fp_roundtrip.lua

function fp_to_bytes(fp, bytes, is_double)
  local val = tonumber(fp)

  -- it's a NaN or inf
  if val ~= val or val == math.huge or val == -math.huge then
    bytes[1] = (val ~= val or val == math.huge) and 0x7f or 0xff
    bytes[2] = (val ~= val and 0xf9 or 0xf8)
    local max = is_double and 8 or 4
    for i = 3, max do
      bytes[i] = 0
    end
    return
  end
  
  local sign = 0

  if val < 0 then
    sign = 1
    val = -val
  end

  local mantissa, exponent = math.frexp(val)
  if val == 0 then
    mantissa = 0
    exponent = 0
  else
    mantissa = (mantissa * 2 - 1) * math.ldexp(0.5, is_double and 53 or 24)
    exponent = exponent + (is_double and 1022 or 126)
  end

  local pos
  if is_double then
    val = mantissa
    for i = 8, 3, -1 do
      bytes[i] = math.floor(val) % (2 ^ 8)
      val = math.floor(val / (2 ^ 8))
    end
  else
    bytes[4] = math.floor(mantissa) % (2 ^ 8)
    val = math.floor(mantissa / (2 ^ 8))
    bytes[3] = math.floor(val) % (2 ^ 8)
    val = math.floor(val / (2 ^ 8))
  end

  bytes[2] = math.floor(exponent * (is_double and 16 or 128) + val) % (2 ^ 8)
  val = math.floor((exponent * (is_double and 16 or 128) + val) / (2 ^ 8))
  bytes[1] = math.floor(sign * 128 + val) % (2 ^ 8)
end

function bytes_to_fp(bytes, is_double)
  local n = is_double and 8 or 4

  -- NaN or inf
  if (bytes[1] == 0x7F or bytes[1] == 0xff) and bytes[2] >= 0xf8 then
    if bytes[2] == 0xf8 then
      local all_zero = true
      for i = 3, n do
        if bytes[i] ~= 0 then
          all_zero = false
          break
        end
      end
      if all_zero then
        return bytes[1] == 0x7F and 1/0 or -1/0
      end
    end
    return 0/0
  end
  
  local sign = 1
  if bytes[1] > 127 then
    sign = -1
  end
  local mantissa = bytes[2] % (is_double and 16 or 128)
  for i = 3, n  do
    mantissa = mantissa * (2 ^ 8) + bytes[i]
  end

  local exponent = (bytes[1] % 128) * (is_double and 16 or 2) + math.floor(bytes[2] / (is_double and 16 or 128))
  if exponent == 0 then
    return 0.0
  else
    mantissa = (math.ldexp(mantissa, is_double and -52 or -23) + 1) * sign
    return math.ldexp(mantissa, exponent - (is_double and 1023 or 127))
  end
end

function test_roundtrip(inp)
  bytes = {}
  for i = 1, 8 do
    bytes[i] = 0
  end

  fp_to_bytes(inp, bytes, true)

  -- for i, v in ipairs(bytes) do
  --  print (i, string.format("%x", v))
  -- end
  -- print(bytes)

  print(inp, "==", bytes_to_fp(bytes, true))
end

test_roundtrip(0)
test_roundtrip(1.234)
test_roundtrip(-9876.5432)
test_roundtrip(1/0)
test_roundtrip(-1/0)
test_roundtrip(0/0)

results.txt

0       ==      0
1.234   ==      1.234
-9876.5432      ==      -9876.5432
inf     ==      inf
-inf    ==      -inf
nan     ==      nan