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Loss of precision in (complex) arcsinh & arctanh (Trac #1008) #1606

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@thouis

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@thouis

Original ticket http://projects.scipy.org/numpy/ticket/1008 on 2009-02-15 by @pv, assigned to unknown.

Numpy's complex arcsinh and arctanh suffer from loss of precision at small arguments:

>>> import numpy as np
>>> np.__version__
'1.3.0.dev6366'
>>> np.arcsinh(1e-50)
1e-50
>>> np.arcsinh(1e-50+0j)
0j
>>> np.arctanh(1e-50)
1e-50
>>> np.arctanh(1e-50+0j)
0j

However, complex arcsin and arctan are OK:

>>> np.arcsin(1e-50 + 0j)
(1e-50-0j)
>>> np.arctan(1e-50 + 0j)
(1e-50+0j)

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