pow.exs

[#HashDict<[{"number", 3400}, {"comments", 14},
  {"title", "Float.round is inconsistent"},
  {"created_at", "2015-06-17T13:04:45Z"}, {"state", "open"}, {"locked", false},
  {"url", "https://api.github.com/repos/elixir-lang/elixir/issues/3400"},
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  {"body",
   "The rounding from Float.round is inconsistent, eg\r\n\r\niex(121)> Kernel.round(1.255 * 100) / 100\r\n1.25\r\n\r\niex(123)> Kernel.round(125.5) / 100\r\n1.26\r\n\r\niex> Kernel.round(Kernel.round(1.255 * 1000) / 10) / 100\r\n1.26\r\n\r\n\r\nThe core issue is numerical instability due to the multiplication by a power of 10 (which itself has to be encoded as an approximation in floating point format)\r\n\r\nThe following *appears* to correctly implement the same rounding function as Kernel.round (ie round away from zero) without instability.  However, it would be sensible to include a test harness for very large/small numbers and also floats in \"denomalised\" form.\r\n\r\n```\r\n  @spec round(float, 0..15) :: float\r\n  def round(number, precision \\\\ 0) when is_float(number) and precision in 0..15 do\r\n    power = power_of_10(precision)\r\n    power2 = power_of_10(precision+1)\r\n    # Avoid numerical instability by pre-rounding to one extra digit of precision\r\n    Kernel.round(Kernel.round(number * power2) / 10) / power\r\n  end\r\n\r\n  Enum.reduce 0..21, 1, fn x, acc ->\r\n    defp power_of_10(unquote(x)), do: unquote(acc)\r\n    acc * 10\r\n  end\r\n```"},
  {"assignee", :null}, {"closed_at", :null}, {"milestone", :null},
  {"updated_at", "2015-06-22T11:55:15Z"}]>]