      function alnrel (x)
c april 1977 version.  w. fullerton, c3, los alamos scientific lab.
      dimension alnrcs(23)
      external alog, csevl, inits, r1mach, sqrt
c
c series for alnr       on the interval -3.75000d-01 to  3.75000d-01
c                                        with weighted error   1.93e-17
c                                         log weighted error  16.72
c                               significant figures required  16.44
c                                    decimal places required  17.40
c
      data alnrcs( 1) /   1.0378693562 743770e0 /
      data alnrcs( 2) /   -.1336430150 4908918e0 /
      data alnrcs( 3) /    .0194082491 35520563e0 /
      data alnrcs( 4) /   -.0030107551 12753577e0 /
      data alnrcs( 5) /    .0004869461 47971548e0 /
      data alnrcs( 6) /   -.0000810548 81893175e0 /
      data alnrcs( 7) /    .0000137788 47799559e0 /
      data alnrcs( 8) /   -.0000023802 21089435e0 /
      data alnrcs( 9) /    .0000004164 04162138e0 /
      data alnrcs(10) /   -.0000000735 95828378e0 /
      data alnrcs(11) /    .0000000131 17611876e0 /
      data alnrcs(12) /   -.0000000023 54670931e0 /
      data alnrcs(13) /    .0000000004 25227732e0 /
      data alnrcs(14) /   -.0000000000 77190894e0 /
      data alnrcs(15) /    .0000000000 14075746e0 /
      data alnrcs(16) /   -.0000000000 02576907e0 /
      data alnrcs(17) /    .0000000000 00473424e0 /
      data alnrcs(18) /   -.0000000000 00087249e0 /
      data alnrcs(19) /    .0000000000 00016124e0 /
      data alnrcs(20) /   -.0000000000 00002987e0 /
      data alnrcs(21) /    .0000000000 00000554e0 /
      data alnrcs(22) /   -.0000000000 00000103e0 /
      data alnrcs(23) /    .0000000000 00000019e0 /
c
      data nlnrel, xmin /0, 0./
c
      if (nlnrel.ne.0) go to 10
      nlnrel = inits (alnrcs, 23, 0.1*r1mach(3))
      xmin = -1.0 + sqrt(r1mach(4))
c
 10   if (x.le.(-1.0)) call seteru (
     1  18halnrel  x is le -1, 18, 2, 2)
      if (x.lt.xmin) call seteru (
     1  54halnrel  answer lt half precision because x too near -1, 54,
     2  1, 1)
c
      if (abs(x).le.0.375) alnrel = x*(1. -
     1  x*csevl (x/.375, alnrcs, nlnrel))
      if (abs(x).gt.0.375) alnrel = alog (1.0+x)
c
      return
      end