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, 114 insertions, 0 deletions

diff --git a/src/math/atan2l.c b/src/math/atan2l.c
new file mode 100644
index 00000000..64ec12e7
--- /dev/null
+++ b/src/math/atan2l.c
@@ -0,0 +1,114 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2l.c */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ *
+ */
+/*
+ * See comments in atan2.c.
+ * Converted to long double by David Schultz <das@FreeBSD.ORG>.
+ */
+
+#include "libm.h"
+
+#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
+long double atan2l(long double y, long double x)
+{
+	return atan2(y, x);
+}
+#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
+#include "__invtrigl.h"
+static volatile long double
+tiny = 1.0e-300;
+static const long double
+zero = 0.0;
+/* XXX Work around the fact that gcc truncates long double constants on i386 */
+static volatile double
+pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1  */
+pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
+#define pi ((long double)pi1 + pi2)
+#if 0
+static const long double
+pi = 3.14159265358979323846264338327950280e+00L;
+#endif
+
+long double atan2l(long double y, long double x)
+{
+	union IEEEl2bits ux, uy;
+	long double z;
+	int32_t k,m;
+	int16_t exptx, expsignx, expty, expsigny;
+
+	uy.e = y;
+	expsigny = uy.xbits.expsign;
+	expty = expsigny & 0x7fff;
+	ux.e = x;
+	expsignx = ux.xbits.expsign;
+	exptx = expsignx & 0x7fff;
+	if ((exptx==BIAS+LDBL_MAX_EXP &&
+	     ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
+	    (expty==BIAS+LDBL_MAX_EXP &&
+	     ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0))   /* y is NaN */
+		return x+y;
+	if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
+		return atanl(y);
+	m = ((expsigny>>15)&1) | ((expsignx>>14)&2);  /* 2*sign(x)+sign(y) */
+
+	/* when y = 0 */
+	if (expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==0) {
+		switch(m) {
+		case 0:
+		case 1: return y;        /* atan(+-0,+anything)=+-0 */
+		case 2: return  pi+tiny; /* atan(+0,-anything) = pi */
+		case 3: return -pi-tiny; /* atan(-0,-anything) =-pi */
+		}
+	}
+	/* when x = 0 */
+	if (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
+		return expsigny < 0 ? -pio2_hi-tiny : pio2_hi+tiny;
+	/* when x is INF */
+	if (exptx == BIAS+LDBL_MAX_EXP) {
+		if (expty == BIAS+LDBL_MAX_EXP) {
+			switch(m) {
+			case 0: return  pio2_hi*0.5+tiny; /* atan(+INF,+INF) */
+			case 1: return -pio2_hi*0.5-tiny; /* atan(-INF,+INF) */
+			case 2: return  1.5*pio2_hi+tiny; /*atan(+INF,-INF)*/
+			case 3: return -1.5*pio2_hi-tiny; /*atan(-INF,-INF)*/
+			}
+		} else {
+			switch(m) {
+			case 0: return  zero;    /* atan(+...,+INF) */
+			case 1: return -zero;    /* atan(-...,+INF) */
+			case 2: return  pi+tiny; /* atan(+...,-INF) */
+			case 3: return -pi-tiny; /* atan(-...,-INF) */
+			}
+		}
+	}
+	/* when y is INF */
+	if (expty == BIAS+LDBL_MAX_EXP)
+		return expsigny < 0 ? -pio2_hi-tiny : pio2_hi+tiny;
+
+	/* compute y/x */
+	k = expty-exptx;
+	if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
+		z = pio2_hi+pio2_lo;
+		m &= 1;
+	} else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
+		z = 0.0;
+	else                     /* safe to do y/x */
+		z = atanl(fabsl(y/x));
+	switch (m) {
+	case 0: return z;              /* atan(+,+) */
+	case 1: return -z;             /* atan(-,+) */
+	case 2: return pi - (z-pi_lo); /* atan(+,-) */
+	default: /* case 3 */
+		return (z-pi_lo) - pi; /* atan(-,-) */
+	}
+}
+#endif