Category : C Source Code
Archive   : CEPHES22.ZIP
Filename : ELLPK.C

 
Output of file : ELLPK.C contained in archive : CEPHES22.ZIP
/* ellpk.c
*
* Complete elliptic integral of the first kind
*
*
*
* SYNOPSIS:
*
* double m1, y, ellpk();
*
* y = ellpk( m1 );
*
*
*
* DESCRIPTION:
*
* Approximates the integral
*
*
*
* pi/2
* -
* | |
* | dt
* K(m) = | ------------------
* | 2
* | | sqrt( 1 - m sin t )
* -
* 0
*
* where m = 1 - m1, using the approximation
*
* P(x) - log x Q(x).
*
* The argument m1 is used rather than m so that the logarithmic
* singularity at m = 1 will be shifted to the origin; this
* preserves maximum accuracy.
*
* K(0) = pi/2.
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0,1 16000 3.5e-17 1.1e-17
* IEEE 0,1 30000 2.5e-16 6.8e-17
*
* ERROR MESSAGES:
*
* message condition value returned
* ellpk domain x<0, x>1 0.0
*
*/

/* ellpk.c */


/*
Cephes Math Library, Release 2.0: April, 1987
Copyright 1984, 1987 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/

#include "mconf.h"

#ifdef DEC
static short P[] =
{
0035020,0127576,0040430,0051544,
0036025,0070136,0042703,0153716,
0036402,0122614,0062555,0077777,
0036441,0102130,0072334,0025172,
0036341,0043320,0117242,0172076,
0036312,0146456,0077242,0154141,
0036420,0003467,0013727,0035407,
0036564,0137263,0110651,0020237,
0036775,0001330,0144056,0020305,
0037305,0144137,0157521,0141734,
0040261,0071027,0173721,0147572
};
static short Q[] =
{
0034366,0130371,0103453,0077633,
0035557,0122745,0173515,0113016,
0036302,0124470,0167304,0074473,
0036575,0132403,0117226,0117576,
0036703,0156271,0047124,0147733,
0036766,0137465,0002053,0157312,
0037031,0014423,0154274,0176515,
0037107,0177747,0143216,0016145,
0037217,0177777,0172621,0074000,
0037377,0177777,0177776,0156435,
0040000,0000000,0000000,0000000
};
static short ac1[] = {0040261,0071027,0173721,0147572};
#define C1 (*(double *)ac1)
#endif

#ifdef IBMPC
static short P[] =
{
0x0a6d,0xc823,0x15ef,0x3f22,
0x7afa,0xc8b8,0xae0b,0x3f62,
0xb000,0x8cad,0x54b1,0x3f80,
0x854f,0x0e9b,0x308b,0x3f84,
0x5e88,0x13d4,0x28da,0x3f7c,
0x5b0c,0xcfd4,0x59a5,0x3f79,
0xe761,0xe2fa,0x00e6,0x3f82,
0x2414,0x7235,0x97d6,0x3f8e,
0xc419,0x1905,0xa05b,0x3f9f,
0x387c,0xfbea,0xb90b,0x3fb8,
0x39ef,0xfefa,0x2e42,0x3ff6
};
static short Q[] =
{
0x6ff3,0x30e5,0xd61f,0x3efe,
0xb2c2,0xbee9,0xf4bc,0x3f4d,
0x8f27,0x1dd8,0x5527,0x3f78,
0xd3f0,0x73d2,0xb6a0,0x3f8f,
0x99fb,0x29ca,0x7b97,0x3f98,
0x7bd9,0xa085,0xd7e6,0x3f9e,
0x9faa,0x7b17,0x2322,0x3fa3,
0xc38d,0xf8d1,0xfffc,0x3fa8,
0x2f00,0xfeb2,0xffff,0x3fb1,
0xdba4,0xffff,0xffff,0x3fbf,
0x0000,0x0000,0x0000,0x3fe0
};
static short ac1[] = {0x39ef,0xfefa,0x2e42,0x3ff6};
#define C1 (*(double *)ac1)
#endif

#ifdef MIEEE
static short P[] =
{
0x3f22,0x15ef,0xc823,0x0a6d,
0x3f62,0xae0b,0xc8b8,0x7afa,
0x3f80,0x54b1,0x8cad,0xb000,
0x3f84,0x308b,0x0e9b,0x854f,
0x3f7c,0x28da,0x13d4,0x5e88,
0x3f79,0x59a5,0xcfd4,0x5b0c,
0x3f82,0x00e6,0xe2fa,0xe761,
0x3f8e,0x97d6,0x7235,0x2414,
0x3f9f,0xa05b,0x1905,0xc419,
0x3fb8,0xb90b,0xfbea,0x387c,
0x3ff6,0x2e42,0xfefa,0x39ef
};
static short Q[] =
{
0x3efe,0xd61f,0x30e5,0x6ff3,
0x3f4d,0xf4bc,0xbee9,0xb2c2,
0x3f78,0x5527,0x1dd8,0x8f27,
0x3f8f,0xb6a0,0x73d2,0xd3f0,
0x3f98,0x7b97,0x29ca,0x99fb,
0x3f9e,0xd7e6,0xa085,0x7bd9,
0x3fa3,0x2322,0x7b17,0x9faa,
0x3fa8,0xfffc,0xf8d1,0xc38d,
0x3fb1,0xffff,0xfeb2,0x2f00,
0x3fbf,0xffff,0xffff,0xdba4,
0x3fe0,0x0000,0x0000,0x0000
};
static short ac1[] = {
0x3ff6,0x2e42,0xfefa,0x39ef
};
#define C1 (*(double *)ac1)
#endif

#ifdef UNK
static double P[] =
{
1.37982864606273237150E-4,
2.28025724005875567385E-3,
7.97404013220415179367E-3,
9.85821379021226008714E-3,
6.87489687449949877925E-3,
6.18901033637687613229E-3,
8.79078273952743772254E-3,
1.49380448916805252718E-2,
3.08851465246711995998E-2,
9.65735902811690126535E-2,
1.38629436111989062502E0
};

static double Q[] =
{
2.94078955048598507511E-5,
9.14184723865917226571E-4,
5.94058303753167793257E-3,
1.54850516649762399335E-2,
2.39089602715924892727E-2,
3.01204715227604046988E-2,
3.73774314173823228969E-2,
4.88280347570998239232E-2,
7.03124996963957469739E-2,
1.24999999999870820058E-1,
4.99999999999999999821E-1
};
static double C1 = 1.3862943611198906188E0; /* log(4) */
#endif

extern double MACHEP, MAXNUM;

double ellpk(x)
double x;
{
double polevl(), p1evl(), log();


if( (x < 0.0) || (x > 1.0) )
{
mtherr( "ellpk", DOMAIN );
return( 0.0 );
}

if( x > MACHEP )
{
return( polevl(x,P,10) - log(x) * polevl(x,Q,10) );
}
else
{
if( x == 0.0 )
{
mtherr( "ellpk", SING );
return( MAXNUM );
}
else
{
return( C1 - 0.5 * log(x) );
}
}
}


  3 Responses to “Category : C Source Code
Archive   : CEPHES22.ZIP
Filename : ELLPK.C

  1. Very nice! Thank you for this wonderful archive. I wonder why I found it only now. Long live the BBS file archives!

  2. This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.

  3. But one thing that puzzles me is the “mtswslnkmcjklsdlsbdmMICROSOFT” string. There is an article about it here. It is definitely worth a read: http://www.os2museum.com/wp/mtswslnk/