1
2 /*
3 * M_APM - mapm5sin.c
4 *
5 * Copyright (C) 1999 - 2007 Michael C. Ring
6 *
7 * Permission to use, copy, and distribute this software and its
8 * documentation for any purpose with or without fee is hereby granted,
9 * provided that the above copyright notice appear in all copies and
10 * that both that copyright notice and this permission notice appear
11 * in supporting documentation.
12 *
13 * Permission to modify the software is granted. Permission to distribute
14 * the modified code is granted. Modifications are to be distributed by
15 * using the file 'license.txt' as a template to modify the file header.
16 * 'license.txt' is available in the official MAPM distribution.
17 *
18 * This software is provided "as is" without express or implied warranty.
19 */
20
21 /*
22 * $Id: mapm5sin.c,v 1.10 2007/12/03 01:26:16 mike Exp $
23 *
24 * This file contains the functions that implement the sin (5x)
25 * and cos (4x) multiple angle relations
26 *
27 * $Log: mapm5sin.c,v $
28 * Revision 1.10 2007/12/03 01:26:16 mike
29 * Update license
30 *
31 * Revision 1.9 2002/11/03 21:50:36 mike
32 * Updated function parameters to use the modern style
33 *
34 * Revision 1.8 2001/03/25 20:57:03 mike
35 * move cos_to_sin func in here
36 *
37 * Revision 1.7 2000/05/04 23:50:21 mike
38 * use multiple angle identity 4 times of larger COS angles
39 *
40 * Revision 1.6 1999/06/30 00:08:53 mike
41 * pass more decimal places to raw functions
42 *
43 * Revision 1.5 1999/06/20 23:41:32 mike
44 * changed COS to use 4x multiple angle identity instead of 5x
45 *
46 * Revision 1.4 1999/06/20 19:42:26 mike
47 * tweak number of dec places passed to sub-functions
48 *
49 * Revision 1.3 1999/06/20 19:03:56 mike
50 * changed local static variables to MAPM stack variables
51 *
52 * Revision 1.2 1999/05/12 21:30:09 mike
53 * replace local 5.0 with global
54 *
55 * Revision 1.1 1999/05/10 20:56:31 mike
56 * Initial revision
57 */
58
59 #include "m_apm_lc.h"
60
61 /****************************************************************************/
M_5x_sin(M_APM r,int places,M_APM x)62 void M_5x_sin(M_APM r, int places, M_APM x)
63 {
64 M_APM tmp8, tmp9;
65
66 tmp8 = M_get_stack_var();
67 tmp9 = M_get_stack_var();
68
69 m_apm_multiply(tmp9, x, MM_5x_125R); /* 1 / (5*5*5) */
70 M_raw_sin(tmp8, (places + 6), tmp9);
71 M_5x_do_it(tmp9, (places + 4), tmp8);
72 M_5x_do_it(tmp8, (places + 4), tmp9);
73 M_5x_do_it(r, places, tmp8);
74
75 M_restore_stack(2);
76 }
77 /****************************************************************************/
M_4x_cos(M_APM r,int places,M_APM x)78 void M_4x_cos(M_APM r, int places, M_APM x)
79 {
80 M_APM tmp8, tmp9;
81
82 tmp8 = M_get_stack_var();
83 tmp9 = M_get_stack_var();
84
85 /*
86 * if |x| >= 1.0 use multiple angle identity 4 times
87 * if |x| < 1.0 use multiple angle identity 3 times
88 */
89
90 if (x->m_apm_exponent > 0)
91 {
92 m_apm_multiply(tmp9, x, MM_5x_256R); /* 1 / (4*4*4*4) */
93 M_raw_cos(tmp8, (places + 8), tmp9);
94 M_4x_do_it(tmp9, (places + 8), tmp8);
95 M_4x_do_it(tmp8, (places + 6), tmp9);
96 M_4x_do_it(tmp9, (places + 4), tmp8);
97 M_4x_do_it(r, places, tmp9);
98 }
99 else
100 {
101 m_apm_multiply(tmp9, x, MM_5x_64R); /* 1 / (4*4*4) */
102 M_raw_cos(tmp8, (places + 6), tmp9);
103 M_4x_do_it(tmp9, (places + 4), tmp8);
104 M_4x_do_it(tmp8, (places + 4), tmp9);
105 M_4x_do_it(r, places, tmp8);
106 }
107
108 M_restore_stack(2);
109 }
110 /****************************************************************************/
111 /*
112 * calculate the multiple angle identity for sin (5x)
113 *
114 * sin (5x) == 16 * sin^5 (x) - 20 * sin^3 (x) + 5 * sin(x)
115 */
M_5x_do_it(M_APM rr,int places,M_APM xx)116 void M_5x_do_it(M_APM rr, int places, M_APM xx)
117 {
118 M_APM tmp0, tmp1, t2, t3, t5;
119
120 tmp0 = M_get_stack_var();
121 tmp1 = M_get_stack_var();
122 t2 = M_get_stack_var();
123 t3 = M_get_stack_var();
124 t5 = M_get_stack_var();
125
126 m_apm_multiply(tmp1, xx, xx);
127 m_apm_round(t2, (places + 4), tmp1); /* x ^ 2 */
128
129 m_apm_multiply(tmp1, t2, xx);
130 m_apm_round(t3, (places + 4), tmp1); /* x ^ 3 */
131
132 m_apm_multiply(t5, t2, t3); /* x ^ 5 */
133
134 m_apm_multiply(tmp0, xx, MM_Five);
135 m_apm_multiply(tmp1, t5, MM_5x_Sixteen);
136 m_apm_add(t2, tmp0, tmp1);
137 m_apm_multiply(tmp1, t3, MM_5x_Twenty);
138 m_apm_subtract(tmp0, t2, tmp1);
139
140 m_apm_round(rr, places, tmp0);
141 M_restore_stack(5);
142 }
143 /****************************************************************************/
144 /*
145 * calculate the multiple angle identity for cos (4x)
146 *
147 * cos (4x) == 8 * [ cos^4 (x) - cos^2 (x) ] + 1
148 */
M_4x_do_it(M_APM rr,int places,M_APM xx)149 void M_4x_do_it(M_APM rr, int places, M_APM xx)
150 {
151 M_APM tmp0, tmp1, t2, t4;
152
153 tmp0 = M_get_stack_var();
154 tmp1 = M_get_stack_var();
155 t2 = M_get_stack_var();
156 t4 = M_get_stack_var();
157
158 m_apm_multiply(tmp1, xx, xx);
159 m_apm_round(t2, (places + 4), tmp1); /* x ^ 2 */
160 m_apm_multiply(t4, t2, t2); /* x ^ 4 */
161
162 m_apm_subtract(tmp0, t4, t2);
163 m_apm_multiply(tmp1, tmp0, MM_5x_Eight);
164 m_apm_add(tmp0, MM_One, tmp1);
165 m_apm_round(rr, places, tmp0);
166 M_restore_stack(4);
167 }
168 /****************************************************************************/
169 /*
170 * compute r = sqrt(1 - a ^ 2).
171 */
M_cos_to_sin(M_APM r,int places,M_APM a)172 void M_cos_to_sin(M_APM r, int places, M_APM a)
173 {
174 M_APM tmp1, tmp2;
175
176 tmp1 = M_get_stack_var();
177 tmp2 = M_get_stack_var();
178
179 m_apm_multiply(tmp1, a, a);
180 m_apm_subtract(tmp2, MM_One, tmp1);
181 m_apm_sqrt(r, places, tmp2);
182 M_restore_stack(2);
183 }
184 /****************************************************************************/
185