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March 2014 update

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This commit is contained in:
Ingy döt Net 2014-04-02 16:56:35 +00:00
parent 09687c4926
commit a25938f123
1846 changed files with 21876 additions and 5203 deletions
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60
Task/Gamma-function/D/gamma-function.d
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@ -1,17 +1,22 @@
import std.stdio, std.mathspecial;
import std.stdio, std.math, std.mathspecial;
real myGamma(in real x) pure nothrow {
real taylorGamma(in real x) pure nothrow {
static immutable real[30] table = [
1.00000000000000000000, 0.57721566490153286061, -0.65587807152025388108,
-0.04200263503409523553, 0.16653861138229148950, -0.04219773455554433675,
-0.00962197152787697356, 0.00721894324666309954, -0.00116516759185906511,
-0.00021524167411495097, 0.00012805028238811619, -0.00002013485478078824,
-0.00000125049348214267, 0.00000113302723198170, -0.00000020563384169776,
0.00000000611609510448, 0.00000000500200764447, -0.00000000118127457049,
0.00000000010434267117, 0.00000000000778226344, -0.00000000000369680562,
0.00000000000051003703, -0.00000000000002058326, -0.00000000000000534812,
0.00000000000000122678, -0.00000000000000011813, 0.00000000000000000119,
0.00000000000000000141, -0.00000000000000000023, 0.00000000000000000002];
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];
immutable real y = x - 1.0L;
real sm = table[$ - 1];
@ -20,9 +25,38 @@ real myGamma(in real x) pure nothrow {
return 1.0L / sm;
}
real lanczosGamma(real z) pure nothrow {
// Coefficients used by the GNU Scientific Library.
// http://en.wikipedia.org/wiki/Lanczos_approximation
enum g = 7;
static immutable real[9] table =
[ 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 < 0.5L) {
return PI / (sin(PI * z) * lanczosGamma(1 - z));
} else {
z -= 1;
real x = table[0];
foreach (immutable i; 1 .. g + 2)
x += table[i] / (z + i);
immutable real t = z + g + 0.5L;
return sqrt(2 * PI) * t ^^ (z + 0.5L) * exp(-t) * x;
}
}
void main() {
foreach (immutable i; 1 .. 11) {
immutable real x = i / 3.0L;
writefln("%f: %20.19e %20.19e", x, myGamma(x), gamma(x));
writefln("%f: %20.19e %20.19e %20.19e", x,
x.taylorGamma, x.lanczosGamma, x.gamma);
}
}