Is floating point addition commutative in C++?

Question

For floating point values, is it guaranteed that a + b == b + a ?

I believe this is guaranteed in IEEE754, however the C++ standard does not specify tha

Answer 1

No, the C++ language generally wouldn't make such a requirement of the hardware. Only the associativity of operators is defined.

All kinds of crazy things do happen in floating-point arithmetic. Perhaps, on some machine, adding zero to an denormal number produces zero. Conceivable that a machine could avoid updating memory in the case of adding a zero-valued register to a denormal in memory. Possible that a really dumb compiler would always put the LHS in memory and the RHS in a register.

Note, though, that a machine with non-commutative addition would need to specifically define how expressions map to instructions, if you're going to have any control over which operation you get. Does the left-hand side go into the first machine operand or the second?

Such an ABI specification, mentioning the construction of expressions and instructions in the same breath, would be quite pathological.