253 lines
10 KiB
C
253 lines
10 KiB
C
/* 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
|