Data commit

2023-07-01 11:58:00 -04:00 · 2023-07-01 11:58:00 -04:00 · cb5bb5e222
commit cb5bb5e222
parent 7387c8f97b
199093 changed files with 3378972 additions and 0 deletions
--- a/Task/Gamma-function/00-META.yaml
+++ b/Task/Gamma-function/00-META.yaml
@ -0,0 +1,3 @@
+---
+from: http://rosettacode.org/wiki/Gamma_function
+note: Mathematical operations
--- a/Task/Gamma-function/00-TASK.txt
+++ b/Task/Gamma-function/00-TASK.txt
@ -0,0 +1,17 @@
+;Task:
+Implement one algorithm (or more) to compute the [[wp:Gamma function|Gamma]] (<math>\Gamma</math>) function (in the real field only). 
+
+If your language has the function as built-in or you know a library which has it, compare your implementation's results with the results of the built-in/library function.
+
+The Gamma function can be defined as:
+
+:::::: <big><big> <math>\Gamma(x) = \displaystyle\int_0^\infty t^{x-1}e^{-t} dt</math></big></big>
+
+This suggests a straightforward (but inefficient) way of computing the <math>\Gamma</math> through numerical integration.
+
+
+Better suggested methods:
+* [[wp:Lanczos approximation|Lanczos approximation]]
+* [[wp:Stirling's approximation|Stirling's approximation]]
+<br><br>
+
--- a/Task/Gamma-function/11l/gamma-function.11l
+++ b/Task/Gamma-function/11l/gamma-function.11l
@ -0,0 +1,20 @@
+V _a = [  1.00000000000000000000,  0.57721566490153286061, -0.65587807152025388108,
+         -0.04200263503409523553,  0.16653861138229148950, -0.04219773455554433675,
+         -0.00962197152787697356,  0.00721894324666309954, -0.00116516759185906511,
+         -0.00021524167411495097,  0.00012805028238811619, -0.00002013485478078824,
+         -0.00000125049348214267,  0.00000113302723198170, -0.00000020563384169776,
+          0.00000000611609510448,  0.00000000500200764447, -0.00000000118127457049,
+          0.00000000010434267117,  0.00000000000778226344, -0.00000000000369680562,
+          0.00000000000051003703, -0.00000000000002058326, -0.00000000000000534812,
+          0.00000000000000122678, -0.00000000000000011813,  0.00000000000000000119,
+          0.00000000000000000141, -0.00000000000000000023,  0.00000000000000000002
+       ]
+F gamma(x)
+   V y = x - 1.0
+   V sm = :_a.last
+   L(n) (:_a.len-2 .. 0).step(-1)
+      sm = sm * y + :_a[n]
+   R 1.0 / sm
+
+L(i) 1..10
+   print(‘#.14’.format(gamma(i / 3.0)))
--- a/Task/Gamma-function/360-Assembly/gamma-function.360
+++ b/Task/Gamma-function/360-Assembly/gamma-function.360
@ -0,0 +1,159 @@
+GAMMAT   CSECT
+         USING GAMMAT,R13
+SAVEAR   B     STM-SAVEAR(R15)
+         DC    17F'0'
+         DC    CL8'GAMMAT'
+STM      STM   R14,R12,12(R13)
+         ST    R13,4(R15)
+         ST    R15,8(R13)
+         LR    R13,R15
+*        ----  CODE
+         LE    F4,=E'0'
+         LH    R2,NI
+LOOPI    EQU   *
+         AE    F4,=E'1'         xi=xi+1
+         LER   F0,F4
+         DE    F0,=E'10'        x=xi/10
+         STE   F0,X
+         LE    F6,X
+         SE    F6,=E'1'         xx=x-1.0
+         LH    R4,NT
+         BCTR  R4,0
+         SLA   R4,2
+         LE    F0,T(R4)
+         STE   F0,SUM           sum=t(nt)
+         LH    R3,NT
+         BCTR  R3,0
+         SH    R4,=H'4'
+LOOPJ    CH    R3,=H'1'         for j=nt-1 downto 1
+         BL    ENDLOOPJ
+         LE    F0,SUM
+         MER   F0,F6            sum*xx
+         LE    F2,T(R4)         t(j)
+         AER   F0,F2
+         STE   F0,SUM           sum=sum*xx+t(j)
+         BCTR  R3,0
+         SH    R4,=H'4'
+         B     LOOPJ
+ENDLOOPJ EQU   *
+         LE    F0,=E'1'
+         DE    F0,SUM
+         STE   F0,GAMMA         gamma=1/sum
+         LE    F0,X
+         BAL   R14,CONVERT
+         MVC   BUF(8),CONVERTM
+         LE    F0,GAMMA
+         BAL   R14,CONVERT
+         MVC   BUF+9(13),CONVERTM
+         WTO   MF=(E,WTOMSG)		
+         BCT   R2,LOOPI
+*        ----  END CODE
+         CNOP  0,4
+         L     R13,4(0,R13)
+         LM    R14,R12,12(R13)
+         XR    R15,R15
+         BR    R14
+*        ----  DATA
+NI       DC    H'30'
+NT       DC    AL2((TEND-T)/4)
+T        DC    E'1.00000000000000000000'
+         DC    E'0.57721566490153286061'
+         DC    E'-0.65587807152025388108'
+         DC    E'-0.04200263503409523553'
+         DC    E'0.16653861138229148950'
+         DC    E'-0.04219773455554433675'
+         DC    E'-0.00962197152787697356'
+         DC    E'0.00721894324666309954'
+         DC    E'-0.00116516759185906511'
+         DC    E'-0.00021524167411495097'
+         DC    E'0.00012805028238811619'
+         DC    E'-0.00002013485478078824'
+         DC    E'-0.00000125049348214267'
+         DC    E'0.00000113302723198170'
+         DC    E'-0.00000020563384169776'
+         DC    E'0.00000000611609510448'
+         DC    E'0.00000000500200764447'
+         DC    E'-0.00000000118127457049'
+         DC    E'0.00000000010434267117'
+         DC    E'0.00000000000778226344'
+         DC    E'-0.00000000000369680562'
+         DC    E'0.00000000000051003703'
+         DC    E'-0.00000000000002058326'
+         DC    E'-0.00000000000000534812'
+         DC    E'0.00000000000000122678'
+         DC    E'-0.00000000000000011813'
+         DC    E'0.00000000000000000119'
+         DC    E'0.00000000000000000141'
+         DC    E'-0.00000000000000000023'
+         DC    E'0.00000000000000000002'
+TEND     DS    0E
+X        DS    E
+SUM      DS    E
+GAMMA    DS    E
+WTOMSG   DS    0F
+         DC    AL2(L'BUF),XL2'0000'
+BUF      DC    CL80' '
+*        Subroutine             Convertion Float->Display
+CONVERT  CNOP  0,4
+         ME    F0,CONVERTC
+         STE   F0,CONVERTF
+         MVI   CONVERTS,X'00'
+         L     R9,CONVERTF
+         CH    R9,=H'0'
+         BZ    CONVERT7
+         BNL   CONVERT1         is negative?
+         MVI   CONVERTS,X'80'
+         N     R9,=X'7FFFFFFF'  sign bit
+CONVERT1 LR    R8,R9
+         N     R8,=X'00FFFFFF'
+         BNZ   CONVERT2
+         SR    R9,R9
+         B     CONVERT7
+CONVERT2 LR    R8,R9
+         N     R8,=X'FF000000'  characteristic
+         SRL   R8,24
+         CH    R8,=H'64'
+         BH    CONVERT3
+         SR    R9,R9
+         B     CONVERT7
+CONVERT3 CH    R8,=H'72'        2**32
+         BNH   CONVERT4
+         L     R9,=X'7FFFFFFF'  biggest
+         B     CONVERT6
+CONVERT4 SR    R8,R8
+         SLDL  R8,8
+         CH    R8,=H'72'
+         BL    CONVERT5
+         CH    R9,=H'0'
+         BP    CONVERT5
+         L     R9,=X'7FFFFFFF'
+         B     CONVERT6
+CONVERT5 SH    R8,=H'72'
+         LCR   R8,R8
+         SLL   R8,2
+         SRL   R9,0(R8)
+CONVERT6 SR    R8,R8
+         IC    R8,CONVERTS
+         CH    R8,=H'0'         sign bit set?
+         BZ    CONVERT7
+         LCR   R9,R9
+CONVERT7 ST    R9,CONVERTB
+         CVD   R9,CONVERTP
+         MVC   CONVERTD,=X'402020202120202020202020'
+         ED    CONVERTD,CONVERTP+2
+         MVC   CONVERTM(6),CONVERTD
+         MVI   CONVERTM+6,C'.'
+         MVC   CONVERTM+7(6),CONVERTD+6
+         BR    R14
+*
+CONVERTC DC    E'1E6'           X'45F42400'
+CONVERTF DS    F
+CONVERTB DS    F
+CONVERTS DS    X
+CONVERTM DS    CL13
+CONVERTD DS    CL12
+CONVERTP DS    PL8
+*
+         EQUREGS
+         EQUREGS REGS=FPR
+         END   GAMMAT
--- a/Task/Gamma-function/ALGOL-68/gamma-function.alg
+++ b/Task/Gamma-function/ALGOL-68/gamma-function.alg
@ -0,0 +1,131 @@
+# Coefficients used by the GNU Scientific Library #
+[]LONG REAL p = ( LONG    0.99999 99999 99809 93,
+                  LONG  676.52036 81218 851,
+                 -LONG 1259.13921 67224 028,
+                  LONG  771.32342 87776 5313,
+                 -LONG  176.61502 91621 4059,
+                  LONG   12.50734 32786 86905,
+                 -LONG    0.13857 10952 65720 12,
+                  LONG    9.98436 95780 19571 6e-6,
+                  LONG    1.50563 27351 49311 6e-7);
+
+PROC lanczos gamma = (LONG REAL in z)LONG REAL: (
+  # Reflection formula #
+  LONG REAL z := in z;
+  IF z < LONG 0.5 THEN
+    long pi / (long sin(long pi*z)*lanczos gamma(1-z))
+  ELSE
+    z -:= 1;
+    LONG REAL x := p[1];
+    FOR i TO UPB p - 1 DO x +:= p[i+1]/(z+i) OD;
+    LONG REAL t = z + UPB p - LONG 1.5;
+    long sqrt(2*long pi) * t**(z+LONG 0.5) * long exp(-t) * x
+  FI
+);
+
+PROC taylor gamma = (LONG REAL x)LONG REAL:
+BEGIN # good for values between 0 and 1 #
+    []LONG REAL a =
+        ( LONG 1.00000 00000 00000 00000,
+          LONG 0.57721 56649 01532 86061,
+         -LONG 0.65587 80715 20253 88108,
+         -LONG 0.04200 26350 34095 23553,
+          LONG 0.16653 86113 82291 48950,
+         -LONG 0.04219 77345 55544 33675,
+         -LONG 0.00962 19715 27876 97356,
+          LONG 0.00721 89432 46663 09954,
+         -LONG 0.00116 51675 91859 06511,
+         -LONG 0.00021 52416 74114 95097,
+          LONG 0.00012 80502 82388 11619,
+         -LONG 0.00002 01348 54780 78824,
+         -LONG 0.00000 12504 93482 14267,
+          LONG 0.00000 11330 27231 98170,
+         -LONG 0.00000 02056 33841 69776,
+          LONG 0.00000 00061 16095 10448,
+          LONG 0.00000 00050 02007 64447,
+         -LONG 0.00000 00011 81274 57049,
+          LONG 0.00000 00001 04342 67117,
+          LONG 0.00000 00000 07782 26344,
+         -LONG 0.00000 00000 03696 80562,
+          LONG 0.00000 00000 00510 03703,
+         -LONG 0.00000 00000 00020 58326,
+         -LONG 0.00000 00000 00005 34812,
+          LONG 0.00000 00000 00001 22678,
+         -LONG 0.00000 00000 00000 11813,
+          LONG 0.00000 00000 00000 00119,
+          LONG 0.00000 00000 00000 00141,
+         -LONG 0.00000 00000 00000 00023,
+          LONG 0.00000 00000 00000 00002
+        );
+    LONG REAL y = x - 1;
+    LONG REAL sum := a [UPB a];
+    FOR n FROM UPB a - 1 DOWNTO LWB a DO
+       sum := sum * y + a [n]
+    OD;
+    1/sum
+END # taylor gamma #;
+
+LONG REAL long e = long exp(1);
+
+PROC sterling gamma = (LONG REAL n)LONG REAL:
+( # improves for values much greater then 1 #
+  long sqrt(2*long pi/n)*(n/long e)**n
+);
+
+PROC factorial = (LONG INT n)LONG REAL:
+(
+  IF n=0 OR n=1 THEN 1
+  ELIF n=2 THEN 2
+  ELSE n*factorial(n-1) FI
+);
+
+REF[]LONG REAL fm := NIL;
+
+PROC sponge gamma = (LONG REAL x)LONG REAL:
+(
+  INT a = 12; # alter to get required precision #
+  REF []LONG REAL fm := NIL;
+  LONG REAL res;
+
+  IF fm :=: REF[]LONG REAL(NIL) THEN
+    fm := HEAP[0:a-1]LONG REAL;
+    fm[0] := long sqrt(LONG 2*long pi);
+    FOR k TO a-1 DO
+      fm[k] := (((k-1) MOD 2=0) | 1 | -1) * long exp(a-k) *
+	(a-k) **(k-LONG 0.5) / factorial(k-1)
+    OD
+  FI;
+  res := fm[0];
+  FOR k TO a-1 DO
+    res +:= fm[k] / ( x + k )
+  OD;
+  res *:= long exp(-(x+a)) * (x+a)**(x + LONG 0.5);
+  res/x
+);
+
+FORMAT real fmt = $g(-real width, real width - 2)$;
+FORMAT long real fmt16 = $g(-17, 17 - 2)$; # accurate to about 16 decimal places #
+
+[]STRING methods = ("Genie", "Lanczos", "Sponge", "Taylor","Stirling");
+
+printf(($11xg12xg12xg13xg13xgl$,methods));
+
+FORMAT sample fmt = $"gamma("g(-3,1)")="f(real fmt)n(UPB methods-1)(", "f(long real fmt16))l$;
+FORMAT sqr sample fmt = $"gamma("g(-3,1)")**2="f(real fmt)n(UPB methods-1)(", "f(long real fmt16))l$;
+FORMAT sample exp fmt = $"gamma("g(-3)")="g(-15,11,0)n(UPB methods-1)(","g(-18,14,0))l$;
+
+PROC sample = (LONG REAL x)[]LONG REAL:
+  (gamma(SHORTEN x), lanczos gamma(x), sponge gamma(x), taylor gamma(x), sterling gamma(x));
+
+FOR i FROM 1 TO 20 DO
+  LONG REAL x = i / LONG 10;
+  printf((sample fmt, x, sample(x)));
+  IF i = 5 THEN # insert special case of a half #
+    printf((sqr sample fmt,
+            x, gamma(SHORTEN x)**2,  lanczos gamma(x)**2, sponge gamma(x)**2,
+            taylor gamma(x)**2, sterling gamma(x)**2))
+  FI
+OD;
+FOR x FROM 10 BY 10 TO 70 DO
+  printf((sample exp fmt, x, sample(x)))
+OD
--- a/Task/Gamma-function/ANSI-BASIC/gamma-function.basic
+++ b/Task/Gamma-function/ANSI-BASIC/gamma-function.basic
@ -0,0 +1,26 @@
+100 DECLARE EXTERNAL FUNCTION FNlngamma
+110
+120 DEF FNgamma(z) = EXP(FNlngamma(z))
+130
+140 FOR x = 0.1 TO 2.05 STEP 0.1
+150    PRINT USING$("#.#",x), USING$("##.############", FNgamma(x))
+160 NEXT x
+170 END
+180
+190 EXTERNAL FUNCTION FNlngamma(z)
+200 DIM lz(0 TO 6)
+210 RESTORE
+220 MAT READ lz
+230 DATA 1.000000000190015, 76.18009172947146, -86.50532032941677, 24.01409824083091, -1.231739572450155, 0.0012086509738662, -0.000005395239385
+240 IF z < 0.5 THEN
+250    LET FNlngamma = LOG(PI / SIN(PI * z)) - FNlngamma(1.0 - z)
+260    EXIT FUNCTION
+270 END IF
+280 LET z = z - 1.0
+290 LET b = z + 5.5
+300 LET a = lz(0)
+310 FOR i = 1 TO 6
+320    LET a  = a + lz(i) / (z + i)
+330 NEXT i
+340 LET FNlngamma = (LOG(SQR(2*PI)) + LOG(a) - b) + LOG(b) * (z+0.5)
+350 END FUNCTION
--- a/Task/Gamma-function/AWK/gamma-function.awk
+++ b/Task/Gamma-function/AWK/gamma-function.awk
@ -0,0 +1,18 @@
+# syntax: GAWK -f GAMMA_FUNCTION.AWK
+BEGIN {
+    e = (1+1/100000)^100000
+    pi = atan2(0,-1)
+
+    print("X    Stirling")
+    for (i=1; i<=20; i++) {
+      d = i / 10
+      printf("%4.2f %9.5f\n",d,gamma_stirling(d))
+    }
+    exit(0)
+}
+function gamma_stirling(x) {
+    return sqrt(2*pi/x) * pow(x/e,x)
+}
+function pow(a,b) {
+    return exp(b*log(a))
+}
--- a/Task/Gamma-function/Ada/gamma-function-1.ada
+++ b/Task/Gamma-function/Ada/gamma-function-1.ada
@ -0,0 +1,41 @@
+function Gamma (X : Long_Float) return Long_Float is
+   A : constant array (0..29) of Long_Float :=
+       (  1.00000_00000_00000_00000,
+          0.57721_56649_01532_86061,
+         -0.65587_80715_20253_88108,
+         -0.04200_26350_34095_23553,
+          0.16653_86113_82291_48950,
+         -0.04219_77345_55544_33675,
+         -0.00962_19715_27876_97356,
+          0.00721_89432_46663_09954,
+         -0.00116_51675_91859_06511,
+         -0.00021_52416_74114_95097,
+          0.00012_80502_82388_11619,
+         -0.00002_01348_54780_78824,
+         -0.00000_12504_93482_14267,
+          0.00000_11330_27231_98170,
+         -0.00000_02056_33841_69776,
+          0.00000_00061_16095_10448,
+          0.00000_00050_02007_64447,
+         -0.00000_00011_81274_57049,
+          0.00000_00001_04342_67117,
+          0.00000_00000_07782_26344,
+         -0.00000_00000_03696_80562,
+          0.00000_00000_00510_03703,
+         -0.00000_00000_00020_58326,
+         -0.00000_00000_00005_34812,
+          0.00000_00000_00001_22678,
+         -0.00000_00000_00000_11813,
+          0.00000_00000_00000_00119,
+          0.00000_00000_00000_00141,
+         -0.00000_00000_00000_00023,
+          0.00000_00000_00000_00002
+       );
+   Y   : constant Long_Float := X - 1.0;
+   Sum : Long_Float := A (A'Last);
+begin
+   for N in reverse A'First..A'Last - 1 loop
+      Sum := Sum * Y + A (N);
+   end loop;
+   return 1.0 / Sum;
+end Gamma;
--- a/Task/Gamma-function/Ada/gamma-function-2.ada
+++ b/Task/Gamma-function/Ada/gamma-function-2.ada
@ -0,0 +1,9 @@
+with Ada.Text_IO;  use Ada.Text_IO;
+with Gamma;
+
+procedure Test_Gamma is
+begin
+   for I in 1..10 loop
+      Put_Line (Long_Float'Image (Gamma (Long_Float (I) / 3.0)));
+   end loop;
+end Test_Gamma;
--- a/Task/Gamma-function/Arturo/gamma-function.arturo
+++ b/Task/Gamma-function/Arturo/gamma-function.arturo
@ -0,0 +1,32 @@
+A: @[
+    1.00000000000000000000     0.57721566490153286061 neg 0.65587807152025388108
+neg 0.04200263503409523553     0.16653861138229148950 neg 0.04219773455554433675
+neg 0.00962197152787697356     0.00721894324666309954 neg 0.00116516759185906511
+neg 0.00021524167411495097     0.00012805028238811619 neg 0.00002013485478078824
+neg 0.00000125049348214267     0.00000113302723198170 neg 0.00000020563384169776
+    0.00000000611609510448     0.00000000500200764447 neg 0.00000000118127457049
+    0.00000000010434267117     0.00000000000778226344 neg 0.00000000000369680562
+    0.00000000000051003703 neg 0.00000000000002058326 neg 0.00000000000000534812
+    0.00000000000000122678 neg 0.00000000000000011813     0.00000000000000000119
+    0.00000000000000000141 neg 0.00000000000000000023     0.00000000000000000002
+]
+
+ourGamma: function [x][
+    y: x - 1
+    result: last A
+    loop ((size A)-1)..0 'n ->
+        result: (result*y) + get A n
+    result: 1 // result
+    return result
+]
+
+loop 1..10 'z [
+    v1: ourGamma z // 3
+    v2: gamma z // 3
+    print [
+        pad (to :string z)++" =>" 10
+        pad (to :string v1)++" ~" 30
+        pad (to :string v2)++" :" 30
+        pad (to :string v1-v2) 30
+    ]
+]
--- a/Task/Gamma-function/AutoHotkey/gamma-function.ahk
+++ b/Task/Gamma-function/AutoHotkey/gamma-function.ahk
@ -0,0 +1,82 @@
+/*
+Here is the upper incomplete Gamma function. Omitting or setting
+the second parameter to 0 we get the (complete) Gamma function.
+The code is based on: "Computation of Special Functions" Zhang and Jin,
+John Wiley and Sons, 1996
+*/
+
+SetFormat FloatFast, 0.9e
+
+Loop 10
+   MsgBox % GAMMA(A_Index/3) "`n" GAMMA(A_Index*10)
+
+GAMMA(a,x=0) {  ; upper incomplete gamma: Integral(t**(a-1)*e**-t, t = x..inf)
+   If (a > 171 || x < 0)
+      Return 2.e308   ; overflow
+
+   xam := x > 0 ? -x+a*ln(x) : 0
+   If (xam > 700)
+      Return 2.e308   ; overflow
+
+   If (x > 1+a) {     ; no need for gamma(a)
+      t0 := 0, k := 60
+      Loop 60
+          t0 := (k-a)/(1+k/(x+t0)), --k
+      Return exp(xam) / (x+t0)
+   }
+
+   r := 1, ga := 1.0  ; compute ga = gamma(a) ...
+   If (a = round(a))  ; if integer: factorial
+      If (a > 0)
+         Loop % a-1
+            ga *= A_Index
+      Else            ; negative integer
+         ga := 1.7976931348623157e+308 ; Dmax
+   Else {             ; not integer
+      If (abs(a) > 1) {
+         z := abs(a)
+         m := floor(z)
+         Loop %m%
+             r *= (z-A_Index)
+         z -= m
+      }
+      Else
+         z := a
+
+      gr := (((((((((((((((((((((((       0.14e-14
+          *z - 0.54e-14)             *z - 0.206e-13)          *z + 0.51e-12)
+          *z - 0.36968e-11)          *z + 0.77823e-11)        *z + 0.1043427e-9)
+          *z - 0.11812746e-8)        *z + 0.50020075e-8)      *z + 0.6116095e-8)
+          *z - 0.2056338417e-6)      *z + 0.1133027232e-5)    *z - 0.12504934821e-5)
+          *z - 0.201348547807e-4)    *z + 0.1280502823882e-3) *z - 0.2152416741149e-3)
+          *z - 0.11651675918591e-2)  *z + 0.7218943246663e-2) *z - 0.9621971527877e-2)
+          *z - 0.421977345555443e-1) *z + 0.1665386113822915) *z - 0.420026350340952e-1)
+          *z - 0.6558780715202538)   *z + 0.5772156649015329) *z + 1
+
+      ga := 1.0/(gr*z) * r
+      If (a < -1)
+         ga := -3.1415926535897931/(a*ga*sin(3.1415926535897931*a))
+   }
+
+   If (x = 0)         ; complete gamma requested
+      Return ga
+
+   s := 1/a           ; here x <= 1+a
+   r := s
+   Loop 60 {
+      r *= x/(a+A_Index)
+      s += r
+      If (abs(r/s) < 1.e-15)
+         break
+   }
+   Return ga - exp(xam)*s
+}
+
+/*
+The 10 results shown:
+2.678938535e+000  1.354117939e+000  1.0               8.929795115e-001  9.027452930e-001
+3.628800000e+005  1.216451004e+017  8.841761994e+030  2.039788208e+046  6.082818640e+062
+
+1.000000000e+000  1.190639348e+000  1.504575489e+000  2.000000000e+000  2.778158479e+000
+1.386831185e+080  1.711224524e+098  8.946182131e+116  1.650795516e+136  9.332621544e+155
+*/
--- a/Task/Gamma-function/BASIC256/gamma-function.basic
+++ b/Task/Gamma-function/BASIC256/gamma-function.basic
@ -0,0 +1,29 @@
+print " x       Stirling         Lanczos"
+print
+for i = 1 to 20
+    d = i / 10.0
+    print d;
+    print chr(9); ljust(string(gammaStirling(d)), 13, "0");
+    print chr(9); ljust(string(gammaLanczos(d)),  13, "0")
+next i
+end
+
+function gammaStirling (x)
+    e = exp(1)	# e is not predefined in BASIC256
+    return sqr(2.0 * pi / x) * ((x / e) ^ x)
+end function
+
+function gammaLanczos (x)
+    dim p = {0.99999999999980993, 676.5203681218851, -1259.1392167224028, 771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7}
+
+    g = 7
+    if x < 0.5 then return pi / (sin(pi * x) * gammaLanczos(1-x))
+    x -= 1
+    a = p[0]
+    t = x + g + 0.5
+
+    for i = 1 to 8
+	a += p[i] / (x + i)
+    next i
+    return sqr(2.0 * pi) * (t ^ (x + 0.5)) * exp(-t) * a
+end function
--- a/Task/Gamma-function/BBC-BASIC/gamma-function.basic
+++ b/Task/Gamma-function/BBC-BASIC/gamma-function.basic
@ -0,0 +1,23 @@
+      *FLOAT64
+      INSTALL @lib$+"FNUSING"
+
+      FOR x = 0.1 TO 2.05 STEP 0.1
+        PRINT FNusing("#.#",x), FNusing("##.############", FNgamma(x))
+      NEXT
+      END
+
+      DEF FNgamma(z) = EXP(FNlngamma(z))
+
+      DEF FNlngamma(z)
+      LOCAL a, b, i%, lz()
+      DIM lz(6)
+      lz() = 1.000000000190015, 76.18009172947146, -86.50532032941677, \
+      \ 24.01409824083091, -1.231739572450155, 0.0012086509738662, -0.000005395239385
+      IF z < 0.5 THEN = LN(PI / SIN(PI * z)) - FNlngamma(1.0 - z)
+      z -= 1.0
+      b = z + 5.5
+      a = lz(0)
+      FOR i% = 1 TO 6
+        a += lz(i%) / (z + i%)
+      NEXT
+      = (LNSQR(2*PI) + LN(a) - b) + LN(b) * (z+0.5)
--- a/Task/Gamma-function/C++/gamma-function.cpp
+++ b/Task/Gamma-function/C++/gamma-function.cpp
@ -0,0 +1,58 @@
+#include <math.h>
+#include <numbers>
+#include <stdio.h>
+#include <vector>
+
+// Calculate the coefficients used by Spouge's approximation (based on the C
+// implemetation)
+std::vector<double> CalculateCoefficients(int numCoeff)
+{
+    std::vector<double> c(numCoeff);
+    double k1_factrl = 1.0;
+    c[0] = sqrt(2.0 * std::numbers::pi);
+    for(size_t k=1; k < numCoeff; k++)
+    {
+        c[k] = exp(numCoeff-k) * pow(numCoeff-k, k-0.5) / k1_factrl;
+        k1_factrl *= -(double)k;
+    }
+    return c;
+}
+
+// The Spouge approximation
+double Gamma(const std::vector<double>& coeffs, double x)
+{
+        const size_t numCoeff = coeffs.size();
+        double accm = coeffs[0];
+        for(size_t k=1; k < numCoeff; k++)
+        {
+            accm += coeffs[k] / ( x + k );
+        }
+        accm *= exp(-(x+numCoeff)) * pow(x+numCoeff, x+0.5);
+        return accm/x;
+}
+
+int main()
+{
+    // estimate the gamma function with 1, 4, and 10 coefficients
+    const auto coeff1 = CalculateCoefficients(1);
+    const auto coeff4 = CalculateCoefficients(4);
+    const auto coeff10 = CalculateCoefficients(10);
+
+    const auto inputs = std::vector<double>{
+        0.001, 0.01, 0.1, 0.5, 1.0,
+        1.461632145, // minimum of the gamma function
+        2, 2.5, 3, 4, 5, 6, 7, 8, 9, 10, 50, 100,
+        150 // causes overflow for this implemetation
+        };
+
+    printf("%16s%16s%16s%16s%16s\n", "gamma( x ) =", "Spouge 1", "Spouge 4", "Spouge 10", "built-in");
+    for(auto x : inputs)
+    {
+        printf("gamma(%7.3f) = %16.10g %16.10g %16.10g %16.10g\n",
+            x,
+            Gamma(coeff1, x),
+            Gamma(coeff4, x),
+            Gamma(coeff10, x),
+            std::tgamma(x)); // built-in gamma function
+    }
+}
--- a/Task/Gamma-function/C-sharp/gamma-function.cs
+++ b/Task/Gamma-function/C-sharp/gamma-function.cs
@ -0,0 +1,27 @@
+using System;
+using System.Numerics;
+
+static int g = 7;
+static double[] p = {0.99999999999980993, 676.5203681218851, -1259.1392167224028,
+	     771.32342877765313, -176.61502916214059, 12.507343278686905,
+	     -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7};
+		
+Complex Gamma(Complex z)
+{
+    // Reflection formula
+    if (z.Real < 0.5)
+	{
+        return Math.PI / (Complex.Sin( Math.PI * z) * Gamma(1 - z));
+	}
+    else
+	{
+        z -= 1;
+        Complex x = p[0];
+        for (var i = 1; i < g + 2; i++)
+		{
+            x += p[i]/(z+i);
+		}
+        Complex t = z + g + 0.5;
+        return Complex.Sqrt(2 * Math.PI) * (Complex.Pow(t, z + 0.5)) * Complex.Exp(-t) * x;
+	}
+}
--- a/Task/Gamma-function/C/gamma-function.c
+++ b/Task/Gamma-function/C/gamma-function.c
@ -0,0 +1,52 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <gsl/gsl_sf_gamma.h>
+#ifndef M_PI
+#define M_PI 3.14159265358979323846
+#endif
+
+/* very simple approximation */
+double st_gamma(double x)
+{
+  return sqrt(2.0*M_PI/x)*pow(x/M_E, x);
+}
+
+#define A 12
+double sp_gamma(double z)
+{
+  const int a = A;
+  static double c_space[A];
+  static double *c = NULL;
+  int k;
+  double accm;
+
+  if ( c == NULL ) {
+    double k1_factrl = 1.0; /* (k - 1)!*(-1)^k with 0!==1*/
+    c = c_space;
+    c[0] = sqrt(2.0*M_PI);
+    for(k=1; k < a; k++) {
+      c[k] = exp(a-k) * pow(a-k, k-0.5) / k1_factrl;
+	  k1_factrl *= -k;
+    }
+  }
+  accm = c[0];
+  for(k=1; k < a; k++) {
+    accm += c[k] / ( z + k );
+  }
+  accm *= exp(-(z+a)) * pow(z+a, z+0.5); /* Gamma(z+1) */
+  return accm/z;
+}
+
+int main()
+{
+  double x;
+
+
+  printf("%15s%15s%15s%15s\n", "Stirling", "Spouge", "GSL", "libm");
+  for(x=1.0; x <= 10.0; x+=1.0) {
+    printf("%15.8lf%15.8lf%15.8lf%15.8lf\n", st_gamma(x/3.0), sp_gamma(x/3.0),
+	   gsl_sf_gamma(x/3.0), tgamma(x/3.0));
+  }
+  return 0;
+}
--- a/Task/Gamma-function/Clojure/gamma-function-1.clj
+++ b/Task/Gamma-function/Clojure/gamma-function-1.clj
@ -0,0 +1,15 @@
+(defn gamma
+  "Returns Gamma(z + 1 = number) using Lanczos approximation."
+  [number]
+  (if (< number 0.5)
+       (/ Math/PI (* (Math/sin (* Math/PI number))
+	             (gamma (- 1 number))))
+       (let [n (dec number)
+      	     c [0.99999999999980993 676.5203681218851 -1259.1392167224028
+	        771.32342877765313 -176.61502916214059 12.507343278686905
+	        -0.13857109526572012 9.9843695780195716e-6 1.5056327351493116e-7]]
+         (* (Math/sqrt (* 2 Math/PI))
+	    (Math/pow (+ n 7 0.5) (+ n 0.5))
+	    (Math/exp (- (+ n 7 0.5)))
+            (+ (first c)
+               (apply + (map-indexed #(/ %2 (+ n %1 1)) (next c))))))))
--- a/Task/Gamma-function/Clojure/gamma-function-2.clj
+++ b/Task/Gamma-function/Clojure/gamma-function-2.clj
@ -0,0 +1 @@
+(map #(printf "%.1f %.4f\n" % (gamma %)) (map #(float (/ % 10)) (range 1 31)))
--- a/Task/Gamma-function/Common-Lisp/gamma-function.lisp
+++ b/Task/Gamma-function/Common-Lisp/gamma-function.lisp
@ -0,0 +1,26 @@
+; Taylor series coefficients
+(defconstant tcoeff
+  '( 1.00000000000000000000  0.57721566490153286061 -0.65587807152025388108
+    -0.04200263503409523553  0.16653861138229148950 -0.04219773455554433675
+    -0.00962197152787697356  0.00721894324666309954 -0.00116516759185906511
+    -0.00021524167411495097  0.00012805028238811619 -0.00002013485478078824
+    -0.00000125049348214267  0.00000113302723198170 -0.00000020563384169776
+     0.00000000611609510448  0.00000000500200764447 -0.00000000118127457049
+     0.00000000010434267117  0.00000000000778226344 -0.00000000000369680562
+     0.00000000000051003703 -0.00000000000002058326 -0.00000000000000534812
+     0.00000000000000122678 -0.00000000000000011813  0.00000000000000000119
+     0.00000000000000000141 -0.00000000000000000023  0.00000000000000000002))
+
+; number of coefficients
+(defconstant numcoeff (length tcoeff))
+
+(defun gamma (x)
+  (let ((y (- x 1.0))
+        (sum (nth (- numcoeff 1) tcoeff)))
+    (loop for i from (- numcoeff 2) downto 0 do
+          (setf sum (+ (* sum y) (nth i tcoeff))))
+    (/ 1.0 sum)))
+
+(loop for i from 1 to 10
+   do (
+     format t "~12,10f~%" (gamma (/ i 3.0))))
--- a/Task/Gamma-function/Crystal/gamma-function.crystal
+++ b/Task/Gamma-function/Crystal/gamma-function.crystal
@ -0,0 +1,42 @@
+# Taylor Series
+def a
+   [ 1.00000_00000_00000_00000,  0.57721_56649_01532_86061, -0.65587_80715_20253_88108,
+    -0.04200_26350_34095_23553,  0.16653_86113_82291_48950, -0.04219_77345_55544_33675,
+    -0.00962_19715_27876_97356,  0.00721_89432_46663_09954, -0.00116_51675_91859_06511,
+    -0.00021_52416_74114_95097,  0.00012_80502_82388_11619, -0.00002_01348_54780_78824,
+    -0.00000_12504_93482_14267,  0.00000_11330_27231_98170, -0.00000_02056_33841_69776,
+     0.00000_00061_16095_10448,  0.00000_00050_02007_64447, -0.00000_00011_81274_57049,
+     0.00000_00001_04342_67117,  0.00000_00000_07782_26344, -0.00000_00000_03696_80562,
+     0.00000_00000_00510_03703, -0.00000_00000_00020_58326, -0.00000_00000_00005_34812,
+     0.00000_00000_00001_22678, -0.00000_00000_00000_11813,  0.00000_00000_00000_00119,
+     0.00000_00000_00000_00141, -0.00000_00000_00000_00023,  0.00000_00000_00000_00002 ]
+end
+
+def taylor_gamma(x)
+  y = x.to_f - 1
+  1.0 / a.reverse.reduce(0) { |sum, an| sum * y + an }
+end
+
+# Lanczos Method
+def p
+  [ 0.99999_99999_99809_93, 676.52036_81218_851, -1259.13921_67224_028,
+    771.32342_87776_5313, -176.61502_91621_4059,  12.50734_32786_86905,
+    -0.13857_10952_65720_12, 9.98436_95780_19571_6e-6, 1.50563_27351_49311_6e-7 ]
+end
+
+def lanczos_gamma(z)
+  # Reflection formula
+  z = z.to_f
+  if z < 0.5
+    Math::PI / (Math.sin(Math::PI * z) * lanczos_gamma(1 - z))
+  else
+    z -= 1
+    x = p[0]
+    (1..p.size - 1).each { |i| x += p[i] / (z + i) }
+    t = z + p.size - 1.5
+    Math.sqrt(2 * Math::PI) * t**(z + 0.5) * Math.exp(-t) * x
+  end
+end
+
+puts "                Taylor Series         Lanczos Method        Builtin Function"
+(1..27).each { |i| n = i/3.0; puts "gamma(%.2f) = %.14e  %.14e  %.14e" % [n, taylor_gamma(n), lanczos_gamma(n), Math.gamma(n)] }
--- a/Task/Gamma-function/D/gamma-function.d
+++ b/Task/Gamma-function/D/gamma-function.d
@ -0,0 +1,62 @@
+import std.stdio, std.math, std.mathspecial;
+
+real taylorGamma(in real x) pure nothrow @safe @nogc {
+    static immutable real[30] table = [
+     0x1p+0,                    0x1.2788cfc6fb618f4cp-1,
+    -0x1.4fcf4026afa2dcecp-1,  -0x1.5815e8fa27047c8cp-5,
+     0x1.5512320b43fbe5dep-3,  -0x1.59af103c340927bep-5,
+    -0x1.3b4af28483e214e4p-7,   0x1.d919c527f60b195ap-8,
+    -0x1.317112ce3a2a7bd2p-10, -0x1.c364fe6f1563ce9cp-13,
+     0x1.0c8a78cd9f9d1a78p-13, -0x1.51ce8af47eabdfdcp-16,
+    -0x1.4fad41fc34fbb2p-20,    0x1.302509dbc0de2c82p-20,
+    -0x1.b9986666c225d1d4p-23,  0x1.a44b7ba22d628acap-28,
+     0x1.57bc3fc384333fb2p-28, -0x1.44b4cedca388f7c6p-30,
+     0x1.cae7675c18606c6p-34,   0x1.11d065bfaf06745ap-37,
+    -0x1.0423bac8ca3faaa4p-38,  0x1.1f20151323cd0392p-41,
+    -0x1.72cb88ea5ae6e778p-46, -0x1.815f72a05f16f348p-48,
+     0x1.6198491a83bccbep-50,  -0x1.10613dde57a88bd6p-53,
+     0x1.5e3fee81de0e9c84p-60,  0x1.a0dc770fb8a499b6p-60,
+    -0x1.0f635344a29e9f8ep-62,  0x1.43d79a4b90ce8044p-66];
+
+    immutable real y = x - 1.0L;
+    real sm = table[$ - 1];
+    foreach_reverse (immutable an; table[0 .. $ - 1])
+        sm = sm * y + an;
+    return 1.0L / sm;
+}
+
+real lanczosGamma(real z) pure nothrow @safe @nogc {
+    // Coefficients used by the GNU Scientific Library.
+    // http://en.wikipedia.org/wiki/Lanczos_approximation
+    enum g = 7;
+    static immutable real[9] table =
+        [    0.99999_99999_99809_93,
+           676.52036_81218_851,
+         -1259.13921_67224_028,
+           771.32342_87776_5313,
+          -176.61502_91621_4059,
+            12.50734_32786_86905,
+            -0.13857_10952_65720_12,
+             9.98436_95780_19571_6e-6,
+             1.50563_27351_49311_6e-7];
+
+    // Reflection formula.
+    if (z < 0.5L) {
+        return PI / (sin(PI * z) * lanczosGamma(1 - z));
+    } else {
+        z -= 1;
+        real x = table[0];
+        foreach (immutable i; 1 .. g + 2)
+            x += table[i] / (z + i);
+        immutable real t = z + g + 0.5L;
+        return sqrt(2 * PI) * t ^^ (z + 0.5L) * exp(-t) * x;
+    }
+}
+
+void main() {
+    foreach (immutable i; 1 .. 11) {
+        immutable real x = i / 3.0L;
+        writefln("%f: %20.19e %20.19e %20.19e", x,
+                 x.taylorGamma, x.lanczosGamma, x.gamma);
+    }
+}
--- a/Task/Gamma-function/Delphi/gamma-function.delphi
+++ b/Task/Gamma-function/Delphi/gamma-function.delphi
@ -0,0 +1,26 @@
+program Gamma_function;
+
+{$APPTYPE CONSOLE}
+
+uses
+  System.SysUtils,
+  System.Math;
+
+function lanczos7(z: double): Double;
+begin
+  var t := z + 6.5;
+  var x := 0.99999999999980993 + 676.5203681218851 / z - 1259.1392167224028 / (z
+    + 1) + 771.32342877765313 / (z + 2) - 176.61502916214059 / (z + 3) +
+    12.507343278686905 / (z + 4) - 0.13857109526572012 / (z + 5) +
+    9.9843695780195716e-6 / (z + 6) + 1.5056327351493116e-7 / (z + 7);
+
+  Result := Sqrt(2) * Sqrt(pi) * Power(t, z - 0.5) * exp(-t) * x;
+end;
+
+begin
+  var xs: TArray<double> := [-0.5, 0.1, 0.5, 1, 1.5, 2, 3, 10, 140, 170];
+  writeln('    x              Lanczos7');
+  for var x in xs do
+    writeln(format('%5.1f %24.16g', [x, lanczos7(x)]));
+  readln;
+end.
--- a/Task/Gamma-function/Elixir/gamma-function.elixir
+++ b/Task/Gamma-function/Elixir/gamma-function.elixir
@ -0,0 +1,21 @@
+defmodule Gamma do
+  @a [ 1.00000_00000_00000_00000,  0.57721_56649_01532_86061, -0.65587_80715_20253_88108,
+      -0.04200_26350_34095_23553,  0.16653_86113_82291_48950, -0.04219_77345_55544_33675,
+      -0.00962_19715_27876_97356,  0.00721_89432_46663_09954, -0.00116_51675_91859_06511,
+      -0.00021_52416_74114_95097,  0.00012_80502_82388_11619, -0.00002_01348_54780_78824,
+      -0.00000_12504_93482_14267,  0.00000_11330_27231_98170, -0.00000_02056_33841_69776,
+       0.00000_00061_16095_10448,  0.00000_00050_02007_64447, -0.00000_00011_81274_57049,
+       0.00000_00001_04342_67117,  0.00000_00000_07782_26344, -0.00000_00000_03696_80562,
+       0.00000_00000_00510_03703, -0.00000_00000_00020_58326, -0.00000_00000_00005_34812,
+       0.00000_00000_00001_22678, -0.00000_00000_00000_11813,  0.00000_00000_00000_00119,
+       0.00000_00000_00000_00141, -0.00000_00000_00000_00023,  0.00000_00000_00000_00002 ]
+     |> Enum.reverse
+  def taylor(x) do
+    y = x - 1
+    1 / Enum.reduce(@a, 0, fn a,sum -> sum * y + a end)
+  end
+end
+
+Enum.each(Enum.map(1..10, &(&1/3)), fn x ->
+  :io.format "~f  ~18.15f~n", [x, Gamma.taylor(x)]
+end)
--- a/Task/Gamma-function/F-Sharp/gamma-function-1.fs
+++ b/Task/Gamma-function/F-Sharp/gamma-function-1.fs
@ -0,0 +1,14 @@
+open System
+
+let gamma z =
+    let lanczosCoefficients = [76.18009172947146;-86.50532032941677;24.01409824083091;-1.231739572450155;0.1208650973866179e-2;-0.5395239384953e-5]
+    let rec sumCoefficients acc i coefficients =
+        match coefficients with
+        | []   -> acc
+        | h::t -> sumCoefficients (acc + (h/i)) (i+1.0) t
+    let gamma = 5.0
+    let x = z - 1.0
+    Math.Pow(x + gamma + 0.5, x + 0.5) * Math.Exp( -(x + gamma + 0.5) ) * Math.Sqrt( 2.0 * Math.PI ) * sumCoefficients 1.000000000190015 (x + 1.0) lanczosCoefficients
+
+seq { for i in 1 .. 20 do yield ((double)i/10.0) } |> Seq.iter ( fun v -> System.Console.WriteLine("{0} : {1}", v, gamma v ) )
+seq { for i in 1 .. 10 do yield ((double)i*10.0) } |> Seq.iter ( fun v -> System.Console.WriteLine("{0} : {1}", v, gamma v ) )
--- a/Task/Gamma-function/F-Sharp/gamma-function-2.fs
+++ b/Task/Gamma-function/F-Sharp/gamma-function-2.fs
@ -0,0 +1,21 @@
+open System.Numerics
+open System
+
+let rec gamma (z: Complex) =
+    let mutable z = z
+    let lanczosCoefficients = [| 676.520368121885; -1259.1392167224; 771.323428777653; -176.615029162141; 12.5073432786869; -0.13857109526572; 9.98436957801957E-06; 1.50563273514931E-07 |]
+
+    if z.Real < 0.5 then
+        Math.PI / (sin (Math.PI * z) * gamma (1.0 - z))
+    else
+        let mutable x = Complex.One
+        z <- z - 1.0
+
+        for i = 0 to lanczosCoefficients.Length - 1 do
+            x <- x + lanczosCoefficients.[i] / (z + Complex(i, 0) + 1.0)
+
+        let t = z + float lanczosCoefficients.Length - 0.5
+        sqrt (2.0 * Math.PI) * (t ** (z + 0.5)) * exp (-t) * x
+
+Seq.iter (fun i -> printfn "Gamma(%f) = %A" i (gamma (Complex(i, 0)))) [ 0 .. 100 ]
+Seq.iter2 (fun i j -> printfn "Gamma(%f + i%f) = %A" i j (gamma (Complex(i, j)))) [ 0 .. 100 ] [ 0 .. 100 ]
--- a/Task/Gamma-function/Factor/gamma-function.factor
+++ b/Task/Gamma-function/Factor/gamma-function.factor
@ -0,0 +1,5 @@
+! built in
+USING: picomath prettyprint ;
+0.1 gamma .  ! 9.513507698668723
+2.0 gamma .  ! 1.0
+10. gamma .  ! 362880.0
--- a/Task/Gamma-function/Forth/gamma-function-1.fth
+++ b/Task/Gamma-function/Forth/gamma-function-1.fth
@ -0,0 +1,15 @@
+8 constant (gamma-shift)
+
+: (mortici)                            ( f1 -- f2)
+  -1 s>f f+ 1 s>f
+  fover 271828183e-8 f* 12 s>f f* f/
+  fover 271828183e-8 f/ f+
+  fover f** fswap
+  628318530e-8 f* fsqrt f*             \ 2*pi
+;
+
+: gamma                                ( f1 -- f2)
+  fdup f0< >r fdup f0= r> or abort" Gamma less or equal to zero"
+  fdup (gamma-shift) s>f f+ (mortici) fswap
+  1 s>f (gamma-shift) 0 do fover i s>f f+ f* loop fswap fdrop f/
+;
--- a/Task/Gamma-function/Forth/gamma-function-2.fth
+++ b/Task/Gamma-function/Forth/gamma-function-2.fth
@ -0,0 +1,25 @@
+2 constant (gamma-shift)               \ don't change this
+                                       \ an approximation of the d(x) function
+: ~d(x)                                ( f1 -- f2)
+  fdup 10 s>f f<                       \ use first symmetrical sigmoidal
+  if                                   \ for range 1-10
+    -2705443e-8 fswap 2280802e-6 f/ 1428045e-6 f** 1 s>f f+ f/ 3187831e-8 f+
+  else                                 \ use second symmetrical sigmoidal
+    -29372563e-9 fswap 1841693e-6 f/ 1052779e-6 f** 1 s>f f+ f/ 3330828e-8 f+
+  then 333333333e-10 fover f< if fdrop 1 s>f 30 s>f f/ then
+;                                      \ perform some sane clipping to infinity
+
+: (ramanujan)                          ( f1 -- f2)
+  fdup fdup f* 4 s>f f*                ( n 4n2)
+  fover fover f* fdup f+ f+ fover f+   ( n 8n3+4n2+n)
+  fover ~d(x) f+                       ( n 8n3+4n2+n+d[x])
+  1 s>f 6 s>f f/ f**                   ( n 8n3+4n2+n+d[x]^1/6)
+  fswap fdup 2.7182818284590452353e f/ ( 8n3+4n2+n+d[x]^1/6 n n/e)
+  fswap f** f* pi fsqrt f*             ( f)
+;
+
+: gamma                                ( f1 -- f2)
+  fdup f0< >r fdup f0= r> or abort" Gamma less or equal to zero"
+  fdup (gamma-shift) 1- s>f f+ (ramanujan) fswap
+  1 s>f (gamma-shift) 0 do fover i s>f f+ f* loop fswap fdrop f/
+;
--- a/Task/Gamma-function/Fortran/gamma-function.f
+++ b/Task/Gamma-function/Fortran/gamma-function.f
@ -0,0 +1,98 @@
+program ComputeGammaInt
+
+  implicit none
+
+  integer :: i
+
+  write(*, "(3A15)") "Simpson", "Lanczos", "Builtin"
+  do i=1, 10
+     write(*, "(3F15.8)") my_gamma(i/3.0), lacz_gamma(i/3.0), gamma(i/3.0)
+  end do
+
+contains
+
+  pure function intfuncgamma(x, y) result(z)
+    real :: z
+    real, intent(in) :: x, y
+
+    z = x**(y-1.0) * exp(-x)
+  end function intfuncgamma
+
+
+  function my_gamma(a) result(g)
+    real :: g
+    real, intent(in) :: a
+
+    real, parameter :: small = 1.0e-4
+    integer, parameter :: points = 100000
+
+    real :: infty, dx, p, sp(2, points), x
+    integer :: i
+    logical :: correction
+
+    x = a
+
+    correction = .false.
+    ! value with x<1 gives \infty, so we use
+    ! \Gamma(x+1) = x\Gamma(x)
+    ! to avoid the problem
+    if ( x < 1.0 ) then
+       correction = .true.
+       x = x + 1
+    end if
+
+    ! find a "reasonable" infinity...
+    ! we compute this integral indeed
+    ! \int_0^M dt t^{x-1} e^{-t}
+    ! where M is such that M^{x-1} e^{-M} ≤ \epsilon
+    infty = 1.0e4
+    do while ( intfuncgamma(infty, x) > small )
+       infty = infty * 10.0
+    end do
+
+    ! using simpson
+    dx = infty/real(points)
+    sp = 0.0
+    forall(i=1:points/2-1) sp(1, 2*i) = intfuncgamma(2.0*(i)*dx, x)
+    forall(i=1:points/2) sp(2, 2*i - 1) = intfuncgamma((2.0*(i)-1.0)*dx, x)
+    g = (intfuncgamma(0.0, x) + 2.0*sum(sp(1,:)) + 4.0*sum(sp(2,:)) + &
+         intfuncgamma(infty, x))*dx/3.0
+
+    if ( correction ) g = g/a
+
+  end function my_gamma
+
+
+  recursive function lacz_gamma(a) result(g)
+    real, intent(in) :: a
+    real :: g
+
+    real, parameter :: pi = 3.14159265358979324
+    integer, parameter :: cg = 7
+
+    ! these precomputed values are taken by the sample code in Wikipedia,
+    ! and the sample itself takes them from the GNU Scientific Library
+    real, dimension(0:8), parameter :: p = &
+         (/ 0.99999999999980993, 676.5203681218851, -1259.1392167224028, &
+         771.32342877765313, -176.61502916214059, 12.507343278686905, &
+         -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7 /)
+
+    real :: t, w, x
+    integer :: i
+
+    x = a
+
+    if ( x < 0.5 ) then
+       g = pi / ( sin(pi*x) * lacz_gamma(1.0-x) )
+    else
+       x = x - 1.0
+       t = p(0)
+       do i=1, cg+2
+          t = t + p(i)/(x+real(i))
+       end do
+       w = x + real(cg) + 0.5
+       g = sqrt(2.0*pi) * w**(x+0.5) * exp(-w) * t
+    end if
+  end function lacz_gamma
+
+end program ComputeGammaInt
--- a/Task/Gamma-function/FreeBASIC/gamma-function.basic
+++ b/Task/Gamma-function/FreeBASIC/gamma-function.basic
@ -0,0 +1,47 @@
+' FB 1.05.0 Win64
+
+Const pi = 3.1415926535897932
+Const e  = 2.7182818284590452
+
+Function gammaStirling (x As Double) As Double
+  Return Sqr(2.0 * pi / x) * ((x / e) ^ x)
+End Function
+
+Function gammaLanczos (x As Double) As Double
+  Dim p(0 To 8) As Double = _
+  { _
+       0.99999999999980993, _
+     676.5203681218851, _
+   -1259.1392167224028, _			     	
+     771.32342877765313, _
+    -176.61502916214059, _
+      12.507343278686905, _
+      -0.13857109526572012, _
+       9.9843695780195716e-6, _
+       1.5056327351493116e-7 _
+  }
+
+  Dim As Integer g = 7
+  If x < 0.5 Then Return pi / (Sin(pi * x) * gammaLanczos(1-x))
+  x -= 1
+  Dim a As Double = p(0)
+  Dim t As Double = x + g + 0.5
+
+  For i As Integer = 1 To 8
+    a += p(i) / (x + i)
+  Next		
+
+  Return Sqr(2.0 * pi) * (t ^ (x + 0.5)) * Exp(-t) * a
+End Function
+
+Print " x", "    Stirling",, "    Lanczos"
+Print
+For i As Integer = 1 To 20
+   Dim As Double d = i / 10.0
+   Print   Using "#.##"; d;
+   Print , Using "#.###############"; gammaStirling(d);
+   Print , Using "#.###############"; gammaLanczos(d)
+Next
+Print
+Print "Press any key to quit"
+Sleep
--- a/Task/Gamma-function/Go/gamma-function.go
+++ b/Task/Gamma-function/Go/gamma-function.go
@ -0,0 +1,27 @@
+package main
+
+import (
+    "fmt"
+    "math"
+)
+
+func main() {
+    fmt.Println("    x               math.Gamma                 Lanczos7")
+    for _, x := range []float64{-.5, .1, .5, 1, 1.5, 2, 3, 10, 140, 170} {
+        fmt.Printf("%5.1f %24.16g %24.16g\n", x, math.Gamma(x), lanczos7(x))
+    }
+}
+
+func lanczos7(z float64) float64 {
+    t := z + 6.5
+    x := .99999999999980993 +
+        676.5203681218851/z -
+        1259.1392167224028/(z+1) +
+        771.32342877765313/(z+2) -
+        176.61502916214059/(z+3) +
+        12.507343278686905/(z+4) -
+        .13857109526572012/(z+5) +
+        9.9843695780195716e-6/(z+6) +
+        1.5056327351493116e-7/(z+7)
+    return math.Sqrt2 * math.SqrtPi * math.Pow(t, z-.5) * math.Exp(-t) * x
+}
--- a/Task/Gamma-function/Groovy/gamma-function.groovy
+++ b/Task/Gamma-function/Groovy/gamma-function.groovy
@ -0,0 +1,14 @@
+a = [ 1.00000000000000000000, 0.57721566490153286061, -0.65587807152025388108,
+     -0.04200263503409523553, 0.16653861138229148950, -0.04219773455554433675,
+     -0.00962197152787697356, 0.00721894324666309954, -0.00116516759185906511,
+     -0.00021524167411495097, 0.00012805028238811619, -0.00002013485478078824,
+     -0.00000125049348214267, 0.00000113302723198170, -0.00000020563384169776,
+      0.00000000611609510448, 0.00000000500200764447, -0.00000000118127457049,
+      0.00000000010434267117, 0.00000000000778226344, -0.00000000000369680562,
+      0.00000000000051003703, -0.00000000000002058326, -0.00000000000000534812,
+      0.00000000000000122678, -0.00000000000000011813, 0.00000000000000000119,
+      0.00000000000000000141, -0.00000000000000000023, 0.00000000000000000002].reverse()
+
+def gamma = { 1.0 / a.inject(0) { sm, a_i -> sm * (it - 1) + a_i } }
+
+(1..10).each{ printf("%  1.9e\n", gamma(it / 3.0)) }
--- a/Task/Gamma-function/Haskell/gamma-function-1.hs
+++ b/Task/Gamma-function/Haskell/gamma-function-1.hs
@ -0,0 +1,21 @@
+cof :: [Double]
+cof =
+  [ 76.18009172947146
+  , -86.50532032941677
+  , 24.01409824083091
+  , -1.231739572450155
+  , 0.001208650973866179
+  , -0.000005395239384953
+  ]
+
+ser :: Double
+ser = 1.000000000190015
+
+gammaln :: Double -> Double
+gammaln xx =
+  let tmp_ = (xx + 5.5) - (xx + 0.5) * log (xx + 5.5)
+      ser_ = ser + sum (zipWith (/) cof [xx + 1 ..])
+  in -tmp_ + log (2.5066282746310005 * ser_ / xx)
+
+main :: IO ()
+main = mapM_ print $ gammaln <$> [0.1,0.2 .. 1.0]
--- a/Task/Gamma-function/Haskell/gamma-function-2.hs
+++ b/Task/Gamma-function/Haskell/gamma-function-2.hs
@ -0,0 +1,22 @@
+import Control.Applicative
+
+cof :: [Double]
+cof =
+  [ 76.18009172947146
+  , -86.50532032941677
+  , 24.01409824083091
+  , -1.231739572450155
+  , 0.001208650973866179
+  , -0.000005395239384953
+  ]
+
+gammaln :: Double -> Double
+gammaln =
+  ((+) . negate . (((-) . (5.5 +)) <*> (((*) . (0.5 +)) <*> (log . (5.5 +))))) <*>
+  (log .
+   ((/) =<<
+    (2.5066282746310007 *) .
+    (1.000000000190015 +) . sum . zipWith (/) cof . enumFrom . (1 +)))
+
+main :: IO ()
+main = mapM_ print $ gammaln <$> [0.1,0.2 .. 1.0]
--- a/Task/Gamma-function/Haskell/gamma-function-3.hs
+++ b/Task/Gamma-function/Haskell/gamma-function-3.hs
@ -0,0 +1,7 @@
+procedure main()
+    every write(left(i := !10/10.0,5),gamma(.i))
+end
+
+procedure gamma(z)	# Stirling's approximation
+    return (2*&pi/z)^0.5 * (z/&e)^z
+end
--- a/Task/Gamma-function/J/gamma-function-1.j
+++ b/Task/Gamma-function/J/gamma-function-1.j
@ -0,0 +1 @@
+gamma=: !@<:
--- a/Task/Gamma-function/J/gamma-function-2.j
+++ b/Task/Gamma-function/J/gamma-function-2.j
@ -0,0 +1,3 @@
+sbase =: %:@(2p1&%) * %&1x1 ^ ]
+scorr =: 1 1r12 1r288 _139r51840 _571r2488320&p.@%
+stirlg=: sbase * scorr
--- a/Task/Gamma-function/J/gamma-function-3.j
+++ b/Task/Gamma-function/J/gamma-function-3.j
@ -0,0 +1,6 @@
+   (,. stirlg ,. gamma) 10 1p1 1x1 1.5 1
+     10   362880   362880
+3.14159  2.28803  2.28804
+2.71828  1.56746  1.56747
+    1.5 0.886155 0.886227
+      1 0.999499        1
--- a/Task/Gamma-function/Java/gamma-function.java
+++ b/Task/Gamma-function/Java/gamma-function.java
@ -0,0 +1,31 @@
+public class GammaFunction {
+
+	public double st_gamma(double x){
+		return Math.sqrt(2*Math.PI/x)*Math.pow((x/Math.E), x);
+	}
+	
+	public double la_gamma(double x){
+		double[] p = {0.99999999999980993, 676.5203681218851, -1259.1392167224028,
+			     	  771.32342877765313, -176.61502916214059, 12.507343278686905,
+			     	  -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7};
+		int g = 7;
+		if(x < 0.5) return Math.PI / (Math.sin(Math.PI * x)*la_gamma(1-x));
+
+		x -= 1;
+		double a = p[0];
+		double t = x+g+0.5;
+		for(int i = 1; i < p.length; i++){
+			a += p[i]/(x+i);
+		}
+		
+		return Math.sqrt(2*Math.PI)*Math.pow(t, x+0.5)*Math.exp(-t)*a;
+	}
+	
+	public static void main(String[] args) {
+		GammaFunction test = new GammaFunction();
+		System.out.println("Gamma \t\tStirling \t\tLanczos");
+		for(double i = 1; i <= 20; i += 1){
+			System.out.println("" + i/10.0 + "\t\t" + test.st_gamma(i/10.0) + "\t" + test.la_gamma(i/10.0));
+		}
+	}
+}
--- a/Task/Gamma-function/JavaScript/gamma-function.js
+++ b/Task/Gamma-function/JavaScript/gamma-function.js
@ -0,0 +1,20 @@
+function gamma(x) {
+    var p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,
+        771.32342877765313, -176.61502916214059, 12.507343278686905,
+        -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7
+    ];
+
+    var g = 7;
+    if (x < 0.5) {
+        return Math.PI / (Math.sin(Math.PI * x) * gamma(1 - x));
+    }
+
+    x -= 1;
+    var a = p[0];
+    var t = x + g + 0.5;
+    for (var i = 1; i < p.length; i++) {
+        a += p[i] / (x + i);
+    }
+
+    return Math.sqrt(2 * Math.PI) * Math.pow(t, x + 0.5) * Math.exp(-t) * a;
+}
--- a/Task/Gamma-function/Jq/gamma-function-1.jq
+++ b/Task/Gamma-function/Jq/gamma-function-1.jq
@ -0,0 +1,16 @@
+def gamma:
+  [
+    1.00000000000000000000,  0.57721566490153286061,  -0.65587807152025388108, -0.04200263503409523553,
+    0.16653861138229148950, -0.04219773455554433675,  -0.00962197152787697356,  0.00721894324666309954,
+   -0.00116516759185906511, -0.00021524167411495097,   0.00012805028238811619, -0.00002013485478078824,
+   -0.00000125049348214267,  0.00000113302723198170,  -0.00000020563384169776,  0.00000000611609510448,
+    0.00000000500200764447, -0.00000000118127457049,   0.00000000010434267117,  0.00000000000778226344,
+   -0.00000000000369680562,  0.00000000000051003703,  -0.00000000000002058326, -0.00000000000000534812,
+    0.00000000000000122678, -0.00000000000000011813,   0.00000000000000000119,  0.00000000000000000141,
+   -0.00000000000000000023,  0.00000000000000000002
+  ] as $a
+  | (. - 1) as $y
+  | ($a|length) as $n
+  | reduce range(2; 1+$n) as $an
+      ($a[$n-1]; (. * $y) + $a[$n - $an])
+  | 1 / . ;
--- a/Task/Gamma-function/Jq/gamma-function-2.jq
+++ b/Task/Gamma-function/Jq/gamma-function-2.jq
@ -0,0 +1,16 @@
+# for reals, but easily extended to complex values
+def gamma_by_lanczos:
+  def pow(x): if x == 0 then 1 elif x == 1 then . else x * log | exp end;
+  . as $x
+  | ((1|atan) * 4) as $pi
+  | if $x < 0.5 then $pi / ((($pi * $x) | sin) * ((1-$x)|gamma_by_lanczos ))
+    else
+      [   0.99999999999980993, 676.5203681218851,     -1259.1392167224028,
+        771.32342877765313,   -176.61502916214059,       12.507343278686905,
+         -0.13857109526572012,   9.9843695780195716e-6,   1.5056327351493116e-7] as $p
+    | ($x - 1) as $x
+    | ($x + 7.5) as $t
+    |  reduce range(1; $p|length) as $i
+          ($p[0]; . + ($p[$i]/($x + $i) ))
+       * ((2*$pi) | sqrt) * ($t | pow($x+0.5)) * ((-$t)|exp)
+    end;
--- a/Task/Gamma-function/Jq/gamma-function-3.jq
+++ b/Task/Gamma-function/Jq/gamma-function-3.jq
@ -0,0 +1,5 @@
+def gamma_by_stirling:
+  def pow(x): if x == 0 then 1 elif x == 1 then . else x * log | exp end;
+  ((1|atan) * 8) as $twopi
+  | . as $x
+  | (($twopi/$x) | sqrt) * ( ($x / (1|exp)) | pow($x));
--- a/Task/Gamma-function/Jq/gamma-function-4.jq
+++ b/Task/Gamma-function/Jq/gamma-function-4.jq
@ -0,0 +1,6 @@
+def pad(n): tostring | . + (n - length) * " ";
+
+"                 i:      gamma                lanczos              tgamma",
+(range(1;11)
+ | . / 3.0
+ | "\(pad(18)): \(gamma|pad(18)) : \(gamma_by_lanczos|pad(18)) : \(tgamma)")
--- a/Task/Gamma-function/Jq/gamma-function-5.jq
+++ b/Task/Gamma-function/Jq/gamma-function-5.jq
@ -0,0 +1,12 @@
+$ jq -M -r -n -f Gamma_function_Stirling.jq
+                 i:      gamma                lanczos              tgamma
+0.3333333333333333: 2.6789385347077483 : 2.6789385347077483 : 2.678938534707748
+0.6666666666666666: 1.3541179394264005 : 1.3541179394263998 : 1.3541179394264005
+1                 : 1                  : 0.9999999999999998 : 1
+1.3333333333333333: 0.8929795115692493 : 0.8929795115692494 : 0.8929795115692493
+1.6666666666666667: 0.9027452929509336 : 0.9027452929509342 : 0.9027452929509336
+2                 : 1                  : 1.0000000000000002 : 1
+2.3333333333333335: 1.190639348758999  : 1.1906393487589995 : 1.190639348758999
+2.6666666666666665: 1.5045754882515399 : 1.5045754882515576 : 1.5045754882515558
+3                 : 1.9999999999939684 : 2.0000000000000013 : 2
+3.3333333333333335: 2.778158479338573  : 2.778158480437665  : 2.7781584804376647
--- a/Task/Gamma-function/Jsish/gamma-function.jsish
+++ b/Task/Gamma-function/Jsish/gamma-function.jsish
@ -0,0 +1,56 @@
+#!/usr/bin/env jsish
+/* Gamma function, in Jsish, using the Lanczos approximation */
+function gamma(x) {
+    var p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,
+        771.32342877765313, -176.61502916214059, 12.507343278686905,
+        -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7
+    ];
+
+    var g = 7;
+    if (x < 0.5) {
+        return Math.PI / (Math.sin(Math.PI * x) * gamma(1 - x));
+    }
+
+    x -= 1;
+    var a = p[0];
+    var t = x + g + 0.5;
+    for (var i = 1; i < p.length; i++) {
+        a += p[i] / (x + i);
+    }
+
+    return Math.sqrt(2 * Math.PI) * Math.pow(t, x + 0.5) * Math.exp(-t) * a;
+}
+
+if (Interp.conf('unitTest')) {
+    for (var i=-5.5; i <= 5.5; i += 0.5) {
+        printf('%2.1f %+e\n', i, gamma(i));
+    }
+}
+
+/*
+=!EXPECTSTART!=
+-5.5 +1.091265e-02
+-5.0 -4.275508e+13
+-4.5 -6.001960e-02
+-4.0 +2.672193e+14
+-3.5 +2.700882e-01
+-3.0 -1.425169e+15
+-2.5 -9.453087e-01
+-2.0 +6.413263e+15
+-1.5 +2.363272e+00
+-1.0 -2.565305e+16
+-0.5 -3.544908e+00
+0.0 +inf
+0.5 +1.772454e+00
+1.0 +1.000000e+00
+1.5 +8.862269e-01
+2.0 +1.000000e+00
+2.5 +1.329340e+00
+3.0 +2.000000e+00
+3.5 +3.323351e+00
+4.0 +6.000000e+00
+4.5 +1.163173e+01
+5.0 +2.400000e+01
+5.5 +5.234278e+01
+=!EXPECTEND!=
+*/
--- a/Task/Gamma-function/Julia/gamma-function-1.julia
+++ b/Task/Gamma-function/Julia/gamma-function-1.julia
@ -0,0 +1 @@
+@show gamma(1)
--- a/Task/Gamma-function/Julia/gamma-function-2.julia
+++ b/Task/Gamma-function/Julia/gamma-function-2.julia
@ -0,0 +1,3 @@
+using QuadGK
+gammaquad(t::Float64) = first(quadgk(x -> x ^ (t - 1) * exp(-x), zero(t), Inf, reltol = 100eps(t)))
+@show gammaquad(1.0)
--- a/Task/Gamma-function/Julia/gamma-function-3.julia
+++ b/Task/Gamma-function/Julia/gamma-function-3.julia
@ -0,0 +1,2 @@
+using SpecialFunctions
+gamma(1/2) - sqrt(pi)
--- a/Task/Gamma-function/Kotlin/gamma-function.kotlin
+++ b/Task/Gamma-function/Kotlin/gamma-function.kotlin
@ -0,0 +1,35 @@
+// version 1.0.6
+
+fun gammaStirling(x: Double): Double = Math.sqrt(2.0 * Math.PI / x) * Math.pow(x / Math.E, x)
+
+fun gammaLanczos(x: Double): Double {
+    var xx = x
+    val p = doubleArrayOf(
+        0.99999999999980993,
+      676.5203681218851,
+    -1259.1392167224028,			     	
+      771.32342877765313,
+     -176.61502916214059,
+       12.507343278686905,
+       -0.13857109526572012,
+        9.9843695780195716e-6,
+        1.5056327351493116e-7
+    )
+    val g = 7
+    if (xx < 0.5) return Math.PI / (Math.sin(Math.PI * xx) * gammaLanczos(1.0 - xx))
+    xx--
+    var a = p[0]
+    val t = xx + g + 0.5
+    for (i in 1 until p.size) a += p[i] / (xx + i)
+    return Math.sqrt(2.0 * Math.PI) * Math.pow(t, xx + 0.5) * Math.exp(-t) * a
+}
+
+fun main(args: Array<String>) {
+    println(" x\tStirling\t\tLanczos\n")
+    for (i in 1 .. 20) {
+        val d = i / 10.0
+        print("%4.2f\t".format(d))
+        print("%17.15f\t".format(gammaStirling(d)))
+        println("%17.15f".format(gammaLanczos(d)))
+    }
+}
--- a/Task/Gamma-function/Lambdatalk/gamma-function.lambdatalk
+++ b/Task/Gamma-function/Lambdatalk/gamma-function.lambdatalk
@ -0,0 +1,65 @@
+{def gamma.p
+ {A.new 0.99999999999980993
+      676.5203681218851
+    -1259.1392167224028
+      771.32342877765313
+     -176.61502916214059
+       12.507343278686905
+       -0.13857109526572012
+        9.9843695780195716e-6
+        1.5056327351493116e-7
+}}
+-> gamma.p
+
+{def gamma.rec
+ {lambda {:x :a :i}
+  {if {< :i {A.length {gamma.p}}}
+   then {gamma.rec :x
+                   {+ :a {/ {A.get :i {gamma.p}} {+ :x :i}} }
+                   {+ :i 1}}
+   else :a
+}}}
+-> gamma.rec
+
+{def gamma
+ {lambda {:x}
+  {if {< :x 0.5}
+   then {/ {PI}
+           {* {sin {* {PI} :x}}
+              {gamma {- 1 :x}}}}
+   else {let { {:x {- :x 1}}
+               {:t {+ {- :x 1} 7 0.5}}
+             } {* {sqrt {* 2 {PI}}}
+                  {pow :t {+ :x 0.5}}
+                  {exp -:t}
+                  {gamma.rec :x {A.first {gamma.p}} 1}}
+}}}}
+-> gamma
+
+{S.map {lambda {:i}
+               {div} Γ(:i) = {gamma :i}}
+       {S.serie -5.5 5.5 0.5}}
+
+ Γ(-5.5) = 0.010912654781909836
+ Γ(-5) = -42755084646679.17
+ Γ(-4.5) = -0.06001960130050417
+ Γ(-4) = 267219279041745.34
+ Γ(-3.5) = 0.27008820585226917
+ Γ(-3) = -1425169488222640
+ Γ(-2.5) = -0.9453087204829418
+ Γ(-2) = 6413262697001885
+ Γ(-1.5) = 2.363271801207352
+ Γ(-1) = -25653050788007544
+ Γ(-0.5) = -3.5449077018110295
+ Γ(0) = Infinity
+ Γ(0.5) = 1.7724538509055159
+ Γ(1) = 0.9999999999999998
+ Γ(1.5) = 0.8862269254527586
+ Γ(2) = 1.0000000000000002
+ Γ(2.5) = 1.3293403881791384
+ Γ(3) = 2.000000000000001
+ Γ(3.5) = 3.3233509704478426
+ Γ(4) = 6.000000000000007
+ Γ(4.5) = 11.631728396567446
+ Γ(5) = 23.999999999999996
+ Γ(5.5) = 52.34277778455358
--- a/Task/Gamma-function/Limbo/gamma-function.limbo
+++ b/Task/Gamma-function/Limbo/gamma-function.limbo
@ -0,0 +1,44 @@
+implement Lanczos7;
+
+include "sys.m"; sys: Sys;
+include "draw.m";
+include "math.m"; math: Math;
+	lgamma, exp, pow, sqrt: import math;
+
+Lanczos7: module {
+	init: fn(nil: ref Draw->Context, nil: list of string);
+};
+
+init(nil: ref Draw->Context, nil: list of string)
+{
+	sys = load Sys Sys->PATH;
+	math = load Math Math->PATH;
+	# We ignore some floating point exceptions:
+	math->FPcontrol(0, Math->OVFL|Math->UNFL);
+	ns : list of real = -0.5 :: 0.1 :: 0.5 :: 1.0 :: 1.5 :: 2.0 :: 3.0 :: 10.0 :: 140.0 :: 170.0 :: nil;
+
+	sys->print("%5s %24s %24s\n", "x", "math->lgamma", "lanczos7");
+	while(ns != nil) {
+		x := hd ns;
+		ns = tl ns;
+		# math->lgamma returns a tuple.
+		(i, r) := lgamma(x);
+		g := real i * exp(r);
+		sys->print("%5.1f %24.16g %24.16g\n", x, g, lanczos7(x));
+	}
+}
+
+lanczos7(z: real): real
+{
+	t := z + 6.5;
+	x := 0.99999999999980993 +
+		676.5203681218851/z -
+		1259.1392167224028/(z+1.0) +
+		771.32342877765313/(z+2.0) -
+		176.61502916214059/(z+3.0) +
+		12.507343278686905/(z+4.0) -
+		0.13857109526572012/(z+5.0) +
+		9.9843695780195716e-6/(z+6.0) +
+		1.5056327351493116e-7/(z+7.0);
+	return sqrt(2.0) * sqrt(Math->Pi) * pow(t, z - 0.5) * exp(-t) * x;
+}
--- a/Task/Gamma-function/Lua/gamma-function.lua
+++ b/Task/Gamma-function/Lua/gamma-function.lua
@ -0,0 +1,11 @@
+gamma, coeff, quad, qui, set = 0.577215664901, -0.65587807152056, -0.042002635033944, 0.16653861138228,	-0.042197734555571
+function recigamma(z)
+  return z + gamma * z^2 + coeff * z^3 + quad * z^4 + qui * z^5 + set * z^6
+end
+
+function gammafunc(z)
+  if z == 1 then return 1
+  elseif math.abs(z) <= 0.5 then return 1 / recigamma(z)
+  else return (z - 1) * gammafunc(z-1)
+  end
+end
--- a/Task/Gamma-function/M2000-Interpreter/gamma-function.m2000
+++ b/Task/Gamma-function/M2000-Interpreter/gamma-function.m2000
@ -0,0 +1,39 @@
+Module PrepareLambdaFunctions {
+      Const e = 2.7182818284590452@
+      Exp= Lambda e (x) -> e^x
+      gammaStirling=lambda e (x As decimal)->Sqrt(2.0 * pi / x) * ((x / e) ^ x)
+      Rad2Deg =Lambda pidivby180=pi/180 (RadAngle)->RadAngle / pidivby180
+      Dim p(9)
+      p(0)=0.99999999999980993@, 676.5203681218851@,   -1259.1392167224028@,  771.32342877765313@
+      p(4)=-176.61502916214059@,  12.507343278686905@,  -0.13857109526572012@,  0.0000099843695780195716@
+      p(8)=0.00000015056327351493116@
+      gammaLanczos =Lambda p(), Rad2Deg, Exp (x As decimal) -> {
+            Def Decimal a, t
+            If x < 0.5 Then =pi / (Sin(Rad2Deg(pi * x)) *Lambda(1-x)) : Exit
+            x -= 1@
+            a=p(0)
+            t = x + 7.5@
+            For i= 1@ To 8@ {
+                  a += p(i) / (x + i)
+            }
+             = Sqrt(2.0 * pi) * (t ^ (x + 0.5)) * Exp(-t) * a
+      }
+      Push gammaStirling, gammaLanczos
+}
+Call PrepareLambdaFunctions
+Read gammaLanczos, gammaStirling
+Font "Courier New"
+Form 120, 40
+document doc$="     χ                        Stirling                     Lanczos"+{
+}
+Print $(2,20),"x", "Stirling",@(55),"Lanczos", $(0)
+Print
+For d = 0.1 To 2 step 0.1
+      Print   $("0.00"), d,
+      Print  $("0.000000000000000"), gammaStirling(d),
+      Print  $("0.0000000000000000000000000000"), gammaLanczos(d)
+      doc$=format$("{0:-10}  {1:-30}   {2:-34}",str$(d,"0.00"), str$(gammaStirling(d),"0.000000000000000"), str$(gammaLanczos(d),"0.0000000000000000000000000000"))+{
+      }
+Next d
+Print $("")
+clipboard doc$
--- a/Task/Gamma-function/Maple/gamma-function.maple
+++ b/Task/Gamma-function/Maple/gamma-function.maple
@ -0,0 +1,4 @@
+GAMMA(17/2);
+GAMMA(7*I);
+M := Matrix(2, 3, 'fill' = -3.6);
+MTM:-gamma(M);
--- a/Task/Gamma-function/Mathematica/gamma-function.math
+++ b/Task/Gamma-function/Mathematica/gamma-function.math
@ -0,0 +1 @@
+Gamma[x]
--- a/Task/Gamma-function/Maxima/gamma-function.maxima
+++ b/Task/Gamma-function/Maxima/gamma-function.maxima
@ -0,0 +1,21 @@
+fpprec: 30$
+
+gamma_coeff(n) := block([a: makelist(1, n)],
+   a[2]: bfloat(%gamma),
+   for k from 3 thru n do
+      a[k]: bfloat((sum((-1)^j * zeta(j) * a[k - j], j, 2, k - 1) - a[2] * a[k - 1]) / (1 - k * a[1])),
+   a)$
+
+poleval(a, x) := block([y: 0],
+   for k from length(a) thru 1 step -1 do
+      y: y * x + a[k],
+   y)$
+
+gc: gamma_coeff(20)$
+
+gamma_approx(x) := block([y: 1],
+   while x > 2 do (x: x - 1, y: y * x),
+   y / (poleval(gc, x - 1)))$
+
+gamma_approx(12.3b0) - gamma(12.3b0);
+/* -9.25224705314470500985141176997b-15 */
--- a/Task/Gamma-function/Modula-3/gamma-function.mod3
+++ b/Task/Gamma-function/Modula-3/gamma-function.mod3
@ -0,0 +1,37 @@
+MODULE Gamma EXPORTS Main;
+
+FROM IO IMPORT Put;
+FROM Fmt IMPORT Extended, Style;
+
+PROCEDURE Taylor(x: EXTENDED): EXTENDED =
+  CONST a = ARRAY [0..29] OF EXTENDED {
+    1.00000000000000000000X0, 0.57721566490153286061X0,
+    -0.65587807152025388108X0, -0.04200263503409523553X0,
+    0.16653861138229148950X0, -0.04219773455554433675X0,
+    -0.00962197152787697356X0, 0.00721894324666309954X0,
+    -0.00116516759185906511X0, -0.00021524167411495097X0,
+    0.00012805028238811619X0, -0.00002013485478078824X0,
+    -0.00000125049348214267X0, 0.00000113302723198170X0,
+    -0.00000020563384169776X0, 0.00000000611609510448X0,
+    0.00000000500200764447X0, -0.00000000118127457049X0,
+    0.00000000010434267117X0, 0.00000000000778226344X0,
+    -0.00000000000369680562X0, 0.00000000000051003703X0,
+    -0.00000000000002058326X0, -0.00000000000000534812X0,
+    0.00000000000000122678X0, -0.00000000000000011813X0,
+    0.00000000000000000119X0, 0.00000000000000000141X0,
+    -0.00000000000000000023X0, 0.00000000000000000002X0 };
+  VAR y := x - 1.0X0;
+      sum := a[LAST(a)];
+
+  BEGIN
+    FOR i := LAST(a) - 1 TO FIRST(a) BY -1 DO
+      sum := sum * y + a[i];
+    END;
+    RETURN 1.0X0 / sum;
+  END Taylor;
+
+BEGIN
+  FOR i := 1 TO 10 DO
+    Put(Extended(Taylor(FLOAT(i, EXTENDED) / 3.0X0), style := Style.Sci) & "\n");
+  END;
+END Gamma.
--- a/Task/Gamma-function/Nim/gamma-function.nim
+++ b/Task/Gamma-function/Nim/gamma-function.nim
@ -0,0 +1,27 @@
+import math, strformat
+
+const A = [
+ 1.00000000000000000000,  0.57721566490153286061, -0.65587807152025388108,
+-0.04200263503409523553,  0.16653861138229148950, -0.04219773455554433675,
+-0.00962197152787697356,  0.00721894324666309954, -0.00116516759185906511,
+-0.00021524167411495097,  0.00012805028238811619, -0.00002013485478078824,
+-0.00000125049348214267,  0.00000113302723198170, -0.00000020563384169776,
+ 0.00000000611609510448,  0.00000000500200764447, -0.00000000118127457049,
+ 0.00000000010434267117,  0.00000000000778226344, -0.00000000000369680562,
+ 0.00000000000051003703, -0.00000000000002058326, -0.00000000000000534812,
+ 0.00000000000000122678, -0.00000000000000011813,  0.00000000000000000119,
+ 0.00000000000000000141, -0.00000000000000000023,  0.00000000000000000002 ]
+
+proc gamma(x: float): float =
+  let y = x - 1
+  result = A[^1]
+  for n in countdown(A.high - 1, A.low):
+    result = result * y + A[n]
+  result = 1 / result
+
+echo "Our gamma function     Nim gamma function      Difference"
+echo "------------------     ------------------      ----------"
+for i in 1..10:
+  let val1 = gamma(i.toFloat / 3)
+  let val2 = math.gamma(i.toFloat / 3)
+  echo &"{val1:18.16f}     {val2:18.16f}     {val1 - val2:11.4e}"
--- a/Task/Gamma-function/OCaml/gamma-function.ocaml
+++ b/Task/Gamma-function/OCaml/gamma-function.ocaml
@ -0,0 +1,63 @@
+let e = exp 1.
+let pi = 4. *. atan 1.
+let sqrttwopi = sqrt (2. *. pi)
+
+module Lanczos = struct
+  (* Lanczos method *)
+  (* Coefficients used by the GNU Scientific Library *)
+  let g = 7.
+  let c = [|0.99999999999980993; 676.5203681218851; -1259.1392167224028;
+	    771.32342877765313; -176.61502916214059; 12.507343278686905;
+	    -0.13857109526572012; 9.9843695780195716e-6; 1.5056327351493116e-7|]
+
+  let rec ag z d =
+    if d = 0 then c.(0) +. ag z 1
+    else if d < 8 then c.(d) /. (z +. float d) +. ag z (succ d)
+    else c.(d) /. (z +. float d)
+
+  let gamma z =
+    let z = z -. 1. in
+    let p = z +. g +. 0.5 in
+    sqrttwopi *. p ** (z +. 0.5) *. exp (-. p) *. ag z 0
+end
+
+module Stirling = struct
+  (* Stirling method *)
+  let gamma z =
+    sqrttwopi /. sqrt z *. (z /. e) ** z
+
+end
+
+module Stirling2 = struct
+  (* Extended Stirling method seen in Abramowitz and Stegun *)
+  let d = [|1./.12.; 1./.288.; -139./.51840.; -571./.2488320.|]
+
+  let rec corr z x n =
+    if n < Array.length d - 1 then d.(n) /. x +. corr z (x *. z) (succ n)
+    else d.(n) /. x
+
+  let gamma z = Stirling.gamma z *. (1. +. corr z z 0)
+end
+
+let mirror gma z =
+  if z > 0.5 then gma z
+  else pi /. sin (pi *. z) /. gma (1. -. z)
+
+let _ =
+  Printf.printf "z\t\tLanczos\t\tStirling\tStirling2\n";
+  for i = 1 to 20 do
+    let z = float i /. 10. in
+    Printf.printf "%-10.8g\t%10.8e\t%10.8e\t%10.8e\n"
+    		  z
+		  (mirror Lanczos.gamma z)
+		  (mirror Stirling.gamma z)
+		  (mirror Stirling2.gamma z)
+  done;
+  for i = 1 to 7 do
+    let z = 10. *. float i in
+    Printf.printf "%-10.8g\t%10.8e\t%10.8e\t%10.8e\n"
+    		  z
+		  (Lanczos.gamma z)
+		  (Stirling.gamma z)
+		  (Stirling2.gamma z)
+  done
--- a/Task/Gamma-function/Octave/gamma-function.octave
+++ b/Task/Gamma-function/Octave/gamma-function.octave
@ -0,0 +1,22 @@
+function g = lacz_gamma(a, cg=7)
+  p = [ 0.99999999999980993, 676.5203681218851, -1259.1392167224028, \
+        771.32342877765313, -176.61502916214059, 12.507343278686905, \
+        -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7 ];
+  x=a;
+  if ( x < 0.5 )
+    g = pi / ( sin(pi*x) * lacz_gamma(1.0-x) );
+  else
+    x = x - 1.0;
+    t = p(1);
+    for i=1:(cg+1)
+      t = t + p(i+1)/(x+double(i));
+    endfor
+    w = x + double(cg) + 0.5;
+    g = sqrt(2.0*pi) * w**(x+0.5) * exp(-w) * t;
+  endif
+endfunction
+
+
+for i = 1:10
+  printf("%f %f\n", gamma(i/3.0), lacz_gamma(i/3.0));
+endfor
--- a/Task/Gamma-function/Oforth/gamma-function.fth
+++ b/Task/Gamma-function/Oforth/gamma-function.fth
@ -0,0 +1,17 @@
+import: math
+
+[
+   676.5203681218851,  -1259.1392167224028, 771.32342877765313,
+  -176.61502916214059, 12.507343278686905, -0.13857109526572012,
+   9.9843695780195716e-6, 1.5056327351493116e-7
+] const: Gamma.Lanczos
+
+: gamma(z)
+| i t |
+   z 0.5 < ifTrue: [ Pi dup z * sin 1.0 z - gamma * / return ]
+   z 1.0 - ->z
+   0.99999999999980993 Gamma.Lanczos size loop: i [ i Gamma.Lanczos at z i + / + ]
+   z Gamma.Lanczos size + 0.5 - ->t
+   2 Pi * sqrt *
+   t z 0.5 + powf *
+   t neg exp * ;
--- a/Task/Gamma-function/PARI-GP/gamma-function-1.parigp
+++ b/Task/Gamma-function/PARI-GP/gamma-function-1.parigp
@ -0,0 +1 @@
+gamma(x)
--- a/Task/Gamma-function/PARI-GP/gamma-function-2.parigp
+++ b/Task/Gamma-function/PARI-GP/gamma-function-2.parigp
@ -0,0 +1 @@
+Gamma(x)=intnum(t=0,[+oo,1],t^(x-1)/exp(t))
--- a/Task/Gamma-function/PARI-GP/gamma-function-3.parigp
+++ b/Task/Gamma-function/PARI-GP/gamma-function-3.parigp
@ -0,0 +1 @@
+Gamma(x)=intnumromb(t=0,9,t^(x-1)/exp(t),0)+intnumromb(t=9,max(x,99)^9,t^(x-1)/exp(t),2)
--- a/Task/Gamma-function/PARI-GP/gamma-function-4.parigp
+++ b/Task/Gamma-function/PARI-GP/gamma-function-4.parigp
@ -0,0 +1 @@
+Stirling(x)=x--;sqrt(2*Pi*x)*(x/exp(1))^x
--- a/Task/Gamma-function/PL-I/gamma-function.pli
+++ b/Task/Gamma-function/PL-I/gamma-function.pli
@ -0,0 +1,45 @@
+/* From Rosetta Fortran */
+test: procedure options (main);
+
+  declare i fixed binary;
+
+  on underflow ;
+
+  put skip list ('Lanczos', 'Builtin' );
+  do i = 1 to 10;
+     put skip list (lanczos_gamma(i/3.0q0), gamma(i/3.0q0) );
+  end;
+
+
+lanczos_gamma: procedure (a) returns (float (18)) recursive;
+    declare a float (18);
+    declare pi float (18) value (3.14159265358979324E0);
+    declare cg fixed binary initial ( 7 );
+
+    /* these precomputed values are taken by the sample code in Wikipedia, */
+    /* and the sample itself takes them from the GNU Scientific Library */
+    declare p(0:8) float (18) static initial
+         ( 0.99999999999980993e0, 676.5203681218851e0, -1259.1392167224028e0,
+         771.32342877765313e0, -176.61502916214059e0, 12.507343278686905e0,
+         -0.13857109526572012e0, 9.9843695780195716e-6, 1.5056327351493116e-7 );
+
+    declare ( t, w, x ) float (18);
+    declare i fixed binary;
+
+    x = a;
+
+    if x < 0.5 then
+       return ( pi / ( sin(pi*x) * lanczos_gamma(1.0-x) ) );
+    else
+       do;
+          x = x - 1.0;
+          t = p(0);
+          do i = 1 to cg+2;
+             t = t + p(i)/(x+i);
+          end;
+          w = x + float(cg) + 0.5;
+          return ( sqrt(2*pi) * w**(x+0.5) * exp(-w) * t );
+       end;
+  end lanczos_gamma;
+
+end test;
--- a/Task/Gamma-function/Pascal/gamma-function.pas
+++ b/Task/Gamma-function/Pascal/gamma-function.pas
@ -0,0 +1,76 @@
+program GammaTest;
+{$mode objfpc}{$H+}
+uses SysUtils;
+
+function Gamma( x : extended) : extended;
+const COF : array [0..14] of extended =
+(  0.999999999999997092, // may as well include this in the array
+  57.1562356658629235,
+ -59.5979603554754912,
+  14.1360979747417471,
+ -0.491913816097620199,
+  0.339946499848118887e-4,
+  0.465236289270485756e-4,
+ -0.983744753048795646e-4,
+  0.158088703224912494e-3,
+ -0.210264441724104883e-3,
+  0.217439618115212643e-3,
+ -0.164318106536763890e-3,
+  0.844182239838527433e-4,
+ -0.261908384015814087e-4,
+  0.368991826595316234e-5);
+const
+  K = 2.5066282746310005;
+  PI_OVER_K = PI / K;
+var
+  j : integer;
+  tmp, w, ser : extended;
+  reflect : boolean;
+begin
+  reflect := (x < 0.5);
+  if reflect then w := 1.0 - x else w := x;
+  tmp := w + 5.2421875;
+  tmp := (w + 0.5)*Ln(tmp) - tmp;
+  ser := COF[0];
+  for j := 1 to 14 do ser := ser + COF[j]/(w + j);
+  try
+    if reflect then
+      result := PI_OVER_K * w * Exp(-tmp) / (Sin(PI*x) * ser)
+    else
+      result := K * Exp(tmp) * ser / w;
+  except
+    raise SysUtils.Exception.CreateFmt(
+        'Gamma(%g) is undefined or out of floating-point range', [x]);
+  end;
+end;
+
+// Main routine for testing the Gamma function
+var
+    x, k : extended;
+begin
+  WriteLn( 'Is it seamless at x = 1/2 ?');
+  x := 0.49999999999999;
+  WriteLn( SysUtils.Format( 'Gamma(%g) = %g', [x, Gamma(x)]));
+  x := 0.50000000000001;
+  WriteLn( SysUtils.Format( 'Gamma(%g) = %g', [x, Gamma(x)]));
+  WriteLn( 'Test a few values:');
+  WriteLn( SysUtils.Format( 'Gamma(1)   = %g', [Gamma(1)]));
+  WriteLn( SysUtils.Format( 'Gamma(2)   = %g', [Gamma(2)]));
+  WriteLn( SysUtils.Format( 'Gamma(3)   = %g', [Gamma(3)]));
+  WriteLn( SysUtils.Format( 'Gamma(10)  = %g', [Gamma(10)]));
+  WriteLn( SysUtils.Format( 'Gamma(101) = %g', [Gamma(101)]));
+  WriteLn( '      100! = 9.33262154439442E157');
+  WriteLn( SysUtils.Format( 'Gamma(1/2) = %g', [Gamma(0.5)]));
+  WriteLn( SysUtils.Format( 'Sqrt(pi)   = %g', [Sqrt(PI)]));
+  WriteLn( SysUtils.Format( 'Gamma(-7/2)       =  %g', [Gamma(-3.5)]));
+(*
+  Note here a bug or misfeature in Lazarus (doesn't occur in Delphi):
+  Putting (16.0/105.0)*Sqrt(PI) does not give the required precision.
+  We have to explicitly define the integers as extended floating-point.
+*)
+  k := extended(16.0)/extended(105.0);
+  WriteLn( SysUtils.Format( ' (16/105)Sqrt(pi) =  %g', [k*Sqrt(PI)]));
+  WriteLn( SysUtils.Format( 'Gamma(-9/2)       = %g', [Gamma(-4.5)]));
+  k := extended(32.0)/extended(945.0);
+  WriteLn( SysUtils.Format( '-(32/945)Sqrt(pi) = %g', [-k*Sqrt(PI)]));
+end.
--- a/Task/Gamma-function/Perl/gamma-function.pl
+++ b/Task/Gamma-function/Perl/gamma-function.pl
@ -0,0 +1,70 @@
+use strict;
+use warnings;
+use constant pi => 4*atan2(1, 1);
+use constant e  => exp(1);
+
+# Normally would be:  use Math::MPFR
+# but this will use it if it's installed and ignore otherwise
+my $have_MPFR = eval { require Math::MPFR; Math::MPFR->import(); 1; };
+
+sub Gamma {
+    my $z = shift;
+    my $method = shift // 'lanczos';
+    if ($method eq 'lanczos') {
+        use constant g => 9;
+        $z <  .5 ?  pi / sin(pi * $z) / Gamma(1 - $z, $method) :
+        sqrt(2* pi) *
+        ($z + g - .5)**($z - .5) *
+        exp(-($z + g - .5)) *
+        do {
+            my @coeff = qw{
+            1.000000000000000174663
+        5716.400188274341379136
+      -14815.30426768413909044
+       14291.49277657478554025
+       -6348.160217641458813289
+        1301.608286058321874105
+        -108.1767053514369634679
+           2.605696505611755827729
+          -0.7423452510201416151527e-2
+           0.5384136432509564062961e-7
+          -0.4023533141268236372067e-8
+            };
+            my ($sum, $i) = (shift(@coeff), 0);
+            $sum += $_ / ($z + $i++) for @coeff;
+            $sum;
+        }
+    } elsif ($method eq 'taylor') {
+        $z <  .5 ? Gamma($z+1, $method)/$z     :
+        $z > 1.5 ? ($z-1)*Gamma($z-1, $method) :
+	do {
+	    my $s = 0; ($s *= $z-1) += $_ for qw{
+	    0.00000000000000000002 -0.00000000000000000023 0.00000000000000000141
+	    0.00000000000000000119 -0.00000000000000011813 0.00000000000000122678
+	    -0.00000000000000534812 -0.00000000000002058326 0.00000000000051003703
+	    -0.00000000000369680562 0.00000000000778226344 0.00000000010434267117
+	    -0.00000000118127457049 0.00000000500200764447 0.00000000611609510448
+	    -0.00000020563384169776 0.00000113302723198170 -0.00000125049348214267
+	    -0.00002013485478078824 0.00012805028238811619 -0.00021524167411495097
+	    -0.00116516759185906511 0.00721894324666309954 -0.00962197152787697356
+	    -0.04219773455554433675 0.16653861138229148950 -0.04200263503409523553
+	    -0.65587807152025388108 0.57721566490153286061 1.00000000000000000000
+	    }; 1/$s;
+	}
+    } elsif ($method eq 'stirling') {
+        no warnings qw(recursion);
+        $z < 100 ? Gamma($z + 1, $method)/$z :
+        sqrt(2*pi*$z)*($z/e + 1/(12*e*$z))**$z / $z;
+    } elsif ($method eq 'MPFR') {
+        my $result = Math::MPFR->new();
+        Math::MPFR::Rmpfr_gamma($result, Math::MPFR->new($z), 0);
+        $result;
+    } else { die "unknown method '$method'" }
+}
+
+for my $method (qw(MPFR lanczos taylor stirling)) {
+    next if $method eq 'MPFR' && !$have_MPFR;
+    printf "%10s: ", $method;
+    print join(' ', map { sprintf "%.12f", Gamma($_/3, $method) } 1 .. 10);
+    print "\n";
+}
--- a/Task/Gamma-function/Phix/gamma-function-1.phix
+++ b/Task/Gamma-function/Phix/gamma-function-1.phix
@ -0,0 +1,116 @@
+(phixonline)-->
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
+ <span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">function</span> <span style="color: #000000;">spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">atom</span> <span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
+     <span style="color: #008080;">if</span> <span style="color: #000000;">accm</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
+         <span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span>
+         <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">accm</span>
+         <span style="color: #004080;">atom</span> <span style="color: #000000;">k1_factrl</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>  <span style="color: #000080;font-style:italic;">-- (k - 1)!*(-1)^k with 0!==1</span>
+         <span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">12</span> <span style="color: #008080;">do</span>
+             <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">13</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">13</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">k1_factrl</span>
+             <span style="color: #000000;">k1_factrl</span> <span style="color: #0000FF;">*=</span> <span style="color: #0000FF;">-(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">12</span> <span style="color: #008080;">do</span>
+         <span style="color: #000000;">accm</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]/(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #000000;">accm</span> <span style="color: #0000FF;">*=</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(-(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span><span style="color: #0000FF;">))*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Gamma(z+1)</span>
+     <span style="color: #008080;">return</span> <span style="color: #000000;">accm</span><span style="color: #0000FF;">/</span><span style="color: #000000;">z</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+
+ <span style="color: #008080;">function</span> <span style="color: #000000;">taylor_gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000080;font-style:italic;">-- (good for values between 0 and 1, apparently)</span>
+     <span style="color: #008080;">constant</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">1.00000_00000_00000_00000</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.57721_56649_01532_86061</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.65587_80715_20253_88108</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.04200_26350_34095_23553</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.16653_86113_82291_48950</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.04219_77345_55544_33675</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00962_19715_27876_97356</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00721_89432_46663_09954</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00116_51675_91859_06511</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00021_52416_74114_95097</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00012_80502_82388_11619</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00002_01348_54780_78824</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_12504_93482_14267</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_11330_27231_98170</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_02056_33841_69776</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_00061_16095_10448</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_00050_02007_64447</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00011_81274_57049</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_00001_04342_67117</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_00000_07782_26344</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_03696_80562</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_00000_00510_03703</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_00020_58326</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_00005_34812</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_00000_00001_22678</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_00000_11813</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_00000_00000_00119</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_00000_00000_00141</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">0.00000_00000_00000_00023</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">0.00000_00000_00000_00002</span> <span style="color: #0000FF;">}</span>
+     <span style="color: #004080;">atom</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span>
+          <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[$]</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
+         <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">*</span><span style="color: #000000;">y</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">return</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">s</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+
+ <span style="color: #008080;">function</span> <span style="color: #000000;">lanczos_gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">if</span> <span style="color: #000000;">z</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0.5</span> <span style="color: #008080;">then</span>
+         <span style="color: #008080;">return</span> <span style="color: #004600;">PI</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">*</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">lanczos_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">z</span><span style="color: #0000FF;">))</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #000080;font-style:italic;">-- use a lanczos approximation:</span>
+     <span style="color: #004080;">atom</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.99999999999980993</span><span style="color: #0000FF;">,</span>
+          <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">6.5</span><span style="color: #0000FF;">;</span>
+     <span style="color: #004080;">sequence</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">676.5203681218851</span><span style="color: #0000FF;">,</span>
+                  <span style="color: #0000FF;">-</span><span style="color: #000000;">1259.1392167224028</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">771.32342877765313</span><span style="color: #0000FF;">,</span>
+                   <span style="color: #0000FF;">-</span><span style="color: #000000;">176.61502916214059</span><span style="color: #0000FF;">,</span>
+                     <span style="color: #000000;">12.507343278686905</span><span style="color: #0000FF;">,</span>
+                     <span style="color: #0000FF;">-</span><span style="color: #000000;">0.13857109526572012</span><span style="color: #0000FF;">,</span>
+                      <span style="color: #000000;">9.9843695780195716e-6</span><span style="color: #0000FF;">,</span>
+                      <span style="color: #000000;">1.5056327351493116e-7</span> <span style="color: #0000FF;">}</span>
+     <span style="color: #000000;">z</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
+         <span style="color: #000000;">x</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">z</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">return</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">x</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+
+ <span style="color: #008080;">constant</span> <span style="color: #000000;">sqPI</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span>
+
+ <span style="color: #008080;">procedure</span> <span style="color: #000000;">sq</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">zm</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"%19.16f"</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">atom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mul</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">zm</span>
+     <span style="color: #004080;">atom</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">mul</span>
+     <span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">),</span>
+                   <span style="color: #000000;">taylor_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">),</span>
+                   <span style="color: #000000;">lanczos_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)},</span>
+          <span style="color: #000000;">error</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_abs</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">))</span>
+     <span style="color: #004080;">string</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">",  "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">", "</span>
+     <span style="color: #004080;">integer</span> <span style="color: #000000;">bdx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">smallest</span><span style="color: #0000FF;">(</span><span style="color: #000000;">error</span><span style="color: #0000FF;">,</span><span style="color: #000000;">return_index</span><span style="color: #0000FF;">:=</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">atom</span> <span style="color: #000000;">best</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bdx</span><span style="color: #0000FF;">],</span>
+          <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">bdx</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">mul</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000080;font-style:italic;">-- (potentially mark &gt;1)</span>
+         <span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">best</span> <span style="color: #008080;">then</span>
+             <span style="color: #000000;">t</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">22</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">22</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"*,"</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #004080;">string</span> <span style="color: #000000;">es</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">e</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%5g: %s %s,  %19.16f\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">es</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #000000;">p</span><span style="color: #0000FF;">})</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
+
+ <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"   z    ------ spouge -----   ----- taylor ------   ----- lanczos -----   ---- expected -----  %19.16f\n"</span><span style="color: #0000FF;">,</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span>
+ <span style="color: #7060A8;">papply</span><span style="color: #0000FF;">({{-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">/</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">/</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">7</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">/</span><span style="color: #000000;">15</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">sq</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">0.001</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">999.4237725</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.15f"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">0.01</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">99.43258512</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.16f"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">0.1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">9.513507699</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.16f"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">362880</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.12f"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">9.332621544e155</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.13g"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">if</span> <span style="color: #7060A8;">machine_bits</span><span style="color: #0000FF;">()=</span><span style="color: #000000;">64</span> <span style="color: #008080;">then</span>
+     <span style="color: #000000;">sq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">150</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sqPI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">3.808922638e260</span><span style="color: #0000FF;">},</span><span style="color: #008000;">"%19.13g"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (fatal power overflow error on 32 bits)</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+<!--
--- a/Task/Gamma-function/Phix/gamma-function-2.phix
+++ b/Task/Gamma-function/Phix/gamma-function-2.phix
@ -0,0 +1,109 @@
+-->
+ <span style="color: #008080;">without</span> <span style="color: #008080;">javascript_semantics</span> <span style="color: #000080;font-style:italic;">-- (no mpfr_exp(), mpfr_gamma() in pwa/p2js)</span>
+ <span style="color: #008080;">constant</span> <span style="color: #000000;">dp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">30</span>
+ <span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"%5s:  %33s,  %33s,  %32s\n"</span>
+ <span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (mpfr_get_fixed(maxlen), mpfr_gamma)</span>
+ <span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
+ <span style="color: #7060A8;">mpfr_set_default_precision</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">87</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- 87 decimal places. </span>
+ <span style="color: #004080;">sequence</span> <span style="color: #000000;">mc</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">40</span><span style="color: #0000FF;">)</span>
+
+ <span style="color: #008080;">function</span> <span style="color: #000000;">mpfr_spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpfr</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">mpfr</span> <span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
+     <span style="color: #008080;">if</span> <span style="color: #7060A8;">mpfr_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
+         <span style="color: #000080;font-style:italic;">-- mc[1] := sqrt(2*PI)</span>
+         <span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">)</span>
+         <span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
+         <span style="color: #7060A8;">mpfr_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">)</span>
+         <span style="color: #000080;font-style:italic;">-- k1_factrl = (k - 1)!*(-1)^k with 0!==1</span>
+         <span style="color: #004080;">mpfr</span> <span style="color: #000000;">k1_factrl</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
+              <span style="color: #000000;">tmk</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span>
+              <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
+         <span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
+             <span style="color: #000080;font-style:italic;">-- mc[k] = exp(13-k)*power(13-k,k-1.5)/k1_factrl</span>
+             <span style="color: #7060A8;">mpfr_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmk</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)</span>
+             <span style="color: #000000;">mpfr_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">tmk</span><span style="color: #0000FF;">)</span>
+             <span style="color: #7060A8;">mpfr_set_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">)</span>
+             <span style="color: #000000;">mpfr_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tmk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
+             <span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k1_factrl</span><span style="color: #0000FF;">)</span>
+             <span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">],</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
+             <span style="color: #000080;font-style:italic;">-- k1_factrl *= -(k-1)</span>
+             <span style="color: #7060A8;">mpfr_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">k1_factrl</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k1_factrl</span><span style="color: #0000FF;">,-(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
+         <span style="color: #000080;font-style:italic;">-- accm += mc[k]/(z+k-1)</span>
+         <span style="color: #004080;">mpfr</span> <span style="color: #000000;">ck</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]),</span>
+              <span style="color: #000000;">zk</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+         <span style="color: #7060A8;">mpfr_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zk</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+         <span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ck</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ck</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zk</span><span style="color: #0000FF;">)</span>
+         <span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ck</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #000080;font-style:italic;">-- atom zc = z+length(mc)
+     -- accm *= exp(-zc)*power(zc,z+0.5) -- Gamma(z+1)</span>
+     <span style="color: #004080;">mpfr</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">),</span>
+          <span style="color: #000000;">ez</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span>
+          <span style="color: #000000;">zh</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mc</span><span style="color: #0000FF;">))</span>
+     <span style="color: #7060A8;">mpfr_neg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000000;">mpfr_exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zh</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zh</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000000;">mpfr_pow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">zh</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ez</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000080;font-style:italic;">-- return accm/z</span>
+     <span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">accm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">return</span> <span style="color: #000000;">accm</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+
+ <span style="color: #008080;">constant</span> <span style="color: #000000;">mPI</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(),</span>
+         <span style="color: #000000;">mqPI</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
+ <span style="color: #7060A8;">mpfr_const_pi</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mPI</span><span style="color: #0000FF;">)</span>
+ <span style="color: #004080;">string</span> <span style="color: #000000;">pistr</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">)</span>
+ <span style="color: #7060A8;">mpfr_sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mPI</span><span style="color: #0000FF;">)</span>
+
+ <span style="color: #008080;">function</span> <span style="color: #000000;">makempfr</span><span style="color: #0000FF;">(</span><span style="color: #004080;">object</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">mpfr</span> <span style="color: #000000;">res</span>
+     <span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
+         <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'/'</span><span style="color: #0000FF;">)</span>
+         <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
+         <span style="color: #7060A8;">mpfr_div_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">to_integer</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]))</span>
+     <span style="color: #008080;">elsif</span> <span style="color: #004080;">sequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
+         <span style="color: #0000FF;">{</span><span style="color: #004080;">mpfr</span> <span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">object</span> <span style="color: #000000;">x2</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
+         <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x1</span><span style="color: #0000FF;">)</span>
+         <span style="color: #008080;">if</span> <span style="color: #004080;">string</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
+             <span style="color: #004080;">mpfr</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
+             <span style="color: #7060A8;">mpfr_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
+         <span style="color: #008080;">else</span>
+             <span style="color: #7060A8;">mpfr_div_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x2</span><span style="color: #0000FF;">)</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #008080;">else</span>
+         <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+
+ <span style="color: #008080;">procedure</span> <span style="color: #000000;">mq</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">zm</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">=</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">mpfr</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mul</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zm</span><span style="color: #0000FF;">,</span><span style="color: #000000;">makempfr</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">mpfr</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">mpfr_spouge_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">string</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxlen</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">mpfr</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">()</span>
+     <span style="color: #7060A8;">mpfr_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">mpfr</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mul</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">string</span> <span style="color: #000000;">zs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">),</span>
+            <span style="color: #000000;">es</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">e</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxlen</span><span style="color: #0000FF;">:=</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span>
+            <span style="color: #000000;">ps</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_get_fixed</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">zs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">es</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ps</span><span style="color: #0000FF;">})</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
+
+ <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"   z     %s    %s   %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">pad</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" spouge "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"BOTH"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">pad</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" expected "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dp</span><span style="color: #0000FF;">+</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"BOTH"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">),</span><span style="color: #000000;">pistr</span><span style="color: #0000FF;">})</span>
+ <span style="color: #7060A8;">papply</span><span style="color: #0000FF;">({{-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.75</span><span style="color: #0000FF;">},{-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}},{</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}},{</span><span style="color: #000000;">2.5</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"4/3"</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}},{</span><span style="color: #000000;">3.5</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"8/15"</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}},</span><span style="color: #000000;">mq</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #008000;">"1/1000"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"999.4237724845954661149822012996"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">28</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #008000;">"1/100"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"99.43258511915060371353298887051"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">29</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #008000;">"1/10"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"9.513507698668731836292487177265"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">30</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #000000;">362880</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">25</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"9.332621544394415268169923885627e155"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000000;">mq</span><span style="color: #0000FF;">({</span><span style="color: #000000;">150</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mqPI</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"3.80892263763056972698595524350735e260"</span><span style="color: #0000FF;">}},</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
+<!--
--- a/Task/Gamma-function/Phixmonti/gamma-function.phixmonti
+++ b/Task/Gamma-function/Phixmonti/gamma-function.phixmonti
@ -0,0 +1,41 @@
+0.577215664901 var gamma
+-0.65587807152056 var coeff
+-0.042002635033944 var quad
+0.16653861138228 var qui
+-0.042197734555571 var theSet
+
+def recigamma var z /# n -- n #/
+    z 6 power theSet *
+    z 5 power qui *
+    z 4 power quad *
+    z 3 power coeff *
+    z 2 power gamma *
+    z + + + + +
+enddef
+
+/# without var
+def recigamma
+    dup 6 power theSet * swap
+    dup 5 power qui * swap
+    dup 4 power quad * swap
+    dup 3 power coeff * swap
+    dup 2 power gamma * swap
+    + + + + +
+enddef
+#/
+
+def gammafunc   /# n -- n #/
+    dup 1 == if
+    else
+        dup abs 0.5 <= if
+            recigamma 1 swap /
+        else
+            dup 1 - gammafunc swap 1 - *
+        endif
+    endif
+enddef
+
+0.1 2.1 .1 3 tolist
+for
+    dup print " = " print gammafunc print nl
+endfor
--- a/Task/Gamma-function/PicoLisp/gamma-function.l
+++ b/Task/Gamma-function/PicoLisp/gamma-function.l
@ -0,0 +1,20 @@
+(scl 28)
+
+(de *A
+   ~(flip
+      (1.00000000000000000000  0.57721566490153286061 -0.65587807152025388108
+      -0.04200263503409523553  0.16653861138229148950 -0.04219773455554433675
+      -0.00962197152787697356  0.00721894324666309954 -0.00116516759185906511
+      -0.00021524167411495097  0.00012805028238811619 -0.00002013485478078824
+      -0.00000125049348214267  0.00000113302723198170 -0.00000020563384169776
+       0.00000000611609510448  0.00000000500200764447 -0.00000000118127457049
+       0.00000000010434267117  0.00000000000778226344 -0.00000000000369680562
+       0.00000000000051003703 -0.00000000000002058326 -0.00000000000000534812
+       0.00000000000000122678 -0.00000000000000011813  0.00000000000000000119
+       0.00000000000000000141 -0.00000000000000000023  0.00000000000000000002 ) ) )
+
+(de gamma (X)
+   (let (Y (- X 1.0)  Sum (car *A))
+      (for A (cdr *A)
+         (setq Sum (+ A (*/ Sum Y 1.0))) )
+      (*/ 1.0 1.0 Sum) ) )
--- a/Task/Gamma-function/PowerShell/gamma-function.psh
+++ b/Task/Gamma-function/PowerShell/gamma-function.psh
@ -0,0 +1,3 @@
+Add-Type -Path "C:\Program Files (x86)\Math\MathNet.Numerics.3.12.0\lib\net40\MathNet.Numerics.dll"
+
+1..20 | ForEach-Object {[MathNet.Numerics.SpecialFunctions]::Gamma($_ / 10)}
--- a/Task/Gamma-function/Prolog/gamma-function.pro
+++ b/Task/Gamma-function/Prolog/gamma-function.pro
@ -0,0 +1,36 @@
+gamma_coefficients(
+     [ 1.00000000000000000000000,  0.57721566490153286060651, -0.65587807152025388107701,
+      -0.04200263503409523552900,  0.16653861138229148950170, -0.04219773455554433674820,
+      -0.00962197152787697356211,  0.00721894324666309954239, -0.00116516759185906511211,
+      -0.00021524167411495097281,  0.00012805028238811618615, -0.00002013485478078823865,
+      -0.00000125049348214267065,  0.00000113302723198169588, -0.00000020563384169776071,
+       0.00000000611609510448141,  0.00000000500200764446922, -0.00000000118127457048702,
+       0.00000000010434267116911,  0.00000000000778226343990, -0.00000000000369680561864,
+       0.00000000000051003702874, -0.00000000000002058326053, -0.00000000000000534812253,
+       0.00000000000000122677862, -0.00000000000000011812593,  0.00000000000000000118669,
+       0.00000000000000000141238, -0.00000000000000000022987,  0.00000000000000000001714
+    ]).
+
+tolerance(1e-17).
+
+gamma(X, _) :- X =< 0.0, !, fail.
+gamma(X, Y) :-
+    X < 1.0, small_gamma(X, Y), !.
+gamma(1, 1) :- !.
+gamma(1.0, 1) :- !.
+gamma(X, Y) :-
+    X1 is X - 1,
+    gamma(X1, Y1),
+    Y is X1 * Y1.
+
+small_gamma(X, Y) :-
+    gamma_coefficients(Cs),
+    recip_gamma(X, 1.0, Cs, 1.0, 0.0, Y0),
+    Y is 1 / Y0.
+
+recip_gamma(_, _, [], _, Y, Y) :- !.
+recip_gamma(_, _, [], X0, X1, Y) :- tolerance(Tol), abs(X1 - X0) < Tol, Y = X1, !. % early exit
+recip_gamma(X, PrevPow, [C|Cs], _, X1, Y) :-
+    Power is PrevPow * X,
+    X2 is X1 + C*Power,
+    recip_gamma(X, Power, Cs, X1, X2, Y).
--- a/Task/Gamma-function/PureBasic/gamma-function-1.basic
+++ b/Task/Gamma-function/PureBasic/gamma-function-1.basic
@ -0,0 +1,82 @@
+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
--- a/Task/Gamma-function/PureBasic/gamma-function-2.basic
+++ b/Task/Gamma-function/PureBasic/gamma-function-2.basic
@ -0,0 +1,8 @@
+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
--- a/Task/Gamma-function/Python/gamma-function-1.py
+++ b/Task/Gamma-function/Python/gamma-function-1.py
@ -0,0 +1,22 @@
+_a =    ( 1.00000000000000000000, 0.57721566490153286061, -0.65587807152025388108,
+         -0.04200263503409523553, 0.16653861138229148950, -0.04219773455554433675,
+         -0.00962197152787697356, 0.00721894324666309954, -0.00116516759185906511,
+         -0.00021524167411495097, 0.00012805028238811619, -0.00002013485478078824,
+         -0.00000125049348214267, 0.00000113302723198170, -0.00000020563384169776,
+          0.00000000611609510448, 0.00000000500200764447, -0.00000000118127457049,
+          0.00000000010434267117, 0.00000000000778226344, -0.00000000000369680562,
+          0.00000000000051003703, -0.00000000000002058326, -0.00000000000000534812,
+          0.00000000000000122678, -0.00000000000000011813, 0.00000000000000000119,
+          0.00000000000000000141, -0.00000000000000000023, 0.00000000000000000002
+       )
+def gamma (x):
+   y  = float(x) - 1.0;
+   sm = _a[-1];
+   for an in _a[-2::-1]:
+      sm = sm * y + an;
+   return 1.0 / sm;
+
+
+if __name__ == '__main__':
+    for i in range(1,11):
+        print "  %20.14e" % gamma(i/3.0)
--- a/Task/Gamma-function/Python/gamma-function-2.py
+++ b/Task/Gamma-function/Python/gamma-function-2.py
@ -0,0 +1,82 @@
+'''Gamma function'''
+
+from functools import reduce
+
+
+# gamma_ :: [Float] -> Float -> Float
+def gamma_(tbl):
+    '''Gamma function.'''
+    def go(x):
+        y = float(x) - 1.0
+        return 1.0 / reduce(
+            lambda a, x: a * y + x,
+            tbl[-2::-1],
+            tbl[-1]
+        )
+    return lambda x: go(x)
+
+
+# TBL :: [Float]
+TBL = [
+    1.00000000000000000000, 0.57721566490153286061,
+    -0.65587807152025388108, -0.04200263503409523553,
+    0.16653861138229148950, -0.04219773455554433675,
+    -0.00962197152787697356, 0.00721894324666309954,
+    -0.00116516759185906511, -0.00021524167411495097,
+    0.00012805028238811619, -0.00002013485478078824,
+    -0.00000125049348214267, 0.00000113302723198170,
+    -0.00000020563384169776, 0.00000000611609510448,
+    0.00000000500200764447, -0.00000000118127457049,
+    0.00000000010434267117, 0.00000000000778226344,
+    -0.00000000000369680562, 0.00000000000051003703,
+    -0.00000000000002058326, -0.00000000000000534812,
+    0.00000000000000122678, -0.00000000000000011813,
+    0.00000000000000000119, 0.00000000000000000141,
+    -0.00000000000000000023, 0.00000000000000000002
+]
+
+
+# TEST ----------------------------------------------------
+# main :: IO()
+def main():
+    '''Gamma function over a range of values.'''
+
+    gamma = gamma_(TBL)
+    print(
+        fTable(' i -> gamma(i/3):\n')(repr)(lambda x: "%0.7e" % x)(
+            lambda x: gamma(x / 3.0)
+        )(enumFromTo(1)(10))
+    )
+
+
+# GENERIC -------------------------------------------------
+
+# enumFromTo :: (Int, Int) -> [Int]
+def enumFromTo(m):
+    '''Integer enumeration from m to n.'''
+    return lambda n: list(range(m, 1 + n))
+
+
+# FORMATTING -------------------------------------------------
+
+# fTable :: String -> (a -> String) ->
+#                     (b -> String) -> (a -> b) -> [a] -> String
+def fTable(s):
+    '''Heading -> x display function -> fx display function ->
+                     f -> xs -> tabular string.
+    '''
+    def go(xShow, fxShow, f, xs):
+        ys = [xShow(x) for x in xs]
+        w = max(map(len, ys))
+        return s + '\n' + '\n'.join(map(
+            lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
+            xs, ys
+        ))
+    return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
+        xShow, fxShow, f, xs
+    )
+
+
+# MAIN ---
+if __name__ == '__main__':
+    main()
--- a/Task/Gamma-function/R/gamma-function.r
+++ b/Task/Gamma-function/R/gamma-function.r
@ -0,0 +1,53 @@
+stirling <- function(z) sqrt(2*pi/z) * (exp(-1)*z)^z
+
+nemes <- function(z) sqrt(2*pi/z) * (exp(-1)*(z + (12*z - (10*z)^-1)^-1))^z
+
+lanczos <- function(z)
+{
+   if(length(z) > 1)
+   {
+      sapply(z, lanczos)
+   } else
+   {
+     g <- 7
+      p <- c(0.99999999999980993, 676.5203681218851, -1259.1392167224028,
+        771.32342877765313, -176.61502916214059, 12.507343278686905,
+        -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7)
+      z <- as.complex(z)
+      if(Re(z) < 0.5)
+      {
+         pi / (sin(pi*z) * lanczos(1-z))
+      } else
+      {
+         z <- z - 1
+         x <- p[1]
+         for (i in 1:8) {
+           x <- x+p[i+1]/(z+i)
+         }
+         tt <- z + g + 0.5
+         sqrt(2*pi) * tt^(z+0.5) * exp(-tt) * x
+      }
+   }
+}
+
+spouge <- function(z, a=49)
+{
+   if(length(z) > 1)
+   {
+      sapply(z, spouge)
+   } else
+   {
+      z <- z-1
+      k <- seq.int(1, a-1)
+      ck <- rep(c(1, -1), len=a-1) / factorial(k-1) * (a-k)^(k-0.5) * exp(a-k)
+      (z + a)^(z+0.5) * exp(-z - a) * (sqrt(2*pi) + sum(ck/(z+k)))
+   }
+}
+
+# Checks
+z <- (1:10)/3
+all.equal(gamma(z), stirling(z))             # Mean relative difference: 0.07181942
+all.equal(gamma(z), nemes(z))                # Mean relative difference: 0.003460549
+all.equal(as.complex(gamma(z)), lanczos(z))  # TRUE
+all.equal(gamma(z), spouge(z))               # TRUE
+data.frame(z=z, stirling=stirling(z), nemes=nemes(z), lanczos=lanczos(z), spouge=spouge(z), builtin=gamma(z))
--- a/Task/Gamma-function/REXX/gamma-function-1.rexx
+++ b/Task/Gamma-function/REXX/gamma-function-1.rexx
@ -0,0 +1,68 @@
+/*REXX program calculates GAMMA using the Taylor series coefficients; ≈80 decimal digits*/
+                            /*The GAMMA function symbol is the Greek capital letter:  Γ */
+numeric digits 90                                /*be able to handle extended precision.*/
+parse arg LO HI .                                /*allow specification of gamma arg/args*/
+                                                 /* [↓]  either show a range or a ···   */
+        do j=word(LO 1, 1)  to word(HI LO 9, 1)  /*              ··· single gamma value.*/
+        say 'gamma('j") ="  gamma(j)             /*compute gamma of J and display value.*/
+        end   /*j*/                              /* [↑]  default LO is one;  HI is nine.*/
+exit                                             /*stick a fork in it,  we're all done. */
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+gamma:  procedure;   parse arg x;    xm=x-1;    sum=0
+                                /*coefficients thanks to: Arne Fransén & Staffan Wrigge.*/
+ #.1 =  1                       /* [↓]    #.2   is the   Euler-Mascheroni  constant.    */
+ #.2 =  0.57721566490153286060651209008240243104215933593992359880576723488486772677766467
+ #.3 = -0.65587807152025388107701951514539048127976638047858434729236244568387083835372210
+ #.4 = -0.04200263503409523552900393487542981871139450040110609352206581297618009687597599
+ #.5 =  0.16653861138229148950170079510210523571778150224717434057046890317899386605647425
+ #.6 = -0.04219773455554433674820830128918739130165268418982248637691887327545901118558900
+ #.7 = -0.00962197152787697356211492167234819897536294225211300210513886262731167351446074
+ #.8 =  0.00721894324666309954239501034044657270990480088023831800109478117362259497415854
+ #.9 = -0.00116516759185906511211397108401838866680933379538405744340750527562002584816653
+#.10 = -0.00021524167411495097281572996305364780647824192337833875035026748908563946371678
+#.11 =  0.00012805028238811618615319862632816432339489209969367721490054583804120355204347
+#.12 = -0.00002013485478078823865568939142102181838229483329797911526116267090822918618897
+#.13 = -0.00000125049348214267065734535947383309224232265562115395981534992315749121245561
+#.14 =  0.00000113302723198169588237412962033074494332400483862107565429550539546040842730
+#.15 = -0.00000020563384169776071034501541300205728365125790262933794534683172533245680371
+#.16 =  0.00000000611609510448141581786249868285534286727586571971232086732402927723507435
+#.17 =  0.00000000500200764446922293005566504805999130304461274249448171895337887737472132
+#.18 = -0.00000000118127457048702014458812656543650557773875950493258759096189263169643391
+#.19 =  0.00000000010434267116911005104915403323122501914007098231258121210871073927347588
+#.20 =  0.00000000000778226343990507125404993731136077722606808618139293881943550732692987
+#.21 = -0.00000000000369680561864220570818781587808576623657096345136099513648454655443000
+#.22 =  0.00000000000051003702874544759790154813228632318027268860697076321173501048565735
+#.23 = -0.00000000000002058326053566506783222429544855237419746091080810147188058196444349
+#.24 = -0.00000000000000534812253942301798237001731872793994898971547812068211168095493211
+#.25 =  0.00000000000000122677862823826079015889384662242242816545575045632136601135999606
+#.26 = -0.00000000000000011812593016974587695137645868422978312115572918048478798375081233
+#.27 =  0.00000000000000000118669225475160033257977724292867407108849407966482711074006109
+#.28 =  0.00000000000000000141238065531803178155580394756670903708635075033452562564122263
+#.29 = -0.00000000000000000022987456844353702065924785806336992602845059314190367014889830
+#.30 =  0.00000000000000000001714406321927337433383963370267257066812656062517433174649858
+#.31 =  0.00000000000000000000013373517304936931148647813951222680228750594717618947898583
+#.32 = -0.00000000000000000000020542335517666727893250253513557337960820379352387364127301
+#.33 =  0.00000000000000000000002736030048607999844831509904330982014865311695836363370165
+#.34 = -0.00000000000000000000000173235644591051663905742845156477979906974910879499841377
+#.35 = -0.00000000000000000000000002360619024499287287343450735427531007926413552145370486
+#.36 =  0.00000000000000000000000001864982941717294430718413161878666898945868429073668232
+#.37 = -0.00000000000000000000000000221809562420719720439971691362686037973177950067567580
+#.38 =  0.00000000000000000000000000012977819749479936688244144863305941656194998646391332
+#.39 =  0.00000000000000000000000000000118069747496652840622274541550997151855968463784158
+#.40 = -0.00000000000000000000000000000112458434927708809029365467426143951211941179558301
+#.41 =  0.00000000000000000000000000000012770851751408662039902066777511246477487720656005
+#.42 = -0.00000000000000000000000000000000739145116961514082346128933010855282371056899245
+#.43 =  0.00000000000000000000000000000000001134750257554215760954165259469306393008612196
+#.44 =  0.00000000000000000000000000000000004639134641058722029944804907952228463057968680
+#.45 = -0.00000000000000000000000000000000000534733681843919887507741819670989332090488591
+#.46 =  0.00000000000000000000000000000000000032079959236133526228612372790827943910901464
+#.47 = -0.00000000000000000000000000000000000000444582973655075688210159035212464363740144
+#.48 = -0.00000000000000000000000000000000000000131117451888198871290105849438992219023663
+#.49 =  0.00000000000000000000000000000000000000016470333525438138868182593279063941453996
+#.50 = -0.00000000000000000000000000000000000000001056233178503581218600561071538285049997
+#.51 =  0.00000000000000000000000000000000000000000026784429826430494783549630718908519485
+#.52 =  0.00000000000000000000000000000000000000000002424715494851782689673032938370921241
+#=52;                           do k=#  by -1  for #
+                                sum=sum*xm  +  #.k
+                                end   /*k*/
+return 1/sum
--- a/Task/Gamma-function/REXX/gamma-function-2.rexx
+++ b/Task/Gamma-function/REXX/gamma-function-2.rexx
@ -0,0 +1,69 @@
+/*REXX program calculates the gamma function using Spouge's approximation with 87 digits*/
+e=2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138
+numeric digits length(e)   -  length(.)          /*use the number of decimal digits in E*/
+c.=  0
+# = 40                                           /*#:  the number of steps in GAMMA func*/
+                    call sq gamma(-3/2),  3/4
+                    call sq gamma(-1/2), -1/2
+                    call sq gamma( 1/2),   1
+                    call si gamma(  1 )
+                    call sq gamma( 3/2),   2
+                    call si gamma(  2 )
+                    call sq gamma( 5/2),  4/3
+                    call si gamma(  3 )
+                    call sq gamma( 7/2),  8/15
+                    call si gamma(  4 )
+exit                                             /*stick a fork in it,  we're all done. */
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+gamma: procedure expose c. e #; parse arg z;         #p= # + 1
+       accm = c.1
+       if accm==0  then do;  accm= sqrt( 2*pi() )
+                             c.1 = accm
+                             kfact = 1
+                                         do k=2  to #
+                                         c.k= exp(#p-k) * pow(#p-k, k-1.5) / kfact
+                                         kfact = kfact  *  -(k-1)
+                                         end   /*k*/
+                        end
+
+           do j=2  to #;   accm = accm   +   c.j / (z+j-1)
+           end   /*k*/
+
+       return (accm * exp(-(z+#)) * pow(z+#, z+0.5) ) / z
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+pi: return 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348
+fmt:    parse arg n,p,a;  _= format(n,p,a);  L= length(_);      return left( strip0(_), L)
+isInt:  return datatype(arg(1), 'W')                      /*is the argument an integer? */
+sq:     procedure expose #; parse arg x,mu; say fmt(x,9,#)  fmt((x*mu)**2,9,#);   return
+si:     procedure expose #; parse arg x;    say fmt(x,9,#);                       return
+strip0: procedure; arg _; if pos(., _)\==0  then _= strip(strip(_,'T',0),'T',.);  return _
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+exp: procedure expose e; arg x; ix= x%1; if abs(x-ix)>.5  then ix=ix+sign(x); x= x-ix; z=1
+     _=1;  w=1;    do j=1;  _= _*x/j;    z= (z+_)/1;      if z==w  then leave;         w=z
+                   end  /*j*/;           if z\==0  then z= e**ix * z;             return z
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+ln:     procedure; parse arg x; call e; ig= x>1.5; is= 1-2*(ig\==1); ii= 0; xx= x
+          do while ig & xx>1.5 | \ig & xx<.5; _=e
+        do k=-1; iz=xx*_**-is; if k>=0&(ig&iz<1|\ig&iz>.5)  then leave; _=_*_; izz=iz; end
+        xx= izz; ii= ii+is*2**k;   end   /*while*/;      x= x*e**-ii-1;  z=0;  _= -1;  p=z
+          do k=1; _=-_*x;  z=z+_/k;  if z=p  then leave;  p=z; end;  /*k*/;    return z+ii
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+pow:    procedure; parse arg x,y;  if y=0  then return 1;  if x=0  then return 0
+        if isInt(y)  then return x**y;          if isInt(1/y)  then return root(x, 1/y)
+        if abs(y//1)=.5  then return sqrt(x)**sign(y)*x**(y%1);     return exp( y*ln(x) )
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+root:   procedure; parse arg x 1 ox,y 1 oy;     if x=0 | y=1  then return x/1
+        if \isInt(y)  then return $pow(x, 1/y)
+        if y==2  then return sqrt(x); if y==-2  then return 1/sqrt(x); return rooti(x,y)/1
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+rooti:  x=abs(x); y=abs(y); a= digits() + 5;  m= y-1;  d= 5
+        parse value format(x,2,1,,0) 'E0'  with  ? 'E' _ .;   g= (?/y'E'_ % y) + (x>1)
+          do until d==a;   d=min(d+d, a);  numeric digits d;  o=0
+            do until o=g;  o=g;  g= format((m*g**y+x)/y/g**m,,d-2);  end;  end
+        _= g*sign(ox);  if oy<0  then _= 1/_;                                     return _
+/*──────────────────────────────────────────────────────────────────────────────────────*/
+sqrt: procedure; parse arg x;  if x=0  then return 0;  d=digits();  numeric digits;  h=d+6
+      numeric form; m.=9; parse value format(x,2,1,,0) 'E0' with g "E" _ .; g=g *.5'e'_ %2
+            do j=0  while h>9;        m.j=h;                 h=h%2+1;          end  /*j*/
+            do k=j+5  to 0  by -1;    numeric digits m.k;    g=(g+x/g)*.5;     end  /*k*/
+      numeric digits d;     return g/1
--- a/Task/Gamma-function/Racket/gamma-function.rkt
+++ b/Task/Gamma-function/Racket/gamma-function.rkt
@ -0,0 +1,29 @@
+#lang racket
+(define (gamma number)
+  (if (> 1/2 number)
+      (/ pi (* (sin (* pi number))
+               (gamma (- 1.0 number))))
+      (let ((n (sub1 number))
+            (c '(0.99999999999980993 676.5203681218851 -1259.1392167224028
+                 771.32342877765313 -176.61502916214059 12.507343278686905
+	             -0.13857109526572012 9.9843695780195716e-6 1.5056327351493116e-7)))
+        (* (sqrt (* pi 2))
+           (expt (+ n 7 0.5) (+ n 0.5))
+           (exp (- (+ n 7 0.5)))
+           (+ (car c)
+              (apply +
+                (for/list ((i (in-range (length (cdr c)))) (x (in-list (cdr c))))
+                  (/ x (+ 1 n i)))))))))
+
+(map gamma '(0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0))
+;->
+;'(9.513507698668736
+;  4.590843711998802
+;  2.9915689876875904
+;  2.218159543757687
+;  1.7724538509055159
+;  1.489192248812818
+;  1.2980553326475577
+;  1.1642297137253037
+;  1.068628702119319
+;  1.0)
--- a/Task/Gamma-function/Raku/gamma-function.raku
+++ b/Task/Gamma-function/Raku/gamma-function.raku
@ -0,0 +1,22 @@
+sub Γ(\z) {
+    constant g = 9;
+    z < .5 ?? pi/ sin(pi * z) / Γ(1 - z) !!
+    sqrt(2*pi) *
+    (z + g - 1/2)**(z - 1/2) *
+    exp(-(z + g - 1/2)) *
+    [+] <
+        1.000000000000000174663
+     5716.400188274341379136
+   -14815.30426768413909044
+    14291.49277657478554025
+    -6348.160217641458813289
+     1301.608286058321874105
+     -108.1767053514369634679
+        2.605696505611755827729
+       -0.7423452510201416151527e-2
+        0.5384136432509564062961e-7
+       -0.4023533141268236372067e-8
+    > Z* 1, |map 1/(z + *), 0..*
+}
+
+say Γ($_) for 1/3, 2/3 ... 10/3;
--- a/Task/Gamma-function/Ring/gamma-function.ring
+++ b/Task/Gamma-function/Ring/gamma-function.ring
@ -0,0 +1,18 @@
+decimals(3)
+gamma = 0.577
+coeff = -0.655
+quad = -0.042
+qui = 0.166
+set = -0.042
+
+for i=1 to 10
+    see gammafunc(i / 3.0) + nl
+next
+
+func recigamma z
+     return z + gamma * pow(z,2) + coeff * pow(z,3) + quad * pow(z,4) + qui * pow(z,5) + set * pow(z,6)
+
+func gammafunc z
+     if z = 1 return 1
+     but fabs(z) <= 0.5 return 1 / recigamma(z)
+     else return (z - 1) * gammafunc(z-1) ok
--- a/Task/Gamma-function/Ruby/gamma-function-1.rb
+++ b/Task/Gamma-function/Ruby/gamma-function-1.rb
@ -0,0 +1,17 @@
+$a = [ 1.00000_00000_00000_00000,  0.57721_56649_01532_86061, -0.65587_80715_20253_88108,
+      -0.04200_26350_34095_23553,  0.16653_86113_82291_48950, -0.04219_77345_55544_33675,
+      -0.00962_19715_27876_97356,  0.00721_89432_46663_09954, -0.00116_51675_91859_06511,
+      -0.00021_52416_74114_95097,  0.00012_80502_82388_11619, -0.00002_01348_54780_78824,
+      -0.00000_12504_93482_14267,  0.00000_11330_27231_98170, -0.00000_02056_33841_69776,
+       0.00000_00061_16095_10448,  0.00000_00050_02007_64447, -0.00000_00011_81274_57049,
+       0.00000_00001_04342_67117,  0.00000_00000_07782_26344, -0.00000_00000_03696_80562,
+       0.00000_00000_00510_03703, -0.00000_00000_00020_58326, -0.00000_00000_00005_34812,
+       0.00000_00000_00001_22678, -0.00000_00000_00000_11813,  0.00000_00000_00000_00119,
+       0.00000_00000_00000_00141, -0.00000_00000_00000_00023,  0.00000_00000_00000_00002 ]
+
+def gamma(x)
+  y = Float(x) - 1
+  1.0 / $a.reverse.inject {|sum, an| sum * y + an}
+end
+
+(1..10).each {|i| puts format("%.14e", gamma(i/3.0))}
--- a/Task/Gamma-function/Ruby/gamma-function-2.rb
+++ b/Task/Gamma-function/Ruby/gamma-function-2.rb
@ -0,0 +1 @@
+(1..10).each{|i| puts Math.gamma(i/3.0)}
--- a/Task/Gamma-function/Scala/gamma-function.scala
+++ b/Task/Gamma-function/Scala/gamma-function.scala
@ -0,0 +1,26 @@
+import java.util.Locale._
+
+object Gamma {
+  def stGamma(x:Double):Double=math.sqrt(2*math.Pi/x)*math.pow((x/math.E), x)
+
+  def laGamma(x:Double):Double={
+    val p=Seq(676.5203681218851, -1259.1392167224028, 771.32342877765313,
+             -176.61502916214059, 12.507343278686905, -0.13857109526572012,
+                9.9843695780195716e-6, 1.5056327351493116e-7)
+
+    if(x < 0.5) {
+      math.Pi/(math.sin(math.Pi*x)*laGamma(1-x))
+    } else {
+      val x2=x-1
+      val t=x2+7+0.5
+      val a=p.zipWithIndex.foldLeft(0.99999999999980993)((r,v) => r+v._1/(x2+v._2+1))
+      math.sqrt(2*math.Pi)*math.pow(t, x2+0.5)*math.exp(-t)*a
+    }
+  }
+
+  def main(args: Array[String]): Unit = {
+    println("Gamma    Stirling             Lanczos")
+    for(x <- 0.1 to 2.0 by 0.1)
+      println("%.1f  ->  %.16f   %.16f".formatLocal(ENGLISH, x, stGamma(x), laGamma(x)))
+  }
+}
--- a/Task/Gamma-function/Scheme/gamma-function.ss
+++ b/Task/Gamma-function/Scheme/gamma-function.ss
@ -0,0 +1,62 @@
+(import (scheme base)
+        (scheme inexact)
+        (scheme write))
+
+(define PI 3.14159265358979323846264338327950)
+(define e 2.7182818284590452353602875)
+
+(define gamma-lanczos
+  (let ((p '(676.5203681218851 -1259.1392167224028 771.32342877765313
+             -176.61502916214059 12.507343278686905 -0.13857109526572012
+             9.9843695780195716e-6 1.5056327351493116e-7)))
+    (lambda (x)
+      (if (< x 0.5)
+        (/ PI (* (sin (* PI x)) (gamma-lanczos (- 1 x))))
+        (let* ((x2 (- x 1))
+               (t (+ x2 7 0.5))
+               (a (do ((ps p (cdr ps))
+                       (idx 0 (+ 1 idx))
+                       (res 0.99999999999980993 (+ res
+                                                   (/ (car ps)
+                                                      (+ x2 idx 1)))))
+                    ((null? ps) res))))
+          (* (sqrt (* 2 PI)) (expt t (+ x2 0.5)) (exp (- t)) a))))))
+
+(define (gamma-stirling x)
+  (* (sqrt (* 2 (/ PI x))) (expt (/ x e) x)))
+
+(define gamma-taylor
+  (let ((a (reverse
+             '(1.00000000000000000000  0.57721566490153286061
+               -0.65587807152025388108 -0.04200263503409523553
+               0.16653861138229148950 -0.04219773455554433675
+               -0.00962197152787697356  0.00721894324666309954
+               -0.00116516759185906511 -0.00021524167411495097
+               0.00012805028238811619 -0.00002013485478078824
+               -0.00000125049348214267  0.00000113302723198170
+               -0.00000020563384169776 0.00000000611609510448
+               0.00000000500200764447 -0.00000000118127457049
+               0.00000000010434267117 0.00000000000778226344
+               -0.00000000000369680562 0.00000000000051003703
+               -0.00000000000002058326 -0.00000000000000534812
+               0.00000000000000122678 -0.00000000000000011813
+               0.00000000000000000119 0.00000000000000000141
+               -0.00000000000000000023  0.00000000000000000002))))
+    (lambda (x)
+      (let ((y (- x 1)))
+        (do ((as a (cdr as))
+             (res 0 (+ (car as) (* res y))))
+          ((null? as) (/ 1 res)))))))
+
+(do ((i 0.1 (+ i 0.1)))
+  ((> i 2.01) )
+  (display (string-append "Gamma ("
+                          (number->string i)
+                          "): "
+                          "\n --- Lanczos : "
+                          (number->string (gamma-lanczos i))
+                          "\n --- Stirling: "
+                          (number->string (gamma-stirling i))
+                          "\n --- Taylor  : "
+                          (number->string (gamma-taylor i))
+                          "\n")))
--- a/Task/Gamma-function/Scilab/gamma-function.scilab
+++ b/Task/Gamma-function/Scilab/gamma-function.scilab
@ -0,0 +1,22 @@
+function x=gammal(z)  // Lanczos'
+    lz=[  1.000000000190015 ..
+          76.18009172947146  -86.50532032941677      24.01409824083091    ..
+         -1.231739572450155   1.208650973866179e-3  -5.395239384953129e-6 ]
+    if z < 0.5 then
+        x=%pi/sin(%pi*z)-gammal(1-z)
+    else
+        z=z-1.0
+        b=z+5.5
+        a=lz(1)
+        for i=1:6
+            a=a+(lz(i+1)/(z+i))
+        end
+        x=exp((log(sqrt(2*%pi))+log(a)-b)+log(b)*(z+0.5))
+    end
+endfunction
+
+printf("%4s %-9s %-9s\n","x","gamma(x)","gammal(x)")
+for i=1:30
+    x=i/10
+    printf("%4.1f %9f %9f\n",x,gamma(x),gammal(x))
+end
--- a/Task/Gamma-function/Seed7/gamma-function.seed7
+++ b/Task/Gamma-function/Seed7/gamma-function.seed7
@ -0,0 +1,42 @@
+$ include "seed7_05.s7i";
+  include "float.s7i";
+
+const func float: gamma (in float: X) is func
+  result
+    var float: result is 0.0;
+  local
+    const array float: A is [] (
+         1.00000000000000000000,  0.57721566490153286061,
+        -0.65587807152025388108, -0.04200263503409523553,
+         0.16653861138229148950, -0.04219773455554433675,
+        -0.00962197152787697356,  0.00721894324666309954,
+        -0.00116516759185906511, -0.00021524167411495097,
+         0.00012805028238811619, -0.00002013485478078824,
+        -0.00000125049348214267,  0.00000113302723198170,
+        -0.00000020563384169776,  0.00000000611609510448,
+         0.00000000500200764447, -0.00000000118127457049,
+         0.00000000010434267117,  0.00000000000778226344,
+        -0.00000000000369680562,  0.00000000000051003703,
+        -0.00000000000002058326, -0.00000000000000534812,
+         0.00000000000000122678, -0.00000000000000011813,
+         0.00000000000000000119,  0.00000000000000000141,
+        -0.00000000000000000023,  0.00000000000000000002);
+    var float: Y is 0.0;
+    var float: Sum is A[maxIdx(A)];
+    var integer: N is 0;
+  begin
+    Y := X - 1.0;
+    for N range pred(maxIdx(A)) downto minIdx(A) do
+      Sum := Sum * Y + A[N];
+    end for;
+    result := 1.0 / Sum;
+  end func;
+
+const proc: main is func
+  local
+    var integer: I is 0;
+  begin
+    for I range 1 to 10 do
+      writeln((gamma(flt(I) / 3.0)) digits 15);
+    end for;
+  end func;
--- a/Task/Gamma-function/Sidef/gamma-function-1.sidef
+++ b/Task/Gamma-function/Sidef/gamma-function-1.sidef
@ -0,0 +1,19 @@
+var a = [ 1.00000_00000_00000_00000,  0.57721_56649_01532_86061, -0.65587_80715_20253_88108,
+         -0.04200_26350_34095_23553,  0.16653_86113_82291_48950, -0.04219_77345_55544_33675,
+         -0.00962_19715_27876_97356,  0.00721_89432_46663_09954, -0.00116_51675_91859_06511,
+         -0.00021_52416_74114_95097,  0.00012_80502_82388_11619, -0.00002_01348_54780_78824,
+         -0.00000_12504_93482_14267,  0.00000_11330_27231_98170, -0.00000_02056_33841_69776,
+          0.00000_00061_16095_10448,  0.00000_00050_02007_64447, -0.00000_00011_81274_57049,
+          0.00000_00001_04342_67117,  0.00000_00000_07782_26344, -0.00000_00000_03696_80562,
+          0.00000_00000_00510_03703, -0.00000_00000_00020_58326, -0.00000_00000_00005_34812,
+          0.00000_00000_00001_22678, -0.00000_00000_00000_11813,  0.00000_00000_00000_00119,
+          0.00000_00000_00000_00141, -0.00000_00000_00000_00023,  0.00000_00000_00000_00002 ]
+
+func gamma(x) {
+    var y = (x - 1)
+    1 / a.reverse.reduce {|sum, an| sum*y + an}
+}
+
+for i in 1..10 {
+    say ("%.14e" % gamma(i/3))
+}
--- a/Task/Gamma-function/Sidef/gamma-function-2.sidef
+++ b/Task/Gamma-function/Sidef/gamma-function-2.sidef
@ -0,0 +1,37 @@
+func gamma(z) {
+    var epsilon = 0.0000001
+    func withinepsilon(x) {
+        abs(x - abs(x)) <= epsilon
+    }
+ 
+    var p = [
+        676.5203681218851,     -1259.1392167224028,
+        771.32342877765313,    -176.61502916214059,
+        12.507343278686905,    -0.13857109526572012,
+        9.9843695780195716e-6,  1.5056327351493116e-7,
+    ]
+ 
+    var result = 0
+    const pi = Num.pi
+ 
+    if (z.re < 0.5) {
+        result = (pi / (sin(pi * z) * gamma(1 - z)))
+    }
+    else {
+        z -= 1
+        var x = 0.99999999999980993
+ 
+        p.each_kv { |i, v|
+            x += v/(z + i + 1)
+        }
+ 
+        var t = (z + p.len - 0.5)
+        result = (sqrt(pi*2) * t**(z+0.5) * exp(-t) * x)
+    }
+ 
+    withinepsilon(result.im) ? result.re : result
+}
+ 
+for i in 1..10 {
+    say ("%.14e" % gamma(i/3))
+}
--- a/Task/Gamma-function/Sidef/gamma-function-3.sidef
+++ b/Task/Gamma-function/Sidef/gamma-function-3.sidef
@ -0,0 +1,11 @@
+define ℯ = Num.e
+define τ = Num.tau
+ 
+func Γ(t) {
+    t < 20 ? (__FUNC__(t + 1) / t)
+           : (sqrt(τ*t) * pow(t/ℯ + 1/(12*ℯ*t), t) / t)
+}
+ 
+for i in (1..10) {
+    say ("%.14e" % Γ(i/3))
+}
--- a/Task/Gamma-function/Stata/gamma-function-1.stata
+++ b/Task/Gamma-function/Stata/gamma-function-1.stata
@ -0,0 +1,61 @@
+mata
+_gamma_coef = 1.0,
+ 5.772156649015328606065121e-1,
+-6.558780715202538810770195e-1,
+-4.200263503409523552900393e-2,
+ 1.665386113822914895017008e-1,
+-4.219773455554433674820830e-2,
+-9.621971527876973562114922e-3,
+ 7.218943246663099542395010e-3,
+-1.165167591859065112113971e-3,
+-2.152416741149509728157300e-4,
+ 1.280502823881161861531986e-4,
+-2.013485478078823865568939e-5,
+-1.250493482142670657345359e-6,
+ 1.133027231981695882374130e-6,
+-2.056338416977607103450154e-7,
+ 6.116095104481415817862499e-9,
+ 5.002007644469222930055665e-9,
+-1.181274570487020144588127e-9,
+ 1.04342671169110051049154e-10,
+ 7.782263439905071254049937e-12,
+-3.696805618642205708187816e-12,
+ 5.100370287454475979015481e-13,
+-2.05832605356650678322243e-14,
+-5.348122539423017982370017e-15,
+ 1.226778628238260790158894e-15,
+-1.181259301697458769513765e-16,
+ 1.186692254751600332579777e-18,
+ 1.412380655318031781555804e-18,
+-2.298745684435370206592479e-19,
+ 1.714406321927337433383963e-20
+
+function gamma_(x_) {
+    external _gamma_coef
+    x = x_
+    y = 1
+    while (x<0.5) y = y/x++
+    while (x>1.5) y = --x*y
+    z = _gamma_coef[30]
+    x--
+    for (i=29; i>=1; i--) z = z*x+_gamma_coef[i]
+    return(y/z)
+}
+
+function map(f,a) {
+    n = rows(a)
+    p = cols(a)
+    b = J(n,p,.)
+    for (i=1; i<=n; i++) {
+        for (j=1; j<=p; j++) {
+            b[i,j] = (*f)(a[i,j])
+        }
+    }
+    return(b)
+}
+
+x=(1::1000)/100
+u=map(&gamma(),x)
+v=map(&gamma_(),x)
+max(abs((v-u):/u))
+end
--- a/Task/Gamma-function/Stata/gamma-function-2.stata
+++ b/Task/Gamma-function/Stata/gamma-function-2.stata
@ -0,0 +1,31 @@
+from mpmath import mp
+
+mp.dps = 50
+
+def gamma_coef(n):
+    a = [mp.mpf(1), mp.mpf(mp.euler)]
+    for k in range(3, n + 1):
+        s = sum((-1)**j * mp.zeta(j) * a[k - j - 1] for j in range(2, k))
+        a.append((s - a[1] * a[k - 2]) / (1 - k * a[0]))
+    return a
+
+def horner(a, x):
+    y = 0
+    for s in reversed(a):
+        y = y * x + s
+    return y
+
+gc = gamma_coef(30)
+
+def gamma_approx(x):
+    y = mp.mpf(1)
+    while x < 0.5:
+        y /= x
+        x += 1
+    while x > 1.5:
+        x -= 1
+        y *= x
+    return y / horner(gc, x - 1)
+
+for x in gc:
+    print(mp.nstr(x, 25))
--- a/Task/Gamma-function/TI-83-BASIC/gamma-function-1.basic
+++ b/Task/Gamma-function/TI-83-BASIC/gamma-function-1.basic
@ -0,0 +1,6 @@
+for(I,1,10)
+I/2→X
+X^(X-1/2)e^(-X)√(2π)→Y
+Disp X,(X-1)!,Y
+Pause
+End
--- a/Task/Gamma-function/TI-83-BASIC/gamma-function-2.basic
+++ b/Task/Gamma-function/TI-83-BASIC/gamma-function-2.basic
@ -0,0 +1,14 @@
+for(I,1,10)
+I/2→X
+e^(ln((1.0
+76.18009173/(X+1)
+-86.50532033/(X+2)
+24.01409824/(X+3)
+-1.231739572/(X+4)
+1.208650974E-3/(X+5)
+-5.395239385E-6/(X+6)
+)√(2π)/X)
+(X+.5)ln(X+5.5)-X-5.5)->Y
+Disp X,(X-1)!,Y
+Pause
+End
--- a/Task/Gamma-function/TXR/gamma-function-1.txr
+++ b/Task/Gamma-function/TXR/gamma-function-1.txr
@ -0,0 +1,20 @@
+(defun gamma (x)
+  (/ (rpoly (- x 1.0)
+            #( 1.00000,00000,00000,00000  0.57721,56649,01532,86061
+              -0.65587,80715,20253,88108 -0.04200,26350,34095,23553
+               0.16653,86113,82291,48950 -0.04219,77345,55544,33675
+              -0.00962,19715,27876,97356  0.00721,89432,46663,09954
+              -0.00116,51675,91859,06511 -0.00021,52416,74114,95097
+               0.00012,80502,82388,11619 -0.00002,01348,54780,78824
+              -0.00000,12504,93482,14267  0.00000,11330,27231,98170
+              -0.00000,02056,33841,69776  0.00000,00061,16095,10448
+               0.00000,00050,02007,64447 -0.00000,00011,81274,57049
+               0.00000,00001,04342,67117  0.00000,00000,07782,26344
+              -0.00000,00000,03696,80562  0.00000,00000,00510,03703
+              -0.00000,00000,00020,58326 -0.00000,00000,00005,34812
+               0.00000,00000,00001,22678 -0.00000,00000,00000,11813
+               0.00000,00000,00000,00119  0.00000,00000,00000,00141
+              -0.00000,00000,00000,00023  0.00000,00000,00000,00002))))
+
+(each ((i 1..11))
+  (put-line (pic "##.######" (gamma (/ i 3.0)))))
--- a/Task/Gamma-function/TXR/gamma-function-2.txr
+++ b/Task/Gamma-function/TXR/gamma-function-2.txr
@ -0,0 +1,7 @@
+(defun gamma (x)
+  (* (sqrt (/ (* 2 %pi%)
+              x))
+     (expt (/ x %e%) x)))
+
+(each ((i 1..11))
+  (put-line (pic "##.######" (gamma (/ i 3.0)))))
--- a/Show more
+++ b/Show more
				`@ -0,0 +1 @@`
				`(map #(printf "%.1f %.4f\n" % (gamma %)) (map #(float (/ % 10)) (range 1 31)))`
				`@ -0,0 +1 @@`
				`Gamma(x)=intnumromb(t=0,9,t^(x-1)/exp(t),0)+intnumromb(t=9,max(x,99)^9,t^(x-1)/exp(t),2)`