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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
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 "fdlibm.h"
#ifdef _NEED_FLOAT64
#include <limits.h>
#include <math.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 __float64 Zero[] = {_F_64(0.0), _F_64(-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.
*/
__float64
remquo64(__float64 x, __float64 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 = fabs64(y);
if (y < _F_64(0x1p-1021)) {
if (x+x>y || (x+x==y && (q & 1))) {
q++;
x-=y;
}
} else if (x>_F_64(0.5)*y || (x==_F_64(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;
}
_MATH_ALIAS_d_ddI(remquo)
#endif /* _NEED_FLOAT64 */
|
