math/big: handle negative moduli in ModInverse

[bmkessler]

What version of Go are you using (go version)?

go version go1.10 linux/amd64

Does this issue reproduce with the latest release?

yes

What did you do?

Calculate ModInverse with positive and negative moduli.

https://play.golang.org/p/oCjaCyBdbp7

What did you expect to see?

Both should give the same result for ModInverse.

What did you see instead?

Negative moduli returns 0.

[gopherbot]

Change https://golang.org/cl/108115 mentions this issue: math/big: handle negative moduli in ModInverse

[FiloSottile]

When the modulus is negative, shouldn't the result be negative as well?

[bmkessler]

I think the result should always be non-negative per the definition of Euclidean modulus from the go docs

DivMod implements Euclidean division and modulus (unlike Go):
q = x div y such that
m = x - y*q with 0 <= m < |y|

So, I would expect the result of ModInverse to always be non-negative as well, such that taking the Mod of the ModInverse would be the identity. If the ModInverse result was negative, taking the Mod of the result would return the positive value.