Perf quick wins - 10% Fp12 mul (#235)

* improve FP12_mul  perf by 10%

* update README [skip ci]

README.md

@@ -37,7 +37,9 @@ The implementations are accompanied with SAGE code used as reference implementat
     - [In blockchain](#in-blockchain)
     - [In zero-knowledge proofs](#in-zero-knowledge-proofs)
     - [Measuring performance](#measuring-performance)
-      - [BLS12_381 Clang + inline Assembly](#bls12_381-clang--inline-assembly)
+      - [Ethereum BLS signatures over BLS12-381 G2](#ethereum-bls-signatures-over-bls12-381-g2)
+      - [BLS12-381 detailed benchmarks](#bls12-381-detailed-benchmarks)
+      - [BN254-Snarks Multi-Scalar-Multiplication benchmarks](#bn254-snarks-multi-scalar-multiplication-benchmarks)
       - [Parallelism](#parallelism)
   - [Why Nim](#why-nim)
   - [Compiler caveats](#compiler-caveats)
@@ -304,7 +306,11 @@ The full list of benchmarks is available in the [`benchmarks`](./benchmarks) fol
 
 As mentioned in the [Compiler caveats](#compiler-caveats) section, GCC is up to 2x slower than Clang due to mishandling of carries and register usage.
 
-#### BLS12_381 (Clang + inline Assembly)
+#### Ethereum BLS signatures (over BLS12-381 G2)
+
+![Bench Ethereum BLS signature](./media/ethereum_bls_signatures.png)
+
+#### BLS12-381 detailed benchmarks
 
 On my machine i9-11980HK (8 cores 2.6GHz, turbo 5GHz), for Clang + Assembly, **all being constant-time** (including scalar multiplication, square root and inversion).
 
@@ -314,9 +320,11 @@ On my machine i9-11980HK (8 cores 2.6GHz, turbo 5GHz), for Clang + Assembly, **a
 ![BLS12-381 Multi-Scalar multiplication 2](./media/bls12_381_msm_i9-11980HK-8cores_2.png)
 ![BLS12-381 Multi-Scalar multiplication 3](./media/bls12_381_msm_i9-11980HK-8cores_3.png)
 
+#### BN254-Snarks Multi-Scalar-Multiplication benchmarks
+
 On a i9-9980XE (18 cores,watercooled, overclocked, 4.1GHz all core turbo)
 
-![BN254-Snarks multi-sclar multiplication](./media/bn254_snarks_msm-i9-9980XE-18cores.png)
+![BN254-Snarks multi-scalar multiplication](./media/bn254_snarks_msm-i9-9980XE-18cores.png)
 
 #### Parallelism
 

benchmarks/bench_elliptic_template.nim

@@ -45,7 +45,7 @@ macro fixEllipticDisplay(EC: typedesc): untyped =
   var name = $instantiated[1][0] # EllipticEquationFormCoordinates
   let fieldName = $instantiated[1][1][0]
   let curveName = $Curve(instantiated[1][1][1].intVal)
-  name.add "[" & fieldName & "[" & curveName & "]]"
+  name.add "[" & fieldName & "[" & curveName & ']'
   result = newLit name
 
 proc report(op, elliptic: string, start, stop: MonoTime, startClk, stopClk: int64, iters: int) =

constantine/math/extension_fields/assembly/fp2_asm_x86_adx_bmi2.nim

@@ -76,12 +76,11 @@ func sqrx_complex_sparebit_asm_adx*(
 
   static: doAssert Fp.has1extraBit()
 
-  var v0 {.noInit.}, v1 {.noInit.}: typeof(r.c0)
+  var v0 {.noInit.}, v1 {.noInit.}, v2{.noInit.}: typeof(r.c0)
+  v2.double(a.c1)
   v0.diff(a.c0, a.c1)
   v1.sum(a.c0, a.c1)
-  r.c1.mres.limbs.mulMont_CIOS_sparebit_asm_adx(a.c0.mres.limbs, a.c1.mres.limbs, Fp.fieldMod().limbs, Fp.getNegInvModWord())
+  r.c1.mres.limbs.mulMont_CIOS_sparebit_asm_adx(a.c0.mres.limbs, v2.mres.limbs, Fp.fieldMod().limbs, Fp.getNegInvModWord())
-  # aliasing: a unneeded now
-  r.c1.double()
   r.c0.mres.limbs.mulMont_CIOS_sparebit_asm_adx(v0.mres.limbs, v1.mres.limbs, Fp.fieldMod().limbs, Fp.getNegInvModWord())
 
 # 𝔽p2 multiplication

constantine/math/extension_fields/towers.nim

@@ -57,8 +57,8 @@ type
     CubicExt[Fp2[C]]
 
   Fp12*[C: static Curve] =
-    # CubicExt[Fp4[C]]
+    CubicExt[Fp4[C]]
-    QuadraticExt[Fp6[C]]
+    # QuadraticExt[Fp6[C]]
 
 template c0*(a: ExtensionField): auto =
   a.coords[0]