Benchmark: BigInt -> Montgomery conversion:

- shlAddMod (with assembly division) is already 4x slower than Montgomery Multiplication based.
- constant-time division will be even slower
- use montgomery-multiplication based conversion

benchmarks/big_to_fq.nim

@@ -0,0 +1,48 @@
+# Constantine
+# Copyright (c) 2018-2019    Status Research & Development GmbH
+# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
+# Licensed and distributed under either of
+#   * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
+#   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
+# at your option. This file may not be copied, modified, or distributed except according to those terms.
+
+# ############################################################
+#
+#        Benchmark of the conversion from Big Int to Fq
+#
+# ############################################################
+
+# 2 implementations are possible
+# - 1 based on Montgomery Multiplication
+# - 1 based on modular left shift which involves multiple divisions
+
+import
+  ../constantine/config/[common, curves],
+  ../constantine/math/[bigints_checked, finite_fields],
+  random, std/monotimes, times, strformat
+
+const Iters = 1_000_000
+
+randomize(1234)
+
+proc main() =
+  var x: BigInt[381]
+  x.setInternalBitLength()
+  for i in 0 ..< x.limbs.len - 1:
+    # Set x to a random value guaranteed below the prime
+    x.limbs[i] = Word(rand(BaseType.high.int))
+
+
+  let start = getMonotime()
+  for _ in 0 ..< Iters:
+    let y = Fq[BLS12_381].fromBig(x)
+  let stop = getMonotime()
+
+  echo &"Time for {Iters} iterations: {inMilliseconds(stop-start)} ms"
+
+
+main()
+# 1_000_000 iterations with -d:danger on i9-9980XE all-core turbo 4.1GHz
+# Montgomery Multiplication based: 254ms
+# shlAddMod based (using assembly div2n1n!!): 907 ms
+# Note: shlAddMod will be even slower when division is made constant-time

constantine/math/bigints_checked.nim

@@ -120,14 +120,7 @@ func unsafeMontyResidue*[mBits](mres: var BigInt[mBits], a, N, r2modN: BigInt[mB
   ## Caller must take care of properly switching between
   ## the natural and montgomery domain.
   ## Nesting Montgomery form is possible by applying this function twice.
-  # TODO: benchmark
-  when true:
-    # Montgomery multiplication based
   montyResidue(mres.view, a.view, N.view, r2modN.view, Word(negInvModWord))
-  else:
-    # Modular left shift based
-    mres = a
-    montyResidue(mres.view, N.view)
 
 func unsafeRedc*[mBits](mres: var BigInt[mBits], N: BigInt[mBits], negInvModWord: static BaseType) =
   ## Convert a BigInt from its Montgomery n-residue form

constantine/math/finite_fields.nim

@@ -49,11 +49,11 @@ debug:
 #
 # ############################################################
 
-func fromBig*(T: type Fq, src: BigInt): T =
+func fromBig*[C: static Curve](T: type Fq[C], src: BigInt): Fq[C] {.noInit.} =
   ## Convert a BigInt to its Montgomery form
-  result.mres.unsafeMontyResidue(src, Fq.C.Mod.mres, Fq.C.getR2modP(), Fq.C.getNegInvModWord())
+  result.mres.unsafeMontyResidue(src, C.Mod.mres, C.getR2modP(), C.getNegInvModWord())
 
-func toBig*(src: Fq): auto =
+func toBig*(src: Fq): auto {.noInit.} =
   ## Convert a finite-field element to a BigInt in natral representation
   result = src.mres
   result.unsafeRedC(Fq.C.Mod.mres, Fq.C.getNegInvModWord())