class num2
    static function ipow(i, exp)
        assert(math.type(i) == "integer", "receiver must be an integer")
        assert(math.type(exp) == "integer", "exponent must be an integer")
        if i == 1 or exp == 0 then return 1 end
        if i == -1 then return exp % 2 == 0 ? 1 : -1 end
        assert(exp >= 0, "exponent cannot be negative for non-unit values")
        local ans = 1
        local base = i
        local e = exp
        while e > 1 do
            if e % 2 == 1 then ans *= base end
            e //= 2
            base *= base
        end
        return ans * base
    end

    static function fpow(f, exp)
       assert(type(f) == "number", "receiver must be a number")
       assert(math.type(exp) == "integer", "exponent must be an integer")
       local ans = 1.0
       local e = exp
       local base = e < 0 ? 1 / f : f
       if e < 0 then e = -e end
       while e > 0 do
            if e % 2 == 1 then ans *= base end
            e //= 2
            base *= base
       end
       return ans
    end

    public n

    function __construct(n)
        assert(type(n) == "number", "argument must be a number")
        self.n = n
    end

    -- Overloads '^' operator.
    function __pow(exp)
        assert(math.type(exp) == "integer", "exponent must be an integer")
        if math.type(n) == "integer" and (exp >= 0 or math.abs(self.n) == 1) then
            return num2.ipow(self.n, exp)
        else
            return num2.fpow(self.n, exp)
        end
    end
end

print("Using static methods:")
print($"  2 ^   3   = {num2.ipow( 2,   3)}")
print($"  1 ^ -10   = {num2.ipow( 1, -10)}")
print($" -1 ^  -3   = {num2.ipow(-1,  -3)}")
print()
print($"  2.0 ^ -3  = {num2.fpow(2.0, -3)}")
print($"  1.5 ^  0  = {num2.fpow(1.5,  0)}")
print($"  4.5 ^  2  = {num2.fpow(4.5,  2)}")

print("\nUsing the ^ operator:")
print($"  2 ^   3   = {new num2(2)  ^   3}")
print($"  1 ^ -10   = {new num2(1)  ^ -10}")
print($" -1 ^  -3   = {new num2(-1) ^  -3}")
print()
print($"  2.0 ^ -3  = {new num2(2.0) ^ -3}")
print($"  1.5 ^  0  = {new num2(1.5) ^  0}")
print($"  4.5 ^  2  = {new num2(4.5) ^  2}")