The Chudnovsky algorithm - https://en.wikipedia.org/wiki/Chudnovsky_algorithm - is supposed to have the fastest convergence for pi (or 1/pi, to be exact). I had tried this one which is OK but only seems to add one digit for each power of 10: 6!:2 'pi=. 4*-/%>:+:i. 1e6' 0.0145579 20j18":pi 3.141591653589793420 6!:2 'pi=. 4*-/%>:+:i. 1e7' 0.140673 20j18":pi 3.141592553589793280 6!:2 'pi=. 4*-/%>:+:i. 1e8' 1.44487 20j18":pi 3.141592643589793177 6!:2 'pi=. 4*-/%>:+:i. 1e9' 16.7988 20j18":pi 3.141592652589793477
The Chudnovsky series is fast and gives me 15 correct decimal digits for only 2 iterations but fails to improve after that presumably because of floating point limitations: 20j18":%12*-/chudSeries i.2 3.141592653589795336 20j18":%12*-/chudSeries i.3 3.141592653589795336 20j18":%12*-/chudSeries i.4 3.141592653589795336 chudSeries i.4 0.0265258 4.98422e_16 2.59929e_30 1.45271e_44 However, when I try to use extended precision, it does not seem to give me extended precision results: chudSeries=: 13 : '((!6x*x: y)*13591409x+545140134x*x: y)%(!3x*x: y)*(3x^~!x: y)*640320x^3r2+3x*x: y' I get the same fp values for the "i.4" argument as shown above. Am I doing something wrong or overlooking something? Thanks, Devon -- Devon McCormick, CFA Quantitative Consultant ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
