/** Program to calculate pi to a large number of digits using the Chudnovsky algorithm with binary splitting. see: http://numbers.computation.free.fr/Constants/Algorithms/splitting.html This program is a testbed for timing the performance of this algorithm and prints extraneous output. If you want a quieter, cached version that you can use in your own library, see pi.frink instead. This is a new version that's intended to be used with Frink: The Next Generation. It uses mostly fast floating-point algorithms. See: https://frinklang.org/experimental.html */ //input["Hit Enter. "] // This is so we can attach jvirtualvm profiler. //use sqrtWayne.frink digits = million if length[ARGS] >= 1 digits = eval[ARGS@0] digitsPerIteration = 14.1816474627254776555 // Find number of terms to calculate k = floor[digits/digitsPerIteration] setPrecision[digits+3] println["Calculating $digits digits."] //println["k=$k"] start1 = now[]; // pi = p[0,k] * (C/D) * sqrt[C] / (q[0,k] + A * p) p = p[0,k] q = q[0,k] end = now[]; println["Time spent in binary splitting: " + format[end-start1, "s", 3]]; start = now[]; sqC = sqrt[640320, digits+2] end = now[]; println["Time spent in square root: " + format[end-start, "s", 3]]; start = now[]; piprime = p * 53360. / (q + 13591409 * p) pi = piprime * sqC end = now[]; println["Time spent in combining operations " + format[end-start, "s", 3]] println["Calculation complete."] setPrecision[digits] start = now[] value = 1. * pi end = now[] println["Time spent in floating-point calculation: " + format[end-start, "s", 3]] start = now[] println[value] end = now[] println["Time spent in printing: " + format[end-start, "s", 3]] end = now[] println["Total time is " + format[end-start1, "s", 3]] q[a,b] := { if (b-a)==1 return (-1)^b * g[a,b] * (13591409 + 545140134 b) m = (a+b) div 2 return q[a,m] p[m,b] + q[m,b] g[a,m] } p[a,b] := { if (b-a) == 1 return 10939058860032000 b^3 // Constant is C^3/24 m = (a+b) div 2 return p[a,m] p[m,b] } g[a,b] := { if (b-a) == 1 return (6b-5)(2b-1)(6b-1) m = (a+b) div 2 return g[a,m] g[m,b] }