In late 2001, I wrote the skeleton
of a pure /bin/sh implementation of various mathematical
operations (doesn't even use test or echo).
It includes the boolean operators and conversion between binary and
decimal, plus a few helper functions.
The code is notionally arbitrary-precision, but will in fact be limited
by how long a particular Bourne shell implementation allows variables
to be.
A sample script calculates a broadcast address given IP address and netmask, and is merely proof-of-concept code to disprove Randal L. Schwartz's assertion, on the SAGE mailing list, that it couldn't be done. He had written:
There are no solutions in sh (other than brute force). Sh has insufficient computing ability - it'll have to call some other program (and I bet a lot of the answers will probably try using bc or expr).
Of course, Clarke's First Law applies here.
Coming back to it a year later, I realized that the code doesn't understand negative numbers. I'm not entirely sure how to rectify that; while the code does have all the boolean operators, it is arbitrary precision, and so I don't think normal digital-computer like operations will work. It's been over a decade since I studied that sort of thing. And, do I really care?