split file

cmd/crt.go

@@ -53,7 +53,7 @@ func crt(cmd *cobra.Command, args []string) {
 		log.Fatalf("moduli %v are not pairwise coprime", moduli)
 	}
 
-	x, N := lib.CRTSolutionGeneral(rs, ns)
+	x, N := lib.CRTSolution(rs, ns)
 
 	fmt.Println(x)
 	fmt.Println(N)

internal/lib/continuedFrac.go

@@ -0,0 +1,38 @@
+package lib
+
+import (
+	"errors"
+	"math/big"
+)
+
+func SqrtRepetend(x *big.Int) ([]*big.Int, error) {
+	m := big.NewInt(0)
+	d := big.NewInt(1)
+	a0 := new(big.Int).Sqrt(x)
+
+	s := new(big.Int).Exp(a0, big.NewInt(2), nil)
+	if x.Cmp(s) == 0 {
+		return nil, errors.New("input is a perfect square")
+	}
+
+	repetend := make([]*big.Int, 0)
+
+	a := new(big.Int).Set(a0)
+	twoa0 := new(big.Int).Mul(big.NewInt(2), a0)
+	for a.Cmp(twoa0) != 0 {
+		// m = d * a - m
+		tmp := new(big.Int)
+		m.Sub(tmp.Mul(d, a), m)
+
+		// d = (x - m^2) // d
+		tmp.Exp(m, big.NewInt(2), nil)
+		d.Div(tmp.Sub(x, tmp), d)
+
+		// a = (a0 + m) // d
+		a.Div(tmp.Add(a0, m), d)
+
+		repetend = append(repetend, new(big.Int).Set(a))
+	}
+
+	return repetend, nil
+}

internal/lib/crt.go

@@ -0,0 +1,62 @@
+package lib
+
+import (
+	"math/big"
+)
+
+func solveCRT(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 CRTSolution(remainders, moduli []*big.Int) (*big.Int, *big.Int) {
+	n1 := new(big.Int)
+	a1 := new(big.Int)
+	for i, n2 := range moduli {
+		a2 := remainders[i]
+		if i == 0 {
+			a1.Set(a2)
+			n1.Set(n2)
+			continue
+		}
+
+		a1, n1 = solveCRT(a1, n1, a2, n2)
+	}
+
+	return a1, n1
+}
+
+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
+}

internal/lib/primitiveRoot.go

@@ -5,95 +5,6 @@ import (
 	"math/big"
 )
 
-func SqrtRepetend(x *big.Int) ([]*big.Int, error) {
-	m := big.NewInt(0)
-	d := big.NewInt(1)
-	a0 := new(big.Int).Sqrt(x)
-
-	s := new(big.Int).Exp(a0, big.NewInt(2), nil)
-	if x.Cmp(s) == 0 {
-		return nil, errors.New("input is a perfect square")
-	}
-
-	repetend := make([]*big.Int, 0)
-
-	a := new(big.Int).Set(a0)
-	twoa0 := new(big.Int).Mul(big.NewInt(2), a0)
-	for a.Cmp(twoa0) != 0 {
-		// m = d * a - m
-		tmp := new(big.Int)
-		m.Sub(tmp.Mul(d, a), m)
-
-		// d = (x - m^2) // d
-		tmp.Exp(m, big.NewInt(2), nil)
-		d.Div(tmp.Sub(x, tmp), d)
-
-		// a = (a0 + m) // d
-		a.Div(tmp.Add(a0, m), d)
-
-		repetend = append(repetend, new(big.Int).Set(a))
-	}
-
-	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 CRTSolutionGeneral(remainders, moduli []*big.Int) (*big.Int, *big.Int) {
-	n1 := new(big.Int)
-	a1 := new(big.Int)
-	for i, n2 := range moduli {
-		a2 := remainders[i]
-		if i == 0 {
-			a1.Set(a2)
-			n1.Set(n2)
-			continue
-		}
-
-		a1, n1 = CRTSolution(a1, n1, a2, n2)
-	}
-
-	return a1, n1
-}
-
-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 Totient(n *big.Int) *big.Int {
 	N := new(big.Int).Set(n)