "gamma"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if(floor(x)==x&&x<=0.0) { + /* gamma(-integer) or gamma(0) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* gamma(finite) overflow */ + exc.type = OVERFLOW; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return y; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wr_lgamma.c b/newlib/libm/math/wr_lgamma.c new file mode 100644 index 00000000000..c59c1cce9af --- /dev/null +++ b/newlib/libm/math/wr_lgamma.c @@ -0,0 +1,77 @@ + +/* @(#)wr_lgamma.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. + * ==================================================== + */ + +/* + * wrapper double lgamma_r(double x, int *signgamp) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifndef _DOUBLE_IS_32BITS + +#ifdef __STDC__ + double lgamma_r(double x, int *signgamp) /* wrapper lgamma_r */ +#else + double lgamma_r(x,signgamp) /* wrapper lgamma_r */ + double x; int *signgamp; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_lgamma_r(x,signgamp); +#else + double y; + struct exception exc; + y = __ieee754_lgamma_r(x,signgamp); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "lgamma"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if(floor(x)==x&&x<=0.0) { + /* lgamma(-integer) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + + } else { + /* lgamma(finite) overflow */ + exc.type = OVERFLOW; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + } + if (exc.err != 0) + errno = exc.err; + return exc.retval; + } else + return y; +#endif +} + +#endif /* defined(_DOUBLE_IS_32BITS) */ diff --git a/newlib/libm/math/wrf_gamma.c b/newlib/libm/math/wrf_gamma.c new file mode 100644 index 00000000000..ae285f56488 --- /dev/null +++ b/newlib/libm/math/wrf_gamma.c @@ -0,0 +1,74 @@ +/* wrf_gamma.c -- float version of wr_gamma.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. + * ==================================================== + */ + +/* + * wrapper float gammaf_r(float x, int *signgamp) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float gammaf_r(float x, int *signgamp) /* wrapper lgammaf_r */ +#else + float gammaf_r(x,signgamp) /* wrapper lgammaf_r */ + float x; int *signgamp; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_gammaf_r(x,signgamp); +#else + float y; + struct exception exc; + y = __ieee754_gammaf_r(x,signgamp); + if(_LIB_VERSION == _IEEE_) return y; + if(!finitef(y)&&finitef(x)) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "gammaf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if(floorf(x)==x&&x<=(float)0.0) { + /* gammaf(-integer) or gamma(0) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + } else { + /* gammaf(finite) overflow */ + exc.type = OVERFLOW; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return y; +#endif +} diff --git a/newlib/libm/math/wrf_lgamma.c b/newlib/libm/math/wrf_lgamma.c new file mode 100644 index 00000000000..73985e2714e --- /dev/null +++ b/newlib/libm/math/wrf_lgamma.c @@ -0,0 +1,75 @@ +/* wrf_lgamma.c -- float version of wr_lgamma.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. + * ==================================================== + */ + +/* + * wrapper float lgammaf_r(float x, int *signgamp) + */ + +#include "fdlibm.h" +#include <errno.h> + +#ifdef __STDC__ + float lgammaf_r(float x, int *signgamp) /* wrapper lgammaf_r */ +#else + float lgammaf_r(x,signgamp) /* wrapper lgammaf_r */ + float x; int *signgamp; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_lgammaf_r(x,signgamp); +#else + float y; + struct exception exc; + y = __ieee754_lgammaf_r(x,signgamp); + if(_LIB_VERSION == _IEEE_) return y; + if(!finitef(y)&&finitef(x)) { +#ifndef HUGE_VAL +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + exc.name = "lgammaf"; + exc.err = 0; + exc.arg1 = exc.arg2 = (double)x; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if(floorf(x)==x&&x<=(float)0.0) { + /* lgammaf(-integer) or lgamma(0) */ + exc.type = SING; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + errno = EDOM; + } + + } else { + /* lgammaf(finite) overflow */ + exc.type = OVERFLOW; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + } + if (exc.err != 0) + errno = exc.err; + return (float)exc.retval; + } else + return y; +#endif +} |