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extint.f
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cc************************************************************************
c Old version that generated the q-array internally.
cc Initial evaluation of the two components of the function
c subroutine initext(next,phibye,phiei,rb,xlambda)
c integer next
c real phibye(next),phiei(next)
c real rb
cc statement function:
c eeih(x)=alog(1.+1./x)-.56/(1.+4.1*x+0.9*x*x)
c
cc precalculate values for an integration from q=0 to 1/rb, (r=infty to rb )
c if(rb.gt.0.) then
c qrb=1./rb
c else
c write(*,*)"initext zero rb error"
c stop
c endif
c rbol=rb/xlambda
cc Values multiplied by exp functions.
c if(rbol.lt.50.)then
c E1rb=exp(rbol)*Eone(rbol)
c else
c E1rb=eeih(rbol)
c endif
c Eirb=EXPEi(rbol)
c do i=1,next
c q=qrb*(i-0.5)/next
c rol=1./(q*xlambda)
c if(rol-rbol.gt.50) then
c phibye(i)=0.
c else
c phibye(i)=exp(rbol-rol)*rb*q
c endif
c if(rol.gt.50.)then
cc ee1=eeih(rol)
c ee1=1/rol
c else
c ee1=exp(rol)*Eone(rol)
c endif
c phiei(i)=-( 1./(2.*rol))*(
c $ exp(rbol-rol)*(E1rb+Eirb)
c $ -ee1
c $ -(EXPEi(rol)) )
cc phiei(i)=-( 1./(2.*rol))*(exp(2.*rbol-rol)*...
cc $ -exp(rol)*Eone(rol)
cc $ -exp(-rol)*(Ei(rol)-...) )
c enddo
c end
c************************************************************************
c Initial evaluation of the two components of the function
c Here qp is an array going from 0 to 1. Corresponding to r running from
c infinity to rmax=rb.
subroutine initext(next,qp,phibye,phiei,rb,xlambda)
integer next
real qp(next),phibye(next),phiei(next)
real rb
c statement function:
eeih(x)=alog(1.+1./x)-.56/(1.+4.1*x+0.9*x*x)
c precalculate values for an integration over qp range.
rbol=rb/xlambda
c Values multiplied by exp functions.
if(rbol.lt.50.)then
E1rb=exp(rbol)*Eone(rbol)
else
E1rb=eeih(rbol)
endif
Eirb=EXPEi(rbol)
do i=1,next
c Get q in proper units.
q=qp(i)/rb
rol=1./(q*xlambda)
if(rol-rbol.gt.50) then
phibye(i)=0.
else
phibye(i)=exp(rbol-rol)*rb*q
endif
if(rol.gt.50.)then
c ee1=eeih(rol)
ee1=1/rol
else
ee1=exp(rol)*Eone(rol)
endif
phiei(i)=-( 1./(2.*rol))*(
$ exp(rbol-rol)*(E1rb+Eirb)
$ -ee1
$ -(EXPEi(rol)) )
enddo
end
c********************************************************************
c From here on is the NETLIB Exponential integral package.
SUBROUTINE CALCEI(ARG,RESULT,INT)
C----------------------------------------------------------------------
C
C This Fortran 77 packet computes the exponential integrals Ei(x),
C E1(x), and exp(-x)*Ei(x) for real arguments x where
C
C integral (from t=-infinity to t=x) (exp(t)/t), x > 0,
C Ei(x) =
C -integral (from t=-x to t=infinity) (exp(t)/t), x < 0,
C
C and where the first integral is a principal value integral.
C The packet contains three function type subprograms: EI, EONE,
C and EXPEI; and one subroutine type subprogram: CALCEI. The
C calling statements for the primary entries are
C
C Y = EI(X), where X .NE. 0,
C
C Y = EONE(X), where X .GT. 0,
C and
C Y = EXPEI(X), where X .NE. 0,
C
C and where the entry points correspond to the functions Ei(x),
C E1(x), and exp(-x)*Ei(x), respectively. The routine CALCEI
C is intended for internal packet use only, all computations within
C the packet being concentrated in this routine. The function
C subprograms invoke CALCEI with the Fortran statement
C CALL CALCEI(ARG,RESULT,INT)
C where the parameter usage is as follows
C
C Function Parameters for CALCEI
C Call ARG RESULT INT
C
C EI(X) X .NE. 0 Ei(X) 1
C EONE(X) X .GT. 0 -Ei(-X) 2
C EXPEI(X) X .NE. 0 exp(-X)*Ei(X) 3
C
C The main computation involves evaluation of rational Chebyshev
C approximations published in Math. Comp. 22, 641-649 (1968), and
C Math. Comp. 23, 289-303 (1969) by Cody and Thacher. This
C transportable program is patterned after the machine-dependent
C FUNPACK packet NATSEI, but cannot match that version for
C efficiency or accuracy. This version uses rational functions
C that theoretically approximate the exponential integrals to
C at least 18 significant decimal digits. The accuracy achieved
C depends on the arithmetic system, the compiler, the intrinsic
C functions, and proper selection of the machine-dependent
C constants.
C
C
C*******************************************************************
C*******************************************************************
C
C Explanation of machine-dependent constants
C
C beta = radix for the floating-point system.
C minexp = smallest representable power of beta.
C maxexp = smallest power of beta that overflows.
C XBIG = largest argument acceptable to EONE; solution to
C equation:
C exp(-x)/x * (1 + 1/x) = beta ** minexp.
C XINF = largest positive machine number; approximately
C beta ** maxexp
C XMAX = largest argument acceptable to EI; solution to
C equation: exp(x)/x * (1 + 1/x) = beta ** maxexp.
C
C Approximate values for some important machines are:
C
C beta minexp maxexp
C
C CRAY-1 (S.P.) 2 -8193 8191
C Cyber 180/185
C under NOS (S.P.) 2 -975 1070
C IEEE (IBM/XT,
C SUN, etc.) (S.P.) 2 -126 128
C IEEE (IBM/XT,
C SUN, etc.) (D.P.) 2 -1022 1024
C IBM 3033 (D.P.) 16 -65 63
C VAX D-Format (D.P.) 2 -128 127
C VAX G-Format (D.P.) 2 -1024 1023
C
C XBIG XINF XMAX
C
C CRAY-1 (S.P.) 5670.31 5.45E+2465 5686.21
C Cyber 180/185
C under NOS (S.P.) 669.31 1.26E+322 748.28
C IEEE (IBM/XT,
C SUN, etc.) (S.P.) 82.93 3.40E+38 93.24
C IEEE (IBM/XT,
C SUN, etc.) (D.P.) 701.84 1.79D+308 716.35
C IBM 3033 (D.P.) 175.05 7.23D+75 179.85
C VAX D-Format (D.P.) 84.30 1.70D+38 92.54
C VAX G-Format (D.P.) 703.22 8.98D+307 715.66
C
C*******************************************************************
C*******************************************************************
C
C Error returns
C
C The following table shows the types of error that may be
C encountered in this routine and the function value supplied
C in each case.
C
C Error Argument Function values for
C Range EI EXPEI EONE
C
C UNDERFLOW (-)X .GT. XBIG 0 - 0
C OVERFLOW X .GE. XMAX XINF - -
C ILLEGAL X X = 0 -XINF -XINF XINF
C ILLEGAL X X .LT. 0 - - USE ABS(X)
C
C Intrinsic functions required are:
C
C ABS, SQRT, EXP
C
C
C Author: W. J. Cody
C Mathematics abd Computer Science Division
C Argonne National Laboratory
C Argonne, IL 60439
C
C Latest modification: September 9, 1988
C
C----------------------------------------------------------------------
INTEGER I,INT
REAL
CD DOUBLE PRECISION
1 A,ARG,B,C,D,EXP40,E,EI,F,FOUR,FOURTY,FRAC,HALF,ONE,P,
2 PLG,PX,P037,P1,P2,Q,QLG,QX,Q1,Q2,R,RESULT,S,SIX,SUMP,
3 SUMQ,T,THREE,TWELVE,TWO,TWO4,W,X,XBIG,XINF,XMAX,XMX0,
4 X0,X01,X02,X11,Y,YSQ,ZERO
DIMENSION A(7),B(6),C(9),D(9),E(10),F(10),P(10),Q(10),R(10),
1 S(9),P1(10),Q1(9),P2(10),Q2(9),PLG(4),QLG(4),PX(10),QX(10)
C----------------------------------------------------------------------
C Mathematical constants
C EXP40 = exp(40)
C X0 = zero of Ei
C X01/X11 + X02 = zero of Ei to extra precision
C----------------------------------------------------------------------
DATA ZERO,P037,HALF,ONE,TWO/0.0E0,0.037E0,0.5E0,1.0E0,2.0E0/,
1 THREE,FOUR,SIX,TWELVE,TWO4/3.0E0,4.0E0,6.0E0,12.E0,24.0E0/,
2 FOURTY,EXP40/40.0E0,2.3538526683701998541E17/,
3 X01,X11,X02/381.5E0,1024.0E0,-5.1182968633365538008E-5/,
4 X0/3.7250741078136663466E-1/
CD DATA ZERO,P037,HALF,ONE,TWO/0.0D0,0.037D0,0.5D0,1.0D0,2.0D0/,
CD 1 THREE,FOUR,SIX,TWELVE,TWO4/3.0D0,4.0D0,6.0D0,12.D0,24.0D0/,
CD 2 FOURTY,EXP40/40.0D0,2.3538526683701998541D17/,
CD 3 X01,X11,X02/381.5D0,1024.0D0,-5.1182968633365538008D-5/,
CD 4 X0/3.7250741078136663466D-1/
C----------------------------------------------------------------------
C Machine-dependent constants
C----------------------------------------------------------------------
DATA XINF/3.40E+38/,XMAX/93.246E0/,XBIG/82.93E0/
CD DATA XINF/1.79D+308/,XMAX/716.351D0/,XBIG/701.84D0/
C----------------------------------------------------------------------
C Coefficients for -1.0 <= X < 0.0
C----------------------------------------------------------------------
DATA A/1.1669552669734461083368E2, 2.1500672908092918123209E3,
1 1.5924175980637303639884E4, 8.9904972007457256553251E4,
2 1.5026059476436982420737E5,-1.4815102102575750838086E5,
3 5.0196785185439843791020E0/
DATA B/4.0205465640027706061433E1, 7.5043163907103936624165E2,
1 8.1258035174768735759855E3, 5.2440529172056355429883E4,
2 1.8434070063353677359298E5, 2.5666493484897117319268E5/
CD DATA A/1.1669552669734461083368D2, 2.1500672908092918123209D3,
CD 1 1.5924175980637303639884D4, 8.9904972007457256553251D4,
CD 2 1.5026059476436982420737D5,-1.4815102102575750838086D5,
CD 3 5.0196785185439843791020D0/
CD DATA B/4.0205465640027706061433D1, 7.5043163907103936624165D2,
CD 1 8.1258035174768735759855D3, 5.2440529172056355429883D4,
CD 2 1.8434070063353677359298D5, 2.5666493484897117319268D5/
C----------------------------------------------------------------------
C Coefficients for -4.0 <= X < -1.0
C----------------------------------------------------------------------
DATA C/3.828573121022477169108E-1, 1.107326627786831743809E+1,
1 7.246689782858597021199E+1, 1.700632978311516129328E+2,
2 1.698106763764238382705E+2, 7.633628843705946890896E+1,
3 1.487967702840464066613E+1, 9.999989642347613068437E-1,
4 1.737331760720576030932E-8/
DATA D/8.258160008564488034698E-2, 4.344836335509282083360E+0,
1 4.662179610356861756812E+1, 1.775728186717289799677E+2,
2 2.953136335677908517423E+2, 2.342573504717625153053E+2,
3 9.021658450529372642314E+1, 1.587964570758947927903E+1,
4 1.000000000000000000000E+0/
CD DATA C/3.828573121022477169108D-1, 1.107326627786831743809D+1,
CD 1 7.246689782858597021199D+1, 1.700632978311516129328D+2,
CD 2 1.698106763764238382705D+2, 7.633628843705946890896D+1,
CD 3 1.487967702840464066613D+1, 9.999989642347613068437D-1,
CD 4 1.737331760720576030932D-8/
CD DATA D/8.258160008564488034698D-2, 4.344836335509282083360D+0,
CD 1 4.662179610356861756812D+1, 1.775728186717289799677D+2,
CD 2 2.953136335677908517423D+2, 2.342573504717625153053D+2,
CD 3 9.021658450529372642314D+1, 1.587964570758947927903D+1,
CD 4 1.000000000000000000000D+0/
C----------------------------------------------------------------------
C Coefficients for X < -4.0
C----------------------------------------------------------------------
DATA E/1.3276881505637444622987E+2,3.5846198743996904308695E+4,
1 1.7283375773777593926828E+5,2.6181454937205639647381E+5,
2 1.7503273087497081314708E+5,5.9346841538837119172356E+4,
3 1.0816852399095915622498E+4,1.0611777263550331766871E03,
4 5.2199632588522572481039E+1,9.9999999999999999087819E-1/
DATA F/3.9147856245556345627078E+4,2.5989762083608489777411E+5,
1 5.5903756210022864003380E+5,5.4616842050691155735758E+5,
2 2.7858134710520842139357E+5,7.9231787945279043698718E+4,
3 1.2842808586627297365998E+4,1.1635769915320848035459E+3,
4 5.4199632588522559414924E+1,1.0E0/
CD DATA E/1.3276881505637444622987D+2,3.5846198743996904308695D+4,
CD 1 1.7283375773777593926828D+5,2.6181454937205639647381D+5,
CD 2 1.7503273087497081314708D+5,5.9346841538837119172356D+4,
CD 3 1.0816852399095915622498D+4,1.0611777263550331766871D03,
CD 4 5.2199632588522572481039D+1,9.9999999999999999087819D-1/
CD DATA F/3.9147856245556345627078D+4,2.5989762083608489777411D+5,
CD 1 5.5903756210022864003380D+5,5.4616842050691155735758D+5,
CD 2 2.7858134710520842139357D+5,7.9231787945279043698718D+4,
CD 3 1.2842808586627297365998D+4,1.1635769915320848035459D+3,
CD 4 5.4199632588522559414924D+1,1.0D0/
C----------------------------------------------------------------------
C Coefficients for rational approximation to ln(x/a), |1-x/a| < .1
C----------------------------------------------------------------------
DATA PLG/-2.4562334077563243311E+01,2.3642701335621505212E+02,
1 -5.4989956895857911039E+02,3.5687548468071500413E+02/
DATA QLG/-3.5553900764052419184E+01,1.9400230218539473193E+02,
1 -3.3442903192607538956E+02,1.7843774234035750207E+02/
CD DATA PLG/-2.4562334077563243311D+01,2.3642701335621505212D+02,
CD 1 -5.4989956895857911039D+02,3.5687548468071500413D+02/
CD DATA QLG/-3.5553900764052419184D+01,1.9400230218539473193D+02,
CD 1 -3.3442903192607538956D+02,1.7843774234035750207D+02/
C----------------------------------------------------------------------
C Coefficients for 0.0 < X < 6.0,
C ratio of Chebyshev polynomials
C----------------------------------------------------------------------
DATA P/-1.2963702602474830028590E01,-1.2831220659262000678155E03,
1 -1.4287072500197005777376E04,-1.4299841572091610380064E06,
2 -3.1398660864247265862050E05,-3.5377809694431133484800E08,
3 3.1984354235237738511048E08,-2.5301823984599019348858E10,
4 1.2177698136199594677580E10,-2.0829040666802497120940E11/
DATA Q/ 7.6886718750000000000000E01,-5.5648470543369082846819E03,
1 1.9418469440759880361415E05,-4.2648434812177161405483E06,
2 6.4698830956576428587653E07,-7.0108568774215954065376E08,
3 5.4229617984472955011862E09,-2.8986272696554495342658E10,
4 9.8900934262481749439886E10,-8.9673749185755048616855E10/
CD DATA P/-1.2963702602474830028590D01,-1.2831220659262000678155D03,
CD 1 -1.4287072500197005777376D04,-1.4299841572091610380064D06,
CD 2 -3.1398660864247265862050D05,-3.5377809694431133484800D08,
CD 3 3.1984354235237738511048D08,-2.5301823984599019348858D10,
CD 4 1.2177698136199594677580D10,-2.0829040666802497120940D11/
CD DATA Q/ 7.6886718750000000000000D01,-5.5648470543369082846819D03,
CD 1 1.9418469440759880361415D05,-4.2648434812177161405483D06,
CD 2 6.4698830956576428587653D07,-7.0108568774215954065376D08,
CD 3 5.4229617984472955011862D09,-2.8986272696554495342658D10,
CD 4 9.8900934262481749439886D10,-8.9673749185755048616855D10/
C----------------------------------------------------------------------
C J-fraction coefficients for 6.0 <= X < 12.0
C----------------------------------------------------------------------
DATA R/-2.645677793077147237806E00,-2.378372882815725244124E00,
1 -2.421106956980653511550E01, 1.052976392459015155422E01,
2 1.945603779539281810439E01,-3.015761863840593359165E01,
3 1.120011024227297451523E01,-3.988850730390541057912E00,
4 9.565134591978630774217E00, 9.981193787537396413219E-1/
DATA S/ 1.598517957704779356479E-4, 4.644185932583286942650E00,
1 3.697412299772985940785E02,-8.791401054875438925029E00,
2 7.608194509086645763123E02, 2.852397548119248700147E01,
3 4.731097187816050252967E02,-2.369210235636181001661E02,
4 1.249884822712447891440E00/
CD DATA R/-2.645677793077147237806D00,-2.378372882815725244124D00,
CD 1 -2.421106956980653511550D01, 1.052976392459015155422D01,
CD 2 1.945603779539281810439D01,-3.015761863840593359165D01,
CD 3 1.120011024227297451523D01,-3.988850730390541057912D00,
CD 4 9.565134591978630774217D00, 9.981193787537396413219D-1/
CD DATA S/ 1.598517957704779356479D-4, 4.644185932583286942650D00,
CD 1 3.697412299772985940785D02,-8.791401054875438925029D00,
CD 2 7.608194509086645763123D02, 2.852397548119248700147D01,
CD 3 4.731097187816050252967D02,-2.369210235636181001661D02,
CD 4 1.249884822712447891440D00/
C----------------------------------------------------------------------
C J-fraction coefficients for 12.0 <= X < 24.0
C----------------------------------------------------------------------
DATA P1/-1.647721172463463140042E00,-1.860092121726437582253E01,
1 -1.000641913989284829961E01,-2.105740799548040450394E01,
2 -9.134835699998742552432E-1,-3.323612579343962284333E01,
3 2.495487730402059440626E01, 2.652575818452799819855E01,
4 -1.845086232391278674524E00, 9.999933106160568739091E-1/
DATA Q1/ 9.792403599217290296840E01, 6.403800405352415551324E01,
1 5.994932325667407355255E01, 2.538819315630708031713E02,
2 4.429413178337928401161E01, 1.192832423968601006985E03,
3 1.991004470817742470726E02,-1.093556195391091143924E01,
4 1.001533852045342697818E00/
CD DATA P1/-1.647721172463463140042D00,-1.860092121726437582253D01,
CD 1 -1.000641913989284829961D01,-2.105740799548040450394D01,
CD 2 -9.134835699998742552432D-1,-3.323612579343962284333D01,
CD 3 2.495487730402059440626D01, 2.652575818452799819855D01,
CD 4 -1.845086232391278674524D00, 9.999933106160568739091D-1/
CD DATA Q1/ 9.792403599217290296840D01, 6.403800405352415551324D01,
CD 1 5.994932325667407355255D01, 2.538819315630708031713D02,
CD 2 4.429413178337928401161D01, 1.192832423968601006985D03,
CD 3 1.991004470817742470726D02,-1.093556195391091143924D01,
CD 4 1.001533852045342697818D00/
C----------------------------------------------------------------------
C J-fraction coefficients for X .GE. 24.0
C----------------------------------------------------------------------
DATA P2/ 1.75338801265465972390E02,-2.23127670777632409550E02,
1 -1.81949664929868906455E01,-2.79798528624305389340E01,
2 -7.63147701620253630855E00,-1.52856623636929636839E01,
3 -7.06810977895029358836E00,-5.00006640413131002475E00,
4 -3.00000000320981265753E00, 1.00000000000000485503E00/
DATA Q2/ 3.97845977167414720840E04, 3.97277109100414518365E00,
1 1.37790390235747998793E02, 1.17179220502086455287E02,
2 7.04831847180424675988E01,-1.20187763547154743238E01,
3 -7.99243595776339741065E00,-2.99999894040324959612E00,
4 1.99999999999048104167E00/
CD DATA P2/ 1.75338801265465972390D02,-2.23127670777632409550D02,
CD 1 -1.81949664929868906455D01,-2.79798528624305389340D01,
CD 2 -7.63147701620253630855D00,-1.52856623636929636839D01,
CD 3 -7.06810977895029358836D00,-5.00006640413131002475D00,
CD 4 -3.00000000320981265753D00, 1.00000000000000485503D00/
CD DATA Q2/ 3.97845977167414720840D04, 3.97277109100414518365D00,
CD 1 1.37790390235747998793D02, 1.17179220502086455287D02,
CD 2 7.04831847180424675988D01,-1.20187763547154743238D01,
CD 3 -7.99243595776339741065D00,-2.99999894040324959612D00,
CD 4 1.99999999999048104167D00/
C----------------------------------------------------------------------
X = ARG
IF (X .EQ. ZERO) THEN
EI = -XINF
IF (INT .EQ. 2) EI = -EI
ELSE IF ((X .LT. ZERO) .OR. (INT .EQ. 2)) THEN
C----------------------------------------------------------------------
C Calculate EI for negative argument or for E1.
C----------------------------------------------------------------------
Y = ABS(X)
IF (Y .LE. ONE) THEN
SUMP = A(7) * Y + A(1)
SUMQ = Y + B(1)
DO 110 I = 2, 6
SUMP = SUMP * Y + A(I)
SUMQ = SUMQ * Y + B(I)
110 CONTINUE
EI = LOG(Y) - SUMP / SUMQ
IF (INT .EQ. 3) EI = EI * EXP(Y)
ELSE IF (Y .LE. FOUR) THEN
W = ONE / Y
SUMP = C(1)
SUMQ = D(1)
DO 130 I = 2, 9
SUMP = SUMP * W + C(I)
SUMQ = SUMQ * W + D(I)
130 CONTINUE
EI = - SUMP / SUMQ
IF (INT .NE. 3) EI = EI * EXP(-Y)
ELSE
IF ((Y .GT. XBIG) .AND. (INT .LT. 3)) THEN
EI = ZERO
ELSE
W = ONE / Y
SUMP = E(1)
SUMQ = F(1)
DO 150 I = 2, 10
SUMP = SUMP * W + E(I)
SUMQ = SUMQ * W + F(I)
150 CONTINUE
EI = -W * (ONE - W * SUMP / SUMQ )
IF (INT .NE. 3) EI = EI * EXP(-Y)
END IF
END IF
IF (INT .EQ. 2) EI = -EI
ELSE IF (X .LT. SIX) THEN
C----------------------------------------------------------------------
C To improve conditioning, rational approximations are expressed
C in terms of Chebyshev polynomials for 0 <= X < 6, and in
C continued fraction form for larger X.
C----------------------------------------------------------------------
T = X + X
T = T / THREE - TWO
PX(1) = ZERO
QX(1) = ZERO
PX(2) = P(1)
QX(2) = Q(1)
DO 210 I = 2, 9
PX(I+1) = T * PX(I) - PX(I-1) + P(I)
QX(I+1) = T * QX(I) - QX(I-1) + Q(I)
210 CONTINUE
SUMP = HALF * T * PX(10) - PX(9) + P(10)
SUMQ = HALF * T * QX(10) - QX(9) + Q(10)
FRAC = SUMP / SUMQ
XMX0 = (X - X01/X11) - X02
IF (ABS(XMX0) .GE. P037) THEN
EI = LOG(X/X0) + XMX0 * FRAC
IF (INT .EQ. 3) EI = EXP(-X) * EI
ELSE
C----------------------------------------------------------------------
C Special approximation to ln(X/X0) for X close to X0
C----------------------------------------------------------------------
Y = XMX0 / (X + X0)
YSQ = Y*Y
SUMP = PLG(1)
SUMQ = YSQ + QLG(1)
DO 220 I = 2, 4
SUMP = SUMP*YSQ + PLG(I)
SUMQ = SUMQ*YSQ + QLG(I)
220 CONTINUE
EI = (SUMP / (SUMQ*(X+X0)) + FRAC) * XMX0
IF (INT .EQ. 3) EI = EXP(-X) * EI
END IF
ELSE IF (X .LT. TWELVE) THEN
FRAC = ZERO
DO 230 I = 1, 9
FRAC = S(I) / (R(I) + X + FRAC)
230 CONTINUE
EI = (R(10) + FRAC) / X
IF (INT .NE. 3) EI = EI * EXP(X)
ELSE IF (X .LE. TWO4) THEN
FRAC = ZERO
DO 240 I = 1, 9
FRAC = Q1(I) / (P1(I) + X + FRAC)
240 CONTINUE
EI = (P1(10) + FRAC) / X
IF (INT .NE. 3) EI = EI * EXP(X)
ELSE
IF ((X .GE. XMAX) .AND. (INT .LT. 3)) THEN
EI = XINF
ELSE
Y = ONE / X
FRAC = ZERO
DO 250 I = 1, 9
FRAC = Q2(I) / (P2(I) + X + FRAC)
250 CONTINUE
FRAC = P2(10) + FRAC
EI = Y + Y * Y * FRAC
IF (INT .NE. 3) THEN
IF (X .LE. XMAX-TWO4) THEN
EI = EI * EXP(X)
ELSE
C----------------------------------------------------------------------
C Calculation reformulated to avoid premature overflow
C----------------------------------------------------------------------
EI = (EI * EXP(X-FOURTY)) * EXP40
END IF
END IF
END IF
END IF
RESULT = EI
RETURN
C---------- Last line of CALCEI ----------
END
FUNCTION EI(X)
C--------------------------------------------------------------------
C
C This function program computes approximate values for the
C exponential integral Ei(x), where x is real.
C
C Author: W. J. Cody
C
C Latest modification: January 12, 1988
C
C--------------------------------------------------------------------
INTEGER INT
REAL EI, X, RESULT
CD DOUBLE PRECISION EI, X, RESULT
C--------------------------------------------------------------------
INT = 1
CALL CALCEI(X,RESULT,INT)
EI = RESULT
RETURN
C---------- Last line of EI ----------
END
FUNCTION EXPEI(X)
C--------------------------------------------------------------------
C
C This function program computes approximate values for the
C function exp(-x) * Ei(x), where Ei(x) is the exponential
C integral, and x is real.
C
C Author: W. J. Cody
C
C Latest modification: January 12, 1988
C
C--------------------------------------------------------------------
INTEGER INT
REAL EXPEI, X, RESULT
CD DOUBLE PRECISION EXPEI, X, RESULT
C--------------------------------------------------------------------
INT = 3
CALL CALCEI(X,RESULT,INT)
EXPEI = RESULT
RETURN
C---------- Last line of EXPEI ----------
END
FUNCTION EONE(X)
C--------------------------------------------------------------------
C
C This function program computes approximate values for the
C exponential integral E1(x), where x is real.
C
C Author: W. J. Cody
C
C Latest modification: January 12, 1988
C
C--------------------------------------------------------------------
INTEGER INT
REAL EONE, X, RESULT
CD DOUBLE PRECISION EONE, X, RESULT
C--------------------------------------------------------------------
INT = 2
CALL CALCEI(X,RESULT,INT)
EONE = RESULT
RETURN
C---------- Last line of EONE ----------
END