refactor general crt algorithm into separate function

cmd/crt.go

@@ -34,12 +34,18 @@ func crt(cmd *cobra.Command, args []string) {
 	}
 
 	ns := make([]*big.Int, len(moduli))
+	rs := make([]*big.Int, len(remainders))
 	for i := range moduli {
 		var ok bool
 		ns[i], ok = new(big.Int).SetString(moduli[i], 10)
 		if !ok {
 			log.Fatal("invalid input " + moduli[i])
 		}
+
+		rs[i], ok = new(big.Int).SetString(remainders[i], 10)
+		if !ok {
+			log.Fatal("invalid input " + remainders[i])
+		}
 	}
 
 	// TODO: support non-pairwise coprime moduli
@@ -47,27 +53,10 @@ func crt(cmd *cobra.Command, args []string) {
 		log.Fatalf("moduli %v are not pairwise coprime", moduli)
 	}
 
-	n1 := new(big.Int)
-	a1 := new(big.Int)
-	for i, n2 := range ns {
-		a2, ok := new(big.Int).SetString(remainders[i], 10)
-		if !ok {
-			log.Fatal("invalid input " + remainders[i])
-		}
+	x, N := lib.CRTSolutionGeneral(rs, ns)
 
-		if i == 0 {
-			a1.Set(a2)
-			n1.Set(n2)
-			continue
-		}
-
-		x, N := lib.CRTSolution(a1, n1, a2, n2)
-		a1.Set(x)
-		n1.Set(N)
-	}
-
-	fmt.Println(a1)
-	fmt.Println(n1)
+	fmt.Println(x)
+	fmt.Println(N)
 }
 
 // crtCmd represents the crt command