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|
CC
CC various special functions, taken from netlib's specfun package
CC
double precision function erf_xx(arg,jint)
C------------------------------------------------------------------
C
C This packet evaluates erf(x), erfc(x), and exp(x*x)*erfc(x)
C for a real argument x. It contains three FUNCTION type
C subprograms: ERF, ERFC, and ERFCX (or DERF, DERFC, and DERFCX),
C and one SUBROUTINE type subprogram, ERF_XX. The calling
C statements for the primary entries are:
C
C Y=ERF(X) (or Y=DERF(X)),
C
C Y=ERFC(X) (or Y=DERFC(X)),
C and
C Y=ERFCX(X) (or Y=DERFCX(X)).
C
C The routine ERF_XX is intended for internal packet use only,
C all computations within the packet being concentrated in this
C routine. The function subprograms invoke ERF_XX with the
C statement
C
C CALL ERF_XX(ARG,RESULT,JINT)
C
C where the parameter usage is as follows
C
C Function Parameters for ERF_XX
C call ARG Result JINT
C
C ERF(ARG) ANY REAL ARGUMENT ERF(ARG) 0
C ERFC(ARG) ABS(ARG) .LT. XBIG ERFC(ARG) 1
C ERFCX(ARG) XNEG .LT. ARG .LT. XMAX ERFCX(ARG) 2
C
C The main computation evaluates near-minimax approximations
C from "Rational Chebyshev approximations for the error function"
C by W. J. Cody, Math. Comp., 1969, PP. 631-638. This
C transportable program uses rational functions that theoretically
C approximate erf(x) and erfc(x) to at least 18 significant
C decimal digits. The accuracy achieved depends on the arithmetic
C system, the compiler, the intrinsic functions, and proper
C selection of the machine-dependent constants.
C
C*******************************************************************
C*******************************************************************
C
C Explanation of machine-dependent constants
C
C XMIN = the smallest positive floating-point number.
C XINF = the largest positive finite floating-point number.
C XNEG = the largest negative argument acceptable to ERFCX;
C the negative of the solution to the equation
C 2*exp(x*x) = XINF.
C XSMALL = argument below which erf(x) may be represented by
C 2*x/sqrt(pi) and above which x*x will not underflow.
C A conservative value is the largest machine number X
C such that 1.0 + X = 1.0 to machine precision.
C XBIG = largest argument acceptable to ERFC; solution to
C the equation: W(x) * (1-0.5/x**2) = XMIN, where
C W(x) = exp(-x*x)/[x*sqrt(pi)].
C XHUGE = argument above which 1.0 - 1/(2*x*x) = 1.0 to
C machine precision. A conservative value is
C 1/[2*sqrt(XSMALL)]
C XMAX = largest acceptable argument to ERFCX; the minimum
C of XINF and 1/[sqrt(pi)*XMIN].
C
C*******************************************************************
C*******************************************************************
C
C Error returns
C
C The program returns ERFC = 0 for ARG .GE. XBIG;
C
C ERFCX = XINF for ARG .LT. XNEG;
C and
C ERFCX = 0 for ARG .GE. XMAX.
C
C Intrinsic functions required are:
C
C ABS, INT, EXP
C
C
C Author: W. J. Cody
C Mathematics and Computer Science Division
C Argonne National Laboratory
C Argonne, IL 60439
C
C Latest modification: March 19, 1990
C
c------------------------------------------------------------------
integer i,jint
double precision arg,del,four,half,one, y, ysq, sixteen
double precision sqrpi,two,thresh,x,xbig,xden,xhuge
double precision xinf,xmax,xneg,xnum,xsmall, zero
double precision a(5),b(4),c(9),d(8),p(6),q(5)
c------------------------------------------------------------------
c mathematical constants
c------------------------------------------------------------------
parameter(four=4.d0,
parameter(sqrpi=5.6418958354775628695d-1,thresh=0.46875d0)
parameter(sixten=16.0d0)
c------------------------------------------------------------------
c machine-dependent constants
c------------------------------------------------------------------
parameter(xinf =1.d50, xneg=-22.d0, xsmall=1.d-16)
parameter(xbig =22.d0, xhuge=6.d6, xmax=xinf)
c------------------------------------------------------------------
c coefficients for approximation to erf in first interval
c------------------------------------------------------------------
data a/3.16112374387056560d00,1.13864154151050156d02,
1 3.77485237685302021d02,3.20937758913846947d03,
2 1.85777706184603153d-1/
data b/2.36012909523441209d01,2.44024637934444173d02,
1 1.28261652607737228d03,2.84423683343917062d03/
c------------------------------------------------------------------
c coefficients for approximation to erfc in second interval
c------------------------------------------------------------------
data c/5.64188496988670089d-1,8.88314979438837594d0,
1 6.61191906371416295d01,2.98635138197400131d02,
2 8.81952221241769090d02,1.71204761263407058d03,
3 2.05107837782607147d03,1.23033935479799725d03,
4 2.15311535474403846d-8/
data d/1.57449261107098347d01,1.17693950891312499d02,
1 5.37181101862009858d02,1.62138957456669019d03,
2 3.29079923573345963d03,4.36261909014324716d03,
3 3.43936767414372164d03,1.23033935480374942d03/
c------------------------------------------------------------------
c coefficients for approximation to erfc in third interval
c------------------------------------------------------------------
data p/3.05326634961232344d-1,3.60344899949804439d-1,
1 1.25781726111229246d-1,1.60837851487422766d-2,
2 6.58749161529837803d-4,1.63153871373020978d-2/
data q/2.56852019228982242d00,1.87295284992346047d00,
1 5.27905102951428412d-1,6.05183413124413191d-2,
2 2.33520497626869185d-3/
c------------------------------------------------------------------
x = arg
y = abs(x)
if (y .le. thresh) then
c------------------------------------------------------------------
c evaluate erf for |x| <= 0.46875
c------------------------------------------------------------------
ysq = zero
if (y .gt. xsmall) ysq = y * y
xnum = a(5)*ysq
xden = ysq
do 20 i = 1, 3
xnum = (xnum + a(i)) * ysq
xden = (xden + b(i)) * ysq
20 continue
erf_xx = x * (xnum + a(4)) / (xden + b(4))
if (jint .ne. 0) erf_xx = one - erf_xx
if (jint .eq. 2) erf_xx = exp(ysq) * erf_xx
go to 800
c------------------------------------------------------------------
c evaluate erfc for 0.46875 <= |x| <= 4.0
c------------------------------------------------------------------
else if (y .le. four) then
xnum = c(9)*y
xden = y
do 120 i = 1, 7
xnum = (xnum + c(i)) * y
xden = (xden + d(i)) * y
120 continue
erf_xx = (xnum + c(8)) / (xden + d(8))
if (jint .ne. 2) then
ysq = int(y*sixten)/sixten
del = (y-ysq)*(y+ysq)
erf_xx = exp(-ysq*ysq) * exp(-del) * erf_xx
end if
c------------------------------------------------------------------
c evaluate erfc for |x| > 4.0
c------------------------------------------------------------------
else
erf_xx = zero
if (y .ge. xbig) then
if ((jint .ne. 2) .or. (y .ge. xmax)) go to 300
if (y .ge. xhuge) then
erf_xx = sqrpi / y
go to 300
end if
end if
ysq = one / (y * y)
xnum = p(6)*ysq
xden = ysq
do 240 i = 1, 4
xnum = (xnum + p(i)) * ysq
xden = (xden + q(i)) * ysq
240 continue
erf_xx = ysq *(xnum + p(5)) / (xden + q(5))
erf_xx = (sqrpi - erf_xx) / y
if (jint .ne. 2) then
ysq = int(y*sixten)/sixten
del = (y-ysq)*(y+ysq)
erf_xx = exp(-ysq*ysq) * exp(-del) * erf_xx
end if
end if
c------------------------------------------------------------------
c fix up for negative argument, erf, etc.
c------------------------------------------------------------------
300 if (jint .eq. 0) then
erf_xx = (half - erf_xx) + half
if (x .lt. zero) erf_xx = -erf_xx
else if (jint .eq. 1) then
if (x .lt. zero) erf_xx = two - erf_xx
else
if (x .lt. zero) then
if (x .lt. xneg) then
erf_xx = xinf
else
ysq = int(x*sixten)/sixten
del = (x-ysq)*(x+ysq)
y = exp(ysq*ysq) * exp(del)
erf_xx = (y+y) - erf_xx
end if
end if
end if
800 return
end
DOUBLE PRECISION FUNCTION DGAMMA(X)
C----------------------------------------------------------------------
C
C This routine calculates the GAMMA function for a real argument X.
C Computation is based on an algorithm outlined in reference 1.
C The program uses rational functions that approximate the GAMMA
C function to at least 20 significant decimal digits. Coefficients
C for the approximation over the interval (1,2) are unpublished.
C Those for the approximation for X .GE. 12 are from reference 2.
C The accuracy achieved depends on the arithmetic system, the
C compiler, the intrinsic functions, and proper selection of the
C machine-dependent constants.
C
C
C*******************************************************************
C*******************************************************************
C
C Explanation of machine-dependent constants
C
C beta - radix for the floating-point representation
C maxexp - the smallest positive power of beta that overflows
C XBIG - the largest argument for which GAMMA(X) is representable
C in the machine, i.e., the solution to the equation
C GAMMA(XBIG) = beta**maxexp
C XINF - the largest machine representable floating-point number;
C approximately beta**maxexp
C EPS - the smallest positive floating-point number such that
C 1.0+EPS .GT. 1.0
C XMININ - the smallest positive floating-point number such that
C 1/XMININ is machine representable
C
C Approximate values for some important machines are:
C
C beta maxexp XBIG
C
C CRAY-1 (S.P.) 2 8191 966.961
C Cyber 180/855
C under NOS (S.P.) 2 1070 177.803
C IEEE (IBM/XT,
C SUN, etc.) (S.P.) 2 128 35.040
C IEEE (IBM/XT,
C SUN, etc.) (D.P.) 2 1024 171.624
C IBM 3033 (D.P.) 16 63 57.574
C VAX D-Format (D.P.) 2 127 34.844
C VAX G-Format (D.P.) 2 1023 171.489
C
C XINF EPS XMININ
C
C CRAY-1 (S.P.) 5.45E+2465 7.11E-15 1.84E-2466
C Cyber 180/855
C under NOS (S.P.) 1.26E+322 3.55E-15 3.14E-294
C IEEE (IBM/XT,
C SUN, etc.) (S.P.) 3.40E+38 1.19E-7 1.18E-38
C IEEE (IBM/XT,
C SUN, etc.) (D.P.) 1.79D+308 2.22D-16 2.23D-308
C IBM 3033 (D.P.) 7.23D+75 2.22D-16 1.39D-76
C VAX D-Format (D.P.) 1.70D+38 1.39D-17 5.88D-39
C VAX G-Format (D.P.) 8.98D+307 1.11D-16 1.12D-308
C
C*******************************************************************
C*******************************************************************
C
C Error returns
C
C The program returns the value XINF for singularities or
C when overflow would occur. The computation is believed
C to be free of underflow and overflow.
C
C
C Intrinsic functions required are:
C
C INT, DBLE, EXP, LOG, REAL, SIN
C
C
C References: "An Overview of Software Development for Special
C Functions", W. J. Cody, Lecture Notes in Mathematics,
C 506, Numerical Analysis Dundee, 1975, G. A. Watson
C (ed.), Springer Verlag, Berlin, 1976.
C
C Computer Approximations, Hart, Et. Al., Wiley and
C sons, New York, 1968.
C
C Latest modification: October 12, 1989
C
C Authors: W. J. Cody and L. Stoltz
C Applied Mathematics Division
C Argonne National Laboratory
C Argonne, IL 60439
C
C----------------------------------------------------------------------
INTEGER I,N
LOGICAL PARITY
DOUBLE PRECISION
1 C,CONV,EPS,FACT,HALF,ONE,P,PI,Q,RES,SQRTPI,SUM,TWELVE,
2 TWO,X,XBIG,XDEN,XINF,XMININ,XNUM,Y,Y1,YSQ,Z,ZERO
DIMENSION C(7),P(8),Q(8)
C----------------------------------------------------------------------
C Mathematical constants
C----------------------------------------------------------------------
DATA ONE,HALF,TWELVE,TWO,ZERO/1.0D0,0.5D0,12.0D0,2.0D0,0.0D0/,
1 SQRTPI/0.9189385332046727417803297D0/,
2 PI/3.1415926535897932384626434D0/
C----------------------------------------------------------------------
C Machine dependent parameters
C----------------------------------------------------------------------
DATA XBIG,XMININ,EPS/171.624D0,2.23D-308,2.22D-16/,
1 XINF/1.79D308/
C----------------------------------------------------------------------
C Numerator and denominator coefficients for rational minimax
C approximation over (1,2).
C----------------------------------------------------------------------
DATA P/-1.71618513886549492533811D+0,2.47656508055759199108314D+1,
1 -3.79804256470945635097577D+2,6.29331155312818442661052D+2,
2 8.66966202790413211295064D+2,-3.14512729688483675254357D+4,
3 -3.61444134186911729807069D+4,6.64561438202405440627855D+4/
DATA Q/-3.08402300119738975254353D+1,3.15350626979604161529144D+2,
1 -1.01515636749021914166146D+3,-3.10777167157231109440444D+3,
2 2.25381184209801510330112D+4,4.75584627752788110767815D+3,
3 -1.34659959864969306392456D+5,-1.15132259675553483497211D+5/
C----------------------------------------------------------------------
C Coefficients for minimax approximation over (12, INF).
C----------------------------------------------------------------------
DATA C/-1.910444077728D-03,8.4171387781295D-04,
1 -5.952379913043012D-04,7.93650793500350248D-04,
2 -2.777777777777681622553D-03,8.333333333333333331554247D-02,
3 5.7083835261D-03/
C----------------------------------------------------------------------
C Statement functions for conversion between integer and float
C----------------------------------------------------------------------
CONV(I) = DBLE(I)
PARITY = .FALSE.
FACT = ONE
N = 0
Y = X
IF (Y .LE. ZERO) THEN
C----------------------------------------------------------------------
C Argument is negative
C----------------------------------------------------------------------
Y = -X
Y1 = AINT(Y)
RES = Y - Y1
IF (RES .NE. ZERO) THEN
IF (Y1 .NE. AINT(Y1*HALF)*TWO) PARITY = .TRUE.
FACT = -PI / SIN(PI*RES)
Y = Y + ONE
ELSE
RES = XINF
GO TO 900
END IF
END IF
C----------------------------------------------------------------------
C Argument is positive
C----------------------------------------------------------------------
IF (Y .LT. EPS) THEN
C----------------------------------------------------------------------
C Argument .LT. EPS
C----------------------------------------------------------------------
IF (Y .GE. XMININ) THEN
RES = ONE / Y
ELSE
RES = XINF
GO TO 900
END IF
ELSE IF (Y .LT. TWELVE) THEN
Y1 = Y
IF (Y .LT. ONE) THEN
C----------------------------------------------------------------------
C 0.0 .LT. argument .LT. 1.0
C----------------------------------------------------------------------
Z = Y
Y = Y + ONE
ELSE
C----------------------------------------------------------------------
C 1.0 .LT. argument .LT. 12.0, reduce argument if necessary
C----------------------------------------------------------------------
N = INT(Y) - 1
Y = Y - CONV(N)
Z = Y - ONE
END IF
C----------------------------------------------------------------------
C Evaluate approximation for 1.0 .LT. argument .LT. 2.0
C----------------------------------------------------------------------
XNUM = ZERO
XDEN = ONE
DO 260 I = 1, 8
XNUM = (XNUM + P(I)) * Z
XDEN = XDEN * Z + Q(I)
260 CONTINUE
RES = XNUM / XDEN + ONE
IF (Y1 .LT. Y) THEN
C----------------------------------------------------------------------
C Adjust result for case 0.0 .LT. argument .LT. 1.0
C----------------------------------------------------------------------
RES = RES / Y1
ELSE IF (Y1 .GT. Y) THEN
C----------------------------------------------------------------------
C Adjust result for case 2.0 .LT. argument .LT. 12.0
C----------------------------------------------------------------------
DO 290 I = 1, N
RES = RES * Y
Y = Y + ONE
290 CONTINUE
END IF
ELSE
C----------------------------------------------------------------------
C Evaluate for argument .GE. 12.0,
C----------------------------------------------------------------------
IF (Y .LE. XBIG) THEN
YSQ = Y * Y
SUM = C(7)
DO 350 I = 1, 6
SUM = SUM / YSQ + C(I)
350 CONTINUE
SUM = SUM/Y - Y + SQRTPI
SUM = SUM + (Y-HALF)*LOG(Y)
RES = EXP(SUM)
ELSE
RES = XINF
GO TO 900
END IF
END IF
C----------------------------------------------------------------------
C Final adjustments and return
C----------------------------------------------------------------------
IF (PARITY) RES = -RES
IF (FACT .NE. ONE) RES = FACT / RES
900 DGAMMA = RES
RETURN
C ---------- Last line of GAMMA ----------
END
DOUBLE PRECISION FUNCTION DLGAMA(X)
C----------------------------------------------------------------------
C
C This routine calculates the LOG(GAMMA) function for a positive real
C argument X. Computation is based on an algorithm outlined in
C references 1 and 2. The program uses rational functions that
C theoretically approximate LOG(GAMMA) to at least 18 significant
C decimal digits. The approximation for X > 12 is from reference
C 3, while approximations for X < 12.0 are similar to those in
C reference 1, but are unpublished. The accuracy achieved depends
C on the arithmetic system, the compiler, the intrinsic functions,
C and proper selection of the machine-dependent constants.
C
C
C*********************************************************************
C*********************************************************************
C
C Explanation of machine-dependent constants
C
C beta - radix for the floating-point representation
C maxexp - the smallest positive power of beta that overflows
C XBIG - largest argument for which LN(GAMMA(X)) is representable
C in the machine, i.e., the solution to the equation
C LN(GAMMA(XBIG)) = beta**maxexp
C XINF - largest machine representable floating-point number;
C approximately beta**maxexp.
C EPS - The smallest positive floating-point number such that
C 1.0+EPS .GT. 1.0
C FRTBIG - Rough estimate of the fourth root of XBIG
C
C
C Approximate values for some important machines are:
C
C beta maxexp XBIG
C
C CRAY-1 (S.P.) 2 8191 9.62E+2461
C Cyber 180/855
C under NOS (S.P.) 2 1070 1.72E+319
C IEEE (IBM/XT,
C SUN, etc.) (S.P.) 2 128 4.08E+36
C IEEE (IBM/XT,
C SUN, etc.) (D.P.) 2 1024 2.55D+305
C IBM 3033 (D.P.) 16 63 4.29D+73
C VAX D-Format (D.P.) 2 127 2.05D+36
C VAX G-Format (D.P.) 2 1023 1.28D+305
C
C
C XINF EPS FRTBIG
C
C CRAY-1 (S.P.) 5.45E+2465 7.11E-15 3.13E+615
C Cyber 180/855
C under NOS (S.P.) 1.26E+322 3.55E-15 6.44E+79
C IEEE (IBM/XT,
C SUN, etc.) (S.P.) 3.40E+38 1.19E-7 1.42E+9
C IEEE (IBM/XT,
C SUN, etc.) (D.P.) 1.79D+308 2.22D-16 2.25D+76
C IBM 3033 (D.P.) 7.23D+75 2.22D-16 2.56D+18
C VAX D-Format (D.P.) 1.70D+38 1.39D-17 1.20D+9
C VAX G-Format (D.P.) 8.98D+307 1.11D-16 1.89D+76
C
C**************************************************************
C**************************************************************
C
C Error returns
C
C The program returns the value XINF for X .LE. 0.0 or when
C overflow would occur. The computation is believed to
C be free of underflow and overflow.
C
C
C Intrinsic functions required are:
C
C LOG
C
C
C References:
C
C 1) W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for
C the Natural Logarithm of the Gamma Function,' Math. Comp. 21,
C 1967, pp. 198-203.
C
C 2) K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May,
C 1969.
C
C 3) Hart, Et. Al., Computer Approximations, Wiley and sons, New
C York, 1968.
C
C
C Authors: W. J. Cody and L. Stoltz
C Argonne National Laboratory
C
C Latest modification: June 16, 1988
C
C----------------------------------------------------------------------
INTEGER I
DOUBLE PRECISION
1 C,CORR,D1,D2,D4,EPS,FRTBIG,FOUR,HALF,ONE,PNT68,P1,P2,P4,
2 Q1,Q2,Q4,RES,SQRTPI,THRHAL,TWELVE,TWO,X,XBIG,XDEN,XINF,
3 XM1,XM2,XM4,XNUM,Y,YSQ,ZERO
DIMENSION C(7),P1(8),P2(8),P4(8),Q1(8),Q2(8),Q4(8)
C----------------------------------------------------------------------
C Mathematical constants
C----------------------------------------------------------------------
DATA ONE,HALF,TWELVE,ZERO/1.0D0,0.5D0,12.0D0,0.0D0/,
1 FOUR,THRHAL,TWO,PNT68/4.0D0,1.5D0,2.0D0,0.6796875D0/,
2 SQRTPI/0.9189385332046727417803297D0/
C----------------------------------------------------------------------
C Machine dependent parameters
C----------------------------------------------------------------------
DATA XBIG,XINF,EPS,FRTBIG/2.55D305,1.79D308,2.22D-16,2.25D76/
C----------------------------------------------------------------------
C Numerator and denominator coefficients for rational minimax
C approximation over (0.5,1.5).
C----------------------------------------------------------------------
DATA D1/-5.772156649015328605195174D-1/
DATA P1/4.945235359296727046734888D0,2.018112620856775083915565D2,
1 2.290838373831346393026739D3,1.131967205903380828685045D4,
2 2.855724635671635335736389D4,3.848496228443793359990269D4,
3 2.637748787624195437963534D4,7.225813979700288197698961D3/
DATA Q1/6.748212550303777196073036D1,1.113332393857199323513008D3,
1 7.738757056935398733233834D3,2.763987074403340708898585D4,
2 5.499310206226157329794414D4,6.161122180066002127833352D4,
3 3.635127591501940507276287D4,8.785536302431013170870835D3/
C----------------------------------------------------------------------
C Numerator and denominator coefficients for rational minimax
C Approximation over (1.5,4.0).
C----------------------------------------------------------------------
DATA D2/4.227843350984671393993777D-1/
DATA P2/4.974607845568932035012064D0,5.424138599891070494101986D2,
1 1.550693864978364947665077D4,1.847932904445632425417223D5,
2 1.088204769468828767498470D6,3.338152967987029735917223D6,
3 5.106661678927352456275255D6,3.074109054850539556250927D6/
DATA Q2/1.830328399370592604055942D2,7.765049321445005871323047D3,
1 1.331903827966074194402448D5,1.136705821321969608938755D6,
2 5.267964117437946917577538D6,1.346701454311101692290052D7,
3 1.782736530353274213975932D7,9.533095591844353613395747D6/
C----------------------------------------------------------------------
C Numerator and denominator coefficients for rational minimax
C Approximation over (4.0,12.0).
C----------------------------------------------------------------------
DATA D4/1.791759469228055000094023D0/
DATA P4/1.474502166059939948905062D4,2.426813369486704502836312D6,
1 1.214755574045093227939592D8,2.663432449630976949898078D9,
2 2.940378956634553899906876D10,1.702665737765398868392998D11,
3 4.926125793377430887588120D11,5.606251856223951465078242D11/
DATA Q4/2.690530175870899333379843D3,6.393885654300092398984238D5,
2 4.135599930241388052042842D7,1.120872109616147941376570D9,
3 1.488613728678813811542398D10,1.016803586272438228077304D11,
4 3.417476345507377132798597D11,4.463158187419713286462081D11/
C----------------------------------------------------------------------
C Coefficients for minimax approximation over (12, INF).
C----------------------------------------------------------------------
DATA C/-1.910444077728D-03,8.4171387781295D-04,
1 -5.952379913043012D-04,7.93650793500350248D-04,
2 -2.777777777777681622553D-03,8.333333333333333331554247D-02,
3 5.7083835261D-03/
C----------------------------------------------------------------------
Y = X
IF ((Y .GT. ZERO) .AND. (Y .LE. XBIG)) THEN
IF (Y .LE. EPS) THEN
RES = -LOG(Y)
ELSE IF (Y .LE. THRHAL) THEN
C----------------------------------------------------------------------
C EPS .LT. X .LE. 1.5
C----------------------------------------------------------------------
IF (Y .LT. PNT68) THEN
CORR = -LOG(Y)
XM1 = Y
ELSE
CORR = ZERO
XM1 = (Y - HALF) - HALF
END IF
IF ((Y .LE. HALF) .OR. (Y .GE. PNT68)) THEN
XDEN = ONE
XNUM = ZERO
DO 140 I = 1, 8
XNUM = XNUM*XM1 + P1(I)
XDEN = XDEN*XM1 + Q1(I)
140 CONTINUE
RES = CORR + (XM1 * (D1 + XM1*(XNUM/XDEN)))
ELSE
XM2 = (Y - HALF) - HALF
XDEN = ONE
XNUM = ZERO
DO 220 I = 1, 8
XNUM = XNUM*XM2 + P2(I)
XDEN = XDEN*XM2 + Q2(I)
220 CONTINUE
RES = CORR + XM2 * (D2 + XM2*(XNUM/XDEN))
END IF
ELSE IF (Y .LE. FOUR) THEN
C----------------------------------------------------------------------
C 1.5 .LT. X .LE. 4.0
C----------------------------------------------------------------------
XM2 = Y - TWO
XDEN = ONE
XNUM = ZERO
DO 240 I = 1, 8
XNUM = XNUM*XM2 + P2(I)
XDEN = XDEN*XM2 + Q2(I)
240 CONTINUE
RES = XM2 * (D2 + XM2*(XNUM/XDEN))
ELSE IF (Y .LE. TWELVE) THEN
C----------------------------------------------------------------------
C 4.0 .LT. X .LE. 12.0
C----------------------------------------------------------------------
XM4 = Y - FOUR
XDEN = -ONE
XNUM = ZERO
DO 340 I = 1, 8
XNUM = XNUM*XM4 + P4(I)
XDEN = XDEN*XM4 + Q4(I)
340 CONTINUE
RES = D4 + XM4*(XNUM/XDEN)
ELSE
C----------------------------------------------------------------------
C Evaluate for argument .GE. 12.0,
C----------------------------------------------------------------------
RES = ZERO
IF (Y .LE. FRTBIG) THEN
RES = C(7)
YSQ = Y * Y
DO 450 I = 1, 6
RES = RES / YSQ + C(I)
450 CONTINUE
END IF
RES = RES/Y
CORR = LOG(Y)
RES = RES + SQRTPI - HALF*CORR
RES = RES + Y*(CORR-ONE)
END IF
ELSE
C----------------------------------------------------------------------
C Return for bad arguments
C----------------------------------------------------------------------
RES = XINF
END IF
C----------------------------------------------------------------------
C Final adjustments and return
C----------------------------------------------------------------------
DLGAMA = RES
RETURN
C ---------- Last line of DLGAMA ----------
END
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