dlngam.f

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*DECK DLNGAM
      DOUBLE PRECISION FUNCTION dlngam (X)
C***BEGIN PROLOGUE  DLNGAM
C***PURPOSE  Compute the logarithm of the absolute value of the Gamma
C            function.
C***LIBRARY   SLATEC (FNLIB)
C***CATEGORY  C7A
C***TYPE      DOUBLE PRECISION (ALNGAM-S, DLNGAM-D, CLNGAM-C)
C***KEYWORDS  ABSOLUTE VALUE, COMPLETE GAMMA FUNCTION, FNLIB, LOGARITHM,
C             SPECIAL FUNCTIONS
C***AUTHOR  Fullerton, W., (LANL)
C***DESCRIPTION
C
C DLNGAM(X) calculates the double precision logarithm of the
C absolute value of the Gamma function for double precision
C argument X.
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH, D9LGMC, DGAMMA, 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   900727  Added EXTERNAL statement.  (WRB)
C***END PROLOGUE  DLNGAM
      DOUBLE PRECISION X, DXREL, PI, SINPIY, SQPI2L, SQ2PIL, XMAX,
     1  y, dgamma, d9lgmc, d1mach, temp
      LOGICAL FIRST
      EXTERNAL dgamma
      SAVE sq2pil, sqpi2l, pi, xmax, dxrel, first
      DATA sq2pil / 0.9189385332 0467274178 0329736405 62 d0 /
      DATA sqpi2l / +.2257913526 4472743236 3097614947 441 d+0    /
      DATA pi / 3.1415926535 8979323846 2643383279 50 d0 /
      DATA first /.true./
C***FIRST EXECUTABLE STATEMENT  DLNGAM
      IF (first) THEN
         temp = 1.d0/log(d1mach(2))
         xmax = temp*d1mach(2)
         dxrel = sqrt(d1mach(4))
      ENDIF
      first = .false.
C
      y = abs(x)
      IF (y.GT.10.d0) go to 20
C
C LOG (ABS (DGAMMA(X)) ) FOR ABS(X) .LE. 10.0
C
      dlngam = log(abs(dgamma(x)) )
      RETURN
C
C LOG ( ABS (DGAMMA(X)) ) FOR ABS(X) .GT. 10.0
C
 20   IF (y .GT. xmax) CALL xermsg('SLATEC', 'DLNGAM',
     +   'ABS(X) SO BIG DLNGAM OVERFLOWS', 2, 2)
C
      IF (x.GT.0.d0) dlngam = sq2pil + (x-0.5d0)*log(x) - x + d9lgmc(y)
      IF (x.GT.0.d0) RETURN
C
      sinpiy = abs(sin(pi*y))
      IF (sinpiy .EQ. 0.d0) CALL xermsg('SLATEC', 'DLNGAM',
     +   'X IS A NEGATIVE INTEGER', 3, 2)
C
      IF (abs((x-aint(x-0.5d0))/x) .LT. dxrel) CALL xermsg('SLATEC',
     +   'DLNGAM',
     +   'ANSWER LT HALF PRECISION BECAUSE X TOO NEAR NEGATIVE INTEGER',
     +   1, 1)
C
      dlngam = sqpi2l + (x-0.5d0)*log(y) - x - log(sinpiy) - d9lgmc(y)
      RETURN
C
      END