complex function clngam (zin) c august 1980 edition. w. fullerton c3, los alamos scientific lab. c eventually clngam should make use of c8lgmc for all z except for c z in the vicinity of 1 and 2. complex zin, z, corr, cexp, clog, clnrel, c9lgmc external c9lgmc, carg, clnrel, 1 r1mach data pi / 3.1415926535 8979324e0 / data sq2pil / 0.9189385332 0467274e0 / c data bound, dxrel, rmax / 3*0.0 / c if (bound.ne.0.) go to 10 n = -0.30*alog(r1mach(3)) c bound = n*(0.1*eps)**(-1/(2*n-1))/(pi*exp(1)) bound = 0.1171*float(n)*(0.1*r1mach(3))**(-1./(2.*float(n)-1.)) dxrel = sqrt (r1mach(4)) rmax = r1mach(2)/alog(r1mach(2)) c 10 z = zin x = real(zin) y = aimag(zin) c corr = (0.0, 0.0) cabsz = cabs(z) if (cabsz.gt.rmax) call seteru ( 1 44hclngam cabs(z) so large result may overflow, 44, 2, 2) if (x.ge.0.0 .and. cabsz.gt.bound) go to 50 if (x.lt.0.0 .and. abs(y).gt.bound) go to 50 c if (cabsz.lt.bound) go to 20 c c use the reflection formula for real(z) negative, cabs(z) large, and c abs(aimag(y)) small. c call entsrc (irold, 1) if (y.gt.0.0) z = conjg (z) corr = cexp (-cmplx(0.0,2.0*pi)*z) if (real(corr).eq.1.0 .and. aimag(corr).eq.0.0) call seteru ( 1 31hclngam z is a negative integer, 31, 3, 2) c clngam = sq2pil + 1.0 - cmplx(0.0,pi)*(z-0.5) - clnrel(-corr) 1 + (z-0.5)*clog(1.0-z) - z - c9lgmc(1.0-z) if (y.gt.0.0) clngam = conjg (clngam) c call erroff call entsrc (ir, irold) if (abs(y).gt.dxrel) return c X in sequence field on next line is to preserve trailing blank if (0.5*cabs((1.-corr)*clngam/z).lt.dxrel) call seteru (68hclngam X 1 answer lt half precision because z too near negative integer, 68, 2 1, 1) return c c use the recursion relation for cabs(z) small. c 20 if (x.ge.(-0.5) .or. abs(y).gt.dxrel) go to 30 if (cabs((z-aint(x-0.5))/x).lt.dxrel) call seteru ( 68hclngam ans 1wer lt half precision because z too near negative integer, 68,1,1) c 30 n = sqrt (bound**2 - y**2) - x + 1.0 argsum = 0.0 corr = (1.0, 0.0) do 40 i=1,n argsum = argsum + carg(z) corr = z*corr z = 1.0 + z 40 continue c if (real(corr).eq.0.0 .and. aimag(corr).eq.0.0) call seteru ( 1 31hclngam z is a negative integer, 31, 3, 2) corr = -cmplx (alog(cabs(corr)), argsum) c c use stirling-s approximation for large z. c 50 clngam = sq2pil + (z-0.5)*clog(z) - z + corr + c9lgmc(z) return c end