create a cFracConvergents function

cmd/convergents.go

@@ -35,10 +35,14 @@ func cycle(seq []*big.Int) <-chan *big.Int {
 	return ch
 }
 
-func gaussianBrackets(x, xprev *big.Int, ch <-chan *big.Int) <-chan *big.Int {
+func gaussianBrackets(ch <-chan *big.Int) <-chan *big.Int {
 	out := make(chan *big.Int)
 
+	xprev := big.NewInt(0)
+	x := big.NewInt(1)
+
 	go func() {
+		out <- big.NewInt(1)
 		for a := range ch {
 			tmp := new(big.Int).Mul(a, x)
 			tmp.Add(tmp, xprev)
@@ -51,6 +55,32 @@ func gaussianBrackets(x, xprev *big.Int, ch <-chan *big.Int) <-chan *big.Int {
 	return out
 }
 
+func cFracConvergents(a0 *big.Int, denoms []*big.Int) <-chan *big.Rat {
+	f := cycle(denoms)
+	_ = <-f
+	g := cycle(denoms)
+
+	hch := gaussianBrackets(f)
+	kch := gaussianBrackets(g)
+	_ = <-kch
+
+	a := new(big.Rat).SetInt(a0)
+
+	out := make(chan *big.Rat)
+
+	go func() {
+		for {
+			r := new(big.Rat)
+			h, k := <-hch, <-kch
+			r.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 {
@@ -66,13 +96,7 @@ func convergents(cmd *cobra.Command, args []string) {
 		}
 	}
 
-	hch := gaussianBrackets(a0, big.NewInt(1), cycle(denoms))
+	for r := range cFracConvergents(a0, denoms) {
-	kch := gaussianBrackets(big.NewInt(1), big.NewInt(0), cycle(denoms))
-
-	r := new(big.Rat)
-	for {
-		h, k := <-hch, <-kch
-		r.SetFrac(h, k)
 		fmt.Println(r)
 	}
 }

cmd/pell.go

@@ -47,13 +47,12 @@ func pell(cmd *cobra.Command, args []string) {
 		period = 2 * r
 	}
 
-	hch := gaussianBrackets(a0, big.NewInt(1), cycle(repetend))
+	ch := cFracConvergents(a0, repetend)
-	kch := gaussianBrackets(big.NewInt(1), big.NewInt(0), cycle(repetend))
 
 	for i := 1; true; i = (i + 1) % period {
-		h, k := <-hch, <-kch
+		r := <-ch
 		if i == period-1 {
-			fmt.Println(h, k)
+			fmt.Println(r.Num(), r.Denom())
 		}
 	}
 }