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glibc  2.9
mpatan.c
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00001 
00002 /*
00003  * IBM Accurate Mathematical Library
00004  * written by International Business Machines Corp.
00005  * Copyright (C) 2001 Free Software Foundation
00006  *
00007  * This program is free software; you can redistribute it and/or modify
00008  * it under the terms of the GNU Lesser General Public License as published by
00009  * the Free Software Foundation; either version 2.1 of the License, or
00010  * (at your option) any later version.
00011  *
00012  * This program is distributed in the hope that it will be useful,
00013  * but WITHOUT ANY WARRANTY; without even the implied warranty of
00014  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00015  * GNU Lesser General Public License for more details.
00016  *
00017  * You should have received a copy of the GNU  Lesser General Public License
00018  * along with this program; if not, write to the Free Software
00019  * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
00020  */
00021 /******************************************************************/
00022 /*                                                                */
00023 /* MODULE_NAME:mpatan.c                                           */
00024 /*                                                                */
00025 /* FUNCTIONS:mpatan                                               */
00026 /*                                                                */
00027 /* FILES NEEDED: mpa.h endian.h mpatan.h                          */
00028 /*               mpa.c                                            */
00029 /*                                                                */
00030 /* Multi-Precision Atan function subroutine, for precision p >= 4.*/
00031 /* The relative error of the result is bounded by 34.32*r**(1-p), */
00032 /* where r=2**24.                                                 */
00033 /******************************************************************/
00034 
00035 #include "endian.h"
00036 #include "mpa.h"
00037 void __mpsqrt(mp_no *, mp_no *, int);
00038 
00039 void __mpatan(mp_no *x, mp_no *y, int p) {
00040 #include "mpatan.h"
00041 
00042   int i,m,n;
00043   double dx;
00044   mp_no
00045     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,
00046               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,
00047               0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
00048     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,
00049               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,
00050               0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
00051     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,
00052               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,
00053               0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
00054 
00055   mp_no mps,mpsm,mpt,mpt1,mpt2,mpt3;
00056 
00057                       /* Choose m and initiate mpone, mptwo & mptwoim1 */
00058     if      (EX>0) m=7;
00059     else if (EX<0) m=0;
00060     else {
00061       __mp_dbl(x,&dx,p);  dx=ABS(dx);
00062       for (m=6; m>0; m--)
00063         {if (dx>xm[m].d) break;}
00064     }
00065     mpone.e    = mptwo.e    = mptwoim1.e = 1;
00066     mpone.d[0] = mpone.d[1] = mptwo.d[0] = mptwoim1.d[0] = ONE;
00067     mptwo.d[1] = TWO;
00068 
00069                                  /* Reduce x m times */
00070     __mul(x,x,&mpsm,p);
00071     if (m==0) __cpy(x,&mps,p);
00072     else {
00073       for (i=0; i<m; i++) {
00074        __add(&mpone,&mpsm,&mpt1,p);
00075        __mpsqrt(&mpt1,&mpt2,p);
00076        __add(&mpt2,&mpt2,&mpt1,p);
00077        __add(&mptwo,&mpsm,&mpt2,p);
00078        __add(&mpt1,&mpt2,&mpt3,p);
00079        __dvd(&mpsm,&mpt3,&mpt1,p);
00080        __cpy(&mpt1,&mpsm,p);
00081       }
00082       __mpsqrt(&mpsm,&mps,p);    mps.d[0] = X[0];
00083     }
00084 
00085                     /* Evaluate a truncated power series for Atan(s) */
00086     n=np[p];    mptwoim1.d[1] = twonm1[p].d;
00087     __dvd(&mpsm,&mptwoim1,&mpt,p);
00088     for (i=n-1; i>1; i--) {
00089       mptwoim1.d[1] -= TWO;
00090       __dvd(&mpsm,&mptwoim1,&mpt1,p);
00091       __mul(&mpsm,&mpt,&mpt2,p);
00092       __sub(&mpt1,&mpt2,&mpt,p);
00093     }
00094     __mul(&mps,&mpt,&mpt1,p);
00095     __sub(&mps,&mpt1,&mpt,p);
00096 
00097                           /* Compute Atan(x) */
00098     mptwoim1.d[1] = twom[m].d;
00099     __mul(&mptwoim1,&mpt,y,p);
00100 
00101   return;
00102 }