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106 lines
3.4 KiB
C
106 lines
3.4 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2012 Free Software Foundation
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/******************************************************************/
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/* */
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/* MODULE_NAME:mpatan.c */
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/* */
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/* FUNCTIONS:mpatan */
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/* */
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/* FILES NEEDED: mpa.h endian.h mpatan.h */
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/* mpa.c */
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/* */
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/* Multi-Precision Atan function subroutine, for precision p >= 4.*/
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/* The relative error of the result is bounded by 34.32*r**(1-p), */
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/* where r=2**24. */
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/******************************************************************/
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#include "endian.h"
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#include "mpa.h"
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#ifndef SECTION
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# define SECTION
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#endif
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#include "mpatan.h"
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void __mpsqrt(mp_no *, mp_no *, int);
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void
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SECTION
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__mpatan(mp_no *x, mp_no *y, int p) {
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int i,m,n;
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double dx;
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mp_no
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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,
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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,
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0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}},
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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,
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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,
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0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0}};
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mp_no mps,mpsm,mpt,mpt1,mpt2,mpt3;
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/* Choose m and initiate mptwo & mptwoim1 */
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if (EX>0) m=7;
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else if (EX<0) m=0;
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else {
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__mp_dbl(x,&dx,p); dx=ABS(dx);
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for (m=6; m>0; m--)
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{if (dx>__atan_xm[m].d) break;}
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}
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mptwo.e = mptwoim1.e = 1;
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mptwo.d[0] = mptwoim1.d[0] = ONE;
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mptwo.d[1] = TWO;
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/* Reduce x m times */
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__mul(x,x,&mpsm,p);
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if (m==0) __cpy(x,&mps,p);
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else {
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for (i=0; i<m; i++) {
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__add(&mpone,&mpsm,&mpt1,p);
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__mpsqrt(&mpt1,&mpt2,p);
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__add(&mpt2,&mpt2,&mpt1,p);
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__add(&mptwo,&mpsm,&mpt2,p);
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__add(&mpt1,&mpt2,&mpt3,p);
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__dvd(&mpsm,&mpt3,&mpt1,p);
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__cpy(&mpt1,&mpsm,p);
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}
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__mpsqrt(&mpsm,&mps,p); mps.d[0] = X[0];
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}
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/* Evaluate a truncated power series for Atan(s) */
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n=__atan_np[p]; mptwoim1.d[1] = __atan_twonm1[p].d;
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__dvd(&mpsm,&mptwoim1,&mpt,p);
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for (i=n-1; i>1; i--) {
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mptwoim1.d[1] -= TWO;
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__dvd(&mpsm,&mptwoim1,&mpt1,p);
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__mul(&mpsm,&mpt,&mpt2,p);
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__sub(&mpt1,&mpt2,&mpt,p);
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}
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__mul(&mps,&mpt,&mpt1,p);
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__sub(&mps,&mpt1,&mpt,p);
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/* Compute Atan(x) */
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mptwoim1.d[1] = 1 << m;
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__mul(&mptwoim1,&mpt,y,p);
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return;
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}
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