The Computation of π to 29,360,000 Decimal Digits Using Borweins’ Quartically Convergent Algorithm

  • David H. Bailey


In a recent work [6], Borwein and Borwein derived a class of algorithms based on the theory of elliptic integrals that yield very rapidly convergent approximations to elementary constants. The author has implemented Borweins’ quartically convergent algorithm for 1/π, using a prime modulus transform multi-precision technique, to compute over 29,360,000 digits of the decimal expansion of π. The result was checked by using a different algorithm, also due to the Borweins, that converges quadratically to π. These computations were performed as a system test of the Cray-2 operated by the Numerical Aerodynamical Simulation (NAS) Program at NASA Ames Research Center. The calculations were made possible by the very large memory of the Cray-2.


Fast Fourier Transform Discrete Fourier Transform Main Memory Chinese Remainder Theorem Decimal Digit 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • David H. Bailey
    • 1
  1. 1.NAS Systems DivisionNASA Ames Research CenterMoffett FieldUSA

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