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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 <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
#else
#define LDBL_NBIT 0x80000000
#define SET_NBIT(hx) (hx)
#define HFRAC_BITS (EXT_FRACHBITS - 1)
#endif
#define MANL_SHIFT (EXT_FRACLBITS - 1)
static const long double one = 1.0, Zero[] = {0.0, -0.0,};
/*
* fmodl(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*
* 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
fmodl(long double x, long double y)
{
union {
long double e;
struct ieee_ext bits;
} ux, uy;
int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
uint32_t hy;
uint32_t lx,ly,lz;
int ix,iy,n,sx;
ux.e = x;
uy.e = y;
sx = ux.bits.ext_sign;
/* purge off exception values */
if((uy.bits.ext_exp|uy.bits.ext_frach|uy.bits.ext_fracl)==0 || /* y=0 */
(ux.bits.ext_exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
(uy.bits.ext_exp == BIAS + LDBL_MAX_EXP &&
((uy.bits.ext_frach&~LDBL_NBIT)|uy.bits.ext_fracl)!=0)) /* or y is NaN */
return (x*y)/(x*y);
if(ux.bits.ext_exp<=uy.bits.ext_exp) {
if((ux.bits.ext_exp<uy.bits.ext_exp) ||
(ux.bits.ext_frach<=uy.bits.ext_frach &&
(ux.bits.ext_frach<uy.bits.ext_frach ||
ux.bits.ext_fracl<uy.bits.ext_fracl))) {
return x; /* |x|<|y| return x or x-y */
}
if(ux.bits.ext_frach==uy.bits.ext_frach &&
ux.bits.ext_fracl==uy.bits.ext_fracl) {
return Zero[sx]; /* |x|=|y| return x*0*/
}
}
/* determine ix = ilogb(x) */
if(ux.bits.ext_exp == 0) { /* subnormal x */
ux.e *= 0x1.0p512;
ix = ux.bits.ext_exp - (BIAS + 512);
} else {
ix = ux.bits.ext_exp - BIAS;
}
/* determine iy = ilogb(y) */
if(uy.bits.ext_exp == 0) { /* subnormal y */
uy.e *= 0x1.0p512;
iy = uy.bits.ext_exp - (BIAS + 512);
} else {
iy = uy.bits.ext_exp - BIAS;
}
/* set up {hx,lx}, {hy,ly} and align y to x */
hx = SET_NBIT(ux.bits.ext_frach);
hy = SET_NBIT(uy.bits.ext_frach);
lx = ux.bits.ext_fracl;
ly = uy.bits.ext_fracl;
/* fix point fmod */
n = ix - iy;
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 {
if ((hz|lz)==0) /* return sign(x)*0 */
return Zero[sx];
hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
}
}
hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
if(hz>=0) {hx=hz;lx=lz;}
/* convert back to floating value and restore the sign */
if((hx|lx)==0) /* return sign(x)*0 */
return Zero[sx];
while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */
hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
iy -= 1;
}
ux.bits.ext_frach = hx; /* The mantissa is truncated here if needed. */
ux.bits.ext_fracl = lx;
if (iy < LDBL_MIN_EXP) {
ux.bits.ext_exp = iy + (BIAS + 512);
ux.e *= 0x1p-512;
} else {
ux.bits.ext_exp = iy + BIAS;
}
x = ux.e * one; /* create necessary signal */
return x; /* exact output */
}
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