math.finite, math.isinf & math.isnan functions in pure Lua. Completely covered (all tests passed). https://i.imgur.com/1vzo2x9.png

math_inf_nan.lua

local NAN  =  0.0 / 0.0
local NINF = -math.huge
local PINF =  math.huge

--- Returns true if given value is a finite number; otherwise false or nil if value is not of type string nor number.
function math.finite(value)
  if type(value) == "string" then
    value = tonumber(value)
    if value == nil then return nil end
  elseif type(value) ~= "number" then
    return nil
  end
  return value > NINF and value < PINF
end

--- Returns 1 if given value is a positive infinity or -1 if given value is a negative infinity; otherwise 0 or nil if value is not of type string nor number.
function math.isinf(value)
  if type(value) == "string" then
    value = tonumber(value)
    if value == nil then return nil end
  elseif type(value) ~= "number" then
    return nil
  end
  if value == PINF then return 1 end
  if value == NINF then return -1 end
  return 0
end

--- Returns true if given value is not a number (NaN); otherwise false or nil if value is not of type string nor number.
function math.isnan(value)
  if type(value) == "string" then
    value = tonumber(value)
    if value == nil then return nil end
  elseif type(value) ~= "number" then
    return nil
  end
  return value ~= value
end

--
-- Unit tests.
--
local tests_index = {
  "Finite_1",
  "Finite_2",
  "Finite_3",
  "Finite_4",
  "Finite_5",
  "Finite_6",
  "Infinity_1",
  "Infinity_2",
  "Infinity_3",
  "Infinity_4",
  "Infinity_5",
  "Infinity_6",
  "NaN_1",
  "NaN_2",
  "NaN_3",
  "NaN_4",
  "NaN_5",
  "NaN_6",
}
local tests = {
  Finite_1 = function() return math.finite(PINF) == false end,
  Finite_2 = function() return math.finite(NINF) == false end,
  Finite_3 = function() return math.finite(NAN) == false end,
  Finite_4 = function() return math.finite(math.random(10000000000000.0, 10000000000000.0)) == true end,
  Finite_5 = function() return math.finite("invalid number") == nil end,
  Finite_6 = function() return math.finite("123456789") == true end,
  Infinity_1 = function() return math.isinf(PINF) == 1 end,
  Infinity_2 = function() return math.isinf(NINF) == -1 end,
  Infinity_3 = function() return math.isinf(NAN) == 0 end,
  Infinity_4 = function() return math.isinf(math.random(10000000000000.0, 10000000000000.0)) == 0 end,
  Infinity_5 = function() return math.isinf("invalid number") == nil end,
  Infinity_6 = function() return math.isinf("123456789") == 0 end,
  NaN_1 = function() return math.isnan(PINF) == false end,
  NaN_2 = function() return math.isnan(NINF) == false end,
  NaN_3 = function() return math.isnan(NAN) == true end,
  NaN_4 = function() return math.isnan(math.random(10000000000000.0, 10000000000000.0)) == false end,
  NaN_5 = function() return math.isnan("invalid number") == nil end,
  NaN_6 = function() return math.isnan("123456789") == false end,
}
local pass_count, fail_count, total_count = 0, 0, 0
for _, test_name in ipairs(tests_index) do
  local test_func = tests[test_name]
  total_count = total_count + 1
  test_name = test_name:gsub("_", " ")
  local test_result = test_func()
  if test_result then
    pass_count = pass_count + 1
  else
    fail_count = fail_count + 1
  end
  local test_result_text = test_result and "Test passed." or "Test FAILED!!!"
  print("[" .. os.date("%d-%m-%Y %H:%M:%S") .. "] [" .. ("%0" .. tostring(#tests_index):len() .. ".0f"):format(total_count) .. "] " .. test_name .. ": " .. test_result_text)
end
print("-----------------------------------")
print("Total: " .. total_count .. " tests.")
print("Passed: " .. pass_count .. " / " .. total_count .. " (" .. ("%.2f"):format((pass_count / total_count) * 100.0) .. "% covered).")
print("Failed: " .. fail_count .. " / " .. total_count .. " (" .. ("%.2f"):format((fail_count / total_count) * 100.0) .. "% not covered).")