/* Adapted for Newlib, 2009. (Allow for int < 32 bits; return *quo=0 during
|
/* Adapted for Newlib, 2009. (Allow for int < 32 bits; return *quo=0 during
|
* errors to make test scripts easier.) */
|
* errors to make test scripts easier.) */
|
/* @(#)e_fmod.c 1.3 95/01/18 */
|
/* @(#)e_fmod.c 1.3 95/01/18 */
|
/*-
|
/*-
|
* ====================================================
|
* ====================================================
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
*
|
*
|
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
* Developed at SunSoft, 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.
|
* ====================================================
|
* ====================================================
|
*/
|
*/
|
/*
|
/*
|
FUNCTION
|
FUNCTION
|
<<remquo>>, <<remquof>>--remainder and part of quotient
|
<<remquo>>, <<remquof>>--remainder and part of quotient
|
INDEX
|
INDEX
|
remquo
|
remquo
|
INDEX
|
INDEX
|
remquof
|
remquof
|
|
|
ANSI_SYNOPSIS
|
ANSI_SYNOPSIS
|
#include <math.h>
|
#include <math.h>
|
double remquo(double <[x]>, double <[y]>, int *<[quo]>);
|
double remquo(double <[x]>, double <[y]>, int *<[quo]>);
|
float remquof(float <[x]>, float <[y]>, int *<[quo]>);
|
float remquof(float <[x]>, float <[y]>, int *<[quo]>);
|
|
|
DESCRIPTION
|
DESCRIPTION
|
The <<remquo>> functions compute the same remainder as the <<remainder>>
|
The <<remquo>> functions compute the same remainder as the <<remainder>>
|
functions; this value is in the range -<[y]>/2 ... +<[y]>/2. In the object
|
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>>
|
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
|
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 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
|
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.
|
bits or more, otherwise, n is 1 less than the width of int.
|
|
|
For example:
|
For example:
|
. remquo(-29.0, 3.0, &<[quo]>)
|
. remquo(-29.0, 3.0, &<[quo]>)
|
returns -1.0 and sets <[quo]>=10, and
|
returns -1.0 and sets <[quo]>=10, and
|
. remquo(-98307.0, 3.0, &<[quo]>)
|
. remquo(-98307.0, 3.0, &<[quo]>)
|
returns -0.0 and sets <[quo]>=-32769, although for 16-bit int, <[quo]>=-1. In
|
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
|
the latter case, the actual quotient of -(32769=0x8001) is reduced to -1
|
because of the 15-bit limitation for the quotient.
|
because of the 15-bit limitation for the quotient.
|
|
|
RETURNS
|
RETURNS
|
When either argument is NaN, NaN is returned. If <[y]> is 0 or <[x]> is
|
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"
|
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
|
floating point exception is raised or errno is set to EDOM), and NaN is
|
returned.
|
returned.
|
Otherwise, the <<remquo>> functions return <[x]> REM <[y]>.
|
Otherwise, the <<remquo>> functions return <[x]> REM <[y]>.
|
|
|
BUGS
|
BUGS
|
IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow"
|
IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow"
|
floating-point exception. This implementation does not.
|
floating-point exception. This implementation does not.
|
|
|
PORTABILITY
|
PORTABILITY
|
C99, POSIX.
|
C99, POSIX.
|
|
|
*/
|
*/
|
|
|
#include <limits.h>
|
#include <limits.h>
|
#include <math.h>
|
#include <math.h>
|
#include "fdlibm.h"
|
#include "fdlibm.h"
|
|
|
/* For quotient, return either all 31 bits that can from calculation (using
|
/* 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. */
|
* int32_t), or as many as can fit into an int that is smaller than 32 bits. */
|
#if INT_MAX > 0x7FFFFFFFL
|
#if INT_MAX > 0x7FFFFFFFL
|
#define QUO_MASK 0x7FFFFFFF
|
#define QUO_MASK 0x7FFFFFFF
|
# else
|
# else
|
#define QUO_MASK INT_MAX
|
#define QUO_MASK INT_MAX
|
#endif
|
#endif
|
|
|
static const double Zero[] = {0.0, -0.0,};
|
static const double Zero[] = {0.0, -0.0,};
|
|
|
/*
|
/*
|
* Return the IEEE remainder and set *quo to the last n bits of the
|
* 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--
|
* 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
|
* 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
|
* 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
|
* method. In practice, this is far more bits than are needed to use
|
* remquo in reduction algorithms.
|
* remquo in reduction algorithms.
|
*/
|
*/
|
double
|
double
|
remquo(double x, double y, int *quo)
|
remquo(double x, double y, int *quo)
|
{
|
{
|
__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,q,sxy;
|
__uint32_t lx,ly,lz,q,sxy;
|
|
|
EXTRACT_WORDS(hx,lx,x);
|
EXTRACT_WORDS(hx,lx,x);
|
EXTRACT_WORDS(hy,ly,y);
|
EXTRACT_WORDS(hy,ly,y);
|
sxy = (hx ^ hy) & 0x80000000;
|
sxy = (hx ^ hy) & 0x80000000;
|
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 */
|
*quo = 0; /* Not necessary, but return consistent value */
|
*quo = 0; /* Not necessary, but return consistent value */
|
return (x*y)/(x*y);
|
return (x*y)/(x*y);
|
}
|
}
|
if(hx<=hy) {
|
if(hx<=hy) {
|
if((hx<hy)||(lx<ly)) {
|
if((hx<hy)||(lx<ly)) {
|
q = 0;
|
q = 0;
|
goto fixup; /* |x|<|y| return x or x-y */
|
goto fixup; /* |x|<|y| return x or x-y */
|
}
|
}
|
if(lx==ly) {
|
if(lx==ly) {
|
*quo = (sxy ? -1 : 1);
|
*quo = (sxy ? -1 : 1);
|
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;
|
q = 0;
|
q = 0;
|
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 {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
|
else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
|
q <<= 1;
|
q <<= 1;
|
}
|
}
|
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;q++;}
|
if(hz>=0) {hx=hz;lx=lz;q++;}
|
|
|
/* 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 */
|
q &= QUO_MASK;
|
q &= QUO_MASK;
|
*quo = (sxy ? -q : q);
|
*quo = (sxy ? -q : q);
|
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));
|
} 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;
|
}
|
}
|
}
|
}
|
fixup:
|
fixup:
|
INSERT_WORDS(x,hx,lx);
|
INSERT_WORDS(x,hx,lx);
|
y = fabs(y);
|
y = fabs(y);
|
if (y < 0x1p-1021) {
|
if (y < 0x1p-1021) {
|
if (x+x>y || (x+x==y && (q & 1))) {
|
if (x+x>y || (x+x==y && (q & 1))) {
|
q++;
|
q++;
|
x-=y;
|
x-=y;
|
}
|
}
|
} else if (x>0.5*y || (x==0.5*y && (q & 1))) {
|
} else if (x>0.5*y || (x==0.5*y && (q & 1))) {
|
q++;
|
q++;
|
x-=y;
|
x-=y;
|
}
|
}
|
GET_HIGH_WORD(hx,x);
|
GET_HIGH_WORD(hx,x);
|
SET_HIGH_WORD(x,hx^sx);
|
SET_HIGH_WORD(x,hx^sx);
|
q &= QUO_MASK;
|
q &= QUO_MASK;
|
*quo = (sxy ? -q : q);
|
*quo = (sxy ? -q : q);
|
return x;
|
return x;
|
}
|
}
|
|
|
