/*
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 lib

import (
	"errors"
	"math/big"
)

/*
SqrtRepetend returns the repetend of the continued fraction of sqrt(x). It returns an error if x is a perfect square.
*/
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 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
}

/*
GaussianBrackets returns a channel that outputs the sequence [], [a1], [a1, a2], ... where each value comes from the input channel and [] denotes Gaussian brackets.
*/
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
}

/*
CFracConvergents returns a channel that outputs convergents of a periodic continued fraction with initial term a0 and repetend stored in denoms.
*/
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
}