e_fmod.c

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/* @(#)e_fmod.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, 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 "math.h"
#include "math_private.h"

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

double
fmod(double x, double y)
{
    int32_t n,hx,hy,hz,ix,iy,sx,i;
    u_int32_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)) return x;  /* |x|<|y| return x */
        if(lx==ly) 
        return Zero[(u_int32_t)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[(u_int32_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[(u_int32_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)|((u_int32_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);
        x *= one;       /* create necessary signal */
    }
    return x;       /* exact output */
}