mirror of
https://github.com/opelly27/Y-Cruncher.git
synced 2026-05-20 01:47:34 +00:00
opelly27
80 lines
2.8 KiB
INI
80 lines
2.8 KiB
INI
// y-cruncher Custom Formula File
|
|
//
|
|
// This can be loaded directly from the Custom Compute menu or
|
|
// entered from the command line as "custom:filename.cfg".
|
|
// y-cruncher custom custom:"filename.cfg"
|
|
//
|
|
//
|
|
// Author: Alexander J. Yee
|
|
// Date: September 30, 2018
|
|
//
|
|
// Value: 3.14159265358979323846264338327950288419716939937510...
|
|
//
|
|
// Formula: Chien-Lih Hwang's 6-term formula (1997)
|
|
//
|
|
// Pi = 732 ArcTan(1/239) + 128 ArcTan(1/1023) - 272 ArcTan(1/5832)
|
|
// + 48 ArcTan(1/110443) - 48 ArcTan(1/4841182) - 400 ArcTan(1/6826318)
|
|
//
|
|
// This uses Euler's ArcTan formula which is slightly faster
|
|
// than the usual Taylor series.
|
|
//
|
|
|
|
{
|
|
NameShort : "Pi"
|
|
NameLong : "Pi"
|
|
AlgorithmShort : "Hwang"
|
|
AlgorithmLong : "Hwang's 6-term Formula (1997)"
|
|
Formula : {
|
|
LinearCombination : [
|
|
[87474 {SeriesHypergeometric : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 1
|
|
CoefficientD : 28561
|
|
PolynomialP : [0 1]
|
|
PolynomialQ : [28561 57122]
|
|
PolynomialR : [0 1]
|
|
}}]
|
|
[65472 {SeriesHypergeometric : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 1
|
|
CoefficientD : 523265
|
|
PolynomialP : [0 1]
|
|
PolynomialQ : [523265 1046530]
|
|
PolynomialR : [0 1]
|
|
}}]
|
|
[-1586304 {SeriesHypergeometric : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 1
|
|
CoefficientD : 34012225
|
|
PolynomialP : [0 2]
|
|
PolynomialQ : [34012225 68024450]
|
|
PolynomialR : [0 2]
|
|
}}]
|
|
[2650632 {SeriesHypergeometric : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 1
|
|
CoefficientD : 6098828125
|
|
PolynomialP : [0 1]
|
|
PolynomialQ : [6098828125 12197656250]
|
|
PolynomialR : [0 1]
|
|
}}]
|
|
[-232376736 {SeriesHypergeometric : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 1
|
|
CoefficientD : 23437043157125
|
|
PolynomialP : [0 2]
|
|
PolynomialQ : [23437043157125 46874086314250]
|
|
PolynomialR : [0 2]
|
|
}}]
|
|
[-109221088 {SeriesHypergeometric : {
|
|
CoefficientP : 1
|
|
CoefficientQ : 1
|
|
CoefficientD : 1863944697485
|
|
PolynomialP : [0 2]
|
|
PolynomialQ : [46598617437125 93197234874250]
|
|
PolynomialR : [0 2]
|
|
}}]
|
|
]
|
|
}
|
|
}
|