From c8617da8e134cc1e1065ec03f00316af42e2b9bb Mon Sep 17 00:00:00 2001
From: filifa <filifa.breath652@8alias.com>
Date: Tue, 12 Aug 2025 21:27:37 -0400
Subject: [PATCH] add sqrtRepetend command

---
 cmd/sqrtRepetend.go | 105 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 105 insertions(+)
 create mode 100644 cmd/sqrtRepetend.go

diff --git a/cmd/sqrtRepetend.go b/cmd/sqrtRepetend.go
new file mode 100644
index 0000000..d6292e8
--- /dev/null
+++ b/cmd/sqrtRepetend.go
@@ -0,0 +1,105 @@
+/*
+Copyright © 2025 filifa
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+package cmd
+
+import (
+	"errors"
+	"fmt"
+	"log"
+	"math/big"
+
+	"github.com/spf13/cobra"
+)
+
+func computeSqrtRepetend(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 sqrtRepetend(cmd *cobra.Command, args []string) {
+	x := new(big.Int)
+
+	for _, s := range args {
+		_, ok := x.SetString(s, 10)
+		if !ok {
+			log.Print("invalid input " + s)
+			continue
+		}
+
+		repetend, err := computeSqrtRepetend(x)
+		if err != nil {
+			log.Print(s + " is a perfect square")
+			continue
+		}
+
+		fmt.Print(repetend[0])
+		for _, r := range repetend[1:] {
+			fmt.Printf(" %s", r)
+		}
+		fmt.Println()
+	}
+}
+
+// sqrtRepetendCmd represents the sqrtRepetend command
+var sqrtRepetendCmd = &cobra.Command{
+	Use:   "sqrt-repetend N [N ...]",
+	Short: "Compute the repetend of the square root of the input",
+	Long:  `Compute the repetend of the square root of the input.`,
+	Args:  cobra.MinimumNArgs(1),
+	Run:   sqrtRepetend,
+}
+
+func init() {
+	rootCmd.AddCommand(sqrtRepetendCmd)
+
+	// Here you will define your flags and configuration settings.
+
+	// Cobra supports Persistent Flags which will work for this command
+	// and all subcommands, e.g.:
+	// sqrtRepetendCmd.PersistentFlags().String("foo", "", "A help for foo")
+
+	// Cobra supports local flags which will only run when this command
+	// is called directly, e.g.:
+	// sqrtRepetendCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+}