Initial import

libc/math/hypot.c

@@ -0,0 +1,65 @@
+#include "libc/math/math.h"
+
+#if FLT_EVAL_METHOD > 1U && LDBL_MANT_DIG == 64
+#define SPLIT (0x1p32 + 1)
+#else
+#define SPLIT (0x1p27 + 1)
+#endif
+
+static void sq(double_t *hi, double_t *lo, double x)
+{
+	double_t xh, xl, xc;
+
+	xc = (double_t)x*SPLIT;
+	xh = x - xc + xc;
+	xl = x - xh;
+	*hi = (double_t)x*x;
+	*lo = xh*xh - *hi + 2*xh*xl + xl*xl;
+}
+
+double hypot(double x, double y)
+{
+	union {double f; uint64_t i;} ux = {x}, uy = {y}, ut;
+	int ex, ey;
+	double_t hx, lx, hy, ly, z;
+
+	/* arrange |x| >= |y| */
+	ux.i &= -1ULL>>1;
+	uy.i &= -1ULL>>1;
+	if (ux.i < uy.i) {
+		ut = ux;
+		ux = uy;
+		uy = ut;
+	}
+
+	/* special cases */
+	ex = ux.i>>52;
+	ey = uy.i>>52;
+	x = ux.f;
+	y = uy.f;
+	/* note: hypot(inf,nan) == inf */
+	if (ey == 0x7ff)
+		return y;
+	if (ex == 0x7ff || uy.i == 0)
+		return x;
+	/* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */
+	/* 64 difference is enough for ld80 double_t */
+	if (ex - ey > 64)
+		return x + y;
+
+	/* precise sqrt argument in nearest rounding mode without overflow */
+	/* xh*xh must not overflow and xl*xl must not underflow in sq */
+	z = 1;
+	if (ex > 0x3ff+510) {
+		z = 0x1p700;
+		x *= 0x1p-700;
+		y *= 0x1p-700;
+	} else if (ey < 0x3ff-450) {
+		z = 0x1p-700;
+		x *= 0x1p700;
+		y *= 0x1p700;
+	}
+	sq(&hx, &lx, x);
+	sq(&hy, &ly, y);
+	return z*sqrt(ly+lx+hy+hx);
+}