musl/src/math/hypot.c

/* 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)
		w = scalbn(w, k);
	return w;
}