March 2014 update

2014-04-02 16:56:35 +00:00 · 2014-04-02 16:56:35 +00:00 · a25938f123
commit a25938f123
parent 09687c4926
1846 changed files with 21876 additions and 5203 deletions
--- a/Task/Gamma-function/Perl-6/gamma-function.pl6
+++ b/Task/Gamma-function/Perl-6/gamma-function.pl6
@ -1,18 +1,51 @@
-sub Γ($x) {
-    1 / <
-	 0.00000_00000_00000_00002 -0.00000_00000_00000_00023  0.00000_00000_00000_00141
-	 0.00000_00000_00000_00119 -0.00000_00000_00000_11813  0.00000_00000_00001_22678
-	-0.00000_00000_00005_34812 -0.00000_00000_00020_58326  0.00000_00000_00510_03703
-	-0.00000_00000_03696_80562  0.00000_00000_07782_26344  0.00000_00001_04342_67117
-	-0.00000_00011_81274_57049  0.00000_00050_02007_64447  0.00000_00061_16095_10448
-	-0.00000_02056_33841_69776  0.00000_11330_27231_98170 -0.00000_12504_93482_14267
-	-0.00002_01348_54780_78824  0.00012_80502_82388_11619 -0.00021_52416_74114_95097
-	-0.00116_51675_91859_06511  0.00721_89432_46663_09954 -0.00962_19715_27876_97356
-	-0.04219_77345_55544_33675  0.16653_86113_82291_48950 -0.04200_26350_34095_23553
-	-0.65587_80715_20253_88108  0.57721_56649_01532_86061  1.00000_00000_00000_00000
-    >.reduce: * *($x-1) + *
+sub Γ(\z, :$method = 'lanczos') {
+    given $method {
+	when 'lanczos' {
+	    constant g = 9;
+	    z < .5 ?? pi/ sin(pi * z) / Γ(1 - z, :$method) !!
+	    sqrt(2*pi) *
+	    (z + g - 1/2)**(z - 1/2) *
+	    exp(-(z + g - 1/2)) *
+	    [+] <
+		1.000000000000000174663
+	     5716.400188274341379136
+	   -14815.30426768413909044
+	    14291.49277657478554025
+	    -6348.160217641458813289
+	     1301.608286058321874105
+	     -108.1767053514369634679
+		2.605696505611755827729
+	       -0.7423452510201416151527e-2
+		0.5384136432509564062961e-7
+	       -0.4023533141268236372067e-8
+	    > Z* 1, map 1/(z + *), 0..*
+	}
+	when 'stirling' {
+	    z < 10 ?? Γ(z + 1, :$method) / z !!
+	    sqrt(2*pi*z)*(z/e + 1/(12*z*e))**z / z
+	}
+	when 'taylor' {
+	    z > 3/2 ?? (z - 1)*Γ(z - 1, :$method) !!
+	    z < 1/2 ?? Γ(z + 1, :$method)/z       !!
+	    1 / <
+		 0.00000_00000_00000_00002 -0.00000_00000_00000_00023  0.00000_00000_00000_00141
+		 0.00000_00000_00000_00119 -0.00000_00000_00000_11813  0.00000_00000_00001_22678
+		-0.00000_00000_00005_34812 -0.00000_00000_00020_58326  0.00000_00000_00510_03703
+		-0.00000_00000_03696_80562  0.00000_00000_07782_26344  0.00000_00001_04342_67117
+		-0.00000_00011_81274_57049  0.00000_00050_02007_64447  0.00000_00061_16095_10448
+		-0.00000_02056_33841_69776  0.00000_11330_27231_98170 -0.00000_12504_93482_14267
+		-0.00002_01348_54780_78824  0.00012_80502_82388_11619 -0.00021_52416_74114_95097
+		-0.00116_51675_91859_06511  0.00721_89432_46663_09954 -0.00962_19715_27876_97356
+		-0.04219_77345_55544_33675  0.16653_86113_82291_48950 -0.04200_26350_34095_23553
+		-0.65587_80715_20253_88108  0.57721_56649_01532_86061  1.00000_00000_00000_00000
+	    >.reduce: * *(z-1) + *
+	}
+	default { die "unknow method '$method'" }
+    }
 }
- 
-for 1/3, 2/3 ... 10/3 {
-    printf "Γ(%.5f) ≈ %.14f\n", $_, Γ($_);
+
+for <lanczos taylor stirling> -> $method {
+    # a bug in fmt forces us to round numbers before displaying them
+    say "{$method.fmt("%10s")}: ",
+    map { Γ($_, :$method).round(1e-12).fmt("%.12f") }, (1/3, 2/3 ... 10/3);
 }