Source code for xorbits._mars.tensor.arithmetic.log1p

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# Licensed under the Apache License, Version 2.0 (the "License");
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#      http://www.apache.org/licenses/LICENSE-2.0
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import numpy as np

from ... import opcodes as OperandDef
from ..utils import infer_dtype
from .core import TensorUnaryOp
from .utils import arithmetic_operand


@arithmetic_operand(sparse_mode="unary")
class TensorLog1p(TensorUnaryOp):
    _op_type_ = OperandDef.LOG1P
    _func_name = "log1p"


@infer_dtype(np.log1p)
def log1p(x, out=None, where=None, **kwargs):
    """
    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 : Tensor
        Natural logarithm of `1 + x`, element-wise.

    See Also
    --------
    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
    """
    op = TensorLog1p(**kwargs)
    return op(x, out=out, where=where)