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  2. Chudnovsky algorithm - Wikipedia

    en.wikipedia.org/wiki/Chudnovsky_algorithm

    The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae.Published by the Chudnovsky brothers in 1988, [1] it was used to calculate π to a billion decimal places.

  3. Bailey–Borwein–Plouffe formula - Wikipedia

    en.wikipedia.org/wiki/Bailey–Borwein–Plouffe...

    This algorithm computes π without requiring custom data types having thousands or even millions of digits. The method calculates the nth digit without calculating the first n − 1 digits and can use small, efficient data types. Fabrice Bellard found a variant of BBP, Bellard's formula, which is faster.

  4. Gauss–Legendre algorithm - Wikipedia

    en.wikipedia.org/wiki/Gauss–Legendre_algorithm

    The Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π . However, it has some drawbacks (for example, it is computer memory -intensive) and therefore all record-breaking calculations for many years have used other ...

  5. Borwein's algorithm - Wikipedia

    en.wikipedia.org/wiki/Borwein's_algorithm

    Start by setting [4] = = = + Then iterate + = + + = (+) + + = (+ +) + + + Then p k converges quadratically to π; that is, each iteration approximately doubles the number of correct digits.The algorithm is not self-correcting; each iteration must be performed with the desired number of correct digits for π 's final result.

  6. Machin-like formula - Wikipedia

    en.wikipedia.org/wiki/Machin-like_formula

    For the first term in the Taylor series, all digits must be processed. In the last term of the Taylor series, however, there's only one digit remaining to be processed. In all of the intervening terms, the number of digits to be processed can be approximated by linear interpolation. Thus the total is given by:

  7. Spigot algorithm - Wikipedia

    en.wikipedia.org/wiki/Spigot_algorithm

    The same approach can be used to calculate digits of the binary expansion of ln(2) starting from an arbitrary nth position. The number of terms in the "head" sum increases linearly with n , but the complexity of each term only increases with the logarithm of n if an efficient method of modular exponentiation is used.

  8. A Google employee broke the world record for calculating pi - AOL

    www.aol.com/2019-03-14-a-google-employee-broke...

    Google engineer Emma Haruka Iwao has calculated pi to 31 trillion digits, breaking the world record.

  9. List of arbitrary-precision arithmetic software - Wikipedia

    en.wikipedia.org/wiki/List_of_arbitrary...

    SmartXML, a free programming language with integrated development environment (IDE) for mathematical calculations. Variables of BigNumber type can be used, or regular numbers can be converted to big numbers using conversion operator # (e.g., #2.3^2000.1). SmartXML big numbers can have up to 100,000,000 decimal digits and up to 100,000,000 whole ...