Optimize BN254 ecmul with the field endomorphism

[rodiazet]

• ecmul is optimized using curve endomorphism and "Shamir's trick" multiplication.
• Based on Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
• v1 and v2 vectors taken from cloudflare implementation

Before:

(vvenv) rodia@MacBook-Pro-2 evmone % ./build/bin/evmone-precompiles-bench --benchmark_filter=ecmul
Unable to determine clock rate from sysctl: hw.cpufrequency: No such file or directory
This does not affect benchmark measurements, only the metadata output.
***WARNING*** Failed to set thread affinity. Estimated CPU frequency may be incorrect.
2025-12-02T12:37:39+01:00
Running ./build/bin/evmone-precompiles-bench
Run on (12 X 24 MHz CPU s)
CPU Caches:
  L1 Data 64 KiB
  L1 Instruction 128 KiB
  L2 Unified 4096 KiB (x12)
Load Average: 1.82, 2.09, 1.99
------------------------------------------------------------------------------------------------------
Benchmark                                            Time             CPU   Iterations UserCounters...
------------------------------------------------------------------------------------------------------
precompile<PrecompileId::ecmul, evmmax_cpp>      56080 ns        56081 ns        12380 gas_rate=106.989M/s gas_used=60k

After:

(vvenv) rodia@MacBook-Pro-2 evmone % ./build/bin/evmone-precompiles-bench --benchmark_filter=ecmul
Unable to determine clock rate from sysctl: hw.cpufrequency: No such file or directory
This does not affect benchmark measurements, only the metadata output.
***WARNING*** Failed to set thread affinity. Estimated CPU frequency may be incorrect.
2025-12-02T12:38:10+01:00
Running ./build/bin/evmone-precompiles-bench
Run on (12 X 24 MHz CPU s)
CPU Caches:
  L1 Data 64 KiB
  L1 Instruction 128 KiB
  L2 Unified 4096 KiB (x12)
Load Average: 1.75, 2.05, 1.97
------------------------------------------------------------------------------------------------------
Benchmark                                            Time             CPU   Iterations UserCounters...
------------------------------------------------------------------------------------------------------
precompile<PrecompileId::ecmul, evmmax_cpp>      37996 ns        37987 ns        18480 gas_rate=157.947M/s gas_used=60k

[codecov[bot]]

Codecov Report

:x: Patch coverage is 96.50000% with 7 lines in your changes missing coverage. Please review. :white_check_mark: Project coverage is 81.66%. Comparing base (eeb288a) to head (c09a5a9). :warning: Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
test/unittests/evmmax_bn254_mul_test.cpp	96.64%	0 Missing and 5 partials :warning:
lib/evmone_precompiles/ecc.hpp	95.34%	1 Missing and 1 partial :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1389      +/-   ##
==========================================
+ Coverage   81.44%   81.66%   +0.22%     
==========================================
  Files         152      152              
  Lines       13396    13596     +200     
  Branches     3211     3226      +15     
==========================================
+ Hits        10910    11103     +193     
- Misses        342      343       +1     
- Partials     2144     2150       +6     

Flag	Coverage Δ
eest-develop	91.13% <100.00%> (+0.04%)	:arrow_up:
eest-develop-gmp	29.08% <17.00%> (-0.26%)	:arrow_down:
eest-legacy	15.32% <0.00%> (-0.23%)	:arrow_down:
eest-legacy-silkpre	24.42% <17.00%> (-0.19%)	:arrow_down:
evmone-unittests	76.21% <96.50%> (+0.30%)	:arrow_up:

Flags with carried forward coverage won't be shown. Click here to find out more.

Components	Coverage Δ
core	94.42% <96.07%> (+0.01%)	:arrow_up:
tooling	83.63% <ø> (ø)
tests	73.55% <96.64%> (+0.46%)	:arrow_up:

Files with missing lines	Coverage Δ
lib/evmone_precompiles/bn254.cpp	100.00% <100.00%> (ø)
lib/evmone_precompiles/ecc.hpp	95.81% <95.34%> (-0.10%)	:arrow_down:
test/unittests/evmmax_bn254_mul_test.cpp	92.26% <96.64%> (+34.36%)	:arrow_up:

:rocket: New features to boost your workflow:

• :snowflake: Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[chfast]

Improvement 72 Mgas/s → 117 Mgas/s (+63%).

[chfast]

Comparing o/ecmul to o/ecmul-endo
Benchmark                                                            Time             CPU      Time Old      Time New       CPU Old       CPU New
-------------------------------------------------------------------------------------------------------------------------------------------------
precompile<PrecompileId::ecmul, evmmax_cpp>_pvalue                 0.0001          0.0001      U Test, Repetitions: 11 vs 11
precompile<PrecompileId::ecmul, evmmax_cpp>_mean                  -0.3707         -0.3707         80940         50937         80920         50925
precompile<PrecompileId::ecmul, evmmax_cpp>_median                -0.3695         -0.3695         80762         50922         80746         50909
precompile<PrecompileId::ecmul, evmmax_cpp>_stddev                -0.8101         -0.8133           367            70           371            69
precompile<PrecompileId::ecmul, evmmax_cpp>_cv                    -0.6982         -0.7034             0             0             0             0
OVERALL_GEOMEAN                                                   -0.3707         -0.3707             0             0             0             0

[chfast]

The cost of decompose is 0.20%, out of which 0.14% is the division by DET.