114 lines
3.8 KiB
C
114 lines
3.8 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:slowpow.c */
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/* */
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/* FUNCTION:slowpow */
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/* */
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/*FILES NEEDED:mpa.h */
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/* mpa.c mpexp.c mplog.c halfulp.c */
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/* */
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/* Given two IEEE double machine numbers y,x , routine computes the */
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/* correctly rounded (to nearest) value of x^y. Result calculated by */
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/* multiplication (in halfulp.c) or if result isn't accurate enough */
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/* then routine converts x and y into multi-precision doubles and */
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/* calls to mpexp routine */
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/*************************************************************************/
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#include "mpa.h"
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#include <math_private.h>
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#ifndef SECTION
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# define SECTION
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#endif
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void __mpexp (mp_no *x, mp_no *y, int p);
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void __mplog (mp_no *x, mp_no *y, int p);
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double ulog (double);
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double __halfulp (double x, double y);
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double
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SECTION
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__slowpow (double x, double y, double z)
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{
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double res, res1;
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mp_no mpx, mpy, mpz, mpw, mpp, mpr, mpr1;
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static const mp_no eps = {-3, {1.0, 4.0}};
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int p;
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/* __HALFULP returns -10 or X^Y. */
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res = __halfulp (x, y);
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/* Return if the result was computed by __HALFULP. */
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if (res >= 0)
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return res;
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/* Compute pow as long double. This is currently only used by powerpc, where
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one may get 106 bits of accuracy. */
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#ifdef USE_LONG_DOUBLE_FOR_MP
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long double ldw, ldz, ldpp;
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static const long double ldeps = 0x4.0p-96;
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ldz = __ieee754_logl ((long double) x);
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ldw = (long double) y *ldz;
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ldpp = __ieee754_expl (ldw);
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res = (double) (ldpp + ldeps);
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res1 = (double) (ldpp - ldeps);
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/* Return the result if it is accurate enough. */
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if (res == res1)
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return res;
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#endif
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/* Or else, calculate using multiple precision. P = 10 implies accuracy of
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240 bits accuracy, since MP_NO has a radix of 2^24. */
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p = 10;
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__dbl_mp (x, &mpx, p);
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__dbl_mp (y, &mpy, p);
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__dbl_mp (z, &mpz, p);
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/* z = x ^ y
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log (z) = y * log (x)
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z = exp (y * log (x)) */
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__mplog (&mpx, &mpz, p);
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__mul (&mpy, &mpz, &mpw, p);
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__mpexp (&mpw, &mpp, p);
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/* Add and subtract EPS to ensure that the result remains unchanged, i.e. we
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have last bit accuracy. */
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__add (&mpp, &eps, &mpr, p);
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__mp_dbl (&mpr, &res, p);
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__sub (&mpp, &eps, &mpr1, p);
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__mp_dbl (&mpr1, &res1, p);
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if (res == res1)
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return res;
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/* If we don't, then we repeat using a higher precision. 768 bits of
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precision ought to be enough for anybody. */
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p = 32;
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__dbl_mp (x, &mpx, p);
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__dbl_mp (y, &mpy, p);
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__dbl_mp (z, &mpz, p);
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__mplog (&mpx, &mpz, p);
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__mul (&mpy, &mpz, &mpw, p);
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__mpexp (&mpw, &mpp, p);
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__mp_dbl (&mpp, &res, p);
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return res;
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}
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