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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2025 Free Software Foundation, Inc.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public License as published by
* the Free Software Foundation; either version 2.1 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this program; if not, see <https://www.gnu.org/licenses/>.
*/
/**************************************************************************/
/* MODULE_NAME urem.c */
/* */
/* FUNCTION: uremainder */
/* */
/* An ultimate remainder routine. Given two IEEE double machine numbers x */
/* ,y it computes the correctly rounded (to nearest) value of remainder */
/* of dividing x by y. */
/* Assumption: Machine arithmetic operations are performed in */
/* round to nearest mode of IEEE 754 standard. */
/* */
/* ************************************************************************/
#include "endian.h"
#include "mydefs.h"
#include "urem.h"
#include <math.h>
#include <math_private.h>
#include <fenv_private.h>
#include <libm-alias-finite.h>
/**************************************************************************/
/* An ultimate remainder routine. Given two IEEE double machine numbers x */
/* ,y it computes the correctly rounded (to nearest) value of remainder */
/**************************************************************************/
double
__ieee754_remainder (double x, double y)
{
double z, d, xx;
int4 kx, ky, n, nn, n1, m1, l;
mynumber u, t, w = { { 0, 0 } }, v = { { 0, 0 } }, ww = { { 0, 0 } }, r;
u.x = x;
t.x = y;
kx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign for x*/
t.i[HIGH_HALF] &= 0x7fffffff; /*no sign for y */
ky = t.i[HIGH_HALF];
/*------ |x| < 2^1023 and 2^-970 < |y| < 2^1024 ------------------*/
if (kx < 0x7fe00000 && ky < 0x7ff00000 && ky >= 0x03500000)
{
SET_RESTORE_ROUND_NOEX (FE_TONEAREST);
if (kx + 0x00100000 < ky)
return x;
if ((kx - 0x01500000) < ky)
{
z = x / t.x;
v.i[HIGH_HALF] = t.i[HIGH_HALF];
d = (z + big.x) - big.x;
xx = (x - d * v.x) - d * (t.x - v.x);
if (d - z != 0.5 && d - z != -0.5)
return (xx != 0) ? xx : ((x > 0) ? ZERO.x : nZERO.x);
else
{
if (fabs (xx) > 0.5 * t.x)
return (z > d) ? xx - t.x : xx + t.x;
else
return xx;
}
} /* (kx<(ky+0x01500000)) */
else
{
r.x = 1.0 / t.x;
n = t.i[HIGH_HALF];
nn = (n & 0x7ff00000) + 0x01400000;
w.i[HIGH_HALF] = n;
ww.x = t.x - w.x;
l = (kx - nn) & 0xfff00000;
n1 = ww.i[HIGH_HALF];
m1 = r.i[HIGH_HALF];
while (l > 0)
{
r.i[HIGH_HALF] = m1 - l;
z = u.x * r.x;
w.i[HIGH_HALF] = n + l;
ww.i[HIGH_HALF] = (n1) ? n1 + l : n1;
d = (z + big.x) - big.x;
u.x = (u.x - d * w.x) - d * ww.x;
l = (u.i[HIGH_HALF] & 0x7ff00000) - nn;
}
r.i[HIGH_HALF] = m1;
w.i[HIGH_HALF] = n;
ww.i[HIGH_HALF] = n1;
z = u.x * r.x;
d = (z + big.x) - big.x;
u.x = (u.x - d * w.x) - d * ww.x;
if (fabs (u.x) < 0.5 * t.x)
return (u.x != 0) ? u.x : ((x > 0) ? ZERO.x : nZERO.x);
else
if (fabs (u.x) > 0.5 * t.x)
return (d > z) ? u.x + t.x : u.x - t.x;
else
{
z = u.x / t.x; d = (z + big.x) - big.x;
return ((u.x - d * w.x) - d * ww.x);
}
}
} /* (kx<0x7fe00000&&ky<0x7ff00000&&ky>=0x03500000) */
else
{
if (kx < 0x7fe00000 && ky < 0x7ff00000 && (ky > 0 || t.i[LOW_HALF] != 0))
{
y = fabs (y) * t128.x;
z = __ieee754_remainder (x, y) * t128.x;
z = __ieee754_remainder (z, y) * tm128.x;
return z;
}
else
{
if ((kx & 0x7ff00000) == 0x7fe00000 && ky < 0x7ff00000 &&
(ky > 0 || t.i[LOW_HALF] != 0))
{
y = fabs (y);
z = 2.0 * __ieee754_remainder (0.5 * x, y);
d = fabs (z);
if (d <= fabs (d - y))
return z;
else if (d == y)
return 0.0 * x;
else
return (z > 0) ? z - y : z + y;
}
else /* if x is too big */
{
if (ky == 0 && t.i[LOW_HALF] == 0) /* y = 0 */
return (x * y) / (x * y);
else if (kx >= 0x7ff00000 /* x not finite */
|| (ky > 0x7ff00000 /* y is NaN */
|| (ky == 0x7ff00000 && t.i[LOW_HALF] != 0)))
return (x * y) / (x * y);
else
return x;
}
}
}
}
libm_alias_finite (__ieee754_remainder, __remainder)
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