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/* Adapted for Newlib, 2009.  (Allow for int < 32 bits; return *quo=0 during

 * errors to make test scripts easier.)  */

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

/*-

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

 * 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.

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

 */

/*

FUNCTION

<<remquo>>, <<remquof>>--remainder and part of quotient

INDEX

        remquo

INDEX

        remquof

ANSI_SYNOPSIS

        #include <math.h>

        double remquo(double <[x]>, double <[y]>, int *<[quo]>);

        float remquof(float <[x]>, float <[y]>, int *<[quo]>);

DESCRIPTION

The <<remquo>> functions compute the same remainder as the <<remainder>>

functions; this value is in the range -<[y]>/2 ... +<[y]>/2.  In the object

pointed to by <<quo>> they store a value whose sign is the sign of <<x>>/<<y>>

and whose magnitude is congruent modulo 2**n to the magnitude of the integral

quotient of <<x>>/<<y>>.  (That is, <<quo>> is given the n lsbs of the

quotient, not counting the sign.)  This implementation uses n=31 if int is 32

bits or more, otherwise, n is 1 less than the width of int.

For example:

.       remquo(-29.0, 3.0, &<[quo]>)

returns -1.0 and sets <[quo]>=10, and

.       remquo(-98307.0, 3.0, &<[quo]>)

returns -0.0 and sets <[quo]>=-32769, although for 16-bit int, <[quo]>=-1.  In

the latter case, the actual quotient of -(32769=0x8001) is reduced to -1

because of the 15-bit limitation for the quotient.

RETURNS

When either argument is NaN, NaN is returned.  If <[y]> is 0 or <[x]> is

infinite (and neither is NaN), a domain error occurs (i.e. the "invalid"

floating point exception is raised or errno is set to EDOM), and NaN is

returned.

Otherwise, the <<remquo>> functions return <[x]> REM <[y]>.

BUGS

IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow"

floating-point exception.  This implementation does not.

PORTABILITY

C99, POSIX.

*/

#include <limits.h>

#include <math.h>

#include "fdlibm.h"

/* For quotient, return either all 31 bits that can from calculation (using

 * int32_t), or as many as can fit into an int that is smaller than 32 bits.  */

#if INT_MAX > 0x7FFFFFFFL

  #define QUO_MASK 0x7FFFFFFF

# else

  #define QUO_MASK INT_MAX

#endif

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

/*

 * Return the IEEE remainder and set *quo to the last n bits of the

 * quotient, rounded to the nearest integer.  We choose n=31--if that many fit--

 * 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.

 */

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 */

            *quo = 0;    /* Not necessary, but return consistent value */

            return (x*y)/(x*y);

        }

        if(hx<=hy) {

            if((hx<hy)||(lx<ly)) {

                q = 0;

                goto fixup;     /* |x|<|y| return x or x-y */

            }

            if(lx==ly) {

                *quo = (sxy ? -1 : 1);

                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;

        q = 0;

        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 {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}

            q <<= 1;

        }

        hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;

        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 */

            q &= QUO_MASK;

            *quo = (sxy ? -q : q);

            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));

        } 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 &= QUO_MASK;

        *quo = (sxy ? -q : q);

        return x;

}