first commit of the new libm!

thanks to the hard work of Szabolcs Nagy (nsz), identifying the best
(from correctness and license standpoint) implementations from freebsd
and openbsd and cleaning them up! musl should now fully support c99
float and long double math functions, and has near-complete complex
math support. tgmath should also work (fully on gcc-compatible
compilers, and mostly on any c99 compiler).

based largely on commit 0376d44a890fea261506f1fc63833e7a686dca19 from
nsz's libm git repo, with some additions (dummy versions of a few
missing long double complex functions, etc.) by me.

various cleanups still need to be made, including re-adding (if
they're correct) some asm functions that were dropped.

1 files changed, 127 insertions, 0 deletions

diff --git a/src/complex/ctanh.c b/src/complex/ctanh.c
new file mode 100644
index 00000000..dd569fc3
--- /dev/null
+++ b/src/complex/ctanh.c
@@ -0,0 +1,127 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_ctanh.c */
+/*-
+ * 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 "libm.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(x + i NAN) = NaN + i NaN
+	 * ctanh(x +- i Inf) = NaN + i NaN
+	 */
+	if (!isfinite(y))
+		return cpack(y - y, y - 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);
+}