Data commit

Task/Gamma-function/Sidef/gamma-function-1.sidef

@@ -0,0 +1,19 @@
+var a = [ 1.00000_00000_00000_00000,  0.57721_56649_01532_86061, -0.65587_80715_20253_88108,
+         -0.04200_26350_34095_23553,  0.16653_86113_82291_48950, -0.04219_77345_55544_33675,
+         -0.00962_19715_27876_97356,  0.00721_89432_46663_09954, -0.00116_51675_91859_06511,
+         -0.00021_52416_74114_95097,  0.00012_80502_82388_11619, -0.00002_01348_54780_78824,
+         -0.00000_12504_93482_14267,  0.00000_11330_27231_98170, -0.00000_02056_33841_69776,
+          0.00000_00061_16095_10448,  0.00000_00050_02007_64447, -0.00000_00011_81274_57049,
+          0.00000_00001_04342_67117,  0.00000_00000_07782_26344, -0.00000_00000_03696_80562,
+          0.00000_00000_00510_03703, -0.00000_00000_00020_58326, -0.00000_00000_00005_34812,
+          0.00000_00000_00001_22678, -0.00000_00000_00000_11813,  0.00000_00000_00000_00119,
+          0.00000_00000_00000_00141, -0.00000_00000_00000_00023,  0.00000_00000_00000_00002 ]
+
+func gamma(x) {
+    var y = (x - 1)
+    1 / a.reverse.reduce {|sum, an| sum*y + an}
+}
+
+for i in 1..10 {
+    say ("%.14e" % gamma(i/3))
+}

Task/Gamma-function/Sidef/gamma-function-2.sidef

@@ -0,0 +1,37 @@
+func gamma(z) {
+    var epsilon = 0.0000001
+    func withinepsilon(x) {
+        abs(x - abs(x)) <= epsilon
+    }
+ 
+    var p = [
+        676.5203681218851,     -1259.1392167224028,
+        771.32342877765313,    -176.61502916214059,
+        12.507343278686905,    -0.13857109526572012,
+        9.9843695780195716e-6,  1.5056327351493116e-7,
+    ]
+ 
+    var result = 0
+    const pi = Num.pi
+ 
+    if (z.re < 0.5) {
+        result = (pi / (sin(pi * z) * gamma(1 - z)))
+    }
+    else {
+        z -= 1
+        var x = 0.99999999999980993
+ 
+        p.each_kv { |i, v|
+            x += v/(z + i + 1)
+        }
+ 
+        var t = (z + p.len - 0.5)
+        result = (sqrt(pi*2) * t**(z+0.5) * exp(-t) * x)
+    }
+ 
+    withinepsilon(result.im) ? result.re : result
+}
+ 
+for i in 1..10 {
+    say ("%.14e" % gamma(i/3))
+}

Task/Gamma-function/Sidef/gamma-function-3.sidef

@@ -0,0 +1,11 @@
+define ℯ = Num.e
+define τ = Num.tau
+ 
+func Γ(t) {
+    t < 20 ? (__FUNC__(t + 1) / t)
+           : (sqrt(τ*t) * pow(t/ℯ + 1/(12*ℯ*t), t) / t)
+}
+ 
+for i in (1..10) {
+    say ("%.14e" % Γ(i/3))
+}