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).
Re:Floating point oddity
by thethirdone on Monday November 11, 2019 @10:05PM
(#21511204)
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.
Re:Floating point oddity
by elcaminocomplex on Monday November 11, 2019 @09:09PM
(#21510896)
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.
Re:Floating point oddity
by thethirdone on Monday November 11, 2019 @10:08PM
(#21511211)
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.
Note: That is of course no longer true under -ffast-math.