numpy.log1p(x[, out])

Return the natural logarithm of one plus the input array, element-wise.

Calculates log(1 + x).

Parameters :

x : array_like

Input values.

Returns :

y : ndarray

Natural logarithm of 1 + x, element-wise.

See also

exp(x) - 1, the inverse of log1p.


For real-valued input, log1p is accurate also for x so small that 1 + x == 1 in floating-point 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 real-valued 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 complex-valued input, log1p is a complex analytical function that has a branch cut [-inf, -1] and is continuous from above on it. log1p handles the floating-point negative zero as an infinitesimal negative number, conforming to the C99 standard.


[R45]M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67.
[R46]Wikipedia, “Logarithm”.


>>> np.log1p(1e-99)
>>> np.log(1 + 1e-99)

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