bisection <- function ( f, a, b, tol = 1.0e-3, m = 100 )

#*****************************************************************************80
#
## bisection seeks the root of a function using the bisection 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:
#
#    13 March 2020
#
#  Author:
#
#    Original R code 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.
#
{
  iter <- 0
  f.a <- f ( a )
  f.b <- f ( b )

  while ( tol < abs ( b - a ) )
  {
    iter <- iter + 1
    if ( m < iter )
    {
      warning ( 'bisection: iteration limit exceeded.' )
      break
    }

    xmid <- 0.5 * ( a + b )
    ymid <- f ( xmid )

    if ( 0.0 < f.a * ymid )
    {
      a <- xmid
      f.a <- ymid
    }
    else
    {
      b <- xmid
      f.b <- ymid
    }
  }

  value <- 0.5 * ( a + b )

  return ( value )
}