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117 lines
3.4 KiB
C
117 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) 2001-2015 Free Software Foundation, Inc.
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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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#include <math.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
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SECTION
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__mpatan (mp_no *x, mp_no *y, int p)
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{
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int i, m, n;
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double dx;
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mp_no mptwoim1 =
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{
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0,
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{
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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, 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
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}
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};
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mp_no mps, mpsm, mpt, mpt1, mpt2, mpt3;
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/* Choose m and initiate mptwoim1. */
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if (EX > 0)
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m = 7;
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else if (EX < 0)
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m = 0;
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else
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{
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__mp_dbl (x, &dx, p);
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dx = fabs (dx);
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for (m = 6; m > 0; m--)
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{
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if (dx > __atan_xm[m].d)
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break;
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}
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}
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mptwoim1.e = 1;
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mptwoim1.d[0] = 1;
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/* Reduce x m times. */
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__sqr (x, &mpsm, p);
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if (m == 0)
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__cpy (x, &mps, p);
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else
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{
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for (i = 0; i < m; i++)
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{
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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);
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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];
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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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{
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mptwoim1.d[1] -= 2;
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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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}
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