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, 83 insertions, 0 deletions

diff --git a/src/math/tanhl.c b/src/math/tanhl.c
new file mode 100644
index 00000000..e62be59b
--- /dev/null
+++ b/src/math/tanhl.c
@@ -0,0 +1,83 @@
+/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_tanhl.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+/* tanhl(x)
+ * Return the Hyperbolic Tangent of x
+ *
+ * Method :
+ *                                      x    -x
+ *                                     e  - e
+ *      0. tanhl(x) is defined to be -----------
+ *                                      x    -x
+ *                                     e  + e
+ *      1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
+ *      2.  0      <= x <= 2**-55 : tanhl(x) := x*(one+x)
+ *                                               -t
+ *          2**-55 <  x <=  1     : tanhl(x) := -----; t = expm1l(-2x)
+ *                                              t + 2
+ *                                                    2
+ *          1      <= x <=  23.0  : tanhl(x) := 1-  ----- ; t=expm1l(2x)
+ *                                                  t + 2
+ *          23.0   <  x <= INF    : tanhl(x) := 1.
+ *
+ * Special cases:
+ *      tanhl(NaN) is NaN;
+ *      only tanhl(0)=0 is exact for finite argument.
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double tanhl(long double x)
+{
+	return tanh(x);
+}
+#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
+
+long double tanhl(long double x)
+{
+	long double t,z;
+	int32_t se;
+	uint32_t jj0,jj1,ix;
+
+	/* High word of |x|. */
+	GET_LDOUBLE_WORDS(se, jj0, jj1, x);
+	ix = se & 0x7fff;
+
+	/* x is INF or NaN */
+	if (ix == 0x7fff) {
+		/* for NaN it's not important which branch: tanhl(NaN) = NaN */
+		if (se & 0x8000)
+			return one/x-one;  /* tanhl(-inf)= -1; */
+		return one/x+one;          /* tanhl(+inf)= +1 */
+	}
+
+	/* |x| < 23 */
+	if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {
+		if ((ix|jj0|jj1) == 0) /* x == +- 0 */
+			return x;
+		if (ix < 0x3fc8)       /* |x| < 2**-55 */
+			return x*(one+tiny);  /* tanh(small) = small */
+		if (ix >= 0x3fff) {    /* |x| >= 1  */
+			t = expm1l(two*fabsl(x));
+			z = one - two/(t+two);
+		} else {
+			t = expm1l(-two*fabsl(x));
+			z = -t/(t+two);
+		}
+	/* |x| > 23, return +-1 */
+	} else {
+		z = one - tiny;  /* raise inexact flag */
+	}
+	return se & 0x8000 ? -z : z;
+}
+#endif