How about an ijulia notebook of 101 ways to compute pi in Julia, ideally with accompanying graphics?
On Sunday, 8 March 2015 13:16:26 UTC, Johan Sigfrids wrote: > > Because calling out to mpfr is cheating here is a implementation of > Gauss-Legendre in Julia calculating Pi to the desired number of digits > (Still relying on BigFloats though). > > function gaussLegendrePi(d::Integer) > prec = get_bigfloat_precision() > set_bigfloat_precision(iceil(d*log(10)/log(2))+10) > n = iceil(log2(d)) > a = BigFloat(1) > b = a / sqrt(BigFloat(2)) > t = a / BigFloat(4) > x = a > while n > 0 > y = a > a = (a + b) / 2 > b = sqrt(b * y) > t = t - x * (y - a)^2 > x = 2 * x > n -= 1 > end > p = ((a + b)^2) / (4 * t) > println(string(p)[1:d+1]) > set_bigfloat_precision(prec) > nothing > end > > I haven't done any validation beyond checking that it and Mathematica > agree on the millionth digit of Pi. >
