// Program to calculate e using binary splitting. There is now a new library // e.frink which allows resumable calculations and caching of e. This program // contains a simpler version of the algorithm for benchmarking and testing. // // See: // http://numbers.computation.free.fr/Constants/Algorithms/splitting.html // http://www.ginac.de/CLN/binsplit.pdf digits = 10000 if length[ARGS] >= 1 digits = eval[ARGS@0] // Find number of terms to calculate. ln[x!] = ln[1] + ln[2] + ... + ln[x] k = 1 logFactorial = 0. logMax = digits * ln[10] while (logFactorial < logMax) { logFactorial = logFactorial + ln[k]; k = k + 1; } setPrecision[digits+3] //println["k=\$k"] s1 = now[] start = now[] p = P[0,k] q = Q[0,k] end = now[] println["Time spent in binary splitting: " + format[end-start, "s", 3]] start = now[] e = 1 + (1. * p)/q end = now[] println["Time spent in combining operations: " + format[end-start, "s", 3]] //println[e] // Rational number setPrecision[digits] start = now[] e = 1. * e end = now[] println["Time spent in floating-point conversion: " + format[end-start, "s", 3]] start = now[] es = toString[e] end = now[] println["Time spent in radix conversion: " + format[end-start, "s", 3]] println[e] e1 = now[] println["Total time spent: " + format[e1-s1, "s", 3]] println[e] P[a,b] := { if (b-a) == 1 return 1 m = (a+b) div 2 r = P[a,m] Q[m,b] + P[m,b] return r } Q[a,b] := { if (b-a) == 1 return b m = (a+b) div 2 return Q[a,m] Q[m,b] }