title: Unexpected behavior of numpy.fft.fft with high precision numbers
body: <p>I have the following code...Note the two lines under # generate sine curve.  One uses a higher precision value for 2pi than the other, they should still give near identical results though.</p>
  
  <pre><code>import numpy as np
  import matplotlib.pyplot as plt
  
  
  t1 = np.arange(0., 1., .01)
  
  # generate sine curve
  y1 = np.sin(6.28318*5.*t1)  
  #y1 = np.sin(6.283185307179586*5.*t1) # equivalent to np.sin(2*np.pi*t1)
  
  # calculate the fft (no averaging!) of the time series
  ffty = np.fft.fft(y1)
  
  fig, ax_list = plt.subplots(3,1)
  ax_list[0].plot(t1,y1, '.-')
  
  ax_list[1].plot(ffty.real, '.-', label='Real Part')
  ax_list[1].legend()
  
  ax_list[2].plot(ffty.imag, '.-', label='Imag Part')
  ax_list[2].legend()
  
  
  plt.show()
  </code></pre>
  
  <p>If you run the code with the lower precision 6.28318 you get the expected result for the fft...
  <a href="https://i.stack.imgur.com/wiDTa.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/wiDTa.png" alt="enter image description here"></a></p>
  
  <p>However, if you run the code with the higher precision 6.283185307179586 which is equal to 2.*numpy.pi, you get the unexpected result below... the real part is drastically wrong...The amplitudes are way off, it's not symmetric, it doesn't make any sense.
  <a href="https://i.stack.imgur.com/miOb5.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/miOb5.png" alt="enter image description here"></a></p>
  
  <p>I'm at a loss as to what is causing this.  Anyone have any ideas?</p>