create internal library

internal/lib/lib.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
+}