mirror of
https://github.com/opelly27/Y-Cruncher.git
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opelly27
135 lines
4.9 KiB
INI
135 lines
4.9 KiB
INI
// y-cruncher Custom Formula File
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//
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// This can be loaded directly from the Custom Compute menu or
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// entered from the command line as "custom:filename.cfg".
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// y-cruncher custom custom:"filename.cfg"
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//
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//
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// Author: Alexander J. Yee
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// Date: October 2, 2018
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//
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// Value = 0.91596559417721901505460351493238411077414937428167...
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//
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// Formula: G. Huvent (2006)
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//
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// 3 inf ( 1 ( 2 2 1 ))
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// Catalan = --- SUM (-------- (---------- - ---------- + ----------))
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// 4 k=0 ( (-4)^k ( (4k+1)^2 (4k+2)^2 (4k+3)^2 ))
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//
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// 1 inf ( 1 ( 8 4 1 ))
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// - ---- SUM (--------- (---------- + ---------- + ----------))
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// 32 k=0 ( (-64)^k ( (4k+1)^2 (4k+2)^2 (4k+3)^2 ))
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//
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//
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// Optimized by Alex Yee (2013) to:
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//
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// 1 inf ( 1 ( 576 144 72 18
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// Catalan = ----- SUM (--------- (----------- - ----------- - ----------- - ------------
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// 384 k=0 ( (-64)^k ( (12k+1)^2 (12k+5)^2 (12k+7)^2 (12k+11)^2
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//
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// 144 9 64 8 8 ))
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// - ---------- - ---------- - ---------- - ---------- - ---------- ))
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// (6k+1)^2 (6k+5)^2 (4k+1)^2 (4k+3)^2 (2k+1)^2 ))
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//
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{
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NameShort : "Catalan"
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NameLong : "Catalan's Constant"
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AlgorithmShort : "Huvent (optimized)"
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AlgorithmLong : "Huvent (2006) (optimized)"
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Formula : {
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LinearCombination : [
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1
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Alternating : "true"
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PowerCoef : -6
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PowerShift : 5
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PolynomialP : [3]
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PolynomialQ : [121 -264 144]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1
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Alternating : "true"
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PowerCoef : -6
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PowerShift : 3
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PolynomialP : [3]
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PolynomialQ : [49 -168 144]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1
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Alternating : "true"
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PowerCoef : -6
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PowerShift : 2
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PolynomialP : [3]
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PolynomialQ : [25 -120 144]
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}}]
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[-1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1
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Alternating : "true"
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PowerCoef : -6
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PowerShift : 0
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PolynomialP : [3]
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PolynomialQ : [1 -24 144]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 1
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Alternating : "true"
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PowerCoef : -6
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PowerShift : 3
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PolynomialP : [3]
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PolynomialQ : [25 -60 36]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 2
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Alternating : "true"
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PowerCoef : -6
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PowerShift : 0
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PolynomialP : [3]
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PolynomialQ : [1 -12 36]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 3
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Alternating : "true"
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PowerCoef : -6
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PowerShift : 5
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PolynomialP : [1]
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PolynomialQ : [9 -24 16]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 3
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Alternating : "true"
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PowerCoef : -6
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PowerShift : 2
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PolynomialP : [1]
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PolynomialQ : [1 -8 16]
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}}]
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[1 {SeriesBinaryBBP : {
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CoefficientP : 1
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CoefficientQ : 0
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CoefficientD : 3
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Alternating : "true"
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PowerCoef : -6
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PowerShift : 2
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PolynomialP : [1]
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PolynomialQ : [1 -4 4]
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}}]
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]
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}
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}
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