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/** Program to calculate pi to arbitrary precision. This algorithm uses
binary splitting.
This version has been updated to be fastest with
Frink: The Next Generation. Due to limitations in Java's BigDecimal
class, this is limited to a little over 101 million digits.
You usually use this by calling Pi.getPi[digits] which will return pi
to the number of digits you specify. You can also call Pi.get2Pi[digits]
to return 2 pi.
See http://numbers.computation.free.fr/Constants/Algorithms/splitting.html
*/
use sqrtWayne.frink
class Pi
{
class var digitsPerIteration = 14.1816474627254776555
class var largestDigits = -1
class var cachePi = undef
/** This is the main public method to get the value of pi to a certain
number of digits, calculating it if need be. If pi has already been
calculated to a sufficient number of digits, this returns it from the
cache.
*/
class getPi[digits = getPrecision[]] :=
{
origPrec = getPrecision[]
try
{
setPrecision[digits]
if (largestDigits >= digits)
return 1. * cachePi
else
return 1. * calcPi[digits]
}
finally
setPrecision[origPrec]
}
/** This is the main public method to get the value of 2 * pi to a certain
number of digits, calculating it if need be. If pi has already been
calculated to a sufficient number of digits, this returns it from the
cache.
*/
class get2Pi[digits = getPrecision[]] :=
{
origPrec = getPrecision[]
try
{
setPrecision[digits]
if (largestDigits != undef) and (largestDigits >= digits)
return 2 * cachePi
else
return 2 * calcPi[digits]
}
finally
setPrecision[origPrec]
}
/** This is an internal method that calculates the digits of pi if
necessary. */
class calcPi[digits] :=
{
oldPrec = getPrecision[]
// Find number of terms to calculate
k = max[floor[digits/digitsPerIteration], 1]
try
{
setPrecision[digits+5]
sum = 0
p = p[0,k]
q = q[0,k]
sqC = sqrt[640320, digits+8]
piprime = p * 53360. / (q + 13591409 * p)
piFull = piprime * sqC
// Truncate to the desired number of digits
setPrecision[digits]
pi = 1. * piFull
largestDigits = digits
cachePi = pi
return pi
}
finally
setPrecision[oldPrec]
}
/** Internal method for binary splitting. */
class q[a,b] :=
{
if (b-a) == 1
return (-1)^b * g[a,b] * (13591409 + 545140134 b)
m = (a+b) div 2
return q[a,m] p[m,b] + q[m,b] g[a,m]
}
/** Internal method for binary splitting. */
class p[a,b] :=
{
if (b-a) == 1
return 10939058860032000 b^3
m = (a+b) div 2
return p[a,m] p[m,b]
}
/** Internal method for binary splitting. */
class g[a,b] :=
{
if (b-a) == 1
return (6b-5)(2b-1)(6b-1)
m = (a+b) div 2
return g[a,m] g[m,b]
}
}
Download or view pi.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 19970 days, 10 hours, 12 minutes ago.