function gamic (a, x)
  c july 1977 edition.  w. fullerton, c3, los alamos scientific lab.
  c
  c evaluate the complementary incomplete gamma function
  c
  c gamic = integral from t = x to infinity of exp(-t) * t**(a-1.)  .
  c
  c gamic is evaluated for arbitrary real values of a and for non-negative
  c values of x (even though gamic is defined for x .lt. 0.0), except that
  c for x = 0 and a .le. 0.0, gamic is undefined.
  c
  c      a slight deterioration of 2 or 3 digits accuracy will occur when
  c gamic is very large or very small in absolute value, because log-
  c arithmic variables are used.  also, if the parameter a is very close
  c to a negative integer (but not a negative integer), there is a loss
  c of accuracy, which is reported if the result is less than half
  c machine precision.
  c
  c ref. -- w. gautschi, an evaluation procedure for incomplete gamma
  c functions, acm trans. math. software.
  c
        external alngam,  r1mach, r9gmic, r9gmit, r9lgic,
       1  r9lgit
        data eps, sqeps, alneps, bot / 4*0.0 /
  c
        if (eps.ne.0.) go to 10
        eps = 0.5*r1mach(3)
        sqeps = sqrt(r1mach(4))
        alneps = -alog(r1mach(3))
        bot = alog(r1mach(1))
  c
   10   if (x.lt.0.0) call seteru (21hgamic   x is negative, 21, 2, 2)
  c
        if (x.gt.0.0) go to 20
        if (a.le.0.0) call seteru (
       1  46hgamic   x = 0 and a le 0 so gamic is undefined, 46, 3, 2)
  c
        gamic = exp (alngam(a+1.0) - alog(a))
        return
  c
   20   alx = alog(x)
        sga = 1.0
        if (a.ne.0.0) sga = sign (1.0, a)
        ma = a + 0.5*sga
        aeps = a - float(ma)
  c
        izero = 0
        if (x.ge.1.0) go to 60
  c
        if (a.gt.0.5 .or. abs(aeps).gt.0.001) go to 50
        fm = -ma
        e = 2.0
        if (fm.gt.1.0) e = 2.0*(fm+2.0)/(fm*fm-1.0)
        e = e - alx*x**(-0.001)
        if (e*abs(aeps).gt.eps) go to 50
  c
        gamic = r9gmic (a, x, alx)
        return
  c
   50   call algams (a+1.0, algap1, sgngam)
        gstar = r9gmit (a, x, algap1, sgngam, alx)
        if (gstar.eq.0.0) izero = 1
        if (gstar.ne.0.0) alngs = alog (abs(gstar))
        if (gstar.ne.0.0) sgngs = sign (1.0, gstar)
        go to 70
  c
   60   if (a.lt.x) gamic = exp (r9lgic(a, x, alx))
        if (a.lt.x) return
  c
        sgngam = 1.0
        algap1 = alngam (a+1.0)
        sgngs = 1.0
        alngs = r9lgit (a, x, algap1)
  c
  c evaluation of gamic(a,x) in terms of tricomi-s incomplete gamma fn.
  c
   70   h = 1.0
        if (izero.eq.1) go to 80
  c
        t = a*alx + alngs
        if (t.gt.alneps) go to 90
        if (t.gt.(-alneps)) h = 1.0 - sgngs*exp(t)
  c
        if (abs(h).lt.sqeps) call erroff
        if (abs(h).lt.sqeps) call seteru (
       1  32hgamic   result lt half precision, 32, 1, 1)
  c
   80   sgng = sign (1.0, h) * sga * sgngam
        t = alog(abs(h)) + algap1 - alog(abs(a))
        if (t.lt.bot) call erroff
        gamic = sgng * exp(t)
        return
  c
   90   sgng = -sgngs * sga * sgngam
        t = t + algap1 - alog(abs(a))
        if (t.lt.bot) call erroff
        gamic = sgng * exp(t)
        return
  c
        end