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, 118 insertions, 0 deletions

diff --git a/src/math/__tanl.c b/src/math/__tanl.c
new file mode 100644
index 00000000..f842543e
--- /dev/null
+++ b/src/math/__tanl.c
@@ -0,0 +1,118 @@
+/* origin: FreeBSD /usr/src/lib/msun/ld80/k_tanl.c */
+/*
+ * ====================================================
+ * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
+ * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
+ *
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
+/*
+ * ld80 version of __tan.c.  See __tan.c for most comments.
+ */
+/*
+ * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22]
+ * |tan(x)/x - t(x)| < 2**-71.9
+ *
+ * See __cosl.c for more details about the polynomial.
+ */
+
+/* Long double constants are slow on these arches, and broken on i386. */
+static const volatile double
+T3hi =  0.33333333333333331,            /*  0x15555555555555.0p-54 */
+T3lo =  1.8350121769317163e-17,         /*  0x15280000000000.0p-108 */
+T5hi =  0.13333333333333336,            /*  0x11111111111112.0p-55 */
+T5lo =  1.3051083651294260e-17,         /*  0x1e180000000000.0p-109 */
+T7hi =  0.053968253968250494,           /*  0x1ba1ba1ba1b827.0p-57 */
+T7lo =  3.1509625637859973e-18,         /*  0x1d100000000000.0p-111 */
+pio4_hi   =  0.78539816339744828,       /*  0x1921fb54442d18.0p-53 */
+pio4_lo   =  3.0628711372715500e-17,    /*  0x11a80000000000.0p-107 */
+pio4lo_hi = -1.2541394031670831e-20,    /* -0x1d9cceba3f91f2.0p-119 */
+pio4lo_lo =  6.1493048227390915e-37;    /*  0x1a280000000000.0p-173 */
+#define T3      ((long double)T3hi + T3lo)
+#define T5      ((long double)T5hi + T5lo)
+#define T7      ((long double)T7hi + T7lo)
+#define pio4    ((long double)pio4_hi + pio4_lo)
+#define pio4lo  ((long double)pio4lo_hi + pio4lo_lo)
+
+#if 0
+static const long double
+T3 =  0.333333333333333333180L,         /*  0xaaaaaaaaaaaaaaa5.0p-65 */
+T5 =  0.133333333333333372290L,         /*  0x88888888888893c3.0p-66 */
+T7 =  0.0539682539682504975744L,        /*  0xdd0dd0dd0dc13ba2.0p-68 */
+pio4   =  0.785398163397448309628L,     /*  0xc90fdaa22168c235.0p-64 */
+pio4lo = -1.25413940316708300586e-20L;  /* -0xece675d1fc8f8cbb.0p-130 */
+#endif
+
+static const double
+T9  =  0.021869488536312216,            /*  0x1664f4882cc1c2.0p-58 */
+T11 =  0.0088632355256619590,           /*  0x1226e355c17612.0p-59 */
+T13 =  0.0035921281113786528,           /*  0x1d6d3d185d7ff8.0p-61 */
+T15 =  0.0014558334756312418,           /*  0x17da354aa3f96b.0p-62 */
+T17 =  0.00059003538700862256,          /*  0x13559358685b83.0p-63 */
+T19 =  0.00023907843576635544,          /*  0x1f56242026b5be.0p-65 */
+T21 =  0.000097154625656538905,         /*  0x1977efc26806f4.0p-66 */
+T23 =  0.000038440165747303162,         /*  0x14275a09b3ceac.0p-67 */
+T25 =  0.000018082171885432524,         /*  0x12f5e563e5487e.0p-68 */
+T27 =  0.0000024196006108814377,        /*  0x144c0d80cc6896.0p-71 */
+T29 =  0.0000078293456938132840,        /*  0x106b59141a6cb3.0p-69 */
+T31 = -0.0000032609076735050182,        /* -0x1b5abef3ba4b59.0p-71 */
+T33 =  0.0000023261313142559411;        /*  0x13835436c0c87f.0p-71 */
+
+long double __tanl(long double x, long double y, int iy) {
+	long double z, r, v, w, s, a, t;
+	long double osign;
+	int i;
+
+	iy = iy == 1 ? -1 : 1;        /* XXX recover original interface */
+	// FIXME: this is wrong, use copysign, signbit or union bithack
+	osign = x >= 0 ? 1.0 : -1.0;  /* XXX slow, probably wrong for -0 */
+	if (fabsl(x) >= 0.67434) {
+		if (x < 0) {
+			x = -x;
+			y = -y;
+		}
+		z = pio4 - x;
+		w = pio4lo - y;
+		x = z + w;
+		y = 0.0;
+		i = 1;
+	} else
+		i = 0;
+	z = x * x;
+	w = z * z;
+	r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
+	     w * (T25 + w * (T29 + w * T33))))));
+	v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
+	     w * (T27 + w * T31))))));
+	s = z * x;
+	r = y + z * (s * (r + v) + y);
+	r += T3 * s;
+	w = x + r;
+	if (i == 1) {
+		v = (long double)iy;
+		return osign * (v - 2.0 * (x - (w * w / (w + v) - r)));
+	}
+	if (iy == 1)
+		return w;
+
+	/*
+	 * if allow error up to 2 ulp, simply return
+	 * -1.0 / (x+r) here
+	 */
+	/* compute -1.0 / (x+r) accurately */
+	z = w;
+	z = z + 0x1p32 - 0x1p32;
+	v = r - (z - x);        /* z+v = r+x */
+	t = a = -1.0 / w;       /* a = -1.0/w */
+	t = t + 0x1p32 - 0x1p32;
+	s = 1.0 + t * z;
+	return t + a * (s + t * v);
+}
+#endif