Data update

Task/Gamma-function/Loglan82/gamma-function.loglan82

@@ -0,0 +1,53 @@
+(* Gamma function *)
+(* Lanczos approximation *)
+
+block
+var
+  x: real;
+
+  unit gamma: function (z: real): real;
+  const
+    pi = 3.14159265358979;
+  var
+    lz: arrayof real;
+
+    unit ln_gamma: function (z: real): real;
+    (* Uses lz and pi *)
+    var
+      i: integer,
+      b, a: real;
+    begin
+      if z < 0.5 then
+        result := ln(pi / sin(pi * z)) - ln_gamma(1.0 - z)
+      else
+        z := z - 1.0;
+        b := z + 5.5;
+        a := lz(0);
+        for i:= 1 to 6
+        do
+          a:= a + lz(i) / (z + i)
+        od;
+        result := (ln(sqrt(2.0 * pi)) + ln(a) - b) + ln(b) * (z + 0.5)
+      fi;
+    end ln_gamma;
+
+  begin
+    array lz dim (0 : 6);
+    lz(0) := 1.00000000019001;
+    lz(1) := 76.1800917294715;
+    lz(2) := -86.5053203294168;
+    lz(3) := 24.0140982408309;
+    lz(4) := -1.23173957245015;
+    lz(5) := 1.2086509738662E-3;
+    lz(6) := -0.000005395239385;
+    result := exp(ln_gamma(z))
+  end gamma;
+
+begin
+  x:= 0.1;
+  while x < 2.05
+  do
+    writeln(x: 4: 1, "  ", gamma(x): 15: 12);
+    x:= x + 0.1
+  od;
+end