perf(Mux): shared selector decomposition and ±Y symmetry optimization in emulated MSM

[yelhousni]

Description

Optimizes the Mux (multiplexer) function in the selector package and its usage across emulated field arithmetic and elliptic curve scalar multiplication.

The optimizations consist of three key improvements:

1. Share binary decomposition across emulated field limbs

Previously, emulated.Mux decomposed the selector into bits independently for each limb (e.g., 6 limbs × 4 bits = 24 redundant boolean assertions for a 16-to-1 Mux). Now we decompose once and reuse across all limbs.

• Added BinaryMuxUnchecked and GeneralMuxUnchecked variants that skip boolean assertions when bits are already constrained (e.g., from bits.ToBinary).

Also:

• Add constant selector folding: return inputs[sel] directly when sel is compile-time constant
• Add n=2 specialization: use api.Select directly for 2-to-1 Mux

Files: std/math/emulated/field_ops.go, std/selector/mux.go and std/selector/multiplexer.go.

2. Exploit ±Y symmetry in MSM

In GLV-based scalar multiplication, the 16 precomputed points satisfy Y[i] = -Y[15-i]. This allows replacing a 16-to-1 Mux with an 8-to-1 Mux + conditional negation, saving constraints.

Added muxY8Signed helper that selects from 8 Y-values and conditionally negates based on the MSB.

Files: std/algebra/emulated/sw_emulated/point.go, std/algebra/emulated/sw_bls12381/g2.go

Type of change

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

How has this been tested?

• All existing std/selector tests pass
• All existing std/math/emulated tests pass
• All existing std/algebra/emulated/sw_emulated tests pass
• All existing std/algebra/emulated/sw_bls12381 tests pass
• All existing std/evmprecompiles tests pass

How has this been benchmarked?

SCS constraint count comparison:

Single Scalar Multiplication

Circuit	Before	After	Improvement
BLS12-381 G1.ScalarMul	291,552	279,576	-4.1%
BLS12-381 G2.ScalarMul	913,513	891,913	-2.4%

EVM Precompiles

Circuit	Before	After	Improvement
BN254 ECMul	210,369	202,669	-3.7%
BLS12-381 G1MSM(10)	4,397,157	4,277,397	-2.7%
BLS12-381 G2MSM(10)	9,304,517	9,088,517	-2.3%
P256 Verify	666,146	652,482	-2.1%

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

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Note

Medium Risk
Touches low-level constraint-building and mux selection logic used broadly across circuits; while changes are performance-oriented, mistakes could cause unsound or failing constraints across many call sites.

Overview
Speeds up constraint generation for multiplexers and emulated scalar multiplication by reducing redundant selector constraints and leveraging GLV point symmetry.

selector.Mux now short-circuits constant selectors, uses api.Select for 2-way muxes, and replaces the previous bounded-compare check with a builder-level MustBeLessOrEqCst on the already-decomposed selector bits. emulated.Field.Mux is reworked to decompose sel into bits once, reuse them across all limbs via selector.BinaryMux, and pad/check bounds only for non-power-of-two input counts.

Emulated GLV scalar-mul paths in sw_emulated/point.go and BLS12-381 G2 replace 16-to-1 Y-coordinate muxing with an 8-to-1 mux plus conditional negation (muxY8Signed/muxE2Y8Signed), reflecting the Y[i] = -Y[15-i] symmetry. Constraint builders (r1cs/scs) also skip adding trivially satisfied MustBeLessOrEqCst constraints when the compared bit is a constant zero; latest_stats.csv is updated accordingly.

^{Written by Cursor Bugbot for commit de2cef3. This will update automatically on new commits. Configure here.}

[Copilot]

Pull request overview

This PR optimizes selector multiplexing and its use in emulated field arithmetic and GLV-based scalar multiplication to reduce redundant constraints and improve performance.

Changes:

• Add unchecked selector mux variants to reuse already-constrained selector bits.
• Optimize selector.Mux and emulated.Field.Mux to avoid repeated binary decomposition work.
• Exploit ±Y symmetry in GLV tables to replace 16-to-1 Y selection with 8-to-1 + conditional negation.

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
std/selector/mux.go	Adds BinaryMuxUnchecked / GeneralMuxUnchecked wrappers to skip redundant boolean assertions.
std/selector/multiplexer.go	Adds constant-selector fast path, n=2 specialization, and an “unchecked” recursive path for non-power-of-2 muxes.
std/math/emulated/field_ops.go	Reuses a single selector bit decomposition across all limbs and uses unchecked mux variants.
std/algebra/emulated/sw_emulated/point.go	Adds muxY8Signed and switches GLV loops to 8-to-1 Y mux + conditional negation.
std/algebra/emulated/sw_bls12381/g2.go	Adds muxE2Y8Signed for the same 8-to-1 + sign optimization in G2 GLV scalar mul.

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[ivokub]

In general looks good. I can have a check if we can use MarkBoolean more efficiently to avoid redundant binary assertions.

[cursor]

Cursor Bugbot has reviewed your changes and found 1 potential issue.

[ivokub]

Thanks for the fixes! Looks good now!