feat(glv): split scalar strict bounds

[yelhousni]

Description

We re-introduce the original SplitScalar() removed in #213 (now renamed SplitScalarStrict()). For gnark-crypto we continue to use the current SplitScalar() which replaces divisions by right-shifts but we need SplitScalarStrict() for gnark circuits.

Type of change

Please delete options that are not relevant.

• New feature (non-breaking change which adds functionality)

How has this been tested?

TestSplitting in utils_test.go tests both SplitScalar() and SplitScalarStrict().

How has this been benchmarked?

goos: darwin
goarch: arm64
pkg: github.com/consensys/gnark-crypto/ecc
cpu: Apple M1
BenchmarkSplitting256
BenchmarkSplitting256-8                  4004929               253.8 ns/op
BenchmarkSplittingStrict256
BenchmarkSplittingStrict256-8            1352343               884.2 ns/op

Checklist:

• I have performed a self-review of my code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have added tests that prove my fix is effective or that my feature works
• I did not modify files generated from templates
• golangci-lint does not output errors locally
• New and existing unit tests pass locally with my changes
• Any dependent changes have been merged and published in downstream modules

[feltroidprime]

Nice, does this mean the 4 scalars will be i64 in the glv+fakeglv method instead of ~i73 ?

[yelhousni]

Nice, does this mean the 4 scalars will be i64 in the glv+fakeglv method instead of ~i73 ?

unfortunately not. but we can probably save 1 bit.

[ivokub]

Looks good. But I'd add randomized testing for better coverage.

[ivokub]

Could we maybe run the test in gopter? Imo having a test with hardcoded values isn't that useful?