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/* @(#)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.
* ====================================================
*/
#include <sys/types.h>
#include <machine/ieee.h>
#include <float.h>
#include <openlibm_math.h>
#include <stdint.h>
#include "math_private.h"
#define BIAS (LDBL_MAX_EXP - 1)
/*
* These macros add and remove an explicit integer bit in front of the
* fractional mantissa, if the architecture doesn't have such a bit by
* default already.
*/
#ifdef LDBL_IMPLICIT_NBIT
#define LDBL_NBIT 0
#define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
#define HFRAC_BITS (EXT_FRACHBITS + EXT_FRACHMBITS)
#else
#define LDBL_NBIT 0x80000000
#define SET_NBIT(hx) (hx)
#define HFRAC_BITS (EXT_FRACHBITS + EXT_FRACHMBITS - 1)
#endif
#define MANL_SHIFT (EXT_FRACLMBITS + EXT_FRACLBITS - 1)
static const long double Zero[] = {0.0L, -0.0L};
/*
* Return the IEEE remainder and set *quo to the last n bits of the
* quotient, rounded to the nearest integer. We choose n=31 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.
*
* Assumptions:
* - The low part of the mantissa fits in a manl_t exactly.
* - The high part of the mantissa fits in an int64_t with enough room
* for an explicit integer bit in front of the fractional bits.
*/
long double
remquol(long double x, long double y, int *quo)
{
int64_t hx,hz,hy,_hx;
uint64_t lx,ly,lz;
uint64_t sx,sxy;
int ix,iy,n,q;
GET_LDOUBLE_WORDS64(hx,lx,x);
GET_LDOUBLE_WORDS64(hy,ly,y);
sx = (hx>>48)&0x8000;
sxy = sx ^ ((hy>>48)&0x8000);
hx &= 0x7fffffffffffffffLL; /* |x| */
hy &= 0x7fffffffffffffffLL; /* |y| */
SET_LDOUBLE_WORDS64(x,hx,lx);
SET_LDOUBLE_WORDS64(y,hy,ly);
/* purge off exception values */
if((hy|ly)==0 || /* y=0 */
((hx>>48) == BIAS + LDBL_MAX_EXP) || /* or x not finite */
((hy>>48) == BIAS + LDBL_MAX_EXP &&
(((hy&0x0000ffffffffffffLL)&~LDBL_NBIT)|ly)!=0)) /* or y is NaN */
return (x*y)/(x*y);
if((hx>>48)<=(hy>>48)) {
if(((hx>>48)<(hy>>48)) ||
((hx&0x0000ffffffffffffLL)<=(hy&0x0000ffffffffffffLL) &&
((hx&0x0000ffffffffffffLL)<(hy&0x0000ffffffffffffLL) ||
lx<ly))) {
q = 0;
goto fixup; /* |x|<|y| return x or x-y */
}
if((hx&0x0000ffffffffffffLL)==(hy&0x0000ffffffffffffLL) &&
lx==ly) {
*quo = 1;
return Zero[sx!=0]; /* |x|=|y| return x*0*/
}
}
/* determine ix = ilogb(x) */
if((hx>>48) == 0) { /* subnormal x */
x *= 0x1.0p512;
GET_LDOUBLE_WORDS64(hx,lx,x);
ix = (hx>>48) - (BIAS + 512);
} else {
ix = (hx>>48) - BIAS;
}
/* determine iy = ilogb(y) */
if((hy>>48) == 0) { /* subnormal y */
y *= 0x1.0p512;
GET_LDOUBLE_WORDS64(hy,ly,y);
iy = (hy>>48) - (BIAS + 512);
} else {
iy = (hy>>48) - BIAS;
}
/* set up {hx,lx}, {hy,ly} and align y to x */
_hx = SET_NBIT(hx) & 0x0000ffffffffffffLL;
hy = SET_NBIT(hy);
/* 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>>MANL_SHIFT); lx = lx+lx;}
else {_hx = hz+hz+(lz>>MANL_SHIFT); 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 */
*quo = (sxy ? -q : q);
return Zero[sx!=0];
}
while(_hx<(1ULL<<HFRAC_BITS)) { /* normalize x */
_hx = _hx+_hx+(lx>>MANL_SHIFT); lx = lx+lx;
iy -= 1;
}
hx = (hx&0xffff000000000000LL) | (_hx&0x0000ffffffffffffLL);
if (iy < LDBL_MIN_EXP) {
hx = (hx&0x0000ffffffffffffLL) | (uint64_t)(iy + BIAS + 512)<<48;
SET_LDOUBLE_WORDS64(x,hx,lx);
x *= 0x1p-512;
GET_LDOUBLE_WORDS64(hx,lx,x);
} else {
hx = (hx&0x0000ffffffffffffLL) | (uint64_t)(iy + BIAS)<<48;
}
hx &= 0x7fffffffffffffffLL;
SET_LDOUBLE_WORDS64(x,hx,lx);
fixup:
y = fabsl(y);
if (y < LDBL_MIN * 2) {
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_LDOUBLE_MSW64(hx,x);
hx ^= sx;
SET_LDOUBLE_MSW64(x,hx);
q &= 0x7fffffff;
*quo = (sxy ? -q : q);
return x;
}
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