Data commit

Task/Gamma-function/Zkl/gamma-function-1.zkl

@@ -0,0 +1,23 @@
+fcn taylorGamma(x){
+   var table = T(
+     0x1p+0,                    0x1.2788cfc6fb618f4cp-1,
+    -0x1.4fcf4026afa2dcecp-1,  -0x1.5815e8fa27047c8cp-5,
+     0x1.5512320b43fbe5dep-3,  -0x1.59af103c340927bep-5,
+    -0x1.3b4af28483e214e4p-7,   0x1.d919c527f60b195ap-8,
+    -0x1.317112ce3a2a7bd2p-10, -0x1.c364fe6f1563ce9cp-13,
+     0x1.0c8a78cd9f9d1a78p-13, -0x1.51ce8af47eabdfdcp-16,
+    -0x1.4fad41fc34fbb2p-20,    0x1.302509dbc0de2c82p-20,
+    -0x1.b9986666c225d1d4p-23,  0x1.a44b7ba22d628acap-28,
+     0x1.57bc3fc384333fb2p-28, -0x1.44b4cedca388f7c6p-30,
+     0x1.cae7675c18606c6p-34,   0x1.11d065bfaf06745ap-37,
+    -0x1.0423bac8ca3faaa4p-38,  0x1.1f20151323cd0392p-41,
+    -0x1.72cb88ea5ae6e778p-46, -0x1.815f72a05f16f348p-48,
+     0x1.6198491a83bccbep-50,  -0x1.10613dde57a88bd6p-53,
+     0x1.5e3fee81de0e9c84p-60,  0x1.a0dc770fb8a499b6p-60,
+    -0x1.0f635344a29e9f8ep-62,  0x1.43d79a4b90ce8044p-66).reverse();
+
+    y  := x.toFloat() - 1.0;
+    sm := table[1,*].reduce('wrap(sm,an){ sm * y + an },table[0]);
+
+    return(1.0 / sm);
+}

Task/Gamma-function/Zkl/gamma-function-2.zkl

@@ -0,0 +1,28 @@
+fcn lanczosGamma(z) { z = z.toFloat();
+    // Coefficients used by the GNU Scientific Library.
+    // http://en.wikipedia.org/wiki/Lanczos_approximation
+    const g = 7, PI = (0.0).pi;
+    exp := (0.0).e.pow;
+    var table = T(
+             0.99999_99999_99809_93,
+           676.52036_81218_851,
+         -1259.13921_67224_028,
+           771.32342_87776_5313,
+          -176.61502_91621_4059,
+            12.50734_32786_86905,
+            -0.13857_10952_65720_12,
+             9.98436_95780_19571_6e-6,
+             1.50563_27351_49311_6e-7);
+
+    // Reflection formula.
+    if (z < 0.5) {
+        return(PI / ((PI * z).sin() * lanczosGamma(1.0 - z)));
+    } else {
+        z -= 1;
+        x := table[0];
+        foreach i in ([1 .. g + 1]){
+            x += table[i] / (z + i); }
+        t := z + g + 0.5;
+        return((2.0 * PI).sqrt() * t.pow(z + 0.5) * exp(-t) * x);
+    }
+}