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/* e_fmodl.c -- long double version of e_fmod.c.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* __ieee754_fmodl(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
#include <math.h>
#include <math_private.h>
#include <ieee754.h>
#include <libm-alias-finite.h>
static const long double one = 1.0, Zero[] = {0.0, -0.0,};
long double
__ieee754_fmodl (long double x, long double y)
{
int64_t hx, hy, hz, sx, sy;
uint64_t lx, ly, lz;
int n, ix, iy;
double xhi, xlo, yhi, ylo;
ldbl_unpack (x, &xhi, &xlo);
EXTRACT_WORDS64 (hx, xhi);
EXTRACT_WORDS64 (lx, xlo);
ldbl_unpack (y, &yhi, &ylo);
EXTRACT_WORDS64 (hy, yhi);
EXTRACT_WORDS64 (ly, ylo);
sx = hx&0x8000000000000000ULL; /* sign of x */
hx ^= sx; /* |x| */
sy = hy&0x8000000000000000ULL; /* sign of y */
hy ^= sy; /* |y| */
/* purge off exception values */
if(__builtin_expect(hy==0 ||
(hx>=0x7ff0000000000000LL)|| /* y=0,or x not finite */
(hy>0x7ff0000000000000LL),0)) /* or y is NaN */
return (x*y)/(x*y);
if (__glibc_unlikely (hx <= hy))
{
/* If |x| < |y| return x. */
if (hx < hy)
return x;
/* At this point the absolute value of the high doubles of
x and y must be equal. */
if ((lx & 0x7fffffffffffffffLL) == 0
&& (ly & 0x7fffffffffffffffLL) == 0)
/* Both low parts are zero. The result should be an
appropriately signed zero, but the subsequent logic
could treat them as unequal, depending on the signs
of the low parts. */
return Zero[(uint64_t) sx >> 63];
/* If the low double of y is the same sign as the high
double of y (ie. the low double increases |y|)... */
if (((ly ^ sy) & 0x8000000000000000LL) == 0
/* ... then a different sign low double to high double
for x or same sign but lower magnitude... */
&& (int64_t) (lx ^ sx) < (int64_t) (ly ^ sy))
/* ... means |x| < |y|. */
return x;
/* If the low double of x differs in sign to the high
double of x (ie. the low double decreases |x|)... */
if (((lx ^ sx) & 0x8000000000000000LL) != 0
/* ... then a different sign low double to high double
for y with lower magnitude (we've already caught
the same sign for y case above)... */
&& (int64_t) (lx ^ sx) > (int64_t) (ly ^ sy))
/* ... means |x| < |y|. */
return x;
/* If |x| == |y| return x*0. */
if ((lx ^ sx) == (ly ^ sy))
return Zero[(uint64_t) sx >> 63];
}
/* Make the IBM extended format 105 bit mantissa look like the ieee854 112
bit mantissa so the following operations will give the correct
result. */
ldbl_extract_mantissa(&hx, &lx, &ix, x);
ldbl_extract_mantissa(&hy, &ly, &iy, y);
if (__glibc_unlikely (ix == -IEEE754_DOUBLE_BIAS))
{
/* subnormal x, shift x to normal. */
while ((hx & (1LL << 48)) == 0)
{
hx = (hx << 1) | (lx >> 63);
lx = lx << 1;
ix -= 1;
}
}
if (__glibc_unlikely (iy == -IEEE754_DOUBLE_BIAS))
{
/* subnormal y, shift y to normal. */
while ((hy & (1LL << 48)) == 0)
{
hy = (hy << 1) | (ly >> 63);
ly = ly << 1;
iy -= 1;
}
}
/* 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>>63); lx = lx+lx;}
else {
if((hz|lz)==0) /* return sign(x)*0 */
return Zero[(uint64_t)sx>>63];
hx = hz+hz+(lz>>63); 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[(uint64_t)sx>>63];
while(hx<0x0001000000000000LL) { /* normalize x */
hx = hx+hx+(lx>>63); lx = lx+lx;
iy -= 1;
}
if(__builtin_expect(iy>= -1022,0)) { /* normalize output */
x = ldbl_insert_mantissa((sx>>63), iy, hx, lx);
} else { /* subnormal output */
n = -1022 - iy;
/* We know 1 <= N <= 52, and that there are no nonzero
bits in places below 2^-1074. */
lx = (lx >> n) | ((uint64_t) hx << (64 - n));
hx >>= n;
x = ldbl_insert_mantissa((sx>>63), -1023, hx, lx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}
libm_alias_finite (__ieee754_fmodl, __fmodl)
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