gamlim.f

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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