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- /* ellpkf.c
- *
- * Complete elliptic integral of the first kind
- *
- *
- *
- * SYNOPSIS:
- *
- * float m1, y, ellpkf();
- *
- * y = ellpkf( 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
- * IEEE 0,1 30000 1.3e-7 3.4e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ellpkf 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 <math.h>
- static float 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 float 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 float C1 = 1.3862943611198906188E0; /* log(4) */
- extern float MACHEPF, MAXNUMF;
- float polevlf(float, float *, int);
- float p1evlf(float, float *, int);
- float logf(float);
- float ellpkf(float xx)
- {
- float x;
- x = xx;
- if( (x < 0.0) || (x > 1.0) )
- {
- mtherr( "ellpkf", DOMAIN );
- return( 0.0 );
- }
- if( x > MACHEPF )
- {
- return( polevlf(x,P,10) - logf(x) * polevlf(x,Q,10) );
- }
- else
- {
- if( x == 0.0 )
- {
- mtherr( "ellpkf", SING );
- return( MAXNUMF );
- }
- else
- {
- return( C1 - 0.5 * logf(x) );
- }
- }
- }
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