feat: addition of Cmp in the API

frontend/api.go

@@ -32,12 +32,12 @@ type API interface {
 	// Add returns res = i1+i2+...in
 	Add(i1, i2 Variable, in ...Variable) Variable
 
-	// Sub returns res = i1 - i2 - ...in
-	Sub(i1, i2 Variable, in ...Variable) Variable
-
 	// Neg returns -i
 	Neg(i1 Variable) Variable
 
+	// Sub returns res = i1 - i2 - ...in
+	Sub(i1, i2 Variable, in ...Variable) Variable
+
 	// Mul returns res = i1 * i2 * ... in
 	Mul(i1, i2 Variable, in ...Variable) Variable
 
@@ -89,6 +89,9 @@ type API interface {
 	// IsZero returns 1 if a is zero, 0 otherwise
 	IsZero(i1 Variable) Variable
 
+	// Cmp returns 1 if i1>i2, 0 if i1=i2, -1 if i1<i2
+	Cmp(i1, i2 Variable) Variable
+
 	// ---------------------------------------------------------------------------------------------
 	// Assertions
 

frontend/cs/plonk/api.go

@@ -426,6 +426,32 @@ func (system *sparseR1CS) IsZero(i1 frontend.Variable) frontend.Variable {
 	return m
 }
 
+// Cmp returns 1 if i1>i2, 0 if i1=i2, -1 if i1<i2
+func (system *sparseR1CS) Cmp(i1, i2 frontend.Variable) frontend.Variable {
+
+	bi1 := system.ToBinary(i1, system.BitLen())
+	bi2 := system.ToBinary(i2, system.BitLen())
+
+	var res frontend.Variable
+	res = 0
+
+	for i := system.BitLen() - 1; i >= 0; i-- {
+
+		iszeroi1 := system.IsZero(bi1[i])
+		iszeroi2 := system.IsZero(bi2[i])
+
+		i1i2 := system.And(bi1[i], iszeroi2)
+		i2i1 := system.And(bi2[i], iszeroi1)
+
+		n := system.Select(i2i1, -1, 0)
+		m := system.Select(i1i2, 1, n)
+
+		res = system.Select(system.IsZero(res), m, res)
+
+	}
+	return res
+}
+
 // Println behaves like fmt.Println but accepts Variable as parameter
 // whose value will be resolved at runtime when computed by the solver
 // Println enables circuit debugging and behaves almost like fmt.Println()