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
+}

Task/Nth-root/Julia/nth-root.julia

@@ -1,15 +1,17 @@
-function nthroot(n::Integer, A::Real)
-    A < 0 || n == 0 && throw(DomainError())
-    n < 0 && return 1/nthroot(-n, A)
-    A == 0 && return A
-    x = A / n
-    prevdx = A
+function nthroot(n::Integer, r::Real)
+    r < 0 || n == 0 && throw(DomainError())
+    n < 0 && return 1 / nthroot(-n, r)
+    r > 0 || return 0
+    x = r / n
+    prevdx = r
     while true
-        y = x^(n-1)
-        dx = (A - y*x) / (n * y)
-        abs(dx) >= abs(prevdx) && return x
+        y = x ^ (n - 1)
+        dx = (r - y * x) / (n * y)
+        abs(dx) ≥ abs(prevdx) && return x
         x += dx
         prevdx = dx
     end
 end
-@vectorize_2arg Number nthroot
+
+@show nthroot.(-5:2:5, 5.0)
+@show nthroot.(-5:2:5, 5.0) - 5.0 .^ (1 ./ (-5:2:5))

Task/Nth-root/Sidef/nth-root-1.sidef

@@ -1,11 +1,11 @@
 func nthroot(n, a, precision=1e-5) {
-  var x = 1;
-  var prev = 0;
+  var x    = 1.float
+  var prev = 0.float
   while ((prev-x).abs > precision) {
     prev = x;
-    x = (((n-1)*prev + a/(prev**(n-1))) / n);
-  };
-  return x;
+    x = (((n-1)*prev + a/(prev**(n-1))) / n)
+  }
+  return x
 }
 
-say nthroot(5, 34);  # => 2.024397458501034082599817835297912829678
+say nthroot(5, 34)  # => 2.024397458501034082599817835297912829678314204

Task/Nth-root/Sidef/nth-root-2.sidef

@@ -1,6 +1,6 @@
 func nthroot_fast(n, a, precision=1e-5) {
-  { a = nthroot(2, a, precision) } * int(n-1);
-  a ** (2**int(n-1) / n);
+  { a = nthroot(2, a, precision) } * int(n-1)
+  a ** (2**int(n-1) / n)
 }
 
-say nthroot_fast(5, 34, 1e-64);  # => 2.024397458499885042510817245541937419115
+say nthroot_fast(5, 34, 1e-64)  # => 2.02439745849988504251081724554193741911462170107