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, 128 insertions, 0 deletions

diff --git a/src/math/hypot.c b/src/math/hypot.c
new file mode 100644
index 00000000..ba4c7575
--- /dev/null
+++ b/src/math/hypot.c
@@ -0,0 +1,128 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/e_hypot.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.
+ * ====================================================
+ */
+/* hypot(x,y)
+ *
+ * Method :
+ *      If (assume round-to-nearest) z=x*x+y*y
+ *      has error less than sqrt(2)/2 ulp, then
+ *      sqrt(z) has error less than 1 ulp (exercise).
+ *
+ *      So, compute sqrt(x*x+y*y) with some care as
+ *      follows to get the error below 1 ulp:
+ *
+ *      Assume x>y>0;
+ *      (if possible, set rounding to round-to-nearest)
+ *      1. if x > 2y  use
+ *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
+ *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
+ *      2. if x <= 2y use
+ *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
+ *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
+ *      y1= y with lower 32 bits chopped, y2 = y-y1.
+ *
+ *      NOTE: scaling may be necessary if some argument is too
+ *            large or too tiny
+ *
+ * Special cases:
+ *      hypot(x,y) is INF if x or y is +INF or -INF; else
+ *      hypot(x,y) is NAN if x or y is NAN.
+ *
+ * Accuracy:
+ *      hypot(x,y) returns sqrt(x^2+y^2) with error less
+ *      than 1 ulps (units in the last place)
+ */
+
+#include "libm.h"
+
+double hypot(double x, double y)
+{
+	double a,b,t1,t2,y1,y2,w;
+	int32_t j,k,ha,hb;
+
+	GET_HIGH_WORD(ha, x);
+	ha &= 0x7fffffff;
+	GET_HIGH_WORD(hb, y);
+	hb &= 0x7fffffff;
+	if (hb > ha) {
+		a = y;
+		b = x;
+		j=ha; ha=hb; hb=j;
+	} else {
+		a = x;
+		b = y;
+	}
+	a = fabs(a);
+	b = fabs(b);
+	if (ha - hb > 0x3c00000)  /* x/y > 2**60 */
+		return a+b;
+	k = 0;
+	if (ha > 0x5f300000) {    /* a > 2**500 */
+		if(ha >= 0x7ff00000) {  /* Inf or NaN */
+			uint32_t low;
+			/* Use original arg order iff result is NaN; quieten sNaNs. */
+			w = fabs(x+0.0) - fabs(y+0.0);
+			GET_LOW_WORD(low, a);
+			if (((ha&0xfffff)|low) == 0) w = a;
+			GET_LOW_WORD(low, b);
+			if (((hb^0x7ff00000)|low) == 0) w = b;
+			return w;
+		}
+		/* scale a and b by 2**-600 */
+		ha -= 0x25800000; hb -= 0x25800000;  k += 600;
+		SET_HIGH_WORD(a, ha);
+		SET_HIGH_WORD(b, hb);
+	}
+	if (hb < 0x20b00000) {    /* b < 2**-500 */
+		if (hb <= 0x000fffff) {  /* subnormal b or 0 */
+			uint32_t low;
+			GET_LOW_WORD(low, b);
+			if ((hb|low) == 0)
+				return a;
+			t1 = 0;
+			SET_HIGH_WORD(t1, 0x7fd00000);  /* t1 = 2^1022 */
+			b *= t1;
+			a *= t1;
+			k -= 1022;
+		} else {            /* scale a and b by 2^600 */
+			ha += 0x25800000;  /* a *= 2^600 */
+			hb += 0x25800000;  /* b *= 2^600 */
+			k -= 600;
+			SET_HIGH_WORD(a, ha);
+			SET_HIGH_WORD(b, hb);
+		}
+	}
+	/* medium size a and b */
+	w = a - b;
+	if (w > b) {
+		t1 = 0;
+		SET_HIGH_WORD(t1, ha);
+		t2 = a-t1;
+		w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
+	} else {
+		a  = a + a;
+		y1 = 0;
+		SET_HIGH_WORD(y1, hb);
+		y2 = b - y1;
+		t1 = 0;
+		SET_HIGH_WORD(t1, ha+0x00100000);
+		t2 = a - t1;
+		w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
+	}
+	if (k != 0) {
+		uint32_t high;
+		t1 = 1.0;
+		GET_HIGH_WORD(high, t1);
+		SET_HIGH_WORD(t1, high+(k<<20));
+		return t1*w;
+	}
+	return w;
+}