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IEEE floating point is deterministic, to the apparent contradiction of many sentences written by GustafsonWhat about this then, which somebody comments below:
"On old x86 systems, the x87 registers were 80-bits and the bottom bits were undefined. You could theoretically have a 1-bit difference on some results depending on what the bottom 26 bits (that were undefined, because you had 64-bit floats most of the time, even though the machine did things 80-bits at a time)."
And below:
"I spent a long time once debugging an issue arising from this. Code was basically:
double x = y;
[...]
if (x>y) fail;
Nothing in between the assignment and the check changed the value of x or y, yet the check triggered the fail condition. Turned out to be that one of the value stayed in the 80 bit x87 register and one was written to RAM as a 64 bit value, then loaded back into an x87 register for the check, resulting in the inequality. Running in a debugger wrote both values out of the registers before the check, making the problem unreproducible."
This behavior might not be IEEE defined, but even as IEEE undefined (and implementation dependent), it still qualifies those IEEE compliant implementations as non-deterministic.
Or how about:
"parallel systems, most likely GPUs, where it is common to have slightly different results even on the same operation, on the same system. This is due to the fact that several pipelines will do calculations in parallel and depending on which pipeline ends first (which can depend on many factors like current temperature) the sums can happen in a different order, leading to different rounding results."
due to fp associativity?