|
|
/* @(#)e_fmod.c 5.1 93/09/24 */
|
/* @(#)e_fmod.c 5.1 93/09/24 */
|
/*
|
/*
|
* ====================================================
|
* ====================================================
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
*
|
*
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
* Permission to use, copy, modify, and distribute this
|
* Permission to use, copy, modify, and distribute this
|
* software is freely granted, provided that this notice
|
* software is freely granted, provided that this notice
|
* is preserved.
|
* is preserved.
|
* ====================================================
|
* ====================================================
|
*/
|
*/
|
|
|
/*
|
/*
|
* __ieee754_fmod(x,y)
|
* __ieee754_fmod(x,y)
|
* Return x mod y in exact arithmetic
|
* Return x mod y in exact arithmetic
|
* Method: shift and subtract
|
* Method: shift and subtract
|
*/
|
*/
|
|
|
#include "fdlibm.h"
|
#include "fdlibm.h"
|
|
|
#ifndef _DOUBLE_IS_32BITS
|
#ifndef _DOUBLE_IS_32BITS
|
|
|
#ifdef __STDC__
|
#ifdef __STDC__
|
static const double one = 1.0, Zero[] = {0.0, -0.0,};
|
static const double one = 1.0, Zero[] = {0.0, -0.0,};
|
#else
|
#else
|
static double one = 1.0, Zero[] = {0.0, -0.0,};
|
static double one = 1.0, Zero[] = {0.0, -0.0,};
|
#endif
|
#endif
|
|
|
#ifdef __STDC__
|
#ifdef __STDC__
|
double __ieee754_fmod(double x, double y)
|
double __ieee754_fmod(double x, double y)
|
#else
|
#else
|
double __ieee754_fmod(x,y)
|
double __ieee754_fmod(x,y)
|
double x,y ;
|
double x,y ;
|
#endif
|
#endif
|
{
|
{
|
__int32_t n,hx,hy,hz,ix,iy,sx,i;
|
__int32_t n,hx,hy,hz,ix,iy,sx,i;
|
__uint32_t lx,ly,lz;
|
__uint32_t lx,ly,lz;
|
|
|
EXTRACT_WORDS(hx,lx,x);
|
EXTRACT_WORDS(hx,lx,x);
|
EXTRACT_WORDS(hy,ly,y);
|
EXTRACT_WORDS(hy,ly,y);
|
sx = hx&0x80000000; /* sign of x */
|
sx = hx&0x80000000; /* sign of x */
|
hx ^=sx; /* |x| */
|
hx ^=sx; /* |x| */
|
hy &= 0x7fffffff; /* |y| */
|
hy &= 0x7fffffff; /* |y| */
|
|
|
/* purge off exception values */
|
/* purge off exception values */
|
if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
|
if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
|
((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
|
((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
|
return (x*y)/(x*y);
|
return (x*y)/(x*y);
|
if(hx<=hy) {
|
if(hx<=hy) {
|
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
|
if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
|
if(lx==ly)
|
if(lx==ly)
|
return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0*/
|
return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0*/
|
}
|
}
|
|
|
/* determine ix = ilogb(x) */
|
/* determine ix = ilogb(x) */
|
if(hx<0x00100000) { /* subnormal x */
|
if(hx<0x00100000) { /* subnormal x */
|
if(hx==0) {
|
if(hx==0) {
|
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
|
for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
|
} else {
|
} else {
|
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
|
for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
|
}
|
}
|
} else ix = (hx>>20)-1023;
|
} else ix = (hx>>20)-1023;
|
|
|
/* determine iy = ilogb(y) */
|
/* determine iy = ilogb(y) */
|
if(hy<0x00100000) { /* subnormal y */
|
if(hy<0x00100000) { /* subnormal y */
|
if(hy==0) {
|
if(hy==0) {
|
for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
|
for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
|
} else {
|
} else {
|
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
|
for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
|
}
|
}
|
} else iy = (hy>>20)-1023;
|
} else iy = (hy>>20)-1023;
|
|
|
/* set up {hx,lx}, {hy,ly} and align y to x */
|
/* set up {hx,lx}, {hy,ly} and align y to x */
|
if(ix >= -1022)
|
if(ix >= -1022)
|
hx = 0x00100000|(0x000fffff&hx);
|
hx = 0x00100000|(0x000fffff&hx);
|
else { /* subnormal x, shift x to normal */
|
else { /* subnormal x, shift x to normal */
|
n = -1022-ix;
|
n = -1022-ix;
|
if(n<=31) {
|
if(n<=31) {
|
hx = (hx<<n)|(lx>>(32-n));
|
hx = (hx<<n)|(lx>>(32-n));
|
lx <<= n;
|
lx <<= n;
|
} else {
|
} else {
|
hx = lx<<(n-32);
|
hx = lx<<(n-32);
|
lx = 0;
|
lx = 0;
|
}
|
}
|
}
|
}
|
if(iy >= -1022)
|
if(iy >= -1022)
|
hy = 0x00100000|(0x000fffff&hy);
|
hy = 0x00100000|(0x000fffff&hy);
|
else { /* subnormal y, shift y to normal */
|
else { /* subnormal y, shift y to normal */
|
n = -1022-iy;
|
n = -1022-iy;
|
if(n<=31) {
|
if(n<=31) {
|
hy = (hy<<n)|(ly>>(32-n));
|
hy = (hy<<n)|(ly>>(32-n));
|
ly <<= n;
|
ly <<= n;
|
} else {
|
} else {
|
hy = ly<<(n-32);
|
hy = ly<<(n-32);
|
ly = 0;
|
ly = 0;
|
}
|
}
|
}
|
}
|
|
|
/* fix point fmod */
|
/* fix point fmod */
|
n = ix - iy;
|
n = ix - iy;
|
while(n--) {
|
while(n--) {
|
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
|
if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
|
else {
|
else {
|
if((hz|lz)==0) /* return sign(x)*0 */
|
if((hz|lz)==0) /* return sign(x)*0 */
|
return Zero[(__uint32_t)sx>>31];
|
return Zero[(__uint32_t)sx>>31];
|
hx = hz+hz+(lz>>31); lx = lz+lz;
|
hx = hz+hz+(lz>>31); lx = lz+lz;
|
}
|
}
|
}
|
}
|
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
|
if(hz>=0) {hx=hz;lx=lz;}
|
if(hz>=0) {hx=hz;lx=lz;}
|
|
|
/* convert back to floating value and restore the sign */
|
/* convert back to floating value and restore the sign */
|
if((hx|lx)==0) /* return sign(x)*0 */
|
if((hx|lx)==0) /* return sign(x)*0 */
|
return Zero[(__uint32_t)sx>>31];
|
return Zero[(__uint32_t)sx>>31];
|
while(hx<0x00100000) { /* normalize x */
|
while(hx<0x00100000) { /* normalize x */
|
hx = hx+hx+(lx>>31); lx = lx+lx;
|
hx = hx+hx+(lx>>31); lx = lx+lx;
|
iy -= 1;
|
iy -= 1;
|
}
|
}
|
if(iy>= -1022) { /* normalize output */
|
if(iy>= -1022) { /* normalize output */
|
hx = ((hx-0x00100000)|((iy+1023)<<20));
|
hx = ((hx-0x00100000)|((iy+1023)<<20));
|
INSERT_WORDS(x,hx|sx,lx);
|
INSERT_WORDS(x,hx|sx,lx);
|
} else { /* subnormal output */
|
} else { /* subnormal output */
|
n = -1022 - iy;
|
n = -1022 - iy;
|
if(n<=20) {
|
if(n<=20) {
|
lx = (lx>>n)|((__uint32_t)hx<<(32-n));
|
lx = (lx>>n)|((__uint32_t)hx<<(32-n));
|
hx >>= n;
|
hx >>= n;
|
} else if (n<=31) {
|
} else if (n<=31) {
|
lx = (hx<<(32-n))|(lx>>n); hx = sx;
|
lx = (hx<<(32-n))|(lx>>n); hx = sx;
|
} else {
|
} else {
|
lx = hx>>(n-32); hx = sx;
|
lx = hx>>(n-32); hx = sx;
|
}
|
}
|
INSERT_WORDS(x,hx|sx,lx);
|
INSERT_WORDS(x,hx|sx,lx);
|
x *= one; /* create necessary signal */
|
x *= one; /* create necessary signal */
|
}
|
}
|
return x; /* exact output */
|
return x; /* exact output */
|
}
|
}
|
|
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
|
|
