190 lines
8.4 KiB
Fortran
190 lines
8.4 KiB
Fortran
DOUBLE PRECISION FUNCTION DGAMLN(Z,IERR)
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C***BEGIN PROLOGUE DGAMLN
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C***DATE WRITTEN 830501 (YYMMDD)
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C***REVISION DATE 830501 (YYMMDD)
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C***CATEGORY NO. B5F
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C***KEYWORDS GAMMA FUNCTION,LOGARITHM OF GAMMA FUNCTION
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C***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES
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C***PURPOSE TO COMPUTE THE LOGARITHM OF THE GAMMA FUNCTION
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C***DESCRIPTION
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C
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C **** A DOUBLE PRECISION ROUTINE ****
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C DGAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR
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C Z.GT.0. THE ASYMPTOTIC EXPANSION IS USED TO GENERATE VALUES
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C GREATER THAN ZMIN WHICH ARE ADJUSTED BY THE RECURSION
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C G(Z+1)=Z*G(Z) FOR Z.LE.ZMIN. THE FUNCTION WAS MADE AS
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C PORTABLE AS POSSIBLE BY COMPUTIMG ZMIN FROM THE NUMBER OF BASE
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C 10 DIGITS IN A WORD, RLN=AMAX1(-ALOG10(R1MACH(4)),0.5E-18)
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C LIMITED TO 18 DIGITS OF (RELATIVE) ACCURACY.
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C
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C SINCE INTEGER ARGUMENTS ARE COMMON, A TABLE LOOK UP ON 100
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C VALUES IS USED FOR SPEED OF EXECUTION.
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C
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C DESCRIPTION OF ARGUMENTS
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C
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C INPUT Z IS D0UBLE PRECISION
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C Z - ARGUMENT, Z.GT.0.0D0
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C
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C OUTPUT DGAMLN IS DOUBLE PRECISION
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C DGAMLN - NATURAL LOG OF THE GAMMA FUNCTION AT Z.NE.0.0D0
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C IERR - ERROR FLAG
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C IERR=0, NORMAL RETURN, COMPUTATION COMPLETED
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C IERR=1, Z.LE.0.0D0, NO COMPUTATION
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C
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C
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C***REFERENCES COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
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C BY D. E. AMOS, SAND83-0083, MAY, 1983.
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C***ROUTINES CALLED I1MACH,D1MACH
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C***END PROLOGUE DGAMLN
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DOUBLE PRECISION CF, CON, FLN, FZ, GLN, RLN, S, TLG, TRM, TST,
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* T1, WDTOL, Z, ZDMY, ZINC, ZM, ZMIN, ZP, ZSQ, D1MACH
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INTEGER I, IERR, I1M, K, MZ, NZ, I1MACH
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DIMENSION CF(22), GLN(100)
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C LNGAMMA(N), N=1,100
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DATA GLN(1), GLN(2), GLN(3), GLN(4), GLN(5), GLN(6), GLN(7),
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1 GLN(8), GLN(9), GLN(10), GLN(11), GLN(12), GLN(13), GLN(14),
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2 GLN(15), GLN(16), GLN(17), GLN(18), GLN(19), GLN(20),
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3 GLN(21), GLN(22)/
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4 0.00000000000000000D+00, 0.00000000000000000D+00,
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5 6.93147180559945309D-01, 1.79175946922805500D+00,
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6 3.17805383034794562D+00, 4.78749174278204599D+00,
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7 6.57925121201010100D+00, 8.52516136106541430D+00,
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8 1.06046029027452502D+01, 1.28018274800814696D+01,
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9 1.51044125730755153D+01, 1.75023078458738858D+01,
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A 1.99872144956618861D+01, 2.25521638531234229D+01,
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B 2.51912211827386815D+01, 2.78992713838408916D+01,
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C 3.06718601060806728D+01, 3.35050734501368889D+01,
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D 3.63954452080330536D+01, 3.93398841871994940D+01,
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E 4.23356164607534850D+01, 4.53801388984769080D+01/
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DATA GLN(23), GLN(24), GLN(25), GLN(26), GLN(27), GLN(28),
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1 GLN(29), GLN(30), GLN(31), GLN(32), GLN(33), GLN(34),
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2 GLN(35), GLN(36), GLN(37), GLN(38), GLN(39), GLN(40),
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3 GLN(41), GLN(42), GLN(43), GLN(44)/
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4 4.84711813518352239D+01, 5.16066755677643736D+01,
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5 5.47847293981123192D+01, 5.80036052229805199D+01,
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6 6.12617017610020020D+01, 6.45575386270063311D+01,
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7 6.78897431371815350D+01, 7.12570389671680090D+01,
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8 7.46582363488301644D+01, 7.80922235533153106D+01,
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9 8.15579594561150372D+01, 8.50544670175815174D+01,
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A 8.85808275421976788D+01, 9.21361756036870925D+01,
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B 9.57196945421432025D+01, 9.93306124547874269D+01,
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C 1.02968198614513813D+02, 1.06631760260643459D+02,
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D 1.10320639714757395D+02, 1.14034211781461703D+02,
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E 1.17771881399745072D+02, 1.21533081515438634D+02/
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DATA GLN(45), GLN(46), GLN(47), GLN(48), GLN(49), GLN(50),
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1 GLN(51), GLN(52), GLN(53), GLN(54), GLN(55), GLN(56),
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2 GLN(57), GLN(58), GLN(59), GLN(60), GLN(61), GLN(62),
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3 GLN(63), GLN(64), GLN(65), GLN(66)/
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4 1.25317271149356895D+02, 1.29123933639127215D+02,
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5 1.32952575035616310D+02, 1.36802722637326368D+02,
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6 1.40673923648234259D+02, 1.44565743946344886D+02,
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7 1.48477766951773032D+02, 1.52409592584497358D+02,
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8 1.56360836303078785D+02, 1.60331128216630907D+02,
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9 1.64320112263195181D+02, 1.68327445448427652D+02,
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A 1.72352797139162802D+02, 1.76395848406997352D+02,
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B 1.80456291417543771D+02, 1.84533828861449491D+02,
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C 1.88628173423671591D+02, 1.92739047287844902D+02,
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D 1.96866181672889994D+02, 2.01009316399281527D+02,
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E 2.05168199482641199D+02, 2.09342586752536836D+02/
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DATA GLN(67), GLN(68), GLN(69), GLN(70), GLN(71), GLN(72),
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1 GLN(73), GLN(74), GLN(75), GLN(76), GLN(77), GLN(78),
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2 GLN(79), GLN(80), GLN(81), GLN(82), GLN(83), GLN(84),
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3 GLN(85), GLN(86), GLN(87), GLN(88)/
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4 2.13532241494563261D+02, 2.17736934113954227D+02,
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5 2.21956441819130334D+02, 2.26190548323727593D+02,
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6 2.30439043565776952D+02, 2.34701723442818268D+02,
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7 2.38978389561834323D+02, 2.43268849002982714D+02,
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8 2.47572914096186884D+02, 2.51890402209723194D+02,
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9 2.56221135550009525D+02, 2.60564940971863209D+02,
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A 2.64921649798552801D+02, 2.69291097651019823D+02,
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B 2.73673124285693704D+02, 2.78067573440366143D+02,
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C 2.82474292687630396D+02, 2.86893133295426994D+02,
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D 2.91323950094270308D+02, 2.95766601350760624D+02,
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E 3.00220948647014132D+02, 3.04686856765668715D+02/
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DATA GLN(89), GLN(90), GLN(91), GLN(92), GLN(93), GLN(94),
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1 GLN(95), GLN(96), GLN(97), GLN(98), GLN(99), GLN(100)/
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2 3.09164193580146922D+02, 3.13652829949879062D+02,
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3 3.18152639620209327D+02, 3.22663499126726177D+02,
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4 3.27185287703775217D+02, 3.31717887196928473D+02,
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5 3.36261181979198477D+02, 3.40815058870799018D+02,
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6 3.45379407062266854D+02, 3.49954118040770237D+02,
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7 3.54539085519440809D+02, 3.59134205369575399D+02/
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C COEFFICIENTS OF ASYMPTOTIC EXPANSION
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DATA CF(1), CF(2), CF(3), CF(4), CF(5), CF(6), CF(7), CF(8),
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1 CF(9), CF(10), CF(11), CF(12), CF(13), CF(14), CF(15),
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2 CF(16), CF(17), CF(18), CF(19), CF(20), CF(21), CF(22)/
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3 8.33333333333333333D-02, -2.77777777777777778D-03,
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4 7.93650793650793651D-04, -5.95238095238095238D-04,
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5 8.41750841750841751D-04, -1.91752691752691753D-03,
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6 6.41025641025641026D-03, -2.95506535947712418D-02,
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7 1.79644372368830573D-01, -1.39243221690590112D+00,
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8 1.34028640441683920D+01, -1.56848284626002017D+02,
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9 2.19310333333333333D+03, -3.61087712537249894D+04,
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A 6.91472268851313067D+05, -1.52382215394074162D+07,
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B 3.82900751391414141D+08, -1.08822660357843911D+10,
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C 3.47320283765002252D+11, -1.23696021422692745D+13,
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D 4.88788064793079335D+14, -2.13203339609193739D+16/
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C
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C LN(2*PI)
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DATA CON / 1.83787706640934548D+00/
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C
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C***FIRST EXECUTABLE STATEMENT DGAMLN
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IERR=0
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IF (Z.LE.0.0D0) GO TO 70
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IF (Z.GT.101.0D0) GO TO 10
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NZ = INT(SNGL(Z))
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FZ = Z - FLOAT(NZ)
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IF (FZ.GT.0.0D0) GO TO 10
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IF (NZ.GT.100) GO TO 10
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DGAMLN = GLN(NZ)
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RETURN
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10 CONTINUE
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WDTOL = D1MACH(4)
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WDTOL = DMAX1(WDTOL,0.5D-18)
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I1M = I1MACH(14)
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RLN = D1MACH(5)*FLOAT(I1M)
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FLN = DMIN1(RLN,20.0D0)
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FLN = DMAX1(FLN,3.0D0)
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FLN = FLN - 3.0D0
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ZM = 1.8000D0 + 0.3875D0*FLN
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MZ = INT(SNGL(ZM)) + 1
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ZMIN = FLOAT(MZ)
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ZDMY = Z
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ZINC = 0.0D0
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IF (Z.GE.ZMIN) GO TO 20
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ZINC = ZMIN - FLOAT(NZ)
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ZDMY = Z + ZINC
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20 CONTINUE
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ZP = 1.0D0/ZDMY
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T1 = CF(1)*ZP
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S = T1
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IF (ZP.LT.WDTOL) GO TO 40
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ZSQ = ZP*ZP
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TST = T1*WDTOL
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DO 30 K=2,22
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ZP = ZP*ZSQ
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TRM = CF(K)*ZP
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IF (DABS(TRM).LT.TST) GO TO 40
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S = S + TRM
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30 CONTINUE
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40 CONTINUE
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IF (ZINC.NE.0.0D0) GO TO 50
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TLG = DLOG(Z)
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DGAMLN = Z*(TLG-1.0D0) + 0.5D0*(CON-TLG) + S
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RETURN
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50 CONTINUE
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ZP = 1.0D0
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NZ = INT(SNGL(ZINC))
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DO 60 I=1,NZ
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ZP = ZP*(Z+FLOAT(I-1))
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60 CONTINUE
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TLG = DLOG(ZDMY)
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DGAMLN = ZDMY*(TLG-1.0D0) - DLOG(ZP) + 0.5D0*(CON-TLG) + S
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RETURN
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C
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C
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70 CONTINUE
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IERR=1
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RETURN
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END
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