local function from_radix(digits, base)
  local ip = 0
  local fp = 0
  local dp = nil
  for i, v in ipairs(digits) do
    if v == "." then
      dp = i
      break
    end
    if type(v) ~= "number" then
      error("Invalid digit in input")
    end
    if v < 0 or v >= base then
      error("Digit out of range for given base")
    end
  end
  if dp then
    for i = 1, dp - 1 do
      ip = ip * base + digits[i]
    end
    for i = dp + 1, #digits do
      fp = fp + digits[i] / (base ^ (i - dp))
    end
  else
    for i = 1, #digits do
      ip = ip * base + digits[i]
    end
  end
  return ip + fp
end

local function to_radix(x, base, frac_digits)
  if base < 2 then
    error("Base must be at least 2")
  end
  if frac_digits and frac_digits < 0 then
    error("Number of fractional digits must be non-negative")
  end
  local result = {}
  local ip = math.floor(x)
  local fp = x - ip
  repeat
    table.insert(result, 1, ip % base)
    ip = math.floor(ip / base)
  until ip == 0
  if frac_digits and frac_digits > 0 then
    table.insert(result, ".")
    for _ = 1, frac_digits do
      fp = fp * base
      local digit = math.floor(fp)
      table.insert(result, digit)
      fp = fp - digit
    end
  end
  return result
end

local function clock_from_moment(tee)
  local seconds = math.fmod(tee, 86400)
  if seconds < 0 then
    seconds = seconds + 86400
  end
  local hours = math.floor(seconds / 3600)
  seconds = math.fmod(seconds, 3600)
  local minutes = math.floor(seconds / 60)
  seconds = math.fmod(seconds, 60)
  return {hours, minutes, math.floor(seconds)}
end

local function time_from_clock(hms)
  if #hms ~= 3 then
    error("Clock time must have 3 elements: {hours, minutes, seconds}")
  end
  for _, v in ipairs(hms) do
    if type(v) ~= "number" then
      error("Clock time elements must be numbers")
    end
  end
  if hms[1] < 0 or hms[1] > 23 then
    error("Hours must be between 0 and 23")
  end
  if hms[2] < 0 or hms[2] > 59 then
    error("Minutes must be between 0 and 59")
  end
  if hms[3] < 0 or hms[3] > 59 then
    error("Seconds must be between 0 and 59")
  end
  return ((hms[1] * 3600) + (hms[2] * 60) + hms[3]) / 86400
end

local function table_tostring(t)
  if type(t) ~= "table" then
    return tostring(t)
  end
  local s = "{"
  for k, v in pairs(t) do
    s = s .. "[" .. tostring(k) .. "] = " .. tostring(v) .. ", "
  end
  if #s > 1 then
    s = s:sub(1, #s - 2)
  end
  return s .. "}"
end

local function float_equal(a, b, tolerance)
  tolerance = tolerance or 1e-9
  return math.abs(a - b) < tolerance
end

local function assert_eq(actual, expected, message)
  local success = false
  if type(actual) == type(expected) then
    if type(actual) == "table" then
      local actual_count = 0
      local expected_count = 0
      for _ in pairs(actual) do
        actual_count = actual_count + 1
      end
      for _ in pairs(expected) do
        expected_count = expected_count + 1
      end
      if actual_count == expected_count then
        success = true
        for k, exp_v in pairs(expected) do
          local v = actual[k]
          if type(v) == "number" and type(exp_v) == "number" then
            if not float_equal(v, exp_v) then
              success = false
              break
            end
          elseif tostring(v) ~= tostring(exp_v) then
            success = false
            break
          end
        end
      end
    elseif type(actual) == "number" then
      success = float_equal(actual, expected)
    else
      success = actual == expected
    end
  end

  if not success then
    error(
      "Assertion failed: " ..  message .. "\n" ..
      "Expected: " .. table_tostring(expected) .. "\n" ..
      "Got: " .. table_tostring(actual)
    )
  end
end

local tests = {
  {function()
    return from_radix({1, 0, 1, ".", 1, 1}, 2)
  end, 5.75, "Binary 101.11"},
  {function()
    return to_radix(5.75, 2, 5)
  end, {1, 0, 1, ".", 1, 1, 0, 0, 0}, "Decimal 5.75 to binary"},
  {function()
    return to_radix(12345, 16)
  end, {3, 0, 3, 9}, "Decimal 12345 to hex"},
  {function()
    return to_radix(0.3, 2, 10)
  end, {0, ".", 0, 1, 0, 0, 1, 1, 0, 0, 1, 1}, "Decimal 0.3 to binary"},
  {function()
    return clock_from_moment(3723)
  end, {1, 2, 3}, "3723 seconds to clock time"},
  {function()
    return clock_from_moment(0)
  end, {0, 0, 0}, "0 seconds to clock time"},
  {function()
    return clock_from_moment(86400)
  end, {0, 0, 0}, "86400 seconds to clock time"},
  {function()
    return clock_from_moment(86461)
  end, {0, 1, 1}, "86461 seconds to clock time"},
  {function()
    return clock_from_moment(123456)
  end, {10, 17, 36}, "123456 seconds to clock time"},
  {function()
    return time_from_clock({1, 2, 3})
  end, 0.043090277777778, "Clock time 1:2:3 to fraction of day"},
  {function()
    return time_from_clock({0, 0, 0})
  end, 0, "Clock time 0:0:0 to fraction of day"},
  {function()
    return time_from_clock({12, 0, 0})
  end, 0.5, "Clock time 12:0:0 to fraction of day"},
  {function()
    return time_from_clock({23, 59, 59})
  end, 0.99998842592593, "Clock time 23:59:59 to fraction of day"},
  {function()
    return time_from_clock({1, 10, 56})
  end, 0.049259259259259, "Clock time 1:10:56 to fraction of day"}
}

local function run_tests()
  local passed = 0
  local total = #tests

  for i, test in ipairs(tests) do
    local description = test[3]
    local actual = test[1]()
    local expected = test[2]
    assert_eq(actual, expected, description)
    print("Test " .. i .. ": " .. description .. " - PASSED")
    passed = passed + 1
  end

  print("\nPassed " .. passed .. " of " .. total .. " tests.")
end

run_tests()