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/* (C) Copyright John Maddock 2006.
* Use, modification and distribution are subject to the
* Boost Software License, Version 1.0. (See accompanying file
* LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
*/
/* Both lanczos.h and lanczos.c were formed from Boost's lanczos.hpp
*
* Scipy changes:
* - 06-22-2016: Removed all code not related to double precision and
* ported to c for use in Cephes. Note that the order of the
* coefficients is reversed to match the behavior of polevl.
*/
/*
* Optimal values for G for each N are taken from
* http://web.mala.bc.ca/pughg/phdThesis/phdThesis.pdf,
* as are the theoretical error bounds.
*
* Constants calculated using the method described by Godfrey
* http://my.fit.edu/~gabdo/gamma.txt and elaborated by Toth at
* http://www.rskey.org/gamma.htm using NTL::RR at 1000 bit precision.
*/
/*
* Lanczos Coefficients for N=13 G=6.024680040776729583740234375
* Max experimental error (with arbitrary precision arithmetic) 1.196214e-17
* Generated with compiler: Microsoft Visual C++ version 8.0 on Win32 at Mar 23 2006
*
* Use for double precision.
*/
#ifndef LANCZOS_H
#define LANCZOS_H
static const double lanczos_num[13] = {
2.506628274631000270164908177133837338626,
210.8242777515793458725097339207133627117,
8071.672002365816210638002902272250613822,
186056.2653952234950402949897160456992822,
2876370.628935372441225409051620849613599,
31426415.58540019438061423162831820536287,
248874557.8620541565114603864132294232163,
1439720407.311721673663223072794912393972,
6039542586.35202800506429164430729792107,
17921034426.03720969991975575445893111267,
35711959237.35566804944018545154716670596,
42919803642.64909876895789904700198885093,
23531376880.41075968857200767445163675473
};
static const double lanczos_denom[13] = {
1,
66,
1925,
32670,
357423,
2637558,
13339535,
45995730,
105258076,
150917976,
120543840,
39916800,
0
};
static const double lanczos_sum_expg_scaled_num[13] = {
0.006061842346248906525783753964555936883222,
0.5098416655656676188125178644804694509993,
19.51992788247617482847860966235652136208,
449.9445569063168119446858607650988409623,
6955.999602515376140356310115515198987526,
75999.29304014542649875303443598909137092,
601859.6171681098786670226533699352302507,
3481712.15498064590882071018964774556468,
14605578.08768506808414169982791359218571,
43338889.32467613834773723740590533316085,
86363131.28813859145546927288977868422342,
103794043.1163445451906271053616070238554,
56906521.91347156388090791033559122686859
};
static const double lanczos_sum_expg_scaled_denom[13] = {
1,
66,
1925,
32670,
357423,
2637558,
13339535,
45995730,
105258076,
150917976,
120543840,
39916800,
0
};
static const double lanczos_sum_near_1_d[12] = {
0.3394643171893132535170101292240837927725e-9,
-0.2499505151487868335680273909354071938387e-8,
0.8690926181038057039526127422002498960172e-8,
-0.1933117898880828348692541394841204288047e-7,
0.3075580174791348492737947340039992829546e-7,
-0.2752907702903126466004207345038327818713e-7,
-0.1515973019871092388943437623825208095123e-5,
0.004785200610085071473880915854204301886437,
-0.1993758927614728757314233026257810172008,
1.483082862367253753040442933770164111678,
-3.327150580651624233553677113928873034916,
2.208709979316623790862569924861841433016
};
static const double lanczos_sum_near_2_d[12] = {
0.1009141566987569892221439918230042368112e-8,
-0.7430396708998719707642735577238449585822e-8,
0.2583592566524439230844378948704262291927e-7,
-0.5746670642147041587497159649318454348117e-7,
0.9142922068165324132060550591210267992072e-7,
-0.8183698410724358930823737982119474130069e-7,
-0.4506604409707170077136555010018549819192e-5,
0.01422519127192419234315002746252160965831,
-0.5926941084905061794445733628891024027949,
4.408830289125943377923077727900630927902,
-9.8907772644920670589288081640128194231,
6.565936202082889535528455955485877361223
};
static const double lanczos_g = 6.024680040776729583740234375;
#endif
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