prospectively choose to deem waived or otherwise exclude such Section(s) of
the License, but only in their entirety and only with respect to the Combined
Software.
+
+(57) Steven G. Kargl - libm ld128 functions
+
+/*-
+ * 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.
+ */
+
@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.$(OBJEXT) \
@HAVE_LIBM_MACHINE_AARCH64_TRUE@ libm/ld128/libm_a-invtrig.$(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.$(OBJEXT) \
@HAVE_LIBM_MACHINE_I386_FALSE@@HAVE_LIBM_MACHINE_X86_64_TRUE@ libm/ld80/libm_a-invtrig.$(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) \
@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) \
prefix = @prefix@
program_transform_name = @program_transform_name@
psdir = @psdir@
-runstatedir = @runstatedir@
sbindir = @sbindir@
shared_machine_dir = @shared_machine_dir@
sharedstatedir = @sharedstatedir@
@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
@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
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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)/$(am__dirstamp)
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+ libm/ld128/$(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)
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/$(am__dirstamp):
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@: > libm/machine/mips/$(am__dirstamp)
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@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@
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@AMDEP_TRUE@@am__include@ @am__quote@libm/ld128/$(DEPDIR)/libm_a-s_logl.Po@am__quote@
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@AMDEP_TRUE@@am__include@ @am__quote@libm/ld80/$(DEPDIR)/libm_a-b_tgammal.Po@am__quote@
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@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@
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+
+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
@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
}
#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")
%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
--- /dev/null
+/*-
+ * 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));
+}
--- /dev/null
+/*-
+ * 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));
+}
--- /dev/null
+/*
+ * ====================================================
+ * 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);
+ }
+}
--- /dev/null
+/*-
+ * 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);
+}
--- /dev/null
+/*-
+ * 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));
+}
%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
--- /dev/null
+/*
+ * ====================================================
+ * 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);
+ }
+}
git://sourceware.org / newlib-cygwin.git / commitdiff