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
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
|
/* const.c
*
* Globally declared constants
*
*
*
* SYNOPSIS:
*
* extern const double nameofconstant;
*
*
*
*
* DESCRIPTION:
*
* This file contains a number of mathematical constants and
* also some needed size parameters of the computer arithmetic.
* The values are supplied as arrays of hexadecimal integers
* for IEEE arithmetic; arrays of octal constants for DEC
* arithmetic; and in a normal decimal scientific notation for
* other machines. The particular notation used is determined
* by a symbol (DEC, IBMPC, or UNK) defined in the include file
* mconf.h.
*
* The default size parameters are as follows.
*
* For DEC and UNK modes:
* MACHEP = 1.38777878078144567553E-17 2**-56
* MAXLOG = 8.8029691931113054295988E1 log(2**127)
* MINLOG = -8.872283911167299960540E1 log(2**-128)
* MAXNUM = 1.701411834604692317316873e38 2**127
*
* For IEEE arithmetic (IBMPC):
* MACHEP = 1.11022302462515654042E-16 2**-53
* MAXLOG = 7.09782712893383996843E2 log(2**1024)
* MINLOG = -7.08396418532264106224E2 log(2**-1022)
* MAXNUM = 1.7976931348623158E308 2**1024
*
* The global symbols for mathematical constants are
* PI = 3.14159265358979323846 pi
* PIO2 = 1.57079632679489661923 pi/2
* PIO4 = 7.85398163397448309616E-1 pi/4
* SQRT2 = 1.41421356237309504880 sqrt(2)
* SQRTH = 7.07106781186547524401E-1 sqrt(2)/2
* LOG2E = 1.4426950408889634073599 1/log(2)
* SQ2OPI = 7.9788456080286535587989E-1 sqrt( 2/pi )
* LOGE2 = 6.93147180559945309417E-1 log(2)
* LOGSQ2 = 3.46573590279972654709E-1 log(2)/2
* THPIO4 = 2.35619449019234492885 3*pi/4
* TWOOPI = 6.36619772367581343075535E-1 2/pi
*
* These lists are subject to change.
*/
/* const.c */
/*
Cephes Math Library Release 2.3: March, 1995
Copyright 1984, 1995 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
#if 1
const double MACHEP = 1.11022302462515654042E-16; /* 2**-53 */
#else
const double MACHEP = 1.38777878078144567553E-17; /* 2**-56 */
#endif
const double UFLOWTHRESH = 2.22507385850720138309E-308; /* 2**-1022 */
#ifdef DENORMAL
const double MAXLOG = 7.09782712893383996732E2; /* log(MAXNUM) */
/* const double MINLOG = -7.44440071921381262314E2; */ /* log(2**-1074) */
const double MINLOG = -7.451332191019412076235E2; /* log(2**-1075) */
#else
const double MAXLOG = 7.08396418532264106224E2; /* log 2**1022 */
const double MINLOG = -7.08396418532264106224E2; /* log 2**-1022 */
#endif
const double MAXNUM = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */
const double PI = 3.14159265358979323846; /* pi */
const double PIO2 = 1.57079632679489661923; /* pi/2 */
const double PIO4 = 7.85398163397448309616E-1; /* pi/4 */
const double SQRT2 = 1.41421356237309504880; /* sqrt(2) */
const double SQRTH = 7.07106781186547524401E-1; /* sqrt(2)/2 */
const double LOG2E = 1.4426950408889634073599; /* 1/log(2) */
const double SQ2OPI = 7.9788456080286535587989E-1; /* sqrt( 2/pi ) */
const double LOGE2 = 6.93147180559945309417E-1; /* log(2) */
const double LOGSQ2 = 3.46573590279972654709E-1; /* log(2)/2 */
const double THPIO4 = 2.35619449019234492885; /* 3*pi/4 */
const double TWOOPI = 6.36619772367581343075535E-1; /* 2/pi */
#ifdef INFINITIES
const double INFINITY = 1.0/0.0; /* 99e999; */
#else
const double INFINITY = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */
#endif
#ifdef NANS
const double NAN = 1.0/0.0 - 1.0/0.0;
#else
const double NAN = 0.0;
#endif
#ifdef MINUSZERO
const double NEGZERO = -0.0;
#else
const double NEGZERO = 0.0;
#endif
#endif
#ifdef IBMPC
/* 2**-53 = 1.11022302462515654042E-16 */
const unsigned short MACHEP[4] = {0x0000,0x0000,0x0000,0x3ca0};
const unsigned short UFLOWTHRESH[4] = {0x0000,0x0000,0x0000,0x0010};
#ifdef DENORMAL
/* log(MAXNUM) = 7.09782712893383996732224E2 */
const unsigned short MAXLOG[4] = {0x39ef,0xfefa,0x2e42,0x4086};
/* log(2**-1074) = - -7.44440071921381262314E2 */
/*const unsigned short MINLOG[4] = {0x71c3,0x446d,0x4385,0xc087};*/
const unsigned short MINLOG[4] = {0x3052,0xd52d,0x4910,0xc087};
#else
/* log(2**1022) = 7.08396418532264106224E2 */
const unsigned short MAXLOG[4] = {0xbcd2,0xdd7a,0x232b,0x4086};
/* log(2**-1022) = - 7.08396418532264106224E2 */
const unsigned short MINLOG[4] = {0xbcd2,0xdd7a,0x232b,0xc086};
#endif
/* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */
const unsigned short MAXNUM[4] = {0xffff,0xffff,0xffff,0x7fef};
const unsigned short PI[4] = {0x2d18,0x5444,0x21fb,0x4009};
const unsigned short PIO2[4] = {0x2d18,0x5444,0x21fb,0x3ff9};
const unsigned short PIO4[4] = {0x2d18,0x5444,0x21fb,0x3fe9};
const unsigned short SQRT2[4] = {0x3bcd,0x667f,0xa09e,0x3ff6};
const unsigned short SQRTH[4] = {0x3bcd,0x667f,0xa09e,0x3fe6};
const unsigned short LOG2E[4] = {0x82fe,0x652b,0x1547,0x3ff7};
const unsigned short SQ2OPI[4] = {0x3651,0x33d4,0x8845,0x3fe9};
const unsigned short LOGE2[4] = {0x39ef,0xfefa,0x2e42,0x3fe6};
const unsigned short LOGSQ2[4] = {0x39ef,0xfefa,0x2e42,0x3fd6};
const unsigned short THPIO4[4] = {0x21d2,0x7f33,0xd97c,0x4002};
const unsigned short TWOOPI[4] = {0xc883,0x6dc9,0x5f30,0x3fe4};
#ifdef INFINITIES
const unsigned short INFINITY[4] = {0x0000,0x0000,0x0000,0x7ff0};
#else
const unsigned short INFINITY[4] = {0xffff,0xffff,0xffff,0x7fef};
#endif
#ifdef NANS
const unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x7ffc};
#else
const unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
#endif
#ifdef MINUSZERO
const unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x8000};
#else
const unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
#endif
#endif
#ifdef MIEEE
/* 2**-53 = 1.11022302462515654042E-16 */
const unsigned short MACHEP[4] = {0x3ca0,0x0000,0x0000,0x0000};
const unsigned short UFLOWTHRESH[4] = {0x0010,0x0000,0x0000,0x0000};
#ifdef DENORMAL
/* log(2**1024) = 7.09782712893383996843E2 */
const unsigned short MAXLOG[4] = {0x4086,0x2e42,0xfefa,0x39ef};
/* log(2**-1074) = - -7.44440071921381262314E2 */
/* const unsigned short MINLOG[4] = {0xc087,0x4385,0x446d,0x71c3}; */
const unsigned short MINLOG[4] = {0xc087,0x4910,0xd52d,0x3052};
#else
/* log(2**1022) = 7.08396418532264106224E2 */
const unsigned short MAXLOG[4] = {0x4086,0x232b,0xdd7a,0xbcd2};
/* log(2**-1022) = - 7.08396418532264106224E2 */
const unsigned short MINLOG[4] = {0xc086,0x232b,0xdd7a,0xbcd2};
#endif
/* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */
const unsigned short MAXNUM[4] = {0x7fef,0xffff,0xffff,0xffff};
const unsigned short PI[4] = {0x4009,0x21fb,0x5444,0x2d18};
const unsigned short PIO2[4] = {0x3ff9,0x21fb,0x5444,0x2d18};
const unsigned short PIO4[4] = {0x3fe9,0x21fb,0x5444,0x2d18};
const unsigned short SQRT2[4] = {0x3ff6,0xa09e,0x667f,0x3bcd};
const unsigned short SQRTH[4] = {0x3fe6,0xa09e,0x667f,0x3bcd};
const unsigned short LOG2E[4] = {0x3ff7,0x1547,0x652b,0x82fe};
const unsigned short SQ2OPI[4] = {0x3fe9,0x8845,0x33d4,0x3651};
const unsigned short LOGE2[4] = {0x3fe6,0x2e42,0xfefa,0x39ef};
const unsigned short LOGSQ2[4] = {0x3fd6,0x2e42,0xfefa,0x39ef};
const unsigned short THPIO4[4] = {0x4002,0xd97c,0x7f33,0x21d2};
const unsigned short TWOOPI[4] = {0x3fe4,0x5f30,0x6dc9,0xc883};
#ifdef INFINITIES
const unsigned short INFINITY[4] = {0x7ff0,0x0000,0x0000,0x0000};
#else
const unsigned short INFINITY[4] = {0x7fef,0xffff,0xffff,0xffff};
#endif
#ifdef NANS
const unsigned short NAN[4] = {0x7ff8,0x0000,0x0000,0x0000};
#else
const unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
#endif
#ifdef MINUSZERO
const unsigned short NEGZERO[4] = {0x8000,0x0000,0x0000,0x0000};
#else
const unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
#endif
#endif
#ifdef DEC
/* 2**-56 = 1.38777878078144567553E-17 */
const unsigned short MACHEP[4] = {0022200,0000000,0000000,0000000};
const unsigned short UFLOWTHRESH[4] = {0x0080,0x0000,0x0000,0x0000};
/* log 2**127 = 88.029691931113054295988 */
const unsigned short MAXLOG[4] = {041660,007463,0143742,025733,};
/* log 2**-128 = -88.72283911167299960540 */
const unsigned short MINLOG[4] = {0141661,071027,0173721,0147572,};
/* 2**127 = 1.701411834604692317316873e38 */
const unsigned short MAXNUM[4] = {077777,0177777,0177777,0177777,};
const unsigned short PI[4] = {040511,007732,0121041,064302,};
const unsigned short PIO2[4] = {040311,007732,0121041,064302,};
const unsigned short PIO4[4] = {040111,007732,0121041,064302,};
const unsigned short SQRT2[4] = {040265,002363,031771,0157145,};
const unsigned short SQRTH[4] = {040065,002363,031771,0157144,};
const unsigned short LOG2E[4] = {040270,0125073,024534,013761,};
const unsigned short SQ2OPI[4] = {040114,041051,0117241,0131204,};
const unsigned short LOGE2[4] = {040061,071027,0173721,0147572,};
const unsigned short LOGSQ2[4] = {037661,071027,0173721,0147572,};
const unsigned short THPIO4[4] = {040426,0145743,0174631,007222,};
const unsigned short TWOOPI[4] = {040042,0174603,067116,042025,};
/* Approximate infinity by MAXNUM. */
const unsigned short INFINITY[4] = {077777,0177777,0177777,0177777,};
const unsigned short NAN[4] = {0000000,0000000,0000000,0000000};
#ifdef MINUSZERO
const unsigned short NEGZERO[4] = {0000000,0000000,0000000,0100000};
#else
const unsigned short NEGZERO[4] = {0000000,0000000,0000000,0000000};
#endif
#endif
#ifndef UNK
extern const unsigned short MACHEP[];
extern const unsigned short UFLOWTHRESH[];
extern const unsigned short MAXLOG[];
extern const unsigned short UNDLOG[];
extern const unsigned short MINLOG[];
extern const unsigned short MAXNUM[];
extern const unsigned short PI[];
extern const unsigned short PIO2[];
extern const unsigned short PIO4[];
extern const unsigned short SQRT2[];
extern const unsigned short SQRTH[];
extern const unsigned short LOG2E[];
extern const unsigned short SQ2OPI[];
extern const unsigned short LOGE2[];
extern const unsigned short LOGSQ2[];
extern const unsigned short THPIO4[];
extern const unsigned short TWOOPI[];
extern const unsigned short INFINITY[];
extern const unsigned short NAN[];
extern const unsigned short NEGZERO[];
#endif
|
