      function aie (x)
c july 1977 edition.  w. fullerton, c3, los alamos scientific lab.
c
c evaluate ai(x) for x .le. 0.0 and  ai(x)*exp(zeta)  where
c zeta = 2/3 * x**(3/2)  for x .ge. 0.0
c
      dimension aifcs(9), aigcs(8), aipcs(34)
      external cos, csevl, exp, inits, r1mach, sqrt
c
c series for aif        on the interval -1.00000d+00 to  1.00000d+00
c                                        with weighted error   1.09e-19
c                                         log weighted error  18.96
c                               significant figures required  17.76
c                                    decimal places required  19.44
c
      data aif cs( 1) /   -.0379713584 9666999750e0 /
      data aif cs( 2) /    .0591918885 3726363857e0 /
      data aif cs( 3) /    .0009862928 0577279975e0 /
      data aif cs( 4) /    .0000068488 4381907656e0 /
      data aif cs( 5) /    .0000000259 4202596219e0 /
      data aif cs( 6) /    .0000000000 6176612774e0 /
      data aif cs( 7) /    .0000000000 0010092454e0 /
      data aif cs( 8) /    .0000000000 0000012014e0 /
      data aif cs( 9) /    .0000000000 0000000010e0 /
c
c series for aig        on the interval -1.00000d+00 to  1.00000d+00
c                                        with weighted error   1.51e-17
c                                         log weighted error  16.82
c                               significant figures required  15.19
c                                    decimal places required  17.27
c
      data aig cs( 1) /    .0181523655 8116127e0 /
      data aig cs( 2) /    .0215725631 6601076e0 /
      data aig cs( 3) /    .0002567835 6987483e0 /
      data aig cs( 4) /    .0000014265 2141197e0 /
      data aig cs( 5) /    .0000000045 7211492e0 /
      data aig cs( 6) /    .0000000000 0952517e0 /
      data aig cs( 7) /    .0000000000 0001392e0 /
      data aig cs( 8) /    .0000000000 0000001e0 /
c
c series for aip        on the interval  0.          to  1.00000d+00
c                                        with weighted error   5.10e-17
c                                         log weighted error  16.29
c                               significant figures required  14.41
c                                    decimal places required  17.06
c
      data aip cs( 1) /   -.0187519297 793868e0 /
      data aip cs( 2) /   -.0091443848 250055e0 /
      data aip cs( 3) /    .0009010457 337825e0 /
      data aip cs( 4) /   -.0001394184 127221e0 /
      data aip cs( 5) /    .0000273815 815785e0 /
      data aip cs( 6) /   -.0000062750 421119e0 /
      data aip cs( 7) /    .0000016064 844184e0 /
      data aip cs( 8) /   -.0000004476 392158e0 /
      data aip cs( 9) /    .0000001334 635874e0 /
      data aip cs(10) /   -.0000000420 735334e0 /
      data aip cs(11) /    .0000000139 021990e0 /
      data aip cs(12) /   -.0000000047 831848e0 /
      data aip cs(13) /    .0000000017 047897e0 /
      data aip cs(14) /   -.0000000006 268389e0 /
      data aip cs(15) /    .0000000002 369824e0 /
      data aip cs(16) /   -.0000000000 918641e0 /
      data aip cs(17) /    .0000000000 364278e0 /
      data aip cs(18) /   -.0000000000 147475e0 /
      data aip cs(19) /    .0000000000 060851e0 /
      data aip cs(20) /   -.0000000000 025552e0 /
      data aip cs(21) /    .0000000000 010906e0 /
      data aip cs(22) /   -.0000000000 004725e0 /
      data aip cs(23) /    .0000000000 002076e0 /
      data aip cs(24) /   -.0000000000 000924e0 /
      data aip cs(25) /    .0000000000 000417e0 /
      data aip cs(26) /   -.0000000000 000190e0 /
      data aip cs(27) /    .0000000000 000087e0 /
      data aip cs(28) /   -.0000000000 000040e0 /
      data aip cs(29) /    .0000000000 000019e0 /
      data aip cs(30) /   -.0000000000 000009e0 /
      data aip cs(31) /    .0000000000 000004e0 /
      data aip cs(32) /   -.0000000000 000002e0 /
      data aip cs(33) /    .0000000000 000001e0 /
      data aip cs(34) /   -.0000000000 000000e0 /
c
      data naif, naig, naip / 3*0 /
      data x3sml, x32sml, xbig / 3*0.0 /
c
      if (naif.ne.0) go to 10
      eta = 0.1*r1mach(3)
      naif  = inits (aifcs , 9, eta)
      naig  = inits (aigcs , 8, eta)
      naip  = inits (aipcs , 34, eta)
c
      x3sml = eta**0.3333
      x32sml = 1.3104*x3sml**2
      xbig = r1mach(2)**0.6666
c
 10   if (x.ge.(-1.0)) go to 20
      call r9aimp (x, xm, theta)
      aie = xm * cos(theta)
      return
c
 20   if (x.gt.1.0) go to 30
      z = 0.0
      if (abs(x).gt.x3sml) z = x**3
      aie = 0.375 + (csevl (z, aifcs, naif) - x*(0.25 +
     1  csevl (z, aigcs, naig)) )
      if (x.gt.x32sml) aie = aie * exp(2.0*x*sqrt(x)/3.0)
      return
c
 30   sqrtx = sqrt(x)
      z = -1.0
      if (x.lt.xbig) z = 2.0/(x*sqrtx) - 1.0
      aie = (.28125 + csevl (z, aipcs, naip))/sqrt(sqrtx)
      return
c
      end