114 lines
2.2 KiB
Go
114 lines
2.2 KiB
Go
/*
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Copyright © 2025 filifa
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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package lib
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import (
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"errors"
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"math/big"
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)
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func SqrtRepetend(x *big.Int) ([]*big.Int, error) {
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m := big.NewInt(0)
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d := big.NewInt(1)
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a0 := new(big.Int).Sqrt(x)
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s := new(big.Int).Exp(a0, big.NewInt(2), nil)
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if x.Cmp(s) == 0 {
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return nil, errors.New("input is a perfect square")
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}
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repetend := make([]*big.Int, 0)
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a := new(big.Int).Set(a0)
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twoa0 := new(big.Int).Mul(big.NewInt(2), a0)
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for a.Cmp(twoa0) != 0 {
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// m = d * a - m
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tmp := new(big.Int)
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m.Sub(tmp.Mul(d, a), m)
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// d = (x - m^2) // d
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tmp.Exp(m, big.NewInt(2), nil)
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d.Div(tmp.Sub(x, tmp), d)
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// a = (a0 + m) // d
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a.Div(tmp.Add(a0, m), d)
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repetend = append(repetend, new(big.Int).Set(a))
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}
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return repetend, nil
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}
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func cycle(seq []*big.Int) <-chan *big.Int {
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ch := make(chan *big.Int)
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n := len(seq)
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go func() {
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for i := 0; true; i = (i + 1) % n {
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ch <- seq[i]
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}
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}()
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return ch
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}
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func GaussianBrackets(ch <-chan *big.Int) <-chan *big.Int {
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out := make(chan *big.Int)
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xprev := big.NewInt(0)
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x := big.NewInt(1)
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go func() {
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tmp := new(big.Int)
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for a := range ch {
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out <- x
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tmp.Mul(a, x)
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tmp.Add(tmp, xprev)
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xprev.Set(x)
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x = new(big.Int).Set(tmp)
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}
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}()
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return out
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}
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func CFracConvergents(a0 *big.Int, denoms []*big.Int) <-chan *big.Rat {
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hc := cycle(denoms)
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_ = <-hc
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hch := GaussianBrackets(hc)
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kc := cycle(denoms)
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kch := GaussianBrackets(kc)
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_ = <-kch
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a := new(big.Rat).SetInt(a0)
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out := make(chan *big.Rat)
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go func() {
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for {
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h, k := <-hch, <-kch
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r := new(big.Rat).SetFrac(h, k)
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r.Add(r, a)
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out <- r
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}
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}()
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return out
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}
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