| /* |
| * IBM Accurate Mathematical Library |
| * written by International Business Machines Corp. |
| * Copyright (C) 2001-2014 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_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 (ABS (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 (ABS (u.x) < 0.5 * t.x) |
| return (u.x != 0) ? u.x : ((x > 0) ? ZERO.x : nZERO.x); |
| else |
| if (ABS (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 = ABS (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 = ABS (y); |
| z = 2.0 * __ieee754_remainder (0.5 * x, y); |
| d = ABS (z); |
| if (d <= ABS (d - y)) |
| return z; |
| 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) |
