Float.round/2 returns invalid value for 5.0e-324 with precision 1

[hauleth]

Environment

• Elixir & Erlang/OTP versions (elixir --version):

  Erlang/OTP 21 [erts-10.1] [source] [64-bit] [smp:4:4] [ds:4:4:10] [async-threads:1] [hipe] [dtrace]
  
  Elixir 1.8.0 (compiled with Erlang/OTP 21)
  

• Operating system:

  Darwin 18.2.0 Darwin Kernel Version 18.2.0: Fri Oct  5 19:41:49 PDT 2018; root:xnu-4903.221.2~2/RELEASE_X86_64 x86_64
  

Current behavior

refute Float.round(5.0e-324, 1) == 0.0

Expected behavior

assert Float.round(5.0e-324, 1) == 0.0

[eksperimental]

The bug happens for any precision greater than 0.

iex> for precision <- 1..15, do: Float.round(5.0e-324, precision)
[5.0e-324, 5.0e-324, 5.0e-324, 5.0e-324, 5.0e-324, 5.0e-324, 5.0e-324, 5.0e-324,
 5.0e-324, 5.0e-324, 5.0e-324, 5.0e-324, 5.0e-324, 5.0e-324, 5.0e-324]

[eksperimental]

Look, I found the limit where this bug happens. once the exponent is <= -309, that's when it happens.

iex(105)> list = for e <- 0..324, precision <- 1..15, e > precision do float = String.to_float("5.0e-#{e}"); result = Float.round(float, precision); if result !== 0.0, do: {float, precision, result} end; list = Enum.reject(list, &is_nil(&1))  

iex(106)> IO.inspect list, limit: :infinity
[
  {0.05, 1, 0.1},
  {0.005, 2, 0.01},
  {0.0005, 3, 0.001},
  {5.0e-5, 4, 0.0001},
  {5.0e-6, 5, 1.0e-5},
  {5.0e-9, 8, 1.0e-8},
  {5.0e-10, 9, 1.0e-9},
  {5.0e-11, 10, 1.0e-10},
  {5.0e-14, 13, 1.0e-13},
  {5.0e-16, 15, 1.0e-15},
  {5.0e-309, 1, 5.0e-309},
  {5.0e-309, 2, 5.0e-309},
  {5.0e-309, 3, 5.0e-309},
  {5.0e-309, 4, 5.0e-309},
  {5.0e-309, 5, 5.0e-309},
  {5.0e-309, 6, 5.0e-309},
  {5.0e-309, 7, 5.0e-309},
  {5.0e-309, 8, 5.0e-309},
  {5.0e-309, 9, 5.0e-309},
  {5.0e-309, 10, 5.0e-309},
  {5.0e-309, 11, 5.0e-309},
  {5.0e-309, 12, 5.0e-309},
  {5.0e-309, 13, 5.0e-309},
  {5.0e-309, 14, 5.0e-309},
  {5.0e-309, 15, 5.0e-309},
  {5.0e-310, 1, 5.0e-310},
  {5.0e-310, 2, 5.0e-310},
...

See the gist for a full result https://gist.github.com/eksperimental/4a0bcf4db61dea0a441c6a9d2959ffe8

[josevalim]

Closing in favor of #8685. Thanks!

[hauleth]

@josevalim you probably meant #8687