/*
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 (
	"fmt"
	"math/big"

	"github.com/spf13/cobra"
)

var modSqrtQ string
var modSqrtN string

func modSqrt(cmd *cobra.Command, args []string) {
	q, ok := new(big.Int).SetString(modSqrtQ, 10)
	if !ok {
		cobra.CheckErr("invalid input " + modSqrtQ)
	}

	n, ok := new(big.Int).SetString(modSqrtN, 10)
	if !ok {
		cobra.CheckErr("invalid input " + modSqrtN)
	}

	// TODO: support moduli that are not odd primes
	// can use Hansel's lemma for prime powers
	// can use CRT for constructing answers for composite moduli
	// see https://en.wikipedia.org/wiki/Quadratic_residue#Complexity_of_finding_square_roots

	rounds := 10
	z := new(big.Int).Mod(n, big.NewInt(2))
	if z.Cmp(big.NewInt(0)) == 0 || !n.ProbablyPrime(rounds) {
		cobra.CheckErr(modSqrtN + " is not an odd prime")
	}

	res := z.ModSqrt(q, n)
	if res == nil {
		cobra.CheckErr("cannot find a modular square root: " + modSqrtQ + " is not a quadratic residue modulo " + modSqrtN)
	} else {
		fmt.Println(z)
	}
}

// modSqrtCmd represents the modSqrt command
var modSqrtCmd = &cobra.Command{
	Use:   "mod-sqrt -q Q -m M",
	Short: "Compute a modular square root",
	Long: `Compute a modular square root.

Given an integer q and a modulus m, this will compute a value x such that
x^2 = q (mod n)`,
	Run: modSqrt,
}

func init() {
	rootCmd.AddCommand(modSqrtCmd)

	// Here you will define your flags and configuration settings.

	// Cobra supports Persistent Flags which will work for this command
	// and all subcommands, e.g.:
	// modSqrtCmd.PersistentFlags().String("foo", "", "A help for foo")

	// Cobra supports local flags which will only run when this command
	// is called directly, e.g.:
	// modSqrtCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")

	modSqrtCmd.Flags().StringVarP(&modSqrtQ, "residue", "q", "", "candidate to test")
	modSqrtCmd.MarkFlagRequired("residue")

	modSqrtCmd.Flags().StringVarP(&modSqrtN, "modulus", "m", "", "modulus")
	modSqrtCmd.MarkFlagRequired("modulus")
}