libgcc-math/dbl-64/slowpow.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001 Free Software Foundation
   5  *
   6  * This program is free software; you can redistribute it and/or modify
   7  * it under the terms of the GNU Lesser General Public License as published by
   8  * the Free Software Foundation; either version 2.1 of the License, or
   9  * (at your option) any later version.
  10  *
  11  * This program is distributed in the hope that it will be useful,
  12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14  * GNU Lesser General Public License for more details.
  15  *
  16  * You should have received a copy of the GNU Lesser General Public License
  17  * along with this program; if not, write to the Free Software
  18  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
  19  */
  20 /*************************************************************************/
  21 /* MODULE_NAME:slowpow.c                                                 */
  22 /*                                                                       */
  23 /* FUNCTION:slowpow                                                      */
  24 /*                                                                       */
  25 /*FILES NEEDED:mpa.h                                                     */
  26 /*             mpa.c mpexp.c mplog.c halfulp.c                           */
  27 /*                                                                       */
  28 /* Given two IEEE double machine numbers y,x , routine  computes the     */
  29 /* correctly  rounded (to nearest) value of x^y. Result calculated  by   */
  30 /* multiplication (in halfulp.c) or if result isn't accurate enough      */
  31 /* then routine converts x and y into multi-precision doubles     and    */
  32 /* calls to mpexp routine                                                */
  33 /*************************************************************************/
  34
  35 #include "mpa.h"
  36 #include "math_private.h"
  37
  38 void __mpexp(mp_no *x, mp_no *y, int p);
  39 void __mplog(mp_no *x, mp_no *y, int p);
  40 double ulog(double);
  41 double __halfulp(double x,double y);
  42
  43 double __slowpow(double x, double y, double z) {
  44   double res,res1;
  45   mp_no mpx, mpy, mpz,mpw,mpp,mpr,mpr1;
  46   static const mp_no eps = {-3,{1.0,4.0}};
  47   int p;
  48
  49   res = __halfulp(x,y);        /* halfulp() returns -10 or x^y             */
  50   if (res >= 0) return res;  /* if result was really computed by halfulp */
  51                   /*  else, if result was not really computed by halfulp */
  52   p = 10;         /*  p=precision   */
  53   __dbl_mp(x,&mpx,p);
  54   __dbl_mp(y,&mpy,p);
  55   __dbl_mp(z,&mpz,p);
  56   __mplog(&mpx, &mpz, p);     /* log(x) = z   */
  57   __mul(&mpy,&mpz,&mpw,p);    /*  y * z =w    */
  58   __mpexp(&mpw, &mpp, p);     /*  e^w =pp     */
  59   __add(&mpp,&eps,&mpr,p);    /*  pp+eps =r   */
  60   __mp_dbl(&mpr, &res, p);
  61   __sub(&mpp,&eps,&mpr1,p);   /*  pp -eps =r1 */
  62   __mp_dbl(&mpr1, &res1, p);  /*  converting into double precision */
  63   if (res == res1) return res;
  64
  65   p = 32;     /* if we get here result wasn't calculated exactly, continue */
  66   __dbl_mp(x,&mpx,p);                          /* for more exact calculation */
  67   __dbl_mp(y,&mpy,p);
  68   __dbl_mp(z,&mpz,p);
  69   __mplog(&mpx, &mpz, p);   /* log(c)=z  */
  70   __mul(&mpy,&mpz,&mpw,p);  /* y*z =w    */
  71   __mpexp(&mpw, &mpp, p);   /* e^w=pp    */
  72   __mp_dbl(&mpp, &res, p);  /* converting into double precision */
  73   return res;
  74 }