Attachment 229010 Details for Bug 218514 – new new updated patch

[patch] new new updated patch

cospi_20211024.diff (text/plain), 71.06 KB, created by Steve Kargl on 2021-10-25 03:11:17 UTC

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Creator: Steve Kargl

Created: 2021-10-25 03:11:17 UTC

Size: 71.06 KB

patch

obsolete

>diff --git a/lib/msun/Makefile b/lib/msun/Makefile
>index 7107aad56aa..5164aef6020 100644
>--- a/lib/msun/Makefile
>+++ b/lib/msun/Makefile
>@@ -138,6 +138,11 @@ COMMON_SRCS+=	catrig.c catrigf.c \
> 	s_cproj.c s_cprojf.c s_creal.c s_crealf.c s_creall.c \
> 	s_csinh.c s_csinhf.c s_ctanh.c s_ctanhf.c
> 
>+# IEEE-754 2008 and ISO/IEC TS 18661-4 half-cycle trignometric functions
>+COMMON_SRCS+=	s_cospi.c s_cospif.c s_cospil.c \
>+	s_sinpi.c s_sinpif.c s_sinpil.c \
>+	s_tanpi.c s_tanpif.c s_tanpil.c
>+
> # FreeBSD's C library supplies these functions:
> #COMMON_SRCS+=	s_fabs.c s_frexp.c s_isnan.c s_ldexp.c s_modf.c
> 
>@@ -154,7 +159,8 @@ INCS+=	fenv.h math.h
> 
> 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 clog.3 copysign.3 cos.3 cosh.3 cpow.3 csqrt.3 erf.3 \
>+	cimag.3 clog.3 copysign.3 cos.3 cosh.3 cospi.3 \
>+	cpow.3 csqrt.3 erf.3 \
> 	exp.3 fabs.3 fdim.3 \
> 	feclearexcept.3 feenableexcept.3 fegetenv.3 \
> 	fegetround.3 fenv.3 floor.3 \
>@@ -162,7 +168,7 @@ MAN=	acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.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 sincos.3 \
>-	sinh.3 sqrt.3 tan.3 tanh.3 trunc.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
>@@ -192,6 +198,7 @@ MLINKS+=clog.3 clogf.3 clog.3 clogl.3
> 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+=cpow.3 cpowf.3 cpow.3 cpowl.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
>@@ -244,10 +251,12 @@ MLINKS+=scalbn.3 scalbnf.3 scalbn.3 scalbnl.3
> MLINKS+=sin.3 sinf.3 sin.3 sinl.3
> MLINKS+=sincos.3 sincosf.3 sin.3 sincosl.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>
>diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map
>index 51deded732f..317c0de77f9 100644
>--- a/lib/msun/Symbol.map
>+++ b/lib/msun/Symbol.map
>@@ -304,3 +304,16 @@ FBSD_1.5 {
> 	sincosf;
> 	sincosl;
> };
>+
>+/* First added in 14.0-CURRENT */
>+FBSD_1.7{
>+	cospi;
>+	cospif;
>+	cospil;
>+	sinpi;
>+	sinpif;
>+	sinpil;
>+	tanpi;
>+	tanpif;
>+	tanpil;
>+};
>diff --git a/lib/msun/ld128/k_cospil.h b/lib/msun/ld128/k_cospil.h
>new file mode 100644
>index 00000000000..592f1922953
>--- /dev/null
>+++ b/lib/msun/ld128/k_cospil.h
>@@ -0,0 +1,42 @@
>+/*-
>+ * Copyright (c) 2017 Steven G. Kargl
>+ * All rights reserved.
>+ *
>+ * Redistribution and use in source and binary forms, with or without
>+ * modification, are permitted provided that the following conditions
>+ * are met:
>+ * 1. Redistributions of source code must retain the above copyright
>+ *    notice unmodified, this list of conditions, and the following
>+ *    disclaimer.
>+ * 2. Redistributions in binary form must reproduce the above copyright
>+ *    notice, this list of conditions and the following disclaimer in the
>+ *    documentation and/or other materials provided with the distribution.
>+ *
>+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
>+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
>+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
>+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
>+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
>+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
>+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
>+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
>+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
>+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
>+ */
>+
>+/*
>+ * See ../src/k_cospi.c for implementation details.
>+ */
>+
>+static inline long double
>+__kernel_cospil(long double x)
>+{
>+	long double hi, lo;
>+
>+	hi = (double)x;
>+	lo = x - hi;
>+	lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
>+	hi *= pi_hi;
>+	_2sumF(hi, lo);
>+	return (__kernel_cosl(hi, lo));
>+}
>diff --git a/lib/msun/ld128/k_sinpil.h b/lib/msun/ld128/k_sinpil.h
>new file mode 100644
>index 00000000000..fa4e7d6336d
>--- /dev/null
>+++ b/lib/msun/ld128/k_sinpil.h
>@@ -0,0 +1,42 @@
>+/*-
>+ * Copyright (c) 2017 Steven G. Kargl
>+ * All rights reserved.
>+ *
>+ * Redistribution and use in source and binary forms, with or without
>+ * modification, are permitted provided that the following conditions
>+ * are met:
>+ * 1. Redistributions of source code must retain the above copyright
>+ *    notice unmodified, this list of conditions, and the following
>+ *    disclaimer.
>+ * 2. Redistributions in binary form must reproduce the above copyright
>+ *    notice, this list of conditions and the following disclaimer in the
>+ *    documentation and/or other materials provided with the distribution.
>+ *
>+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
>+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
>+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
>+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
>+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
>+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
>+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
>+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
>+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
>+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
>+ */
>+
>+/*
>+ * See ../src/k_sinpi.c for implementation details.
>+ */
>+
>+static inline long double
>+__kernel_sinpil(long double x)
>+{
>+	long double hi, lo;
>+
>+	hi = (double)x;
>+	lo = x - hi;
>+	lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
>+	hi *= pi_hi;
>+	_2sumF(hi, lo);
>+	return (__kernel_sinl(hi, lo, 1));
>+}
>diff --git a/lib/msun/ld128/s_cospil.c b/lib/msun/ld128/s_cospil.c
>new file mode 100644
>index 00000000000..b4bc50bb4d8
>--- /dev/null
>+++ b/lib/msun/ld128/s_cospil.c
>@@ -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"
>+
>+/*
>+ * 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 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.
>+	 */
>+	return (1);
>+}
>diff --git a/lib/msun/ld128/s_sinpil.c b/lib/msun/ld128/s_sinpil.c
>new file mode 100644
>index 00000000000..56ede66dc32
>--- /dev/null
>+++ b/lib/msun/ld128/s_sinpil.c
>@@ -0,0 +1,118 @@
>+/*-
>+ * 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"
>+
>+/*
>+ * 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 ax, hi, lo, 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);
>+				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 (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.
>+	 */
>+	return (copysignl(0, x));
>+}
>diff --git a/lib/msun/ld128/s_tanpil.c b/lib/msun/ld128/s_tanpil.c
>new file mode 100644
>index 00000000000..33a61cf3115
>--- /dev/null
>+++ b/lib/msun/ld128/s_tanpil.c
>@@ -0,0 +1,120 @@
>+/*-
>+ * 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.
>+ */
>+
>+#include "math.h"
>+#include "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;
>+
>+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 * (pi_lo + pi_hi) + hi * pi_lo;
>+		hi *= pi_hi;
>+		_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 * (pi_lo + pi_hi) + hi * pi_lo;
>+		hi *= pi_hi;
>+		_2sumF(hi, lo);
>+		t = - __kernel_tanl(hi, lo, 1);
>+	} else
>+		t = 1;
>+
>+	return (t);
>+}
>+
>+volatile static const double vzero = 0;
>+
>+long double
>+tanpil(long double x)
>+{
>+	long double ax, hi, lo, xf;
>+	uint32_t ix;
>+
>+	ax = fabsl(ax);
>+
>+	if (ax < 1) {
>+		if (ax < 0.5) {
>+			if (ax < 0x1p-60) {
>+				if (x == 0)
>+					return (x);
>+				hi = (double)x;
>+				hi *= 0x1p113L
>+				lo = x * 0x1p113L - hi;
>+				t = (pi_lo + pi_hi) * lo + pi_lo * lo +
>+				    pi_hi * hi;
>+				return (t * 0x1p-113L);
>+			}
>+			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.
>+	 */
>+	return (copysignl(0, x));
>+}
>diff --git a/lib/msun/ld80/k_cospil.h b/lib/msun/ld80/k_cospil.h
>new file mode 100644
>index 00000000000..6e13ef02aea
>--- /dev/null
>+++ b/lib/msun/ld80/k_cospil.h
>@@ -0,0 +1,42 @@
>+/*-
>+ * Copyright (c) 2017 Steven G. Kargl
>+ * All rights reserved.
>+ *
>+ * Redistribution and use in source and binary forms, with or without
>+ * modification, are permitted provided that the following conditions
>+ * are met:
>+ * 1. Redistributions of source code must retain the above copyright
>+ *    notice unmodified, this list of conditions, and the following
>+ *    disclaimer.
>+ * 2. Redistributions in binary form must reproduce the above copyright
>+ *    notice, this list of conditions and the following disclaimer in the
>+ *    documentation and/or other materials provided with the distribution.
>+ *
>+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
>+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
>+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
>+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
>+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
>+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
>+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
>+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
>+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
>+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
>+ */
>+
>+/*
>+ * See ../src/k_cospi.c for implementation details.
>+ */
>+
>+static inline long double
>+__kernel_cospil(long double x)
>+{
>+	long double hi, lo;
>+
>+	hi = (float)x;
>+	lo = x - hi;
>+	lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
>+	hi *= pi_hi;
>+	_2sumF(hi, lo);
>+	return (__kernel_cosl(hi, lo));
>+}
>diff --git a/lib/msun/ld80/k_sinpil.h b/lib/msun/ld80/k_sinpil.h
>new file mode 100644
>index 00000000000..00241b932e9
>--- /dev/null
>+++ b/lib/msun/ld80/k_sinpil.h
>@@ -0,0 +1,42 @@
>+/*-
>+ * Copyright (c) 2017 Steven G. Kargl
>+ * All rights reserved.
>+ *
>+ * Redistribution and use in source and binary forms, with or without
>+ * modification, are permitted provided that the following conditions
>+ * are met:
>+ * 1. Redistributions of source code must retain the above copyright
>+ *    notice unmodified, this list of conditions, and the following
>+ *    disclaimer.
>+ * 2. Redistributions in binary form must reproduce the above copyright
>+ *    notice, this list of conditions and the following disclaimer in the
>+ *    documentation and/or other materials provided with the distribution.
>+ *
>+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
>+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
>+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
>+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
>+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
>+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
>+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
>+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
>+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
>+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
>+ */
>+
>+/*
>+ * See ../src/k_sinpi.c for implementation details.
>+ */
>+
>+static inline long double
>+__kernel_sinpil(long double x)
>+{
>+	long double hi, lo;
>+
>+	hi = (float)x;
>+	lo = x - hi;
>+	lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
>+	hi *= pi_hi;
>+	_2sumF(hi, lo);
>+	return (__kernel_sinl(hi, lo, 1));
>+}
>diff --git a/lib/msun/ld80/s_cospil.c b/lib/msun/ld80/s_cospil.c
>new file mode 100644
>index 00000000000..199479e9eaf
>--- /dev/null
>+++ b/lib/msun/ld80/s_cospil.c
>@@ -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
>+pi_hi = 3.1415926814079285e+00,	/* 0x400921fb 0x58000000 */
>+pi_lo =-2.7818135228334233e-08;	/* 0xbe5dde97 0x3dcb3b3a */
>+
>+#include "k_cospil.h"
>+#include "k_sinpil.h"
>+
>+volatile static const double vzero = 0;
>+
>+long double
>+cospil(long double x)
>+{
>+	long double ax, c;
>+	uint64_t lx, m;
>+	uint32_t j0;
>+	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 {
>+			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.
>+	 */
>+	RETURNI(1);
>+}
>diff --git a/lib/msun/ld80/s_sinpil.c b/lib/msun/ld80/s_sinpil.c
>new file mode 100644
>index 00000000000..4cefa92352e
>--- /dev/null
>+++ b/lib/msun/ld80/s_sinpil.c
>@@ -0,0 +1,140 @@
>+/*-
>+ * 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 union IEEEl2bits
>+pi_hi_u = LD80C(0xc90fdaa200000000,   1, 3.14159265346825122833e+00L),
>+pi_lo_u = LD80C(0x85a308d313198a2e, -33, 1.21542010130123852029e-10L);
>+#define	pi_hi	(pi_hi_u.e)
>+#define	pi_lo	(pi_lo_u.e)
>+
>+#include "k_cospil.h"
>+#include "k_sinpil.h"
>+
>+volatile static const double vzero = 0;
>+
>+long double
>+sinpil(long double x)
>+{
>+	long double ax, hi, lo, s;
>+	uint64_t lx, m;
>+	uint32_t j0;
>+	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);
>+				INSERT_LDBL80_WORDS(hi, hx,
>+				    lx & 0xffffffff00000000ull);
>+				hi *= 0x1p63L;
>+				lo = x * 0x1p63L - hi;
>+				s = (pi_lo + pi_hi) * lo + pi_lo * hi +
>+				    pi_hi * hi;
>+				RETURNI(s * 0x1p-63L);
>+			}
>+			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 {
>+			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.
>+	 */
>+	RETURNI(copysignl(0, x));
>+}
>diff --git a/lib/msun/ld80/s_tanpil.c b/lib/msun/ld80/s_tanpil.c
>new file mode 100644
>index 00000000000..02451e56202
>--- /dev/null
>+++ b/lib/msun/ld80/s_tanpil.c
>@@ -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
>+pi_hi =  3.1415926814079285e+00,	/* 0x400921fb 0x58000000 */
>+pi_lo = -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 * (pi_lo + pi_hi) + hi * pi_lo;
>+		hi *= pi_hi;
>+		_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 * (pi_lo + pi_hi) + hi * pi_lo;
>+		hi *= pi_hi;
>+		_2sumF(hi, lo);
>+		t = - __kernel_tanl(hi, lo, 1);
>+	} else
>+		t = 1;
>+
>+	return (t);
>+}
>+
>+volatile static const double vzero = 0;
>+
>+long double
>+tanpil(long double x)
>+{
>+	long double ax, hi, lo, t;
>+	uint64_t lx, m;
>+	uint32_t j0;
>+	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);
>+				INSERT_LDBL80_WORDS(hi, hx,
>+				    lx & 0xffffffff00000000ull);
>+				hi *= 0x1p63L;
>+				lo = x * 0x1p63L - hi;
>+				t = (pi_lo + pi_hi) * lo + pi_lo * hi +
>+				    pi_hi * hi;
>+				RETURNI(t * 0x1p-63L);
>+			}
>+			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 {
>+			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.
>+	 */
>+	RETURNI(copysignl(0, x));
>+}
>diff --git a/lib/msun/man/cospi.3 b/lib/msun/man/cospi.3
>new file mode 100644
>index 00000000000..b76e1858ed3
>--- /dev/null
>+++ b/lib/msun/man/cospi.3
>@@ -0,0 +1,111 @@
>+.\" Copyright (c) 2017 Steven G. Kargl <kargl@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@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.
>+
>+
>diff --git a/lib/msun/man/sinpi.3 b/lib/msun/man/sinpi.3
>new file mode 100644
>index 00000000000..4ae162bd1c7
>--- /dev/null
>+++ b/lib/msun/man/sinpi.3
>@@ -0,0 +1,102 @@
>+.\" Copyright (c) 2017 Steven G. Kargl <kargl@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@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.
>+
>diff --git a/lib/msun/man/tanpi.3 b/lib/msun/man/tanpi.3
>new file mode 100644
>index 00000000000..9cbbf4efaf2
>--- /dev/null
>+++ b/lib/msun/man/tanpi.3
>@@ -0,0 +1,106 @@
>+.\" Copyright (c) 2017 Steven G. Kargl <kargl@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@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.
>+
>+
>diff --git a/lib/msun/src/k_cospi.h b/lib/msun/src/k_cospi.h
>new file mode 100644
>index 00000000000..32985be809a
>--- /dev/null
>+++ b/lib/msun/src/k_cospi.h
>@@ -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 use the kernel for cos(x), the
>+ * argument to __kernel_cospi() must be multiplied by pi.
>+ */
>+
>+static inline double
>+__kernel_cospi(double x)
>+{
>+	double_t hi, lo;
>+
>+	hi = (float)x;
>+	lo = x - hi;
>+	lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
>+	hi *= pi_hi;
>+	_2sumF(hi, lo);
>+	return (__kernel_cos(hi, lo));
>+}
>+
>diff --git a/lib/msun/src/k_sinpi.h b/lib/msun/src/k_sinpi.h
>new file mode 100644
>index 00000000000..66152ba9931
>--- /dev/null
>+++ b/lib/msun/src/k_sinpi.h
>@@ -0,0 +1,43 @@
>+/*-
>+ * 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 use the kernel for sin(x), the
>+ * argument to __kernel_sinpi() must be multiplied by pi.
>+ */
>+
>+static inline double
>+__kernel_sinpi(double x)
>+{
>+	double_t hi, lo;
>+
>+	hi = (float)x;
>+	lo = x - hi;
>+	lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
>+	hi *= pi_hi;
>+	_2sumF(hi, lo);
>+	return (__kernel_sin(hi, lo, 1));
>+}
>diff --git a/lib/msun/src/math.h b/lib/msun/src/math.h
>index 8156094313e..98601f825bb 100644
>--- a/lib/msun/src/math.h
>+++ b/lib/msun/src/math.h
>@@ -508,6 +508,15 @@ long double	lgammal_r(long double, int *);
> void		sincos(double, double *, double *);
> void		sincosf(float, float *, float *);
> void		sincosl(long double, long double *, long double *);
>+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
>diff --git a/lib/msun/src/s_cospi.c b/lib/msun/src/s_cospi.c
>new file mode 100644
>index 00000000000..92a5f467c97
>--- /dev/null
>+++ b/lib/msun/src/s_cospi.c
>@@ -0,0 +1,151 @@
>+/*-
>+ * 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
>+pi_hi = 3.1415926814079285e+00,	/* 0x400921fb 0x58000000 */
>+pi_lo =-2.7818135228334233e-08;	/* 0xbe5dde97 0x3dcb3b3a */
>+
>+#include "k_cospi.h"
>+#include "k_sinpi.h"
>+
>+volatile static const double vzero = 0;
>+
>+double
>+cospi(double x)
>+{
>+	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.
>+	 */
>+	return (1);
>+}
>+
>+#if LDBL_MANT_DIG == 53
>+__weak_reference(cospi, cospil);
>+#endif
>diff --git a/lib/msun/src/s_cospif.c b/lib/msun/src/s_cospif.c
>new file mode 100644
>index 00000000000..4dd881395ba
>--- /dev/null
>+++ b/lib/msun/src/s_cospif.c
>@@ -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.
>+ */
>+#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)	(__kernel_cosdf(M_PI * (x)))
>+#define	__kernel_sinpif(x)	(__kernel_sindf(M_PI * (x)))
>+
>+volatile static const float vzero = 0;
>+
>+float
>+cospif(float x)
>+{
>+	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.
>+	 */
>+	return (1);
>+}
>diff --git a/lib/msun/src/s_sinpi.c b/lib/msun/src/s_sinpi.c
>new file mode 100644
>index 00000000000..b9731112a7e
>--- /dev/null
>+++ b/lib/msun/src/s_sinpi.c
>@@ -0,0 +1,168 @@
>+/*-
>+ * 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
>+pi_hi = 3.1415926814079285e+00,	/* 0x400921fb 0x58000000 */
>+pi_lo =-2.7818135228334233e-08;	/* 0xbe5dde97 0x3dcb3b3a */
>+
>+#include "k_cospi.h"
>+#include "k_sinpi.h"
>+
>+volatile static const double vzero = 0;
>+
>+double
>+sinpi(double x)
>+{
>+	double ax, hi, lo, 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);
>+				/*
>+				 * To avoid issues with subnormal values,
>+				 * scale the computation and rescale on 
>+				 * return.
>+				 */
>+				INSERT_WORDS(hi, hx, 0);
>+				hi *= 0x1p53;
>+				lo = x * 0x1p53 - hi;
>+				s = (pi_lo + pi_hi) * lo + pi_lo * hi +
>+				    pi_hi * hi;
>+				return (s * 0x1p-53);
>+			}
>+
>+			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.
>+	 */
>+	return (copysign(0, x));
>+}
>+
>+#if LDBL_MANT_DIG == 53
>+__weak_reference(sinpi, sinpil);
>+#endif
>diff --git a/lib/msun/src/s_sinpif.c b/lib/msun/src/s_sinpif.c
>new file mode 100644
>index 00000000000..c9f76f8a235
>--- /dev/null
>+++ b/lib/msun/src/s_sinpif.c
>@@ -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)	(__kernel_cosdf(M_PI * (x)))
>+#define	__kernel_sinpif(x)	(__kernel_sindf(M_PI * (x)))
>+
>+static const float
>+pi_hi =  3.14160156e+00F,	/* 0x40491000 */
>+pi_lo = -8.90890988e-06F;	/* 0xb715777a */
>+
>+volatile static const float vzero = 0;
>+
>+float
>+sinpif(float x)
>+{
>+	float ax, hi, lo, 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(hi, hx & 0xffff0000);
>+				hi *= 0x1p23F;
>+				lo = x * 0x1p23F - hi;
>+				s = (pi_lo + pi_hi) * lo + pi_lo * hi +
>+				    pi_hi * hi;
>+				return (s * 0x1p-23F);
>+			}
>+
>+			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.
>+	 */
>+	return (copysignf(0, x));
>+}
>diff --git a/lib/msun/src/s_tanpi.c b/lib/msun/src/s_tanpi.c
>new file mode 100644
>index 00000000000..e01917c94c1
>--- /dev/null
>+++ b/lib/msun/src/s_tanpi.c
>@@ -0,0 +1,176 @@
>+/*-
>+ * 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 
>+pi_hi =  3.1415926814079285e+00,	/* 0x400921fb 0x58000000 */
>+pi_lo = -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_t hi, lo, t;
>+
>+	if (x < 0.25) {
>+		hi = (float)x;
>+		lo = x - hi;
>+		lo = lo * (pi_lo + pi_hi) + hi * pi_lo;
>+		hi *= pi_hi;
>+		_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 * (pi_lo + pi_hi) + hi * pi_lo;
>+		hi *= pi_hi;
>+		_2sumF(hi, lo);
>+		t = - __kernel_tan(hi, lo, -1);
>+	} else
>+		t = 1;
>+
>+	return (t);
>+}
>+
>+volatile static const double vzero = 0;
>+
>+double
>+tanpi(double x)
>+{
>+	double ax, hi, lo, 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);
>+				/*
>+				 * To avoid issues with subnormal values,
>+				 * scale the computation and rescale on 
>+				 * return.
>+				 */
>+				INSERT_WORDS(hi, hx, 0);
>+				hi *= 0x1p53;
>+				lo = x * 0x1p53 - hi;
>+				t = (pi_lo + pi_hi) * lo + pi_lo * hi +
>+				    pi_hi * hi;
>+				return (t * 0x1p-53);
>+			}
>+			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.
>+	 */
>+	return (copysign(0, x));
>+}
>+
>+#if LDBL_MANT_DIG == 53
>+__weak_reference(tanpi, tanpil);
>+#endif
>diff --git a/lib/msun/src/s_tanpif.c b/lib/msun/src/s_tanpif.c
>new file mode 100644
>index 00000000000..6d4b627d1cf
>--- /dev/null
>+++ b/lib/msun/src/s_tanpif.c
>@@ -0,0 +1,114 @@
>+/*-
>+ * 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
>+pi_hi =  3.14160156e+00F,	/* 0x40491000 */
>+pi_lo = -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);
>+}
>+
>+volatile static const float vzero = 0;
>+
>+float
>+tanpif(float x)
>+{
>+	float ax, hi, lo, 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(hi, hx & 0xffff0000);
>+				hi *= 0x1p23F;
>+				lo = x * 0x1p23F - hi;
>+				t = (pi_lo + pi_hi) * lo + pi_lo * hi +
>+				    pi_hi * hi;
>+				return (t * 0x1p-23F);
>+			}
>+			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.
>+	 */
>+	return (copysignf(0, x));
>+}

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Attachments on bug 218514: 181622 | 182139 | 182648 | 229008 | 229010 | 229037 | 229047 | 229051 | 229108 | 229180 | 229215