Essays/Chudnovsky Algorithm
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The Chudnovsky algorithm is a fast method for computing the digits of . Each term of the series produces an additional 14 decimal digits.
To facilitate its implementation in J, we rewrite the formula so that the terms are rational.
pica=: 3 : 0 k =. x: i. y top=. (!6*k) * 13591409+545140134*k bot=. (!3*k) * ((!k)^3) * 640320^3*k rt =. -:@(+640320&%)^:(>.2^.1+y) x:%:640320 NB. sqrt 640320 to 14*y digits % (12 % 640320*rt) * -/ top % bot )
For example:
0j100 ": pica 7 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170658 0j100 ": t %~ <.@o. t=. 10^100x 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
See also
- Chi Squared CDF
- Normal CDF
- Pi (Chudnovsky Algorithm)
- Sine
- Square Root
- t-Distribution CDF
- Extended Precision Functions
Contributed by Roger Hui.