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Comment by cperciva | Hacker News Reader

As far as I know, floating point add and multiply are commutative (but not associative) in IEEE 754.

Usually, but not always. (+0) + (-0) yields (+0), while (-0) + (+0) yields (-0).

In IEEE 754-1985 and IEEE 754-2008 this is not valid behavior. I have mostly worked on the 2008 revision, so I didn't know if 0 was commutative in the original standard. Thanks for making me look it up.

IEEE 754-2008

> Section 6.3 The sign bit

> When the sum of two operands with opposite signs (or the difference of two operands with like signs) is exactly zero, the sign of that sum (or difference) shall be +0 in all rounding-direction attributes except roundTowardNegative; under that attribute, the sign of an exact zero sum (or difference) shall be −0. However, x + x = x − (−x) retains the same sign as x even when x is zero.

No quote for IEEE 754-1985 because I didn't want to type it out and it is mostly the same.

Huh, interesting. I've definitely seen systems where the sum of two zeroes took the sign of the first value. I assumed they were inheriting 754 behaviour but I guess not.

I can't reproduce this: https://godbolt.org/z/PK4gvZ

It works if the compiler can't do constant folding, like so: https://godbolt.org/z/nQDrSW

Your first line of main is adding -0.0 and -0.0, which is not what I think you intended to show.

Oops, you're right. https://godbolt.org/z/pAwqUA shows it better. Adding a -0 and +0 together in either order gives +0, using the actual x86-64 addsd instruction.

Can you cite any references about this? I don’t recall anything like this at all unless perhaps it’s specific to FENV_ACCESS and non-default rounding modes.

In a sister comment, I quoted IEEE 754-2008 Section 6.3 which shows that 0 is commutative in the newer standard. The older revision has similar language.

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