37 lines
1.5 KiB
Prolog
37 lines
1.5 KiB
Prolog
gamma_coefficients(
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[ 1.00000000000000000000000, 0.57721566490153286060651, -0.65587807152025388107701,
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-0.04200263503409523552900, 0.16653861138229148950170, -0.04219773455554433674820,
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-0.00962197152787697356211, 0.00721894324666309954239, -0.00116516759185906511211,
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-0.00021524167411495097281, 0.00012805028238811618615, -0.00002013485478078823865,
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-0.00000125049348214267065, 0.00000113302723198169588, -0.00000020563384169776071,
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0.00000000611609510448141, 0.00000000500200764446922, -0.00000000118127457048702,
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0.00000000010434267116911, 0.00000000000778226343990, -0.00000000000369680561864,
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0.00000000000051003702874, -0.00000000000002058326053, -0.00000000000000534812253,
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0.00000000000000122677862, -0.00000000000000011812593, 0.00000000000000000118669,
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0.00000000000000000141238, -0.00000000000000000022987, 0.00000000000000000001714
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]).
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tolerance(1e-17).
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gamma(X, _) :- X =< 0.0, !, fail.
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gamma(X, Y) :-
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X < 1.0, small_gamma(X, Y), !.
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gamma(1, 1) :- !.
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gamma(1.0, 1) :- !.
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gamma(X, Y) :-
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X1 is X - 1,
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gamma(X1, Y1),
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Y is X1 * Y1.
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small_gamma(X, Y) :-
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gamma_coefficients(Cs),
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recip_gamma(X, 1.0, Cs, 1.0, 0.0, Y0),
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Y is 1 / Y0.
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recip_gamma(_, _, [], _, Y, Y) :- !.
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recip_gamma(_, _, [], X0, X1, Y) :- tolerance(Tol), abs(X1 - X0) < Tol, Y = X1, !. % early exit
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recip_gamma(X, PrevPow, [C|Cs], _, X1, Y) :-
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Power is PrevPow * X,
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X2 is X1 + C*Power,
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recip_gamma(X, Power, Cs, X1, X2, Y).
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