xref: /openbsd/regress/lib/libm/cephes/const.c (revision fc61954a)
1 /*	$OpenBSD: const.c,v 1.1 2011/05/30 20:23:35 martynas Exp $	*/
2 
3 /*
4  * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5  *
6  * Permission to use, copy, modify, and distribute this software for any
7  * purpose with or without fee is hereby granted, provided that the above
8  * copyright notice and this permission notice appear in all copies.
9  *
10  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13  * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15  * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16  * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17  */
18 
19 /*							const.c
20  *
21  *	Globally declared constants
22  *
23  *
24  *
25  * SYNOPSIS:
26  *
27  * extern double nameofconstant;
28  *
29  *
30  *
31  *
32  * DESCRIPTION:
33  *
34  * This file contains a number of mathematical constants and
35  * also some needed size parameters of the computer arithmetic.
36  * The values are supplied as arrays of hexadecimal integers
37  * for IEEE arithmetic; arrays of octal constants for DEC
38  * arithmetic; and in a normal decimal scientific notation for
39  * other machines.  The particular notation used is determined
40  * by a symbol (DEC, IBMPC, or UNK) defined in the include file
41  * mconf.h.
42  *
43  * The default size parameters are as follows.
44  *
45  * For DEC and UNK modes:
46  * MACHEP =  1.38777878078144567553E-17       2**-56
47  * MAXLOG =  8.8029691931113054295988E1       log(2**127)
48  * MINLOG = -8.872283911167299960540E1        log(2**-128)
49  * MAXNUM =  1.701411834604692317316873e38    2**127
50  *
51  * For IEEE arithmetic (IBMPC):
52  * MACHEP =  1.11022302462515654042E-16       2**-53
53  * MAXLOG =  7.09782712893383996843E2         log(2**1024)
54  * MINLOG = -7.08396418532264106224E2         log(2**-1022)
55  * MAXNUM =  1.7976931348623158E308           2**1024
56  *
57  * The global symbols for mathematical constants are
58  * PI     =  3.14159265358979323846           pi
59  * PIO2   =  1.57079632679489661923           pi/2
60  * PIO4   =  7.85398163397448309616E-1        pi/4
61  * SQRT2  =  1.41421356237309504880           sqrt(2)
62  * SQRTH  =  7.07106781186547524401E-1        sqrt(2)/2
63  * LOG2E  =  1.4426950408889634073599         1/log(2)
64  * SQ2OPI =  7.9788456080286535587989E-1      sqrt( 2/pi )
65  * LOGE2  =  6.93147180559945309417E-1        log(2)
66  * LOGSQ2 =  3.46573590279972654709E-1        log(2)/2
67  * THPIO4 =  2.35619449019234492885           3*pi/4
68  * TWOOPI =  6.36619772367581343075535E-1     2/pi
69  *
70  * These lists are subject to change.
71  */
72 
73 #include "mconf.h"
74 
75 #ifdef UNK
76 #if 1
77 double MACHEP =  1.11022302462515654042E-16;   /* 2**-53 */
78 #else
79 double MACHEP =  1.38777878078144567553E-17;   /* 2**-56 */
80 #endif
81 double UFLOWTHRESH =  2.22507385850720138309E-308; /* 2**-1022 */
82 #ifdef DENORMAL
83 double MAXLOG =  7.09782712893383996732E2;     /* log(MAXNUM) */
84 /* double MINLOG = -7.44440071921381262314E2; */     /* log(2**-1074) */
85 double MINLOG = -7.451332191019412076235E2;     /* log(2**-1075) */
86 #else
87 double MAXLOG =  7.08396418532264106224E2;     /* log 2**1022 */
88 double MINLOG = -7.08396418532264106224E2;     /* log 2**-1022 */
89 #endif
90 double MAXNUM =  1.79769313486231570815E308;    /* 2**1024*(1-MACHEP) */
91 double PI     =  3.14159265358979323846;       /* pi */
92 double PIO2   =  1.57079632679489661923;       /* pi/2 */
93 double PIO4   =  7.85398163397448309616E-1;    /* pi/4 */
94 double SQRT2  =  1.41421356237309504880;       /* sqrt(2) */
95 double SQRTH  =  7.07106781186547524401E-1;    /* sqrt(2)/2 */
96 double LOG2E  =  1.4426950408889634073599;     /* 1/log(2) */
97 double SQ2OPI =  7.9788456080286535587989E-1;  /* sqrt( 2/pi ) */
98 double LOGE2  =  6.93147180559945309417E-1;    /* log(2) */
99 double LOGSQ2 =  3.46573590279972654709E-1;    /* log(2)/2 */
100 double THPIO4 =  2.35619449019234492885;       /* 3*pi/4 */
101 double TWOOPI =  6.36619772367581343075535E-1; /* 2/pi */
102 #ifdef INFINITIES
103 double INFINITY = 1.0/0.0;  /* 99e999; */
104 #else
105 double INFINITY =  1.79769313486231570815E308;    /* 2**1024*(1-MACHEP) */
106 #endif
107 #ifdef NANS
108 double NAN = 1.0/0.0 - 1.0/0.0;
109 #else
110 double NAN = 0.0;
111 #endif
112 #ifdef MINUSZERO
113 double NEGZERO = -0.0;
114 #else
115 double NEGZERO = 0.0;
116 #endif
117 #endif
118 
119 #ifdef IBMPC
120 			/* 2**-53 =  1.11022302462515654042E-16 */
121 unsigned short MACHEP[4] = {0x0000,0x0000,0x0000,0x3ca0};
122 unsigned short UFLOWTHRESH[4] = {0x0000,0x0000,0x0000,0x0010};
123 #ifdef DENORMAL
124 			/* log(MAXNUM) =  7.09782712893383996732224E2 */
125 unsigned short MAXLOG[4] = {0x39ef,0xfefa,0x2e42,0x4086};
126 			/* log(2**-1074) = - -7.44440071921381262314E2 */
127 /*unsigned short MINLOG[4] = {0x71c3,0x446d,0x4385,0xc087};*/
128 unsigned short MINLOG[4] = {0x3052,0xd52d,0x4910,0xc087};
129 #else
130 			/* log(2**1022) =   7.08396418532264106224E2 */
131 unsigned short MAXLOG[4] = {0xbcd2,0xdd7a,0x232b,0x4086};
132 			/* log(2**-1022) = - 7.08396418532264106224E2 */
133 unsigned short MINLOG[4] = {0xbcd2,0xdd7a,0x232b,0xc086};
134 #endif
135 			/* 2**1024*(1-MACHEP) =  1.7976931348623158E308 */
136 unsigned short MAXNUM[4] = {0xffff,0xffff,0xffff,0x7fef};
137 unsigned short PI[4]     = {0x2d18,0x5444,0x21fb,0x4009};
138 unsigned short PIO2[4]   = {0x2d18,0x5444,0x21fb,0x3ff9};
139 unsigned short PIO4[4]   = {0x2d18,0x5444,0x21fb,0x3fe9};
140 unsigned short SQRT2[4]  = {0x3bcd,0x667f,0xa09e,0x3ff6};
141 unsigned short SQRTH[4]  = {0x3bcd,0x667f,0xa09e,0x3fe6};
142 unsigned short LOG2E[4]  = {0x82fe,0x652b,0x1547,0x3ff7};
143 unsigned short SQ2OPI[4] = {0x3651,0x33d4,0x8845,0x3fe9};
144 unsigned short LOGE2[4]  = {0x39ef,0xfefa,0x2e42,0x3fe6};
145 unsigned short LOGSQ2[4] = {0x39ef,0xfefa,0x2e42,0x3fd6};
146 unsigned short THPIO4[4] = {0x21d2,0x7f33,0xd97c,0x4002};
147 unsigned short TWOOPI[4] = {0xc883,0x6dc9,0x5f30,0x3fe4};
148 #ifdef INFINITIES
149 unsigned short INFINITY[4] = {0x0000,0x0000,0x0000,0x7ff0};
150 #else
151 unsigned short INFINITY[4] = {0xffff,0xffff,0xffff,0x7fef};
152 #endif
153 #ifdef NANS
154 unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x7ffc};
155 #else
156 unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
157 #endif
158 #ifdef MINUSZERO
159 unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x8000};
160 #else
161 unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
162 #endif
163 #endif
164 
165 #ifdef MIEEE
166 			/* 2**-53 =  1.11022302462515654042E-16 */
167 unsigned short MACHEP[4] = {0x3ca0,0x0000,0x0000,0x0000};
168 unsigned short UFLOWTHRESH[4] = {0x0010,0x0000,0x0000,0x0000};
169 #ifdef DENORMAL
170 			/* log(2**1024) =   7.09782712893383996843E2 */
171 unsigned short MAXLOG[4] = {0x4086,0x2e42,0xfefa,0x39ef};
172 			/* log(2**-1074) = - -7.44440071921381262314E2 */
173 /* unsigned short MINLOG[4] = {0xc087,0x4385,0x446d,0x71c3}; */
174 unsigned short MINLOG[4] = {0xc087,0x4910,0xd52d,0x3052};
175 #else
176 			/* log(2**1022) =  7.08396418532264106224E2 */
177 unsigned short MAXLOG[4] = {0x4086,0x232b,0xdd7a,0xbcd2};
178 			/* log(2**-1022) = - 7.08396418532264106224E2 */
179 unsigned short MINLOG[4] = {0xc086,0x232b,0xdd7a,0xbcd2};
180 #endif
181 			/* 2**1024*(1-MACHEP) =  1.7976931348623158E308 */
182 unsigned short MAXNUM[4] = {0x7fef,0xffff,0xffff,0xffff};
183 unsigned short PI[4]     = {0x4009,0x21fb,0x5444,0x2d18};
184 unsigned short PIO2[4]   = {0x3ff9,0x21fb,0x5444,0x2d18};
185 unsigned short PIO4[4]   = {0x3fe9,0x21fb,0x5444,0x2d18};
186 unsigned short SQRT2[4]  = {0x3ff6,0xa09e,0x667f,0x3bcd};
187 unsigned short SQRTH[4]  = {0x3fe6,0xa09e,0x667f,0x3bcd};
188 unsigned short LOG2E[4]  = {0x3ff7,0x1547,0x652b,0x82fe};
189 unsigned short SQ2OPI[4] = {0x3fe9,0x8845,0x33d4,0x3651};
190 unsigned short LOGE2[4]  = {0x3fe6,0x2e42,0xfefa,0x39ef};
191 unsigned short LOGSQ2[4] = {0x3fd6,0x2e42,0xfefa,0x39ef};
192 unsigned short THPIO4[4] = {0x4002,0xd97c,0x7f33,0x21d2};
193 unsigned short TWOOPI[4] = {0x3fe4,0x5f30,0x6dc9,0xc883};
194 #ifdef INFINITIES
195 unsigned short INFINITY[4] = {0x7ff0,0x0000,0x0000,0x0000};
196 #else
197 unsigned short INFINITY[4] = {0x7fef,0xffff,0xffff,0xffff};
198 #endif
199 #ifdef NANS
200 unsigned short NAN[4] = {0x7ff8,0x0000,0x0000,0x0000};
201 #else
202 unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000};
203 #endif
204 #ifdef MINUSZERO
205 unsigned short NEGZERO[4] = {0x8000,0x0000,0x0000,0x0000};
206 #else
207 unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000};
208 #endif
209 #endif
210 
211 #ifdef DEC
212 			/* 2**-56 =  1.38777878078144567553E-17 */
213 unsigned short MACHEP[4] = {0022200,0000000,0000000,0000000};
214 unsigned short UFLOWTHRESH[4] = {0x0080,0x0000,0x0000,0x0000};
215 			/* log 2**127 = 88.029691931113054295988 */
216 unsigned short MAXLOG[4] = {041660,007463,0143742,025733,};
217 			/* log 2**-128 = -88.72283911167299960540 */
218 unsigned short MINLOG[4] = {0141661,071027,0173721,0147572,};
219 			/* 2**127 = 1.701411834604692317316873e38 */
220 unsigned short MAXNUM[4] = {077777,0177777,0177777,0177777,};
221 unsigned short PI[4]     = {040511,007732,0121041,064302,};
222 unsigned short PIO2[4]   = {040311,007732,0121041,064302,};
223 unsigned short PIO4[4]   = {040111,007732,0121041,064302,};
224 unsigned short SQRT2[4]  = {040265,002363,031771,0157145,};
225 unsigned short SQRTH[4]  = {040065,002363,031771,0157144,};
226 unsigned short LOG2E[4]  = {040270,0125073,024534,013761,};
227 unsigned short SQ2OPI[4] = {040114,041051,0117241,0131204,};
228 unsigned short LOGE2[4]  = {040061,071027,0173721,0147572,};
229 unsigned short LOGSQ2[4] = {037661,071027,0173721,0147572,};
230 unsigned short THPIO4[4] = {040426,0145743,0174631,007222,};
231 unsigned short TWOOPI[4] = {040042,0174603,067116,042025,};
232 /* Approximate infinity by MAXNUM.  */
233 unsigned short INFINITY[4] = {077777,0177777,0177777,0177777,};
234 unsigned short NAN[4] = {0000000,0000000,0000000,0000000};
235 #ifdef MINUSZERO
236 unsigned short NEGZERO[4] = {0000000,0000000,0000000,0100000};
237 #else
238 unsigned short NEGZERO[4] = {0000000,0000000,0000000,0000000};
239 #endif
240 #endif
241 
242 #ifndef UNK
243 extern unsigned short MACHEP[];
244 extern unsigned short UFLOWTHRESH[];
245 extern unsigned short MAXLOG[];
246 extern unsigned short UNDLOG[];
247 extern unsigned short MINLOG[];
248 extern unsigned short MAXNUM[];
249 extern unsigned short PI[];
250 extern unsigned short PIO2[];
251 extern unsigned short PIO4[];
252 extern unsigned short SQRT2[];
253 extern unsigned short SQRTH[];
254 extern unsigned short LOG2E[];
255 extern unsigned short SQ2OPI[];
256 extern unsigned short LOGE2[];
257 extern unsigned short LOGSQ2[];
258 extern unsigned short THPIO4[];
259 extern unsigned short TWOOPI[];
260 extern unsigned short INFINITY[];
261 extern unsigned short NAN[];
262 extern unsigned short NEGZERO[];
263 #endif
264