mathtools/internal/lib/continuedFrac.go

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
}

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
}