sysdeps/ieee754/dbl-64/mpatan.c

   1
   2 /*
   3  * IBM Accurate Mathematical Library
   4  * written by International Business Machines Corp.
   5  * Copyright (C) 2001 Free Software Foundation
   6  *
   7  * This program is free software; you can redistribute it and/or modify
   8  * it under the terms of the GNU Lesser General Public License as published by
   9  * the Free Software Foundation; either version 2.1 of the License, or
  10  * (at your option) any later version.
  11  *
  12  * This program is distributed in the hope that it will be useful,
  13  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  14  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15  * GNU Lesser General Public License for more details.
  16  *
  17  * You should have received a copy of the GNU  Lesser General Public License
  18  * along with this program; if not, write to the Free Software
  19  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
  20  */
  21 /******************************************************************/
  22 /*                                                                */
  23 /* MODULE_NAME:mpatan.c                                           */
  24 /*                                                                */
  25 /* FUNCTIONS:mpatan                                               */
  26 /*                                                                */
  27 /* FILES NEEDED: mpa.h endian.h mpatan.h                          */
  28 /*               mpa.c                                            */
  29 /*                                                                */
  30 /* Multi-Precision Atan function subroutine, for precision p >= 4.*/
  31 /* The relative error of the result is bounded by 34.32*r**(1-p), */
  32 /* where r=2**24.                                                 */
  33 /******************************************************************/
  34
  35 #include "endian.h"
  36 #include "mpa.h"
  37 void __mpsqrt(mp_no *, mp_no *, int);
  38
  39 void __mpatan(mp_no *x, mp_no *y, int p) {
  40 #include "mpatan.h"
  41
  42   int i,m,n;
  43   double dx;
  44   mp_no
  45     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,
  46                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
  47                 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     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,
  49                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
  50                 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     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,
  52                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,
  53                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
  54
  55   mp_no mps,mpsm,mpt,mpt1,mpt2,mpt3;
  56
  57                       /* Choose m and initiate mpone, mptwo & mptwoim1 */
  58     if      (EX>0) m=7;
  59     else if (EX<0) m=0;
  60     else {
  61       __mp_dbl(x,&dx,p);  dx=ABS(dx);
  62       for (m=6; m>0; m--)
  63         {if (dx>xm[m].d) break;}
  64     }
  65     mpone.e    = mptwo.e    = mptwoim1.e = 1;
  66     mpone.d[0] = mpone.d[1] = mptwo.d[0] = mptwoim1.d[0] = ONE;
  67     mptwo.d[1] = TWO;
  68
  69                                  /* Reduce x m times */
  70     __mul(x,x,&mpsm,p);
  71     if (m==0) __cpy(x,&mps,p);
  72     else {
  73       for (i=0; i<m; i++) {
  74         __add(&mpone,&mpsm,&mpt1,p);
  75         __mpsqrt(&mpt1,&mpt2,p);
  76         __add(&mpt2,&mpt2,&mpt1,p);
  77         __add(&mptwo,&mpsm,&mpt2,p);
  78         __add(&mpt1,&mpt2,&mpt3,p);
  79         __dvd(&mpsm,&mpt3,&mpt1,p);
  80         __cpy(&mpt1,&mpsm,p);
  81       }
  82       __mpsqrt(&mpsm,&mps,p);    mps.d[0] = X[0];
  83     }
  84
  85                     /* Evaluate a truncated power series for Atan(s) */
  86     n=np[p];    mptwoim1.d[1] = twonm1[p].d;
  87     __dvd(&mpsm,&mptwoim1,&mpt,p);
  88     for (i=n-1; i>1; i--) {
  89       mptwoim1.d[1] -= TWO;
  90       __dvd(&mpsm,&mptwoim1,&mpt1,p);
  91       __mul(&mpsm,&mpt,&mpt2,p);
  92       __sub(&mpt1,&mpt2,&mpt,p);
  93     }
  94     __mul(&mps,&mpt,&mpt1,p);
  95     __sub(&mps,&mpt1,&mpt,p);
  96
  97                           /* Compute Atan(x) */
  98     mptwoim1.d[1] = twom[m].d;
  99     __mul(&mptwoim1,&mpt,y,p);
 100
 101   return;
 102 }