*DECK ALNGAM FUNCTION ALNGAM (X) C***BEGIN PROLOGUE ALNGAM C***PURPOSE Compute the logarithm of the absolute value of the Gamma C function. C***LIBRARY SLATEC (FNLIB) C***CATEGORY C7A C***TYPE SINGLE 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 ALNGAM(X) computes the logarithm of the absolute value of the C gamma function at X. C C***REFERENCES (NONE) C***ROUTINES CALLED GAMMA, R1MACH, R9LGMC, 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 900326 Removed duplicate information from DESCRIPTION section. C (WRB) C 900727 Added EXTERNAL statement. (WRB) C***END PROLOGUE ALNGAM LOGICAL FIRST EXTERNAL GAMMA SAVE SQ2PIL, SQPI2L, PI, XMAX, DXREL, FIRST DATA SQ2PIL / 0.9189385332 0467274E0/ DATA SQPI2L / 0.2257913526 4472743E0/ DATA PI / 3.1415926535 8979324E0/ DATA FIRST /.TRUE./ C***FIRST EXECUTABLE STATEMENT ALNGAM IF (FIRST) THEN XMAX = R1MACH(2)/LOG(R1MACH(2)) DXREL = SQRT (R1MACH(4)) ENDIF FIRST = .FALSE. C Y = ABS(X) IF (Y.GT.10.0) GO TO 20 C C LOG (ABS (GAMMA(X))) FOR ABS(X) .LE. 10.0 C ALNGAM = LOG (ABS (GAMMA(X))) RETURN C C LOG (ABS (GAMMA(X))) FOR ABS(X) .GT. 10.0 C 20 IF (Y .GT. XMAX) CALL XERMSG ('SLATEC', 'ALNGAM', + 'ABS(X) SO BIG ALNGAM OVERFLOWS', 2, 2) C IF (X.GT.0.) ALNGAM = SQ2PIL + (X-0.5)*LOG(X) - X + R9LGMC(Y) IF (X.GT.0.) RETURN C SINPIY = ABS (SIN(PI*Y)) IF (SINPIY .EQ. 0.) CALL XERMSG ('SLATEC', 'ALNGAM', + 'X IS A NEGATIVE INTEGER', 3, 2) C IF (ABS((X-AINT(X-0.5))/X) .LT. DXREL) CALL XERMSG ('SLATEC', + 'ALNGAM', 'ANSWER LT HALF PRECISION BECAUSE X TOO NEAR ' // + 'NEGATIVE INTEGER', 1, 1) C ALNGAM = SQPI2L + (X-0.5)*LOG(Y) - X - LOG(SINPIY) - R9LGMC(Y) RETURN C END