double precision function dcinh (x)
c december 1980 edition.  w. fullerton, bell labs.
c
c evaluate the hyperbolic cin function.
c           cinh(x) = integral from 0 to x of  (cosh(t)-1)/t dt.
c
      double precision x, cinhcs(16), eul, xsml, xmin, absx, y,
     1  dchi, dcsevl, d1mach, dlog, dsqrt
      external d1mach, dchi, dcsevl, dlog, dsqrt, initds
c
c series for cinh on the interval  0.00000e+00 to  9.00000e+00
c                                        with weighted error   4.84e-32
c                                         log weighted error  31.32
c                               significant figures required  30.21
c                                    decimal places required  31.92
c
      data cinhcs(  1) /     0.1093291636 5207344314 0742519979 5917d0/
      data cinhcs(  2) /     0.0573928847 5503796764 4532342982 5108d0/
      data cinhcs(  3) /     0.0028095756 9788303534 1640420894 0774d0/
      data cinhcs(  4) /     0.0000828780 8407213566 5573176506 9792d0/
      data cinhcs(  5) /     0.0000016278 5961739141 8557772601 8815d0/
      data cinhcs(  6) /     0.0000000227 8095192558 5661985908 3591d0/
      data cinhcs(  7) /     0.0000000002 3844848424 6305925728 4002d0/
      data cinhcs(  8) /     0.0000000000 0193608297 8078195747 1028d0/
      data cinhcs(  9) /     0.0000000000 0001254536 9832817255 9683d0/
      data cinhcs( 10) /     0.0000000000 0000006636 3744949726 2300d0/
      data cinhcs( 11) /     0.0000000000 0000000029 1963926359 4744d0/
      data cinhcs( 12) /     0.0000000000 0000000000 1084912395 6107d0/
      data cinhcs( 13) /     0.0000000000 0000000000 0003449908 0805d0/
      data cinhcs( 14) /     0.0000000000 0000000000 0000009493 6664d0/
      data cinhcs( 15) /     0.0000000000 0000000000 0000000022 8291d0/
      data cinhcs( 16) /     0.0000000000 0000000000 0000000000 0484d0/
c
      data eul / 0.5772156649 0153286060 6512090082 40 d0 /
      data ncinh, xsml, xmin /0, 2*0.0d0/
c
      if (ncinh.ne.0) go to 10
      ncinh = initds (cinhcs, 16, 0.1*sngl(d1mach(3)))
      xsml = dsqrt (d1mach(3))
      xmin = 2.0d0*dsqrt(d1mach(1))
c
 10   absx = dabs(x)
      if (absx.gt.3.0d0) go to 20
c
      dcinh = 0.0d0
      if (x.ne.0.d0 .and. absx.le.xmin) call seteru (
     1  39hdcinh   abs(x) so small cinh underflows, 39, 1, 0)
      if (absx.le.xmin) return
c
      y = -1.0d0
      if (absx.gt.xsml) y = x*x/9.d0 - 1.0d0
      dcinh = x*x* (0.25d0 + dcsevl (y, cinhcs, ncinh))
      return
c
 20   dcinh = dchi(absx) - eul - dlog(absx)
c
      return
      end