0,0 → 1,208 |
/* 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 |
|
ANSI_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 <limits.h> |
#include <math.h> |
#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<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 = 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; |
} |