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-rw-r--r--libm/double/ellik.c148
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diff --git a/libm/double/ellik.c b/libm/double/ellik.c
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-/* 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 m in [0, 1] and phi as indicated.
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE -10,10 200000 7.4e-16 1.0e-16
- *
- *
- */
-
-
-/*
-Cephes Math Library Release 2.8: June, 2000
-Copyright 1984, 1987, 2000 by Stephen L. Moshier
-*/
-
-/* Incomplete elliptic integral of first kind */
-
-#include <math.h>
-#ifdef ANSIPROT
-extern double sqrt ( double );
-extern double fabs ( double );
-extern double log ( double );
-extern double tan ( double );
-extern double atan ( double );
-extern double floor ( double );
-extern double ellpk ( double );
-double ellik ( double, double );
-#else
-double sqrt(), fabs(), log(), tan(), atan(), floor(), ellpk();
-double ellik();
-#endif
-extern double PI, PIO2, MACHEP, MAXNUM;
-
-double ellik( phi, m )
-double phi, m;
-{
-double a, b, c, e, temp, t, K;
-int d, mod, sign, npio2;
-
-if( m == 0.0 )
- return( phi );
-a = 1.0 - m;
-if( a == 0.0 )
- {
- if( fabs(phi) >= PIO2 )
- {
- mtherr( "ellik", SING );
- return( MAXNUM );
- }
- return( log( tan( (PIO2 + phi)/2.0 ) ) );
- }
-npio2 = floor( phi/PIO2 );
-if( npio2 & 1 )
- npio2 += 1;
-if( npio2 )
- {
- K = ellpk( a );
- phi = phi - npio2 * PIO2;
- }
-else
- K = 0.0;
-if( phi < 0.0 )
- {
- phi = -phi;
- sign = -1;
- }
-else
- sign = 0;
-b = sqrt(a);
-t = tan( phi );
-if( fabs(t) > 10.0 )
- {
- /* Transform the amplitude */
- e = 1.0/(b*t);
- /* ... but avoid multiple recursions. */
- if( fabs(e) < 10.0 )
- {
- e = atan(e);
- if( npio2 == 0 )
- K = ellpk( a );
- temp = K - ellik( e, m );
- goto done;
- }
- }
-a = 1.0;
-c = sqrt(m);
-d = 1;
-mod = 0;
-
-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);
-
-done:
-if( sign < 0 )
- temp = -temp;
-temp += npio2 * K;
-return( temp );
-}