| /* |
| * 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:slowpow.c */ |
| /* */ |
| /* FUNCTION:slowpow */ |
| /* */ |
| /*FILES NEEDED:mpa.h */ |
| /* mpa.c mpexp.c mplog.c halfulp.c */ |
| /* */ |
| /* Given two IEEE double machine numbers y,x , routine computes the */ |
| /* correctly rounded (to nearest) value of x^y. Result calculated by */ |
| /* multiplication (in halfulp.c) or if result isn't accurate enough */ |
| /* then routine converts x and y into multi-precision doubles and */ |
| /* calls to mpexp routine */ |
| /*************************************************************************/ |
| |
| #include "mpa.h" |
| #include <math_private.h> |
| |
| #include <stap-probe.h> |
| |
| #ifndef SECTION |
| # define SECTION |
| #endif |
| |
| void __mpexp (mp_no *x, mp_no *y, int p); |
| void __mplog (mp_no *x, mp_no *y, int p); |
| double ulog (double); |
| double __halfulp (double x, double y); |
| |
| double |
| SECTION |
| __slowpow (double x, double y, double z) |
| { |
| double res, res1; |
| mp_no mpx, mpy, mpz, mpw, mpp, mpr, mpr1; |
| static const mp_no eps = {-3, {1.0, 4.0}}; |
| int p; |
| |
| /* __HALFULP returns -10 or X^Y. */ |
| res = __halfulp (x, y); |
| |
| /* Return if the result was computed by __HALFULP. */ |
| if (res >= 0) |
| return res; |
| |
| /* Compute pow as long double. This is currently only used by powerpc, where |
| one may get 106 bits of accuracy. */ |
| #ifdef USE_LONG_DOUBLE_FOR_MP |
| long double ldw, ldz, ldpp; |
| static const long double ldeps = 0x4.0p-96; |
| |
| ldz = __ieee754_logl ((long double) x); |
| ldw = (long double) y *ldz; |
| ldpp = __ieee754_expl (ldw); |
| res = (double) (ldpp + ldeps); |
| res1 = (double) (ldpp - ldeps); |
| |
| /* Return the result if it is accurate enough. */ |
| if (res == res1) |
| return res; |
| #endif |
| |
| /* Or else, calculate using multiple precision. P = 10 implies accuracy of |
| 240 bits accuracy, since MP_NO has a radix of 2^24. */ |
| p = 10; |
| __dbl_mp (x, &mpx, p); |
| __dbl_mp (y, &mpy, p); |
| __dbl_mp (z, &mpz, p); |
| |
| /* z = x ^ y |
| log (z) = y * log (x) |
| z = exp (y * log (x)) */ |
| __mplog (&mpx, &mpz, p); |
| __mul (&mpy, &mpz, &mpw, p); |
| __mpexp (&mpw, &mpp, p); |
| |
| /* Add and subtract EPS to ensure that the result remains unchanged, i.e. we |
| have last bit accuracy. */ |
| __add (&mpp, &eps, &mpr, p); |
| __mp_dbl (&mpr, &res, p); |
| __sub (&mpp, &eps, &mpr1, p); |
| __mp_dbl (&mpr1, &res1, p); |
| if (res == res1) |
| { |
| /* Track how often we get to the slow pow code plus |
| its input/output values. */ |
| LIBC_PROBE (slowpow_p10, 4, &x, &y, &z, &res); |
| return res; |
| } |
| |
| /* If we don't, then we repeat using a higher precision. 768 bits of |
| precision ought to be enough for anybody. */ |
| p = 32; |
| __dbl_mp (x, &mpx, p); |
| __dbl_mp (y, &mpy, p); |
| __dbl_mp (z, &mpz, p); |
| __mplog (&mpx, &mpz, p); |
| __mul (&mpy, &mpz, &mpw, p); |
| __mpexp (&mpw, &mpp, p); |
| __mp_dbl (&mpp, &res, p); |
| |
| /* Track how often we get to the uber-slow pow code plus |
| its input/output values. */ |
| LIBC_PROBE (slowpow_p32, 4, &x, &y, &z, &res); |
| |
| return res; |
| } |