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, 141 insertions, 0 deletions

diff --git a/src/complex/csinh.c b/src/complex/csinh.c
new file mode 100644
index 00000000..fe16f06b
--- /dev/null
+++ b/src/complex/csinh.c
@@ -0,0 +1,141 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_csinh.c */
+/*-
+ * 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 "libm.h"
+
+static const double huge = 0x1p1023;
+
+double complex csinh(double complex z)
+{
+	double x, y, h;
+	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);
+		if (ix < 0x40360000)    /* small x: normal case */
+			return cpack(sinh(x) * cos(y), cosh(x) * sin(y));
+
+		/* |x| >= 22, so cosh(x) ~= exp(|x|) */
+		if (ix < 0x40862e42) {
+			/* x < 710: exp(|x|) won't overflow */
+			h = exp(fabs(x)) * 0.5;
+			return cpack(copysign(h, x) * cos(y), h * sin(y));
+		} else if (ix < 0x4096bbaa) {
+			/* x < 1455: scale to avoid overflow */
+			z = __ldexp_cexp(cpack(fabs(x), y), -1);
+			return cpack(creal(z) * copysign(1, x), cimag(z));
+		} else {
+			/* x >= 1455: the result always overflows */
+			h = huge * x;
+			return cpack(h * cos(y), h * h * 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, 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));
+}