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, 55 insertions, 0 deletions

diff --git a/src/math/__tandf.c b/src/math/__tandf.c
new file mode 100644
index 00000000..36a8214e
--- /dev/null
+++ b/src/math/__tandf.c
@@ -0,0 +1,55 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/k_tanf.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Optimized by Bruce D. Evans.
+ */
+/*
+ * ====================================================
+ * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#include "libm.h"
+
+/* |tan(x)/x - t(x)| < 2**-25.5 (~[-2e-08, 2e-08]). */
+static const double T[] = {
+  0x15554d3418c99f.0p-54, /* 0.333331395030791399758 */
+  0x1112fd38999f72.0p-55, /* 0.133392002712976742718 */
+  0x1b54c91d865afe.0p-57, /* 0.0533812378445670393523 */
+  0x191df3908c33ce.0p-58, /* 0.0245283181166547278873 */
+  0x185dadfcecf44e.0p-61, /* 0.00297435743359967304927 */
+  0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
+};
+
+float __tandf(double x, int iy)
+{
+	double z,r,w,s,t,u;
+
+	z = x*x;
+	/*
+	 * Split up the polynomial into small independent terms to give
+	 * opportunities for parallel evaluation.  The chosen splitting is
+	 * micro-optimized for Athlons (XP, X64).  It costs 2 multiplications
+	 * relative to Horner's method on sequential machines.
+	 *
+	 * We add the small terms from lowest degree up for efficiency on
+	 * non-sequential machines (the lowest degree terms tend to be ready
+	 * earlier).  Apart from this, we don't care about order of
+	 * operations, and don't need to to care since we have precision to
+	 * spare.  However, the chosen splitting is good for accuracy too,
+	 * and would give results as accurate as Horner's method if the
+	 * small terms were added from highest degree down.
+	 */
+	r = T[4] + z*T[5];
+	t = T[2] + z*T[3];
+	w = z*z;
+	s = z*x;
+	u = T[0] + z*T[1];
+	r = (x + s*u) + (s*w)*(t + w*r);
+	if(iy==1) return r;
+	else return -1.0/r;
+}