Re: [PATCH] newlib: Add more FreeBSD files for non LDBL_EQ_DBL support
Joel Sherrill <[email protected]>
| Newsgroups | gmane.comp.lib.newlib |
|---|---|
| Message-ID | <CAF9ehCXCwXTO+HnyxFY8ECVO7D5KrKvZN14UM7aY6O5V-tcgTA@mail.gmail.com> |
Thanks! I'm thrilled to see issues get fixed for the long double support! It was a mess to sort out enough to get it in initially. --joel On Tue, Jul 16, 2024 at 2:22 PM Jeff Johnston <[email protected]> wrote: > Thanks Kito. Patch applied. > > -- Jeff J. > > On Tue, Jul 16, 2024 at 5:32 AM Corinna Vinschen <[email protected]> > wrote: > >> >> Jeff, ping? I think that looks ok, but it's libm, yuk. >> >> Thanks, >> Corinna >> >> On Jul 10 17:44, Kito Cheng wrote: >> > For RISC-V, AArch64, i386, and x86_64 >> > >> > - k_tanl.c is required for tanl; the linker will report `__kernel_tanl` >> > not found when tanl is called. >> > - s_cospil.c and s_sinpil.c are added for cospil and sinpil, which are >> already >> > available for ld80 but not for ld128. >> > --- >> > newlib/Makefile.in | 97 ++++++++++++++++++++++++--- >> > newlib/libm/ld/math_private.h | 53 +++++++++++++++ >> > newlib/libm/ld128/Makefile.inc | 3 +- >> > newlib/libm/ld128/k_cospil.h | 42 ++++++++++++ >> > newlib/libm/ld128/k_sinpil.h | 42 ++++++++++++ >> > newlib/libm/ld128/k_tanl.c | 114 +++++++++++++++++++++++++++++++ >> > newlib/libm/ld128/s_cospil.c | 108 ++++++++++++++++++++++++++++++ >> > newlib/libm/ld128/s_sinpil.c | 111 ++++++++++++++++++++++++++++++ >> > newlib/libm/ld80/Makefile.inc | 4 +- >> > newlib/libm/ld80/k_tanl.c | 119 +++++++++++++++++++++++++++++++++ >> > 10 files changed, 681 insertions(+), 12 deletions(-) >> > create mode 100644 newlib/libm/ld128/k_cospil.h >> > create mode 100644 newlib/libm/ld128/k_sinpil.h >> > create mode 100644 newlib/libm/ld128/k_tanl.c >> > create mode 100644 newlib/libm/ld128/s_cospil.c >> > create mode 100644 newlib/libm/ld128/s_sinpil.c >> > create mode 100644 newlib/libm/ld80/k_tanl.c >> > >> > diff --git a/newlib/Makefile.in b/newlib/Makefile.in >> > index b45c42c36..a051c2760 100644 >> > --- a/newlib/Makefile.in >> > +++ b/newlib/Makefile.in >> > @@ -3244,7 +3244,10 @@ am__objects_159 = >> libm/fenv/libm_a-feclearexcept.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_AARCH64_FALSE@@HAVE_LIBM_MACHINE_RISCV_TRUE@ >> libm/ld128/libm_a-invtrig.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_AARCH64_FALSE@@HAVE_LIBM_MACHINE_RISCV_TRUE@ >> libm/ld128/libm_a-e_lgammal_r.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_AARCH64_FALSE@@HAVE_LIBM_MACHINE_RISCV_TRUE@ >> libm/ld128/libm_a-k_cosl.$(OBJEXT) \ >> > -@HAVE_LIBM_MACHINE_AARCH64_FALSE@@HAVE_LIBM_MACHINE_RISCV_TRUE@ >> libm/ld128/libm_a-k_sinl.$(OBJEXT) >> > +@HAVE_LIBM_MACHINE_AARCH64_FALSE@@HAVE_LIBM_MACHINE_RISCV_TRUE@ >> libm/ld128/libm_a-k_sinl.$(OBJEXT) \ >> > +@HAVE_LIBM_MACHINE_AARCH64_FALSE@@HAVE_LIBM_MACHINE_RISCV_TRUE@ >> libm/ld128/libm_a-k_tanl.$(OBJEXT) \ >> > +@HAVE_LIBM_MACHINE_AARCH64_FALSE@@HAVE_LIBM_MACHINE_RISCV_TRUE@ >> libm/ld128/libm_a-s_sinpil.$(OBJEXT) \ >> > +@HAVE_LIBM_MACHINE_AARCH64_FALSE@@HAVE_LIBM_MACHINE_RISCV_TRUE@ >> libm/ld128/libm_a-s_cospil.$(OBJEXT) >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@am__objects_162 = >> libm/ld128/libm_a-e_powl.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-s_erfl.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-s_exp2l.$(OBJEXT) \ >> > @@ -3254,7 +3257,10 @@ am__objects_159 = >> libm/fenv/libm_a-feclearexcept.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-invtrig.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-e_lgammal_r.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-k_cosl.$(OBJEXT) \ >> > -@HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-k_sinl.$(OBJEXT) >> > +@HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-k_sinl.$(OBJEXT) \ >> > +@HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-k_tanl.$(OBJEXT) \ >> > +@HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-s_sinpil.$(OBJEXT) \ >> > +@HAVE_LIBM_MACHINE_AARCH64_TRUE@ >> libm/ld128/libm_a-s_cospil.$(OBJEXT) >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@@HAVE_LONG_DOUBLE_TRUE@am__objects_163 >> = $(am__objects_162) >> > @HAVE_LIBM_MACHINE_AMDGCN_TRUE@am__objects_164 = >> libm/machine/amdgcn/libm_a-v64_mathcnst.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_AMDGCN_TRUE@ >> libm/machine/amdgcn/libm_a-v64_reent.$(OBJEXT) \ >> > @@ -3426,7 +3432,8 @@ am__objects_159 = >> libm/fenv/libm_a-feclearexcept.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_I386_FALSE@@HAVE_LIBM_MACHINE_X86_64_TRUE@ >> libm/ld80/libm_a-invtrig.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_I386_FALSE@@HAVE_LIBM_MACHINE_X86_64_TRUE@ >> libm/ld80/libm_a-e_lgammal_r.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_I386_FALSE@@HAVE_LIBM_MACHINE_X86_64_TRUE@ >> libm/ld80/libm_a-k_cosl.$(OBJEXT) \ >> > -@HAVE_LIBM_MACHINE_I386_FALSE@@HAVE_LIBM_MACHINE_X86_64_TRUE@ >> libm/ld80/libm_a-k_sinl.$(OBJEXT) >> > +@HAVE_LIBM_MACHINE_I386_FALSE@@HAVE_LIBM_MACHINE_X86_64_TRUE@ >> libm/ld80/libm_a-k_sinl.$(OBJEXT) \ >> > +@HAVE_LIBM_MACHINE_I386_FALSE@@HAVE_LIBM_MACHINE_X86_64_TRUE@ >> libm/ld80/libm_a-k_tanl.$(OBJEXT) >> > @HAVE_LIBM_MACHINE_I386_TRUE@am__objects_170 = >> libm/ld80/libm_a-b_tgammal.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_I386_TRUE@ >> libm/ld80/libm_a-e_powl.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_I386_TRUE@ >> libm/ld80/libm_a-s_erfl.$(OBJEXT) \ >> > @@ -3438,7 +3445,8 @@ am__objects_159 = >> libm/fenv/libm_a-feclearexcept.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_I386_TRUE@ >> libm/ld80/libm_a-invtrig.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_I386_TRUE@ >> libm/ld80/libm_a-e_lgammal_r.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_I386_TRUE@ >> libm/ld80/libm_a-k_cosl.$(OBJEXT) \ >> > -@HAVE_LIBM_MACHINE_I386_TRUE@ libm/ld80/libm_a-k_sinl.$(OBJEXT) >> > +@HAVE_LIBM_MACHINE_I386_TRUE@ >> libm/ld80/libm_a-k_sinl.$(OBJEXT) \ >> > +@HAVE_LIBM_MACHINE_I386_TRUE@ libm/ld80/libm_a-k_tanl.$(OBJEXT) >> > @HAVE_LIBM_MACHINE_I386_TRUE@@HAVE_LONG_DOUBLE_TRUE@am__objects_171 = >> $(am__objects_170) >> > @HAVE_LIBM_MACHINE_MIPS_TRUE@am__objects_172 = >> libm/machine/mips/libm_a-feclearexcept.$(OBJEXT) \ >> > @HAVE_LIBM_MACHINE_MIPS_TRUE@ >> libm/machine/mips/libm_a-fegetenv.$(OBJEXT) \ >> > @@ -3971,7 +3979,6 @@ pdfdir = @pdfdir@ >> > prefix = @prefix@ >> > program_transform_name = @program_transform_name@ >> > psdir = @psdir@ >> > -runstatedir = @runstatedir@ >> > sbindir = @sbindir@ >> > shared_machine_dir = @shared_machine_dir@ >> > sharedstatedir = @sharedstatedir@ >> > @@ -5066,12 +5073,14 @@ libm_test_test_LDADD = $(CRT0) libm.a libc.a >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@libm_ld128_lsrc = \ >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@ libm/ld128/e_powl.c >> libm/ld128/s_erfl.c libm/ld128/s_exp2l.c libm/ld128/s_expl.c \ >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@ libm/ld128/s_logl.c >> libm/ld128/b_tgammal.c libm/ld128/invtrig.c \ >> > -@HAVE_LIBM_MACHINE_AARCH64_TRUE@ libm/ld128/e_lgammal_r.c >> libm/ld128/k_cosl.c libm/ld128/k_sinl.c >> > +@HAVE_LIBM_MACHINE_AARCH64_TRUE@ libm/ld128/e_lgammal_r.c >> libm/ld128/k_cosl.c libm/ld128/k_sinl.c \ >> > +@HAVE_LIBM_MACHINE_AARCH64_TRUE@ libm/ld128/k_tanl.c >> libm/ld128/s_sinpil.c libm/ld128/s_cospil.c >> > >> > @HAVE_LIBM_MACHINE_RISCV_TRUE@libm_ld128_lsrc = \ >> > @HAVE_LIBM_MACHINE_RISCV_TRUE@ libm/ld128/e_powl.c >> libm/ld128/s_erfl.c libm/ld128/s_exp2l.c libm/ld128/s_expl.c \ >> > @HAVE_LIBM_MACHINE_RISCV_TRUE@ libm/ld128/s_logl.c >> libm/ld128/b_tgammal.c libm/ld128/invtrig.c \ >> > -@HAVE_LIBM_MACHINE_RISCV_TRUE@ libm/ld128/e_lgammal_r.c >> libm/ld128/k_cosl.c libm/ld128/k_sinl.c >> > +@HAVE_LIBM_MACHINE_RISCV_TRUE@ libm/ld128/e_lgammal_r.c >> libm/ld128/k_cosl.c libm/ld128/k_sinl.c \ >> > +@HAVE_LIBM_MACHINE_RISCV_TRUE@ libm/ld128/k_tanl.c >> libm/ld128/s_sinpil.c libm/ld128/s_cospil.c >> > >> > @HAVE_LIBM_MACHINE_AARCH64_TRUE@libm_a_CFLAGS_libm_ld128 = -fbuiltin >> -fno-math-errno >> > @HAVE_LIBM_MACHINE_RISCV_TRUE@libm_a_CFLAGS_libm_ld128 = -fbuiltin >> -fno-math-errno >> > @@ -5212,12 +5221,14 @@ libm_test_test_LDADD = $(CRT0) libm.a libc.a >> > @HAVE_LIBM_MACHINE_I386_TRUE@libm_ld80_lsrc = \ >> > @HAVE_LIBM_MACHINE_I386_TRUE@ libm/ld80/b_tgammal.c >> libm/ld80/e_powl.c libm/ld80/s_erfl.c libm/ld80/s_exp2l.c \ >> > @HAVE_LIBM_MACHINE_I386_TRUE@ libm/ld80/s_expl.c >> libm/ld80/s_logl.c libm/ld80/s_sinpil.c libm/ld80/s_cospil.c \ >> > -@HAVE_LIBM_MACHINE_I386_TRUE@ libm/ld80/invtrig.c >> libm/ld80/e_lgammal_r.c libm/ld80/k_cosl.c libm/ld80/k_sinl.c >> > +@HAVE_LIBM_MACHINE_I386_TRUE@ libm/ld80/invtrig.c >> libm/ld80/e_lgammal_r.c libm/ld80/k_cosl.c libm/ld80/k_sinl.c \ >> > +@HAVE_LIBM_MACHINE_I386_TRUE@ libm/ld80/k_tanl.c >> > >> > @HAVE_LIBM_MACHINE_X86_64_TRUE@libm_ld80_lsrc = \ >> > @HAVE_LIBM_MACHINE_X86_64_TRUE@ libm/ld80/b_tgammal.c >> libm/ld80/e_powl.c libm/ld80/s_erfl.c libm/ld80/s_exp2l.c \ >> > @HAVE_LIBM_MACHINE_X86_64_TRUE@ libm/ld80/s_expl.c >> libm/ld80/s_logl.c libm/ld80/s_sinpil.c libm/ld80/s_cospil.c \ >> > -@HAVE_LIBM_MACHINE_X86_64_TRUE@ libm/ld80/invtrig.c >> libm/ld80/e_lgammal_r.c libm/ld80/k_cosl.c libm/ld80/k_sinl.c >> > +@HAVE_LIBM_MACHINE_X86_64_TRUE@ libm/ld80/invtrig.c >> libm/ld80/e_lgammal_r.c libm/ld80/k_cosl.c libm/ld80/k_sinl.c \ >> > +@HAVE_LIBM_MACHINE_X86_64_TRUE@ libm/ld80/k_tanl.c >> > >> > @HAVE_LIBM_MACHINE_I386_TRUE@libm_a_CFLAGS_libm_ld80 = -fbuiltin >> -fno-math-errno >> > @HAVE_LIBM_MACHINE_X86_64_TRUE@libm_a_CFLAGS_libm_ld80 = -fbuiltin >> -fno-math-errno >> > @@ -11059,6 +11070,12 @@ libm/ld128/libm_a-k_cosl.$(OBJEXT): >> libm/ld128/$(am__dirstamp) \ >> > libm/ld128/$(DEPDIR)/$(am__dirstamp) >> > libm/ld128/libm_a-k_sinl.$(OBJEXT): libm/ld128/$(am__dirstamp) \ >> > libm/ld128/$(DEPDIR)/$(am__dirstamp) >> > +libm/ld128/libm_a-k_tanl.$(OBJEXT): libm/ld128/$(am__dirstamp) \ >> > + libm/ld128/$(DEPDIR)/$(am__dirstamp) >> > +libm/ld128/libm_a-s_sinpil.$(OBJEXT): libm/ld128/$(am__dirstamp) \ >> > + libm/ld128/$(DEPDIR)/$(am__dirstamp) >> > +libm/ld128/libm_a-s_cospil.$(OBJEXT): libm/ld128/$(am__dirstamp) \ >> > + libm/ld128/$(DEPDIR)/$(am__dirstamp) >> > libm/machine/amdgcn/$(am__dirstamp): >> > @$(MKDIR_P) libm/machine/amdgcn >> > @: > libm/machine/amdgcn/$(am__dirstamp) >> > @@ -11575,6 +11592,8 @@ libm/ld80/libm_a-k_cosl.$(OBJEXT): >> libm/ld80/$(am__dirstamp) \ >> > libm/ld80/$(DEPDIR)/$(am__dirstamp) >> > libm/ld80/libm_a-k_sinl.$(OBJEXT): libm/ld80/$(am__dirstamp) \ >> > libm/ld80/$(DEPDIR)/$(am__dirstamp) >> > +libm/ld80/libm_a-k_tanl.$(OBJEXT): libm/ld80/$(am__dirstamp) \ >> > + libm/ld80/$(DEPDIR)/$(am__dirstamp) >> > libm/machine/mips/$(am__dirstamp): >> > @$(MKDIR_P) libm/machine/mips >> > @: > libm/machine/mips/$(am__dirstamp) >> > @@ -14427,16 +14446,20 @@ distclean-compile: >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-invtrig.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-k_cosl.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-k_sinl.Po@am__quote@ >> > +@AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-k_tanl.Po@am__quote@ >> > +@AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-s_cospil.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-s_erfl.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-s_exp2l.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-s_expl.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-s_logl.Po@am__quote@ >> > +@AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld128/$(DEPDIR)/libm_a-s_sinpil.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-b_tgammal.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-e_lgammal_r.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-e_powl.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-invtrig.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-k_cosl.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-k_sinl.Po@am__quote@ >> > +@AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-k_tanl.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-s_cospil.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-s_erfl.Po@am__quote@ >> > @AMDEP_TRUE@@am__include@ @am__quote@libm >> /ld80/$(DEPDIR)/libm_a-s_exp2l.Po@am__quote@ >> > @@ -44350,6 +44373,48 @@ libm/ld128/libm_a-k_sinl.obj: >> libm/ld128/k_sinl.c >> > @AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > @am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld128/libm_a-k_sinl.obj `if test -f >> 'libm/ld128/k_sinl.c'; then $(CYGPATH_W) 'libm/ld128/k_sinl.c'; else >> $(CYGPATH_W) '$(srcdir)/libm/ld128/k_sinl.c'; fi` >> > >> > +libm/ld128/libm_a-k_tanl.o: libm/ld128/k_tanl.c >> > +@am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/ld128/libm_a-k_tanl.o -MD -MP -MF >> libm/ld128/$(DEPDIR)/libm_a-k_tanl.Tpo -c -o libm/ld128/libm_a-k_tanl.o >> `test -f 'libm/ld128/k_tanl.c' || echo '$(srcdir)/'`libm/ld128/k_tanl.c >> > +@am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/ld128/$(DEPDIR)/libm_a-k_tanl.Tpo libm/ld128/$(DEPDIR)/libm_a-k_tanl.Po >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ >> $(AM_V_CC)source='libm/ld128/k_tanl.c' object='libm/ld128/libm_a-k_tanl.o' >> libtool=no @AMDEPBACKSLASH@ >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > +@am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld128/libm_a-k_tanl.o `test -f >> 'libm/ld128/k_tanl.c' || echo '$(srcdir)/'`libm/ld128/k_tanl.c >> > + >> > +libm/ld128/libm_a-k_tanl.obj: libm/ld128/k_tanl.c >> > +@am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/ld128/libm_a-k_tanl.obj -MD -MP -MF >> libm/ld128/$(DEPDIR)/libm_a-k_tanl.Tpo -c -o libm/ld128/libm_a-k_tanl.obj >> `if test -f 'libm/ld128/k_tanl.c'; then $(CYGPATH_W) 'libm/ld128/k_tanl.c'; >> else $(CYGPATH_W) '$(srcdir)/libm/ld128/k_tanl.c'; fi` >> > +@am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/ld128/$(DEPDIR)/libm_a-k_tanl.Tpo libm/ld128/$(DEPDIR)/libm_a-k_tanl.Po >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ >> $(AM_V_CC)source='libm/ld128/k_tanl.c' >> object='libm/ld128/libm_a-k_tanl.obj' libtool=no @AMDEPBACKSLASH@ >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > +@am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld128/libm_a-k_tanl.obj `if test -f >> 'libm/ld128/k_tanl.c'; then $(CYGPATH_W) 'libm/ld128/k_tanl.c'; else >> $(CYGPATH_W) '$(srcdir)/libm/ld128/k_tanl.c'; fi` >> > + >> > +libm/ld128/libm_a-s_sinpil.o: libm/ld128/s_sinpil.c >> > +@am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/ld128/libm_a-s_sinpil.o -MD -MP -MF >> libm/ld128/$(DEPDIR)/libm_a-s_sinpil.Tpo -c -o libm/ld128/libm_a-s_sinpil.o >> `test -f 'libm/ld128/s_sinpil.c' || echo '$(srcdir)/'`libm/ld128/s_sinpil.c >> > +@am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/ld128/$(DEPDIR)/libm_a-s_sinpil.Tpo >> libm/ld128/$(DEPDIR)/libm_a-s_sinpil.Po >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ >> $(AM_V_CC)source='libm/ld128/s_sinpil.c' >> object='libm/ld128/libm_a-s_sinpil.o' libtool=no @AMDEPBACKSLASH@ >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > +@am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld128/libm_a-s_sinpil.o `test -f >> 'libm/ld128/s_sinpil.c' || echo '$(srcdir)/'`libm/ld128/s_sinpil.c >> > + >> > +libm/ld128/libm_a-s_sinpil.obj: libm/ld128/s_sinpil.c >> > +@am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/ld128/libm_a-s_sinpil.obj -MD -MP -MF >> libm/ld128/$(DEPDIR)/libm_a-s_sinpil.Tpo -c -o >> libm/ld128/libm_a-s_sinpil.obj `if test -f 'libm/ld128/s_sinpil.c'; then >> $(CYGPATH_W) 'libm/ld128/s_sinpil.c'; else $(CYGPATH_W) >> '$(srcdir)/libm/ld128/s_sinpil.c'; fi` >> > +@am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/ld128/$(DEPDIR)/libm_a-s_sinpil.Tpo >> libm/ld128/$(DEPDIR)/libm_a-s_sinpil.Po >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ >> $(AM_V_CC)source='libm/ld128/s_sinpil.c' >> object='libm/ld128/libm_a-s_sinpil.obj' libtool=no @AMDEPBACKSLASH@ >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > +@am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld128/libm_a-s_sinpil.obj `if test -f >> 'libm/ld128/s_sinpil.c'; then $(CYGPATH_W) 'libm/ld128/s_sinpil.c'; else >> $(CYGPATH_W) '$(srcdir)/libm/ld128/s_sinpil.c'; fi` >> > + >> > +libm/ld128/libm_a-s_cospil.o: libm/ld128/s_cospil.c >> > +@am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/ld128/libm_a-s_cospil.o -MD -MP -MF >> libm/ld128/$(DEPDIR)/libm_a-s_cospil.Tpo -c -o libm/ld128/libm_a-s_cospil.o >> `test -f 'libm/ld128/s_cospil.c' || echo '$(srcdir)/'`libm/ld128/s_cospil.c >> > +@am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/ld128/$(DEPDIR)/libm_a-s_cospil.Tpo >> libm/ld128/$(DEPDIR)/libm_a-s_cospil.Po >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ >> $(AM_V_CC)source='libm/ld128/s_cospil.c' >> object='libm/ld128/libm_a-s_cospil.o' libtool=no @AMDEPBACKSLASH@ >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > +@am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld128/libm_a-s_cospil.o `test -f >> 'libm/ld128/s_cospil.c' || echo '$(srcdir)/'`libm/ld128/s_cospil.c >> > + >> > +libm/ld128/libm_a-s_cospil.obj: libm/ld128/s_cospil.c >> > +@am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/ld128/libm_a-s_cospil.obj -MD -MP -MF >> libm/ld128/$(DEPDIR)/libm_a-s_cospil.Tpo -c -o >> libm/ld128/libm_a-s_cospil.obj `if test -f 'libm/ld128/s_cospil.c'; then >> $(CYGPATH_W) 'libm/ld128/s_cospil.c'; else $(CYGPATH_W) >> '$(srcdir)/libm/ld128/s_cospil.c'; fi` >> > +@am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/ld128/$(DEPDIR)/libm_a-s_cospil.Tpo >> libm/ld128/$(DEPDIR)/libm_a-s_cospil.Po >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ >> $(AM_V_CC)source='libm/ld128/s_cospil.c' >> object='libm/ld128/libm_a-s_cospil.obj' libtool=no @AMDEPBACKSLASH@ >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > +@am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld128/libm_a-s_cospil.obj `if test -f >> 'libm/ld128/s_cospil.c'; then $(CYGPATH_W) 'libm/ld128/s_cospil.c'; else >> $(CYGPATH_W) '$(srcdir)/libm/ld128/s_cospil.c'; fi` >> > + >> > libm/machine/amdgcn/libm_a-v64_mathcnst.o: >> libm/machine/amdgcn/v64_mathcnst.c >> > @am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/machine/amdgcn/libm_a-v64_mathcnst.o -MD -MP -MF >> libm/machine/amdgcn/$(DEPDIR)/libm_a-v64_mathcnst.Tpo -c -o >> libm/machine/amdgcn/libm_a-v64_mathcnst.o `test -f >> 'libm/machine/amdgcn/v64_mathcnst.c' || echo >> '$(srcdir)/'`libm/machine/amdgcn/v64_mathcnst.c >> > @am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/machine/amdgcn/$(DEPDIR)/libm_a-v64_mathcnst.Tpo >> libm/machine/amdgcn/$(DEPDIR)/libm_a-v64_mathcnst.Po >> > @@ -46534,6 +46599,20 @@ libm/ld80/libm_a-k_sinl.obj: libm/ld80/k_sinl.c >> > @AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > @am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld80/libm_a-k_sinl.obj `if test -f >> 'libm/ld80/k_sinl.c'; then $(CYGPATH_W) 'libm/ld80/k_sinl.c'; else >> $(CYGPATH_W) '$(srcdir)/libm/ld80/k_sinl.c'; fi` >> > >> > +libm/ld80/libm_a-k_tanl.o: libm/ld80/k_tanl.c >> > +@am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/ld80/libm_a-k_tanl.o -MD -MP -MF libm/ld80/$(DEPDIR)/libm_a-k_tanl.Tpo >> -c -o libm/ld80/libm_a-k_tanl.o `test -f 'libm/ld80/k_tanl.c' || echo >> '$(srcdir)/'`libm/ld80/k_tanl.c >> > +@am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/ld80/$(DEPDIR)/libm_a-k_tanl.Tpo libm/ld80/$(DEPDIR)/libm_a-k_tanl.Po >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ >> $(AM_V_CC)source='libm/ld80/k_tanl.c' object='libm/ld80/libm_a-k_tanl.o' >> libtool=no @AMDEPBACKSLASH@ >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > +@am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld80/libm_a-k_tanl.o `test -f >> 'libm/ld80/k_tanl.c' || echo '$(srcdir)/'`libm/ld80/k_tanl.c >> > + >> > +libm/ld80/libm_a-k_tanl.obj: libm/ld80/k_tanl.c >> > +@am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/ld80/libm_a-k_tanl.obj -MD -MP -MF >> libm/ld80/$(DEPDIR)/libm_a-k_tanl.Tpo -c -o libm/ld80/libm_a-k_tanl.obj `if >> test -f 'libm/ld80/k_tanl.c'; then $(CYGPATH_W) 'libm/ld80/k_tanl.c'; else >> $(CYGPATH_W) '$(srcdir)/libm/ld80/k_tanl.c'; fi` >> > +@am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/ld80/$(DEPDIR)/libm_a-k_tanl.Tpo libm/ld80/$(DEPDIR)/libm_a-k_tanl.Po >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ >> $(AM_V_CC)source='libm/ld80/k_tanl.c' object='libm/ld80/libm_a-k_tanl.obj' >> libtool=no @AMDEPBACKSLASH@ >> > +@AMDEP_TRUE@@am__fastdepCC_FALSE@ DEPDIR=$(DEPDIR) $(CCDEPMODE) >> $(depcomp) @AMDEPBACKSLASH@ >> > +@am__fastdepCC_FALSE@ $(AM_V_CC@am__nodep@)$(CC) $(DEFS) >> $(DEFAULT_INCLUDES) $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) >> $(libm_a_CFLAGS) $(CFLAGS) -c -o libm/ld80/libm_a-k_tanl.obj `if test -f >> 'libm/ld80/k_tanl.c'; then $(CYGPATH_W) 'libm/ld80/k_tanl.c'; else >> $(CYGPATH_W) '$(srcdir)/libm/ld80/k_tanl.c'; fi` >> > + >> > libm/machine/mips/libm_a-feclearexcept.o: >> libm/machine/mips/feclearexcept.c >> > @am__fastdepCC_TRUE@ $(AM_V_CC)$(CC) $(DEFS) $(DEFAULT_INCLUDES) >> $(INCLUDES) $(libm_a_CPPFLAGS) $(CPPFLAGS) $(libm_a_CFLAGS) $(CFLAGS) -MT >> libm/machine/mips/libm_a-feclearexcept.o -MD -MP -MF >> libm/machine/mips/$(DEPDIR)/libm_a-feclearexcept.Tpo -c -o >> libm/machine/mips/libm_a-feclearexcept.o `test -f >> 'libm/machine/mips/feclearexcept.c' || echo >> '$(srcdir)/'`libm/machine/mips/feclearexcept.c >> > @am__fastdepCC_TRUE@ $(AM_V_at)$(am__mv) >> libm/machine/mips/$(DEPDIR)/libm_a-feclearexcept.Tpo >> libm/machine/mips/$(DEPDIR)/libm_a-feclearexcept.Po >> > diff --git a/newlib/libm/ld/math_private.h >> b/newlib/libm/ld/math_private.h >> > index c5b88f65e..6d0183e3c 100644 >> > --- a/newlib/libm/ld/math_private.h >> > +++ b/newlib/libm/ld/math_private.h >> > @@ -705,6 +705,59 @@ irintl(long double x) >> > } >> > #endif >> > >> > +/* >> > + * The following are fast floor macros for 0 <= |x| < 0x1p(N-1), where >> > + * N is the precision of the type of x. These macros are used in the >> > + * half-cycle trignometric functions (e.g., sinpi(x)). >> > + */ >> > +#define FFLOORF(x, j0, ix) do { \ >> > + (j0) = (((ix) >> 23) & 0xff) - 0x7f; \ >> > + (ix) &= ~(0x007fffff >> (j0)); \ >> > + SET_FLOAT_WORD((x), (ix)); \ >> > +} while (0) >> > + >> > +#define FFLOOR(x, j0, ix, lx) do { \ >> > + (j0) = (((ix) >> 20) & 0x7ff) - 0x3ff; \ >> > + if ((j0) < 20) { \ >> > + (ix) &= ~(0x000fffff >> (j0)); \ >> > + (lx) = 0; \ >> > + } else { \ >> > + (lx) &= ~((uint32_t)0xffffffff >> ((j0) - 20)); \ >> > + } \ >> > + INSERT_WORDS((x), (ix), (lx)); \ >> > +} while (0) >> > + >> > +#define FFLOORL80(x, j0, ix, lx) do { \ >> > + j0 = ix - 0x3fff + 1; \ >> > + if ((j0) < 32) { \ >> > + (lx) = ((lx) >> 32) << 32; \ >> > + (lx) &= ~((((lx) << 32)-1) >> (j0)); \ >> > + } else { \ >> > + uint64_t _m; \ >> > + _m = (uint64_t)-1 >> (j0); \ >> > + if ((lx) & _m) (lx) &= ~_m; \ >> > + } \ >> > + INSERT_LDBL80_WORDS((x), (ix), (lx)); \ >> > +} while (0) >> > + >> > +#define FFLOORL128(x, ai, ar) do { \ >> > + union IEEEl2bits u; \ >> > + uint64_t m; \ >> > + int e; \ >> > + u.e = (x); \ >> > + e = u.bits.exp - 16383; \ >> > + if (e < 48) { \ >> > + m = ((1llu << 49) - 1) >> (e + 1); \ >> > + u.bits.manh &= ~m; \ >> > + u.bits.manl = 0; \ >> > + } else { \ >> > + m = (uint64_t)-1 >> (e - 48); \ >> > + u.bits.manl &= ~m; \ >> > + } \ >> > + (ai) = u.e; \ >> > + (ar) = (x) - (ai); \ >> > +} while (0) >> > + >> > #ifdef DEBUG >> > #if defined(__amd64__) || defined(__i386__) >> > #define breakpoint() asm("int $3") >> > diff --git a/newlib/libm/ld128/Makefile.inc >> b/newlib/libm/ld128/Makefile.inc >> > index 337284d69..3a04b99a1 100644 >> > --- a/newlib/libm/ld128/Makefile.inc >> > +++ b/newlib/libm/ld128/Makefile.inc >> > @@ -1,7 +1,8 @@ >> > %C%_lsrc = \ >> > %D%/e_powl.c %D%/s_erfl.c %D%/s_exp2l.c %D%/s_expl.c \ >> > %D%/s_logl.c %D%/b_tgammal.c %D%/invtrig.c \ >> > - %D%/e_lgammal_r.c %D%/k_cosl.c %D%/k_sinl.c >> > + %D%/e_lgammal_r.c %D%/k_cosl.c %D%/k_sinl.c \ >> > + %D%/k_tanl.c %D%/s_sinpil.c %D%/s_cospil.c >> > >> > libm_a_CFLAGS_%C% = -fbuiltin -fno-math-errno >> > >> > diff --git a/newlib/libm/ld128/k_cospil.h b/newlib/libm/ld128/k_cospil.h >> > new file mode 100644 >> > index 000000000..592f19229 >> > --- /dev/null >> > +++ b/newlib/libm/ld128/k_cospil.h >> > @@ -0,0 +1,42 @@ >> > +/*- >> > + * Copyright (c) 2017 Steven G. Kargl >> > + * All rights reserved. >> > + * >> > + * Redistribution and use in source and binary forms, with or without >> > + * modification, are permitted provided that the following conditions >> > + * are met: >> > + * 1. Redistributions of source code must retain the above copyright >> > + * notice unmodified, this list of conditions, and the following >> > + * disclaimer. >> > + * 2. Redistributions in binary form must reproduce the above copyright >> > + * notice, this list of conditions and the following disclaimer in >> the >> > + * documentation and/or other materials provided with the >> distribution. >> > + * >> > + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR >> > + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED >> WARRANTIES >> > + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE >> DISCLAIMED. >> > + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, >> > + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES >> (INCLUDING, BUT >> > + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS >> OF USE, >> > + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON >> ANY >> > + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT >> > + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE >> USE OF >> > + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. >> > + */ >> > + >> > +/* >> > + * See ../src/k_cospi.c for implementation details. >> > + */ >> > + >> > +static inline long double >> > +__kernel_cospil(long double x) >> > +{ >> > + long double hi, lo; >> > + >> > + hi = (double)x; >> > + lo = x - hi; >> > + lo = lo * (pi_lo + pi_hi) + hi * pi_lo; >> > + hi *= pi_hi; >> > + _2sumF(hi, lo); >> > + return (__kernel_cosl(hi, lo)); >> > +} >> > diff --git a/newlib/libm/ld128/k_sinpil.h b/newlib/libm/ld128/k_sinpil.h >> > new file mode 100644 >> > index 000000000..fa4e7d633 >> > --- /dev/null >> > +++ b/newlib/libm/ld128/k_sinpil.h >> > @@ -0,0 +1,42 @@ >> > +/*- >> > + * Copyright (c) 2017 Steven G. Kargl >> > + * All rights reserved. >> > + * >> > + * Redistribution and use in source and binary forms, with or without >> > + * modification, are permitted provided that the following conditions >> > + * are met: >> > + * 1. Redistributions of source code must retain the above copyright >> > + * notice unmodified, this list of conditions, and the following >> > + * disclaimer. >> > + * 2. Redistributions in binary form must reproduce the above copyright >> > + * notice, this list of conditions and the following disclaimer in >> the >> > + * documentation and/or other materials provided with the >> distribution. >> > + * >> > + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR >> > + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED >> WARRANTIES >> > + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE >> DISCLAIMED. >> > + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, >> > + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES >> (INCLUDING, BUT >> > + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS >> OF USE, >> > + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON >> ANY >> > + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT >> > + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE >> USE OF >> > + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. >> > + */ >> > + >> > +/* >> > + * See ../src/k_sinpi.c for implementation details. >> > + */ >> > + >> > +static inline long double >> > +__kernel_sinpil(long double x) >> > +{ >> > + long double hi, lo; >> > + >> > + hi = (double)x; >> > + lo = x - hi; >> > + lo = lo * (pi_lo + pi_hi) + hi * pi_lo; >> > + hi *= pi_hi; >> > + _2sumF(hi, lo); >> > + return (__kernel_sinl(hi, lo, 1)); >> > +} >> > diff --git a/newlib/libm/ld128/k_tanl.c b/newlib/libm/ld128/k_tanl.c >> > new file mode 100644 >> > index 000000000..9a58cd264 >> > --- /dev/null >> > +++ b/newlib/libm/ld128/k_tanl.c >> > @@ -0,0 +1,114 @@ >> > +/* >> > + * ==================================================== >> > + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. >> > + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. >> > + * >> > + * Permission to use, copy, modify, and distribute this >> > + * software is freely granted, provided that this notice >> > + * is preserved. >> > + * ==================================================== >> > + */ >> > + >> > +/* >> > + * ld128 version of k_tan.c. See ../src/k_tan.c for most comments. >> > + */ >> > + >> > +#include "math.h" >> > +#include "../ld/math_private.h" >> > + >> > +/* >> > + * Domain [-0.67434, 0.67434], range ~[-3.37e-36, 1.982e-37] >> > + * |tan(x)/x - t(x)| < 2**-117.8 (XXX should be ~1e-37) >> > + * >> > + * See ../ld80/k_cosl.c for more details about the polynomial. >> > + */ >> > +static const long double >> > +T3 = 0x1.5555555555555555555555555553p-2L, >> > +T5 = 0x1.1111111111111111111111111eb5p-3L, >> > +T7 = 0x1.ba1ba1ba1ba1ba1ba1ba1b694cd6p-5L, >> > +T9 = 0x1.664f4882c10f9f32d6bbe09d8bcdp-6L, >> > +T11 = 0x1.226e355e6c23c8f5b4f5762322eep-7L, >> > +T13 = 0x1.d6d3d0e157ddfb5fed8e84e27b37p-9L, >> > +T15 = 0x1.7da36452b75e2b5fce9ee7c2c92ep-10L, >> > +T17 = 0x1.355824803674477dfcf726649efep-11L, >> > +T19 = 0x1.f57d7734d1656e0aceb716f614c2p-13L, >> > +T21 = 0x1.967e18afcb180ed942dfdc518d6cp-14L, >> > +T23 = 0x1.497d8eea21e95bc7e2aa79b9f2cdp-15L, >> > +T25 = 0x1.0b132d39f055c81be49eff7afd50p-16L, >> > +T27 = 0x1.b0f72d33eff7bfa2fbc1059d90b6p-18L, >> > +T29 = 0x1.5ef2daf21d1113df38d0fbc00267p-19L, >> > +T31 = 0x1.1c77d6eac0234988cdaa04c96626p-20L, >> > +T33 = 0x1.cd2a5a292b180e0bdd701057dfe3p-22L, >> > +T35 = 0x1.75c7357d0298c01a31d0a6f7d518p-23L, >> > +T37 = 0x1.2f3190f4718a9a520f98f50081fcp-24L, >> > +pio4 = 0x1.921fb54442d18469898cc51701b8p-1L, >> > +pio4lo = 0x1.cd129024e088a67cc74020bbea60p-116L; >> > + >> > +static const double >> > +T39 = 0.000000028443389121318352, /* 0x1e8a7592977938.0p-78 */ >> > +T41 = 0.000000011981013102001973, /* 0x19baa1b1223219.0p-79 */ >> > +T43 = 0.0000000038303578044958070, /* 0x107385dfb24529.0p-80 */ >> > +T45 = 0.0000000034664378216909893, /* 0x1dc6c702a05262.0p-81 */ >> > +T47 = -0.0000000015090641701997785, /* -0x19ecef3569ebb6.0p-82 */ >> > +T49 = 0.0000000029449552300483952, /* 0x194c0668da786a.0p-81 */ >> > +T51 = -0.0000000022006995706097711, /* -0x12e763b8845268.0p-81 */ >> > +T53 = 0.0000000015468200913196612, /* 0x1a92fc98c29554.0p-82 */ >> > +T55 = -0.00000000061311613386849674, /* -0x151106cbc779a9.0p-83 */ >> > +T57 = 1.4912469681508012e-10; /* >> 0x147edbdba6f43a.0p-85 */ >> > + >> > +long double >> > +__kernel_tanl(long double x, long double y, int iy) { >> > + long double z, r, v, w, s; >> > + long double osign; >> > + int i; >> > + >> > + iy = (iy == 1 ? -1 : 1); /* XXX recover original interface >> */ >> > + osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for >> -0 */ >> > + if (fabsl(x) >= 0.67434) { >> > + if (x < 0) { >> > + x = -x; >> > + y = -y; >> > + } >> > + z = pio4 - x; >> > + w = pio4lo - y; >> > + x = z + w; >> > + y = 0.0; >> > + i = 1; >> > + } else >> > + i = 0; >> > + z = x * x; >> > + w = z * z; >> > + r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + >> > + w * (T25 + w * (T29 + w * (T33 + >> > + w * (T37 + w * (T41 + w * (T45 + w * (T49 + w * (T53 + >> > + w * T57)))))))))))); >> > + v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + >> > + w * (T27 + w * (T31 + w * (T35 + >> > + w * (T39 + w * (T43 + w * (T47 + w * (T51 + w * >> T55)))))))))))); >> > + s = z * x; >> > + r = y + z * (s * (r + v) + y); >> > + r += T3 * s; >> > + w = x + r; >> > + if (i == 1) { >> > + v = (long double) iy; >> > + return osign * >> > + (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 */ >> > + long double a, t; >> > + z = w; >> > + z = z + 0x1p32 - 0x1p32; >> > + v = r - (z - x); /* z+v = r+x */ >> > + t = a = -1.0 / w; /* a = -1.0/w */ >> > + t = t + 0x1p32 - 0x1p32; >> > + s = 1.0 + t * z; >> > + return t + a * (s + t * v); >> > + } >> > +} >> > diff --git a/newlib/libm/ld128/s_cospil.c b/newlib/libm/ld128/s_cospil.c >> > new file mode 100644 >> > index 000000000..0ef31775f >> > --- /dev/null >> > +++ b/newlib/libm/ld128/s_cospil.c >> > @@ -0,0 +1,108 @@ >> > +/*- >> > + * Copyright (c) 2017-2023 Steven G. Kargl >> > + * All rights reserved. >> > + * >> > + * Redistribution and use in source and binary forms, with or without >> > + * modification, are permitted provided that the following conditions >> > + * are met: >> > + * 1. Redistributions of source code must retain the above copyright >> > + * notice unmodified, this list of conditions, and the following >> > + * disclaimer. >> > + * 2. Redistributions in binary form must reproduce the above copyright >> > + * notice, this list of conditions and the following disclaimer in >> the >> > + * documentation and/or other materials provided with the >> distribution. >> > + * >> > + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR >> > + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED >> WARRANTIES >> > + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE >> DISCLAIMED. >> > + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, >> > + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES >> (INCLUDING, BUT >> > + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS >> OF USE, >> > + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON >> ANY >> > + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT >> > + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE >> USE OF >> > + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. >> > + */ >> > + >> > +/* >> > + * See ../src/s_cospi.c for implementation details. >> > + */ >> > + >> > +#include "../ld/fpmath.h" >> > +#include "math.h" >> > +#include "../ld/math_private.h" >> > + >> > +/* >> > + * pi_hi contains the leading 56 bits of a 169 bit approximation for >> pi. >> > + */ >> > +static const long double >> > +pi_hi = 3.14159265358979322702026593105983920e+00L, >> > +pi_lo = 1.14423774522196636802434264184180742e-17L; >> > + >> > +#include "k_cospil.h" >> > +#include "k_sinpil.h" >> > + >> > +volatile static const double vzero = 0; >> > + >> > +long double >> > +cospil(long double x) >> > +{ >> > + long double ai, ar, ax, c; >> > + >> > + ax = fabsl(x); >> > + >> > + if (ax <= 1) { >> > + if (ax < 0.25) { >> > + if (ax < 0x1p-60) { >> > + if ((int)x == 0) >> > + return (1); >> > + } >> > + return (__kernel_cospil(ax)); >> > + } >> > + >> > + if (ax < 0.5) >> > + c = __kernel_sinpil(0.5 - ax); >> > + else if (ax < 0.75) { >> > + if (ax == 0.5) >> > + return (0); >> > + c = -__kernel_sinpil(ax - 0.5); >> > + } else >> > + c = -__kernel_cospil(1 - ax); >> > + return (c); >> > + } >> > + >> > + if (ax < 0x1p112) { >> > + /* Split ax = ai + ar with 0 <= ar < 1. */ >> > + FFLOORL128(ax, ai, ar); >> > + >> > + if (ar < 0.5) { >> > + if (ar < 0.25) >> > + c = ar == 0 ? 1 : __kernel_cospil(ar); >> > + else >> > + c = __kernel_sinpil(0.5 - ar); >> > + } else { >> > + if (ar < 0.75) { >> > + if (ar == 0.5) >> > + return (0); >> > + c = -__kernel_sinpil(ar - 0.5); >> > + } else >> > + c = -__kernel_cospil(1 - ar); >> > + } >> > + return (fmodl(ai, 2.L) == 0 ? c : -c); >> > + } >> > + >> > + if (isinf(x) || isnan(x)) >> > + return (vzero / vzero); >> > + >> > + /* >> > + * For |x| >= 0x1p113, it is always an even integer, so return 1. >> > + */ >> > + if (ax >= 0x1p113) >> > + return (1); >> > + /* >> > + * For 0x1p112 <= |x| < 0x1p113 need to determine if x is an even >> > + * or odd integer to return 1 or -1. >> > + */ >> > + >> > + return (fmodl(ax, 2.L) == 0 ? 1 : -1); >> > +} >> > diff --git a/newlib/libm/ld128/s_sinpil.c b/newlib/libm/ld128/s_sinpil.c >> > new file mode 100644 >> > index 000000000..30d1881b8 >> > --- /dev/null >> > +++ b/newlib/libm/ld128/s_sinpil.c >> > @@ -0,0 +1,111 @@ >> > +/*- >> > + * Copyright (c) 2017-2023 Steven G. Kargl >> > + * All rights reserved. >> > + * >> > + * Redistribution and use in source and binary forms, with or without >> > + * modification, are permitted provided that the following conditions >> > + * are met: >> > + * 1. Redistributions of source code must retain the above copyright >> > + * notice unmodified, this list of conditions, and the following >> > + * disclaimer. >> > + * 2. Redistributions in binary form must reproduce the above copyright >> > + * notice, this list of conditions and the following disclaimer in >> the >> > + * documentation and/or other materials provided with the >> distribution. >> > + * >> > + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR >> > + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED >> WARRANTIES >> > + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE >> DISCLAIMED. >> > + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, >> > + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES >> (INCLUDING, BUT >> > + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS >> OF USE, >> > + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON >> ANY >> > + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT >> > + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE >> USE OF >> > + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. >> > + */ >> > + >> > +/* >> > + * See ../src/s_sinpi.c for implementation details. >> > + */ >> > + >> > +#include "../ld/fpmath.h" >> > +#include "math.h" >> > +#include "../ld/math_private.h" >> > + >> > +/* >> > + * pi_hi contains the leading 56 bits of a 169 bit approximation for >> pi. >> > + */ >> > +static const long double >> > +pi_hi = 3.14159265358979322702026593105983920e+00L, >> > +pi_lo = 1.14423774522196636802434264184180742e-17L; >> > + >> > +#include "k_cospil.h" >> > +#include "k_sinpil.h" >> > + >> > +volatile static const double vzero = 0; >> > + >> > +long double >> > +sinpil(long double x) >> > +{ >> > + long double ai, ar, ax, hi, lo, s, xhi, xlo; >> > + >> > + ax = fabsl(x); >> > + >> > + if (ax < 1) { >> > + if (ax < 0.25) { >> > + if (ax < 0x1p-60) { >> > + if (x == 0) >> > + return (x); >> > + hi = (double)x; >> > + hi *= 0x1p113L; >> > + lo = x * 0x1p113L - hi; >> > + s = (pi_lo + pi_hi) * lo + pi_lo * lo + >> > + pi_hi * hi; >> > + return (s * 0x1p-113L); >> > + } >> > + >> > + s = __kernel_sinpil(ax); >> > + return (x < 0 ? -s : s); >> > + } >> > + >> > + if (ax < 0.5) >> > + s = __kernel_cospil(0.5 - ax); >> > + else if (ax < 0.75) >> > + s = __kernel_cospil(ax - 0.5); >> > + else >> > + s = __kernel_sinpil(1 - ax); >> > + return (x < 0 ? -s : s); >> > + } >> > + >> > + if (ax < 0x1p112) { >> > + /* Split ax = ai + ar with 0 <= ar < 1. */ >> > + FFLOORL128(ax, ai, ar); >> > + >> > + if (ar == 0) { >> > + s = 0; >> > + } else { >> > + if (ar < 0.5) { >> > + if (ar <= 0.25) >> > + s = __kernel_sinpil(ar); >> > + else >> > + s = __kernel_cospil(0.5 - ar); >> > + } else { >> > + if (ar < 0.75) >> > + s = __kernel_cospil(ar - 0.5); >> > + else >> > + s = __kernel_sinpil(1 - ar); >> > + } >> > + >> > + s = fmodl(ai, 2.L) == 0 ? s : -s; >> > + } >> > + return (x < 0 ? -s : s); >> > + } >> > + >> > + if (isinf(x) || isnan(x)) >> > + return (vzero / vzero); >> > + >> > + /* >> > + * |x| >= 0x1p112 is always an integer, so return +-0. >> > + */ >> > + return (copysignl(0, x)); >> > +} >> > diff --git a/newlib/libm/ld80/Makefile.inc >> b/newlib/libm/ld80/Makefile.inc >> > index 97fbacdda..7bb20f743 100644 >> > --- a/newlib/libm/ld80/Makefile.inc >> > +++ b/newlib/libm/ld80/Makefile.inc >> > @@ -1,8 +1,8 @@ >> > %C%_lsrc = \ >> > %D%/b_tgammal.c %D%/e_powl.c %D%/s_erfl.c %D%/s_exp2l.c \ >> > %D%/s_expl.c %D%/s_logl.c %D%/s_sinpil.c %D%/s_cospil.c \ >> > - %D%/invtrig.c %D%/e_lgammal_r.c %D%/k_cosl.c %D%/k_sinl.c >> > - >> > + %D%/invtrig.c %D%/e_lgammal_r.c %D%/k_cosl.c %D%/k_sinl.c \ >> > + %D%/k_tanl.c >> > >> > libm_a_CFLAGS_%C% = -fbuiltin -fno-math-errno >> > >> > diff --git a/newlib/libm/ld80/k_tanl.c b/newlib/libm/ld80/k_tanl.c >> > new file mode 100644 >> > index 000000000..c55303f01 >> > --- /dev/null >> > +++ b/newlib/libm/ld80/k_tanl.c >> > @@ -0,0 +1,119 @@ >> > +/* >> > + * ==================================================== >> > + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. >> > + * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. >> > + * >> > + * Permission to use, copy, modify, and distribute this >> > + * software is freely granted, provided that this notice >> > + * is preserved. >> > + * ==================================================== >> > + */ >> > + >> > +/* >> > + * ld80 version of k_tan.c. See ../src/k_tan.c for most comments. >> > + */ >> > + >> > +#include "math.h" >> > +#include "../ld/math_private.h" >> > + >> > +/* >> > + * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22] >> > + * |tan(x)/x - t(x)| < 2**-71.9 >> > + * >> > + * See k_cosl.c for more details about the polynomial. >> > + */ >> > +#if defined(__amd64__) || defined(__i386__) >> > +/* Long double constants are slow on these arches, and broken on i386. >> */ >> > +static const volatile double >> > +T3hi = 0.33333333333333331, /* 0x15555555555555.0p-54 */ >> > +T3lo = 1.8350121769317163e-17, /* >> 0x15280000000000.0p-108 */ >> > +T5hi = 0.13333333333333336, /* 0x11111111111112.0p-55 */ >> > +T5lo = 1.3051083651294260e-17, /* >> 0x1e180000000000.0p-109 */ >> > +T7hi = 0.053968253968250494, /* >> 0x1ba1ba1ba1b827.0p-57 */ >> > +T7lo = 3.1509625637859973e-18, /* >> 0x1d100000000000.0p-111 */ >> > +pio4_hi = 0.78539816339744828, /* >> 0x1921fb54442d18.0p-53 */ >> > +pio4_lo = 3.0628711372715500e-17, /* 0x11a80000000000.0p-107 */ >> > +pio4lo_hi = -1.2541394031670831e-20, /* -0x1d9cceba3f91f2.0p-119 */ >> > +pio4lo_lo = 6.1493048227390915e-37; /* 0x1a280000000000.0p-173 */ >> > +#define T3 ((long double)T3hi + T3lo) >> > +#define T5 ((long double)T5hi + T5lo) >> > +#define T7 ((long double)T7hi + T7lo) >> > +#define pio4 ((long double)pio4_hi + pio4_lo) >> > +#define pio4lo ((long double)pio4lo_hi + pio4lo_lo) >> > +#else >> > +static const long double >> > +T3 = 0.333333333333333333180L, /* 0xaaaaaaaaaaaaaaa5.0p-65 */ >> > +T5 = 0.133333333333333372290L, /* 0x88888888888893c3.0p-66 */ >> > +T7 = 0.0539682539682504975744L, /* 0xdd0dd0dd0dc13ba2.0p-68 */ >> > +pio4 = 0.785398163397448309628L, /* 0xc90fdaa22168c235.0p-64 */ >> > +pio4lo = -1.25413940316708300586e-20L; /* >> -0xece675d1fc8f8cbb.0p-130 */ >> > +#endif >> > + >> > +static const double >> > +T9 = 0.021869488536312216, /* 0x1664f4882cc1c2.0p-58 */ >> > +T11 = 0.0088632355256619590, /* >> 0x1226e355c17612.0p-59 */ >> > +T13 = 0.0035921281113786528, /* >> 0x1d6d3d185d7ff8.0p-61 */ >> > +T15 = 0.0014558334756312418, /* >> 0x17da354aa3f96b.0p-62 */ >> > +T17 = 0.00059003538700862256, /* >> 0x13559358685b83.0p-63 */ >> > +T19 = 0.00023907843576635544, /* >> 0x1f56242026b5be.0p-65 */ >> > +T21 = 0.000097154625656538905, /* >> 0x1977efc26806f4.0p-66 */ >> > +T23 = 0.000038440165747303162, /* >> 0x14275a09b3ceac.0p-67 */ >> > +T25 = 0.000018082171885432524, /* >> 0x12f5e563e5487e.0p-68 */ >> > +T27 = 0.0000024196006108814377, /* 0x144c0d80cc6896.0p-71 */ >> > +T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */ >> > +T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */ >> > +T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */ >> > + >> > +long double >> > +__kernel_tanl(long double x, long double y, int iy) { >> > + long double z, r, v, w, s; >> > + long double osign; >> > + int i; >> > + >> > + iy = (iy == 1 ? -1 : 1); /* XXX recover original interface >> */ >> > + osign = (x >= 0 ? 1.0 : -1.0); /* XXX slow, probably wrong for >> -0 */ >> > + if (fabsl(x) >= 0.67434) { >> > + if (x < 0) { >> > + x = -x; >> > + y = -y; >> > + } >> > + z = pio4 - x; >> > + w = pio4lo - y; >> > + x = z + w; >> > + y = 0.0; >> > + i = 1; >> > + } else >> > + i = 0; >> > + z = x * x; >> > + w = z * z; >> > + r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + >> > + w * (T25 + w * (T29 + w * T33)))))); >> > + v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 + >> > + w * (T27 + w * T31)))))); >> > + s = z * x; >> > + r = y + z * (s * (r + v) + y); >> > + r += T3 * s; >> > + w = x + r; >> > + if (i == 1) { >> > + v = (long double) iy; >> > + return osign * >> > + (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 */ >> > + long double a, t; >> > + z = w; >> > + z = z + 0x1p32 - 0x1p32; >> > + v = r - (z - x); /* z+v = r+x */ >> > + t = a = -1.0 / w; /* a = -1.0/w */ >> > + t = t + 0x1p32 - 0x1p32; >> > + s = 1.0 + t * z; >> > + return t + a * (s + t * v); >> > + } >> > +} >> > -- >> > 2.34.1 >> >>