Output of file : ELLIK.C contained in archive : CEPHES22.ZIP
/* ellik.c
*
* Incomplete elliptic integral of the first kind
*
*
*
* SYNOPSIS:
*
* double phi, m, y, ellik();
*
* y = ellik( phi, m );
*
*
*
* DESCRIPTION:
*
* Approximates the integral
*
*
*
* phi
* -
* | |
* | dt
* F(phi_\m) = | ------------------
* | 2
* | | sqrt( 1 - m sin t )
* -
* 0
*
* of amplitude phi and modulus m, using the arithmetic -
* geometric mean algorithm.
*
*
*
*
* ACCURACY:
*
* Tested at random points with phi in [0, 2] and m in
* [0, 1].
* Relative error:
* arithmetic domain # trials peak rms
* DEC 0,2 3700 8.1e-17 2.5e-17
* IEEE 0,2 10000 6.0e-16 1.4e-16
*
*
*/

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

/* Incomplete elliptic integral of first kind */

extern double PI, PIO2, MACHEP;

double ellik( phi, m )
double phi, m;
{
double a, b, c, temp;
double t, step;
double sqrt(), fabs(), log(), tan(), atan();
int d, mod, sign;

if( m == 0.0 )
return( phi );
if( phi < 0.0 )
{
phi = -phi;
sign = -1;
}
else
sign = 0;
a = 1.0;
b = 1.0 - m;
if( b == 0.0 )
return( log( tan( (PIO2 + phi)/2.0 ) ) );
b = sqrt(b);
c = sqrt(m);
d = 1;
t = tan( phi );
mod = (phi + PIO2)/PI;

while( fabs(c/a) > MACHEP )
{
temp = b/a;
phi = phi + atan(t*temp) + mod * PI;
mod = (phi + PIO2)/PI;
t = t * ( 1.0 + temp )/( 1.0 - temp * t * t );
c = ( a - b )/2.0;
temp = sqrt( a * b );
a = ( a + b )/2.0;
b = temp;
d += d;
}

temp = (atan(t) + mod * PI)/(d * a);
if( sign < 0 )
temp = -temp;
return( temp );
}

### 3 Responses to “Category : C Source CodeArchive   : CEPHES22.ZIPFilename : ELLIK.C”

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