we all know floating point numbers can be treacherous, but what are specific examples of when they've betrayed you?
so far I have:
* money calculations where you need to get the exact correct answer
* twitter's tweet IDs are bigger than 2^53 and can't be represented as a Javascript number, you have to use a string
* implementing numerical algorithms (like matrix multiplication) (I've never done this)
I would phrase the money thing rather as "the exact correct answer _according to rules incompatible with ones for FP_".
I think there are very many problems that are instances of "implementing a numerical algorithm", even if people who don't think in these terms won't call them that. For example, computing a sum of a long sequence of numbers (where you can acquire errors by adding many numbers that are below the smallest representable difference in the sum accumulated so far).
