Root, Lua - rextester

Language: Layout:

--lua 5.3

-- Port of https://rextester.com/discussion/TAGOI61149 to Lua.

local function checkNumber(num)
    assert(math.type(num), tostring(num) .. " is not a number")
    assert(num == num and num ~= math.huge, tostring(num) .. " is not finite")
end

local function checkInteger(num)
    checkNumber(num)
    assert(math.type(num) == "integer", tostring(num) .. " is not an integer")
end

local function integralRoot(num, pow)
    pow = (pow ~= nil) and pow or 2
    checkNumber(num)
    checkInteger(pow)
    
    for i = 1, num do
        if i ^ pow == num then
            return i
        elseif i ^ pow > num then
            return i - 1
        end
    end
end

local function root(num, pow, prc)
    pow = (pow ~= nil) and pow or 2
    prc = (prc ~= nil) and prc or 15
    checkNumber(num)
    checkInteger(pow)
    checkInteger(prc)
    
    local int_root = integralRoot(num, pow)
    if int_root ^ pow == num then
        return int_root
    end
    
    local str = int_root .. "."
    for i = 1, prc do
        local added = false
        
        for j = 1, 9 do
            local n = tonumber(str .. j)
            
            if n ^ pow == num then
                return n
            elseif n ^ pow > num then
                str = str .. (j - 1)
                added = true
                break
            end
        end
        
        if not added then str = str .. "9" end
    end
    
    return tonumber(str)
end

local x = 125096235
print(root(x), math.sqrt(x))

[ + ] Show input
Absolute running time: 0.19 sec, cpu time: 0.02 sec, memory peak: 5 Mb, absolute service time: 0,3 sec