double precision function dchi (x)
  c december 1980 edition.  w. fullerton, bell labs.
  c
  c evaluate the hyperbolic cosine integral.  when x is negative, the
  c principal value is used.
  c
        double precision x, dei, de1
        external de1, dei
  c
        dchi = 0.5d0 * (dei(x) - de1(x))
  c
        return
        end