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61 lines
2 KiB
Fortran
61 lines
2 KiB
Fortran
*DECK GAMLIM
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SUBROUTINE GAMLIM (XMIN, XMAX)
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C***BEGIN PROLOGUE GAMLIM
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C***PURPOSE Compute the minimum and maximum bounds for the argument in
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C the Gamma function.
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C***LIBRARY SLATEC (FNLIB)
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C***CATEGORY C7A, R2
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C***TYPE SINGLE PRECISION (GAMLIM-S, DGAMLM-D)
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C***KEYWORDS COMPLETE GAMMA FUNCTION, FNLIB, LIMITS, SPECIAL FUNCTIONS
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C***AUTHOR Fullerton, W., (LANL)
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C***DESCRIPTION
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C
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C Calculate the minimum and maximum legal bounds for X in GAMMA(X).
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C XMIN and XMAX are not the only bounds, but they are the only non-
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C trivial ones to calculate.
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C
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C Output Arguments --
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C XMIN minimum legal value of X in GAMMA(X). Any smaller value of
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C X might result in underflow.
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C XMAX maximum legal value of X in GAMMA(X). Any larger value will
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C cause overflow.
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C
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C***REFERENCES (NONE)
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C***ROUTINES CALLED R1MACH, XERMSG
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C***REVISION HISTORY (YYMMDD)
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C 770401 DATE WRITTEN
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C 890531 Changed all specific intrinsics to generic. (WRB)
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C 890531 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
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C***END PROLOGUE GAMLIM
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C***FIRST EXECUTABLE STATEMENT GAMLIM
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ALNSML = LOG(R1MACH(1))
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XMIN = -ALNSML
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DO 10 I=1,10
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XOLD = XMIN
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XLN = LOG(XMIN)
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XMIN = XMIN - XMIN*((XMIN+0.5)*XLN - XMIN - 0.2258 + ALNSML)
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1 / (XMIN*XLN + 0.5)
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IF (ABS(XMIN-XOLD).LT.0.005) GO TO 20
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10 CONTINUE
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CALL XERMSG ('SLATEC', 'GAMLIM', 'UNABLE TO FIND XMIN', 1, 2)
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C
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20 XMIN = -XMIN + 0.01
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C
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ALNBIG = LOG(R1MACH(2))
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XMAX = ALNBIG
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DO 30 I=1,10
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XOLD = XMAX
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XLN = LOG(XMAX)
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XMAX = XMAX - XMAX*((XMAX-0.5)*XLN - XMAX + 0.9189 - ALNBIG)
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1 / (XMAX*XLN - 0.5)
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IF (ABS(XMAX-XOLD).LT.0.005) GO TO 40
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30 CONTINUE
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CALL XERMSG ('SLATEC', 'GAMLIM', 'UNABLE TO FIND XMAX', 2, 2)
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C
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40 XMAX = XMAX - 0.01
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XMIN = MAX (XMIN, -XMAX+1.)
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C
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RETURN
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END
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