*********************************************************************** * * * Program for generating Electromagnetic Structure Functions using * * consistent treatment of charm and bottom structure functions * * Not included are the effects due to NLO corrections to photon- * * gluon fusion. Charm mass = 1.35 GeV Bottom mass = 4.3 GeV * * * * A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne * * University of Durham preprint DTP/98/10 * * Rutherford Appleton Laboratory preprint RAL-TR-98-029 * * * * Setting MODE=1 gives MRST L(4)=300 MeV a_s(M_Z)=0.1175 * * Setting MODE=2 gives MRST(g^^) L(4)=300 MeV a_s(M_Z)=0.1175 * * Setting MODE=3 gives MRST(gvv) L(4)=300 MeV a_s(M_Z)=0.1175 * * Setting MODE=4 gives MRST(avv) L(4)=229 MeV a_s(M_Z)=0.1125 * * Setting MODE=5 gives MRST(a^^) L(4)=383 MeV a_s(M_Z)=0.1225 * * * * The program should be run only with iord set to 1 * * The calculation of F_L includes the full order(alpha_s^2) * * contribution * * The program is self contained, only requiring the subroutine * * mrs98.f and the grid files to be accessible * * * *********************************************************************** implicit real*8(a-h,o-z) COMMON/GAUS96/XI(96),WI(96),XX(97),NTERMS COMMON/INPUT/alambda,flavor,qsct,qsdt,iord call wate96 iord=1 flavor=3 qsdt=7.29 qsct=74. 99 read(5,*) mode,x,q2 if(mode.eq.1) alambda=0.300 if(mode.eq.2) alambda=0.300 if(mode.eq.3) alambda=0.300 if(mode.eq.4) alambda=0.229 if(mode.eq.5) alambda=0.383 call sfun(x,q2,mode,f2p,flp,f1p,rp,f2n,fln,f1n,rn, xf2c,flc,f1c,f2b,flb,f1b) print 100,x,q2,f2p,flp,f1p,f2n,fln,f1n print 101,f2c,flc,f1c,f2b,flb,f1b go to 99 100 format(1x,'x= ',f10.6,' Q2= ',f14.3/ 11x,' Proton Structure Functions '/ 25x,' F2= ',f8.4,' FL= ',f8.4,' 2xF1= ',f8.4/ 31x,' Neutron Structure Functions '/ 45x,' F2= ',f8.4,' FL= ',f8.4,' 2xF1= ',f8.4/) 101 format(1x,' Contributions from Charm'/ 15x,' F2(c)= ',f8.4,' FL(c)= ',f8.4,' 2xF1(c)= ',f8.4/ 21x,' Contributions from Bottom'/ 35x,' F2(b)= ',f8.4,' FL(b)= ',f8.4,' 2xF1(b)= ',f8.4/) end subroutine sfun(x,q2,mode,f2p,flp,f1p,rp,f2n,fln,f1n,rn, xf2c,flc,f1c,f2b,flb,f1b) implicit real*8(a-h,o-z) COMMON/GAUS96/XI(96),WI(96),XX(97),NTERMS COMMON/INPUT/alambda,flavor,qsct,qsdt,iord data pi,pi2/3.14159,9.8696/ XLAM=alambda IFL=4 xlam2=xlam*xlam t=dlog(q2/xlam2) al=alpha(t)/(4.*pi) argmin=qsdt/4./xlam2 scale=dsqrt(q2) cf=4./3. ca=3. enf=flavor iorder=iord dpsi2=2./9. ZETA2=1.64493406684823 ZETA3=1.20205690315959 ww2=(1.-x)*q2/x epsc4=qsdt/q2 fpsc4=qsdt/ww2 epsc=epsc4/4. thcq=1. if(epsc.gt.1.) thcq=0. thcw=1. if(fpsc4.gt.1.) thcw=0. epsb4=qsct/q2 fpsb4=qsct/ww2 epsb=epsb4/4. thbq=1. if(epsb.gt.1.) thbq=0. thbw=1. if(fpsb4.gt.1.) thbw=0. call mrs98(x,scale,mode,upv,dnv,usea,dsea,str,chm,bot,glu) if(epsc.gt.1.) chm=0. if(epsb.gt.1.) bot=0. fp=(4.*upv+dnv+8.*usea+2.*dsea+2.*str)/9. fn=(4.*dnv+upv+2.*usea+8.*dsea+2.*str)/9. fc=8.*chm/9. fb=2.*bot/9. ffp=0. ffn=0. ffc=0. ffb=0. chmq=0. chmg=0. chmgsw=0. chmdcg=0. chmlq=0. chmlg=0. botq=0. botg=0. botgsw=0. botdcg=0. fflp=0. ffln=0. fflc=0. fflb=0. IF(IORD.LE.0.) THEN GO TO 27 ELSE GO TO 22 ENDIF 22 CONTINUE IF3=0 FAC=FLAVOR facc=1. facb=1. IF(ifl.EQ.3.OR.ifl.EQ.4) then FAC=6./9. facc=4./9. facb=1./9. endif IF(IFL.EQ.1) IF3=1 CF=4./3. AL1=dLOG(1.-X) ffp=Fp+Fp*AL*CF*(-9.-2.*PI2/3.+AL1*(-3.+2.*AL1)) ffn=Fn+Fn*AL*CF*(-9.-2.*PI2/3.+AL1*(-3.+2.*AL1)) c ffc=ffc+fc*AL*CF*(-9.-2.*PI2/3.+AL1*(-3.+2.*AL1)) c ffb=ffb+fb*AL*CF*(-9.-2.*PI2/3.+AL1*(-3.+2.*AL1)) DO 23 I=1,NTERMS Y=0.5*(1.-X)*XI(I)+0.5*(1.+X) XY=X/Y AL1=dLOG(1.-Y) call mrs98(xy,scale,mode,upv,dnv,usea,dsea,str,chm,bot,glu) if(epsc.gt.1.) chm=0. if(epsb.gt.1.) bot=0. fpxy=(4.*upv+dnv+8.*usea+2.*dsea+2.*str)/9. fnxy=(4.*dnv+upv+2.*usea+8.*dsea+2.*str)/9. fcxy=8.*chm/9. fbxy=2.*bot/9. gluxy=glu C22=CF*(6.+4.*Y-2.*(1.+Y*Y)/(1.-Y)*dLOG(Y)-2.*(1.+Y)*AL1 2-IF3*2.*(1.+Y)) C23=CF*(-3.+4.*AL1)/(1.-Y) CG2=2.*FAC*(-1.+8.*Y*(1.-Y)+(1.-2.*Y+2.*Y*Y)*dLOG(1./Y-1.)) f1lq=4.*cf*y f1lg=8.*enf*y*(1.-y) ffp=ffp+.5*(1.-X)*WI(I)*AL*(C22*fpxy+C23*(fpxy-fp)) ffn=ffn+.5*(1.-X)*WI(I)*AL*(C22*fnxy+C23*(fnxy-fn)) c ffc=ffc+.5*(1.-X)*WI(I)*AL*(C22*fcxy+C23*(fcxy-fc)) c ffb=ffb+.5*(1.-X)*WI(I)*AL*(C22*fbxy+C23*(fbxy-fb)) fflp=fflp+.5*(1.-x)*wi(i)*al*f1lq*fpxy ffln=ffln+.5*(1.-x)*wi(i)*al*f1lq*fnxy IF(IFL-1) 23,23,24 24 CONTINUE ffp=ffp+.5*(1.-X)*WI(I)*AL*CG2*gluxy ffn=ffn+.5*(1.-X)*WI(I)*AL*CG2*gluxy fflp=fflp+.5*(1.-x)*wi(i)*al*dpsi2*f1lg*gluxy ffln=ffln+.5*(1.-x)*wi(i)*al*dpsi2*f1lg*gluxy FSXY=DPSI2*(UPV+DNV+2.*USEA+2.*DSEA+2.*STR) Y1=1.-Y Y2=Y*Y Y3=Y*Y2 Y4=Y3*Y Y5=Y4*Y DL=DLOG(Y) DL2=DL*DL DLM1=DLOG(Y1) YP1=Y+1. DLP1=DLOG(YP1) DLM2=DLOG(1.-Y2) DL3=DLOG(Y/Y1) DL4=DLOG(Y2/Y1) ALI2 =FASTLI2(Y) ALI2M=FASTLI2(-Y) ALI21=FASTLI2(Y1) ALI3 =FASTLI3(Y) ALI3M=FASTLI3(-Y) S12M =FASTS12(-Y) FACT1=4.*DL*(6.-3.*Y+47.*Y2-9.*Y3)/(15.*Y2) X-4.*ALI2M*(DL-2.*DLP1)-8.*ZETA3-2.*DL2*DLM2 X+4.*DL*DLP1*DLP1-4.*DL*ALI2+0.4*(5.-3.*Y2)*DL2 X-4.*(2.+10.*Y2+5.*Y3-3.*Y5)*(ALI2M+DL*DLP1)/(5.*Y3) X+4.*ZETA2*(DLM2-0.2*(5.-3.*Y2))+8.*S12M+4.*ALI3+4.*ALI3M X-23.*DLM1/3.-(144.+294.*Y-1729.*Y2+216.*Y3)/(90.*Y2) FACT2=ALI2+DL3*DL3-3.*ZETA2-(3.-22.*Y)*DL/(3.*Y) X+(6.-25.*Y)*DLM1/(6.*Y)-(78.-355.*Y)/(36.*Y) FACT3=DL4-(6.-25.*Y)/(6.*Y) FNS2LQ=4.*CF*(CA-2.*CF)*Y*FACT1 X+8.*CF*CF*Y*FACT2-(8./3.)*CF*ENF*Y*FACT3 FS2LQ=(16./9.)*CF*ENF*(3.*(1.-2.*Y-2.*Y2)*Y1*DLM1/Y X+9.*Y*(ALI2+DL2-ZETA2)+9.*(1.-Y-2.*Y2)*DL X-9.*Y*Y1-Y1*Y1*Y1/Y) FACT4=(1.-3.*Y-27.*Y2+29.*Y3)*DLM1/(3.*Y2) X-2.*Y1*DL*DLM1+2.*YP1*ALI2M+4.*ALI2+3.*DL2 X+2.*(Y-2.)*ZETA2+Y1*DLM1*DLM1+2.*YP1*DL*DLP1 X+(24.+192.*Y-317.*Y2)*DL/(24.*Y)+(-8.+24.*Y+501.*Y2-517.*Y3) X/(72.*Y2) FACT5=ALI2+2.*(5.+3.*Y2)*DL2/15.-(1.+3.*Y-4.*Y2)*DLM1/ X(2.*Y)+(-2.+10.*Y3-12.*Y5)*(ALI2M+DL*DLP1)/(15.*Y3) X-(5.+12.*Y2)*ZETA2/15.+(4.+13.*Y+48.*Y2-36.*Y3)*DL/(30.*Y2) X-(4.-Y-198.*Y2+195.*Y3)/(30.*Y2) FACT6=-4.*ALI21+2.*YP1*(ALI2M+DL*DLP1)+Y1*DLM1*DLM1 X+(-6.+2.*Y)*DL*DLM1+(-1./Y-9.+29./3.*Y+1./3./Y2)*DLM1 X+3.*DL2+(1./Y+8.-13.*Y)*DL+2.*Y*ZETA2+1./3./Y+17./3.-53./9.*Y X-1./9./Y2 FACT7=ALI21+DL*DLM1+(-2./3.+4./5.*Y2+2./15./Y3)*(ALI2M+DL*DLP1) X+(1./2./Y+3./2.-2.*Y)*DLM1-(2./3.+2./5.*Y2)*DL2 X+(-13./2./Y-39.+18.*Y-2./Y2)/15.*DL X+(-2./3.+4./5.*Y2)*ZETA2-8./15./Y-19./5.+21./5.*Y+2./15./Y2 F2LG=16.*CA*ENF*Y*FACT6+16.*CF*ENF*Y*FACT7 fflp=fflp+0.5*(1.-x)*WI(I)*AL*AL* X(FNS2LQ*fpxy+FS2LQ*FSXY+DPSI2*F2LG*gluxy) ffln=ffln+0.5*(1.-x)*WI(I)*AL*AL* X(FNS2LQ*fnxy+FS2LQ*FSXY+DPSI2*F2LG*gluxy) 23 CONTINUE 21 CONTINUE r7=dsqrt(7.d0) xcmax=1./(1.+epsc4) if(xcmax.le.x) go to 321 DO 323 I=1,NTERMS Y=0.5*(xcmax-X)*XI(I)+0.5*(xcmax+X) XY=X/Y call mrs98(xy,scale,mode,upv,dnv,usea,dsea,str,chm,bot,glu) if(epsc.gt.1.) chm=0. gluxy=glu fcxy=8.*chm/9. del=0.01 xyu=xy*(1.+0.5*del) if(xyu.gt.1.d0) then dfcxy=0.d0 go to 1324 endif call mrs98(xyu,scale,mode,upv,dnv,usea,dsea,str,chm,bot,glu) if(epsc.gt.1.) chm=0. fcxyu=8.*chm/9. xyl=xy*(1.-0.5*del) call mrs98(xyl,scale,mode,upv,dnv,usea,dsea,str,chm,bot,glu) if(epsc.gt.1.) chm=0. fcxyl=8.*chm/9. dfcxy=(fcxyu-fcxyl)/del 1324 c0c=cheavy(2,y,epsc) if(epsc.gt.1.d0) c0c=0.d0 cg21c=2.*facc*cheavy(1,y,epsc) cg22c=2.*facc*c0c*dlog(1./epsc) clg2c=2.*facc*cheavy(3,y,epsc) f1lq=cheavy(4,y,epsc) ffc=ffc+0.5*(xcmax-x)*wi(i)*c0c*(-dfcxy+3.*fcxy) ffc=ffc+0.5*(xcmax-x)*wi(i)*al*(cg21c-cg22c)*gluxy fflc=fflc+0.5*(xcmax-x)*wi(i)*al*f1lq*fcxy fflc=fflc+0.5*(xcmax-x)*wi(i)*al*clg2c*gluxy chmg=chmg+.5*(xcmax-X)*WI(I)*AL*(cg21c-cg22c)*gluxy chmgsw=chmgsw+.5*(xcmax-X)*WI(I)*AL*(cg21c )*gluxy chmdcg=chmdcg+.5*(xcmax-X)*WI(I)*AL*(cg22c )*gluxy chmlg=chmlg+0.5*(xcmax-x)*wi(i)*al*clg2c*gluxy fcextra=coeff2(y,epsc) ffc=ffc+0.5*(xcmax-x)*wi(i)*fcxy*fcextra c1c=cheavy(5,y,epsc) fflc=fflc+0.5*(xcmax-x)*wi(i)*al*al*c1c*fcxy cl1c=4.*cf*(1.+y-2.*y*y+2.*y*dlog(y)) clg22c=2.*facc*cl1c*dlog(1./epsc) fflc=fflc-0.5*(xcmax-x)*wi(i)*al*al*clg22c*gluxy chmlg=chmlg-0.5*(xcmax-x)*wi(i)*al*al*clg22c*gluxy 323 CONTINUE 321 CONTINUE xbmax=1./(1.+epsb4) if(xbmax.le.x) go to 421 DO 423 I=1,NTERMS Y=0.5*(xbmax-X)*XI(I)+0.5*(xbmax+X) XY=X/Y call mrs98(xy,scale,mode,upv,dnv,usea,dsea,str,chm,bot,glu) if(epsb.gt.1.) bot=0. gluxy=glu fbxy=2.*bot/9. del=0.01 xyu=xy*(1.+0.5*del) if(xyu.gt.1.d0) then dfbxy=0.d0 go to 1424 endif call mrs98(xyu,scale,mode,upv,dnv,usea,dsea,str,chm,bot,glu) if(epsb.gt.1.) bot=0. fbxyu=2.*bot/9. xyl=xy*(1.-0.5*del) call mrs98(xyl,scale,mode,upv,dnv,usea,dsea,str,chm,bot,glu) if(epsb.gt.1.) bot=0. fbxyl=2.*bot/9. dfbxy=(fbxyu-fbxyl)/del 1424 c0b=cheavy(2,y,epsb) if(epsb.gt.1.d0) c0b=0.d0 cg21b=2.*facb*cheavy(1,y,epsb) cg22b=2.*facb*c0b*dlog(1./epsb) clg2b=2.*facb*cheavy(3,y,epsb) f1lq=cheavy(4,y,epsb) ffb=ffb+0.5*(xbmax-x)*wi(i)*c0b*(-dfbxy+3.*fbxy) ffb=ffb+0.5*(xbmax-x)*wi(i)*al*(cg21b-cg22b)*gluxy fflb=fflb+0.5*(xcmax-x)*wi(i)*al*f1lq*fbxy fflb=fflb+0.5*(xcmax-x)*wi(i)*al*clg2b*gluxy botg=botg+.5*(xbmax-X)*WI(I)*AL*(cg21b-cg22b)*gluxy botgsw=botgsw+.5*(xbmax-X)*WI(I)*AL*(cg21b )*gluxy botdcg=botdcg+.5*(xbmax-X)*WI(I)*AL*(cg22b )*gluxy fbextra=coeff2(y,epsb) ffb=ffb+0.5*(xbmax-x)*wi(i)*fbxy*fbextra c1b=cheavy(5,y,epsb) fflb=fflb+0.5*(xbmax-x)*wi(i)*al*al*c1b*fbxy cl1b=4.*cf*(1.+y-2.*y*y+2.*y*dlog(y)) clg22b=2.*facb*cl1b*dlog(1./epsb) fflb=fflb-0.5*(xbmax-x)*wi(i)*al*al*clg22b*gluxy botlg=botlg-0.5*(xbmax-x)*wi(i)*al*al*clg22b*gluxy 423 CONTINUE 421 CONTINUE if(ffc.lt.0.) ffc=0. if(ffb.lt.0.) ffb=0. f2p=ffp+ffc+ffb f2n=ffn+ffc+ffb f2c=ffc f2b=ffb chmq=ffc-chmg chmlq=fflc-chmlg botq=ffb-botg flp=fflp+fflc+fflb fln=ffln+fflc+fflb flc=fflc flb=fflb f1p=f2p-flp f1n=f2n-fln f1c=f2c-flc f1b=f2b-flb rp=flp/f1p rn=fln/f1n 27 RETURN END real*8 function coeff2(y,eps) implicit real*8(a-h,o-z) dimension z1(17),z2(17) data z1/-0.183E+01,0.400E+01,0.159E+02,-0.357E+02, .-0.186E+00,-0.988E+02,0.712E+02,0.631E+02,-0.136E+01, .0.175E+03,-0.158E+03,-0.433E+02,0.375E+01,-0.913E+02, .0.842E+02,0.107E+02,0.629E+00/ data z2/-0.204E+01,-0.127E+01,0.117E+01,-0.208E+00, .-0.228E+02,0.261E+03,-0.340E+03,0.153E+03,-0.591E+02, .-0.199E+04,-0.113E+04,0.299E+04,-0.408E+04,-0.446E+04, . 0.307E+05,-0.282E+05,0.144E+02/ epsl=eps eps4=4.d0*eps x0=1.d0/(1.d0+eps4) yx0=y/x0 yx01=1.d0-yx0 epsl2=epsl*epsl epsl3=epsl2*epsl if(y.lt.0.05) go to 100 a0=z1(1)+z1(2)*epsl+z1(3)*epsl2+z1(4)*epsl3 a1=z1(5)+z1(6)*epsl+z1(7)*epsl2+z1(8)*epsl3 a2=z1(9)+z1(10)*epsl+z1(11)*epsl2+z1(12)*epsl3 a3=z1(13)+z1(14)*epsl+z1(15)*epsl2+z1(16)*epsl3 fac=a0+a1*yx0+a2*yx0*yx0+a3*yx0*yx0*yx0 coeff2=fac*yx01**z1(17) return 100 continue a0=z2(1)+z2(2)*epsl+z2(3)*epsl2+z2(4)*epsl3 a1=z2(5)+z2(6)*epsl+z2(7)*epsl2+z2(8)*epsl3 a2=z2(9)+z2(10)*epsl+z2(11)*epsl2+z2(12)*epsl3 a3=z2(13)+z2(14)*epsl+z2(15)*epsl2+z2(16)*epsl3 fac=a0+a1*yx0+a2*yx0*yx0+a3*yx0*yx0*yx0 coeff2=fac*yx01**z2(17) return end real*8 function coeff3(y,eps) implicit real*8(a-h,o-z) dimension z1(17),z2(17) data z1/-0.857E+00,0.217E+02,-0.199E+02,0.162E+02, .0.204E+00,-0.142E+03,0.101E+03,-0.575E+02,0.832E+00, .0.175E+03,-0.139E+03,0.604E+02,0.344E-01,-0.648E+02, .0.538E+02,-0.160E+02,0.000E+00/ data z2/-0.334E-03,0.677E-02,-0.108E-02,0.825E-03, .-0.425E+04,0.883E+05,-0.562E+05,0.601E+05,0.562E+07, .-0.122E+09,0.912E+08,-0.928E+08,-0.236E+10,0.499E+11, .-0.449E+11,0.412E+11,0.000E+00/ epsl=eps eps4=4.d0*eps x0=1.d0/(1.d0+eps) yx0=y/x0 yx01=1.d0-yx0 epsl2=epsl*epsl epsl3=epsl2*epsl if(y.lt.0.05) go to 100 a0=z1(1)+z1(2)*epsl+z1(3)*epsl2+z1(4)*epsl3 a1=z1(5)+z1(6)*epsl+z1(7)*epsl2+z1(8)*epsl3 a2=z1(9)+z1(10)*epsl+z1(11)*epsl2+z1(12)*epsl3 a3=z1(13)+z1(14)*epsl+z1(15)*epsl2+z1(16)*epsl3 fac=a0+a1*yx0+a2*yx0*yx0+a3*yx0*yx0*yx0 coeff3=fac*yx01**z1(17) return 100 continue a0=z2(1)+z2(2)*epsl+z2(3)*epsl2+z2(4)*epsl3 a1=z2(5)+z2(6)*epsl+z2(7)*epsl2+z2(8)*epsl3 a2=z2(9)+z2(10)*epsl+z2(11)*epsl2+z2(12)*epsl3 a3=z2(13)+z2(14)*epsl+z2(15)*epsl2+z2(16)*epsl3 fac=a0+a1*yx0+a2*yx0*yx0+a3*yx0*yx0*yx0 coeff3=fac*yx01**z2(17) return end DOUBLE PRECISION FUNCTION ALPHA(T) IMPLICIT REAL*8(A-H,O-Z) COMMON/INPUT/alambda,flavor,qsct,qsdt,iord DATA PI/3.14159/ DATA TOL/.0005/ ITH=0 TT=T qsdtt=qsdt/4. qsctt=qsct/4. AL=ALAMBDA AL2=AL*AL FLAV=4. QS=AL2*dEXP(T) if(qs.lt.0.5d0) then !! running stops below 0.5 qs=0.5d0 t=dlog(qs/al2) tt=t endif IF(QS.gt.QSCTT) GO TO 12 IF(QS.lt.QSDTT) GO TO 312 11 CONTINUE B0=11-2.*FLAV/3. IF(IORD)1,1,2 c IF(IORD)2,2,2 !TAKE CARE !! 1 CONTINUE ALPHA=4.*PI/B0/T RETURN 2 CONTINUE X1=4.*PI/B0 B1=102.-38.*FLAV/3. X2=B1/B0**2 AS=X1/T*(1.-X2*dLOG(T)/T) 5 CONTINUE F=-T+X1/AS-X2*dLOG(X1/AS+X2) FP=-X1/AS**2*(1.-X2/(X1/AS+X2)) AS2=AS-F/FP DEL=ABS(F/FP/AS) IF(DEL-TOL)3,3,4 3 CONTINUE ALPHA=AS2 IF(ITH.EQ.0) RETURN GO TO (13,14,15) ITH 4 CONTINUE AS=AS2 GO TO 5 12 ITH=1 T=dLOG(QSCTT/AL2) GO TO 11 13 ALFQC4=ALPHA FLAV=5. ITH=2 GO TO 11 14 ALFQC5=ALPHA ITH=3 T=TT GO TO 11 15 ALFQS5=ALPHA ALFINV=1./ALFQS5+1./ALFQC4-1./ALFQC5 ALPHA=1./ALFINV RETURN 311 CONTINUE B0=11-2.*FLAV/3. IF(IORD)31,31,32 c IF(IORD)32,32,32 !TAKE CARE !! 31 CONTINUE ALPHA=4.*PI/B0/T RETURN 32 CONTINUE X1=4.*PI/B0 B1=102.-38.*FLAV/3. X2=B1/B0**2 AS=X1/T*(1.-X2*dLOG(T)/T) 35 CONTINUE F=-T+X1/AS-X2*dLOG(X1/AS+X2) FP=-X1/AS**2*(1.-X2/(X1/AS+X2)) AS2=AS-F/FP DEL=ABS(F/FP/AS) IF(DEL-TOL)33,33,34 33 CONTINUE ALPHA=AS2 IF(ITH.EQ.0) RETURN GO TO (313,314,315) ITH 34 CONTINUE AS=AS2 GO TO 35 312 ITH=1 T=dLOG(QSDTT/AL2) GO TO 311 313 ALFQC4=ALPHA FLAV=3. ITH=2 GO TO 311 314 ALFQC3=ALPHA ITH=3 T=TT GO TO 311 315 ALFQS3=ALPHA ALFINV=1./ALFQS3+1./ALFQC4-1./ALFQC3 ALPHA=1./ALFINV RETURN END SUBROUTINE WATE96 C******************************************************************* C***** ***** C***** THE X(I) AND W(I) ARE THE DIRECT OUTPUT FROM A PROGRAM ***** C***** USING NAG ROUTINE D01BCF TO CALCULATE THE ***** C***** GAUSS-LEGENDRE WEIGHTS FOR 96 POINT INTEGRATION. ***** C***** THEY AGREE TO TYPICALLY 14 DECIMAL PLACES WITH THE ***** C***** TABLE IN ABRAMOWITZ & STEGUN, PAGE 919. ***** C***** ***** C***** ----> PETER HARRIMAN, APRIL 3RD 1990. ***** C***** ***** C******************************************************************* IMPLICIT REAL*8 (A-H,O-Z) DIMENSION X(48),W(48) COMMON/GAUS96/XI(96),WI(96),XX(97),NTERMS NTERMS=96 X( 1)= 0.01627674484960183561 X( 2)= 0.04881298513604856015 X( 3)= 0.08129749546442434360 X( 4)= 0.11369585011066471632 X( 5)= 0.14597371465489567682 X( 6)= 0.17809688236761733390 X( 7)= 0.21003131046056591064 X( 8)= 0.24174315616383866556 X( 9)= 0.27319881259104774468 X(10)= 0.30436494435449495954 X(11)= 0.33520852289262397655 X(12)= 0.36569686147231213885 X(13)= 0.39579764982890709712 X(14)= 0.42547898840729897474 X(15)= 0.45470942216774136446 X(16)= 0.48345797392059470382 X(17)= 0.51169417715466604391 X(18)= 0.53938810832435567233 X(19)= 0.56651041856139533470 X(20)= 0.59303236477757022282 X(21)= 0.61892584012546672523 X(22)= 0.64416340378496526886 X(23)= 0.66871831004391424358 X(24)= 0.69256453664216964528 X(25)= 0.71567681234896561582 X(26)= 0.73803064374439816819 X(27)= 0.75960234117664555964 X(28)= 0.78036904386743123629 X(29)= 0.80030874413913884180 X(30)= 0.81940031073792957139 X(31)= 0.83762351122818502758 X(32)= 0.85495903343459936363 X(33)= 0.87138850590929436968 X(34)= 0.88689451740241818933 X(35)= 0.90146063531585023110 X(36)= 0.91507142312089592706 X(37)= 0.92771245672230655266 X(38)= 0.93937033975275308073 X(39)= 0.95003271778443564022 X(40)= 0.95968829144874048809 X(41)= 0.96832682846326217918 X(42)= 0.97593917458513455843 X(43)= 0.98251726356301274934 X(44)= 0.98805412632962202890 X(45)= 0.99254390032376081654 X(46)= 0.99598184298720747465 X(47)= 0.99836437586317963722 X(48)= 0.99968950388322870559 W( 1)= 0.03255061449236316962 W( 2)= 0.03251611871386883307 W( 3)= 0.03244716371406427668 W( 4)= 0.03234382256857594104 W( 5)= 0.03220620479403026124 W( 6)= 0.03203445623199267876 W( 7)= 0.03182875889441101874 W( 8)= 0.03158933077072719007 W( 9)= 0.03131642559686137819 W(10)= 0.03101033258631386231 W(11)= 0.03067137612366917839 W(12)= 0.03029991542082762553 W(13)= 0.02989634413632842385 W(14)= 0.02946108995816795100 W(15)= 0.02899461415055528410 W(16)= 0.02849741106508543861 W(17)= 0.02797000761684838950 W(18)= 0.02741296272602931385 W(19)= 0.02682686672559184485 W(20)= 0.02621234073567250055 W(21)= 0.02557003600534944960 W(22)= 0.02490063322248370695 W(23)= 0.02420484179236479915 W(24)= 0.02348339908592633665 W(25)= 0.02273706965832950717 W(26)= 0.02196664443874448477 W(27)= 0.02117293989219144572 W(28)= 0.02035679715433347898 W(29)= 0.01951908114014518992 W(30)= 0.01866067962741165898 W(31)= 0.01778250231604547316 W(32)= 0.01688547986424539715 W(33)= 0.01597056290256253144 W(34)= 0.01503872102699521608 W(35)= 0.01409094177231515264 W(36)= 0.01312822956696188190 W(37)= 0.01215160467108866759 W(38)= 0.01116210209983888144 W(39)= 0.01016077053500880978 W(40)= 0.00914867123078384552 W(41)= 0.00812687692569928101 W(42)= 0.00709647079115442616 W(43)= 0.00605854550423662775 W(44)= 0.00501420274292825661 W(45)= 0.00396455433844564804 W(46)= 0.00291073181793626202 W(47)= 0.00185396078894924657 W(48)= 0.00079679206555731759 DO 1 I=1,48 XI(I)=-X(49-I) WI(I)=W(49-I) XI(I+48)=X(I) WI(I+48)=W(I) 1 CONTINUE DO 2 I=1,96 2 XX(I)=0.5*(XI(I)+1.) XX(97)=1.0 EXPON=1.0 DO 3 I=1,96 YI=2.*(0.5*(1.+XI(I)))**EXPON-1. WI(I)=WI(I)/(1.+XI(I))*(1.+YI)*EXPON XI(I)=YI XX(I)=0.5*(1.+YI) 3 CONTINUE RETURN END real*8 function cheavy(i,z,eps) implicit real*8(a-h,o-z) c this function returns the values of C_g(z,Q^2) c and the deriv. wrt log Q^2. Here eps=m^2/Q^2. c If i=1 C_g for F2. If i=2 deriv of C_g for F2 c If i=3 C_g for FL. If i=4 (1-m2/Q2)*beta*Clq(massless) c If i=5 (1-m2/Q2)*beta*Clq(1)(massless) if(i.gt.5) stop z1=1.-z z2=z*z eps2=eps*eps beta2=1.-4.*eps*z/z1 if(beta2.lt.0.) go to 10 beta=dsqrt(beta2) a=z2+z1*z1 b=4.*z*(1.-3.*z) c=-8.*z2 aa=8.*z*z1-1. bb=-4.*z*z1 arg=(1.+beta)/(1.-beta) fac=dlog(arg) cf=4./3. ca=3. enf=4. ZETA2=1.64493406684823 ZETA3=1.20205690315959 go to (1,2,3,4,5) i 1 cheavy=(a+b*eps+c*eps2)*fac+(aa+bb*eps)*beta return 2 cheavy=(-b*eps-2.*c*eps2)*fac+(a+b*eps+c*eps2)/beta . +(-bb*eps)*beta +(aa+bb*eps)*2.*z*eps/z1/beta return 3 cheavy=-bb*beta+c*eps*fac return 4 cheavy=(1.-eps)*beta*4.*cf*z return 5 y=z Y1=1.-Y Y2=Y*Y Y3=Y*Y2 Y4=Y3*Y Y5=Y4*Y DL=DLOG(Y) DL2=DL*DL DLM1=DLOG(Y1) YP1=Y+1. DLP1=DLOG(YP1) DLM2=DLOG(1.-Y2) DL3=DLOG(Y/Y1) DL4=DLOG(Y2/Y1) ALI2 =FASTLI2(Y) ALI2M=FASTLI2(-Y) ALI21=FASTLI2(Y1) ALI3 =FASTLI3(Y) ALI3M=FASTLI3(-Y) S12M =FASTS12(-Y) FACT1=4.*DL*(6.-3.*Y+47.*Y2-9.*Y3)/(15.*Y2) X-4.*ALI2M*(DL-2.*DLP1)-8.*ZETA3-2.*DL2*DLM2 X+4.*DL*DLP1*DLP1-4.*DL*ALI2+0.4*(5.-3.*Y2)*DL2 X-4.*(2.+10.*Y2+5.*Y3-3.*Y5)*(ALI2M+DL*DLP1)/(5.*Y3) X+4.*ZETA2*(DLM2-0.2*(5.-3.*Y2))+8.*S12M+4.*ALI3+4.*ALI3M X-23.*DLM1/3.-(144.+294.*Y-1729.*Y2+216.*Y3)/(90.*Y2) FACT2=ALI2+DL3*DL3-3.*ZETA2-(3.-22.*Y)*DL/(3.*Y) X+(6.-25.*Y)*DLM1/(6.*Y)-(78.-355.*Y)/(36.*Y) FACT3=DL4-(6.-25.*Y)/(6.*Y) FNS2LQ=4.*CF*(CA-2.*CF)*Y*FACT1 X+8.*CF*CF*Y*FACT2-(8./3.)*CF*ENF*Y*FACT3 cheavy=(1.-eps)*beta*FNS2LQ return 10 print 99 99 format(1x,'x > x0') stop end FUNCTION FASTLI2(X) IMPLICIT REAL*8(A-H,O-Z) COMPLEX*16 WGPLG FASTLI2=WGPLG(1,1,X) RETURN END FUNCTION FASTS12(X) IMPLICIT REAL*8(A-H,O-Z) COMPLEX*16 WGPLG FASTS12=WGPLG(1,2,X) RETURN END FUNCTION FASTLI3(X) IMPLICIT REAL*8(A-H,O-Z) COMPLEX*16 WGPLG FASTLI3=WGPLG(2,1,X) RETURN END C C 24/08/89 101231638 MEMBER NAME WGPLG (ZWPROD.S) F77 C NOTE THAT WGPLG(1,1,X) IS DILOG(X) !! COMPLEX FUNCTION WGPLG*16(N,P,X) INTEGER P,P1,NC(10),INDEX(31) DOUBLE PRECISION FCT(0:4),SGN(0:4),U(0:4),S1(4,4),C(4,4) DOUBLE PRECISION A(0:30,10) DOUBLE PRECISION X,X1,H,ALFA,R,Q,C1,C2,B0,B1,B2,ZERO,HALF COMPLEX*16 V(0:5),SK,SM DATA FCT /1.0D0,1.0D0,2.0D0,6.0D0,24.0D0/ DATA SGN /1.0D0,-1.0D0,1.0D0,-1.0D0,1.0D0/ DATA ZERO /0.0D0/, HALF /0.5D0/ DATA C1 /1.33333 33333 333D0/, C2 /0.33333 33333 3333D0/ DATA S1(1,1) /1.64493 40668 482D0/ DATA S1(1,2) /1.20205 69031 596D0/ DATA S1(1,3) /1.08232 32337 111D0/ DATA S1(1,4) /1.03692 77551 434D0/ DATA S1(2,1) /1.20205 69031 596D0/ DATA S1(2,2) /2.70580 80842 778D-1/ DATA S1(2,3) /9.65511 59989 444D-2/ DATA S1(3,1) /1.08232 32337 111D0/ DATA S1(3,2) /9.65511 59989 444D-2/ DATA S1(4,1) /1.03692 77551 434D0/ DATA C(1,1) / 1.64493 40668 482D0/ DATA C(1,2) / 1.20205 69031 596D0/ DATA C(1,3) / 1.08232 32337 111D0/ DATA C(1,4) / 1.03692 77551 434D0/ DATA C(2,1) / 0.00000 00000 000D0/ DATA C(2,2) /-1.89406 56589 945D0/ DATA C(2,3) /-3.01423 21054 407D0/ DATA C(3,1) / 1.89406 56589 945D0/ DATA C(3,2) / 3.01423 21054 407D0/ DATA C(4,1) / 0.00000 00000 000D0/ DATA INDEX /1,2,3,4,6*0,5,6,7,7*0,8,9,8*0,10/ DATA NC /24,26,28,30,22,24,26,19,22,17/ DATA A( 0,1) / .96753 21504 3498D0/ DATA A( 1,1) / .16607 30329 2785D0/ DATA A( 2,1) / .02487 93229 2423D0/ DATA A( 3,1) / .00468 63619 5945D0/ DATA A( 4,1) / .00100 16274 9616D0/ DATA A( 5,1) / .00023 20021 9609D0/ DATA A( 6,1) / .00005 68178 2272D0/ DATA A( 7,1) / .00001 44963 0056D0/ DATA A( 8,1) / .00000 38163 2946D0/ DATA A( 9,1) / .00000 10299 0426D0/ DATA A(10,1) / .00000 02835 7538D0/ DATA A(11,1) / .00000 00793 8705D0/ DATA A(12,1) / .00000 00225 3670D0/ DATA A(13,1) / .00000 00064 7434D0/ DATA A(14,1) / .00000 00018 7912D0/ DATA A(15,1) / .00000 00005 5029D0/ DATA A(16,1) / .00000 00001 6242D0/ DATA A(17,1) / .00000 00000 4827D0/ DATA A(18,1) / .00000 00000 1444D0/ DATA A(19,1) / .00000 00000 0434D0/ DATA A(20,1) / .00000 00000 0131D0/ DATA A(21,1) / .00000 00000 0040D0/ DATA A(22,1) / .00000 00000 0012D0/ DATA A(23,1) / .00000 00000 0004D0/ DATA A(24,1) / .00000 00000 0001D0/ DATA A( 0,2) / .95180 88912 7832D0/ DATA A( 1,2) / .43131 13184 6532D0/ DATA A( 2,2) / .10002 25071 4905D0/ DATA A( 3,2) / .02442 41559 5220D0/ DATA A( 4,2) / .00622 51246 3724D0/ DATA A( 5,2) / .00164 07883 1235D0/ DATA A( 6,2) / .00044 40792 0265D0/ DATA A( 7,2) / .00012 27749 4168D0/ DATA A( 8,2) / .00003 45398 1284D0/ DATA A( 9,2) / .00000 98586 9565D0/ DATA A(10,2) / .00000 28485 6995D0/ DATA A(11,2) / .00000 08317 0847D0/ DATA A(12,2) / .00000 02450 3950D0/ DATA A(13,2) / .00000 00727 6496D0/ DATA A(14,2) / .00000 00217 5802D0/ DATA A(15,2) / .00000 00065 4616D0/ DATA A(16,2) / .00000 00019 8033D0/ DATA A(17,2) / .00000 00006 0204D0/ DATA A(18,2) / .00000 00001 8385D0/ DATA A(19,2) / .00000 00000 5637D0/ DATA A(20,2) / .00000 00000 1735D0/ DATA A(21,2) / .00000 00000 0536D0/ DATA A(22,2) / .00000 00000 0166D0/ DATA A(23,2) / .00000 00000 0052D0/ DATA A(24,2) / .00000 00000 0016D0/ DATA A(25,2) / .00000 00000 0005D0/ DATA A(26,2) / .00000 00000 0002D0/ DATA A( 0,3) / .98161 02799 1365D0/ DATA A( 1,3) / .72926 80632 0726D0/ DATA A( 2,3) / .22774 71490 9321D0/ DATA A( 3,3) / .06809 08329 6197D0/ DATA A( 4,3) / .02013 70118 3064D0/ DATA A( 5,3) / .00595 47848 0197D0/ DATA A( 6,3) / .00176 76901 3959D0/ DATA A( 7,3) / .00052 74821 8502D0/ DATA A( 8,3) / .00015 82746 1460D0/ DATA A( 9,3) / .00004 77492 2076D0/ DATA A(10,3) / .00001 44792 0408D0/ DATA A(11,3) / .00000 44115 4886D0/ DATA A(12,3) / .00000 13500 3870D0/ DATA A(13,3) / .00000 04148 1779D0/ DATA A(14,3) / .00000 01279 3307D0/ DATA A(15,3) / .00000 00395 9070D0/ DATA A(16,3) / .00000 00122 9055D0/ DATA A(17,3) / .00000 00038 2658D0/ DATA A(18,3) / .00000 00011 9459D0/ DATA A(19,3) / .00000 00003 7386D0/ DATA A(20,3) / .00000 00001 1727D0/ DATA A(21,3) / .00000 00000 3687D0/ DATA A(22,3) / .00000 00000 1161D0/ DATA A(23,3) / .00000 00000 0366D0/ DATA A(24,3) / .00000 00000 0116D0/ DATA A(25,3) / .00000 00000 0037D0/ DATA A(26,3) / .00000 00000 0012D0/ DATA A(27,3) / .00000 00000 0004D0/ DATA A(28,3) / .00000 00000 0001D0/ DATA A( 0,4) /1.06405 21184 614 D0/ DATA A( 1,4) /1.06917 20744 981 D0/ DATA A( 2,4) / .41527 19325 1768D0/ DATA A( 3,4) / .14610 33293 6222D0/ DATA A( 4,4) / .04904 73264 8784D0/ DATA A( 5,4) / .01606 34086 0396D0/ DATA A( 6,4) / .00518 88935 0790D0/ DATA A( 7,4) / .00166 29871 7324D0/ DATA A( 8,4) / .00053 05827 9969D0/ DATA A( 9,4) / .00016 88702 9251D0/ DATA A(10,4) / .00005 36832 8059D0/ DATA A(11,4) / .00001 70592 3313D0/ DATA A(12,4) / .00000 54217 4374D0/ DATA A(13,4) / .00000 17239 4082D0/ DATA A(14,4) / .00000 05485 3275D0/ DATA A(15,4) / .00000 01746 7795D0/ DATA A(16,4) / .00000 00556 7550D0/ DATA A(17,4) / .00000 00177 6234D0/ DATA A(18,4) / .00000 00056 7224D0/ DATA A(19,4) / .00000 00018 1313D0/ DATA A(20,4) / .00000 00005 8012D0/ DATA A(21,4) / .00000 00001 8579D0/ DATA A(22,4) / .00000 00000 5955D0/ DATA A(23,4) / .00000 00000 1911D0/ DATA A(24,4) / .00000 00000 0614D0/ DATA A(25,4) / .00000 00000 0197D0/ DATA A(26,4) / .00000 00000 0063D0/ DATA A(27,4) / .00000 00000 0020D0/ DATA A(28,4) / .00000 00000 0007D0/ DATA A(29,4) / .00000 00000 0002D0/ DATA A(30,4) / .00000 00000 0001D0/ DATA A( 0,5) / .97920 86066 9175D0/ DATA A( 1,5) / .08518 81314 8683D0/ DATA A( 2,5) / .00855 98522 2013D0/ DATA A( 3,5) / .00121 17721 4413D0/ DATA A( 4,5) / .00020 72276 8531D0/ DATA A( 5,5) / .00003 99695 8691D0/ DATA A( 6,5) / .00000 83806 4065D0/ DATA A( 7,5) / .00000 18684 8945D0/ DATA A( 8,5) / .00000 04366 6087D0/ DATA A( 9,5) / .00000 01059 1733D0/ DATA A(10,5) / .00000 00264 7892D0/ DATA A(11,5) / .00000 00067 8700D0/ DATA A(12,5) / .00000 00017 7654D0/ DATA A(13,5) / .00000 00004 7342D0/ DATA A(14,5) / .00000 00001 2812D0/ DATA A(15,5) / .00000 00000 3514D0/ DATA A(16,5) / .00000 00000 0975D0/ DATA A(17,5) / .00000 00000 0274D0/ DATA A(18,5) / .00000 00000 0077D0/ DATA A(19,5) / .00000 00000 0022D0/ DATA A(20,5) / .00000 00000 0006D0/ DATA A(21,5) / .00000 00000 0002D0/ DATA A(22,5) / .00000 00000 0001D0/ DATA A( 0,6) / .95021 85196 3952D0/ DATA A( 1,6) / .29052 52916 1433D0/ DATA A( 2,6) / .05081 77406 1716D0/ DATA A( 3,6) / .00995 54376 7280D0/ DATA A( 4,6) / .00211 73389 5031D0/ DATA A( 5,6) / .00047 85947 0550D0/ DATA A( 6,6) / .00011 33432 1308D0/ DATA A( 7,6) / .00002 78473 3104D0/ DATA A( 8,6) / .00000 70478 8108D0/ DATA A( 9,6) / .00000 18278 8740D0/ DATA A(10,6) / .00000 04838 7492D0/ DATA A(11,6) / .00000 01303 3842D0/ DATA A(12,6) / .00000 00356 3769D0/ DATA A(13,6) / .00000 00098 7174D0/ DATA A(14,6) / .00000 00027 6586D0/ DATA A(15,6) / .00000 00007 8279D0/ DATA A(16,6) / .00000 00002 2354D0/ DATA A(17,6) / .00000 00000 6435D0/ DATA A(18,6) / .00000 00000 1866D0/ DATA A(19,6) / .00000 00000 0545D0/ DATA A(20,6) / .00000 00000 0160D0/ DATA A(21,6) / .00000 00000 0047D0/ DATA A(22,6) / .00000 00000 0014D0/ DATA A(23,6) / .00000 00000 0004D0/ DATA A(24,6) / .00000 00000 0001D0/ DATA A( 0,7) / .95064 03218 6777D0/ DATA A( 1,7) / .54138 28546 5171D0/ DATA A( 2,7) / .13649 97959 0321D0/ DATA A( 3,7) / .03417 94232 8207D0/ DATA A( 4,7) / .00869 02788 3583D0/ DATA A( 5,7) / .00225 28408 4155D0/ DATA A( 6,7) / .00059 51608 9806D0/ DATA A( 7,7) / .00015 99561 7766D0/ DATA A( 8,7) / .00004 36521 3096D0/ DATA A( 9,7) / .00001 20747 4688D0/ DATA A(10,7) / .00000 33801 8176D0/ DATA A(11,7) / .00000 09563 2476D0/ DATA A(12,7) / .00000 02731 3129D0/ DATA A(13,7) / .00000 00786 6968D0/ DATA A(14,7) / .00000 00228 3195D0/ DATA A(15,7) / .00000 00066 7205D0/ DATA A(16,7) / .00000 00019 6191D0/ DATA A(17,7) / .00000 00005 8018D0/ DATA A(18,7) / .00000 00001 7246D0/ DATA A(19,7) / .00000 00000 5151D0/ DATA A(20,7) / .00000 00000 1545D0/ DATA A(21,7) / .00000 00000 0465D0/ DATA A(22,7) / .00000 00000 0141D0/ DATA A(23,7) / .00000 00000 0043D0/ DATA A(24,7) / .00000 00000 0013D0/ DATA A(25,7) / .00000 00000 0004D0/ DATA A(26,7) / .00000 00000 0001D0/ DATA A( 0,8) / .98800 01167 2229D0/ DATA A( 1,8) / .04364 06760 9601D0/ DATA A( 2,8) / .00295 09117 8278D0/ DATA A( 3,8) / .00031 47780 9720D0/ DATA A( 4,8) / .00004 31484 6029D0/ DATA A( 5,8) / .00000 69381 8230D0/ DATA A( 6,8) / .00000 12464 0350D0/ DATA A( 7,8) / .00000 02429 3628D0/ DATA A( 8,8) / .00000 00504 0827D0/ DATA A( 9,8) / .00000 00109 9075D0/ DATA A(10,8) / .00000 00024 9467D0/ DATA A(11,8) / .00000 00005 8540D0/ DATA A(12,8) / .00000 00001 4127D0/ DATA A(13,8) / .00000 00000 3492D0/ DATA A(14,8) / .00000 00000 0881D0/ DATA A(15,8) / .00000 00000 0226D0/ DATA A(16,8) / .00000 00000 0059D0/ DATA A(17,8) / .00000 00000 0016D0/ DATA A(18,8) / .00000 00000 0004D0/ DATA A(19,8) / .00000 00000 0001D0/ DATA A( 0,9) / .95768 50654 6350D0/ DATA A( 1,9) / .19725 24967 9534D0/ DATA A( 2,9) / .02603 37031 3918D0/ DATA A( 3,9) / .00409 38216 8261D0/ DATA A( 4,9) / .00072 68170 7110D0/ DATA A( 5,9) / .00014 09187 9261D0/ DATA A( 6,9) / .00002 92045 8914D0/ DATA A( 7,9) / .00000 63763 1144D0/ DATA A( 8,9) / .00000 14516 7850D0/ DATA A( 9,9) / .00000 03420 5281D0/ DATA A(10,9) / .00000 00829 4302D0/ DATA A(11,9) / .00000 00206 0784D0/ DATA A(12,9) / .00000 00052 2823D0/ DATA A(13,9) / .00000 00013 5066D0/ DATA A(14,9) / .00000 00003 5451D0/ DATA A(15,9) / .00000 00000 9436D0/ DATA A(16,9) / .00000 00000 2543D0/ DATA A(17,9) / .00000 00000 0693D0/ DATA A(18,9) / .00000 00000 0191D0/ DATA A(19,9) / .00000 00000 0053D0/ DATA A(20,9) / .00000 00000 0015D0/ DATA A(21,9) / .00000 00000 0004D0/ DATA A(22,9) / .00000 00000 0001D0/ DATA A( 0,10) / .99343 65167 1347D0/ DATA A( 1,10) / .02225 77012 6826D0/ DATA A( 2,10) / .00101 47557 4703D0/ DATA A( 3,10) / .00008 17515 6250D0/ DATA A( 4,10) / .00000 89997 3547D0/ DATA A( 5,10) / .00000 12082 3987D0/ DATA A( 6,10) / .00000 01861 6913D0/ DATA A( 7,10) / .00000 00317 4723D0/ DATA A( 8,10) / .00000 00058 5215D0/ DATA A( 9,10) / .00000 00011 4739D0/ DATA A(10,10) / .00000 00002 3652D0/ DATA A(11,10) / .00000 00000 5082D0/ DATA A(12,10) / .00000 00000 1131D0/ DATA A(13,10) / .00000 00000 0259D0/ DATA A(14,10) / .00000 00000 0061D0/ DATA A(15,10) / .00000 00000 0015D0/ DATA A(16,10) / .00000 00000 0004D0/ DATA A(17,10) / .00000 00000 0001D0/ IF(N .LT. 1 .OR. N .GT. 4 .OR. P .LT. 1 .OR. P .GT. 4 .OR. 1 N+P .GT. 5) THEN WGPLG=ZERO PRINT 1000, N,P RETURN END IF IF(X .EQ. SGN(0)) THEN WGPLG=S1(N,P) RETURN END IF IF(X .GT. FCT(2) .OR. X .LT. SGN(1)) THEN X1=SGN(0)/X H=C1*X1+C2 ALFA=H+H V(0)=SGN(0) V(1)=LOG(DCMPLX(-X,ZERO)) DO 33 L = 2,N+P 33 V(L)=V(1)*V(L-1)/L SK=ZERO DO 34 K = 0,P-1 P1=P-K R=X1**P1/(FCT(P1)*FCT(N-1)) SM=ZERO DO 35 M = 0,K N1=N+K-M L=INDEX(10*N1+P1-10) B1=ZERO B2=ZERO DO 31 I = NC(L),0,-1 B0=A(I,L)+ALFA*B1-B2 B2=B1 31 B1=B0 Q=(FCT(N1-1)/FCT(K-M))*(B0-H*B2)*R/P1**N1 35 SM=SM+V(M)*Q 34 SK=SK+SGN(K)*SM SM=ZERO DO 36 M = 0,N-1 36 SM=SM+V(M)*C(N-M,P) WGPLG=SGN(N)*SK+SGN(P)*(SM+V(N+P)) RETURN END IF IF(X .GT. HALF) THEN X1=SGN(0)-X H=C1*X1+C2 ALFA=H+H V(0)=SGN(0) U(0)=SGN(0) V(1)=LOG(DCMPLX(X1,ZERO)) U(1)=LOG(X) DO 23 L = 2,P 23 V(L)=V(1)*V(L-1)/L DO 26 L = 2,N 26 U(L)=U(1)*U(L-1)/L SK=ZERO DO 24 K = 0,N-1 P1=N-K R=X1**P1/FCT(P1) SM=ZERO DO 25 M = 0,P-1 N1=P-M L=INDEX(10*N1+P1-10) B1=ZERO B2=ZERO DO 12 I = NC(L),0,-1 B0=A(I,L)+ALFA*B1-B2 B2=B1 12 B1=B0 Q=SGN(M)*(B0-H*B2)*R/P1**N1 25 SM=SM+V(M)*Q 24 SK=SK+U(K)*(S1(P1,P)-SM) WGPLG=SK+SGN(P)*U(N)*V(P) RETURN END IF L=INDEX(10*N+P-10) H=C1*X+C2 ALFA=H+H B1=ZERO B2=ZERO DO 11 I = NC(L),0,-1 B0=A(I,L)+ALFA*B1-B2 B2=B1 11 B1=B0 WGPLG=(B0-H*B2)*X**P/(FCT(P)*P**N) RETURN 1000 FORMAT(/' ***** CERN SUBROUTINE WGPLG ... ILLEGAL VALUES', 1 ' N = ',I3,' P = ',I3) END