title: Can I lose precision going from float32 -> float64 back to float32?
body: <p>Is it possible to lose any fidelity or precision going from a numpy float32 to a python float (float64) back to a numpy float32?</p>
  
  <p>I can't seem to find a case where there is data lost but everyone around me is claiming that the world will end because there is data lost.  I just need to find a document/example that proves that data is lost before I continue.</p>
  
  <p>Any help pointing me in the right direction is appreciated.</p>
  
  <p>Here is a typical use case I'm seeing:</p>
  
  <pre><code>def serialize(val):
      # val is a np.float32
      return val.astype(float)
  
  
  def deserialize(msg):
      return np.float32(msg)
  
  message = '1.23456789'
  outgoing = serialize(message)
  incoming = deserialize(message)
  </code></pre>