relibc_openlibm/slatec/gamln.f

*DECK GAMLN
      REAL FUNCTION GAMLN (Z, IERR)
C***BEGIN PROLOGUE  GAMLN
C***SUBSIDIARY
C***PURPOSE  Compute the logarithm of the Gamma function
C***LIBRARY   SLATEC
C***CATEGORY  C7A
C***TYPE      SINGLE PRECISION (GAMLN-S, DGAMLN-D)
C***KEYWORDS  LOGARITHM OF GAMMA FUNCTION
C***AUTHOR  Amos, D. E., (SNL)
C***DESCRIPTION
C
C         GAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR
C         Z.GT.0.  THE ASYMPTOTIC EXPANSION IS USED TO GENERATE VALUES
C         GREATER THAN ZMIN WHICH ARE ADJUSTED BY THE RECURSION
C         G(Z+1)=Z*G(Z) FOR Z.LE.ZMIN.  THE FUNCTION WAS MADE AS
C         PORTABLE AS POSSIBLE BY COMPUTING ZMIN FROM THE NUMBER OF BASE
C         10 DIGITS IN A WORD, RLN=MAX(-ALOG10(R1MACH(4)),0.5E-18)
C         LIMITED TO 18 DIGITS OF (RELATIVE) ACCURACY.
C
C         SINCE INTEGER ARGUMENTS ARE COMMON, A TABLE LOOK UP ON 100
C         VALUES IS USED FOR SPEED OF EXECUTION.
C
C     DESCRIPTION OF ARGUMENTS
C
C         INPUT
C           Z      - REAL ARGUMENT, Z.GT.0.0E0
C
C         OUTPUT
C           GAMLN  - NATURAL LOG OF THE GAMMA FUNCTION AT Z
C           IERR   - ERROR FLAG
C                    IERR=0, NORMAL RETURN, COMPUTATION COMPLETED
C                    IERR=1, Z.LE.0.0E0,    NO COMPUTATION
C
C***REFERENCES  COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT
C                 BY D. E. AMOS, SAND83-0083, MAY, 1983.
C***ROUTINES CALLED  I1MACH, R1MACH
C***REVISION HISTORY  (YYMMDD)
C   830501  DATE WRITTEN
C   830501  REVISION DATE from Version 3.2
C   910415  Prologue converted to Version 4.0 format.  (BAB)
C   920128  Category corrected.  (WRB)
C   921215  GAMLN defined for Z negative.  (WRB)
C***END PROLOGUE  GAMLN
C
      INTEGER I, I1M, K, MZ, NZ, IERR, I1MACH
      REAL CF, CON, FLN, FZ, GLN, RLN, S, TLG, TRM, TST, T1, WDTOL, Z,
     * ZDMY, ZINC, ZM, ZMIN, ZP, ZSQ
      REAL R1MACH
      DIMENSION CF(22), GLN(100)
C           LNGAMMA(N), N=1,100
      DATA GLN(1), GLN(2), GLN(3), GLN(4), GLN(5), GLN(6), GLN(7),
     1     GLN(8), GLN(9), GLN(10), GLN(11), GLN(12), GLN(13), GLN(14),
     2     GLN(15), GLN(16), GLN(17), GLN(18), GLN(19), GLN(20),
     3     GLN(21), GLN(22)/
     4     0.00000000000000000E+00,     0.00000000000000000E+00,
     5     6.93147180559945309E-01,     1.79175946922805500E+00,
     6     3.17805383034794562E+00,     4.78749174278204599E+00,
     7     6.57925121201010100E+00,     8.52516136106541430E+00,
     8     1.06046029027452502E+01,     1.28018274800814696E+01,
     9     1.51044125730755153E+01,     1.75023078458738858E+01,
     A     1.99872144956618861E+01,     2.25521638531234229E+01,
     B     2.51912211827386815E+01,     2.78992713838408916E+01,
     C     3.06718601060806728E+01,     3.35050734501368889E+01,
     D     3.63954452080330536E+01,     3.93398841871994940E+01,
     E     4.23356164607534850E+01,     4.53801388984769080E+01/
      DATA GLN(23), GLN(24), GLN(25), GLN(26), GLN(27), GLN(28),
     1     GLN(29), GLN(30), GLN(31), GLN(32), GLN(33), GLN(34),
     2     GLN(35), GLN(36), GLN(37), GLN(38), GLN(39), GLN(40),
     3     GLN(41), GLN(42), GLN(43), GLN(44)/
     4     4.84711813518352239E+01,     5.16066755677643736E+01,
     5     5.47847293981123192E+01,     5.80036052229805199E+01,
     6     6.12617017610020020E+01,     6.45575386270063311E+01,
     7     6.78897431371815350E+01,     7.12570389671680090E+01,
     8     7.46582363488301644E+01,     7.80922235533153106E+01,
     9     8.15579594561150372E+01,     8.50544670175815174E+01,
     A     8.85808275421976788E+01,     9.21361756036870925E+01,
     B     9.57196945421432025E+01,     9.93306124547874269E+01,
     C     1.02968198614513813E+02,     1.06631760260643459E+02,
     D     1.10320639714757395E+02,     1.14034211781461703E+02,
     E     1.17771881399745072E+02,     1.21533081515438634E+02/
      DATA GLN(45), GLN(46), GLN(47), GLN(48), GLN(49), GLN(50),
     1     GLN(51), GLN(52), GLN(53), GLN(54), GLN(55), GLN(56),
     2     GLN(57), GLN(58), GLN(59), GLN(60), GLN(61), GLN(62),
     3     GLN(63), GLN(64), GLN(65), GLN(66)/
     4     1.25317271149356895E+02,     1.29123933639127215E+02,
     5     1.32952575035616310E+02,     1.36802722637326368E+02,
     6     1.40673923648234259E+02,     1.44565743946344886E+02,
     7     1.48477766951773032E+02,     1.52409592584497358E+02,
     8     1.56360836303078785E+02,     1.60331128216630907E+02,
     9     1.64320112263195181E+02,     1.68327445448427652E+02,
     A     1.72352797139162802E+02,     1.76395848406997352E+02,
     B     1.80456291417543771E+02,     1.84533828861449491E+02,
     C     1.88628173423671591E+02,     1.92739047287844902E+02,
     D     1.96866181672889994E+02,     2.01009316399281527E+02,
     E     2.05168199482641199E+02,     2.09342586752536836E+02/
      DATA GLN(67), GLN(68), GLN(69), GLN(70), GLN(71), GLN(72),
     1     GLN(73), GLN(74), GLN(75), GLN(76), GLN(77), GLN(78),
     2     GLN(79), GLN(80), GLN(81), GLN(82), GLN(83), GLN(84),
     3     GLN(85), GLN(86), GLN(87), GLN(88)/
     4     2.13532241494563261E+02,     2.17736934113954227E+02,
     5     2.21956441819130334E+02,     2.26190548323727593E+02,
     6     2.30439043565776952E+02,     2.34701723442818268E+02,
     7     2.38978389561834323E+02,     2.43268849002982714E+02,
     8     2.47572914096186884E+02,     2.51890402209723194E+02,
     9     2.56221135550009525E+02,     2.60564940971863209E+02,
     A     2.64921649798552801E+02,     2.69291097651019823E+02,
     B     2.73673124285693704E+02,     2.78067573440366143E+02,
     C     2.82474292687630396E+02,     2.86893133295426994E+02,
     D     2.91323950094270308E+02,     2.95766601350760624E+02,
     E     3.00220948647014132E+02,     3.04686856765668715E+02/
      DATA GLN(89), GLN(90), GLN(91), GLN(92), GLN(93), GLN(94),
     1     GLN(95), GLN(96), GLN(97), GLN(98), GLN(99), GLN(100)/
     2     3.09164193580146922E+02,     3.13652829949879062E+02,
     3     3.18152639620209327E+02,     3.22663499126726177E+02,
     4     3.27185287703775217E+02,     3.31717887196928473E+02,
     5     3.36261181979198477E+02,     3.40815058870799018E+02,
     6     3.45379407062266854E+02,     3.49954118040770237E+02,
     7     3.54539085519440809E+02,     3.59134205369575399E+02/
C             COEFFICIENTS OF ASYMPTOTIC EXPANSION
      DATA CF(1), CF(2), CF(3), CF(4), CF(5), CF(6), CF(7), CF(8),
     1     CF(9), CF(10), CF(11), CF(12), CF(13), CF(14), CF(15),
     2     CF(16), CF(17), CF(18), CF(19), CF(20), CF(21), CF(22)/
     3     8.33333333333333333E-02,    -2.77777777777777778E-03,
     4     7.93650793650793651E-04,    -5.95238095238095238E-04,
     5     8.41750841750841751E-04,    -1.91752691752691753E-03,
     6     6.41025641025641026E-03,    -2.95506535947712418E-02,
     7     1.79644372368830573E-01,    -1.39243221690590112E+00,
     8     1.34028640441683920E+01,    -1.56848284626002017E+02,
     9     2.19310333333333333E+03,    -3.61087712537249894E+04,
     A     6.91472268851313067E+05,    -1.52382215394074162E+07,
     B     3.82900751391414141E+08,    -1.08822660357843911E+10,
     C     3.47320283765002252E+11,    -1.23696021422692745E+13,
     D     4.88788064793079335E+14,    -2.13203339609193739E+16/
C
C             LN(2*PI)
      DATA CON                    /     1.83787706640934548E+00/
C
C***FIRST EXECUTABLE STATEMENT  GAMLN
      IERR=0
      IF (Z.LE.0.0E0) GO TO 70
      IF (Z.GT.101.0E0) GO TO 10
      NZ = Z
      FZ = Z - NZ
      IF (FZ.GT.0.0E0) GO TO 10
      IF (NZ.GT.100) GO TO 10
      GAMLN = GLN(NZ)
      RETURN
   10 CONTINUE
      WDTOL = R1MACH(4)
      WDTOL = MAX(WDTOL,0.5E-18)
      I1M = I1MACH(11)
      RLN = R1MACH(5)*I1M
      FLN = MIN(RLN,20.0E0)
      FLN = MAX(FLN,3.0E0)
      FLN = FLN - 3.0E0
      ZM = 1.8000E0 + 0.3875E0*FLN
      MZ = ZM + 1
      ZMIN = MZ
      ZDMY = Z
      ZINC = 0.0E0
      IF (Z.GE.ZMIN) GO TO 20
      ZINC = ZMIN - NZ
      ZDMY = Z + ZINC
   20 CONTINUE
      ZP = 1.0E0/ZDMY
      T1 = CF(1)*ZP
      S = T1
      IF (ZP.LT.WDTOL) GO TO 40
      ZSQ = ZP*ZP
      TST = T1*WDTOL
      DO 30 K=2,22
        ZP = ZP*ZSQ
        TRM = CF(K)*ZP
        IF (ABS(TRM).LT.TST) GO TO 40
        S = S + TRM
   30 CONTINUE
   40 CONTINUE
      IF (ZINC.NE.0.0E0) GO TO 50
      TLG = ALOG(Z)
      GAMLN = Z*(TLG-1.0E0) + 0.5E0*(CON-TLG) + S
      RETURN
   50 CONTINUE
      ZP = 1.0E0
      NZ = ZINC
      DO 60 I=1,NZ
        ZP = ZP*(Z+(I-1))
   60 CONTINUE
      TLG = ALOG(ZDMY)
      GAMLN = ZDMY*(TLG-1.0E0) - ALOG(ZP) + 0.5E0*(CON-TLG) + S
      RETURN
C
C
   70 CONTINUE
      GAMLN = R1MACH(2)
      IERR=1
      RETURN
      END