An interesting modern variant of Casio's venerable low-end programmable scientific calculator series, the fx-3600Pv also happens to be a machine with a curious bug, a bug not present in its predecessor, the fx-3600P. I encountered this as I was trying to create a program to compute the Gamma function, which of course is my favorite programming example for calculators. Take a look at this simple program:

+
ln
Kin+1
1
=
x<=M
0
x-K 1

This program should compute the logarithm of the products of numbers starting from the number in the display, up to and including the number in the calculator's independent memory. For instance, if the number on the display is 5, and the number in memory is 9, running this program should produce 9.62377..., i.e., the natural logarithm of 15120 (=5×6×7×8×9). What it does compute instead is something completely different: 13.57639..., which is the logarithm of 787320. It took me some time to figure out this riddle: 787320=9×18×27×36×5! I.e., while we're decrementing the single-digit argument in the display register, a phantom digit in the second position appears in the multiplication. The same effect is not reproduced if you perform this calculation by hand; nor is this effect present if the independent memory contains a number greater than, or equal to, 10.

Oh well, scratch one useful method for shortening my Gamma function program. Here is a program anyway, one that performs a somewhat lengthier calculation but avoids this bug.

Kin 2
ln
Kin+ 1
9
Min
Kout 2
+
1
=
x<=M
X
Min
ln
-
MR
+
(
2
*
π 
/
MR
)
√ 
ln
+
1
2
1/x
/
MR
-
0
x-K 1
=