# xarray.ufuncs.log1p

### xarray.ufuncs.log1p *= <xarray.ufuncs._unary_ufunc object>*

xarray specific variant of `numpy.log1p()`. Handles xarray objects by dispatching to the appropriate function for the underlying array type.

Documentation from numpy:

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

Calculates `log(1 + x)`.

* **Parameters:**
  * **x** ([array_like](https://numpy.org/doc/stable/glossary.html#term-array_like)) – Input values.
  * **out** ([`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray), [`None`](https://docs.python.org/3/builtins/constants.html#None), or [`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple) of [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray) and [`None`](https://docs.python.org/3/builtins/constants.html#None), *optional*) – A location into which the result is stored. If provided, it must have
    a shape that the inputs broadcast to. If not provided or None,
    a freshly-allocated array is returned. A tuple (possible only as a
    keyword argument) must have length equal to the number of outputs.
  * **where** ([array_like](https://numpy.org/doc/stable/glossary.html#term-array_like), *optional*) – This condition is broadcast over the input. At locations where the
    condition is True, the out array will be set to the ufunc result.
    Elsewhere, the out array will retain its original value.
    Note that if an uninitialized out array is created via the default
    `out=None`, locations within it where the condition is False will
    remain uninitialized.
  * **\*\*kwargs** – For other keyword-only arguments, see the
    [ufunc docs](https://numpy.org/doc/stable/reference/ufuncs.html#ufuncs-kwargs).
* **Returns:**
  **y** ([`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray)) – Natural logarithm of 1 + x, element-wise.
  This is a scalar if x is a scalar.

#### SEE ALSO
[`expm1`](xarray.ufuncs.expm1.html.md#xarray.ufuncs.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.
   [https://personal.math.ubc.ca/~cbm/aands/page_67.htm](https://personal.math.ubc.ca/~cbm/aands/page_67.htm)
2. Wikipedia, “Logarithm”. [https://en.wikipedia.org/wiki/Logarithm](https://en.wikipedia.org/wiki/Logarithm)

### Examples

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```pycon
>>> import numpy as np
>>> np.log1p(1e-99)
1e-99
>>> np.log(1 + 1e-99)
0.0
```

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