Data commit

Task/Gamma-function/PureBasic/gamma-function-1.basic

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+Procedure.d Gamma(x.d) ; AKJ  01-May-10
+; Complete Gamma function for x>0 and x<2 (approx)
+; Extended outside this range via: Gamma(x+1) = x*Gamma(x)
+; Based on http://rosettacode.org/wiki/Gamma_function  [Ada]
+Protected Dim A.d(28)
+A(0) = 1.0
+A(1) = 0.5772156649015328606
+A(2) =-0.6558780715202538811
+A(3) =-0.0420026350340952355
+A(4) = 0.1665386113822914895
+A(5) =-0.0421977345555443368 ; was ...33675
+A(6) =-0.0096219715278769736
+A(7) = 0.0072189432466630995
+A(8) =-0.0011651675918590651
+A(9) =-0.0002152416741149510
+A(10) = 0.0001280502823881162
+A(11) =-0.0000201348547807882
+A(12) =-0.0000012504934821427
+A(13) = 0.0000011330272319817
+A(14) =-0.0000002056338416978
+A(15) = 0.0000000061160951045
+A(16) = 0.0000000050020076445
+A(17) =-0.0000000011812745705
+A(18) = 0.0000000001043426712
+A(19) = 0.0000000000077822634
+A(20) =-0.0000000000036968056
+A(21) = 0.0000000000005100370
+A(22) =-0.0000000000000205833
+A(23) =-0.0000000000000053481
+A(24) = 0.0000000000000012268
+A(25) =-0.0000000000000001181
+A(26) = 0.0000000000000000012
+A(27) = 0.0000000000000000014
+A(28) =-0.0000000000000000002
+;A(29) = 0.00000000000000000002
+Protected y.d, Prod.d, Sum.d, N
+If x<=0.0: ProcedureReturn 0.0: EndIf ; Error
+y = x-1.0: Prod = 1.0
+While y>=1.0
+  Prod*y: y-1.0 ; Recurse using Gamma(x+1) = x*Gamma(x)
+Wend
+Sum= A(28)
+For N = 27 To 0 Step -1
+  Sum*y+A(N)
+Next N
+If Sum=0.0: ProcedureReturn Infinity(): EndIf
+ProcedureReturn Prod / Sum
+EndProcedure
+
+Procedure.d GammLn(x.d) ; AKJ  01-May-10
+; Returns Ln(Gamma()) or 0 on error
+; Based on Numerical Recipes gamma.h
+Protected j, tmp.d, y.d, ser.d
+Protected Dim cof.d(13)
+cof(0) = 57.1562356658629235
+cof(1) = -59.5979603554754912
+cof(2) = 14.1360979747417471
+cof(3) = -0.491913816097620199
+cof(4) = 0.339946499848118887e-4
+cof(5) = 0.465236289270485756e-4
+cof(6) = -0.983744753048795646e-4
+cof(7) = 0.158088703224912494e-3
+cof(8) = -0.210264441724104883e-3
+cof(9) = 0.217439618115212643e-3
+cof(10) = -0.164318106536763890e-3
+cof(11) = 0.844182239838527433e-4
+cof(12) = -0.261908384015814087e-4
+cof(13) = 0.368991826595316234e-5
+If x<=0: ProcedureReturn 0: EndIf ; Bad argument
+y = x
+tmp = x+5.2421875
+tmp = (x+0.5)*Log(tmp)-tmp
+ser = 0.999999999999997092
+For j=0 To 13
+  y + 1: ser + cof(j)/y
+Next j
+ProcedureReturn tmp+Log(2.5066282746310005*ser/x)
+EndProcedure
+
+Procedure Factorial(x) ; AKJ  01-May-10
+  ProcedureReturn Gamma(x+1)
+EndProcedure

Task/Gamma-function/PureBasic/gamma-function-2.basic

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+Debug "Gamma()"
+For i = 12 To 15
+  Debug StrD(i/3.0, 3)+"   "+StrD(Gamma(i/3.0))
+Next i
+Debug ""
+Debug "Ln(Gamma(5.0)) = "+StrD(GammLn(5.0), 16) ; Ln(24)
+Debug ""
+Debug "Factorial 6 = "+StrD(Factorial(6), 0) ; 72