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*DECK D9GMIT
DOUBLE PRECISION FUNCTION D9GMIT (A, X, ALGAP1, SGNGAM, ALX)
C***BEGIN PROLOGUE D9GMIT
C***SUBSIDIARY
C***PURPOSE Compute Tricomi's incomplete Gamma function for small
C arguments.
C***LIBRARY SLATEC (FNLIB)
C***CATEGORY C7E
C***TYPE DOUBLE PRECISION (R9GMIT-S, D9GMIT-D)
C***KEYWORDS COMPLEMENTARY INCOMPLETE GAMMA FUNCTION, FNLIB, SMALL X,
C SPECIAL FUNCTIONS, TRICOMI
C***AUTHOR Fullerton, W., (LANL)
C***DESCRIPTION
C
C Compute Tricomi's incomplete gamma function for small X.
C
C***REFERENCES (NONE)
C***ROUTINES CALLED D1MACH, DLNGAM, XERMSG
C***REVISION HISTORY (YYMMDD)
C 770701 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890911 Removed unnecessary intrinsics. (WRB)
C 890911 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 900720 Routine changed from user-callable to subsidiary. (WRB)
C***END PROLOGUE D9GMIT
DOUBLE PRECISION A, X, ALGAP1, SGNGAM, ALX, AE, AEPS, ALGS, ALG2,
1 BOT, EPS, FK, S, SGNG2, T, TE, D1MACH, DLNGAM
LOGICAL FIRST
SAVE EPS, BOT, FIRST
DATA FIRST /.TRUE./
C***FIRST EXECUTABLE STATEMENT D9GMIT
IF (FIRST) THEN
EPS = 0.5D0*D1MACH(3)
BOT = LOG (D1MACH(1))
ENDIF
FIRST = .FALSE.
C
IF (X .LE. 0.D0) CALL XERMSG ('SLATEC', 'D9GMIT',
+ 'X SHOULD BE GT 0', 1, 2)
C
MA = A + 0.5D0
IF (A.LT.0.D0) MA = A - 0.5D0
AEPS = A - MA
C
AE = A
IF (A.LT.(-0.5D0)) AE = AEPS
C
T = 1.D0
TE = AE
S = T
DO 20 K=1,200
FK = K
TE = -X*TE/FK
T = TE/(AE+FK)
S = S + T
IF (ABS(T).LT.EPS*ABS(S)) GO TO 30
20 CONTINUE
CALL XERMSG ('SLATEC', 'D9GMIT',
+ 'NO CONVERGENCE IN 200 TERMS OF TAYLOR-S SERIES', 2, 2)
C
30 IF (A.GE.(-0.5D0)) ALGS = -ALGAP1 + LOG(S)
IF (A.GE.(-0.5D0)) GO TO 60
C
ALGS = -DLNGAM(1.D0+AEPS) + LOG(S)
S = 1.0D0
M = -MA - 1
IF (M.EQ.0) GO TO 50
T = 1.0D0
DO 40 K=1,M
T = X*T/(AEPS-(M+1-K))
S = S + T
IF (ABS(T).LT.EPS*ABS(S)) GO TO 50
40 CONTINUE
C
50 D9GMIT = 0.0D0
ALGS = -MA*LOG(X) + ALGS
IF (S.EQ.0.D0 .OR. AEPS.EQ.0.D0) GO TO 60
C
SGNG2 = SGNGAM * SIGN (1.0D0, S)
ALG2 = -X - ALGAP1 + LOG(ABS(S))
C
IF (ALG2.GT.BOT) D9GMIT = SGNG2 * EXP(ALG2)
IF (ALGS.GT.BOT) D9GMIT = D9GMIT + EXP(ALGS)
RETURN
C
60 D9GMIT = EXP (ALGS)
RETURN
C
END
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