[jasone]

I've spent a lot of time over the years using bit shifting to multiply/divide by powers of 2 in low-level code. At some point I grokked the connection with (base 2) logarithms and found myself using them as a mental estimation tool with surprising effectiveness.

Many of us programmers have powers of 2 memorized through at least 2^20 (and 2^10 ~= 1000 is close enough for decomposing and converting larger values), which makes rough conversion to/from the log domain trivial. The trick in estimation is to round to the nearest whole number when converting to the log domain, and try to alternate rounding direction for inputs that are not close to the upper/lower extrema. Keep a running total of the log-domain value as a whole value, and take the antilog as the final step. Given these simple rules, most estimates come within a factor of 2 of the intended value, and with minimal cognitive load. All you need to remember is the current sum and which direction to round the next input.