Discuss: should we panic when powering 0 by 0?

[weikengchen]

Description

This is half PR half discussion.

For pow function, there is a corner case when the base is zero and the pow is also zero.

There are two ways to handle it:

1. panic, as in this PR
2. let it be "1", which is indeed an accepted practice in some fields.

Note that this treatment is sort of for "soundness". It is hard to imagine a concrete application where the developer wants to power a value by "0".

Any opinions? Note that letting it be "1" is simpler.

---

Before we can merge this PR, please make sure that all the following items have been
checked off. If any of the checklist items are not applicable, please leave them but
write a little note why.

• Targeted PR against correct branch (master)
• Linked to Github issue with discussion and accepted design OR have an explanation in the PR that describes this work.
• Wrote unit tests
• Updated relevant documentation in the code
• Re-reviewed Files changed in the Github PR explorer

not ready:

• Added a relevant changelog entry to the Pending section in CHANGELOG.md

[weikengchen]

Note: Rust itself considers 0^0 = 1. I think we just need to consider whether it will ever cause soundness problems in any application. Note that if we panic when 0^0, it may cause additional issues that the program may panic unnecessarily.

if exp == 0 {
     return 1;
}

[ValarDragon]

I think setting it to 1 makes sense personally. I think risk of panic for a core algebraic routine will cause more error handling / cognitive overhead code bloat, for something that seems like a very low risk error to get introduced in natural code.

(Also AFAIK, 0^0 = 1 is relatively common in algebra settings)

[weikengchen]

I think let us settle that 0^0 = 1. I will update arkworks-rs/r1cs-std#72 accordingly.