perf(ecc): faster affine Add

[yelhousni]

Description

Actually, we can optimize affine addition more than #509 with the assumption that both Z1 and Z2 are 1 in Jacobian coordinates. This PR uses these EFD formulas. Also #509 modifies the second input in the Sub method which this PR fixes.

gnark-crypto/internal/generator/ecc/template/point.go.tmpl

Line 128 in 364bbce

b.Y.Neg(&b.Y)

Type of change

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

How has this been tested?

same tests as #509

How has this been benchmarked?

e.g. BLS12-381 G1 addition on a z1d.large AWS machine:

goos: linux
goarch: amd64
pkg: github.com/consensys/gnark-crypto/ecc/bls12-381
cpu: Intel(R) Xeon(R) Platinum 8151 CPU @ 3.40GHz
BenchmarkG1AffineAdd
BenchmarkG1AffineAdd-2   	  232734	      5135 ns/op
PASS

This is a -3.56% saving compared to #509

benchmark                  old ns/op     new ns/op     delta
BenchmarkG1AffineAdd-2     5135          4952          -3.56%

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

[gbotrel]

Code looks correct and match the formulas, however, it is not tested (i.e. G1Affine.Add is not called in any test files, only in fr/lookup and kzg ).

Can you add some basic tests / property based tests now that we have a different code path than Jacobian?

(general addition, doubling, adding of point at infinity, and addition resulting in point at infinity)

[yelhousni]

Code looks correct and match the formulas, however, it is not tested (i.e. G1Affine.Add is not called in any test files, only in fr/lookup and kzg ).

Can you add some basic tests / property based tests now that we have a different code path than Jacobian?

(general addition, doubling, adding of point at infinity, and addition resulting in point at infinity)

I think in TestG*AffineOps we call affine Add, Sub, Double and ScalarMul here for example:

gnark-crypto/ecc/bls12-381/g1_test.go

Line 266 in 3ba464d

properties.Property("[BLS12-381] [2]G = double(G) + G - G", prop.ForAll(

Also this test

gnark-crypto/ecc/bls12-381/g1_test.go

Line 250 in 3ba464d

properties.Property("[BLS12-381] Add should call double when adding the same point", prop.ForAll(

checks the edge case where inputs are equal in Add but I do agree that tests involving the point (0,0) are missing. Will add.