Package org.apache.hadoop.examples.pi.math

Class Bellard

java.lang.Object

org.apache.hadoop.examples.pi.math.Bellard

public final class Bellard
extends java.lang.Object

Bellard's BBP-type Pi formula 1/2^6 \sum_{n=0}^\infty (-1)^n/2^{10n} (-2^5/(4n+1) -1/(4n+3) +2^8/(10n+1) -2^6/(10n+3) -2^2/(10n+5) -2^2/(10n+7) +1/(10n+9)) References: [1] David H. Bailey, Peter B. Borwein and Simon Plouffe. On the Rapid Computation of Various Polylogarithmic Constants. Math. Comp., 66:903-913, 1996. [2] Fabrice Bellard. A new formula to compute the n'th binary digit of pi, 1997. Available at http://fabrice.bellard.free.fr/pi .

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	Bellard.Parameter	Parameters for the sums
static class	Bellard.Sum	The sums in the Bellard's formula

Constructor Summary

Constructors

Constructor	Description
Bellard()

Method Summary

Modifier and Type	Method	Description
static long	bit2terms(long b)	Estimate the number of terms.
static double	computePi(long b)	Compute bits of Pi in the local machine.
static <T extends Container<Summation>> double	computePi(long b, java.util.Map<Bellard.Parameter,T> results)	Compute bits of Pi from the results.
static <T extends Container<Summation>> java.util.Map<Bellard.Parameter,Bellard.Sum>	getSums(long b, int partsPerSum, java.util.Map<Bellard.Parameter,java.util.List<T>> existing)	Get the sums for the Bellard formula.
static void	main(java.lang.String[] args)	main

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Bellard

public Bellard()

Method Detail

getSums

public static <T extends Container<Summation>> java.util.Map<Bellard.Parameter,Bellard.Sum> getSums(long b,
                                                                                                          int partsPerSum,
                                                                                                          java.util.Map<Bellard.Parameter,java.util.List<T>> existing)

Get the sums for the Bellard formula.

computePi

public static <T extends Container<Summation>> double computePi(long b,
                                                                java.util.Map<Bellard.Parameter,T> results)

Compute bits of Pi from the results.

computePi

public static double computePi(long b)

Compute bits of Pi in the local machine.

bit2terms

public static long bit2terms(long b)

Estimate the number of terms.

main

public static void main(java.lang.String[] args)
                 throws java.io.IOException

main

Throws:

java.io.IOException