# mars.tensor.log1p¶

mars.tensor.log1p(x, out=None, where=None, **kwargs)[source]

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

Calculates `log(1 + x)`.

Parameters
• x (array_like) – Input values.

• out (Tensor, None, or tuple of Tensor and 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 tensor is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

• where (array_like, optional) – Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.

• **kwargs

Returns

y – Natural logarithm of 1 + x, element-wise.

Return type

Tensor

`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”. http://en.wikipedia.org/wiki/Logarithm

Examples

```>>> import mars.tensor as mt
```
```>>> mt.log1p(1e-99).execute()
1e-99
>>> mt.log(1 + 1e-99).execute()
0.0
```