slatec-bessel-cpp/fortran/dlngam.f

*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