Update byte_decomposition mode

This updates the `byte_decomposition` model to use the
`fixedFunctionalModel`.  At this stage, more work needs to be done to
enable more useful testing, since there are no accepted traces for this
model which actually compute the desired function.

cmd/testgen/main.go

@@ -83,7 +83,7 @@ type Model struct {
 
 var models []Model = []Model{
 	{"bit_decomposition", bitDecompositionModel},
-	{"byte_decomposition", fixedFunctionModel("ST", "CT", 2, byteDecompositionModel)},
+	{"byte_decomposition", fixedFunctionModel("ST", "CT", 4, byteDecompositionModel)},
 	{"memory", memoryModel},
 	{"word_sorting", wordSortingModel},
 	{"counter", functionalModel("STAMP", counterModel)},
@@ -337,15 +337,19 @@ func byteDecompositionModel(first uint, last uint, schema sc.Schema, trace tr.Tr
 	TWO_8 := fr.NewElement(256)
 	BYTE := findColumn(0, "BYTE", schema, trace).Data()
 	ARG := findColumn(0, "ARG", schema, trace).Data()
+	acc := fr.NewElement(0)
+	// Iterate elements
+	for i := first; i <= last; i++ {
+		byte := BYTE.Get(i)
+		arg := ARG.Get(i)
+		acc := add(mul(acc, TWO_8), byte)
+		// Check accumulator
+		if acc.Cmp(&arg) != 0 {
+			return false
+		}
+	}
 	//
-	arg_0 := ARG.Get(first)
-	arg_1 := ARG.Get(last)
-	byte_0 := BYTE.Get(first)
-	byte_1 := BYTE.Get(last)
-	// Check arg
-	val := add(mul(byte_0, TWO_8), byte_1)
-	//
-	return arg_0.Cmp(&byte_0) == 0 && arg_1.Cmp(&val) == 0
+	return true
 }
 
 func memoryModel(schema sc.Schema, trace tr.Trace) bool {
@@ -472,10 +476,6 @@ func add(lhs fr.Element, rhs fr.Element) fr.Element {
 	return lhs
 }
 
-func add_const(lhs fr.Element, rhs uint64) fr.Element {
-	return add(lhs, fr.NewElement(rhs))
-}
-
 func sub(lhs fr.Element, rhs fr.Element) fr.Element {
 	lhs.Sub(&lhs, &rhs)
 	return lhs
@@ -485,8 +485,3 @@ func mul(lhs fr.Element, rhs fr.Element) fr.Element {
 	lhs.Mul(&lhs, &rhs)
 	return lhs
 }
-
-func eq(lhs fr.Element, rhs fr.Element) bool {
-	d := sub(lhs, rhs)
-	return d.IsZero()
-}

testdata/byte_decomposition.accepts

@@ -1,11 +1,12 @@
 { "ST": [], "CT": [], "BYTE": [], "ARG": [] }
-{ "ST": [1], "CT": [0], "BYTE": [0], "ARG": [0] }
-{ "ST": [1], "CT": [0], "BYTE": [123], "ARG": [123] }
-{ "ST": [1,1], "CT": [0,1], "BYTE": [99,104], "ARG": [99,25448] }
-{ "ST": [1,1,1], "CT": [0,1,2], "BYTE": [99,104,1], "ARG": [99,25448,6514689] }
+{ "ST": [1,1,1,1], "CT": [0,1,2,3], "BYTE": [0,0,0,0], "ARG": [0,0,0,0] }
+{ "ST": [1,1,1,1], "CT": [0,1,2,3], "BYTE": [1,0,0,0], "ARG": [1,256,65536,16777216] }
+{ "ST": [1,1,1,1], "CT": [0,1,2,3], "BYTE": [0,0,0,123], "ARG": [0,0,0,123] }
+{ "ST": [1,1,1,1], "CT": [0,1,2,3], "BYTE": [0,0,123,0], "ARG": [0,0,123,31488] }
+{ "ST": [1,1,1,1], "CT": [0,1,2,3], "BYTE": [0,0,99,104], "ARG": [0,0,99,25448] }
+{ "ST": [1,1,1,1], "CT": [0,1,2,3], "BYTE": [99,104,255,1], "ARG": [99,25448,6514943,1667825409] }
+{ "ST": [1,1,1,1], "CT": [0,1,2,3], "BYTE": [1,2,3,4], "ARG": [1,258,66051,16909060] }
 { "ST": [1,1,1,1], "CT": [0,1,2,3], "BYTE": [99,104,1,11], "ARG": [99,25448,6514689,1667760395] }
-{ "ST": [1,1,1,1,1], "CT": [0,1,2,3,0], "BYTE": [1,2,3,4,5], "ARG": [1,258,66051,16909060,5] }
-{ "ST": [1,1,1,1,1,1], "CT": [0,1,2,3,0,1], "BYTE": [1,2,3,4,5,6], "ARG": [1,258,66051,16909060,5,1286] }
-{ "ST": [1], "CT": [1], "BYTE": [123], "ARG": [123] }
-{ "ST": [1,1], "CT": [1,2], "BYTE": [123,2], "ARG": [123,31490] }
-{ "ST": [1,1,1,1,1], "CT": [4,5,6,7,8], "BYTE": [1,2,3,4,5], "ARG": [1,258,66051,16909060,4328719365] }
+{ "ST": [1,1,1,1,1,1,1,1], "CT": [0,1,2,3,0,1,2,3], "BYTE": [1,0,0,0,1,2,3,4], "ARG": [1,256,65536,16777216,1,258,66051,16909060] }
+{ "ST": [1,1,1,1,1,1,1,1], "CT": [0,1,2,3,0,1,2,3], "BYTE": [0,0,99,104,99,104,1,11], "ARG": [0,0,99,25448,99,25448,6514689,1667760395] }
+{ "ST": [0,1,1,1,1], "CT": [0,0,1,2,3], "BYTE": [123,0,0,0,0], "ARG": [0,0,0,0,0] }