PiDigits Implements the ‘Unbounded Spigot Algorithm for the Digits of Pi’ by Jeremy Gibbons. The paper describing this algorithm can be found at this URL. The same algorithm is used to generate digits of Tau. No matter which circle constant you prefer, you can now generate the decimal expansion using this package.

Usage

PiDigits provides a generator function named piGenerator that yields the digits of Pi as needed. The streaming algorithm based on Lambert’s expression is used for the generator function.

>>> from pidigits import piGenerator >>> mypi = piGenerator() >>> first20pi = [next(mypi) for i in range(20)] >>> first20pi [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4]

Example: Verify the Feynman point.

>>> mypi = piGenerator() >>> first1001 = [next(mypi) for i in range(1001)] >>> feynman = first1001[762:768] >>> print feynman [9, 9, 9, 9, 9, 9]

Alternatively you can also use the getPi(n) function to get the first n digits of Pi.

>>> from pidigits import getPi >>> first20pi = getPi(20) >>> first20pi [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4]

Alternate implementations of streaming algorithms based on Leibniz series and Gosper’s series are also available as generator functions piGenLeibniz and piGenGosper and corresponding getPiLeibniz and getPiGosper functions. These implementations are slower than the one based on Lambert’s series.

Pidigits also provides a generator function name tauGenerator that yields the digits of Tau as needed.

>>> from pidigits import tauGenerator >>> mytau = tauGenerator() >>> first20tau = [next(mytau) for i in range(20)] >>> first20tau [6, 2, 8, 3, 1, 8, 5, 3, 0, 7, 1, 7, 9, 5, 8, 6, 4, 7, 6, 9]

Alternatively you can also use the getTau(n) function to get the first n digits of Tau.