Technically (AFAIK), IEEE754 does need require reproducibility, ergo determinism.
It actually requires more than that:
"Algebraic operations covered by IEEE 754, namely + , - , * , / , square root and Binary <-> Decimal Conversion with rare exceptions, must be Correctly Rounded to the precision of the operationâs destination unless the programmer has specified a rounding other than the default. If it does not Overflow, a correctly rounded operationâs error cannot exceed half the gap between adjacent floating-point numbers astride the operationâs ideal ( unrounded ) result. Half-way cases are rounded to Nearest Even, which means that the neighbor with last digit 0 is chosen."
I don't know if implementation conform exactly to IEEE 754, but I doubt there is any commonly used implementation that isn't deterministic.
