Add c{cos,sin,tan}{,h}{,f} functions. This is joint work with

bde and kargl.

6 files changed, 671 insertions, 0 deletions

diff --git a/lib/msun/src/s_ccosh.c b/lib/msun/src/s_ccosh.c
new file mode 100644
index 0000000..4086394
--- /dev/null
+++ b/lib/msun/src/s_ccosh.c
@@ -0,0 +1,138 @@
+/*-
+ * Copyright (c) 2005 Bruce D. Evans and 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.
+ */
+
+/*
+ * Hyperbolic cosine of a complex argument z = x + i y.
+ *
+ * cosh(z) = cosh(x+iy)
+ *         = cosh(x) cos(y) + i sinh(x) sin(y).
+ *
+ * Exceptional values are noted in the comments within the source code.
+ * These values and the return value were taken from n1124.pdf.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+#include "math_private.h"
+
+double complex
+ccosh(double complex z)
+{
+	double x, y;
+	int32_t hx, hy, ix, iy, lx, ly;
+
+	x = creal(z);
+	y = cimag(z);
+
+	EXTRACT_WORDS(hx, lx, x);
+	EXTRACT_WORDS(hy, ly, y);
+
+	ix = 0x7fffffff & hx;
+	iy = 0x7fffffff & hy;
+
+	/* Handle the nearly-non-exceptional cases where x and y are finite. */
+	if (ix < 0x7ff00000 && iy < 0x7ff00000) {
+		if ((iy | ly) == 0)
+			return (cpack(cosh(x), x * y));
+		/* XXX We don't handle |x| > DBL_MAX ln(2) yet. */
+		return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
+	}
+
+	/*
+	 * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0.
+	 * The sign of 0 in the result is unspecified.  Choice = normally
+	 * the same as dNaN.  Raise the invalid floating-point exception.
+	 *
+	 * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0.
+	 * The sign of 0 in the result is unspecified.  Choice = normally
+	 * the same as d(NaN).
+	 */
+	if ((ix | lx) == 0 && iy >= 0x7ff00000)
+		return (cpack(y - y, copysign(0, x * (y - y))));
+
+	/*
+	 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
+	 *
+	 * cosh(NaN +- I 0)   = d(NaN) + I sign(d(NaN, +-0))0.
+	 * The sign of 0 in the result is unspecified.
+	 */
+	if ((iy | ly) == 0 && ix >= 0x7ff00000) {
+		if (((hx & 0xfffff) | lx) == 0)
+			return (cpack(x * x, copysign(0, x) * y));
+		return (cpack(x * x, copysign(0, (x + x) * y)));
+	}
+
+	/*
+	 * cosh(x +- I Inf) = dNaN + I dNaN.
+	 * Raise the invalid floating-point exception for finite nonzero x.
+	 *
+	 * cosh(x + I NaN) = d(NaN) + I d(NaN).
+	 * Optionally raises the invalid floating-point exception for finite
+	 * nonzero x.  Choice = don't raise (except for signaling NaNs).
+	 */
+	if (ix < 0x7ff00000 && iy >= 0x7ff00000)
+		return (cpack(y - y, x * (y - y)));
+
+	/*
+	 * cosh(+-Inf + I NaN)  = +Inf + I d(NaN).
+	 *
+	 * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
+	 * The sign of Inf in the result is unspecified.  Choice = always +.
+	 * Raise the invalid floating-point exception.
+	 *
+	 * cosh(+-Inf + I y)   = +Inf cos(y) +- I Inf sin(y)
+	 */
+	if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
+		if (iy >= 0x7ff00000)
+			return (cpack(x * x, x * (y - y)));
+		return (cpack((x * x) * cos(y), x * sin(y)));
+	}
+
+	/*
+	 * cosh(NaN + I NaN)  = d(NaN) + I d(NaN).
+	 *
+	 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
+	 * Optionally raises the invalid floating-point exception.
+	 * Choice = raise.
+	 *
+	 * cosh(NaN + I y)    = d(NaN) + I d(NaN).
+	 * Optionally raises the invalid floating-point exception for finite
+	 * nonzero y.  Choice = don't raise (except for signaling NaNs).
+	 */
+	return (cpack((x * x) * (y - y), (x + x) * (y - y)));
+}
+
+double complex
+ccos(double complex z)
+{
+
+	/* ccos(z) = ccosh(I * z) */
+	return (ccosh(cpack(-cimag(z), creal(z))));
+}
diff --git a/lib/msun/src/s_ccoshf.c b/lib/msun/src/s_ccoshf.c
new file mode 100644
index 0000000..bf9b78f
--- /dev/null
+++ b/lib/msun/src/s_ccoshf.c
@@ -0,0 +1,87 @@
+/*-
+ * Copyright (c) 2005 Bruce D. Evans and 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.
+ */
+
+/*
+ * Hyperbolic cosine of a complex argument.  See s_ccosh.c for details.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+#include "math_private.h"
+
+float complex
+ccoshf(float complex z)
+{
+	float x, y;
+	int32_t hx, hy, ix, iy;
+
+	x = crealf(z);
+	y = cimagf(z);
+
+	GET_FLOAT_WORD(hx, x);
+	GET_FLOAT_WORD(hy, y);
+
+	ix = 0x7fffffff & hx;
+	iy = 0x7fffffff & hy;
+
+	if (ix < 0x7f800000 && iy < 0x7f800000) {
+		if (iy == 0)
+			return (cpackf(coshf(x), x * y));
+		/* XXX We don't handle |x| > FLT_MAX ln(2) yet. */
+		return (cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y)));
+	}
+
+	if (ix == 0 && iy >= 0x7f800000)
+		return (cpackf(y - y, copysignf(0, x * (y - y))));
+
+	if (iy == 0 && ix >= 0x7f800000) {
+		if ((hx & 0x7fffff) == 0)
+			return (cpackf(x * x, copysignf(0, x) * y));
+		return (cpackf(x * x, copysignf(0, (x + x) * y)));
+	}
+
+	if (ix < 0x7f800000 && iy >= 0x7f800000)
+		return (cpackf(y - y, x * (y - y)));
+
+	if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
+		if (iy >= 0x7f800000)
+			return (cpackf(x * x, x * (y - y)));
+		return (cpackf((x * x) * cosf(y), x * sinf(y)));
+	}
+
+	return (cpackf((x * x) * (y - y), (x + x) * (y - y)));
+}
+
+float complex
+ccosf(float complex z)
+{
+
+	return (ccoshf(cpackf(-cimagf(z), crealf(z))));
+}
diff --git a/lib/msun/src/s_csinh.c b/lib/msun/src/s_csinh.c
new file mode 100644
index 0000000..74a0aff
--- /dev/null
+++ b/lib/msun/src/s_csinh.c
@@ -0,0 +1,140 @@
+/*-
+ * Copyright (c) 2005 Bruce D. Evans and 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.
+ */
+
+/*
+ * Hyperbolic sine of a complex argument z = x + i y.
+ *
+ * sinh(z) = sinh(x+iy)
+ *         = sinh(x) cos(y) + i cosh(x) sin(y).
+ *
+ * Exceptional values are noted in the comments within the source code.
+ * These values and the return value were taken from n1124.pdf.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+#include "math_private.h"
+
+double complex
+csinh(double complex z)
+{
+	double x, y;
+	int32_t hx, hy, ix, iy, lx, ly;
+
+	x = creal(z);
+	y = cimag(z);
+
+	EXTRACT_WORDS(hx, lx, x);
+	EXTRACT_WORDS(hy, ly, y);
+
+	ix = 0x7fffffff & hx;
+	iy = 0x7fffffff & hy;
+
+	/* Handle the nearly-non-exceptional cases where x and y are finite. */
+	if (ix < 0x7ff00000 && iy < 0x7ff00000) {
+		if ((iy | ly) == 0)
+			return (cpack(sinh(x), y));
+		/* XXX We don't handle |x| > DBL_MAX ln(2) yet. */
+		return (cpack(sinh(x) * cos(y), cosh(x) * sin(y)));
+	}
+
+	/*
+	 * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN.
+	 * The sign of 0 in the result is unspecified.  Choice = normally
+	 * the same as dNaN.  Raise the invalid floating-point exception.
+	 *
+	 * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN).
+	 * The sign of 0 in the result is unspecified.  Choice = normally
+	 * the same as d(NaN).
+	 */
+	if ((ix | lx) == 0 && iy >= 0x7ff00000)
+		return (cpack(copysign(0, x * (y - y)), y - y));
+
+	/*
+	 * sinh(+-Inf +- I 0) = +-Inf + I (+-)(+-)0.
+	 *
+	 * sinh(NaN +- I 0)   = d(NaN) + I +-0.
+	 */
+	if ((iy | ly) == 0 && ix >= 0x7ff00000) {
+		if (((hx & 0xfffff) | lx) == 0)
+			return (cpack(x, copysign(0, x) * y));
+		return (cpack(x, copysign(0, y)));
+	}
+
+	/*
+	 * sinh(x +- I Inf) = dNaN + I dNaN.
+	 * Raise the invalid floating-point exception for finite nonzero x.
+	 *
+	 * sinh(x + I NaN) = d(NaN) + I d(NaN).
+	 * Optionally raises the invalid floating-point exception for finite
+	 * nonzero x.  Choice = don't raise (except for signaling NaNs).
+	 */
+	if (ix < 0x7ff00000 && iy >= 0x7ff00000)
+		return (cpack(y - y, x * (y - y)));
+
+	/*
+	 * sinh(+-Inf + I NaN)  = +-Inf + I d(NaN).
+	 * The sign of Inf in the result is unspecified.  Choice = normally
+	 * the same as d(NaN).
+	 *
+	 * sinh(+-Inf +- I Inf) = +Inf + I dNaN.
+	 * The sign of Inf in the result is unspecified.  Choice = always +.
+	 * Raise the invalid floating-point exception.
+	 *
+	 * sinh(+-Inf + I y)   = +-Inf cos(y) + I Inf sin(y)
+	 */
+	if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
+		if (iy >= 0x7ff00000)
+			return (cpack(x * x, x * (y - y)));
+		return (cpack(x * cos(y), INFINITY * sin(y)));
+	}
+
+	/*
+	 * sinh(NaN + I NaN)  = d(NaN) + I d(NaN).
+	 *
+	 * sinh(NaN +- I Inf) = d(NaN) + I d(NaN).
+	 * Optionally raises the invalid floating-point exception.
+	 * Choice = raise.
+	 *
+	 * sinh(NaN + I y)    = d(NaN) + I d(NaN).
+	 * Optionally raises the invalid floating-point exception for finite
+	 * nonzero y.  Choice = don't raise (except for signaling NaNs).
+	 */
+	return (cpack((x * x) * (y - y), (x + x) * (y - y)));
+}
+
+double complex
+csin(double complex z)
+{
+
+	/* csin(z) = -I * csinh(I * z) */
+	z = csinh(cpack(-cimag(z), creal(z)));
+	return (cpack(cimag(z), -creal(z)));
+}
diff --git a/lib/msun/src/s_csinhf.c b/lib/msun/src/s_csinhf.c
new file mode 100644
index 0000000..e1478ac
--- /dev/null
+++ b/lib/msun/src/s_csinhf.c
@@ -0,0 +1,88 @@
+/*-
+ * Copyright (c) 2005 Bruce D. Evans and 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.
+ */
+
+/*
+ * Hyperbolic sine of a complex argument z.  See s_csinh.c for details.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+#include "math_private.h"
+
+float complex
+csinhf(float complex z)
+{
+	float x, y;
+	int32_t hx, hy, ix, iy;
+
+	x = crealf(z);
+	y = cimagf(z);
+
+	GET_FLOAT_WORD(hx, x);
+	GET_FLOAT_WORD(hy, y);
+
+	ix = 0x7fffffff & hx;
+	iy = 0x7fffffff & hy;
+
+	if (ix < 0x7f800000 && iy < 0x7f800000) {
+		if (iy == 0)
+			return (cpackf(sinhf(x), y));
+		/* XXX We don't handle |x| > FLT_MAX ln(2) yet. */
+		return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
+	}
+
+	if (ix == 0 && iy >= 0x7f800000)
+		return (cpackf(copysignf(0, x * (y - y)), y - y));
+
+	if (iy == 0 && ix >= 0x7f800000) {
+		if ((hx & 0x7fffff) == 0)
+			return (cpackf(x, copysignf(0, x) * y));
+		return (cpackf(x, copysignf(0, y)));
+	}
+
+	if (ix < 0x7f800000 && iy >= 0x7f800000)
+		return (cpackf(y - y, x * (y - y)));
+
+	if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
+		if (iy >= 0x7f800000)
+			return (cpackf(x * x, x * (y - y)));
+		return (cpackf(x * cosf(y), INFINITY * sinf(y)));
+	}
+
+	return (cpackf((x * x) * (y - y), (x + x) * (y - y)));
+}
+
+float complex
+csinf(float complex z)
+{
+
+	z = csinhf(cpackf(-cimagf(z), crealf(z)));
+	return (cpackf(cimagf(z), -crealf(z)));
+}
diff --git a/lib/msun/src/s_ctanh.c b/lib/msun/src/s_ctanh.c
new file mode 100644
index 0000000..1705e90
--- /dev/null
+++ b/lib/msun/src/s_ctanh.c
@@ -0,0 +1,137 @@
+/*-
+ * Copyright (c) 2011 David Schultz
+ * 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.
+ */
+
+/*
+ * Hyperbolic tangent of a complex argument z = x + i y.
+ *
+ * The algorithm is from:
+ *
+ *   W. Kahan.  Branch Cuts for Complex Elementary Functions or Much
+ *   Ado About Nothing's Sign Bit.  In The State of the Art in
+ *   Numerical Analysis, pp. 165 ff.  Iserles and Powell, eds., 1987.
+ *
+ * Method:
+ *
+ *   Let t    = tan(x)
+ *       beta = 1/cos^2(y)
+ *       s    = sinh(x)
+ *       rho  = cosh(x)
+ *
+ *   We have:
+ *
+ *   tanh(z) = sinh(z) / cosh(z)
+ *
+ *             sinh(x) cos(y) + i cosh(x) sin(y)
+ *           = ---------------------------------
+ *             cosh(x) cos(y) + i sinh(x) sin(y)
+ *
+ *             cosh(x) sinh(x) / cos^2(y) + i tan(y)
+ *           = -------------------------------------
+ *                    1 + sinh^2(x) / cos^2(y)
+ *
+ *             beta rho s + i t
+ *           = ----------------
+ *               1 + beta s^2
+ *
+ * Modifications:
+ *
+ *   I omitted the original algorithm's handling of overflow in tan(x) after
+ *   verifying with nearpi.c that this can't happen in IEEE single or double
+ *   precision.  I also handle large x differently.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+#include "math_private.h"
+
+double complex
+ctanh(double complex z)
+{
+	double x, y;
+	double t, beta, s, rho, denom;
+	uint32_t hx, ix, lx;
+
+	x = creal(z);
+	y = cimag(z);
+
+	EXTRACT_WORDS(hx, lx, x);
+	ix = hx & 0x7fffffff;
+
+	/*
+	 * ctanh(NaN + i 0) = NaN + i 0
+	 *
+	 * ctanh(NaN + i y) = NaN + i NaN		for y != 0
+	 *
+	 * The imaginary part has the sign of x*sin(2*y), but there's no
+	 * special effort to get this right.
+	 *
+	 * ctanh(+-Inf +- i Inf) = +-1 +- 0
+	 *
+	 * ctanh(+-Inf + i y) = +-1 + 0 sin(2y)		for y finite
+	 *
+	 * The imaginary part of the sign is unspecified.  This special
+	 * case is only needed to avoid a spurious invalid exception when
+	 * y is infinite.
+	 */
+	if (ix >= 0x7ff00000) {
+		if ((ix & 0xfffff) | lx)	/* x is NaN */
+			return (cpack(x, (y == 0 ? y : x * y)));
+		SET_HIGH_WORD(x, hx - 0x40000000);	/* x = copysign(1, x) */
+		return (cpack(x, copysign(0, isinf(y) ? y : sin(y) * cos(y))));
+	}
+
+	/*
+	 * ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the
+	 * approximation sinh^2(huge) ~= exp(2*huge) / 4.
+	 * We use a modified formula to avoid spurious overflow.
+	 */
+	if (ix >= 0x40360000) {	/* x >= 22 */
+		double exp_mx = exp(-fabs(x));
+		return (cpack(copysign(1, x),
+		    4 * sin(y) * cos(y) * exp_mx * exp_mx));
+	}
+
+	/* Kahan's algorithm */
+	t = tan(y);
+	beta = 1.0 + t * t;	/* = 1 / cos^2(y) */
+	s = sinh(x);
+	rho = sqrt(1 + s * s);	/* = cosh(x) */
+	denom = 1 + beta * s * s;
+	return (cpack((beta * rho * s) / denom, t / denom));
+}
+
+double complex
+ctan(double complex z)
+{
+
+	/* ctan(z) = -I * ctanh(I * z) */
+	z = ctanh(cpack(-cimag(z), creal(z)));
+	return (cpack(cimag(z), -creal(z)));
+}
diff --git a/lib/msun/src/s_ctanhf.c b/lib/msun/src/s_ctanhf.c
new file mode 100644
index 0000000..ae833df
--- /dev/null
+++ b/lib/msun/src/s_ctanhf.c
@@ -0,0 +1,81 @@
+/*-
+ * Copyright (c) 2011 David Schultz
+ * 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.
+ */
+
+/*
+ * Hyperbolic tangent of a complex argument z.  See s_ctanh.c for details.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+#include <complex.h>
+#include <math.h>
+
+#include "math_private.h"
+
+float complex
+ctanhf(float complex z)
+{
+	float x, y;
+	float t, beta, s, rho, denom;
+	uint32_t hx, ix;
+
+	x = crealf(z);
+	y = cimagf(z);
+
+	GET_FLOAT_WORD(hx, x);
+	ix = hx & 0x7fffffff;
+
+	if (ix >= 0x7f800000) {
+		if (ix & 0x7fffff)
+			return (cpackf(x, (y == 0 ? y : x * y)));
+		SET_FLOAT_WORD(x, hx - 0x40000000);
+		return (cpackf(x,
+		    copysignf(0, isinf(y) ? y : sinf(y) * cosf(y))));
+	}
+
+	if (ix >= 0x41300000) {	/* x >= 11 */
+		float exp_mx = expf(-fabsf(x));
+		return (cpackf(copysignf(1, x),
+		    4 * sinf(y) * cosf(y) * exp_mx * exp_mx));
+	}
+
+	t = tanf(y);
+	beta = 1.0 + t * t;
+	s = sinhf(x);
+	rho = sqrtf(1 + s * s);
+	denom = 1 + beta * s * s;
+	return (cpackf((beta * rho * s) / denom, t / denom));
+}
+
+float complex
+ctanf(float complex z)
+{
+
+	z = ctanhf(cpackf(-cimagf(z), crealf(z)));
+	return (cpackf(cimagf(z), -crealf(z)));
+}
+