[431c9e0] | 1 | /* const.c |
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| 2 | * |
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| 3 | * Globally declared constants |
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| 4 | * |
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| 5 | * |
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| 6 | * |
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| 7 | * SYNOPSIS: |
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| 8 | * |
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| 9 | * extern double nameofconstant; |
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| 10 | * |
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| 11 | * |
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| 12 | * |
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| 13 | * |
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| 14 | * DESCRIPTION: |
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| 15 | * |
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| 16 | * This file contains a number of mathematical constants and |
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| 17 | * also some needed size parameters of the computer arithmetic. |
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| 18 | * The values are supplied as arrays of hexadecimal integers |
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| 19 | * for IEEE arithmetic; arrays of octal constants for DEC |
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| 20 | * arithmetic; and in a normal decimal scientific notation for |
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| 21 | * other machines. The particular notation used is determined |
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| 22 | * by a symbol (DEC, IBMPC, or UNK) defined in the include file |
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| 23 | * mconf.h. |
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| 24 | * |
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| 25 | * The default size parameters are as follows. |
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| 26 | * |
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| 27 | * For DEC and UNK modes: |
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| 28 | * MACHEP = 1.38777878078144567553E-17 2**-56 |
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| 29 | * MAXLOG = 8.8029691931113054295988E1 log(2**127) |
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| 30 | * MINLOG = -8.872283911167299960540E1 log(2**-128) |
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| 31 | * MAXNUM = 1.701411834604692317316873e38 2**127 |
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| 32 | * |
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| 33 | * For IEEE arithmetic (IBMPC): |
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| 34 | * MACHEP = 1.11022302462515654042E-16 2**-53 |
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| 35 | * MAXLOG = 7.09782712893383996843E2 log(2**1024) |
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| 36 | * MINLOG = -7.08396418532264106224E2 log(2**-1022) |
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| 37 | * MAXNUM = 1.7976931348623158E308 2**1024 |
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| 38 | * |
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| 39 | * The global symbols for mathematical constants are |
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| 40 | * PI = 3.14159265358979323846 pi |
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| 41 | * PIO2 = 1.57079632679489661923 pi/2 |
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| 42 | * PIO4 = 7.85398163397448309616E-1 pi/4 |
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| 43 | * SQRT2 = 1.41421356237309504880 sqrt(2) |
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| 44 | * SQRTH = 7.07106781186547524401E-1 sqrt(2)/2 |
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| 45 | * LOG2E = 1.4426950408889634073599 1/log(2) |
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| 46 | * SQ2OPI = 7.9788456080286535587989E-1 sqrt( 2/pi ) |
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| 47 | * LOGE2 = 6.93147180559945309417E-1 log(2) |
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| 48 | * LOGSQ2 = 3.46573590279972654709E-1 log(2)/2 |
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| 49 | * THPIO4 = 2.35619449019234492885 3*pi/4 |
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| 50 | * TWOOPI = 6.36619772367581343075535E-1 2/pi |
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| 51 | * |
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| 52 | * These lists are subject to change. |
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| 53 | */ |
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| 54 | |
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| 55 | /* const.c */ |
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| 56 | |
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| 57 | /* |
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| 58 | Cephes Math Library Release 2.3: March, 1995 |
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| 59 | Copyright 1984, 1995 by Stephen L. Moshier |
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| 60 | */ |
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| 61 | |
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| 62 | #include "mconf.h" |
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| 63 | |
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| 64 | #ifdef UNK |
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| 65 | #if 1 |
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| 66 | double MACHEP = 1.11022302462515654042E-16; /* 2**-53 */ |
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| 67 | #else |
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| 68 | double MACHEP = 1.38777878078144567553E-17; /* 2**-56 */ |
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| 69 | #endif |
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| 70 | double UFLOWTHRESH = 2.22507385850720138309E-308; /* 2**-1022 */ |
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| 71 | #ifdef DENORMAL |
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| 72 | double MAXLOG = 7.09782712893383996732E2; /* log(MAXNUM) */ |
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| 73 | /* double MINLOG = -7.44440071921381262314E2; */ /* log(2**-1074) */ |
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| 74 | double MINLOG = -7.451332191019412076235E2; /* log(2**-1075) */ |
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| 75 | #else |
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| 76 | double MAXLOG = 7.08396418532264106224E2; /* log 2**1022 */ |
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| 77 | double MINLOG = -7.08396418532264106224E2; /* log 2**-1022 */ |
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| 78 | #endif |
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| 79 | double MAXNUM = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */ |
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| 80 | double PI = 3.14159265358979323846; /* pi */ |
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| 81 | double PIO2 = 1.57079632679489661923; /* pi/2 */ |
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| 82 | double PIO4 = 7.85398163397448309616E-1; /* pi/4 */ |
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| 83 | double SQRT2 = 1.41421356237309504880; /* sqrt(2) */ |
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| 84 | double SQRTH = 7.07106781186547524401E-1; /* sqrt(2)/2 */ |
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| 85 | double LOG2E = 1.4426950408889634073599; /* 1/log(2) */ |
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| 86 | double SQ2OPI = 7.9788456080286535587989E-1; /* sqrt( 2/pi ) */ |
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| 87 | double LOGE2 = 6.93147180559945309417E-1; /* log(2) */ |
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| 88 | double LOGSQ2 = 3.46573590279972654709E-1; /* log(2)/2 */ |
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| 89 | double THPIO4 = 2.35619449019234492885; /* 3*pi/4 */ |
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| 90 | double TWOOPI = 6.36619772367581343075535E-1; /* 2/pi */ |
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| 91 | #ifdef INFINITIES |
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| 92 | double INFINITY = 1.0/0.0; /* 99e999; */ |
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| 93 | #else |
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| 94 | double INFINITY = 1.79769313486231570815E308; /* 2**1024*(1-MACHEP) */ |
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| 95 | #endif |
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| 96 | #ifdef NANS |
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| 97 | double NAN = 1.0/0.0 - 1.0/0.0; |
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| 98 | #else |
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| 99 | double NAN = 0.0; |
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| 100 | #endif |
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| 101 | #ifdef MINUSZERO |
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| 102 | double NEGZERO = -0.0; |
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| 103 | #else |
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| 104 | double NEGZERO = 0.0; |
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| 105 | #endif |
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| 106 | #endif |
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| 107 | |
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| 108 | #ifdef IBMPC |
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| 109 | /* 2**-53 = 1.11022302462515654042E-16 */ |
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| 110 | unsigned short MACHEP[4] = {0x0000,0x0000,0x0000,0x3ca0}; |
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| 111 | unsigned short UFLOWTHRESH[4] = {0x0000,0x0000,0x0000,0x0010}; |
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| 112 | #ifdef DENORMAL |
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| 113 | /* log(MAXNUM) = 7.09782712893383996732224E2 */ |
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| 114 | unsigned short MAXLOG[4] = {0x39ef,0xfefa,0x2e42,0x4086}; |
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| 115 | /* log(2**-1074) = - -7.44440071921381262314E2 */ |
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| 116 | /*unsigned short MINLOG[4] = {0x71c3,0x446d,0x4385,0xc087};*/ |
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| 117 | unsigned short MINLOG[4] = {0x3052,0xd52d,0x4910,0xc087}; |
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| 118 | #else |
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| 119 | /* log(2**1022) = 7.08396418532264106224E2 */ |
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| 120 | unsigned short MAXLOG[4] = {0xbcd2,0xdd7a,0x232b,0x4086}; |
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| 121 | /* log(2**-1022) = - 7.08396418532264106224E2 */ |
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| 122 | unsigned short MINLOG[4] = {0xbcd2,0xdd7a,0x232b,0xc086}; |
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| 123 | #endif |
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| 124 | /* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */ |
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| 125 | unsigned short MAXNUM[4] = {0xffff,0xffff,0xffff,0x7fef}; |
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| 126 | unsigned short PI[4] = {0x2d18,0x5444,0x21fb,0x4009}; |
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| 127 | unsigned short PIO2[4] = {0x2d18,0x5444,0x21fb,0x3ff9}; |
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| 128 | unsigned short PIO4[4] = {0x2d18,0x5444,0x21fb,0x3fe9}; |
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| 129 | unsigned short SQRT2[4] = {0x3bcd,0x667f,0xa09e,0x3ff6}; |
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| 130 | unsigned short SQRTH[4] = {0x3bcd,0x667f,0xa09e,0x3fe6}; |
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| 131 | unsigned short LOG2E[4] = {0x82fe,0x652b,0x1547,0x3ff7}; |
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| 132 | unsigned short SQ2OPI[4] = {0x3651,0x33d4,0x8845,0x3fe9}; |
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| 133 | unsigned short LOGE2[4] = {0x39ef,0xfefa,0x2e42,0x3fe6}; |
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| 134 | unsigned short LOGSQ2[4] = {0x39ef,0xfefa,0x2e42,0x3fd6}; |
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| 135 | unsigned short THPIO4[4] = {0x21d2,0x7f33,0xd97c,0x4002}; |
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| 136 | unsigned short TWOOPI[4] = {0xc883,0x6dc9,0x5f30,0x3fe4}; |
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| 137 | #ifdef INFINITIES |
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| 138 | unsigned short INFINITY[4] = {0x0000,0x0000,0x0000,0x7ff0}; |
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| 139 | #else |
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| 140 | unsigned short INFINITY[4] = {0xffff,0xffff,0xffff,0x7fef}; |
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| 141 | #endif |
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| 142 | #ifdef NANS |
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| 143 | unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x7ffc}; |
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| 144 | #else |
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| 145 | unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000}; |
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| 146 | #endif |
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| 147 | #ifdef MINUSZERO |
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| 148 | unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x8000}; |
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| 149 | #else |
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| 150 | unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000}; |
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| 151 | #endif |
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| 152 | #endif |
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| 153 | |
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| 154 | #ifdef MIEEE |
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| 155 | /* 2**-53 = 1.11022302462515654042E-16 */ |
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| 156 | unsigned short MACHEP[4] = {0x3ca0,0x0000,0x0000,0x0000}; |
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| 157 | unsigned short UFLOWTHRESH[4] = {0x0010,0x0000,0x0000,0x0000}; |
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| 158 | #ifdef DENORMAL |
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| 159 | /* log(2**1024) = 7.09782712893383996843E2 */ |
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| 160 | unsigned short MAXLOG[4] = {0x4086,0x2e42,0xfefa,0x39ef}; |
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| 161 | /* log(2**-1074) = - -7.44440071921381262314E2 */ |
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| 162 | /* unsigned short MINLOG[4] = {0xc087,0x4385,0x446d,0x71c3}; */ |
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| 163 | unsigned short MINLOG[4] = {0xc087,0x4910,0xd52d,0x3052}; |
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| 164 | #else |
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| 165 | /* log(2**1022) = 7.08396418532264106224E2 */ |
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| 166 | unsigned short MAXLOG[4] = {0x4086,0x232b,0xdd7a,0xbcd2}; |
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| 167 | /* log(2**-1022) = - 7.08396418532264106224E2 */ |
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| 168 | unsigned short MINLOG[4] = {0xc086,0x232b,0xdd7a,0xbcd2}; |
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| 169 | #endif |
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| 170 | /* 2**1024*(1-MACHEP) = 1.7976931348623158E308 */ |
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| 171 | unsigned short MAXNUM[4] = {0x7fef,0xffff,0xffff,0xffff}; |
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| 172 | unsigned short PI[4] = {0x4009,0x21fb,0x5444,0x2d18}; |
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| 173 | unsigned short PIO2[4] = {0x3ff9,0x21fb,0x5444,0x2d18}; |
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| 174 | unsigned short PIO4[4] = {0x3fe9,0x21fb,0x5444,0x2d18}; |
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| 175 | unsigned short SQRT2[4] = {0x3ff6,0xa09e,0x667f,0x3bcd}; |
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| 176 | unsigned short SQRTH[4] = {0x3fe6,0xa09e,0x667f,0x3bcd}; |
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| 177 | unsigned short LOG2E[4] = {0x3ff7,0x1547,0x652b,0x82fe}; |
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| 178 | unsigned short SQ2OPI[4] = {0x3fe9,0x8845,0x33d4,0x3651}; |
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| 179 | unsigned short LOGE2[4] = {0x3fe6,0x2e42,0xfefa,0x39ef}; |
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| 180 | unsigned short LOGSQ2[4] = {0x3fd6,0x2e42,0xfefa,0x39ef}; |
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| 181 | unsigned short THPIO4[4] = {0x4002,0xd97c,0x7f33,0x21d2}; |
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| 182 | unsigned short TWOOPI[4] = {0x3fe4,0x5f30,0x6dc9,0xc883}; |
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| 183 | #ifdef INFINITIES |
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| 184 | unsigned short INFINITY[4] = {0x7ff0,0x0000,0x0000,0x0000}; |
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| 185 | #else |
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| 186 | unsigned short INFINITY[4] = {0x7fef,0xffff,0xffff,0xffff}; |
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| 187 | #endif |
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| 188 | #ifdef NANS |
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| 189 | unsigned short NAN[4] = {0x7ff8,0x0000,0x0000,0x0000}; |
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| 190 | #else |
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| 191 | unsigned short NAN[4] = {0x0000,0x0000,0x0000,0x0000}; |
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| 192 | #endif |
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| 193 | #ifdef MINUSZERO |
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| 194 | unsigned short NEGZERO[4] = {0x8000,0x0000,0x0000,0x0000}; |
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| 195 | #else |
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| 196 | unsigned short NEGZERO[4] = {0x0000,0x0000,0x0000,0x0000}; |
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| 197 | #endif |
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| 198 | #endif |
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| 199 | |
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| 200 | #ifdef DEC |
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| 201 | /* 2**-56 = 1.38777878078144567553E-17 */ |
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| 202 | unsigned short MACHEP[4] = {0022200,0000000,0000000,0000000}; |
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| 203 | unsigned short UFLOWTHRESH[4] = {0x0080,0x0000,0x0000,0x0000}; |
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| 204 | /* log 2**127 = 88.029691931113054295988 */ |
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| 205 | unsigned short MAXLOG[4] = {041660,007463,0143742,025733,}; |
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| 206 | /* log 2**-128 = -88.72283911167299960540 */ |
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| 207 | unsigned short MINLOG[4] = {0141661,071027,0173721,0147572,}; |
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| 208 | /* 2**127 = 1.701411834604692317316873e38 */ |
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| 209 | unsigned short MAXNUM[4] = {077777,0177777,0177777,0177777,}; |
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| 210 | unsigned short PI[4] = {040511,007732,0121041,064302,}; |
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| 211 | unsigned short PIO2[4] = {040311,007732,0121041,064302,}; |
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| 212 | unsigned short PIO4[4] = {040111,007732,0121041,064302,}; |
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| 213 | unsigned short SQRT2[4] = {040265,002363,031771,0157145,}; |
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| 214 | unsigned short SQRTH[4] = {040065,002363,031771,0157144,}; |
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| 215 | unsigned short LOG2E[4] = {040270,0125073,024534,013761,}; |
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| 216 | unsigned short SQ2OPI[4] = {040114,041051,0117241,0131204,}; |
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| 217 | unsigned short LOGE2[4] = {040061,071027,0173721,0147572,}; |
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| 218 | unsigned short LOGSQ2[4] = {037661,071027,0173721,0147572,}; |
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| 219 | unsigned short THPIO4[4] = {040426,0145743,0174631,007222,}; |
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| 220 | unsigned short TWOOPI[4] = {040042,0174603,067116,042025,}; |
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| 221 | /* Approximate infinity by MAXNUM. */ |
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| 222 | unsigned short INFINITY[4] = {077777,0177777,0177777,0177777,}; |
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| 223 | unsigned short NAN[4] = {0000000,0000000,0000000,0000000}; |
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| 224 | #ifdef MINUSZERO |
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| 225 | unsigned short NEGZERO[4] = {0000000,0000000,0000000,0100000}; |
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| 226 | #else |
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| 227 | unsigned short NEGZERO[4] = {0000000,0000000,0000000,0000000}; |
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| 228 | #endif |
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| 229 | #endif |
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| 230 | |
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| 231 | #ifndef UNK |
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| 232 | extern unsigned short MACHEP[]; |
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| 233 | extern unsigned short UFLOWTHRESH[]; |
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| 234 | extern unsigned short MAXLOG[]; |
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| 235 | extern unsigned short UNDLOG[]; |
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| 236 | extern unsigned short MINLOG[]; |
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| 237 | extern unsigned short MAXNUM[]; |
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| 238 | extern unsigned short PI[]; |
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| 239 | extern unsigned short PIO2[]; |
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| 240 | extern unsigned short PIO4[]; |
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| 241 | extern unsigned short SQRT2[]; |
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| 242 | extern unsigned short SQRTH[]; |
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| 243 | extern unsigned short LOG2E[]; |
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| 244 | extern unsigned short SQ2OPI[]; |
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| 245 | extern unsigned short LOGE2[]; |
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| 246 | extern unsigned short LOGSQ2[]; |
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| 247 | extern unsigned short THPIO4[]; |
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| 248 | extern unsigned short TWOOPI[]; |
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| 249 | extern unsigned short INFINITY[]; |
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| 250 | extern unsigned short NAN[]; |
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| 251 | extern unsigned short NEGZERO[]; |
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| 252 | #endif |
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