glibc/sysdeps/ieee754/dbl-64/e_remainder.c
Joseph Myers 444ec6b8d8 Fix dbl-64 remainder sign of zero result (bug 19201).
For some large arguments, the dbl-64 implementation of remainder gives
zero results with the wrong sign, resulting from a subtraction that is
mathematically correct but does not guarantee that a zero result has
the sign of the first argument to remainder.  This patch adds an
appropriate check for this case, similar to other implementations of
remainder in the case of equality, and adds tests of remainder on
inputs already used to test remquo.

Tested for x86_64 and x86.

	[BZ #19201]
	* sysdeps/ieee754/dbl-64/e_remainder.c (__ieee754_remainder):
	Check for zero remainder in case of large exponents and ensure
	correct sign of result in that case.
	* math/libm-test.inc (remainder_test_data): Add more tests.
2015-11-03 00:11:49 +00:00

153 lines
5.0 KiB
C

/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2015 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 <http://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 "MathLib.h"
#include <math.h>
#include <math_private.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;
}
}
}
}
strong_alias (__ieee754_remainder, __remainder_finite)