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- *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
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