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"
37void __mpsqrt(mp_no *, mp_no *, int);
38
39void __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}
103