musl/src/math/fmod.c

/* origin: FreeBSD /usr/src/lib/msun/src/e_fmod.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.
 * ====================================================
 */
/*
 * fmod(x,y)
 * Return x mod y in exact arithmetic
 * Method: shift and subtract
 */

#include "libm.h"

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

double fmod(double x, double y)
{
	int32_t n,hx,hy,hz,ix,iy,sx,i;
	uint32_t lx,ly,lz;

	EXTRACT_WORDS(hx, lx, x);
	EXTRACT_WORDS(hy, ly, y);
	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;
		if (lx == ly)            /* |x| = |y|, return x*0 */
			return Zero[(uint32_t)sx>>31];
	}

	/* determine ix = ilogb(x) */
	if (hx < 0x00100000) {  /* subnormal x */
		if (hx == 0) {
			for (ix = -1043, i = lx; i > 0; i <<= 1)
				ix -= 1;
		} else {
			for (ix = -1022, i = hx<<11; i > 0; i <<= 1)
				ix -= 1;
		}
	} 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 -= 1;
		} else {
			for (iy = -1022, i = hy<<11; i > 0; i <<= 1)
				iy -= 1;
		}
	} 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;
	while (n--) {
		hz = hx-hy;
		lz = lx-ly;
		if (lx < ly)
			hz -= 1;
		if (hz < 0) {
			hx = hx+hx+(lx>>31);
			lx = lx+lx;
		} else {
			if ((hz|lz) == 0)   /* return sign(x)*0 */
				return Zero[(uint32_t)sx>>31];
			hx = hz+hz+(lz>>31);
			lx = lz+lz;
		}
	}
	hz = hx-hy;
	lz = lx-ly;
	if (lx < ly)
		hz -= 1;
	if (hz >= 0) {
		hx = hz;
		lx = lz;
	}

	/* convert back to floating value and restore the sign */
	if ((hx|lx) == 0)          /* return sign(x)*0 */
		return Zero[(uint32_t)sx>>31];
	while (hx < 0x00100000) {  /* normalize x */
		hx = hx+hx+(lx>>31);
		lx = lx+lx;
		iy -= 1;
	}
	if (iy >= -1022) {         /* normalize output */
		hx = ((hx-0x00100000)|((iy+1023)<<20));
		INSERT_WORDS(x, hx|sx, lx);
	} 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;
		}
		INSERT_WORDS(x, hx|sx, lx);
	}
	return x;  /* exact output */
}