horner <- function ( x, coefs )

#*****************************************************************************80
#
## horner evaluates a polynomial using Horner's method.
#
#  Licensing:
#
#    Copyright 2016 James P. Howard, II
#
#    The computer code and data files on this web page are distributed under
#    https://opensource.org/licenses/BSD-2-Clause, the BSD-2-Clause license.
#
#  Modified:
#
#    15 January 2020
#
#  Author:
#
#    Original R version by James Howard.
#    Modifications by John Burkardt.
#
#  Reference:
#
#    James Howard,
#    Computational Methods for Numerical Analysis with R,
#    CRC Press, 2017
#    ISBN13: 978-1-4987-2363-3.
#
#  Input:
#
#    real X, the evaluation points.
#
#    real COEFS, the polynomial coefficients.
#
#  Output:
#
#    real Y, the value of the polynomial at each point X.
{
  y <- rep ( 0.0, length ( x ) )

  for ( i in length ( coefs ) : 1 )
  {
    y <- coefs[i] + x * y
  }

  return ( y )
}