dgamma.f

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*DECK DGAMMA
      DOUBLE PRECISION FUNCTION dgamma (X)
C***BEGIN PROLOGUE  DGAMMA
C***PURPOSE  Compute the complete Gamma function.
C***LIBRARY   SLATEC (FNLIB)
C***CATEGORY  C7A
C***TYPE      DOUBLE PRECISION (GAMMA-S, DGAMMA-D, CGAMMA-C)
C***KEYWORDS  COMPLETE GAMMA FUNCTION, FNLIB, SPECIAL FUNCTIONS
C***AUTHOR  Fullerton, W., (LANL)
C***DESCRIPTION
C
C DGAMMA(X) calculates the double precision complete Gamma function
C for double precision argument X.
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
C***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH, D9LGMC, DCSEVL, DGAMLM, INITDS, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   770601  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890911  Removed unnecessary intrinsics.  (WRB)
C   890911  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
C   920618  Removed space from variable name.  (RWC, WRB)
C***END PROLOGUE  DGAMMA
      DOUBLE PRECISION X, GAMCS(42), DXREL, PI, SINPIY, SQ2PIL, XMAX,
     1  xmin, y, d9lgmc, dcsevl, d1mach
      LOGICAL FIRST
C
      SAVE gamcs, pi, sq2pil, ngam, xmin, xmax, dxrel, first
      DATA gamcs(  1) / +.8571195590 9893314219 2006239994 2 d-2      /
      DATA gamcs(  2) / +.4415381324 8410067571 9131577165 2 d-2      /
      DATA gamcs(  3) / +.5685043681 5993633786 3266458878 9 d-1      /
      DATA gamcs(  4) / -.4219835396 4185605010 1250018662 4 d-2      /
      DATA gamcs(  5) / +.1326808181 2124602205 8400679635 2 d-2      /
      DATA gamcs(  6) / -.1893024529 7988804325 2394702388 6 d-3      /
      DATA gamcs(  7) / +.3606925327 4412452565 7808221722 5 d-4      /
      DATA gamcs(  8) / -.6056761904 4608642184 8554829036 5 d-5      /
      DATA gamcs(  9) / +.1055829546 3022833447 3182350909 3 d-5      /
      DATA gamcs( 10) / -.1811967365 5423840482 9185589116 6 d-6      /
      DATA gamcs( 11) / +.3117724964 7153222777 9025459316 9 d-7      /
      DATA gamcs( 12) / -.5354219639 0196871408 7408102434 7 d-8      /
      DATA gamcs( 13) / +.9193275519 8595889468 8778682594 0 d-9      /
      DATA gamcs( 14) / -.1577941280 2883397617 6742327395 3 d-9      /
      DATA gamcs( 15) / +.2707980622 9349545432 6654043308 9 d-10     /
      DATA gamcs( 16) / -.4646818653 8257301440 8166105893 3 d-11     /
      DATA gamcs( 17) / +.7973350192 0074196564 6076717535 9 d-12     /
      DATA gamcs( 18) / -.1368078209 8309160257 9949917230 9 d-12     /
      DATA gamcs( 19) / +.2347319486 5638006572 3347177168 8 d-13     /
      DATA gamcs( 20) / -.4027432614 9490669327 6657053469 9 d-14     /
      DATA gamcs( 21) / +.6910051747 3721009121 3833697525 7 d-15     /
      DATA gamcs( 22) / -.1185584500 2219929070 5238712619 2 d-15     /
      DATA gamcs( 23) / +.2034148542 4963739552 0102605193 2 d-16     /
      DATA gamcs( 24) / -.3490054341 7174058492 7401294910 8 d-17     /
      DATA gamcs( 25) / +.5987993856 4853055671 3505106602 6 d-18     /
      DATA gamcs( 26) / -.1027378057 8722280744 9006977843 1 d-18     /
      DATA gamcs( 27) / +.1762702816 0605298249 4275966074 8 d-19     /
      DATA gamcs( 28) / -.3024320653 7353062609 5877211204 2 d-20     /
      DATA gamcs( 29) / +.5188914660 2183978397 1783355050 6 d-21     /
      DATA gamcs( 30) / -.8902770842 4565766924 4925160106 6 d-22     /
      DATA gamcs( 31) / +.1527474068 4933426022 7459689130 6 d-22     /
      DATA gamcs( 32) / -.2620731256 1873629002 5732833279 9 d-23     /
      DATA gamcs( 33) / +.4496464047 8305386703 3104657066 6 d-24     /
      DATA gamcs( 34) / -.7714712731 3368779117 0390152533 3 d-25     /
      DATA gamcs( 35) / +.1323635453 1260440364 8657271466 6 d-25     /
      DATA gamcs( 36) / -.2270999412 9429288167 0231381333 3 d-26     /
      DATA gamcs( 37) / +.3896418998 0039914493 2081663999 9 d-27     /
      DATA gamcs( 38) / -.6685198115 1259533277 9212799999 9 d-28     /
      DATA gamcs( 39) / +.1146998663 1400243843 4761386666 6 d-28     /
      DATA gamcs( 40) / -.1967938586 3451346772 9510399999 9 d-29     /
      DATA gamcs( 41) / +.3376448816 5853380903 3489066666 6 d-30     /
      DATA gamcs( 42) / -.5793070335 7821357846 2549333333 3 d-31     /
      DATA pi / 3.1415926535 8979323846 2643383279 50 d0 /
      DATA sq2pil / 0.9189385332 0467274178 0329736405 62 d0 /
      DATA first /.true./
C***FIRST EXECUTABLE STATEMENT  DGAMMA
      IF (first) THEN
         ngam = initds(gamcs, 42, 0.1*REAL(D1MACH(3)) )
C
         CALL dgamlm(xmin, xmax)
         dxrel = sqrt(d1mach(4))
      ENDIF
      first = .false.
C
      y = abs(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 - 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 xermsg('SLATEC', 'DGAMMA', 'X IS 0', 4, 2)
      IF (x .LT. 0.0 .AND. x+n-2 .EQ. 0.d0) CALL xermsg('SLATEC',
     +   'DGAMMA', 'X IS A NEGATIVE INTEGER', 4, 2)
      IF (x .LT. (-0.5d0) .AND. abs((x-aint(x-0.5d0))/x) .LT. dxrel)
     +   CALL xermsg('SLATEC', 'DGAMMA',
     +   'ANSWER LT HALF PRECISION BECAUSE X TOO NEAR NEGATIVE INTEGER',
     +   1, 1)
C
      DO 20 i=1,n
        dgamma = dgamma/(x+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+i) * dgamma
 40   CONTINUE
      RETURN
C
C GAMMA(X) FOR ABS(X) .GT. 10.0.  RECALL Y = ABS(X).
C
 50   IF (x .GT. xmax) CALL xermsg('SLATEC', 'DGAMMA',
     +   'X SO BIG GAMMA OVERFLOWS', 3, 2)
C
      dgamma = 0.d0
      IF (x .LT. xmin) CALL xermsg('SLATEC', 'DGAMMA',
     +   'X SO SMALL GAMMA UNDERFLOWS', 2, 1)
      IF (x.LT.xmin) RETURN
C
      dgamma = exp((y-0.5d0)*log(y) - y + sq2pil + d9lgmc(y) )
      IF (x.GT.0.d0) RETURN
C
      IF (abs((x-aint(x-0.5d0))/x) .LT. dxrel) CALL xermsg('SLATEC',
     +   'DGAMMA',
     +   'ANSWER LT HALF PRECISION, X TOO NEAR NEGATIVE INTEGER', 1, 1)
C
      sinpiy = sin(pi*y)
      IF (sinpiy .EQ. 0.d0) CALL xermsg('SLATEC', 'DGAMMA',
     +   'X IS A NEGATIVE INTEGER', 4, 2)
C
      dgamma = -pi/(y*sinpiy*dgamma)
C
      RETURN
      END