d9lgmc.f

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*DECK D9LGMC
      DOUBLE PRECISION FUNCTION D9LGMC (X)
C***BEGIN PROLOGUE  D9LGMC
C***SUBSIDIARY
C***PURPOSE  Compute the log Gamma correction factor so that
C            LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X
C            + D9LGMC(X).
C***LIBRARY   SLATEC (FNLIB)
C***CATEGORY  C7E
C***TYPE      DOUBLE PRECISION (R9LGMC-S, D9LGMC-D, C9LGMC-C)
C***KEYWORDS  COMPLETE GAMMA FUNCTION, CORRECTION TERM, FNLIB,
C             LOG GAMMA, LOGARITHM, SPECIAL FUNCTIONS
C***AUTHOR  Fullerton, W., (LANL)
C***DESCRIPTION
C
C Compute the log gamma correction factor for X .GE. 10. so that
C LOG (DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X + D9lGMC(X)
C
C Series for ALGM       on the interval  0.          to  1.00000E-02
C                                        with weighted error   1.28E-31
C                                         log weighted error  30.89
C                               significant figures required  29.81
C                                    decimal places required  31.48
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH, DCSEVL, INITDS, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   770601  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890531  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   900720  Routine changed from user-callable to subsidiary.  (WRB)
C***END PROLOGUE  D9LGMC
      DOUBLE PRECISION X, ALGMCS(15), XBIG, XMAX, DCSEVL, D1MACH
      LOGICAL FIRST
      SAVE ALGMCS, NALGM, XBIG, XMAX, FIRST
      DATA ALGMCS(  1) / +.1666389480 4518632472 0572965082 2 D+0      /
      DATA ALGMCS(  2) / -.1384948176 0675638407 3298605913 5 D-4      /
      DATA ALGMCS(  3) / +.9810825646 9247294261 5717154748 7 D-8      /
      DATA ALGMCS(  4) / -.1809129475 5724941942 6330626671 9 D-10     /
      DATA ALGMCS(  5) / +.6221098041 8926052271 2601554341 6 D-13     /
      DATA ALGMCS(  6) / -.3399615005 4177219443 0333059966 6 D-15     /
      DATA ALGMCS(  7) / +.2683181998 4826987489 5753884666 6 D-17     /
      DATA ALGMCS(  8) / -.2868042435 3346432841 4462239999 9 D-19     /
      DATA ALGMCS(  9) / +.3962837061 0464348036 7930666666 6 D-21     /
      DATA ALGMCS( 10) / -.6831888753 9857668701 1199999999 9 D-23     /
      DATA ALGMCS( 11) / +.1429227355 9424981475 7333333333 3 D-24     /
      DATA ALGMCS( 12) / -.3547598158 1010705471 9999999999 9 D-26     /
      DATA ALGMCS( 13) / +.1025680058 0104709120 0000000000 0 D-27     /
      DATA ALGMCS( 14) / -.3401102254 3167487999 9999999999 9 D-29     /
      DATA ALGMCS( 15) / +.1276642195 6300629333 3333333333 3 D-30     /
      DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT  D9LGMC
      IF (FIRST) THEN
         NALGM = INITDS (ALGMCS, 15, REAL(D1MACH(3)) )
         XBIG = 1.0D0/SQRT(D1MACH(3))
         XMAX = EXP (MIN(LOG(D1MACH(2)/12.D0), -LOG(12.D0*D1MACH(1))))
      ENDIF
      FIRST = .FALSE.
C
      IF (X .LT. 10.D0) CALL XERMSG ('SLATEC', 'D9LGMC',
     +   'X MUST BE GE 10', 1, 2)
      IF (X.GE.XMAX) GO TO 20
C
      D9LGMC = 1.D0/(12.D0*X)
      IF (X.LT.XBIG) D9LGMC = DCSEVL (2.0D0*(10.D0/X)**2-1.D0, ALGMCS,
     1  NALGM) / X
      RETURN
C
 20   D9LGMC = 0.D0
      CALL XERMSG ('SLATEC', 'D9LGMC', 'X SO BIG D9LGMC UNDERFLOWS', 2,
     +   1)
      RETURN
C
      END