Re: Compiler optimization and floating point operations

On Mon, Oct 28, 2013 at 6:50 PM, <christian.bau@cbau.wanadoo.co.uk> wrote:
>> [I think you mean they're not associative. I don't know any situations
>> where a+b != b+a, but lots where a+(b+c) != (a+b)+c -John]
>
> Take fused multiply-add, and the expression a*b + c*d.
> It can be evaluated either as fma (a, b, c*d) or fma (c, d, a*b).
>
> It would seem natural that the code for a*b + c*d and for c*d + a*b
> would be different, with different results.


Right, that's called reassociation. The order of operations in the
expression tree has changed, so the finite precision rounding occurs
on different intermediate results. The same problem exists in some
floating point parallel reductions and such.


Most compilers will offer a directive, similar to FP_CONTRACT, for
such critical pieces of code. Some compilers [the good ones ;)] even
have flags to disable optimization passes that involve reassociation.


-Cameron

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