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