I just received this calculator today, a gift from a friend in Hungary (thank you, István!) Battered as it may look, this older Casio machine still works perfectly. Like other lower-end Casio programmable machines of the same vintage, the fx-3600P offers a full complement of scientific functions, but its programming model is very limited. Program storage is limited to 38 program steps. A simple set of conditional instructions allows the program to be restarted from the beginning, but no other control transfer is possible. No facilities are provided for reviewing or editing programs.

The use of conditional instructions is neatly demonstrated by the following simple implementation of the factorial:

Min
×
(
MR
-
1
)
x>0
1
=

Not too long ago, I thought that 38 program steps and a limited branching capability make this calculator inadequate for a problem as complex as my favorite programming example, the Gamma function. But then I received an e-mail from Herman van Elburg who pointed out that this calculator offers full memory arithmetic (all four functions) on its six K-registers; moreover, the operations are fully merged (i.e., Kin × 6 uses only one step in program memory.) Herman quickly followed up with another e-mail, a working implementation of the incomplete Gamma function, and a pretty good one at that! Unlike the algorithms I used for the incomplete Gamma function elsewhere, Herman's even works for negative arguments. Needless to say, I am suitably amazed.

Herman's program is reproduced below. To use the program, clear all registers (INV KAC; needed only when the program is run for the first time), enter the integration limit, hit INV x<->y, enter the argument, and hit P1. The result should usually appear within a minute or so. Choosing a high enough integration limit closely approximates the Gamma function; Herman reports that in integration limit of 1.5z+25 on the fx-3600P provides suitably accurate results.

1		Kin 5				first pass: init z next passes: not needed
2		X<->Y		INV Kin
3		Kin 6				first pass: init x next passes: store 0 (zero)
4		1				(the loop below is only functional during 'next passes')
5		Kin + 1		Kin + 1		inc(z)
6		Kout 1				recall (z+n)
7		Kin ÷ 3		Kin ÷ 3
8		Kout 2				recall n
9		Kin × 3
10		Kout 3				recall next summation term
11		+
12		Kout 4				old sum
13		-
14		X<->K 4		INV Kout 4		put new sum in K4
15		=
16		x>0		INV 7		loop up if sum has changed...
17		+/-
18		x>0		INV 7		... same for negative gammas
19		X<->K 6		INV Kout 6		swap 0 with x (first pass) or 0 (second pass)
20		Kin 2				store x (first pass) or 0 (second pass)
21		xy		INV ×		z^ (first pass) or 0^(unimportant)(2nd pass)
22		Kout 4				recall 0 (first pass) or gamma(z) (second pass)
23		X<->K 5		INV Kout 5		recall z (first pass) or store gamma(z) in K5 (second pass)
24		Kin 1				store z in K1
25		÷
26		Kout 2				divide by exp(x)...
27		ex		INV ln		...
28		÷				divide by z...
29		Kout 1				...
30		=				first summation term done (1st pass) or Zero (second pass)
31		Kin 3				store first term in term memory (K3) (2nd pass: zero)
32		Kin 4				store first term or 0 (2nd pass) in summation memory (K4)
33		x2		INV +/-		square to make negative terms (for half of z<0) positive
34		x>0		INV 7		loop to beginning to calculate gamma, continue if gamma done
35		Kout 5				recall gamma(x,z)
36		Min				store gamma(x,z) in memory.