resema wrote

I guess that the division of -32767 by 10 causing the stack overflow due to the recursion in the Math class.

Does the proposed implementation of the Math division contains such a limitation?

Good guess. It does have issues witn signed integer overflow.

The recursive call doubles the divisor each call until the divisor (y) is greater than the dividend (x). Since the recursive algorithm is wrapped with sign handling code, for -32767/10, x = 32767 and y = 10. The recursive y's are:

hex dec
000A 10
0014 20
0028 40
0050 80
00A0 160
0140 320
0280 640
0500 1280
0A00 2560
1400 5120
2800 10240
5000 20480
A000 -24576
4000 16384
8000 -32768
0000 0
0000 0

Since y is never > 32767, recursion is infinite.

A quick solution is to add (y < 0) into the if at the top of the recursive divide function since a negative value here indicates that y >= 32768.

There are still issues with x or y = -32768. See

this article for more info on signed integer overflow and complete treatment of overflows in the division algorithm.

--Mark