move crt solver

cmd/crt.go

@@ -22,51 +22,12 @@ import (
 	"math/big"
 
 	"github.com/spf13/cobra"
+	"scm.dairydemon.net/filifa/mathtools/internal/lib"
 )
 
 var remainders []string
 var moduli []string
 
-func crtSolve(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
-	// use Bezout's identity to find m1, m2 such that m1*n1 + m2*n2 = 1
-	m1 := new(big.Int)
-	m2 := new(big.Int)
-	tmp := new(big.Int)
-	tmp.GCD(m1, m2, n1, n2)
-
-	// x = a1*m2*n2 + a2*m1*n1
-	x := new(big.Int).Set(a1)
-	x.Mul(x, m2)
-	x.Mul(x, n2)
-
-	tmp.Set(a2)
-	tmp.Mul(tmp, m1)
-	tmp.Mul(tmp, n1)
-
-	x.Add(x, tmp)
-
-	N := new(big.Int).Set(n1)
-	N.Mul(N, n2)
-
-	x.Mod(x, N)
-
-	return x, N
-}
-
-func arePairwiseCoprime(moduli []*big.Int) bool {
-	z := new(big.Int)
-	for i, a := range moduli {
-		for _, b := range moduli[i+1:] {
-			z.GCD(nil, nil, a, b)
-			if z.Cmp(big.NewInt(1)) != 0 {
-				return false
-			}
-		}
-	}
-
-	return true
-}
-
 func crt(cmd *cobra.Command, args []string) {
 	if len(remainders) != len(moduli) {
 		log.Fatal("number of remainders and moduli do not match")
@@ -83,7 +44,7 @@ func crt(cmd *cobra.Command, args []string) {
 	}
 
 	// TODO: support non-pairwise coprime moduli
-	if !arePairwiseCoprime(ns) {
+	if !lib.ArePairwiseCoprime(ns) {
 		log.Fatalf("moduli %v are not pairwise coprime", moduli)
 	}
 
@@ -101,7 +62,7 @@ func crt(cmd *cobra.Command, args []string) {
 			continue
 		}
 
-		x, N := crtSolve(a1, n1, a2, n2)
+		x, N := lib.CRTSolution(a1, n1, a2, n2)
 		a1.Set(x)
 		n1.Set(N)
 	}

internal/lib/lib.go

@@ -36,3 +36,43 @@ func SqrtRepetend(x *big.Int) ([]*big.Int, error) {
 
 	return repetend, nil
 }
+
+func CRTSolution(a1, n1, a2, n2 *big.Int) (*big.Int, *big.Int) {
+	// use Bezout's identity to find m1, m2 such that m1*n1 + m2*n2 = 1
+	m1 := new(big.Int)
+	m2 := new(big.Int)
+	tmp := new(big.Int)
+	tmp.GCD(m1, m2, n1, n2)
+
+	// x = a1*m2*n2 + a2*m1*n1
+	x := new(big.Int).Set(a1)
+	x.Mul(x, m2)
+	x.Mul(x, n2)
+
+	tmp.Set(a2)
+	tmp.Mul(tmp, m1)
+	tmp.Mul(tmp, n1)
+
+	x.Add(x, tmp)
+
+	N := new(big.Int).Set(n1)
+	N.Mul(N, n2)
+
+	x.Mod(x, N)
+
+	return x, N
+}
+
+func ArePairwiseCoprime(moduli []*big.Int) bool {
+	z := new(big.Int)
+	for i, a := range moduli {
+		for _, b := range moduli[i+1:] {
+			z.GCD(nil, nil, a, b)
+			if z.Cmp(big.NewInt(1)) != 0 {
+				return false
+			}
+		}
+	}
+
+	return true
+}