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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/cdefs.h>
__FBSDID("$FreeBSD$");
#include <float.h>
#include <stdint.h>
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
#define BIAS (LDBL_MAX_EXP - 1)
#if LDBL_MANL_SIZE > 32
typedef uint64_t manl_t;
#else
typedef uint32_t manl_t;
#endif
#if LDBL_MANH_SIZE > 32
typedef uint64_t manh_t;
#else
typedef uint32_t manh_t;
#endif
/*
* 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 SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
#define HFRAC_BITS LDBL_MANH_SIZE
#else
#define SET_NBIT(hx) (hx)
#define HFRAC_BITS (LDBL_MANH_SIZE - 1)
#endif
#define MANL_SHIFT (LDBL_MANL_SIZE - 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)
{
union IEEEl2bits ux, uy;
int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
manh_t hy;
manl_t lx,ly,lz;
int ix,iy,n,q,sx,sxy;
ux.e = x;
uy.e = y;
sx = ux.bits.sign;
sxy = sx ^ uy.bits.sign;
ux.bits.sign = 0; /* |x| */
uy.bits.sign = 0; /* |y| */
x = ux.e;
/* purge off exception values */
if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
(ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
(uy.bits.exp == BIAS + LDBL_MAX_EXP &&
((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
return (x*y)/(x*y);
if(ux.bits.exp<=uy.bits.exp) {
if((ux.bits.exp<uy.bits.exp) ||
(ux.bits.manh<=uy.bits.manh &&
(ux.bits.manh<uy.bits.manh ||
ux.bits.manl<uy.bits.manl))) {
q = 0;
goto fixup; /* |x|<|y| return x or x-y */
}
if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
*quo = (sxy ? -1 : 1);
return Zero[sx]; /* |x|=|y| return x*0*/
}
}
/* determine ix = ilogb(x) */
if(ux.bits.exp == 0) { /* subnormal x */
ux.e *= 0x1.0p512;
ix = ux.bits.exp - (BIAS + 512);
} else {
ix = ux.bits.exp - BIAS;
}
/* determine iy = ilogb(y) */
if(uy.bits.exp == 0) { /* subnormal y */
uy.e *= 0x1.0p512;
iy = uy.bits.exp - (BIAS + 512);
} else {
iy = uy.bits.exp - BIAS;
}
/* set up {hx,lx}, {hy,ly} and align y to x */
hx = SET_NBIT(ux.bits.manh);
hy = SET_NBIT(uy.bits.manh);
lx = ux.bits.manl;
ly = uy.bits.manl;
/* 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 */
q &= 0x7fffffff;
*quo = (sxy ? -q : q);
return Zero[sx];
}
while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */
hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
iy -= 1;
}
ux.bits.manh = hx; /* The integer bit is truncated here if needed. */
ux.bits.manl = lx;
if (iy < LDBL_MIN_EXP) {
ux.bits.exp = iy + (BIAS + 512);
ux.e *= 0x1p-512;
} else {
ux.bits.exp = iy + BIAS;
}
ux.bits.sign = 0;
x = ux.e;
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;
}
ux.e = x;
ux.bits.sign ^= sx;
x = ux.e;
q &= 0x7fffffff;
*quo = (sxy ? -q : q);
return x;
}
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