double precision function dgamma (x) c jan 1984 edition. w. fullerton, c3, los alamos scientific lab. c jan 1994 wpp@ips.id.ethz.ch, ehg@research.att.com declare xsml double precision x, gamcs(42), dxrel, pi, sinpiy, sq2pil, xmax, 1 xmin, y, d9lgmc, dcsevl, d1mach, dexp, dint, dlog, 2 dsin, dsqrt, xsml external d1mach, d9lgmc, dcsevl, dexp, dint, dlog, dsin, dsqrt, 1 initds c c series for gam on the interval 0. to 1.00000e+00 c with weighted error 5.79e-32 c log weighted error 31.24 c significant figures required 30.00 c decimal places required 32.05 c data gam cs( 1) / +.8571195590 9893314219 2006239994 2 d-2 / data gam cs( 2) / +.4415381324 8410067571 9131577165 2 d-2 / data gam cs( 3) / +.5685043681 5993633786 3266458878 9 d-1 / data gam cs( 4) / -.4219835396 4185605010 1250018662 4 d-2 / data gam cs( 5) / +.1326808181 2124602205 8400679635 2 d-2 / data gam cs( 6) / -.1893024529 7988804325 2394702388 6 d-3 / data gam cs( 7) / +.3606925327 4412452565 7808221722 5 d-4 / data gam cs( 8) / -.6056761904 4608642184 8554829036 5 d-5 / data gam cs( 9) / +.1055829546 3022833447 3182350909 3 d-5 / data gam cs( 10) / -.1811967365 5423840482 9185589116 6 d-6 / data gam cs( 11) / +.3117724964 7153222777 9025459316 9 d-7 / data gam cs( 12) / -.5354219639 0196871408 7408102434 7 d-8 / data gam cs( 13) / +.9193275519 8595889468 8778682594 0 d-9 / data gam cs( 14) / -.1577941280 2883397617 6742327395 3 d-9 / data gam cs( 15) / +.2707980622 9349545432 6654043308 9 d-10 / data gam cs( 16) / -.4646818653 8257301440 8166105893 3 d-11 / data gam cs( 17) / +.7973350192 0074196564 6076717535 9 d-12 / data gam cs( 18) / -.1368078209 8309160257 9949917230 9 d-12 / data gam cs( 19) / +.2347319486 5638006572 3347177168 8 d-13 / data gam cs( 20) / -.4027432614 9490669327 6657053469 9 d-14 / data gam cs( 21) / +.6910051747 3721009121 3833697525 7 d-15 / data gam cs( 22) / -.1185584500 2219929070 5238712619 2 d-15 / data gam cs( 23) / +.2034148542 4963739552 0102605193 2 d-16 / data gam cs( 24) / -.3490054341 7174058492 7401294910 8 d-17 / data gam cs( 25) / +.5987993856 4853055671 3505106602 6 d-18 / data gam cs( 26) / -.1027378057 8722280744 9006977843 1 d-18 / data gam cs( 27) / +.1762702816 0605298249 4275966074 8 d-19 / data gam cs( 28) / -.3024320653 7353062609 5877211204 2 d-20 / data gam cs( 29) / +.5188914660 2183978397 1783355050 6 d-21 / data gam cs( 30) / -.8902770842 4565766924 4925160106 6 d-22 / data gam cs( 31) / +.1527474068 4933426022 7459689130 6 d-22 / data gam cs( 32) / -.2620731256 1873629002 5732833279 9 d-23 / data gam cs( 33) / +.4496464047 8305386703 3104657066 6 d-24 / data gam cs( 34) / -.7714712731 3368779117 0390152533 3 d-25 / data gam cs( 35) / +.1323635453 1260440364 8657271466 6 d-25 / data gam cs( 36) / -.2270999412 9429288167 0231381333 3 d-26 / data gam cs( 37) / +.3896418998 0039914493 2081663999 9 d-27 / data gam cs( 38) / -.6685198115 1259533277 9212799999 9 d-28 / data gam cs( 39) / +.1146998663 1400243843 4761386666 6 d-28 / data gam cs( 40) / -.1967938586 3451346772 9510399999 9 d-29 / data gam cs( 41) / +.3376448816 5853380903 3489066666 6 d-30 / data gam cs( 42) / -.5793070335 7821357846 2549333333 3 d-31 / c data pi / 3.1415926535 8979323846 2643383279 50 d0 / c sq2pil is 0.5*alog(2*pi) = alog(sqrt(2*pi)) data sq2pil / 0.9189385332 0467274178 0329736405 62 d0 / data ngam, xmin, xmax, xsml, dxrel / 0, 4*0.d0 / c if (ngam.ne.0) go to 10 ngam = initds (gamcs, 42, 0.1*sngl(d1mach(3)) ) c call d9gaml (xmin, xmax) xsml = dexp (dmax1 (dlog(d1mach(1)), -dlog(d1mach(2)))+0.01d0) dxrel = dsqrt (d1mach(4)) c 10 y = dabs(x) if (y.gt.10.d0) go to 50 c c compute gamma(x) for -xbnd .le. x .le. xbnd. reduce interval and find c gamma(1+y) for 0.0 .le. y .lt. 1.0 first of all. c n = x if (x.lt.0.d0) n = n - 1 y = x - dble(float(n)) n = n - 1 dgamma = 0.9375d0 + dcsevl (2.d0*y-1.d0, gamcs, ngam) if (n.eq.0) return c if (n.gt.0) go to 30 c c compute gamma(x) for x .lt. 1.0 c n = -n if (x.eq.0.d0) call seteru (14hdgamma x is 0, 14, 4, 2) if (x.lt.0.0d0 .and. x+dble(float(n-2)).eq.0.d0) call seteru ( 1 31hdgamma x is a negative integer, 31, 4, 2) if (x.lt.(-0.5d0) .and. dabs((x-dint(x-0.5d0))/x).lt.dxrel) call 1 seteru (68hdgamma answer lt half precision because x too near n 2egative integer, 68, 1, 1) if (y.lt.xsml) call seteru ( 1 54hdgamma x is so close to 0.0 that the result overflows, 2 54, 5, 2) c do 20 i=1,n dgamma = dgamma/(x+dble(float(i-1)) ) 20 continue return c c gamma(x) for x .ge. 2.0 and x .le. 10.0 c 30 do 40 i=1,n dgamma = (y+dble(float(i))) * dgamma 40 continue return c c gamma(x) for dabs(x) .gt. 10.0. recall y = dabs(x). c 50 if (x.gt.xmax) call seteru (32hdgamma x so big gamma overflows, 1 32, 3, 2) c dgamma = 0.d0 if (x.lt.xmin) call seteru (35hdgamma x so small gamma underflows 1 , 35, 2, 0) if (x.lt.xmin) return c dgamma = dexp ((y-0.5d0)*dlog(y) - y + sq2pil + d9lgmc(y) ) if (x.gt.0.d0) return c if (dabs((x-dint(x-0.5d0))/x).lt.dxrel) call seteru ( 1 61hdgamma answer lt half precision, x too near negative integer 2 , 61, 1, 1) c sinpiy = dsin (pi*y) if (sinpiy.eq.0.d0) call seteru ( 1 31hdgamma x is a negative integer, 31, 4, 2) c dgamma = -pi/(y*sinpiy*dgamma) c return end