feat(std): add LessThan() and IsEqual()

[vck3000]

Hi guys,

I've found some time to give this a go :).

I have implemented LessThan() and IsEqual() as a new math package under std. Currently, this implementation gives it great isolation and builds on top of the current frontend.api without touching it.

I was hoping to simplify LessThan() to compute a < b, however, I found that I still needed the full functionality of Compare(). If b is greater than a, it needs to be recorded too and persisted to the end of the loop. Without this, if a has a less significant bit set where b's is not, then it will appear as though a > b incorrectly.

As such, I wanted to ask whether you guys wanted to relax the feature from LessThan() to Compare() given both require the same amount of work, but Compare() gives more functionality to the user. I can also see the benefit of simplifying the interface and keeping it as LessThan(), so also happy to keep it just as is and include the reduction done in the final lines of the current implementation:

	// Now, convert output of Convert() into LessThan()
	return m.IsEqual(output, -1)

Another thing I was hoping to do was to add it directly into frontend.api. However, I had some issues getting the tests to run. Here is the link to my attempted commit on my fork: LINK

An example of the error is:

=== RUN   TestCompare/fuzz/bw6_761/plonk
    assert.go:356:
                Error Trace:    assert.go:356
                                                        assert.go:70
                Error:          Received unexpected error:
                                compilation is not deterministic
                Test:           TestCompare/fuzz/bw6_761/plonk

However, this implementation also means that the code has to be duplicated thrice across r1cs, plonk and engine. I could not work out a way to prevent code duplication here if I added it straight into frontend.api.

What do you guys think? I like the idea of having api.LessThan() and api.IsEqual(); however it may be cleaner to have these in a new std/math package.

Open to suggestions and feedback!

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[vck3000]

Hmm, the CLA caught me by surprise. I will have to consult with my research department to see whether I can sign it. Please give me some time to do this. In the meantime, I'd still love to hear your thoughts :).

[vck3000]

Oh, never mind. I just saw #233.

[ThomasPiellard]

Hi @vck3000 , yes I just pushed a similar PR 1hour ago^^ I have added this directly to the api (so the api interface is modified also).

[vck3000]

Sounds good :). Will close this then.