e1xa Subroutine

subroutine e1xa ( x, e1 )

  !*****************************************************************************80
  !
  !! E1XA computes the exponential integral E1(x).
  !
  !  Licensing:
  !
  !    This routine is copyrighted by Shanjie Zhang and Jianming Jin.  However, 
  !    they give permission to incorporate this routine into a user program 
  !    provided that the copyright is acknowledged.
  !
  !  Modified:
  !
  !    06 July 2012
  !
  !  Author:
  !
  !    Shanjie Zhang, Jianming Jin
  !
  !  Reference:
  !
  !    Shanjie Zhang, Jianming Jin,
  !    Computation of Special Functions,
  !    Wiley, 1996,
  !    ISBN: 0-471-11963-6,
  !    LC: QA351.C45.
  !
  !  Parameters:
  !
  !    Input, real ( kind = 8 ) X, the argument.
  !
  !    Output, real ( kind = 8 ) E1, the function value.
  !
  implicit none

  real ( kind = 8 ) e1
  real ( kind = 8 ) es1
  real ( kind = 8 ) es2
  real ( kind = 8 ) x

  if ( x == 0.0D+00 ) then

     e1 = 1.0D+300

  else if ( x <= 1.0D+00 ) then

     e1 = - log ( x ) + (((( &
          1.07857D-03 * x &
          - 9.76004D-03 ) * x &
          + 5.519968D-02 ) * x &
          - 0.24991055D+00 ) * x &
          + 0.99999193D+00 ) * x &
          - 0.57721566D+00

  else

     es1 = ((( x &
          + 8.5733287401D+00 ) * x &
          +18.059016973D+00  ) * x &
          + 8.6347608925D+00 ) * x &
          + 0.2677737343D+00

     es2 = ((( x &
          +  9.5733223454D+00 ) * x &
          + 25.6329561486D+00 ) * x &
          + 21.0996530827D+00 ) * x &
          +  3.9584969228D+00

     e1 = exp ( - x ) / x * es1 / es2

  end if

  return
end subroutine e1xa