immfloat.ml

let is_immediate_float bits =
  let exp = (Int64.(to_int (shift_right_logical bits 52)) land 0x7FF) - 1023 in
  let mant = Int64.logand bits 0xF_FFFF_FFFF_FFFFL in
  exp >= -3 && exp <= 4 && Int64.logand mant 0xF_0000_0000_0000L = mant

let iter_immediate_floats f =
  for sign = 0 to 1 do
    for exp = -3 to 4 do
      for mant = 0 to 15 do
        let bits = Int64.(
          shift_left (of_int sign) 63
          |> logor (shift_left (of_int (exp + 1023)) 52)
          |> logor (shift_left (of_int mant) 48)) in
        f (Int64.float_of_bits bits)
      done
    done
  done

let () =
  iter_immediate_floats (fun f ->
    assert (is_immediate_float (Int64.bits_of_float f));
    if float_of_string (Printf.sprintf "%.7f" f) <> f then
      Printf.printf "%.20f\n" f)

Output with %.7f replaced with %f:

0.13281250000000000000
0.14843750000000000000
0.16406250000000000000
0.17968750000000000000
0.19531250000000000000
0.21093750000000000000
0.22656250000000000000
0.24218750000000000000
-0.13281250000000000000
-0.14843750000000000000
-0.16406250000000000000
-0.17968750000000000000
-0.19531250000000000000
-0.21093750000000000000
-0.22656250000000000000
-0.24218750000000000000