implement the Reducing and ReducingExtension gates

README.md

@@ -47,13 +47,12 @@ Supported gates:
 - [x] PoseidonGate
 - [x] PoseidonMdsGate
 - [x] RandomAccessGate
-- [ ] ReducingGate
-- [ ] ReducingExtensionGate
+- [x] ReducingGate
+- [x] ReducingExtensionGate
 
 Optional features:
 
+- [ ] Supporting different hash functions
 - [ ] Field extensions with degree higher than 2
 - [ ] Being parametric over the field choice
-- [ ] Supporting different hash functions
-
 

src/Gate/Constraints.hs

@@ -22,10 +22,12 @@ import Algebra.Expr
 import Gate.Base
 import Gate.Vars
 import Gate.Computation
+import Misc.Aux
+
 import Gate.Custom.Poseidon
 import Gate.Custom.RandomAccess
 import Gate.Custom.CosetInterp
-import Misc.Aux
+import Gate.Custom.Reducing
 
 --------------------------------------------------------------------------------
 -- * Gate constraints
@@ -98,17 +100,13 @@ gateComputation gate =
       -> randomAccessGateConstraints (MkRACfg (Log2 num_bits) num_copies num_extra_constants)
 
     ReducingGate num_coeffs 
-      -> todo
+      -> reducingGateConstraints num_coeffs
 
     ReducingExtensionGate num_coeffs 
-      -> todo
+      -> reducingExtensionGateConstraints num_coeffs
 
     UnknownGate name -> error ("gateConstraints: unknown gate `" ++ name ++ "`")
 
-  where
- 
-    todo = error $ "gateConstraints: gate `" ++ takeWhile isAlpha (show gate) ++ "` not yet implemented"
-
 --------------------------------------------------------------------------------
 
 -- computes `out = base ^ (sum 2^i e_i)`
@@ -146,5 +144,7 @@ testCosetGate5      = testCompute $ cosetInterpolationGateConstraints $ cosetInt
 testRandAccGate     = testCompute $ randomAccessGateConstraints       $ randomAccessGateConfig       (Log2 4)
 testPoseidonGate    = testCompute $ gateComputation (PoseidonGate    12)
 testPoseidonMdsGate = testCompute $ gateComputation (PoseidonMdsGate 12)
+testReducingGate    = testCompute $ gateComputation (ReducingGate          13)
+testReducingExtGate = testCompute $ gateComputation (ReducingExtensionGate 13)
 
 --------------------------------------------------------------------------------

src/Gate/Custom/Reducing.hs

@@ -0,0 +1,62 @@
+
+-- | The @Reducing@ and @ReducingExtension@ gates
+--
+-- These compute
+--
+-- > initial*alpha^n + sum_{i=0}^{n-1} c[i]*alpha^(n-i)
+--
+
+{-# LANGUAGE StrictData, RecordWildCards #-}
+module Gate.Custom.Reducing where
+
+--------------------------------------------------------------------------------
+
+import Data.Foldable
+import Control.Monad
+
+import Algebra.Goldilocks
+import Algebra.GoldilocksExt
+import Algebra.Expr
+
+import Gate.Vars
+import Gate.Computation
+
+import Misc.Aux
+
+--------------------------------------------------------------------------------
+
+reducingGateConstraints :: Int -> Compute ()
+reducingGateConstraints num_coeffs = do
+
+  forM_ [0..num_coeffs-1] $ \i -> do
+    commitExt $ prev i * alpha + fromBase (coeff i) - accum i
+
+  where
+    
+    -- witness variables
+    output       = wireExt 0
+    alpha        = wireExt 2
+    initial      = wireExt 4
+    coeff i      = wire (6+i)
+    accum i      = if i < num_coeffs - 1 then wireExt (6 + num_coeffs + 2*i) else output
+    prev i       = if i == 0 then initial else accum (i-1)
+
+--------------------------------------------------------------------------------
+
+reducingExtensionGateConstraints :: Int -> Compute ()
+reducingExtensionGateConstraints num_coeffs = do
+
+  forM_ [0..num_coeffs-1] $ \i -> do
+    commitExt $ prev i * alpha + coeff i - accum i
+
+  where
+
+    -- witness variables
+    output       = wireExt 0
+    alpha        = wireExt 2
+    initial      = wireExt 4
+    coeff i      = wireExt (6+2*i)
+    accum i      = if i < num_coeffs - 1 then wireExt (6 + 2*num_coeffs + 2*i) else output
+    prev i       = if i == 0 then initial else accum (i-1)
+
+--------------------------------------------------------------------------------

src/Misc/Aux.hs

@@ -1,7 +1,7 @@
 
 -- | Misc helper functions
 
-{-# LANGUAGE StrictData, DeriveGeneric, DeriveAnyClass #-}
+{-# LANGUAGE StrictData, DeriveGeneric, DeriveAnyClass, GeneralizedNewtypeDeriving, DerivingStrategies #-}
 module Misc.Aux where
 
 --------------------------------------------------------------------------------
@@ -17,7 +17,7 @@ import GHC.Generics
 
 newtype Log2 
   = Log2 Int
-  deriving (Eq,Ord,Show,Num)
+  deriving newtype (Eq,Ord,Show,Num)
 
 fromLog2 :: Log2 -> Int
 fromLog2 (Log2 k) = k