Single vs. double precision issue

[woodward]

Nx: 0.9.2
Elixir: 1.18.1-otp-27
Erlang: 27.2
macOS 14.6.1
Nx default binary backend

Hi:
I'm having some issues with single vs. double precision for floating point math in Nx. Also note that this might not be an actual issue, but might be some misunderstanding or even user error on my part! Here's an example which illustrates the problem in iex:

iex -S mix
Erlang/OTP 27 [erts-15.2] [source] [64-bit] [smp:16:16] [ds:16:16:10] [async-threads:1]
Interactive Elixir (1.18.1) - press Ctrl+C to exit (type h() ENTER for help)

iex> x = Nx.f64(2)
  #Nx.Tensor<
    f64
    2.0
  >

iex> result_f32 = Nx.multiply(x, 0.7)
  #Nx.Tensor<
    f64
    1.399999976158142
  >

iex> result_f64 = Nx.multiply(x, Nx.f64(0.7))
  #Nx.Tensor<
    f64
    1.4
  >

iex> Nx.all_close(result_f64, Nx.f64(1.4), atol: 1.0e-14, rtol: 1.0e-14)
  #Nx.Tensor<
    u8
    1
  >

iex> Nx.all_close(result_f32, Nx.f64(1.4), atol: 1.0e-14, rtol: 1.0e-14)
  #Nx.Tensor<
    u8
    0
  >

iex> Nx.all_close(result_f32, Nx.f64(1.4), atol: 1.0e-07, rtol: 1.0e-07)
  #Nx.Tensor<
    u8
    1
  >

Note that Nx.all_close/3 confirms that result_f64 is accurate to double precision, whereas result_f32 is accurate only to single precision; i.e.,

result_f64: 1.400000000000000
result_f32: 1.399999976158142

Here's a Slack thread in the #machine-learning channel of the EEF Slack where I asked this as a question prior to filing this bug (assuming that it was user error on my part - which it may still be!) There's also an Elixir script in that thread which shows the issue. In the meantime, I can just make sure I use quantities like Nx.f64(0.7) in my code, although it would be nice to use the simpler 0.7 at some point in the future.

I know there are possibly some related GitHub issues such as #448.

Thank you very much for your help,
Greg