Add files via upload

2026-05-20 06:27:37 +00:00 · 2021-11-11 21:34:46 -08:00
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+//  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: Carl Stormer's 4-term formula
+//
+//        Pi = 176 ArcTan(1/57) + 28 ArcTan(1/239) - 48 ArcTan(1/682) + 96 ArcTan(1/12943)
+//
+//    This uses Euler's ArcTan formula which is slightly faster
+//    than the usual Taylor series.
+//
+
+{
+    NameShort : "Pi"
+    NameLong : "Pi"
+    AlgorithmShort : "Stormer"
+    AlgorithmLong : "Stormer's 4-term formula"
+    Formula : {
+        LinearCombination : [
+            [5016 {SeriesHypergeometric : {
+                    CoefficientP : 1
+                    CoefficientQ : 1
+                    CoefficientD : 1625
+                    PolynomialP : [0 1]
+                    PolynomialQ : [1625 3250]
+                    PolynomialR : [0 1]
+            }}]
+            [3346 {SeriesHypergeometric : {
+                    CoefficientP : 1
+                    CoefficientQ : 1
+                    CoefficientD : 28561
+                    PolynomialP : [0 1]
+                    PolynomialQ : [28561 57122]
+                    PolynomialR : [0 1]
+            }}]
+            [-32736 {SeriesHypergeometric : {
+                    CoefficientP : 1
+                    CoefficientQ : 1
+                    CoefficientD : 465125
+                    PolynomialP : [0 2]
+                    PolynomialQ : [465125 930250]
+                    PolynomialR : [0 2]
+            }}]
+            [621264 {SeriesHypergeometric : {
+                    CoefficientP : 1
+                    CoefficientQ : 1
+                    CoefficientD : 83760625
+                    PolynomialP : [0 1]
+                    PolynomialQ : [83760625 167521250]
+                    PolynomialR : [0 1]
+            }}]
+        ]
+    }
+}