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150 lines
5.0 KiB
C
150 lines
5.0 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2015 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/**************************************************************************/
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/* MODULE_NAME urem.c */
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/* */
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/* FUNCTION: uremainder */
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/* */
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/* An ultimate remainder routine. Given two IEEE double machine numbers x */
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/* ,y it computes the correctly rounded (to nearest) value of remainder */
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/* of dividing x by y. */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/* ************************************************************************/
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#include "endian.h"
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#include "mydefs.h"
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#include "urem.h"
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#include "MathLib.h"
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#include <math_private.h>
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/**************************************************************************/
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/* An ultimate remainder routine. Given two IEEE double machine numbers x */
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/* ,y it computes the correctly rounded (to nearest) value of remainder */
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/**************************************************************************/
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double
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__ieee754_remainder (double x, double y)
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{
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double z, d, xx;
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int4 kx, ky, n, nn, n1, m1, l;
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mynumber u, t, w = { { 0, 0 } }, v = { { 0, 0 } }, ww = { { 0, 0 } }, r;
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u.x = x;
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t.x = y;
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kx = u.i[HIGH_HALF] & 0x7fffffff; /* no sign for x*/
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t.i[HIGH_HALF] &= 0x7fffffff; /*no sign for y */
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ky = t.i[HIGH_HALF];
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/*------ |x| < 2^1023 and 2^-970 < |y| < 2^1024 ------------------*/
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if (kx < 0x7fe00000 && ky < 0x7ff00000 && ky >= 0x03500000)
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{
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SET_RESTORE_ROUND_NOEX (FE_TONEAREST);
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if (kx + 0x00100000 < ky)
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return x;
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if ((kx - 0x01500000) < ky)
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{
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z = x / t.x;
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v.i[HIGH_HALF] = t.i[HIGH_HALF];
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d = (z + big.x) - big.x;
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xx = (x - d * v.x) - d * (t.x - v.x);
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if (d - z != 0.5 && d - z != -0.5)
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return (xx != 0) ? xx : ((x > 0) ? ZERO.x : nZERO.x);
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else
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{
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if (ABS (xx) > 0.5 * t.x)
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return (z > d) ? xx - t.x : xx + t.x;
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else
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return xx;
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}
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} /* (kx<(ky+0x01500000)) */
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else
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{
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r.x = 1.0 / t.x;
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n = t.i[HIGH_HALF];
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nn = (n & 0x7ff00000) + 0x01400000;
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w.i[HIGH_HALF] = n;
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ww.x = t.x - w.x;
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l = (kx - nn) & 0xfff00000;
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n1 = ww.i[HIGH_HALF];
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m1 = r.i[HIGH_HALF];
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while (l > 0)
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{
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r.i[HIGH_HALF] = m1 - l;
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z = u.x * r.x;
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w.i[HIGH_HALF] = n + l;
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ww.i[HIGH_HALF] = (n1) ? n1 + l : n1;
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d = (z + big.x) - big.x;
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u.x = (u.x - d * w.x) - d * ww.x;
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l = (u.i[HIGH_HALF] & 0x7ff00000) - nn;
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}
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r.i[HIGH_HALF] = m1;
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w.i[HIGH_HALF] = n;
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ww.i[HIGH_HALF] = n1;
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z = u.x * r.x;
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d = (z + big.x) - big.x;
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u.x = (u.x - d * w.x) - d * ww.x;
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if (ABS (u.x) < 0.5 * t.x)
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return (u.x != 0) ? u.x : ((x > 0) ? ZERO.x : nZERO.x);
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else
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if (ABS (u.x) > 0.5 * t.x)
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return (d > z) ? u.x + t.x : u.x - t.x;
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else
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{
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z = u.x / t.x; d = (z + big.x) - big.x;
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return ((u.x - d * w.x) - d * ww.x);
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}
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}
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} /* (kx<0x7fe00000&&ky<0x7ff00000&&ky>=0x03500000) */
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else
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{
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if (kx < 0x7fe00000 && ky < 0x7ff00000 && (ky > 0 || t.i[LOW_HALF] != 0))
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{
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y = ABS (y) * t128.x;
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z = __ieee754_remainder (x, y) * t128.x;
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z = __ieee754_remainder (z, y) * tm128.x;
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return z;
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}
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else
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{
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if ((kx & 0x7ff00000) == 0x7fe00000 && ky < 0x7ff00000 &&
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(ky > 0 || t.i[LOW_HALF] != 0))
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{
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y = ABS (y);
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z = 2.0 * __ieee754_remainder (0.5 * x, y);
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d = ABS (z);
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if (d <= ABS (d - y))
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return z;
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else
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return (z > 0) ? z - y : z + y;
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}
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else /* if x is too big */
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{
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if (ky == 0 && t.i[LOW_HALF] == 0) /* y = 0 */
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return (x * y) / (x * y);
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else if (kx >= 0x7ff00000 /* x not finite */
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|| (ky > 0x7ff00000 /* y is NaN */
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|| (ky == 0x7ff00000 && t.i[LOW_HALF] != 0)))
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return (x * y) / (x * y);
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else
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return x;
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}
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}
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}
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}
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strong_alias (__ieee754_remainder, __remainder_finite)
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