[jsmith45]

>In particular all basic operations should produce bit-exact results to last ulp.

As long as you are not using a compiler that utilizes x87's extended precision flaots for intermediate calculations, and silently rounding whenever it transfers to memory (That used to be a common issue), and as long as you are not doing dumb stuff with compiler math flags.

Also if you have any code anwhere in your program that relies on correct subnormal handling, then you need to be absolutely sure no code is compiled with `-ffast-math`, including in any dynamically loaded code in your entire program, or your math will break: https://simonbyrne.github.io/notes/fastmath/#flushing_subnor...

And of course if you are doing anything complicated with floating point number, there are entire fields of study about creating numerically stable algorithms, and determining the precision of algorithms with floating point numbers.