1/*
2 * IBM Accurate Mathematical Library
3 * written by International Business Machines Corp.
4 * Copyright (C) 2001-2020 Free Software Foundation, Inc.
5 *
6 * This program is free software; you can redistribute it and/or modify
7 * it under the terms of the GNU Lesser General Public License as published by
8 * the Free Software Foundation; either version 2.1 of the License, or
9 * (at your option) any later version.
10 *
11 * This program is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 * GNU Lesser General Public License for more details.
15 *
16 * You should have received a copy of the GNU Lesser General Public License
17 * along with this program; if not, see <https://www.gnu.org/licenses/>.
18 */
19/********************************************************************/
20/* */
21/* MODULE_NAME: dosincos.c */
22/* */
23/* */
24/* FUNCTIONS: dubsin */
25/* dubcos */
26/* docos */
27/* FILES NEEDED: endian.h mydefs.h dla.h dosincos.h */
28/* sincos.tbl */
29/* */
30/* Routines compute sin() and cos() as Double-Length numbers */
31/********************************************************************/
32
33
34
35#include "endian.h"
36#include "mydefs.h"
37#include <dla.h>
38#include "dosincos.h"
39#include <math_private.h>
40
41#ifndef SECTION
42# define SECTION
43#endif
44
45extern const union
46{
47 int4 i[880];
48 double x[440];
49} __sincostab attribute_hidden;
50
51/***********************************************************************/
52/* Routine receive Double-Length number (x+dx) and computing sin(x+dx) */
53/* as Double-Length number and store it at array v .It computes it by */
54/* arithmetic action on Double-Length numbers */
55/*(x+dx) between 0 and PI/4 */
56/***********************************************************************/
57
58void
59SECTION
60__dubsin (double x, double dx, double v[])
61{
62 double r, s, c, cc, d, dd, d2, dd2, e, ee,
63 sn, ssn, cs, ccs, ds, dss, dc, dcc;
64 mynumber u;
65 int4 k;
66
67 u.x = x + big.x;
68 k = u.i[LOW_HALF] << 2;
69 x = x - (u.x - big.x);
70 d = x + dx;
71 dd = (x - d) + dx;
72 /* sin(x+dx)=sin(Xi+t)=sin(Xi)*cos(t) + cos(Xi)sin(t) where t ->0 */
73 MUL2 (d, dd, d, dd, d2, dd2, c, cc);
74 sn = __sincostab.x[k]; /* */
75 ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */
76 cs = __sincostab.x[k + 2]; /* */
77 ccs = __sincostab.x[k + 3]; /* */
78 /* Taylor series for sin ds=sin(t) */
79 MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, c, cc);
80 ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
81 MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
82 ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
83 MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
84 MUL2 (d, dd, ds, dss, ds, dss, c, cc);
85 ADD2 (ds, dss, d, dd, ds, dss, r, s);
86
87 /* Taylor series for cos dc=cos(t) */
88 MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, c, cc);
89 ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
90 MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
91 ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
92 MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
93 ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
94 MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
95
96 MUL2 (cs, ccs, ds, dss, e, ee, c, cc);
97 MUL2 (dc, dcc, sn, ssn, dc, dcc, c, cc);
98 SUB2 (e, ee, dc, dcc, e, ee, r, s);
99 ADD2 (e, ee, sn, ssn, e, ee, r, s); /* e+ee=sin(x+dx) */
100
101 v[0] = e;
102 v[1] = ee;
103}
104/**********************************************************************/
105/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
106/* as Double-Length number and store it in array v .It computes it by */
107/* arithmetic action on Double-Length numbers */
108/*(x+dx) between 0 and PI/4 */
109/**********************************************************************/
110
111void
112SECTION
113__dubcos (double x, double dx, double v[])
114{
115 double r, s, c, cc, d, dd, d2, dd2, e, ee,
116 sn, ssn, cs, ccs, ds, dss, dc, dcc;
117 mynumber u;
118 int4 k;
119 u.x = x + big.x;
120 k = u.i[LOW_HALF] << 2;
121 x = x - (u.x - big.x);
122 d = x + dx;
123 dd = (x - d) + dx; /* cos(x+dx)=cos(Xi+t)=cos(Xi)cos(t) - sin(Xi)sin(t) */
124 MUL2 (d, dd, d, dd, d2, dd2, c, cc);
125 sn = __sincostab.x[k]; /* */
126 ssn = __sincostab.x[k + 1]; /* sin(Xi) and cos(Xi) */
127 cs = __sincostab.x[k + 2]; /* */
128 ccs = __sincostab.x[k + 3]; /* */
129 MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, c, cc);
130 ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
131 MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
132 ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
133 MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
134 MUL2 (d, dd, ds, dss, ds, dss, c, cc);
135 ADD2 (ds, dss, d, dd, ds, dss, r, s);
136
137 MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, c, cc);
138 ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
139 MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
140 ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
141 MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
142 ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
143 MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
144
145 MUL2 (cs, ccs, ds, dss, e, ee, c, cc);
146 MUL2 (dc, dcc, sn, ssn, dc, dcc, c, cc);
147
148 MUL2 (d2, dd2, s7.x, ss7.x, ds, dss, c, cc);
149 ADD2 (ds, dss, s5.x, ss5.x, ds, dss, r, s);
150 MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
151 ADD2 (ds, dss, s3.x, ss3.x, ds, dss, r, s);
152 MUL2 (d2, dd2, ds, dss, ds, dss, c, cc);
153 MUL2 (d, dd, ds, dss, ds, dss, c, cc);
154 ADD2 (ds, dss, d, dd, ds, dss, r, s);
155 MUL2 (d2, dd2, c8.x, cc8.x, dc, dcc, c, cc);
156 ADD2 (dc, dcc, c6.x, cc6.x, dc, dcc, r, s);
157 MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
158 ADD2 (dc, dcc, c4.x, cc4.x, dc, dcc, r, s);
159 MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
160 ADD2 (dc, dcc, c2.x, cc2.x, dc, dcc, r, s);
161 MUL2 (d2, dd2, dc, dcc, dc, dcc, c, cc);
162 MUL2 (sn, ssn, ds, dss, e, ee, c, cc);
163 MUL2 (dc, dcc, cs, ccs, dc, dcc, c, cc);
164 ADD2 (e, ee, dc, dcc, e, ee, r, s);
165 SUB2 (cs, ccs, e, ee, e, ee, r, s);
166
167 v[0] = e;
168 v[1] = ee;
169}
170/**********************************************************************/
171/* Routine receive Double-Length number (x+dx) and computes cos(x+dx) */
172/* as Double-Length number and store it in array v */
173/**********************************************************************/
174void
175SECTION
176__docos (double x, double dx, double v[])
177{
178 double y, yy, p, w[2];
179 if (x > 0)
180 {
181 y = x; yy = dx;
182 }
183 else
184 {
185 y = -x; yy = -dx;
186 }
187 if (y < 0.5 * hp0.x) /* y< PI/4 */
188 {
189 __dubcos (y, yy, w); v[0] = w[0]; v[1] = w[1];
190 }
191 else if (y < 1.5 * hp0.x) /* y< 3/4 * PI */
192 {
193 p = hp0.x - y; /* p = PI/2 - y */
194 yy = hp1.x - yy;
195 y = p + yy;
196 yy = (p - y) + yy;
197 if (y > 0)
198 {
199 __dubsin (y, yy, w); v[0] = w[0]; v[1] = w[1];
200 }
201 /* cos(x) = sin ( 90 - x ) */
202 else
203 {
204 __dubsin (-y, -yy, w); v[0] = -w[0]; v[1] = -w[1];
205 }
206 }
207 else /* y>= 3/4 * PI */
208 {
209 p = 2.0 * hp0.x - y; /* p = PI- y */
210 yy = 2.0 * hp1.x - yy;
211 y = p + yy;
212 yy = (p - y) + yy;
213 __dubcos (y, yy, w);
214 v[0] = -w[0];
215 v[1] = -w[1];
216 }
217}
218