floating point - In Rust f64 and f32 don't implement total ordering via Ord trait. Why this restriction? -

floating point - In Rust f64 and f32 don't implement total ordering via Ord trait. Why this restriction? -

while integer types in rust implement ord trait emphasizes total ordering, floating point type implement partialord means there floating point values cannot compared. seems bit hard digest since floating point numbers can thought of approximations real numbers happen totally ordered set. add-on of +inf , -inf keeps set of real numbers totally ordered. why odd selection in rust?

this restriction means generic sort/search algorithm can assume partial ordering on numbers. ieee 754 standard seems provide total ordering predicate.

are nan's much of problem in generic code?

what question, precisely? asking whether nan exists, or whether can obtained result of accidental or voluntary computations? yes, , can. sort of info construction requires total order keys breaks downwards when provided order not total order. not want 1 exceptional value different itself, because break invariants of construction , mean can happen henceforth. nan not should assumed innocuous long no problem has been shown, although that has been tried in other languages.

ieee 754's definition of ordinary comparing operators <, <=, … makes them useful in general—if not when need total order. in particular, easy write conditions nan inputs sent error branch:

if (!(x <= max)) { // nan makes status true error(); } if (!(x >= min)) { // nan makes status true error(); }

because < , <= useful, operations implemented single, fast instructions in modern processors—the totalorder predicate ieee 754 typically not implemented in hardware. programming languages map fast instructions constructs in language , leave exceptionally needs totalorder pick library or define themselves.

floating-point order rust