dgamit.f

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*DECK DGAMIT
      DOUBLE PRECISION FUNCTION DGAMIT (A, X)
C***BEGIN PROLOGUE  DGAMIT
C***PURPOSE  Calculate Tricomi's form of the incomplete Gamma function.
C***LIBRARY   SLATEC (FNLIB)
C***CATEGORY  C7E
C***TYPE      DOUBLE PRECISION (GAMIT-S, DGAMIT-D)
C***KEYWORDS  COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB,
C             SPECIAL FUNCTIONS, TRICOMI
C***AUTHOR  Fullerton, W., (LANL)
C***DESCRIPTION
C
C   Evaluate Tricomi's incomplete Gamma function defined by
C
C   DGAMIT = X**(-A)/GAMMA(A) * integral from 0 to X of EXP(-T) *
C              T**(A-1.)
C
C   for A .GT. 0.0 and by analytic continuation for A .LE. 0.0.
C   GAMMA(X) is the complete gamma function of X.
C
C   DGAMIT is evaluated for arbitrary real values of A and for non-
C   negative values of X (even though DGAMIT is defined for X .LT.
C   0.0), except that for X = 0 and A .LE. 0.0, DGAMIT is infinite,
C   which is a fatal error.
C
C   The function and both arguments are DOUBLE PRECISION.
C
C   A slight deterioration of 2 or 3 digits accuracy will occur when
C   DGAMIT is very large or very small in absolute value, because log-
C   arithmic variables are used.  Also, if the parameter  A  is very
C   close to a negative integer (but not a negative integer), there is
C   a loss of accuracy, which is reported if the result is less than
C   half machine precision.
C
C***REFERENCES  W. Gautschi, A computational procedure for incomplete
C                 gamma functions, ACM Transactions on Mathematical
C                 Software 5, 4 (December 1979), pp. 466-481.
C               W. Gautschi, Incomplete gamma functions, Algorithm 542,
C                 ACM Transactions on Mathematical Software 5, 4
C                 (December 1979), pp. 482-489.
C***ROUTINES CALLED  D1MACH, D9GMIT, D9LGIC, D9LGIT, DGAMR, DLGAMS,
C                    DLNGAM, XERCLR, XERMSG
C***REVISION HISTORY  (YYMMDD)
C   770701  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   920528  DESCRIPTION and REFERENCES sections revised.  (WRB)
C***END PROLOGUE  DGAMIT
      DOUBLE PRECISION A, X, AEPS, AINTA, ALGAP1, ALNEPS, ALNG, ALX,
     1  BOT, H, SGA, SGNGAM, SQEPS, T, D1MACH, DGAMR, D9GMIT, D9LGIT,
     2  DLNGAM, D9LGIC
      LOGICAL FIRST
      SAVE ALNEPS, SQEPS, BOT, FIRST
      DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT  DGAMIT
      IF (FIRST) THEN
         ALNEPS = -LOG (D1MACH(3))
         SQEPS = SQRT(D1MACH(4))
         BOT = LOG (D1MACH(1))
      ENDIF
      FIRST = .FALSE.
C
      IF (X .LT. 0.D0) CALL XERMSG ('SLATEC', 'DGAMIT', 'X IS NEGATIVE'
     +   , 2, 2)
C
      IF (X.NE.0.D0) ALX = LOG (X)
      SGA = 1.0D0
      IF (A.NE.0.D0) SGA = SIGN (1.0D0, A)
      AINTA = AINT (A + 0.5D0*SGA)
      AEPS = A - AINTA
C
      IF (X.GT.0.D0) GO TO 20
      DGAMIT = 0.0D0
      IF (AINTA.GT.0.D0 .OR. AEPS.NE.0.D0) DGAMIT = DGAMR(A+1.0D0)
      RETURN
C
 20   IF (X.GT.1.D0) GO TO 30
      IF (A.GE.(-0.5D0) .OR. AEPS.NE.0.D0) CALL DLGAMS (A+1.0D0, ALGAP1,
     1  SGNGAM)
      DGAMIT = D9GMIT (A, X, ALGAP1, SGNGAM, ALX)
      RETURN
C
 30   IF (A.LT.X) GO TO 40
      T = D9LGIT (A, X, DLNGAM(A+1.0D0))
      IF (T.LT.BOT) CALL XERCLR
      DGAMIT = EXP (T)
      RETURN
C
 40   ALNG = D9LGIC (A, X, ALX)
C
C EVALUATE DGAMIT IN TERMS OF LOG (DGAMIC (A, X))
C
      H = 1.0D0
      IF (AEPS.EQ.0.D0 .AND. AINTA.LE.0.D0) GO TO 50
C
      CALL DLGAMS (A+1.0D0, ALGAP1, SGNGAM)
      T = LOG (ABS(A)) + ALNG - ALGAP1
      IF (T.GT.ALNEPS) GO TO 60
C
      IF (T.GT.(-ALNEPS)) H = 1.0D0 - SGA * SGNGAM * EXP(T)
      IF (ABS(H).GT.SQEPS) GO TO 50
C
      CALL XERCLR
      CALL XERMSG ('SLATEC', 'DGAMIT', 'RESULT LT HALF PRECISION', 1,
     +   1)
C
 50   T = -A*ALX + LOG(ABS(H))
      IF (T.LT.BOT) CALL XERCLR
      DGAMIT = SIGN (EXP(T), H)
      RETURN
C
 60   T = T - A*ALX
      IF (T.LT.BOT) CALL XERCLR
      DGAMIT = -SGA * SGNGAM * EXP(T)
      RETURN
C
      END