Autocompute s and c in WBW Montgomery

This allows us to support primes which are not a power of 2.

We also add p484 as an example.

To support this, I added a small parser combinator library which can
parse arithmetic expressions involving `()^*/+-` and decimal digits.

Closes #486
Closes #342

After     | File Name                                    | Before    || Change    | % Change
--------------------------------------------------------------------------------------------
22m14.42s | Total                                        | 12m14.76s || +9m59.65s | +81.61%
--------------------------------------------------------------------------------------------
9m41.91s  | p484_32.c                                    |    N/A    || +9m41.90s | ∞
0m11.51s  | p484_64.c                                    |    N/A    || +0m11.50s | ∞
3m16.22s  | p384_32.c                                    | 3m12.02s  || +0m04.19s | +2.18%
4m12.18s  | PushButtonSynthesis.vo                       | 4m10.16s  || +0m02.02s | +0.80%
0m45.08s  | ExtractionHaskell/word_by_word_montgomery    | 0m45.24s  || -0m00.16s | -0.35%
0m38.14s  | p521_32.c                                    | 0m38.12s  || +0m00.02s | +0.05%
0m31.80s  | p521_64.c                                    | 0m31.78s  || +0m00.01s | +0.06%
0m31.09s  | ExtractionHaskell/unsaturated_solinas        | 0m30.77s  || +0m00.32s | +1.03%
0m24.18s  | ExtractionHaskell/saturated_solinas          | 0m24.21s  || -0m00.03s | -0.12%
0m17.38s  | ExtractionOCaml/word_by_word_montgomery      | 0m17.35s  || +0m00.02s | +0.17%
0m13.39s  | secp256k1_32.c                               | 0m13.59s  || -0m00.19s | -1.47%
0m13.14s  | p256_32.c                                    | 0m13.04s  || +0m00.10s | +0.76%
0m10.58s  | ExtractionOCaml/unsaturated_solinas          | 0m10.73s  || -0m00.15s | -1.39%
0m10.23s  | ExtractionOCaml/word_by_word_montgomery.ml   | 0m10.34s  || -0m00.10s | -1.06%
0m07.88s  | ExtractionOCaml/saturated_solinas            | 0m07.94s  || -0m00.06s | -0.75%
0m06.78s  | ExtractionOCaml/unsaturated_solinas.ml       | 0m06.86s  || -0m00.08s | -1.16%
0m06.28s  | ExtractionHaskell/word_by_word_montgomery.hs | 0m06.42s  || -0m00.13s | -2.18%
0m06.00s  | p224_32.c                                    | 0m05.97s  || +0m00.03s | +0.50%
0m05.50s  | p384_64.c                                    | 0m05.35s  || +0m00.15s | +2.80%
0m05.28s  | ExtractionOCaml/saturated_solinas.ml         | 0m05.08s  || +0m00.20s | +3.93%
0m05.10s  | ExtractionHaskell/unsaturated_solinas.hs     | 0m04.98s  || +0m00.11s | +2.40%
0m04.12s  | ExtractionHaskell/saturated_solinas.hs       | 0m04.15s  || -0m00.03s | -0.72%
0m02.14s  | curve25519_32.c                              | 0m02.28s  || -0m00.13s | -6.14%
0m01.44s  | CLI.vo                                       | 0m01.42s  || +0m00.02s | +1.40%
0m01.44s  | curve25519_64.c                              | 0m01.57s  || -0m00.13s | -8.28%
0m01.14s  | StandaloneOCamlMain.vo                       | 0m01.11s  || +0m00.02s | +2.70%
0m01.12s  | p256_64.c                                    | 0m00.98s  || +0m00.14s | +14.28%
0m01.11s  | StandaloneHaskellMain.vo                     | 0m01.17s  || -0m00.05s | -5.12%
0m01.03s  | secp256k1_64.c                               | 0m01.15s  || -0m00.11s | -10.43%
0m01.02s  | p224_64.c                                    | 0m00.99s  || +0m00.03s | +3.03%
0m00.21s  | Util/Strings/ParseArithmetic.vo              |    N/A    || +0m00.21s | ∞

1 files changed, 23 insertions, 28 deletions

diff --git a/src/CLI.v b/src/CLI.v
index 329937fc4..dc352d9b2 100644
--- a/src/CLI.v
+++ b/src/CLI.v
@@ -6,6 +6,7 @@ Require Import Coq.Strings.String.
 Require Crypto.Util.Strings.String.
 Require Import Crypto.Util.Strings.Decimal.
 Require Import Crypto.Util.Strings.HexString.
+Require Import Crypto.Util.Strings.ParseArithmetic.
 Require Import Crypto.Util.Option.
 Require Import Crypto.Util.Strings.Show.
 Require Import Crypto.PushButtonSynthesis.
@@ -82,6 +83,8 @@ Module ForExtraction.
 
   Definition parse_machine_wordsize (s : string) : Z
     := parse_Z s.
+  Definition parse_m (s : string) : option Z
+    := parseZ_arith s.
 
   Local Open Scope string_scope.
   Local Notation NewLine := (String "010" "") (only parsing).
@@ -127,6 +130,8 @@ Module ForExtraction.
     := "  s                       The largest component of the prime (e.g., '2^255' in '2^255-19')".
   Definition c_help
     := "  c                       The semi-colon separated list of taps, each of which is specified as weight,value (no parentheses) (e.g., '2^96,1;1,-1' in '2^224 - 2^96 + 1')".
+  Definition m_help
+    := "  m                       The prime (e.g., '2^434 - (2^216*3^137 - 1)')".
   Definition machine_wordsize_help
     := "  machine_wordsize        The machine bitwidth (e.g., 32 or 64)".
   Definition function_to_synthesize_help (valid_names : string)
@@ -247,38 +252,31 @@ Module ForExtraction.
   Module WordByWordMontgomery.
     Definition PipelineLines
                (curve_description : string)
-               (s : string)
-               (c : string)
+               (m : string)
                (machine_wordsize : string)
                (requests : list string)
     : list (string * Pipeline.ErrorT (list string)) + list string
       := let prefix := ("fiat_" ++ curve_description ++ "_")%string in
          let str_machine_wordsize := machine_wordsize in
-         let str_c := c in
-         let str_s := s in
+         let str_m := m in
          let machine_wordsize := parse_machine_wordsize machine_wordsize in
          let show_requests := match requests with nil => "(all)" | _ => String.concat ", " requests end in
-         match parse_s s, parse_c c with
-         | None, None
-           => inr ["Could not parse s (" ++ s ++ ") nor c (" ++ c ++ ")"]
-         | None, _
-           => inr ["Could not parse s (" ++ s ++ ")"]
-         | _, None
-           => inr ["Could not parse c (" ++ c ++ ")"]
-         | Some s, Some c
+         match parse_m m with
+         | None
+           => inr ["Could not parse m (" ++ m ++ ")"]
+         | Some m
            => let '(res, types_used)
-                 := WordByWordMontgomery.Synthesize s c machine_wordsize prefix requests in
+                  := WordByWordMontgomery.Synthesize m machine_wordsize prefix requests in
              let header :=
                  ((["/* Autogenerated */";
                        "/* curve description: " ++ curve_description ++ " */";
                        "/* requested operations: " ++ show_requests ++ " */";
-                       "/* s = " ++ Hex.show_Z false s ++ " (from """ ++ str_s ++ """) */";
-                       "/* c = " ++ show false c ++ " (from """ ++ str_c ++ """) */";
+                       "/* m = " ++ Hex.show_Z false m ++ " (from """ ++ str_m ++ """) */";
                        "/* machine_wordsize = " ++ show false machine_wordsize ++ " (from """ ++ str_machine_wordsize ++ """) */";
                        "/*                                                                    */";
                        "/* NOTE: In addition to the bounds specified above each function, all */";
                        "/*   functions synthesized for this Montgomery arithmetic require the */";
-                       "/*   input to be strictly less than the prime modulus (s-c), and also */";
+                       "/*   input to be strictly less than the prime modulus (m), and also   */";
                        "/*   require the input to be in the unique saturated representation.  */";
                        "/*   All functions also ensure that these two properties are true of  */";
                        "/*   return values.                                                   */";
@@ -288,19 +286,18 @@ Module ForExtraction.
              inl
                ([("check_args" ++ NewLine ++ String.concat NewLine header,
                   WordByWordMontgomery.check_args
-                    s c machine_wordsize
+                    m machine_wordsize
                     (ErrorT.Success header))%string]
                   ++ res)%list
          end.
 
     Definition ProcessedLines
                (curve_description : string)
-               (s : string)
-               (c : string)
+               (m : string)
                (machine_wordsize : string)
                (requests : list string)
       : list string + list string
-      := match CollectErrors (PipelineLines curve_description s c machine_wordsize requests) with
+      := match CollectErrors (PipelineLines curve_description m machine_wordsize requests) with
          | inl ls
            => inl
                (List.map (fun s => String.concat NewLine s ++ NewLine ++ NewLine)
@@ -315,14 +312,13 @@ Module ForExtraction.
     Definition Pipeline
                {A}
                (curve_description : string)
-               (s : string)
-               (c : string)
+               (m : string)
                (machine_wordsize : string)
                (requests : list string)
                (success : list string -> A)
                (error : list string -> A)
       : A
-      := match ProcessedLines curve_description s c machine_wordsize requests with
+      := match ProcessedLines curve_description m machine_wordsize requests with
          | inl s => success s
          | inr s => error s
          end.
@@ -334,18 +330,17 @@ Module ForExtraction.
                (error : list string -> A)
       : A
       := match argv with
-         | _::curve_description::s::c::machine_wordsize::requests
+         | _::curve_description::m::machine_wordsize::requests
            => Pipeline
-               curve_description s c machine_wordsize requests
+               curve_description m machine_wordsize requests
                success
                error
          | nil => error ["empty argv"]
          | prog::args
-           => error ["Expected arguments curve_description, s, c, machine_wordsize, [function_to_synthesize*] got " ++ show false (List.length args) ++ " arguments in " ++ prog;
+           => error ["Expected arguments curve_description, m, machine_wordsize, [function_to_synthesize*] got " ++ show false (List.length args) ++ " arguments in " ++ prog;
                        "";
                        curve_description_help;
-                       s_help;
-                       c_help;
+                       m_help;
                        machine_wordsize_help;
                        function_to_synthesize_help WordByWordMontgomery.valid_names;
                        ""]