r8_softplus <- function ( x )

#*****************************************************************************80
#
## r8_softplus() evaluates the softplus function of an R8.
#
#  Discussion:
#
#    An R8 is a double precision real value.
#
#    The softplus function is a smoothed (differentiable) version of 
#    the ReLU (Rectified Linear Unit) activation.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    06 September 2026
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real x: the argument.
#
#  Output:
#
#    real VALUE: the function value.
#
{
  if ( x <= -36.841 )
  {
    value = 0.0
  }
  else if ( +36.841 <= x )
  {
    value = x
  }
  else
  {
    value = log ( 1.0 + exp ( x ) )
  }

  return ( value )
}