Gamma function: Difference between revisions
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<pre>2.220446049250313e-16</pre>
=={{header|Koka}}==
Based on OCaml implementation
<syntaxhighlight lang="koka">
import std/num/float64
fun gamma-lanczos(x)
val g = 7.0
// Coefficients used by the GNU Scientific Library
val c = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,
771.32342877765313, -176.61502916214059, 12.507343278686905,
-0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7]
fun ag(z: float64, d: int)
if d == 0 then c[0].unjust + ag(z, 1)
elif d < 8 then c[d].unjust / (z + d.float64) + ag(z, d.inc)
else c[d].unjust / (z + d.float64)
fun gamma(z)
val z' = z - 1.0
val p = z' + g + 0.5
sqrt(2.0 * pi) * pow(p, (z' + 0.5)) * exp(0.0 - p) * ag(z', 0)
gamma(x)
val e = exp(1.0)
fun gamma-stirling(x)
sqrt(2.0 * pi / x) * pow(x / e, x)
fun gamma-stirling2(x')
// Extended Stirling method seen in Abramowitz and Stegun
val d = [1.0/12.0, 1.0/288.0, -139.0/51840.0, -571.0/2488320.0]
fun corr(z, x, n)
if n < d.length - 1 then d[n].unjust / x + corr(z, x*z, n.inc)
else d[n].unjust / x
fun gamma(z)
gamma-stirling(z)*(1.0 + corr(z, z, 0))
gamma(x')
fun mirror(gma, z)
if z > 0.5 then gma(z) else pi / sin(pi * z) / gma(1.0 - z)
fun main()
println("z\tLanczos\t\t\tStirling\t\tStirling2")
for(1, 20) fn(i)
val z = i.float64 / 10.0
println(z.show(1) ++ "\t" ++ mirror(gamma-lanczos, z).show ++ "\t" ++
mirror(gamma-stirling, z).show ++ "\t" ++ mirror(gamma-stirling2, z).show)
for(1, 7) fn(i)
val z = 10.0 * i.float64
println(z.show ++ "\t" ++ gamma-lanczos(z).show ++ "\t" ++
gamma-stirling(z).show ++ "\t" ++ gamma-stirling2(z).show)
</syntaxhighlight>
{{out}}
<pre>
z Lanczos Stirling Stirling2
0.1 9.5135076986687359 10.405084329555955 9.5210418318004439
0.2 4.5908437119988017 5.0739927535371763 4.596862295030256
0.3 2.9915689876875904 3.3503395433773222 2.9984402802949961
0.4 2.218159543757686 2.5270578096699556 2.2277588907113128
0.5 1.7724538509055157 2.0663656770612464 1.7883901437260497
0.6 1.4891922488128184 1.3071588574483559 1.4827753636029286
0.7 1.2980553326475577 1.1590532921139201 1.2950806801024195
0.8 1.1642297137253037 1.0533709684256085 1.1627054102439229
0.9 1.068628702119319 0.97706150787769541 1.0677830813298756
1.0 1.0000000000000002 0.92213700889578909 0.99949946853364036
1.1 0.95135076986687361 0.88348995316870382 0.95103799705518899
1.2 0.91816874239976076 0.85775533539659088 0.91796405783487933
1.3 0.89747069630627774 0.84267825944839203 0.8973312868034562
1.4 0.88726381750307537 0.8367445486370817 0.88716548484542823
1.5 0.88622692545275827 0.83895655252649626 0.88615538430170204
1.6 0.89351534928769061 0.8486932421525738 0.89346184003019224
1.7 0.90863873285329122 0.86562147179388405 0.90859770150945562
1.8 0.93138377098024272 0.8896396352879945 0.93135158986107858
1.9 0.96176583190738729 0.92084272189422933 0.96174006762796482
2.0 1.0000000000000002 0.95950217574449159 0.99997898067003532
10 362880.00000000105 359869.56187410367 362879.99717458693
20 1.2164510040883245e+17 1.2113934233805675e+17 1.2164510037907557e+17
30 8.841761993739658e+30 8.8172365307655063e+30 8.8417619934546387e+30
40 2.0397882081197221e+46 2.0355431612365591e+46 2.0397882081041343e+46
50 6.0828186403425409e+62 6.0726891878763362e+62 6.0828186403274418e+62
60 1.3868311854568534e+80 1.3849063858294502e+80 1.3868311854555093e+80
70 1.7112245242813438e+98 1.7091885781910795e+98 1.711224524280615e+98
</pre>
=={{header|Kotlin}}==
<syntaxhighlight lang="scala">// version 1.0.6
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