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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2014 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: dosincos.c */
/* */
/* */
/* FUNCTIONS: dubsin */
/* dubcos */
/* docos */
/* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h */
/* sincos.tbl */
/* */
/* Routines compute sin() and cos() as Double-Length numbers */
/********************************************************************/
#include "endian.h"
#include "mydefs.h"
#include <dla.h>
#include "dosincos.h"
#include <math_private.h>
#ifndef SECTION
# define SECTION
#endif
extern const union
{
int4 i[880];
double x[440];
} __sincostab attribute_hidden;
/***********************************************************************/
/* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */
/* as Double-Length number and store it at array v .It computes it by */
/* arithmetic action on Double-Length numbers */
/*(x+dx) between 0 and PI/4 */
/***********************************************************************/
void
SECTION
__dubsin (double x, double dx, double v[])
{
double r, s, c, cc, d, dd, d2, dd2, e, ee,
sn, ssn, cs, ccs, ds, dss, dc, dcc;
#ifndef DLA_FMS
double p, hx, tx, hy, ty, q;
#endif
mynumber u;
int4 k;
u.x = x + big.x;
k = u.i[LOW_HALF] << 2;
x = x - (u.x - big.x);
d = x + dx;
dd = (x - d) + dx;
/* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */
MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc);
sn = __sincostab.x[k]; /* */
ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */
cs = __sincostab.x[k + 2]; /* */
ccs = __sincostab.x[k + 3]; /* */
/* Taylor series for sin ds=sin(t) */
MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc);
ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
ADD2 (ds, dss, d, dd, ds, dss, r, s);
/* Taylor series for cos dc=cos(t) */
MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc);
MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
SUB2 (e, ee, dc, dcc, e, ee, r, s);
ADD2 (e, ee, sn, ssn, e, ee, r, s); /* e+ee=sin(x+dx) */
v[0] = e;
v[1] = ee;
}
/**********************************************************************/
/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
/* as Double-Length number and store it in array v .It computes it by */
/* arithmetic action on Double-Length numbers */
/*(x+dx) between 0 and PI/4 */
/**********************************************************************/
void
SECTION
__dubcos (double x, double dx, double v[])
{
double r, s, c, cc, d, dd, d2, dd2, e, ee,
sn, ssn, cs, ccs, ds, dss, dc, dcc;
#ifndef DLA_FMS
double p, hx, tx, hy, ty, q;
#endif
mynumber u;
int4 k;
u.x = x + big.x;
k = u.i[LOW_HALF] << 2;
x = x - (u.x - big.x);
d = x + dx;
dd = (x - d) + dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
MUL2 (d, dd, d, dd, d2, dd2, p, hx, tx, hy, ty, q, c, cc);
sn = __sincostab.x[k]; /* */
ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */
cs = __sincostab.x[k + 2]; /* */
ccs = __sincostab.x[k + 3]; /* */
MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc);
ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
ADD2 (ds, dss, d, dd, ds, dss, r, s);
MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
MUL2 (cs, ccs, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc);
MUL2 (dc, dcc, sn, ssn, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, p, hx, tx, hy, ty, q, c, cc);
ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
MUL2 (d2, dd2, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
MUL2 (d, dd, ds, dss, ds, dss, p, hx, tx, hy, ty, q, c, cc);
ADD2 (ds, dss, d, dd, ds, dss, r, s);
MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
MUL2 (d2, dd2, dc, dcc, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
MUL2 (sn, ssn, ds, dss, e, ee, p, hx, tx, hy, ty, q, c, cc);
MUL2 (dc, dcc, cs, ccs, dc, dcc, p, hx, tx, hy, ty, q, c, cc);
ADD2 (e, ee, dc, dcc, e, ee, r, s);
SUB2 (cs, ccs, e, ee, e, ee, r, s);
v[0] = e;
v[1] = ee;
}
/**********************************************************************/
/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
/* as Double-Length number and store it in array v */
/**********************************************************************/
void
SECTION
__docos (double x, double dx, double v[])
{
double y, yy, p, w[2];
if (x > 0)
{
y = x; yy = dx;
}
else
{
y = -x; yy = -dx;
}
if (y < 0.5 * hp0.x) /* y< PI/4 */
{
__dubcos (y, yy, w); v[0] = w[0]; v[1] = w[1];
}
else if (y < 1.5 * hp0.x) /* y< 3/4 * PI */
{
p = hp0.x - y; /* p = PI/2 - y */
yy = hp1.x - yy;
y = p + yy;
yy = (p - y) + yy;
if (y > 0)
{
__dubsin (y, yy, w); v[0] = w[0]; v[1] = w[1];
}
/* cos(x) = sin ( 90 - x ) */
else
{
__dubsin (-y, -yy, w); v[0] = -w[0]; v[1] = -w[1];
}
}
else /* y>= 3/4 * PI */
{
p = 2.0 * hp0.x - y; /* p = PI- y */
yy = 2.0 * hp1.x - yy;
y = p + yy;
yy = (p - y) + yy;
__dubcos (y, yy, w);
v[0] = -w[0];
v[1] = -w[1];
}
}
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