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#include <math.h>
#include <stdint.h>
/*
* logfact[k] holds log(k!) for k = 0, 1, 2, ..., 125.
*/
static const double logfact[] = {
0,
0,
0.69314718055994529,
1.791759469228055,
3.1780538303479458,
4.7874917427820458,
6.5792512120101012,
8.5251613610654147,
10.604602902745251,
12.801827480081469,
15.104412573075516,
17.502307845873887,
19.987214495661885,
22.552163853123425,
25.19122118273868,
27.89927138384089,
30.671860106080672,
33.505073450136891,
36.395445208033053,
39.339884187199495,
42.335616460753485,
45.380138898476908,
48.471181351835227,
51.606675567764377,
54.784729398112319,
58.003605222980518,
61.261701761002001,
64.557538627006338,
67.88974313718154,
71.257038967168015,
74.658236348830158,
78.092223553315307,
81.557959456115043,
85.054467017581516,
88.580827542197682,
92.136175603687093,
95.719694542143202,
99.330612454787428,
102.96819861451381,
106.63176026064346,
110.32063971475739,
114.03421178146171,
117.77188139974507,
121.53308151543864,
125.3172711493569,
129.12393363912722,
132.95257503561632,
136.80272263732635,
140.67392364823425,
144.5657439463449,
148.47776695177302,
152.40959258449735,
156.3608363030788,
160.3311282166309,
164.32011226319517,
168.32744544842765,
172.35279713916279,
176.39584840699735,
180.45629141754378,
184.53382886144948,
188.6281734236716,
192.7390472878449,
196.86618167289001,
201.00931639928152,
205.1681994826412,
209.34258675253685,
213.53224149456327,
217.73693411395422,
221.95644181913033,
226.1905483237276,
230.43904356577696,
234.70172344281826,
238.97838956183432,
243.26884900298271,
247.57291409618688,
251.89040220972319,
256.22113555000954,
260.56494097186322,
264.92164979855278,
269.29109765101981,
273.67312428569369,
278.06757344036612,
282.4742926876304,
286.89313329542699,
291.32395009427029,
295.76660135076065,
300.22094864701415,
304.68685676566872,
309.1641935801469,
313.65282994987905,
318.1526396202093,
322.66349912672615,
327.1852877037752,
331.71788719692847,
336.26118197919845,
340.81505887079902,
345.37940706226686,
349.95411804077025,
354.53908551944079,
359.1342053695754,
363.73937555556347,
368.35449607240474,
372.97946888568902,
377.61419787391867,
382.25858877306001,
386.91254912321756,
391.57598821732961,
396.24881705179155,
400.93094827891576,
405.6222961611449,
410.32277652693733,
415.03230672824964,
419.75080559954472,
424.47819341825709,
429.21439186665157,
433.95932399501481,
438.71291418612117,
443.47508812091894,
448.24577274538461,
453.02489623849613,
457.81238798127816,
462.60817852687489,
467.4121995716082,
472.22438392698058,
477.04466549258564,
481.87297922988796
};
/*
* Compute log(k!)
*/
double logfactorial(int64_t k)
{
const double halfln2pi = 0.9189385332046728;
if (k < (int64_t) (sizeof(logfact)/sizeof(logfact[0]))) {
/* Use the lookup table. */
return logfact[k];
}
/*
* Use the Stirling series, truncated at the 1/k**3 term.
* (In a Python implementation of this approximation, the result
* was within 2 ULP of the best 64 bit floating point value for
* k up to 10000000.)
*/
return (k + 0.5)*log(k) - k + (halfln2pi + (1.0/k)*(1/12.0 - 1/(360.0*k*k)));
}
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