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112 lines
3.9 KiB
C
112 lines
3.9 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) 2001-2013 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:mpsqrt.c */
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/* */
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/* FUNCTION:mpsqrt */
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/* fastiroot */
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/* */
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/* FILES NEEDED:endian.h mpa.h mpsqrt.h */
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/* mpa.c */
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/* Multi-Precision square root function subroutine for precision p >= 4. */
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/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */
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/* */
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/****************************************************************************/
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#include "endian.h"
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#include "mpa.h"
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#ifndef SECTION
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# define SECTION
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#endif
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#include "mpsqrt.h"
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/****************************************************************************/
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/* Multi-Precision square root function subroutine for precision p >= 4. */
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/* The relative error is bounded by 3.501*r**(1-p), where r=2**24. */
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/* Routine receives two pointers to Multi Precision numbers: */
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/* x (left argument) and y (next argument). Routine also receives precision */
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/* p as integer. Routine computes sqrt(*x) and stores result in *y */
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/****************************************************************************/
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static double fastiroot (double);
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void
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SECTION
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__mpsqrt (mp_no *x, mp_no *y, int p)
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{
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int i, m, ey;
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double dx, dy;
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static const mp_no mphalf = {0, {1.0, HALFRAD}};
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static const mp_no mp3halfs = {1, {1.0, 1.0, HALFRAD}};
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mp_no mpxn, mpz, mpu, mpt1, mpt2;
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ey = EX / 2;
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__cpy (x, &mpxn, p);
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mpxn.e -= (ey + ey);
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__mp_dbl (&mpxn, &dx, p);
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dy = fastiroot (dx);
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__dbl_mp (dy, &mpu, p);
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__mul (&mpxn, &mphalf, &mpz, p);
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m = __mpsqrt_mp[p];
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for (i = 0; i < m; i++)
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{
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__sqr (&mpu, &mpt1, p);
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__mul (&mpt1, &mpz, &mpt2, p);
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__sub (&mp3halfs, &mpt2, &mpt1, p);
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__mul (&mpu, &mpt1, &mpt2, p);
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__cpy (&mpt2, &mpu, p);
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}
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__mul (&mpxn, &mpu, y, p);
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EY += ey;
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}
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/***********************************************************/
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/* Compute a double precision approximation for 1/sqrt(x) */
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/* with the relative error bounded by 2**-51. */
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/***********************************************************/
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static double
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SECTION
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fastiroot (double x)
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{
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union
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{
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int i[2];
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double d;
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} p, q;
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double y, z, t;
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int n;
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static const double c0 = 0.99674, c1 = -0.53380;
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static const double c2 = 0.45472, c3 = -0.21553;
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p.d = x;
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p.i[HIGH_HALF] = (p.i[HIGH_HALF] & 0x3FFFFFFF) | 0x3FE00000;
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q.d = x;
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y = p.d;
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z = y - 1.0;
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n = (q.i[HIGH_HALF] - p.i[HIGH_HALF]) >> 1;
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z = ((c3 * z + c2) * z + c1) * z + c0; /* 2**-7 */
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z = z * (1.5 - 0.5 * y * z * z); /* 2**-14 */
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p.d = z * (1.5 - 0.5 * y * z * z); /* 2**-28 */
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p.i[HIGH_HALF] -= n;
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t = x * p.d;
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return p.d * (1.5 - 0.5 * p.d * t);
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}
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