The HP-12C is arguably one of the most successful calculators ever made. Introduced almost 20 years ago, this calculator is still in production, and it is the de facto standard shirt-pocket calculator in use by business people.

The HP-12C is a programmable calculator with several business functions, including interest calculations, bonds, amortization, depreciation, and statistical functions. It has a maximum of 99 program steps or 20 data registers. When the calculator is initialized, 8 program steps are available; just like many other HP calculators, the HP-12C converts register memory dynamically into program memory as the user enters additional program steps. When all 99 program steps are used, 7 data registers still remain available for storage.

Although it isn't a scientific calculator, the HP-12C has built-in exponential and logarithm functions. This makes it easier to implement many mathematical algorithms, including that of the Gamma function. As it turns out, an implementation that calculates the function for any real argument fits neatly into the calculator's memory.

In order to run this program, registers 0-6 must be preset with the appropriate values. The program calculates the Gamma function itself (not its logarithm). The result should be accurate to at least 8 digits of precision.

M0:    √2π = 2.506628275
M1:    76.18009173
M2:    86.50532033
M3:    24.01409824
M4:    1.231739572
M5:    1.208650974e-3
M6:    5.395239385e-6

01 -  1 	1
02 - 34 	x-y
03 -  0 	0
04 - 43 34	x<=y
05 - 43,33 16	GTO 16
06 - 33 	Rv
07 - 36 	ENTER
08 - 33 	Rv
09 - 20 	×
10 - 33 	Rv
11 - 33 	Rv
12 - 33 	Rv
13 -  1 	1
14 - 40 	+
15 - 43,33 03	GTO 03
16 - 33 	Rv
17 - 44  7	STO 7
18 - 34 	x-y
19 - 44  8	STO 8
20 - 45  1	RCL 1
21 - 45  7	RCL 7
22 -  1 	1
23 - 40 	+
24 - 10 	÷
25 - 45  2	RCL 2
26 - 45  7	RCL 7
27 -  2 	2
28 - 40 	+
29 - 10 	÷
30 - 30 	-
31 - 45  3	RCL 3
32 - 45  7	RCL 7
33 -  3 	3
34 - 40 	+
35 - 10 	÷
36 - 40 	+
37 - 45  4	RCL 4
38 - 45  7	RCL 7
39 -  4 	4
40 - 40 	+
41 - 10 	÷
42 - 30 	-
43 - 45  5	RCL 5
44 - 45  7	RCL 7
45 -  5 	5
46 - 40 	+
47 - 10 	÷
48 - 40 	+
49 - 45  6	RCL 6
50 - 45  7	RCL 7
51 -  6 	6
52 - 40 	+
53 - 10 	÷
54 - 30 	-
55 -  1 	1
56 - 40 	+
57 - 45  0 	RCL 0
58 - 20 	×
59 - 45  7	RCL 7
60 - 10 	÷
61 - 43 23	LN
62 - 45  7	RCL 7
63 -  5 	5
64 - 48 	.
65 -  5 	5
66 - 40 	+
67 - 43 23	LN
68 - 45  7	RCL 7
69 - 48 	.
70 -  5 	5
71 - 40 	+
72 - 20 	×
73 - 40 	+
74 - 45  7	RCL 7
75 - 30 	-
76 -  5 	5
77 - 48 	.
78 -  5 	5
79 - 30 	-
80 - 43 22	ex
81 - 45  8	RCL 8
82 - 10 	÷