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224 lines
8.4 KiB
C
224 lines
8.4 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) 2001-2017 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: dosincos.c */
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/* */
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/* */
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/* FUNCTIONS: dubsin */
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/* dubcos */
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/* docos */
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/* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h */
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/* sincos.tbl */
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/* */
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/* Routines compute sin() and cos() as Double-Length numbers */
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/********************************************************************/
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#include "endian.h"
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#include "mydefs.h"
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#include <dla.h>
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#include "dosincos.h"
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#include <math_private.h>
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#ifndef SECTION
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# define SECTION
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#endif
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extern const union
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{
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int4 i[880];
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double x[440];
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} __sincostab attribute_hidden;
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/***********************************************************************/
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/* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */
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/* as Double-Length number and store it at array v .It computes it by */
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/* arithmetic action on Double-Length numbers */
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/*(x+dx) between 0 and PI/4 */
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/***********************************************************************/
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void
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SECTION
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__dubsin (double x, double dx, double v[])
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{
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double r, s, c, cc, d, dd, d2, dd2, e, ee,
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sn, ssn, cs, ccs, ds, dss, dc, dcc;
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#ifndef DLA_FMS
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double p, hx, tx, hy, ty, q;
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#endif
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mynumber u;
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int4 k;
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u.x = x + big.x;
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k = u.i[LOW_HALF] << 2;
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x = x - (u.x - big.x);
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d = x + dx;
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dd = (x - d) + dx;
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/* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */
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MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc);
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sn = __sincostab.x[k]; /* */
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ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */
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cs = __sincostab.x[k + 2]; /* */
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ccs = __sincostab.x[k + 3]; /* */
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/* Taylor series for sin ds=sin(t) */
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MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
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MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
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MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (ds, dss, d, dd, ds, dss, r, s);
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/* Taylor series for cos dc=cos(t) */
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MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
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MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
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MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
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MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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SUB2 (e, ee, dc, dcc, e, ee, r, s);
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ADD2 (e, ee, sn, ssn, e, ee, r, s); /* e+ee=sin(x+dx) */
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v[0] = e;
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v[1] = ee;
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}
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/**********************************************************************/
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/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
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/* as Double-Length number and store it in array v .It computes it by */
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/* arithmetic action on Double-Length numbers */
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/*(x+dx) between 0 and PI/4 */
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/**********************************************************************/
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void
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SECTION
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__dubcos (double x, double dx, double v[])
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{
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double r, s, c, cc, d, dd, d2, dd2, e, ee,
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sn, ssn, cs, ccs, ds, dss, dc, dcc;
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#ifndef DLA_FMS
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double p, hx, tx, hy, ty, q;
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#endif
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mynumber u;
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int4 k;
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u.x = x + big.x;
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k = u.i[LOW_HALF] << 2;
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x = x - (u.x - big.x);
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d = x + dx;
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dd = (x - d) + dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
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MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc);
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sn = __sincostab.x[k]; /* */
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ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */
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cs = __sincostab.x[k + 2]; /* */
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ccs = __sincostab.x[k + 3]; /* */
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MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
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MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
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MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (ds, dss, d, dd, ds, dss, r, s);
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MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
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MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
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MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
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MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
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MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
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MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (ds, dss, d, dd, ds, dss, r, s);
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MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
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MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
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MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
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MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (sn, ssn, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc);
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MUL2 (dc, dcc, cs, ccs, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
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ADD2 (e, ee, dc, dcc, e, ee, r, s);
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SUB2 (cs, ccs, e, ee, e, ee, r, s);
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v[0] = e;
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v[1] = ee;
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}
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/**********************************************************************/
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/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
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/* as Double-Length number and store it in array v */
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/**********************************************************************/
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void
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SECTION
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__docos (double x, double dx, double v[])
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{
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double y, yy, p, w[2];
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if (x > 0)
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{
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y = x; yy = dx;
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}
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else
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{
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y = -x; yy = -dx;
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}
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if (y < 0.5 * hp0.x) /* y< PI/4 */
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{
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__dubcos (y, yy, w); v[0] = w[0]; v[1] = w[1];
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}
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else if (y < 1.5 * hp0.x) /* y< 3/4 * PI */
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{
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p = hp0.x - y; /* p = PI/2 - y */
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yy = hp1.x - yy;
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y = p + yy;
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yy = (p - y) + yy;
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if (y > 0)
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{
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__dubsin (y, yy, w); v[0] = w[0]; v[1] = w[1];
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}
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/* cos(x) = sin ( 90 - x ) */
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else
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{
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__dubsin (-y, -yy, w); v[0] = -w[0]; v[1] = -w[1];
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}
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}
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else /* y>= 3/4 * PI */
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{
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p = 2.0 * hp0.x - y; /* p = PI- y */
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yy = 2.0 * hp1.x - yy;
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y = p + yy;
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yy = (p - y) + yy;
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__dubcos (y, yy, w);
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v[0] = -w[0];
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v[1] = -w[1];
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}
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}
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