Perf: Pairing on BN254 using direct Fp12 extension and non-native Eval()

internal/stats/latest_stats.csv

@@ -181,14 +181,14 @@ pairing_bls24315,bls24_315,plonk,0,0
 pairing_bls24315,bls24_317,plonk,0,0
 pairing_bls24315,bw6_761,plonk,0,0
 pairing_bls24315,bw6_633,plonk,141249,141249
-pairing_bn254,bn254,groth16,963003,1603091
+pairing_bn254,bn254,groth16,604783,990919
 pairing_bn254,bls12_377,groth16,0,0
 pairing_bn254,bls12_381,groth16,0,0
 pairing_bn254,bls24_315,groth16,0,0
 pairing_bn254,bls24_317,groth16,0,0
 pairing_bn254,bw6_761,groth16,0,0
 pairing_bn254,bw6_633,groth16,0,0
-pairing_bn254,bn254,plonk,3771397,3534755
+pairing_bn254,bn254,plonk,2319665,2030447
 pairing_bn254,bls12_377,plonk,0,0
 pairing_bn254,bls12_381,plonk,0,0
 pairing_bn254,bls24_315,plonk,0,0

std/algebra/emulated/fields_bn254/doc.go

@@ -1,6 +1,10 @@
-// Package fields_bn254 implements the fields arithmetic of the Fp12 tower
+// Package fields_bn254 implements the fields arithmetic of the direct 𝔽p¹² extension
 // used to compute the pairing over the BN254 curve.
 //
+//	𝔽p¹²[i] = 𝔽p/i¹²-18i⁶+82
+//
+// This direct tower is isomorphic to the 2-3-2 tower:
+//
 //	𝔽p²[u] = 𝔽p/u²+1
 //	𝔽p⁶[v] = 𝔽p²/v³-9-u
 //	𝔽p¹²[w] = 𝔽p⁶/w²-v