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Comment by omoikane | Hacker News Reader

> -Wxor-used-as-pow

This seems to only trigger in limited circumstances, one of my favorite accidentally true expression is still warning-free:

    printf("%d\n", 2^5);  // Warning here.

    assert((3^2) + (4^2) == (5^2));  // No warnings.

https://gcc.godbolt.org/z/4GqdEMfPb

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My understanding is it only triggers when the left side is 2 or 10.

That's quite specific

It's based on the errors the proposers actually found in the wild, which seem to mostly be people attempting to use constant powers of 2 or 10.

should also include e.

Excellent. Now I'm wondering if Fermat's Last Theorem has a bitwise analogue.

> Now I'm wondering if Fermat's Last Theorem has a bitwise analogue.

It hasn’t in this sense. The ^n operator flips the ‘one’ bits in n in its argument, so for any n, we have

  a = a^n^n

So, for all a and b,

  a^n + b^n = ((a^n + b^n)^n)^n

that makes

  c = (a^n + b^n)^n

a solution to

  a^n + b^n = c^n

and that means we can find a c for every n, a and b.

Neat proof!

Bitwise multiplication is bitwise ‘and’, so exponentiation (repeated multiplication) is the identity, so aⁿ+bⁿ=cⁿ iff a+b=c. I have a truly remarkable proof of this, but my filesystem is full.

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