title: Why does numpy's float128 only have 63 bits mantissa?
body: <p>I'm sure this is a daft question but I'm genuinely puzzled:</p>
  
  <pre><code>&gt;&gt;&gt; import numpy as np
  &gt;&gt;&gt; 
  &gt;&gt;&gt; f1, f2, f64 = map(np.float128, (1, 2, -64))
  &gt;&gt;&gt; f1 + f2**f64 == f1
  True
  </code></pre>
  
  <p>Or more directly:</p>
  
  <pre><code>&gt;&gt;&gt; np.finfo(np.float128).nmant
  63
  </code></pre>
  
  <p>Exponent appears to have 15 bits, so where are all those missing bits?</p>