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/* @(#)z_fmod.c 1.0 98/08/13 */

/*

 * ====================================================

 * 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.

 * ====================================================

 */

/*

FUNCTION

<<fmod>>, <<fmodf>>---floating-point remainder (modulo)

INDEX

fmod

INDEX

fmodf

ANSI_SYNOPSIS

#include <math.h>

double fmod(double <[x]>, double <[y]>)

float fmodf(float <[x]>, float <[y]>)

TRAD_SYNOPSIS

#include <math.h>

double fmod(<[x]>, <[y]>)

double (<[x]>, <[y]>);

float fmodf(<[x]>, <[y]>)

float (<[x]>, <[y]>);

DESCRIPTION

The <<fmod>> and <<fmodf>> functions compute the floating-point

remainder of <[x]>/<[y]> (<[x]> modulo <[y]>).

RETURNS

The <<fmod>> function returns the value

@ifnottex

<[x]>-<[i]>*<[y]>,

@end ifnottex

@tex

$x-i\times y$,

@end tex

for the largest integer <[i]> such that, if <[y]> is nonzero, the

result has the same sign as <[x]> and magnitude less than the

magnitude of <[y]>.

<<fmod(<[x]>,0)>> returns NaN, and sets <<errno>> to <<EDOM>>.

You can modify error treatment for these functions using <<matherr>>.

PORTABILITY

<<fmod>> is ANSI C. <<fmodf>> is an extension.

*/

/*

 * fmod(x,y)

 * Return x mod y in exact arithmetic

 * Method: shift and subtract

 */

#include "fdlibm.h"

#include "zmath.h"

#ifndef _DOUBLE_IS_32BITS

#ifdef __STDC__

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

#else

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

#endif

#ifdef __STDC__

        double fmod(double x, double y)

#else

        double fmod(x,y)

        double x,y ;

#endif

{

        __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)) return x;      /* |x|<|y| return x */

            if(lx==ly)

                return Zero[(__uint32_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[(__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);

            x *= one;           /* create necessary signal */

        }

        return x;               /* exact output */

}

#endif /* defined(_DOUBLE_IS_32BITS) */