log(1 + x) in base e, elementwise.
Parameters:  x : array_like


Returns:  y : ndarray

Notes
For realvalued input, log1p is accurate also for x so small that 1 + x == 1 in floatingpoint accuracy.
Logarithm is a multivalued function: for each x there is an infinite number of z such that exp(z) = 1 + x. The convention is to return the z whose imaginary part lies in [pi, pi].
For realvalued input data types, log1p always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.
For complexvalued input, log1p is a complex analytical function that has a branch cut [inf, 1] and is continuous from above on it. log1p handles the floatingpoint negative zero as an infinitesimal negative number, conforming to the C99 standard.
References
[48]  M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/ 
[49]  Wikipedia, “Logarithm”. http://en.wikipedia.org/wiki/Logarithm 
Examples
>>> np.log1p(1e99)
1e99
>>> np.log(1 + 1e99)
0.0