double precision function dgamic (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 double precision a, x, aeps, ainta, algap1, alneps, alngs, alx, 1 bot, e, eps, gstar, h, sga, sgng, sgngam, sgngs, sqeps, t, 2 d1mach, dlngam, d9gmic, d9gmit, d9lgic, d9lgit, dint, 3 dexp, dlog, dsqrt external d1mach, d9gmic, d9gmit, d9lgic, d9lgit 1 dlngam c data eps, sqeps, alneps, bot / 4*0.0d0 / c if (eps.ne.0.d0) go to 10 eps = 0.5d0*d1mach(3) sqeps = dsqrt (d1mach(4)) alneps = -dlog (d1mach(3)) bot = dlog (d1mach(1)) c 10 if (x.lt.0.d0) call seteru (21hdgamic x is negative, 21, 2, 2) c if (x.gt.0.d0) go to 20 if (a.le.0.d0) call seteru ( 1 47hdgamic x = 0 and a le 0 so dgamic is undefined, 47, 3, 2) c dgamic = dexp (dlngam(a+1.d0) - dlog(a)) return c 20 alx = dlog (x) sga = 1.0d0 if (a.ne.0.d0) sga = dsign (1.0d0, a) ainta = dint (a + 0.5d0*sga) aeps = a - ainta c izero = 0 if (x.ge.1.0d0) go to 40 c if (a.gt.0.5d0 .or. dabs(aeps).gt.0.001d0) go to 30 e = 2.0d0 if (-ainta.gt.1.d0) e = 2.d0*(-ainta+2.d0)/(ainta*ainta-1.0d0) e = e - alx * x**(-0.001d0) if (e*dabs(aeps).gt.eps) go to 30 c dgamic = d9gmic (a, x, alx) return c 30 call dlgams (a+1.0d0, algap1, sgngam) gstar = d9gmit (a, x, algap1, sgngam, alx) if (gstar.eq.0.d0) izero = 1 if (gstar.ne.0.d0) alngs = dlog (dabs(gstar)) if (gstar.ne.0.d0) sgngs = dsign (1.0d0, gstar) go to 50 c 40 if (a.lt.x) dgamic = dexp (d9lgic(a, x, alx)) if (a.lt.x) return c sgngam = 1.0d0 algap1 = dlngam (a+1.0d0) sgngs = 1.0d0 alngs = d9lgit (a, x, algap1) c c evaluation of dgamic(a,x) in terms of tricomi-s incomplete gamma fn. c 50 h = 1.d0 if (izero.eq.1) go to 60 c t = a*alx + alngs if (t.gt.alneps) go to 70 if (t.gt.(-alneps)) h = 1.0d0 - sgngs*dexp(t) c if (dabs(h).lt.sqeps) call erroff if (dabs(h).lt.sqeps) call seteru ( 1 32hdgamic result lt half precision, 32, 1, 1) c 60 sgng = dsign (1.0d0, h) * sga * sgngam t = dlog(dabs(h)) + algap1 - dlog(dabs(a)) if (t.lt.bot) call erroff dgamic = sgng * dexp(t) return c 70 sgng = -sgngs * sga * sgngam t = t + algap1 - dlog(dabs(a)) if (t.lt.bot) call erroff dgamic = sgng * dexp(t) return c end