# jax.numpy.log1p¶

jax.numpy.log1p(x)

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

LAX-backend implementation of log1p(). Original docstring below.

log1p(x, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])

Calculates log(1 + x).

Parameters

x (array_like) – Input values.

Returns

y – Natural logarithm of 1 + x, element-wise. This is a scalar if x is a scalar.

Return type

ndarray

expm1()

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

Notes

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.

References

1

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 67. http://www.math.sfu.ca/~cbm/aands/

2

Wikipedia, “Logarithm”. https://en.wikipedia.org/wiki/Logarithm

Examples

>>> np.log1p(1e-99)
1e-99
>>> np.log(1 + 1e-99)
0.0