feat(new-execution): optimize algebra extension e1/e2 execution

[shuklaayush]

• use hardcoded functions for common fields
• replace get_curve_type_from_modulus used in hardcoded ec addition with get_field_type

Reth benchmark (block 21000000) ~2-3% improvement
Reth benchmark (block 21431353) ~5-10% improvement (has 16 ecPairing operations)

[codspeed-hq]

CodSpeed WallTime Performance Report

Merging #1882 will degrade performances by 27.15%

_{Comparing feat/new-exec-optimize-algebra-ext (c8fbbf3) with feat/new-execution (b269dbb)}

⚠️ Unknown Walltime execution environment detected

Using the Walltime instrument on standard Hosted Runners will lead to inconsistent data.

For the most accurate results, we recommend using CodSpeed Macro Runners: bare-metal machines fine-tuned for performance measurement consistency.

Summary

⚡ 2 improvements
❌ 1 regressions
✅ 21 untouched benchmarks

⚠️ Please fix the performance issues or acknowledge them on CodSpeed.

Benchmarks breakdown

	Benchmark	BASE	HEAD	Change
⚡	benchmark_execute[pairing]	296.2 ms	226.1 ms	+31.01%
❌	benchmark_execute[quicksort]	41.4 ms	56.9 ms	-27.15%
⚡	benchmark_execute_metered[pairing]	315.6 ms	246.8 ms	+27.89%

[github-actions]

group	app.proof_time_ms	app.cycles	app.cells_used	leaf.proof_time_ms	leaf.cycles	leaf.cells_used
verify_fibair	1,078	322,700	17,672,408	-	-	-
fibonacci	(+15 [+0.7%]) 2,233	3,000,556	51,508,517	-	-	-
regex	(-70 [-0.9%]) 7,523	8,330,866	165,431,684	-	-	-
ecrecover	(-4 [-0.3%]) 1,148	274,568	8,596,011	-	-	-
pairing	(+61 [+1.6%]) 3,765	3,725,930	93,105,233	-	-	-

Commit: c8fbbf3

Benchmark Workflow