remquo.c

/* origin: FreeBSD /usr/src/lib/msun/src/s_remquo.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.
 * ====================================================
 */
/*
 * Return the IEEE remainder and set *quo to the last n bits of the
 * quotient, rounded to the nearest integer.  We choose n=31 because
 * we wind up computing all the integer bits of the quotient anyway as
 * a side-effect of computing the remainder by the shift and subtract
 * method.  In practice, this is far more bits than are needed to use
 * remquo in reduction algorithms.
 */

#include "libm.h"

static const double Zero[] = {0.0, -0.0,};

double remquo(double x, double y, int *quo)
{
	int32_t n,hx,hy,hz,ix,iy,sx,i;
	uint32_t lx,ly,lz,q,sxy;

	EXTRACT_WORDS(hx, lx, x);
	EXTRACT_WORDS(hy, ly, y);
	sxy = (hx ^ hy) & 0x80000000;
	sx = hx & 0x80000000;   /* sign of x */
	hx ^= sx;               /* |x| */
	hy &= 0x7fffffff;       /* |y| */

	/* purge off exception values */
	if ((hy|ly) == 0 || hx >= 0x7ff00000 ||  /* y = 0, or x not finite */
	    (hy|((ly|-ly)>>31)) > 0x7ff00000)    /* or y is NaN */
		return (x*y)/(x*y);
	if (hx <= hy) {
		if (hx < hy || lx < ly) {  /* |x| < |y| return x or x-y */
			q = 0;
			goto fixup;
		}
		if (lx == ly) {            /* |x| = |y| return x*0 */
			*quo = 1;
			return Zero[(uint32_t)sx>>31];
		}
	}

	// FIXME: use ilogb?

	/* determine ix = ilogb(x) */
	if (hx < 0x00100000) {  /* subnormal x */
		if (hx == 0) {
			for (ix = -1043, i=lx; i>0; i<<=1) ix--;
		} else {
			for (ix = -1022, i=hx<<11; i>0; i<<=1) ix--;
		}
	} else
		ix = (hx>>20) - 1023;

	/* determine iy = ilogb(y) */
	if (hy < 0x00100000) {  /* subnormal y */
		if (hy == 0) {
			for (iy = -1043, i=ly; i>0; i<<=1) iy--;
		} else {
			for (iy = -1022, i=hy<<11; i>0; i<<=1) iy--;
		}
	} else
		iy = (hy>>20) - 1023;

	/* set up {hx,lx}, {hy,ly} and align y to x */
	if (ix >= -1022)
		hx = 0x00100000|(0x000fffff&hx);
	else {  /* subnormal x, shift x to normal */
		n = -1022 - ix;
		if (n <= 31) {
			hx = (hx<<n)|(lx>>(32-n));
			lx <<= n;
		} else {
			hx = lx<<(n-32);
			lx = 0;
		}
	}
	if (iy >= -1022)
		hy = 0x00100000|(0x000fffff&hy);
	else {  /* subnormal y, shift y to normal */
		n = -1022 - iy;
		if (n <= 31) {
			hy = (hy<<n)|(ly>>(32-n));
			ly <<= n;
		} else {
			hy = ly<<(n-32);
			ly = 0;
		}
	}

	/* fix point fmod */
	n = ix - iy;
	q = 0;
	while (n--) {
		hz = hx - hy;
		lz = lx - ly;
		if (lx < ly)
			hz--;
		if (hz < 0) {
			hx = hx + hx + (lx>>31);
			lx = lx + lx;
		} else {
			hx = hz + hz + (lz>>31);
			lx = lz + lz;
			q++;
		}
		q <<= 1;
	}
	hz = hx - hy;
	lz = lx - ly;
	if (lx < ly)
		hz--;
	if (hz >= 0) {
		hx = hz;
		lx = lz;
		q++;
	}

	/* convert back to floating value and restore the sign */
	if ((hx|lx) == 0) {  /* return sign(x)*0 */
		*quo = sxy ? -q : q;
		return Zero[(uint32_t)sx>>31];
	}
	while (hx < 0x00100000) {  /* normalize x */
		hx = hx + hx + (lx>>31);
		lx = lx + lx;
		iy--;
	}
	if (iy >= -1022) {         /* normalize output */
		hx = (hx-0x00100000)|((iy+1023)<<20);
	} else {                   /* subnormal output */
		n = -1022 - iy;
		if (n <= 20) {
			lx = (lx>>n)|((uint32_t)hx<<(32-n));
			hx >>= n;
		} else if (n <= 31) {
			lx = (hx<<(32-n))|(lx>>n);
			hx = sx;
		} else {
			lx = hx>>(n-32);
			hx = sx;
		}
	}
fixup:
	INSERT_WORDS(x, hx, lx);
	y = fabs(y);
	if (y < 0x1p-1021) {
		if (x + x > y || (x + x == y && (q & 1))) {
			q++;
			x -= y;
		}
	} else if (x > 0.5*y || (x == 0.5*y && (q & 1))) {
		q++;
		x -= y;
	}
	GET_HIGH_WORD(hx, x);
	SET_HIGH_WORD(x, hx ^ sx);
	q &= 0x7fffffff;
	*quo = sxy ? -q : q;
	return x;
}