Function log1p

imperative/python/megengine/functional/elemwise.py:712–759

r"""Element-wise :math:`\log(1 + x)` function. Calculates an approximation to :math:`\log(1 + x)`: .. math:: y_i = \log(1 + x_i) where log refers to the natural (base :math:`e`) logarithm, for each element :math:`x_i` of the input tensor :math:`x`. This functio

(x)

def log1p(x):
    r"""Element-wise :math:`\log(1 + x)` function.
    
    Calculates an approximation to :math:`\log(1 + x)`:

    .. math::

         y_i = \log(1 + x_i)

    where log refers to the natural (base :math:`e`) logarithm, 
    for each element :math:`x_i` of the input tensor :math:`x`.

    This function has domain ``[-1, +infinity]`` and codomain ``[-infinity, +infinity]``.

    Args:
        x: input tensor. Should have a floating-point data type.

    Returns:

        a tensor containing the evaluated result for each element in :math:`x`.
        The returned tensor must have a floating-point data type determined by :ref:`dtype-promotion`.
    
    .. note::

       This function is more accurate than :math:`\log(1+x)` for small values of input.
       See FDLIBM, or some other IEEE 754-2019 compliant mathematical library, for a potential reference implementation.
       

    .. admonition:: Special cases

       For floating-point operands,

       * If :math:`x_i` is ``NaN``, the result is ``NaN``.
       * If :math:`x_i` is less than ``-1``, the result is ``NaN``.
       * If :math:`x_i` is ``-1``, the result is ``-infinity``.
       * If :math:`x_i` is ``-0``, the result is ``-0``.
       * If :math:`x_i` is ``+0``, the result is ``+0``.
       * If :math:`x_i` is ``+infinity``, the result is ``+infinity``.

    Examples:

        >>> F.log(1e-10 + 1)
        Tensor(0.0, device=xpux:0)
        >>> F.log1p(1e-10)
        Tensor(1e-10, device=xpux:0)
    
    """
    return _elwise(x, mode=Elemwise.Mode.LOG1P)


def sqrt(x: Tensor) -> Tensor: