Add files via upload

2026-05-20 02:57:34 +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: Kikuo Takano's 4-term formula
+//
+//        Pi = 48 ArcTan(1/49) + 128 ArcTan(1/57) - 20 ArcTan(1/239) + 48 ArcTan(1/110443)
+//
+//    This uses Euler's ArcTan formula which is slightly faster
+//    than the usual Taylor series.
+//
+
+{
+    NameShort : "Pi"
+    NameLong : "Pi"
+    AlgorithmShort : "Takano"
+    AlgorithmLong : "Takano's 4-term Formula"
+    Formula : {
+        LinearCombination : [
+            [1176 {SeriesHypergeometric : {
+                    CoefficientP : 1
+                    CoefficientQ : 1
+                    CoefficientD : 1201
+                    PolynomialP : [0 1]
+                    PolynomialQ : [1201 2402]
+                    PolynomialR : [0 1]
+            }}]
+            [3648 {SeriesHypergeometric : {
+                    CoefficientP : 1
+                    CoefficientQ : 1
+                    CoefficientD : 1625
+                    PolynomialP : [0 1]
+                    PolynomialQ : [1625 3250]
+                    PolynomialR : [0 1]
+            }}]
+            [-2390 {SeriesHypergeometric : {
+                    CoefficientP : 1
+                    CoefficientQ : 1
+                    CoefficientD : 28561
+                    PolynomialP : [0 1]
+                    PolynomialQ : [28561 57122]
+                    PolynomialR : [0 1]
+            }}]
+            [2650632 {SeriesHypergeometric : {
+                    CoefficientP : 1
+                    CoefficientQ : 1
+                    CoefficientD : 6098828125
+                    PolynomialP : [0 1]
+                    PolynomialQ : [6098828125 12197656250]
+                    PolynomialR : [0 1]
+            }}]
+        ]
+    }
+}