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Comment on Why a*a*a*a*a*a cannot be optimized to (a*a*a)*(a*a*a)?parent

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Yes. Multiplication is left associative. I'm not sure that C defines the precision of floating point operations, although I think it sets an upper bound. I may be wrong, and I think that the C99 spec (optionally?) pushes compilers to conform to the iee754

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