*DECK GAMLIM SUBROUTINE GAMLIM (XMIN, XMAX) C***BEGIN PROLOGUE GAMLIM C***PURPOSE Compute the minimum and maximum bounds for the argument in C the Gamma function. C***LIBRARY SLATEC (FNLIB) C***CATEGORY C7A, R2 C***TYPE SINGLE PRECISION (GAMLIM-S, DGAMLM-D) C***KEYWORDS COMPLETE GAMMA FUNCTION, FNLIB, LIMITS, SPECIAL FUNCTIONS C***AUTHOR Fullerton, W., (LANL) C***DESCRIPTION C C Calculate the minimum and maximum legal bounds for X in GAMMA(X). C XMIN and XMAX are not the only bounds, but they are the only non- C trivial ones to calculate. C C Output Arguments -- C XMIN minimum legal value of X in GAMMA(X). Any smaller value of C X might result in underflow. C XMAX maximum legal value of X in GAMMA(X). Any larger value will C cause overflow. C C***REFERENCES (NONE) C***ROUTINES CALLED R1MACH, XERMSG C***REVISION HISTORY (YYMMDD) C 770401 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***END PROLOGUE GAMLIM C***FIRST EXECUTABLE STATEMENT GAMLIM ALNSML = LOG(R1MACH(1)) XMIN = -ALNSML DO 10 I=1,10 XOLD = XMIN XLN = LOG(XMIN) XMIN = XMIN - XMIN*((XMIN+0.5)*XLN - XMIN - 0.2258 + ALNSML) 1 / (XMIN*XLN + 0.5) IF (ABS(XMIN-XOLD).LT.0.005) GO TO 20 10 CONTINUE CALL XERMSG ('SLATEC', 'GAMLIM', 'UNABLE TO FIND XMIN', 1, 2) C 20 XMIN = -XMIN + 0.01 C ALNBIG = LOG(R1MACH(2)) XMAX = ALNBIG DO 30 I=1,10 XOLD = XMAX XLN = LOG(XMAX) XMAX = XMAX - XMAX*((XMAX-0.5)*XLN - XMAX + 0.9189 - ALNBIG) 1 / (XMAX*XLN - 0.5) IF (ABS(XMAX-XOLD).LT.0.005) GO TO 40 30 CONTINUE CALL XERMSG ('SLATEC', 'GAMLIM', 'UNABLE TO FIND XMAX', 2, 2) C 40 XMAX = XMAX - 0.01 XMIN = MAX (XMIN, -XMAX+1.) C RETURN END