sysdeps/ieee754/dbl-64/mpatan.c

   1 /*
   2  * IBM Accurate Mathematical Library
   3  * written by International Business Machines Corp.
   4  * Copyright (C) 2001, 2011 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, see <http://www.gnu.org/licenses/>.
  18  */
  19 /******************************************************************/
  20 /*                                                                */
  21 /* MODULE_NAME:mpatan.c                                           */
  22 /*                                                                */
  23 /* FUNCTIONS:mpatan                                               */
  24 /*                                                                */
  25 /* FILES NEEDED: mpa.h endian.h mpatan.h                          */
  26 /*               mpa.c                                            */
  27 /*                                                                */
  28 /* Multi-Precision Atan function subroutine, for precision p >= 4.*/
  29 /* The relative error of the result is bounded by 34.32*r**(1-p), */
  30 /* where r=2**24.                                                 */
  31 /******************************************************************/
  32
  33 #include "endian.h"
  34 #include "mpa.h"
  35
  36 #ifndef SECTION
  37 # define SECTION
  38 #endif
  39
  40 #include "mpatan.h"
  41
  42 void __mpsqrt(mp_no *, mp_no *, int);
  43
  44 void
  45 SECTION
  46 __mpatan(mp_no *x, mp_no *y, int p) {
  47
  48   int i,m,n;
  49   double dx;
  50   mp_no
  51     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,
  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     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,
  55                 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,
  56                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
  57     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,
  58                 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,
  59                 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
  60
  61   mp_no mps,mpsm,mpt,mpt1,mpt2,mpt3;
  62
  63                       /* Choose m and initiate mpone, mptwo & mptwoim1 */
  64     if      (EX>0) m=7;
  65     else if (EX<0) m=0;
  66     else {
  67       __mp_dbl(x,&dx,p);  dx=ABS(dx);
  68       for (m=6; m>0; m--)
  69         {if (dx>__atan_xm[m].d) break;}
  70     }
  71     mpone.e    = mptwo.e    = mptwoim1.e = 1;
  72     mpone.d[0] = mpone.d[1] = mptwo.d[0] = mptwoim1.d[0] = ONE;
  73     mptwo.d[1] = TWO;
  74
  75                                  /* Reduce x m times */
  76     __mul(x,x,&mpsm,p);
  77     if (m==0) __cpy(x,&mps,p);
  78     else {
  79       for (i=0; i<m; i++) {
  80         __add(&mpone,&mpsm,&mpt1,p);
  81         __mpsqrt(&mpt1,&mpt2,p);
  82         __add(&mpt2,&mpt2,&mpt1,p);
  83         __add(&mptwo,&mpsm,&mpt2,p);
  84         __add(&mpt1,&mpt2,&mpt3,p);
  85         __dvd(&mpsm,&mpt3,&mpt1,p);
  86         __cpy(&mpt1,&mpsm,p);
  87       }
  88       __mpsqrt(&mpsm,&mps,p);    mps.d[0] = X[0];
  89     }
  90
  91                     /* Evaluate a truncated power series for Atan(s) */
  92     n=__atan_np[p];    mptwoim1.d[1] = __atan_twonm1[p].d;
  93     __dvd(&mpsm,&mptwoim1,&mpt,p);
  94     for (i=n-1; i>1; i--) {
  95       mptwoim1.d[1] -= TWO;
  96       __dvd(&mpsm,&mptwoim1,&mpt1,p);
  97       __mul(&mpsm,&mpt,&mpt2,p);
  98       __sub(&mpt1,&mpt2,&mpt,p);
  99     }
 100     __mul(&mps,&mpt,&mpt1,p);
 101     __sub(&mps,&mpt1,&mpt,p);
 102
 103                           /* Compute Atan(x) */
 104     mptwoim1.d[1] = __atan_twom[m].d;
 105     __mul(&mptwoim1,&mpt,y,p);
 106
 107   return;
 108 }