move functions to lib

internal/lib/continuedFrac.go

@@ -36,3 +36,62 @@ func SqrtRepetend(x *big.Int) ([]*big.Int, error) {
 
 	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
+}