musl/src/math/hypotl.c

/* origin: FreeBSD /usr/src/lib/msun/src/e_hypotl.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.
 * ====================================================
 */
/* long double version of hypot().  See comments in hypot.c. */

#include "libm.h"

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double hypotl(long double x, long double y)
{
	return hypot(x, y);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384

#define GET_LDBL_EXPSIGN(i, v) do {     \
	union IEEEl2bits uv;            \
					\
	uv.e = v;                       \
	i = uv.xbits.expsign;           \
} while (0)

#define GET_LDBL_MAN(h, l, v) do {      \
	union IEEEl2bits uv;            \
					\
	uv.e = v;                       \
	h = uv.bits.manh;               \
	l = uv.bits.manl;               \
} while (0)

#define SET_LDBL_EXPSIGN(v, i) do {     \
	union IEEEl2bits uv;            \
					\
	uv.e = v;                       \
	uv.xbits.expsign = i;           \
	v = uv.e;                       \
} while (0)

#undef GET_HIGH_WORD
#define GET_HIGH_WORD(i, v)     GET_LDBL_EXPSIGN(i, v)
#undef SET_HIGH_WORD
#define SET_HIGH_WORD(v, i)     SET_LDBL_EXPSIGN(v, i)

#define DESW(exp)       (exp)           /* delta expsign word */
#define ESW(exp)        (MAX_EXP - 1 + (exp))   /* expsign word */
#define MANT_DIG        LDBL_MANT_DIG
#define MAX_EXP         LDBL_MAX_EXP

#if LDBL_MANL_SIZE > 32
typedef uint64_t man_t;
#else
typedef uint32_t man_t;
#endif

long double hypotl(long double x, long double y)
{
	long double a=x,b=y,t1,t2,y1,y2,w;
	int32_t j,k,ha,hb;

	GET_HIGH_WORD(ha, x);
	ha &= 0x7fff;
	GET_HIGH_WORD(hb, y);
	hb &= 0x7fff;
	if (hb > ha) {
		a = y;
		b = x;
		j=ha; ha=hb; hb=j;
	} else {
		a = x;
		b = y;
	}
	a = fabsl(a);
	b = fabsl(b);
	if (ha - hb > DESW(MANT_DIG+7))  /* x/y > 2**(MANT_DIG+7) */
		return a+b;
	k = 0;
	if (ha > ESW(MAX_EXP/2-12)) {    /* a>2**(MAX_EXP/2-12) */
		if (ha >= ESW(MAX_EXP)) {  /* Inf or NaN */
			man_t manh, manl;
			/* Use original arg order iff result is NaN; quieten sNaNs. */
			w = fabsl(x+0.0)-fabsl(y+0.0);
			GET_LDBL_MAN(manh,manl,a);
			if (manh == LDBL_NBIT && manl == 0) w = a;
			GET_LDBL_MAN(manh,manl,b);
			if (hb >= ESW(MAX_EXP) && manh == LDBL_NBIT && manl == 0) w = b;
			return w;
		}
		/* scale a and b by 2**-(MAX_EXP/2+88) */
		ha -= DESW(MAX_EXP/2+88); hb -= DESW(MAX_EXP/2+88);
		k += MAX_EXP/2+88;
		SET_HIGH_WORD(a, ha);
		SET_HIGH_WORD(b, hb);
	}
	if (hb < ESW(-(MAX_EXP/2-12))) {  /* b < 2**-(MAX_EXP/2-12) */
		if (hb <= 0) {  /* subnormal b or 0 */
			man_t manh, manl;
			GET_LDBL_MAN(manh,manl,b);
			if ((manh|manl) == 0)
				return a;
			t1 = 0;
			SET_HIGH_WORD(t1, ESW(MAX_EXP-2));  /* t1 = 2^(MAX_EXP-2) */
			b *= t1;
			a *= t1;
			k -= MAX_EXP-2;
		} else {            /* scale a and b by 2^(MAX_EXP/2+88) */
			ha += DESW(MAX_EXP/2+88);
			hb += DESW(MAX_EXP/2+88);
			k -= MAX_EXP/2+88;
			SET_HIGH_WORD(a, ha);
			SET_HIGH_WORD(b, hb);
		}
	}
	/* medium size a and b */
	w = a - b;
	if (w > b) {
		t1 = a;
		union IEEEl2bits uv;
		uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
		t2 = a-t1;
		w  = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
	} else {
		a  = a+a;
		y1 = b;
		union IEEEl2bits uv;
		uv.e = y1; uv.bits.manl = 0; y1 = uv.e;
		y2 = b - y1;
		t1 = a;
		uv.e = t1; uv.bits.manl = 0; t1 = uv.e;
		t2 = a - t1;
		w  = sqrtl(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+DESW(k));
		return t1*w;
	}
	return w;
}
#endif