program main

  implicit none

  real ( kind = 8 ) a
  real ( kind = 8 ) b
  integer ( kind = 4 ) i
  integer ( kind = 4 ) it
  real ( kind = 8 ) :: tol = 1.0D-10
  real ( kind = 8 ) w
  real ( kind = 8 ), save, dimension ( 8 ) :: w_vec = (/ &
    0.3517337112491958D+00, &
    0.5671432904097839D+00, &
    0.7258613577662263D+00, &
    0.8526055020137255D+00, &
    0.9585863567287029D+00, &
    0.1000000000000000D+01, &
    0.1745528002740699D+01, &
    0.3385630140290050D+01 /)
  real ( kind = 8 ) x
  real ( kind = 8 ), save, dimension ( 8 ) :: x_vec = (/ &
    0.5000000000000000D+00, &
    0.1000000000000000D+01, &
    0.1500000000000000D+01, &
    0.2000000000000000D+01, &
    0.2500000000000000D+01, &
    0.2718281828459045D+01, &
    0.1000000000000000D+02, &
    0.1000000000000000D+03 /)

  do i = 1, 8

    x = x_vec(i)
    w = x + log ( x )

    it = 0

    do

      if ( 100 < it ) then
        exit
      end if

      if ( abs ( ( x - w * exp ( w ) ) ) < &
        tol * abs ( ( w + 1.0D+00 ) * exp ( w ) ) ) then
        exit
      end if

      a = w * exp ( w ) - x

      b = ( w + 1.0D+00 ) * exp ( w ) &
        - ( w + 2.0D+00 ) * ( w * exp ( w ) - x ) / ( 2.0D+00 * w + 2.0D+00 )

      w = w - a / b

      it = it + 1

    end do

    write ( *, * ) x, it, w, w_vec(i), abs ( w - w_vec(i) )

  end do

  return
end