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/*
* agm.cpp
*
* (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
*/
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <iostream>
#include <gsl/gsl_sf_ellint.h>
int main(int argc, char *argv[]) {
long double a = 1;
long double b = sqrtl(2.)/2;
if (argc >= 3) {
a = std::stod(argv[1]);
b = std::stod(argv[2]);
}
{
long double an = a;
long double bn = b;
for (int i = 0; i < 10; i++) {
printf("%d %24.18Lf %24.18Lf %24.18Lf\n",
i, an, bn, a * M_PI / (2 * an));
long double A = (an + bn) / 2;
bn = sqrtl(an * bn);
an = A;
}
}
{
double k = b/a;
k = sqrt(1 - k*k);
double K = gsl_sf_ellint_Kcomp(k, GSL_PREC_DOUBLE);
printf(" %24.18f %24.18f\n", k, K);
}
return EXIT_SUCCESS;
}
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