sysdeps/ieee754/dbl-64/mpatan.c

   1
   2 /*
   3  * IBM Accurate Mathematical Library
   4  * Copyright (c) International Business Machines Corp., 2001
   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 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 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 /*                                                                */
  22 /* MODULE_NAME:mpatan.c                                           */
  23 /*                                                                */
  24 /* FUNCTIONS:mpatan                                               */
  25 /*                                                                */
  26 /* FILES NEEDED: mpa.h endian.h mpatan.h                          */
  27 /*               mpa.c                                            */
  28 /*                                                                */
  29 /* Multi-Precision Atan function subroutine, for precision p >= 4.*/
  30 /* The relative error of the result is bounded by 34.32*r**(1-p), */
  31 /* where r=2**24.                                                 */
  32 /******************************************************************/
  33
  34 #include "endian.h"
  35 #include "mpa.h"
  36 void __mpsqrt(mp_no *, mp_no *, int);
  37
  38 void __mpatan(mp_no *x, mp_no *y, int p) {
  39 #include "mpatan.h"
  40
  41   int i,m,n;
  42   double dx;
  43   mp_no
  44     mpone    = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
  45                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
  46                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
  47     mptwo    = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
  48                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
  49                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
  50     mptwoim1 = {0,{0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
  51                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
  52                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
  53
  54   mp_no mps,mpsm,mpt,mpt1,mpt2,mpt3;
  55
  56                       /* Choose m and initiate mpone, mptwo & mptwoim1 */
  57     if      (EX>0) m=7;
  58     else if (EX<0) m=0;
  59     else {
  60       __mp_dbl(x,&dx,p);  dx=ABS(dx);
  61       for (m=6; m>0; m--)
  62         {if (dx>xm[m].d) break;}
  63     }
  64     mpone.e    = mptwo.e    = mptwoim1.e = 1;
  65     mpone.d[0] = mpone.d[1] = mptwo.d[0] = mptwoim1.d[0] = ONE;
  66     mptwo.d[1] = TWO;
  67
  68                                  /* Reduce x m times */
  69     __mul(x,x,&mpsm,p);
  70     if (m==0) __cpy(x,&mps,p);
  71     else {
  72       for (i=0; i<m; i++) {
  73         __add(&mpone,&mpsm,&mpt1,p);
  74         __mpsqrt(&mpt1,&mpt2,p);
  75         __add(&mpt2,&mpt2,&mpt1,p);
  76         __add(&mptwo,&mpsm,&mpt2,p);
  77         __add(&mpt1,&mpt2,&mpt3,p);
  78         __dvd(&mpsm,&mpt3,&mpt1,p);
  79         __cpy(&mpt1,&mpsm,p);
  80       }
  81       __mpsqrt(&mpsm,&mps,p);    mps.d[0] = X[0];
  82     }
  83
  84                     /* Evaluate a truncated power series for Atan(s) */
  85     n=np[p];    mptwoim1.d[1] = twonm1[p].d;
  86     __dvd(&mpsm,&mptwoim1,&mpt,p);
  87     for (i=n-1; i>1; i--) {
  88       mptwoim1.d[1] -= TWO;
  89       __dvd(&mpsm,&mptwoim1,&mpt1,p);
  90       __mul(&mpsm,&mpt,&mpt2,p);
  91       __sub(&mpt1,&mpt2,&mpt,p);
  92     }
  93     __mul(&mps,&mpt,&mpt1,p);
  94     __sub(&mps,&mpt1,&mpt,p);
  95
  96                           /* Compute Atan(x) */
  97     mptwoim1.d[1] = twom[m].d;
  98     __mul(&mptwoim1,&mpt,y,p);
  99
 100   return;
 101 }