mathtools/cmd/convergents.go

/*
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"
)

func cycle(seq []*big.Int) <-chan *big.Int {
	ch := make(chan *big.Int)
	n := len(seq)
	go func() {
		for i := 0; true; i = (i + 1) % n {
			ch <- seq[i]
		}
	}()

	return ch
}

func gaussianBrackets(ch <-chan *big.Int) <-chan *big.Int {
	out := make(chan *big.Int)

	xprev := big.NewInt(0)
	x := big.NewInt(1)

	go func() {
		tmp := new(big.Int)
		for a := range ch {
			out <- x

			tmp.Mul(a, x)
			tmp.Add(tmp, xprev)

			xprev.Set(x)
			x = new(big.Int).Set(tmp)
		}
	}()

	return out
}

func cFracConvergents(a0 *big.Int, denoms []*big.Int) <-chan *big.Rat {
	hc := cycle(denoms)
	_ = <-hc
	hch := gaussianBrackets(hc)

	kc := cycle(denoms)
	kch := gaussianBrackets(kc)
	_ = <-kch

	a := new(big.Rat).SetInt(a0)

	out := make(chan *big.Rat)

	go func() {
		for {
			h, k := <-hch, <-kch
			r := new(big.Rat).SetFrac(h, k)
			r.Add(r, a)
			out <- r
		}
	}()

	return out
}

func convergents(cmd *cobra.Command, args []string) {
	a0, ok := new(big.Int).SetString(args[0], 10)
	if !ok {
		cobra.CheckErr("invalid input " + args[0])
	}

	denoms := make([]*big.Int, len(args[1:]))
	for i, d := range args[1:] {
		denoms[i] = new(big.Int)
		_, ok := denoms[i].SetString(d, 10)
		if !ok {
			cobra.CheckErr("invalid input " + d)
		}
	}

	for r := range cFracConvergents(a0, denoms) {
		fmt.Println(r)
	}
}

// FIXME: should support an initial block of non-periodic denominators (will need flags)
// convergentsCmd represents the convergents command
var convergentsCmd = &cobra.Command{
	Use:   "convergents N N [N ...]",
	Short: "Compute convergents of a periodic continued fraction",
	Long:  `Compute convergents of a periodic continued fraction.`,
	Args:  cobra.MinimumNArgs(2),
	Run:   convergents,
}

func init() {
	rootCmd.AddCommand(convergentsCmd)

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

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

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