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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

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

INDEX

	remquo

INDEX

	remquof

ANSI_SYNOPSIS

	#include 

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

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

DESCRIPTION

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

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

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

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

quotient of <>/<>.  (That is, <> 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 <> functions return <[x]> REM <[y]>.

BUGS

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

floating-point exception.  This implementation does not.

PORTABILITY

C99, POSIX.

*/

#include 

#include 

#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

		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<>(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<>(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

	    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

	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;

}