amath/lib/real/fmod.c

/* @(#)e_fmod.c 1.3 95/01/18 */

/*
 * Copyright (c) 2015 Carsten Larsen
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * The origin source code can be obtained from:
 * http://www.netlib.org/fdlibm/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.
 * ====================================================
 *
 */

#include "prim.h"

#ifdef _WIN32
#pragma warning( disable : 4146 )
#endif

static const double one = 1.0, Zero[] = {0.0, -0.0,};

/**
 * @brief   Return x mod y in exact arithmetic
 * @version 1.3
 * @date    95/01/18
 * @details Method: shift and subtract
 */
double fmod(double x, double y)
{
    sword n,hx,hy,hz,ix,iy,sx,i;
    uword 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)) return x;	/* |x|<|y| return x */
        if(lx==ly)
            return Zero[(uword)sx>>31];	/* |x|=|y| return x*0*/
    }

    /* 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[(uword)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[(unsigned)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)|((uword)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);
        x *= one;		/* create necessary signal */
    }
    return x;		/* exact output */
}