sysdeps/powerpc/powerpc32/power4/fpu/slowpow.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001, 2006 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 /* recompute.                                                            */
  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
  44 __slowpow (double x, double y, double z)
  45 {
  46   double res, res1;
  47   long double ldw, ldz, ldpp;
  48   static const long double ldeps = 0x4.0p-96;
  49
  50   res = __halfulp (x, y);       /* halfulp() returns -10 or x^y             */
  51   if (res >= 0)
  52     return res;                 /* if result was really computed by halfulp */
  53   /*  else, if result was not really computed by halfulp */
  54
  55   /* Compute pow as long double, 106 bits */
  56   ldz = __ieee754_logl ((long double) x);
  57   ldw = (long double) y *ldz;
  58   ldpp = __ieee754_expl (ldw);
  59   res = (double) (ldpp + ldeps);
  60   res1 = (double) (ldpp - ldeps);
  61
  62   if (res != res1)              /* if result still not accurate enough */
  63     {                           /* use mpa for higher persision.  */
  64       mp_no mpx, mpy, mpz, mpw, mpp, mpr, mpr1;
  65       static const mp_no eps = { -3, {1.0, 4.0} };
  66       int p;
  67
  68       p = 10;                   /*  p=precision 240 bits  */
  69       __dbl_mp (x, &mpx, p);
  70       __dbl_mp (y, &mpy, p);
  71       __dbl_mp (z, &mpz, p);
  72       __mplog (&mpx, &mpz, p);          /* log(x) = z   */
  73       __mul (&mpy, &mpz, &mpw, p);      /*  y * z =w    */
  74       __mpexp (&mpw, &mpp, p);          /*  e^w =pp     */
  75       __add (&mpp, &eps, &mpr, p);      /*  pp+eps =r   */
  76       __mp_dbl (&mpr, &res, p);
  77       __sub (&mpp, &eps, &mpr1, p);     /*  pp -eps =r1 */
  78       __mp_dbl (&mpr1, &res1, p);       /*  converting into double precision */
  79       if (res == res1)
  80         return res;
  81
  82       /* if we get here result wasn't calculated exactly, continue for
  83          more exact calculation using 768 bits.  */
  84       p = 32;
  85       __dbl_mp (x, &mpx, p);
  86       __dbl_mp (y, &mpy, p);
  87       __dbl_mp (z, &mpz, p);
  88       __mplog (&mpx, &mpz, p);          /* log(c)=z  */
  89       __mul (&mpy, &mpz, &mpw, p);      /* y*z =w    */
  90       __mpexp (&mpw, &mpp, p);          /* e^w=pp    */
  91       __mp_dbl (&mpp, &res, p);         /* converting into double precision */
  92     }
  93   return res;
  94 }