1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
|
/*
* M_APM - mapmrsin.c
*
* Copyright (C) 1999 - 2007 Michael C. Ring
*
* Permission to use, copy, and distribute this software and its
* documentation for any purpose with or without fee is hereby granted,
* provided that the above copyright notice appear in all copies and
* that both that copyright notice and this permission notice appear
* in supporting documentation.
*
* Permission to modify the software is granted. Permission to distribute
* the modified code is granted. Modifications are to be distributed by
* using the file 'license.txt' as a template to modify the file header.
* 'license.txt' is available in the official MAPM distribution.
*
* This software is provided "as is" without express or implied warranty.
*/
/*
*
* This file contains the basic series expansion functions for
* the SIN / COS functions.
*/
#include "pgAdmin3.h"
#include "pgscript/utilities/mapm-lib/m_apm_lc.h"
/****************************************************************************/
/*
x^3 x^5 x^7 x^9
sin(x) = x - --- + --- - --- + --- ...
3! 5! 7! 9!
*/
void M_raw_sin(M_APM rr, int places, M_APM xx)
{
M_APM sum, term, tmp2, tmp7, tmp8;
int tolerance, flag, local_precision, dplaces;
long m1, m2;
sum = M_get_stack_var();
term = M_get_stack_var();
tmp2 = M_get_stack_var();
tmp7 = M_get_stack_var();
tmp8 = M_get_stack_var();
m_apm_copy(sum, xx);
m_apm_copy(term, xx);
m_apm_multiply(tmp8, xx, xx);
m_apm_round(tmp2, (places + 6), tmp8);
dplaces = (places + 8) - xx->m_apm_exponent;
tolerance = xx->m_apm_exponent - (places + 4);
m1 = 2L;
flag = 0;
while (TRUE)
{
m_apm_multiply(tmp8, term, tmp2);
if ((tmp8->m_apm_exponent < tolerance) || (tmp8->m_apm_sign == 0))
break;
local_precision = dplaces + term->m_apm_exponent;
if (local_precision < 20)
local_precision = 20;
m2 = m1 * (m1 + 1);
m_apm_set_long(tmp7, m2);
m_apm_divide(term, local_precision, tmp8, tmp7);
if (flag == 0)
{
m_apm_subtract(tmp7, sum, term);
m_apm_copy(sum, tmp7);
}
else
{
m_apm_add(tmp7, sum, term);
m_apm_copy(sum, tmp7);
}
m1 += 2;
flag = 1 - flag;
}
m_apm_round(rr, places, sum);
M_restore_stack(5);
}
/****************************************************************************/
/*
x^2 x^4 x^6 x^8
cos(x) = 1 - --- + --- - --- + --- ...
2! 4! 6! 8!
*/
void M_raw_cos(M_APM rr, int places, M_APM xx)
{
M_APM sum, term, tmp7, tmp8, tmp9;
int tolerance, flag, local_precision, prev_exp;
long m1, m2;
sum = M_get_stack_var();
term = M_get_stack_var();
tmp7 = M_get_stack_var();
tmp8 = M_get_stack_var();
tmp9 = M_get_stack_var();
m_apm_copy(sum, MM_One);
m_apm_copy(term, MM_One);
m_apm_multiply(tmp8, xx, xx);
m_apm_round(tmp9, (places + 6), tmp8);
local_precision = places + 8;
tolerance = -(places + 4);
prev_exp = 0;
m1 = 1L;
flag = 0;
while (TRUE)
{
m2 = m1 * (m1 + 1);
m_apm_set_long(tmp7, m2);
m_apm_multiply(tmp8, term, tmp9);
m_apm_divide(term, local_precision, tmp8, tmp7);
if (flag == 0)
{
m_apm_subtract(tmp7, sum, term);
m_apm_copy(sum, tmp7);
}
else
{
m_apm_add(tmp7, sum, term);
m_apm_copy(sum, tmp7);
}
if ((term->m_apm_exponent < tolerance) || (term->m_apm_sign == 0))
break;
if (m1 != 1L)
{
local_precision = local_precision + term->m_apm_exponent - prev_exp;
if (local_precision < 20)
local_precision = 20;
}
prev_exp = term->m_apm_exponent;
m1 += 2;
flag = 1 - flag;
}
m_apm_round(rr, places, sum);
M_restore_stack(5);
}
/****************************************************************************/
|
