Implementation of half-cycle trignometric functions
Steve Kargl
sgk at troutmask.apl.washington.edu
Tue May 16 22:46:21 UTC 2017
On Fri, Apr 28, 2017 at 06:00:19PM +1000, Bruce Evans wrote:
> [cc list trimmed]
>
> On Thu, 27 Apr 2017, Steve Kargl wrote:
>
> > I have attached a new diff to the bugzilla report. The
> > diff is 3090 lines and won't be broadcast the mailing list.
>
> But no one will see it there.
>
Picking an almost email to reply to.
I have removed my new kernels and written shims to
use the fdlibm trig kernels. I know that in some
cases this leads to slower code, but a small (if not
tiny) improvement in accuracy. This also leads to
a significant reduction in code size. A couple of
notes:
1) The ld128 routines have not been compiled, and so
by extension these routines are untested. I have
no access to an ld128 platform with sufficient
infrastructure for testing.
2) Argument reduction is of the form x = n + r where n
is an integer and 0 <= r < 1. Thus, this is indeed
a half-cycle implementation. I have found discussions
of argument reduction of the form x = 2 * n + r. I
have no plans to pursue this. For sinpi and tanpi,
one must test for even or odd n to determine the
proper sign.
3) Patch against trunk follows.
Index: lib/msun/Makefile
===================================================================
--- lib/msun/Makefile (revision 318383)
+++ lib/msun/Makefile (working copy)
@@ -59,6 +59,7 @@
s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_carg.c s_cargf.c s_cargl.c \
s_cbrt.c s_cbrtf.c s_ceil.c s_ceilf.c \
s_copysign.c s_copysignf.c s_cos.c s_cosf.c \
+ s_cospi.c s_cospif.c \
s_csqrt.c s_csqrtf.c s_erf.c s_erff.c \
s_exp2.c s_exp2f.c s_expm1.c s_expm1f.c s_fabsf.c s_fdim.c \
s_finite.c s_finitef.c \
@@ -74,7 +75,10 @@
s_rint.c s_rintf.c s_round.c s_roundf.c \
s_scalbln.c s_scalbn.c s_scalbnf.c s_signbit.c \
s_signgam.c s_significand.c s_significandf.c s_sin.c s_sinf.c \
- s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_tgammaf.c s_trunc.c s_truncf.c \
+ s_sinpi.c s_sinpif.c \
+ s_tan.c s_tanf.c s_tanh.c s_tanhf.c \
+ s_tanpi.c s_tanpif.c \
+ s_tgammaf.c s_trunc.c s_truncf.c \
w_cabs.c w_cabsf.c w_drem.c w_dremf.c
# Location of fpmath.h and _fpmath.h
@@ -100,11 +104,16 @@
e_lgammal.c e_lgammal_r.c \
e_remainderl.c e_sinhl.c e_sqrtl.c \
invtrig.c k_cosl.c k_sinl.c k_tanl.c \
- s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c s_cprojl.c \
+ s_asinhl.c s_atanl.c s_cbrtl.c s_ceill.c s_cosl.c \
+ s_cospil.c \
+ s_cprojl.c \
s_csqrtl.c s_erfl.c s_exp2l.c s_expl.c s_floorl.c s_fmal.c \
s_fmaxl.c s_fminl.c s_frexpl.c s_logbl.c s_logl.c s_nanl.c \
s_nextafterl.c s_nexttoward.c s_remquol.c s_rintl.c s_roundl.c \
- s_scalbnl.c s_sinl.c s_tanhl.c s_tanl.c s_truncl.c w_cabsl.c
+ s_scalbnl.c s_sinl.c \
+ s_sinpil.c \
+ s_tanhl.c s_tanl.c \
+ s_tanpil.c s_truncl.c w_cabsl.c
.endif
# C99 complex functions
@@ -131,13 +140,19 @@
MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 \
ceil.3 cacos.3 ccos.3 ccosh.3 cexp.3 \
- cimag.3 copysign.3 cos.3 cosh.3 csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \
+ cimag.3 copysign.3 cos.3 cosh.3 \
+ cospi.3 \
+ csqrt.3 erf.3 exp.3 fabs.3 fdim.3 \
feclearexcept.3 feenableexcept.3 fegetenv.3 \
fegetround.3 fenv.3 floor.3 \
fma.3 fmax.3 fmod.3 hypot.3 ieee.3 ieee_test.3 ilogb.3 j0.3 \
lgamma.3 log.3 lrint.3 lround.3 math.3 nan.3 \
nextafter.3 remainder.3 rint.3 \
- round.3 scalbn.3 signbit.3 sin.3 sinh.3 sqrt.3 tan.3 tanh.3 trunc.3 \
+ round.3 scalbn.3 signbit.3 sin.3 sinh.3 \
+ sinpi.3 \
+ sqrt.3 tan.3 tanh.3 \
+ tanpi.3 \
+ trunc.3 \
complex.3
MLINKS+=acos.3 acosf.3 acos.3 acosl.3
@@ -166,6 +181,7 @@
MLINKS+=copysign.3 copysignf.3 copysign.3 copysignl.3
MLINKS+=cos.3 cosf.3 cos.3 cosl.3
MLINKS+=cosh.3 coshf.3 cosh.3 coshl.3
+MLINKS+=cospi.3 cospif.3 cospi.3 cospil.3
MLINKS+=csqrt.3 csqrtf.3 csqrt.3 csqrtl.3
MLINKS+=erf.3 erfc.3 erf.3 erff.3 erf.3 erfcf.3 erf.3 erfl.3 erf.3 erfcl.3
MLINKS+=exp.3 expm1.3 exp.3 expm1f.3 exp.3 expm1l.3 exp.3 pow.3 exp.3 powf.3 \
@@ -216,10 +232,12 @@
MLINKS+=scalbn.3 scalbnf.3 scalbn.3 scalbnl.3
MLINKS+=sin.3 sinf.3 sin.3 sinl.3
MLINKS+=sinh.3 sinhf.3 sinh.3 sinhl.3
+MLINKS+=sinpi.3 sinpif.3 sinpi.3 sinpil.3
MLINKS+=sqrt.3 cbrt.3 sqrt.3 cbrtf.3 sqrt.3 cbrtl.3 sqrt.3 sqrtf.3 \
sqrt.3 sqrtl.3
MLINKS+=tan.3 tanf.3 tan.3 tanl.3
MLINKS+=tanh.3 tanhf.3 tanh.3 tanhl.3
+MLINKS+=tanpi.3 tanpif.3 tanpi.3 tanpil.3
MLINKS+=trunc.3 truncf.3 trunc.3 truncl.3
.include <src.opts.mk>
Index: lib/msun/Symbol.map
===================================================================
--- lib/msun/Symbol.map (revision 318383)
+++ lib/msun/Symbol.map (working copy)
@@ -294,4 +294,13 @@
casinl;
catanl;
catanhl;
+ cospi;
+ cospif;
+ cospil;
+ sinpi;
+ sinpif;
+ sinpil;
+ tanpi;
+ tanpif;
+ tanpil;
};
Index: lib/msun/ld128/k_cospil.c
===================================================================
--- lib/msun/ld128/k_cospil.c (nonexistent)
+++ lib/msun/ld128/k_cospil.c (working copy)
@@ -0,0 +1,41 @@
+/*-
+ * 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 * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ return (__kernel_cosl(hi, lo));
+}
Property changes on: lib/msun/ld128/k_cospil.c
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Index: lib/msun/ld128/k_sinpil.c
===================================================================
--- lib/msun/ld128/k_sinpil.c (nonexistent)
+++ lib/msun/ld128/k_sinpil.c (working copy)
@@ -0,0 +1,41 @@
+/*-
+ * 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 * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ return (__kernel_sinl(hi, lo, 1));
+}
Property changes on: lib/msun/ld128/k_sinpil.c
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Index: lib/msun/ld128/s_cospil.c
===================================================================
--- lib/msun/ld128/s_cospil.c (nonexistent)
+++ lib/msun/ld128/s_cospil.c (working copy)
@@ -0,0 +1,109 @@
+/*-
+ * 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/s_cospi.c for implementation details.
+ *
+ * FIXME: This has not been compiled nor has it been tested for accuracy.
+ * FIXME: This should use bit twiddling.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const long double
+pihi = 3.14159265358979322702026593105983920e+00L,
+pilo = 1.14423774522196636802434264184180742e-17L;
+
+#include "k_cospil.c"
+#include "k_sinpil.c"
+
+long double
+cospil(long double x)
+{
+ volatile static const double vzero = 0;
+ long double ax, c, xf;
+ uint32_t ix;
+
+ 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) {
+
+ xf = floorl(ax);
+
+ ax -= xf;
+
+ if (x < 0.5) {
+ if (x < 0.25)
+ c = ax == 0 ? 1 : __kernel_cospil(ax);
+ else
+ c = __kernel_sinpil(0.5 - ax);
+ } else {
+ if (x < 0.75) {
+ if (ax == 0.5)
+ return (0);
+ c = -__kernel_sinpil(ax - 0.5);
+ } else
+ c = -__kernel_cospil(1 - ax);
+ }
+
+ if (xf > 0x1p50) xf -= 0x1p50;
+ if (xf > 0x1p30) xf -= 0x1p30;
+ ix = (uint32_t)xf;
+ return (ix & 1 ? -c : c);
+ }
+
+ if (isinf(x) || isnan(x))
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p112 is always an even integer, so return 1.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID.
+ */
+ if (ax + 1 > 1)
+ ax = 1;
+ return (ax);
+}
Property changes on: lib/msun/ld128/s_cospil.c
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Index: lib/msun/ld128/s_sinpil.c
===================================================================
--- lib/msun/ld128/s_sinpil.c (nonexistent)
+++ lib/msun/ld128/s_sinpil.c (working copy)
@@ -0,0 +1,117 @@
+/*-
+ * 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/s_sinpi.c for implementation details.
+ *
+ * FIXME: This has not been compiled nor has it been tested for accuracy.
+ * FIXME: This should use bit twiddling.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const long double
+pihi = 3.14159265358979322702026593105983920e+00L,
+pilo = 1.14423774522196636802434264184180742e-17L;
+
+#include "k_cospil.c"
+#include "k_sinpil.c"
+
+long double
+sinpil(long double x)
+{
+ volatile static const double vzero = 0;
+ long double ax, s, xf, xhi, xlo;
+ uint32_t ix;
+
+ ax = fabsl(x);
+
+ if (ax < 1) {
+ if (ax < 0.25) {
+ if (ax < 0x1p-60) {
+ if (x == 0)
+ return (x);
+ ax = (double)x;
+ x -= ax;
+ s = pilo * x + pihi * x + pilo * ax
+ + pihi * ax;
+ return (s);
+ }
+
+ s = __kernel_sinpil(ax);
+ return (copysignl(s, x));
+ }
+
+ 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 (copysignl(s, x));
+ }
+
+ if (ax < 0x1p112) {
+
+ xf = floorl(ax);
+
+ ax -= xf;
+
+ if (ax == 0) {
+ s = 0;
+ } else {
+ if (ax < 0.5) {
+ if (ax <= 0.25)
+ s = __kernel_sinpil(ax);
+ else
+ s = __kernel_cospil(0.5 - ax);
+ } else {
+ if (ax < 0.75)
+ s = __kernel_cospil(ax - 0.5);
+ else
+ s = __kernel_sinpil(1 - ax);
+ }
+
+ if (xf > 0x1p50) xf -= 0x1p50;
+ if (xf > 0x1p30) xf -= 0x1p30;
+ ix = (uint32_t)xf;
+ if (ix & 1) s = -s;
+ }
+ return (copysignl(s, x));
+ }
+
+ if (isinf(x) || isnan(x))
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p112 is always an integer, so return +-0.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID.
+ */
+ if (ax + 1 > 1)
+ ax = copysignl(0, x);
+ return (ax);
+}
Property changes on: lib/msun/ld128/s_sinpil.c
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Index: lib/msun/ld128/s_tanpil.c
===================================================================
--- lib/msun/ld128/s_tanpil.c (nonexistent)
+++ lib/msun/ld128/s_tanpil.c (working copy)
@@ -0,0 +1,123 @@
+/*-
+ * 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/s_tanpi.c for implementation details.
+ *
+ * FIXME: This has not been compiled nor has it been tested for accuracy.
+ * FIXME: This should use bit twiddling.
+ * FIXME: This should use a polynomial approximation in [0,0.25], but the
+ * FIXME: increase in max ULP is probably small, so who cares.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const long double
+pihi = 3.14159265358979322702026593105983920e+00L,
+pilo = 1.14423774522196636802434264184180742e-17L;
+
+static inline long double
+__kernel_tanpi(long double x)
+{
+ long double hi, lo, t;
+
+ if (x < 0.25) {
+ hi = (double)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ t = __kernel_tanl(hi, lo, -1);
+ } else if (x > 0.25) {
+ x = 0.5 - x;
+ hi = (double)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ t = - __kernel_tanl(hi, lo, 1);
+ } else
+ t = 1;
+
+ return (t);
+}
+
+long double
+tanpil(long double x)
+{
+ volatile static const double vzero = 0;
+ long double ax, xf;
+ uint32_t ix;
+
+ ax = fabsl(ax);
+
+ if (ax < 1) {
+ if (ax < 0.5) {
+ if (ax < 0x1p-60) {
+ if (x == 0)
+ return (x);
+ ax = (double)x;
+ x -= ax;
+ t = pilo * x + pihi * x + pilo * ax
+ + pihi * ax;
+ return (t);
+ }
+ t = __kernel_tanpil(ax);
+ } else if (ax == 0.5)
+ return ((ax - ax) / (ax - ax));
+ else
+ t = -__kernel_tanpil(1 - ax);
+ return (copysignl(t, x));
+ }
+
+ if (ix < 0x1p112) {
+
+ xf = floorl(ax);
+
+ ax -= xf;
+
+ if (ax < 0.5)
+ t = ax == 0 ? 0 : __kernel_tanpil(ax);
+ else if (ax == 0.5)
+ return ((ax - ax) / (ax - ax));
+ else
+ t = -__kernel_tanpil(1 - ax);
+ return (copysignl(t, x));
+ }
+
+ /* x = +-inf or nan. */
+ if (isinf(x) || isnan(x))
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p53 is always an integer, so return +-0.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID.
+ */
+ if (ax + 1 > 1)
+ ax = copysignl(0, x);
+ return (ax);
+}
Property changes on: lib/msun/ld128/s_tanpil.c
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Index: lib/msun/ld80/k_cospil.c
===================================================================
--- lib/msun/ld80/k_cospil.c (nonexistent)
+++ lib/msun/ld80/k_cospil.c (working copy)
@@ -0,0 +1,41 @@
+/*-
+ * 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 = (float)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ return (__kernel_cosl(hi, lo));
+}
Property changes on: lib/msun/ld80/k_cospil.c
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Added: svn:eol-style
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Index: lib/msun/ld80/k_sinpil.c
===================================================================
--- lib/msun/ld80/k_sinpil.c (nonexistent)
+++ lib/msun/ld80/k_sinpil.c (working copy)
@@ -0,0 +1,41 @@
+/*-
+ * 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 = (float)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ return (__kernel_sinl(hi, lo, 1));
+}
Property changes on: lib/msun/ld80/k_sinpil.c
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Added: svn:eol-style
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+FreeBSD=%H
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+text/plain
\ No newline at end of property
Index: lib/msun/ld80/s_cospil.c
===================================================================
--- lib/msun/ld80/s_cospil.c (nonexistent)
+++ lib/msun/ld80/s_cospil.c (working copy)
@@ -0,0 +1,129 @@
+/*-
+ * 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/s_cospi.c for implementation details.
+ */
+
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+#include <stdint.h>
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+
+static const double
+pihi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
+pilo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
+
+#include "k_cospil.c"
+#include "k_sinpil.c"
+
+long double
+cospil(long double x)
+{
+ volatile static const double vzero = 0;
+ long double ax, c;
+ uint32_t j0;
+ uint64_t lx;
+ uint16_t hx, ix;
+
+ EXTRACT_LDBL80_WORDS(hx, lx, x);
+ ix = hx & 0x7fff;
+ INSERT_LDBL80_WORDS(ax, ix, lx);
+
+ ENTERI();
+
+ if (ix < 0x3fff) { /* |x| < 1 */
+ if (ix < 0x3ffd) { /* |x| < 0.25 */
+ if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
+ if ((int)x == 0)
+ RETURNI(1);
+ }
+ RETURNI(__kernel_cospil(ax));
+ }
+
+ if (ix < 0x3ffe) /* |x| < 0.5 */
+ c = __kernel_sinpil(0.5 - ax);
+ else if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
+ if (ax == 0.5)
+ RETURNI(0);
+ c = -__kernel_sinpil(ax - 0.5);
+ } else
+ c = -__kernel_cospil(1 - ax);
+ RETURNI(c);
+ }
+
+ if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
+ /* Determine integer part of ax. */
+ j0 = ix - 0x3fff + 1;
+ if (j0 < 32) {
+ lx = (lx >> 32) << 32;
+ lx &= ~(((lx << 32)-1) >> j0);
+ } else {
+ uint64_t m = (uint64_t)-1 >> (j0 + 1);
+ if (lx & m) lx &= ~m;
+ }
+ INSERT_LDBL80_WORDS(x, ix, lx);
+
+ ax -= x;
+ EXTRACT_LDBL80_WORDS(ix, lx, ax);
+
+ if (ix < 0x3ffe) { /* |x| < 0.5 */
+ if (ix < 0x3ffd) /* |x| < 0.25 */
+ c = ix == 0 ? 1 : __kernel_cospil(ax);
+ else
+ c = __kernel_sinpil(0.5 - ax);
+
+ } else {
+ if (lx < 0xc000000000000000ull) { /* |x| < 0.75 */
+ if (ax == 0.5)
+ RETURNI(0);
+ c = -__kernel_sinpil(ax - 0.5);
+ } else
+ c = -__kernel_cospil(1 - ax);
+ }
+
+ if (j0 > 40) x -= 0x1p40;
+ if (j0 > 30) x -= 0x1p30;
+ j0 = (uint32_t)x;
+
+ RETURNI(j0 & 1 ? -c : c);
+ }
+
+ if (ix >= 0x7fff)
+ RETURNI(vzero / vzero);
+
+ /*
+ * |x| >= 0x1p63 is always an even integer, so return 1.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID.
+ */
+ if (ax + 1 > 1)
+ ax = 1;
+ RETURNI(ax);
+}
Property changes on: lib/msun/ld80/s_cospil.c
___________________________________________________________________
Added: svn:eol-style
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+native
\ No newline at end of property
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\ No newline at end of property
Index: lib/msun/ld80/s_sinpil.c
===================================================================
--- lib/msun/ld80/s_sinpil.c (nonexistent)
+++ lib/msun/ld80/s_sinpil.c (working copy)
@@ -0,0 +1,136 @@
+/*-
+ * 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/s_sinpi.c for implementation details.
+ */
+
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+#include <stdint.h>
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+
+static const double
+pihi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
+pilo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
+
+#include "k_cospil.c"
+#include "k_sinpil.c"
+
+long double
+sinpil(long double x)
+{
+ volatile static const double vzero = 0;
+ long double ax, s;
+ uint32_t j0;
+ uint64_t lx;
+ uint16_t hx, ix;
+
+ EXTRACT_LDBL80_WORDS(hx, lx, x);
+ ix = hx & 0x7fff;
+ INSERT_LDBL80_WORDS(ax, ix, lx);
+
+ ENTERI();
+
+ if (ix < 0x3fff) { /* |x| < 1 */
+ if (ix < 0x3ffd) { /* |x| < 0.25 */
+ if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
+ if (x == 0)
+ RETURNI(x);
+ ax = (float)x;
+ x -= ax;
+ s = pilo * x + pihi * x + pilo * ax
+ + pihi * ax;
+ RETURNI(s);
+ }
+ s = __kernel_sinpil(ax);
+ RETURNI((hx & 0x8000) ? -s : s);
+ }
+
+ if (ix < 0x3ffe) /* |x| < 0.5 */
+ s = __kernel_cospil(0.5 - ax);
+ else if (lx < 0xc000000000000000ull) /* |x| < 0.75 */
+ s = __kernel_cospil(ax - 0.5);
+ else
+ s = __kernel_sinpil(1 - ax);
+ RETURNI((hx & 0x8000) ? -s : s);
+ }
+
+ if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
+ /* Determine integer part of ax. */
+ j0 = ix - 0x3fff + 1;
+ if (j0 < 32) {
+ lx = (lx >> 32) << 32;
+ lx &= ~(((lx << 32)-1) >> j0);
+ } else {
+ uint64_t m = (uint64_t)-1 >> (j0 + 1);
+ if (lx & m) lx &= ~m;
+ }
+ INSERT_LDBL80_WORDS(x, ix, lx);
+
+ ax -= x;
+ EXTRACT_LDBL80_WORDS(ix, lx, ax);
+
+ if (ix == 0) {
+ s = 0;
+ } else {
+ if (ix < 0x3ffe) { /* |x| < 0.5 */
+ if (ix < 0x3ffd) /* |x| < 0.25 */
+ s = __kernel_sinpil(ax);
+ else
+ s = __kernel_cospil(0.5 - ax);
+ } else {
+ /* |x| < 0.75 */
+ if (lx < 0xc000000000000000ull)
+ s = __kernel_cospil(ax - 0.5);
+ else
+ s = __kernel_sinpil(1 - ax);
+ }
+
+ if (j0 > 40) x -= 0x1p40;
+ if (j0 > 30) x -= 0x1p30;
+ j0 = (uint32_t)x;
+ if (j0 & 1) s = -s;
+ }
+ RETURNI((hx & 0x8000) ? -s : s);
+ }
+
+ /* x = +-inf or nan. */
+ if (ix >= 0x7fff)
+ RETURNI(vzero / vzero);
+
+ /*
+ * |x| >= 0x1p63 is always an integer, so return +-0.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID.
+ */
+ if (ax + 1 > 1)
+ ax = copysignl(0, x);
+ RETURNI(ax);
+}
Property changes on: lib/msun/ld80/s_sinpil.c
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
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Index: lib/msun/ld80/s_tanpil.c
===================================================================
--- lib/msun/ld80/s_tanpil.c (nonexistent)
+++ lib/msun/ld80/s_tanpil.c (working copy)
@@ -0,0 +1,139 @@
+/*-
+ * 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/s_tanpi.c for implementation details.
+ */
+
+#ifdef __i386__
+#include <ieeefp.h>
+#endif
+#include <stdint.h>
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+
+static const double
+pihi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
+pilo = -2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
+
+static inline long double
+__kernel_tanpil(long double x)
+{
+ long double hi, lo, t;
+
+ if (x < 0.25) {
+ hi = (float)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ t = __kernel_tanl(hi, lo, -1);
+ } else if (x > 0.25) {
+ x = 0.5 - x;
+ hi = (float)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ t = - __kernel_tanl(hi, lo, 1);
+ } else
+ t = 1;
+
+ return (t);
+}
+
+long double
+tanpil(long double x)
+{
+ volatile static const double vzero = 0;
+ long double ax, t;
+ uint32_t j0;
+ uint64_t lx;
+ uint16_t hx, ix;
+
+ EXTRACT_LDBL80_WORDS(hx, lx, x);
+ ix = hx & 0x7fff;
+ INSERT_LDBL80_WORDS(ax, ix, lx);
+
+ ENTERI();
+
+ if (ix < 0x3fff) { /* |x| < 1 */
+ if (ix < 0x3ffe) { /* |x| < 0.5 */
+ if (ix < 0x3fdd) { /* |x| < 0x1p-34 */
+ if (x == 0)
+ RETURNI(x);
+ ax = (float)x;
+ x -= ax;
+ t = pilo * x + pihi * x + pilo * ax
+ + pihi * ax;
+ RETURNI(t);
+ }
+ t = __kernel_tanpil(ax);
+ } else if (ax == 0.5)
+ RETURNI((ax - ax) / (ax - ax));
+ else
+ t = -__kernel_tanpil(1 - ax);
+ RETURNI((hx & 0x8000) ? -t : t);
+ }
+
+ if (ix < 0x403e) { /* 1 <= |x| < 0x1p63 */
+ /* Determine integer part of ax. */
+ j0 = ix - 0x3fff + 1;
+ if (j0 < 32) {
+ lx = (lx >> 32) << 32;
+ lx &= ~(((lx << 32)-1) >> j0);
+ } else {
+ uint64_t m = (uint64_t)-1 >> (j0 + 1);
+ if (lx & m) lx &= ~m;
+ }
+ INSERT_LDBL80_WORDS(x, ix, lx);
+
+ ax -= x;
+ EXTRACT_LDBL80_WORDS(ix, lx, ax);
+
+ if (ix < 0x3ffe) /* |x| < 0.5 */
+ t = ax == 0 ? 0 : __kernel_tanpil(ax);
+ else if (ax == 0.5)
+ RETURNI((ax - ax) / (ax - ax));
+ else
+ t = -__kernel_tanpil(1 - ax);
+ RETURNI((hx & 0x8000) ? -t : t);
+ }
+
+ /* x = +-inf or nan. */
+ if (ix >= 0x7fff)
+ RETURNI(vzero / vzero);
+
+ /*
+ * |x| >= 0x1p63 is always an integer, so return +-0.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID.
+ */
+ if (ax + 1 > 1)
+ ax = copysignl(0, x);
+ RETURNI(ax);
+}
Property changes on: lib/msun/ld80/s_tanpil.c
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: svn:keywords
## -0,0 +1 ##
+FreeBSD=%H
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## -0,0 +1 ##
+text/plain
\ No newline at end of property
Index: lib/msun/man/cospi.3
===================================================================
--- lib/msun/man/cospi.3 (nonexistent)
+++ lib/msun/man/cospi.3 (working copy)
@@ -0,0 +1,111 @@
+.\" Copyright (c) 2017 Steven G. Kargl <kargl at FreeBSD.org>
+.\" 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, 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 REGENTS AND CONTRIBUTORS ``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 REGENTS OR CONTRIBUTORS 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.
+.\"
+.\" $FreeBSD$
+.\"
+.Dd April 1, 2017
+.Dt COSPI 3
+.Os
+.Sh NAME
+.Nm cospi ,
+.Nm cospif ,
+.Nm cospil
+.Nd half\(encycle cosine functions
+.Sh LIBRARY
+.Lb libm
+.Sh SYNOPSIS
+.In math.h
+.Ft double
+.Fn cospi "double x"
+.Ft float
+.Fn cospif "float x"
+.Ft long double
+.Fn cospil "long double x"
+.Sh DESCRIPTION
+The
+.Fn cospi ,
+.Fn cospif ,
+and
+.Fn cospil
+functions compute the cosine of
+.Fa "\(*p \(mu x" .
+and measure angles in half-cycles.
+.Sh RETURN VALUES
+The
+.Fn cospi ,
+.Fn cospif ,
+and
+.Fn cospil
+functions returns
+.Fn cos "\(*p \(mu x" .
+If \*(Bax\*(Ba \*(Ge 2^(p - 1)
+where p is the floating\(enpoint precision of
+.Ar x ,
+then the returned value is 1 and it has no significance.
+.Sh SPECIAL VALUES
+.Bl -tag
+.It
+.Fn cospi \*(Pm0
+returns 1.
+.It
+.Fn cospi \*(Pmn/2
+returns 0 for positive integers
+.Ar n .
+.It
+.Fn cospi n
+returns 1 for even integers
+.Ar n .
+.It
+.Fn cospi n
+returns \-1 for odd integers
+.Ar n .
+.It
+.Fn cospi \*(Pm\(if
+return an \*(Na and raises an FE_INVALID exception.
+.It
+.Fn cospi \*(Na
+return an \*(Na and raises an FE_INVALID exception.
+.El
+.Sh SEE ALSO
+.Xr cos 3 ,
+.Xr fenv 3 ,
+.Xr math 3 ,
+.Xr sin 3 ,
+.Xr sinpi 3 ,
+.Xr tan 3 ,
+.Xr tanpi 3
+.Sh AUTHORS
+The half\(encycle trignometric functions were written by
+.An Steven G. Kargl Aq Mt kargl at FreeBSD.org .
+.Sh STANDARDS
+These functions conform to
+IEEE Std 754\(tm\(en2008 ,
+\(dqIEEE Standard for Floating-Point Arithmetic\(dq
+and to
+ISO/IEC TS 18661-4 ,
+\(dqInformation technology \(em Programming languages, their environments,
+and system software interfaces \(em Floating\(enpoint extensions for
+C\(dq \(em Part 4: Supplementary functions.
+
+
Property changes on: lib/msun/man/cospi.3
___________________________________________________________________
Added: svn:eol-style
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\ No newline at end of property
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+FreeBSD=%H
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+text/plain
\ No newline at end of property
Index: lib/msun/man/sinpi.3
===================================================================
--- lib/msun/man/sinpi.3 (nonexistent)
+++ lib/msun/man/sinpi.3 (working copy)
@@ -0,0 +1,102 @@
+.\" Copyright (c) 2017 Steven G. Kargl <kargl at FreeBSD.org>
+.\" 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, 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 REGENTS AND CONTRIBUTORS ``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 REGENTS OR CONTRIBUTORS 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.
+.\"
+.\" $FreeBSD$
+.\"
+.Dd April 1, 2017
+.Dt SINPI 3
+.Os
+.Sh NAME
+.Nm sinpi ,
+.Nm sinpif ,
+.Nm sinpil
+.Nd half\(encycle sine functions
+.Sh LIBRARY
+.Lb libm
+.Sh SYNOPSIS
+.In math.h
+.Ft double
+.Fn sinpi "double x"
+.Ft float
+.Fn sinpif "float x"
+.Ft long double
+.Fn sinpil "long double x"
+.Sh DESCRIPTION
+The
+.Fn sinpi ,
+.Fn sinpif ,
+and
+.Fn sinpil
+functions compute the sine of
+.Fa "\(*p \(mu x" .
+and measure angles in half-cycles.
+.Sh RETURN VALUES
+The
+.Fn sinpi ,
+.Fn sinpif ,
+and
+.Fn sinpil
+functions returns
+.Fn sin "\(*p \(mu x" .
+If \*(Bax\*(Ba \*(Ge 2^(p - 1)
+where p is the floating\(enpoint precision of
+.Ar x ,
+then the returned value is \*(Pm0 and it has no significance.
+.Sh SPECIAL VALUES
+.Bl -tag
+.It
+.Fn sinpi \*(Pm0
+returns \*(Pm0.
+.It
+.Fn sinpi \*(Pmn
+returns \*(Pm0 for positive integers
+.Ar n .
+.It
+.Fn sinpi \*(Pm\(if
+return an \*(Na and raises an FE_INVALID exception.
+.It
+.Fn sinpi \*(Na
+return an \*(Na and raises an FE_INVALID exception.
+.El
+.Sh SEE ALSO
+.Xr cos 3 ,
+.Xr cospi 3 ,
+.Xr fenv 3 ,
+.Xr math 3 ,
+.Xr sin 3 ,
+.Xr tan 3 ,
+.Xr tanpi 3
+.Sh AUTHORS
+The half\(encycle trignometric functions were written by
+.An Steven G. Kargl Aq Mt kargl at FreeBSD.org .
+.Sh STANDARDS
+These functions conform to
+IEEE Std 754\(tm\(en2008 ,
+\(dqIEEE Standard for Floating-Point Arithmetic\(dq
+and to
+ISO/IEC TS 18661-4 ,
+\(dqInformation technology \(em Programming languages, their environments,
+and system software interfaces \(em Floating\(enpoint extensions for
+C\(dq \(em Part 4: Supplementary functions.
+
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+text/plain
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Index: lib/msun/man/tanpi.3
===================================================================
--- lib/msun/man/tanpi.3 (nonexistent)
+++ lib/msun/man/tanpi.3 (working copy)
@@ -0,0 +1,106 @@
+.\" Copyright (c) 2017 Steven G. Kargl <kargl at FreeBSD.org>
+.\" 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, 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 REGENTS AND CONTRIBUTORS ``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 REGENTS OR CONTRIBUTORS 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.
+.\"
+.\" $FreeBSD$
+.\"
+.Dd April 1, 2017
+.Dt TANPI 3
+.Os
+.Sh NAME
+.Nm tanpi ,
+.Nm tanpif ,
+.Nm tanpil
+.Nd half\(encycle tangent functions
+.Sh LIBRARY
+.Lb libm
+.Sh SYNOPSIS
+.In math.h
+.Ft double
+.Fn tanpi "double x"
+.Ft float
+.Fn tanpif "float x"
+.Ft long double
+.Fn tanpil "long double x"
+.Sh DESCRIPTION
+The
+.Fn tanpi ,
+.Fn tanpif ,
+and
+.Fn tanpil
+functions compute the tangent of
+.Fa "\(*p \(mu x"
+and measure angles in half-cycles.
+.Sh RETURN VALUES
+The
+.Fn tanpi ,
+.Fn tanpif ,
+and
+.Fn tanpil
+functions returns
+.Fn tan "\(*p \(mu x" .
+If \*(Bax\*(Ba \*(Ge 2^(p - 1)
+where p is the floating\(enpoint precision of
+.Ar x ,
+then the returned value is \*(Pm0 and it has no significance.
+.Sh SPECIAL VALUES
+.Bl -tag
+.It
+.Fn tanpi \*(Pm0
+returns \*(Pm0.
+.It
+.Fn tanpi \*(Pmn
+returns \*(Pm0 for positive integers
+.Ar n .
+.It
+.Fn tanpi \*(Pmn/2
+returns \*(Na for n > 0 and raises an FE_INVALID exception.
+.It
+.Fn tanpi \*(Pm\(if
+return an \*(Na and raises an FE_INVALID exception.
+.It
+.Fn tanpi \*(Na
+return an \*(Na and raises an FE_INVALID exception.
+.El
+.Sh SEE ALSO
+.Xr cos 3 ,
+.Xr cospi 3 ,
+.Xr fenv 3 ,
+.Xr math 3 ,
+.Xr sin 3 ,
+.Xr sinpi 3 ,
+.Xr tan 3 ,
+.Sh AUTHORS
+The half\(encycle trignometric functions were written by
+.An Steven G. Kargl Aq Mt kargl at FreeBSD.org .
+.Sh STANDARDS
+These functions conform to
+IEEE Std 754\(tm\(en2008 ,
+\(dqIEEE Standard for Floating-Point Arithmetic\(dq
+and to
+ISO/IEC TS 18661-4 ,
+\(dqInformation technology \(em Programming languages, their environments,
+and system software interfaces \(em Floating\(enpoint extensions for
+C\(dq \(em Part 4: Supplementary functions.
+
+
Property changes on: lib/msun/man/tanpi.3
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Index: lib/msun/src/k_cospi.c
===================================================================
--- lib/msun/src/k_cospi.c (nonexistent)
+++ lib/msun/src/k_cospi.c (working copy)
@@ -0,0 +1,45 @@
+/*-
+ * 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.
+ */
+
+/*
+ * The basic kernel for x in [0,0.25]. To exploit the kernel for cos(x),
+ * the argument to __kernel_cospi() must be multiply by pi. As pi is an
+ * irrational number, this allows the splitting of pi*x into high and low
+ * parts.
+ */
+
+static inline double
+__kernel_cospi(double x)
+{
+ double hi, lo;
+ hi = (float)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ return (__kernel_cos(hi, lo));
+}
+
Property changes on: lib/msun/src/k_cospi.c
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Index: lib/msun/src/k_sinpi.c
===================================================================
--- lib/msun/src/k_sinpi.c (nonexistent)
+++ lib/msun/src/k_sinpi.c (working copy)
@@ -0,0 +1,44 @@
+/*-
+ * 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.
+ */
+
+/*
+ * The basic kernel for x in [0,0.25]. To exploit the kernel for sin(x),
+ * the argument to __kernel_sinpi() must be multiply by pi. As pi is an
+ * irrational number, this allows the splitting of pi*x into high and low
+ * parts.
+ */
+
+static inline double
+__kernel_sinpi(double x)
+{
+ double hi, lo;
+ hi = (float)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ return (__kernel_sin(hi, lo, 1));
+}
Property changes on: lib/msun/src/k_sinpi.c
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Index: lib/msun/src/math.h
===================================================================
--- lib/msun/src/math.h (revision 318383)
+++ lib/msun/src/math.h (working copy)
@@ -500,6 +500,15 @@
#if __BSD_VISIBLE
long double lgammal_r(long double, int *);
+double cospi(double);
+float cospif(float);
+long double cospil(long double);
+double sinpi(double);
+float sinpif(float);
+long double sinpil(long double);
+double tanpi(double);
+float tanpif(float);
+long double tanpil(long double);
#endif
__END_DECLS
Index: lib/msun/src/s_cospi.c
===================================================================
--- lib/msun/src/s_cospi.c (nonexistent)
+++ lib/msun/src/s_cospi.c (working copy)
@@ -0,0 +1,152 @@
+/*-
+ * 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.
+ */
+
+/**
+ * cospi(x) computes cos(pi*x) without multiplication by pi (almost). First,
+ * note that cospi(-x) = cospi(x), so the algorithm considers only |x|. The
+ * method used depends on the magnitude of x.
+ *
+ * 1. For small |x|, cospi(x) = 1 with FE_INEXACT raised where a sloppy
+ * threshold is used. The threshold is |x| < 0x1pN with N = -(P/2+M).
+ * P is the precision of the floating-point type and M = 2 to 4.
+ *
+ * 2. For |x| < 1, argument reduction is not required and sinpi(x) is
+ * computed by calling a kernel that leverages the kernels for sin(x)
+ * ans cos(x). See k_sinpi.c and k_cospi.c for details.
+ *
+ * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where
+ * |x| = j0 + r with j0 an integer and the remainder r satisfies
+ * 0 <= r < 1. With the given domain, a simplified inline floor(x)
+ * is used. Also, note the following identity
+ *
+ * cospi(x) = cos(pi*(j0+r))
+ * = cos(pi*j0) * cos(pi*r) - sin(pi*j0) * sin(pi*r)
+ * = cos(pi*j0) * cos(pi*r)
+ * = +-cospi(r)
+ *
+ * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1.
+ * cospi(r) is then computed via an appropriate kernel.
+ *
+ * 4. For |x| >= 0x1p(P-1), |x| is integral and cospi(x) = 1.
+ *
+ * 5. Special cases:
+ *
+ * cospi(+-0) = 1.
+ * cospi(n.5) = 0 for n an integer.
+ * cospi(+-inf) = nan. Raises the "invalid" floating-point exception.
+ * cospi(nan) = nan. Raises the "invalid" floating-point exception.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+pihi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
+pilo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
+
+#include "k_cospi.c"
+#include "k_sinpi.c"
+
+double
+cospi(double x)
+{
+ volatile static const double vzero = 0;
+ double ax, c;
+ uint32_t hx, ix, j0, lx;
+
+ EXTRACT_WORDS(hx, lx, x);
+ ix = hx & 0x7fffffff;
+ INSERT_WORDS(ax, ix, lx);
+
+ if (ix < 0x3ff00000) { /* |x| < 1 */
+ if (ix < 0x3fd00000) { /* |x| < 0.25 */
+ if (ix < 0x3e200000) { /* |x| < 0x1p-29 */
+ if ((int)ax == 0)
+ return (1);
+ }
+ return (__kernel_cospi(ax));
+ }
+
+ if (ix < 0x3fe00000) /* |x| < 0.5 */
+ c = __kernel_sinpi(0.5 - ax);
+ else if (ix < 0x3fe80000){ /* |x| < 0.75 */
+ if (ax == 0.5)
+ return (0);
+ c = -__kernel_sinpi(ax - 0.5);
+ } else
+ c = -__kernel_cospi(1 - ax);
+ return (c);
+ }
+
+ if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */
+ /* Determine integer part of ax. */
+ 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);
+
+ ax -= x;
+ EXTRACT_WORDS(ix, lx, ax);
+
+
+ if (ix < 0x3fe00000) { /* |x| < 0.5 */
+ if (ix < 0x3fd00000) /* |x| < 0.25 */
+ c = ix == 0 ? 1 : __kernel_cospi(ax);
+ else
+ c = __kernel_sinpi(0.5 - ax);
+ } else {
+ if (ix < 0x3fe80000) { /* |x| < 0.75 */
+ if (ax == 0.5)
+ return (0);
+ c = -__kernel_sinpi(ax - 0.5);
+ } else
+ c = -__kernel_cospi(1 - ax);
+ }
+
+ if (j0 > 30) x -= 0x1p30;
+ j0 = (uint32_t)x;
+ return (j0 & 1 ? -c : c);
+ }
+
+ if (ix >= 0x7f800000)
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p52 is always an even integer, so return 1.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID?
+ */
+ if (ax + 1 > 1)
+ ax = 1;
+ return (ax);
+}
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(cospi, cospil);
+#endif
Property changes on: lib/msun/src/s_cospi.c
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Index: lib/msun/src/s_cospif.c
===================================================================
--- lib/msun/src/s_cospif.c (nonexistent)
+++ lib/msun/src/s_cospif.c (working copy)
@@ -0,0 +1,111 @@
+/*-
+ * 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/s_cospi.c for implementation details.
+ */
+#define INLINE_KERNEL_SINDF
+#define INLINE_KERNEL_COSDF
+
+#include "math.h"
+#include "math_private.h"
+#include "k_cosf.c"
+#include "k_sinf.c"
+
+#define __kernel_cospif(x) ((float)__kernel_cosdf(M_PI * (x)))
+#define __kernel_sinpif(x) ((float)__kernel_sindf(M_PI * (x)))
+
+float
+cospif(float x)
+{
+ volatile static const float vzero = 0;
+ float ax, c;
+ uint32_t ix, j0;
+
+ GET_FLOAT_WORD(ix, x);
+ ix = ix & 0x7fffffff;
+ SET_FLOAT_WORD(ax, ix);
+
+ if (ix < 0x3f800000) { /* |x| < 1 */
+ if (ix < 0x3e800000) { /* |x| < 0.25 */
+ if (ix < 0x38800000) { /* |x| < 0x1p-14 */
+ /* Raise inexact iff != 0. */
+ if ((int)ax == 0)
+ return (1);
+ }
+ return (__kernel_cospif(ax));
+ }
+
+ if (ix < 0x3f000000) /* |x| < 0.5 */
+ c = __kernel_sinpif(0.5f - ax);
+ else if (ix < 0x3f400000) { /* |x| < 0.75 */
+ if (ix == 0x3f000000)
+ return (0);
+ c = -__kernel_sinpif(ax - 0.5f);
+ } else
+ c = -__kernel_cospif(1 - ax);
+ return (c);
+ }
+
+ if (ix < 0x4b000000) { /* 1 <= |x| < 0x1p23 */
+ /* Determine integer part of ax. */
+ j0 = ((ix >> 23) & 0xff) - 0x7f;
+ ix &= ~(0x007fffff >> j0);
+ SET_FLOAT_WORD(x, ix);
+
+ ax -= x;
+ GET_FLOAT_WORD(ix, ax);
+
+ if (ix < 0x3f000000) { /* |x| < 0.5 */
+ if (ix < 0x3e800000) /* |x| < 0.25 */
+ c = ix == 0 ? 1 : __kernel_cospif(ax);
+ else
+ c = __kernel_sinpif(0.5f - ax);
+ } else {
+ if (ix < 0x3f400000) { /* |x| < 0.75 */
+ if (ix == 0x3f000000)
+ return (0);
+ c = -__kernel_sinpif(ax - 0.5f);
+ } else
+ c = -__kernel_cospif(1 - ax);
+ }
+
+ j0 = (uint32_t)x;
+ return (j0 & 1 ? -c : c);
+ }
+
+ /* x = +-inf or nan. */
+ if (ix >= 0x7f800000)
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p23 is always an even integer, so return 1.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID.
+ */
+ if (ax + 1 > 1)
+ ax = 1;
+ return (ax);
+}
Property changes on: lib/msun/src/s_cospif.c
___________________________________________________________________
Added: svn:eol-style
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Index: lib/msun/src/s_sinpi.c
===================================================================
--- lib/msun/src/s_sinpi.c (nonexistent)
+++ lib/msun/src/s_sinpi.c (working copy)
@@ -0,0 +1,163 @@
+/*-
+ * 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.
+ */
+
+/**
+ * sinpi(x) computes sin(pi*x) without multiplication by pi (almost). First,
+ * note that sinpi(-x) = -sinpi(x), so the algorithm considers only |x| and
+ * includes reflection symmetry by considering the sign of x on output. The
+ * method used depends on the magnitude of x.
+ *
+ * 1. For small |x|, sinpi(x) = pi * x where a sloppy threshold is used. The
+ * threshold is |x| < 0x1pN with N = -(P/2+M). P is the precision of the
+ * floating-point type and M = 2 to 4. To achieve high accuracy, pi is
+ * decomposed into high and low parts with the high part containing a
+ * number of trailing zero bits. x is also split into high and low parts.
+ *
+ * 2. For |x| < 1, argument reduction is not required and sinpi(x) is
+ * computed by calling a kernel that leverages the kernels for sin(x)
+ * ans cos(x). See k_sinpi.c and k_cospi.c for details.
+ *
+ * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where
+ * |x| = j0 + r with j0 an integer and the remainder r satisfies
+ * 0 <= r < 1. With the given domain, a simplified inline floor(x)
+ * is used. Also, note the following identity
+ *
+ * sinpi(x) = sin(pi*(j0+r))
+ * = sin(pi*j0) * cos(pi*r) + cos(pi*j0) * sin(pi*r)
+ * = cos(pi*j0) * sin(pi*r)
+ * = +-sinpi(r)
+ *
+ * If j0 is even, then cos(pi*j0) = 1. If j0 is odd, then cos(pi*j0) = -1.
+ * sinpi(r) is then computed via an appropriate kernel.
+ *
+ * 4. For |x| >= 0x1p(P-1), |x| is integral and sinpi(x) = copysign(0,x).
+ *
+ * 5. Special cases:
+ *
+ * sinpi(+-0) = +-0
+ * sinpi(+-n) = +-0, for positive integers n.
+ * sinpi(+-inf) = nan. Raises the "invalid" floating-point exception.
+ * sinpi(nan) = nan. Raises the "invalid" floating-point exception.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+pihi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
+pilo =-2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
+
+#include "k_cospi.c"
+#include "k_sinpi.c"
+
+double
+sinpi(double x)
+{
+ volatile static const double vzero = 0;
+ double ax, s;
+ uint32_t hx, ix, j0, lx;
+
+ EXTRACT_WORDS(hx, lx, x);
+ ix = hx & 0x7fffffff;
+ INSERT_WORDS(ax, ix, lx);
+
+ if (ix < 0x3ff00000) { /* |x| < 1 */
+ if (ix < 0x3fd00000) { /* |x| < 0.25 */
+ if (ix < 0x3e200000) { /* |x| < 0x1p-29 */
+ if (x == 0)
+ return (x);
+ INSERT_WORDS(ax, hx, 0);
+ x -= ax;
+ s = pilo * x + pihi * x + pilo * ax
+ + pihi * ax;
+ return (s);
+ }
+
+ s = __kernel_sinpi(ax);
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix < 0x3fe00000) /* |x| < 0.5 */
+ s = __kernel_cospi(0.5 - ax);
+ else if (ix < 0x3fe80000) /* |x| < 0.75 */
+ s = __kernel_cospi(ax - 0.5);
+ else
+ s = __kernel_sinpi(1 - ax);
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */
+ /* Determine integer part of ax. */
+ 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);
+
+ ax -= x;
+ EXTRACT_WORDS(ix, lx, ax);
+
+ if (ix == 0)
+ s = 0;
+ else {
+ if (ix < 0x3fe00000) { /* |x| < 0.5 */
+ if (ix < 0x3fd00000) /* |x| < 0.25 */
+ s = __kernel_sinpi(ax);
+ else
+ s = __kernel_cospi(0.5 - ax);
+ } else {
+ if (ix < 0x3fe80000) /* |x| < 0.75 */
+ s = __kernel_cospi(ax - 0.5);
+ else
+ s = __kernel_sinpi(1 - ax);
+ }
+
+ if (j0 > 30) x -= 0x1p30;
+ j0 = (uint32_t)x;
+ if (j0 & 1) s = -s;
+ }
+
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix >= 0x7f800000)
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p52 is always an integer, so return +-0.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID?
+ */
+ if (ax + 1 > 1)
+ ax = copysign(0, x);
+ return (ax);
+}
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(sinpi, sinpil);
+#endif
Property changes on: lib/msun/src/s_sinpi.c
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: svn:keywords
## -0,0 +1 ##
+FreeBSD=%H
\ No newline at end of property
Added: svn:mime-type
## -0,0 +1 ##
+text/plain
\ No newline at end of property
Index: lib/msun/src/s_sinpif.c
===================================================================
--- lib/msun/src/s_sinpif.c (nonexistent)
+++ lib/msun/src/s_sinpif.c (working copy)
@@ -0,0 +1,122 @@
+/*-
+ * 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/s_sinpi.c for implementation details.
+ */
+
+#define INLINE_KERNEL_SINDF
+#define INLINE_KERNEL_COSDF
+
+#include "math.h"
+#include "math_private.h"
+#include "k_cosf.c"
+#include "k_sinf.c"
+
+#define __kernel_cospif(x) ((float)__kernel_cosdf(M_PI * (x)))
+#define __kernel_sinpif(x) ((float)__kernel_sindf(M_PI * (x)))
+
+static const float pihi = 3.14160156e+00f; /* 0x40491000 */
+static const float pilo = -8.90890988e-06f; /* 0xb715777a */
+
+float
+sinpif(float x)
+{
+ volatile static const float vzero = 0;
+ float ax, s;
+ uint32_t hx, ix, j0;
+
+ GET_FLOAT_WORD(hx, x);
+ ix = hx & 0x7fffffff;
+ SET_FLOAT_WORD(ax, ix);
+
+ if (ix < 0x3f800000) { /* |x| < 1 */
+ if (ix < 0x3e800000) { /* |x| < 0.25 */
+ if (ix < 0x38800000) { /* |x| < 0x1p-14 */
+ if (x == 0)
+ return (x);
+ SET_FLOAT_WORD(ax, hx & 0xffff0000);
+ x -= ax;
+ s = pilo * x + pihi * x + pilo * ax
+ + pihi * ax;
+ return (s);
+ }
+
+ s = __kernel_sinpif(ax);
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix < 0x3f000000) /* |x| < 0.5 */
+ s = __kernel_cospif(0.5f - ax);
+ else if (ix < 0x3f400000) /* |x| < 0.75 */
+ s = __kernel_cospif(ax - 0.5f);
+ else
+ s = __kernel_sinpif(1 - ax);
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ if (ix < 0x4b000000) { /* 1 <= |x| < 0x1p23 */
+ /* Determine integer part of ax. */
+ j0 = ((ix >> 23) & 0xff) - 0x7f;
+ ix &= ~(0x007fffff >> j0);
+ SET_FLOAT_WORD(x, ix);
+
+ ax -= x;
+ GET_FLOAT_WORD(ix, ax);
+
+ if (ix == 0)
+ s = 0;
+ else {
+ if (ix < 0x3f000000) { /* |x| < 0.5 */
+ if (ix < 0x3e800000) /* |x| < 0.25 */
+ s = __kernel_sinpif(ax);
+ else
+ s = __kernel_cospif(0.5f - ax);
+ } else {
+ if (ix < 0x3f400000) /* |x| < 0.75 */
+ s = __kernel_cospif(ax - 0.5f);
+ else
+ s = __kernel_sinpif(1 - ax);
+ }
+
+ j0 = (uint32_t)x;
+ s = (j0 & 1) ? -s : s;
+ }
+ return ((hx & 0x80000000) ? -s : s);
+ }
+
+ /* x = +-inf or nan. */
+ if (ix >= 0x7f800000)
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p23 is always an integer, so return +-0.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID?
+ */
+ if (ax + 1 > 1)
+ ax = copysignf(0, x);
+ return (ax);
+}
Property changes on: lib/msun/src/s_sinpif.c
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: svn:keywords
## -0,0 +1 ##
+FreeBSD=%H
\ No newline at end of property
Added: svn:mime-type
## -0,0 +1 ##
+text/plain
\ No newline at end of property
Index: lib/msun/src/s_tanpi.c
===================================================================
--- lib/msun/src/s_tanpi.c (nonexistent)
+++ lib/msun/src/s_tanpi.c (working copy)
@@ -0,0 +1,172 @@
+/*-
+ * 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.
+ */
+
+/**
+ * tanpi(x) computes tan(pi*x) without multiplication by pi (almost). First,
+ * note that tanpi(-x) = -tanpi(x), so the algorithm considers only |x| and
+ * includes reflection symmetry by considering the sign of x on output. The
+ * method used depends on the magnitude of x.
+ *
+ * 1. For small |x|, tanpi(x) = pi * x where a sloppy threshold is used. The
+ * threshold is |x| < 0x1pN with N = -(P/2+M). P is the precision of the
+ * floating-point type and M = 2 to 4. To achieve high accuracy, pi is
+ * decomposed into high and low parts with the high part containing a
+ * number of trailing zero bits. x is also split into high and low parts.
+ *
+ * 2. For |x| < 1, argument reduction is not required and tanpi(x) is
+ * computed by a direct call to a kernel, which uses the kernel for
+ * tan(x). See below.
+ *
+ * 3. For 1 <= |x| < 0x1p(P-1), argument reduction is required where
+ * |x| = j0 + r with j0 an integer and the remainder r satisfies
+ * 0 <= r < 1. With the given domain, a simplified inline floor(x)
+ * is used. Also, note the following identity
+ *
+ * tan(pi*j0) + tan(pi*r)
+ * tanpi(x) = tan(pi*(j0+r)) = ---------------------------- = tanpi(r)
+ * 1 - tan(pi*j0) * tan(pi*r)
+ *
+ * So, after argument reduction, the kernel is again invoked.
+ *
+ * 4. For |x| >= 0x1p(P-1), |x| is integral and tanpi(x) = copysign(0,x).
+ *
+ * 5. Special cases:
+ *
+ * tanpi(+-0) = +-0
+ * tanpi(+-n) = +-0, for positive integers n.
+ * tanpi(+-n+1/4) = +-1, for positive integers n.
+ * tanpi(+-n+1/2) = NaN, for positive integers n.
+ * tanpi(+-inf) = NaN. Raises the "invalid" floating-point exception.
+ * tanpi(nan) = NaN. Raises the "invalid" floating-point exception.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+pihi = 3.1415926814079285e+00, /* 0x400921fb 0x58000000 */
+pilo = -2.7818135228334233e-08; /* 0xbe5dde97 0x3dcb3b3a */
+
+/*
+ * The kernel for tanpi(x) multiplies x by an 80-bit approximation of
+ * pi, where the hi and lo parts are used with with kernel for tan(x).
+ */
+static inline double
+__kernel_tanpi(double x)
+{
+ double hi, lo, t;
+
+ if (x < 0.25) {
+ hi = (float)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ t = __kernel_tan(hi, lo, 1);
+ } else if (x > 0.25) {
+ x = 0.5 - x;
+ hi = (float)x;
+ lo = x - hi;
+ lo = lo * (pilo + pihi) + hi * pilo;
+ hi *= pihi;
+ _2sumF(hi, lo);
+ t = - __kernel_tan(hi, lo, -1);
+ } else
+ t = 1;
+
+ return (t);
+}
+
+double
+tanpi(double x)
+{
+ volatile static const double vzero = 0;
+ double ax, t;
+ uint32_t hx, ix, j0, lx;
+
+ EXTRACT_WORDS(hx, lx, x);
+ ix = hx & 0x7fffffff;
+ INSERT_WORDS(ax, ix, lx);
+
+ if (ix < 0x3ff00000) { /* |x| < 1 */
+ if (ix < 0x3fe00000) { /* |x| < 0.5 */
+ if (ix < 0x3e200000) { /* |x| < 0x1p-29 */
+ if (x == 0)
+ return (x);
+ ax = (float)x;
+ x -= ax;
+ t = pilo * x + pihi * x + pilo * ax
+ + pihi * ax;
+ return (t);
+ }
+ t = __kernel_tanpi(ax);
+ } else if (ax == 0.5)
+ return ((ax - ax) / (ax - ax));
+ else
+ t = - __kernel_tanpi(1 - ax);
+ return ((hx & 0x80000000) ? -t : t);
+ }
+
+ if (ix < 0x43300000) { /* 1 <= |x| < 0x1p52 */
+ /* Determine integer part of ax. */
+ 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);
+
+ ax -= x;
+ EXTRACT_WORDS(ix, lx, ax);
+
+ if (ix < 0x3fe00000) /* |x| < 0.5 */
+ t = ax == 0 ? 0 : __kernel_tanpi(ax);
+ else if (ax == 0.5)
+ return ((ax - ax) / (ax - ax));
+ else
+ t = - __kernel_tanpi(1 - ax);
+
+ return ((hx & 0x80000000) ? -t : t);
+ }
+
+ /* x = +-inf or nan. */
+ if (ix >= 0x7f800000)
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p52 is always an integer, so return +-0.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID?
+ */
+ if (ax + 1 > 1)
+ ax = copysign(0, x);
+ return (ax);
+}
+
+#if LDBL_MANT_DIG == 53
+__weak_reference(tanpi, tanpil);
+#endif
Property changes on: lib/msun/src/s_tanpi.c
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: svn:keywords
## -0,0 +1 ##
+FreeBSD=%H
\ No newline at end of property
Added: svn:mime-type
## -0,0 +1 ##
+text/plain
\ No newline at end of property
Index: lib/msun/src/s_tanpif.c
===================================================================
--- lib/msun/src/s_tanpif.c (nonexistent)
+++ lib/msun/src/s_tanpif.c (working copy)
@@ -0,0 +1,115 @@
+/*-
+ * 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/s_tanpi.c for implementation details.
+ */
+
+#define INLINE_KERNEL_TANDF
+
+#include "math.h"
+#include "math_private.h"
+#include "k_tanf.c"
+
+static const float
+pihi = 3.14160156e+00f, /* 0x40491000 */
+pilo = -8.90890988e-06f; /* 0xb715777a */
+
+static inline float
+__kernel_tanpif(float x)
+{
+ float t;
+
+ if (x < 0.25f)
+ t = __kernel_tandf(M_PI * x, 1);
+ else if (x > 0.25f)
+ t = -__kernel_tandf(M_PI * (0.5 - x), -1);
+ else
+ t = 1;
+
+ return (t);
+}
+
+float
+tanpif(float x)
+{
+ volatile static const float vzero = 0;
+ float ax, t;
+ uint32_t hx, ix, j0;
+
+ GET_FLOAT_WORD(hx, x);
+ ix = hx & 0x7fffffff;
+ SET_FLOAT_WORD(ax, ix);
+
+ if (ix < 0x3f800000) { /* |x| < 1 */
+ if (ix < 0x3f000000) { /* |x| < 0.5 */
+ if (ix < 0x38800000) { /* |x| < 0x1p-14 */
+ if (ix == 0)
+ return (x);
+ SET_FLOAT_WORD(ax, hx & 0xffff0000);
+ x -= ax;
+ t = pilo * x + pihi * x + pilo * ax
+ + pihi * ax;
+ return (t);
+ }
+ t = __kernel_tanpif(ax);
+ } else if (ix == 0x3f000000)
+ return ((ax - ax) / (ax - ax));
+ else
+ t = - __kernel_tanpif(1 - ax);
+ return ((hx & 0x80000000) ? -t : t);
+ }
+
+ if (ix < 0x4b000000) { /* 1 <= |x| < 0x1p23 */
+ /* Determine integer part of ax. */
+ j0 = ((ix >> 23) & 0xff) - 0x7f;
+ ix &= ~(0x007fffff >> j0);
+ SET_FLOAT_WORD(x, ix);
+
+ ax -= x;
+ GET_FLOAT_WORD(ix, ax);
+
+ if (ix < 0x3f000000) /* |x| < 0.5 */
+ t = ix == 0 ? 0 : __kernel_tanpif(ax);
+ else if (ix == 0x3f000000)
+ return ((ax - ax) / (ax - ax));
+ else
+ t = - __kernel_tanpif(1 - ax);
+ return ((hx & 0x80000000) ? -t : t);
+ }
+
+ /* x = +-inf or nan. */
+ if (ix >= 0x7f800000)
+ return (vzero / vzero);
+
+ /*
+ * |x| >= 0x1p23 is always an integer, so return +-0.
+ * FIXME: should this raise FE_INEXACT or FE_INVALID.
+ */
+ if (ax + 1 > 1)
+ ax = copysignf(0, x);
+ return (ax);
+}
Property changes on: lib/msun/src/s_tanpif.c
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: svn:keywords
## -0,0 +1 ##
+FreeBSD=%H
\ No newline at end of property
Added: svn:mime-type
## -0,0 +1 ##
+text/plain
\ No newline at end of property
--
Steve
20170425 https://www.youtube.com/watch?v=VWUpyCsUKR4
20161221 https://www.youtube.com/watch?v=IbCHE-hONow
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