June 2018 Update

Task/Nth-root/Go/nth-root-2.go

@@ -0,0 +1,65 @@
+import "math/big"
+
+func Root(a *big.Float, n uint64) *big.Float {
+	limit := Exp(New(2), 256)
+	n1 := n-1
+	n1f, rn := New(float64(n1)), Div(New(1.0), New(float64(n)))
+	x, x0 := New(1.0), Zero()
+	_ = x0
+	for {
+		potx, t2 := Div(New(1.0), x), a
+		for b:=n1; b>0; b>>=1 {
+			if b&1 == 1 {
+				t2 = Mul(t2, potx)
+			}
+			potx = Mul(potx, potx)
+		}
+		x0, x = x, Mul(rn, Add(Mul(n1f, x), t2) )
+		if Lesser(Mul(Abs(Sub(x, x0)), limit), x) { break }
+	}
+	return x
+}
+
+func Abs(a *big.Float) *big.Float {
+	return Zero().Abs(a)
+}
+
+func Exp(a *big.Float, e uint64) *big.Float {
+	result := Zero().Copy(a)
+	for i:=uint64(0); i<e-1; i++ {
+		result = Mul(result, a)
+	}
+	return result
+}
+
+func New(f float64) *big.Float {
+	r := big.NewFloat(f)
+	r.SetPrec(256)
+	return r
+}
+
+func Div(a, b *big.Float) *big.Float {
+	return Zero().Quo(a, b)
+}
+
+func Zero() *big.Float {
+	r := big.NewFloat(0.0)
+	r.SetPrec(256)
+	return r
+}
+
+func Mul(a, b *big.Float) *big.Float {
+	return Zero().Mul(a, b)
+}
+
+func Add(a, b *big.Float) *big.Float {
+	return Zero().Add(a, b)
+}
+
+func Sub(a, b *big.Float) *big.Float {
+	return Zero().Sub(a, b)
+}
+
+func Lesser(x, y *big.Float) bool {
+	return x.Cmp(y) == -1
+}