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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
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