
    [h<              	          S SK 7  S SKJr  S SKrS\R                  ;   a2  \" \R                  \R                  R                  S5      S-      5      rOSrS\R                  ;   rS q	S r
S	 r/ r\" \" SS
5      5      \" \" SSS5      5      -    H  r\R!                  S\-  S/5        M     \" SS
5       H/  r\R!                  S\-  S/5        \R!                  S\-  S/5        M1     \/ SS/PSS/PSS/PSS/PSS/PSS/PSS/PSS/PSS/PSS/PSS/PSS/PSS/PSS/PS S/PS!S/PS"S/PS#S/PS$S/PS%S/PS"S/PS&S/PS'S/PS(S/PS$S/PS)S/PS*S/PS+S,/PS-S,/PS.S//PS0S1/PS2S3/PS4S5/PS6S7/PS8S9/PS:S/PS;S</PS=S/PS>S/PS?S/PS@S/PSAS/PSBS/PSCS/PSDSE/PSFSG/PSHSI/PSJSK/PSLS/PSMS/PSNS/PSOS/PSPS/PSQS/PSPS/PSRS/PSSS/PSTS/PSUS/PSTS/PSVSW/P-  rSX GH  r\R!                  SY\-  S/5        \R!                  SZ\-  S/5        \R!                  S[\-  S/5        \R!                  S\\-  S/5        \R!                  S]\-  S/5        \R!                  S^\-  S/5        \R!                  S_\-  S/5        \R!                  S`\-  S/5        \R!                  Sa\-  S/5        \R!                  Sb\-  S/5        \R!                  Sc\-  S/5        \R!                  Sd\-  S/5        GM     Se H|  rSf Hs  r\R!                  Sg\< Sh\< Si3S/5        \R!                  Sj\< Sh\< Si3S/5        \R!                  Sg\< Sh\< Sk3S/5        \R!                  Sj\< Sh\< Sk3S/5        Mu     M~     \Sl:X  aY  S SmKJr  Snr\ H4  r\" 5       r\" \5        \" 5       r\" So\\-
  5        \" 5         \\\-
  -  rM6     \" Sp\5        \" Sq[        5        gg)r    )*)ifacNz-dps     z-raisec                     U" U5      nUR                  nUR                  nUR                  nUR                  n	[        S-  n
Sn[        Xh-
  5      [        U5      U
-  :  aj  Sn[        5         [        SU < S[        US5      < S	[        US5      < S
[        [        Xh-
  5      5      < S3	5        [         S-  q [        (       a  [        e[        Xy-
  5      [        U	5      U
-  :  aj  Sn[        5         [        SU < S[        US5      < S	[        U	S5      < S
[        [        Xy-
  5      5      < S3	5        [         S-  q [        (       a  [        eU(       d#  [
        R                  R                  SU -  5        g g !   [         S-  q [        (       a  e [        5         [        U 5        [        S5        SS KnUR	                  [
        R                  " 5       S   5        [        5          g = f)Nr   	EXCEPTIONr         zError! z (re = 
   z	, wanted z, err=)z (im = z%s ok; )errcountraise_print	tracebackprint_tbsysexc_inforealimagepsabsnstr
SystemExitstdoutwrite)namefunczyxr   xreximyreyimtolerrs               T/var/www/auris/envauris/lib/python3.13/site-packages/mpmath/tests/extratest_gamma.pycheckr(      sy   G &&C
&&C
&&C
&&C
a%C
C
37|c#hsl"$SdSVWYl\`adehelam\nopA6
37|c#hsl"$SdSVWYl\`adehelam\nopA6

T)* ?
A6dk3<<>!,-s   E> >A,G,c                     U u  p[        SU5        S[        l        [        U5      n[        S-   [        l        Uc-  [        U5      n[        U5      n[        U5      n[        U5      nO[        U5      n[        U5      nX-  nSU-  nS H  nU[        :  a    g U[        l        [        SU-  5        [        S[
        X5        [        S[        X5        [        S	[        X5        [        S
[        X5        [        5         S[        l        M     g )NzTesting z =i  2   r   )   r         (   <   Z   x      iX  r   i  i  zdps = %sgammargammaloggamma	factorialr,   )r   mpdpsevalmaxdpsr3   r5   r6   r4   expr(   )caser   result	gamma_valloggamma_valfactorial_val
rgamma_valr8   s           r'   testcaserB   4   s    IA	-BFQAb[BF~!H	{!!AY
F|%	y[
K<j3gua+h.j(A4k9a7 L          i     z%s8z%s+0.5z%s+0.37z(0.1+1j)z	(-0.1+1j)z(0.1-1j)z	(-0.1-1j)10jz-10j100j10000jz
-10000000jz(10**100)*jz125+(10**100)*jz-125+(10**100)*jz(10**10)*(1+j)z(10**10)*(-1+j)z(10**100)*(1+j)z(10**100)*(-1+j)z(1.5-1j)z(6+4j)z(4+1j)z(3.5+2j)z(-6-4j)z(-2-3j)z	(-2.5-2j)z(3+3j)z(2-2j)1023zlog(2)4zlog(6)5zlog(24)z0.5z	log(pi)/2z1.5zlog(sqrt(pi)/2)z2.5zlog(3*sqrt(pi)/4)zmpf('0.37')z0.25z)log(sqrt(2*sqrt(2*pi**3)/agm(1,sqrt(2))))z-0.4zmpf('-1.9')zmpf('12.8')zmpf('33.7')zmpf('95.2')zmpf('160.3')zmpf('2057.8')25zlog(ifac(24))80zlog(ifac(79))500zlog(ifac(500-1))8000zlog(ifac(8000-1))z8000.5zmpf('8000.1')zmpf('1.37e10')zmpf('1.37e10')*(1+j)zmpf('1.37e10')*(-1+j)zmpf('1.37e10')*(-1-j)zmpf('1.37e100')zmpf('1.37e100')*(1+j)zmpf('1.37e100')*(-1+j)zmpf('1.37e100')*(-1-j)z3+4ja  mpc('-1.7566267846037841105306041816232757851567066070613445016197619371316057169472361826396083480461846305298860734828967253578064447068977111523651210600259708734715632405373076389685095561916961679704883904239638670319343338908388009531786948197210025029725361069435208930363494971027388382086721660805397916323064321605458016797620170995150951921863546031736733861250062671478363174983174780484475256740163443225458588326103258610863362045919438223029718235161814175530618223688296232894588415495615809337292518431903058265147109853171056894218498782764388681620045286085387381541336752982963143014622747051765799672222008686321794822143126731612769761171322046332838061619713895191371243359764435612951384238091232760634271570950240717650166551484551654327989936028503008171693413044615024511055703811707517257682549003543406938864812466781522545540015867361207626414225907787661003765157377139385212757490499491284143906816424244705094759339932733567910991920631339597278805393743140853391550313363278558195609260225928','4.74266443803465792819488940755002274088830335171164611359052405215840070271590681300937317113976705186354250813687568855081767037900279030487082277549828099966758775645041925653923672591196104389515931289826469459903721798606134294436498090428077839141927485901735557543641049637962003652638924845391650954629013775555010722490760652938524839066763429718336190205584222879898420095911804502117983417158744776290996876098194664579906420307070808945181689246805549314043258530272479246115112769957368212585759640878745385160943755234939803677490810820437032389675754312185365002552976365531236035424489891346371159557028288389233931136182050741628120897320644145308130874835332032440560546577484241423134079056537777170351934430586103623577814746004431994179990531852293907799261385520580149820193022197572124649872089512234542069845198000512157973103058858459643347618317513706729969847568154109777507997488135638784405288158432214886648743541773208808731479748217023665577802702269468013673719173759245720489020315779001'))      "   @   z
(2+j)*%s/3z(-2+j)*%s/3z(1+2*j)*%s/3z
(2-j)*%s/3z(20+j)*%s/3z(-20+j)*%s/3z(1+20*j)*%s/3z(20-j)*%s/3z(200+j)*%s/3z(-200+j)*%s/3z(1+200*j)*%s/3z(200-j)*%s/3)r   r   r	      rU   r-   iiiirG   i7ii߱)z1e-5z1e-20z1e-100z1e-10000zfadd(z,'z',exact=True)zfsub(zj',exact=True)__main__)default_timerg        z
Test time:zTotal time:zErrors:)mpmathmpmath.libmpr   r   argvintindexr:   r   r   r(   rB   	testcaseslistrangenappendr   t__name__timeitr_   clocktot_timer<   t1t2r    rC   r'   <module>rr      s     
	SXX#((..0234FF	SXX	$+L8 	 
eAcl	d5T"#56	6AdQh%& 
7	tCAhlD)*i!mT*+ 
 
 [T [d [ T [ d 	[
 [ [ [ 
4 [ t [  [ D [ T [ 4 [ D [ D [  T ![" T #[$ 
4 %[& 
4 '[( T )[* T +[, D -[. D /[0 d 1[2 
4 3[4 
4 5[6 
4 7[8 c
9[: c
;[< h=[> h?[@ i A[B  C[D  E[F  G[H  I[J 	4 5K[L M[N  O[P  Q[R  S[T  U[V  W[X $ Y[Z  [[\  ][^  _[` 	 a[b 
4 c[d $ e[f 4 g[h  i[j $ k[l $ m[n $ o[p D q[r $ s[t 4  u[v 4  w[x 4  y[z &'{[ [	z 
AlQ&-.ma'./nq($/0lQ&-.ma'./nq($/0o)401ma'./nq($/0o)401&*D12nq($/0 
 
LA41=tDE1=tDEA>EFA>EF	 5 
L z-HWWlBrE"RU  
-"	)X rC   