Catalan's Constant [Ramanujan's Formula]

by Greg Fee

Produced by Greg Fee

Catalan's Constant [Ramanujan's Formula]

Catalan constant to 300000 digits computed on September 29, 1996 by using a Sun Ultra-Sparc in 1 day 8 hour 15 min 15 sec 55 hsec. The algorithm used is the standard series for Catalan, accelerated by an Euler transform. The algorithm was implemented using the LiDIA library for computational number theory and it is part of the multiprecision floating-point arithmetic of the package.

LiDIA is available from

ftp://crypt1.cs.uni-sb.de/pub/systems/LiDIA/LiDIA-1.2.1.tgz http://www-jb.cs.uni-sb.de/LiDIA/linkhtml/lidia/lidia.html

The implementation of the algorithm is:

inline void
const_catalan (bigfloat & y)
{
bigfloat p;
bigfloat t;
int i = 1, j = 3; // j = 2*i+1

// y = t = p = 1/2 divide (y, 1, 2); t.assign (y); p.assign (y);

// while t is greater than the desired accuracy
while (!t.is_approx_zero ())
{
// do
// p = p * (i/j);
// t = (t * i + p) / j;
// y = y + t;
// i++; j+=2;
multiply (p, p, i);
divide (p, p, j);
multiply (t, t, i);
add (t, t, p);
divide (t, t, j);
add (y, y, t);
i++;
j += 2;
}
}

Here is the output of the program: