438 lines
		
	
	
		
			13 KiB
		
	
	
	
		
			Plaintext
		
	
	
	
	
	
		
		
			
		
	
	
			438 lines
		
	
	
		
			13 KiB
		
	
	
	
		
			Plaintext
		
	
	
	
	
	
|   | subroutine ft8b(dd0,newdat,nQSOProgress,nfqso,nftx,ndepth,lapon,napwid,       & | ||
|  |      lsubtract,nagain,iaptype,mygrid6,bcontest,sync0,f1,xdt,xbase,apsym,      & | ||
|  |      nharderrors,dmin,nbadcrc,ipass,iera,message,xsnr)   | ||
|  | 
 | ||
|  |   use timer_module, only: timer | ||
|  |   include 'ft8_params.f90' | ||
|  |   parameter(NRECENT=10,NP2=2812) | ||
|  |   character message*22,msgsent*22 | ||
|  |   character*12 recent_calls(NRECENT) | ||
|  |   character*6 mygrid6 | ||
|  |   logical bcontest | ||
|  |   real a(5) | ||
|  |   real s1(0:7,ND),s2(0:7,NN),s1sort(8*ND) | ||
|  |   real ps(0:7),psl(0:7) | ||
|  |   real bmeta(3*ND),bmetb(3*ND),bmetap(3*ND) | ||
|  |   real llr(3*ND),llra(3*ND),llr0(3*ND),llr1(3*ND),llrap(3*ND)           !Soft symbols | ||
|  |   real dd0(15*12000) | ||
|  |   integer*1 decoded(KK),apmask(3*ND),cw(3*ND) | ||
|  |   integer*1 msgbits(KK) | ||
|  |   integer apsym(KK) | ||
|  |   integer mcq(28),mde(28),mrrr(16),m73(16),mrr73(16) | ||
|  |   integer itone(NN) | ||
|  |   integer indxs1(8*ND) | ||
|  |   integer icos7(0:6),ip(1) | ||
|  |   integer nappasses(0:5)  ! the number of decoding passes to use for each QSO state | ||
|  |   integer naptypes(0:5,4) ! (nQSOProgress, decoding pass)  maximum of 4 passes for now | ||
|  |   complex cd0(3200) | ||
|  |   complex ctwk(32) | ||
|  |   complex csymb(32) | ||
|  |   logical first,newdat,lsubtract,lapon,nagain | ||
|  |   equivalence (s1,s1sort) | ||
|  |   data icos7/2,5,6,0,4,1,3/ | ||
|  |   data mcq/1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,1,1,0,0,1/ | ||
|  |   data mrrr/0,1,1,1,1,1,1,0,1,1,0,0,1,1,1,1/ | ||
|  |   data m73/0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0/ | ||
|  |   data mde/1,1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,1,1,0,1,0,0,0,1/ | ||
|  |   data mrr73/0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,1/ | ||
|  |   data first/.true./ | ||
|  |   save nappasses,naptypes | ||
|  | 
 | ||
|  |   if(first) then | ||
|  |      mcq=2*mcq-1 | ||
|  |      mde=2*mde-1 | ||
|  |      mrrr=2*mrrr-1 | ||
|  |      m73=2*m73-1 | ||
|  |      mrr73=2*mrr73-1 | ||
|  |      nappasses(0)=2 | ||
|  |      nappasses(1)=2 | ||
|  |      nappasses(2)=2 | ||
|  |      nappasses(3)=4 | ||
|  |      nappasses(4)=4 | ||
|  |      nappasses(5)=3 | ||
|  | 
 | ||
|  | ! iaptype | ||
|  | !------------------------ | ||
|  | !   1        CQ     ???    ??? | ||
|  | !   2        MyCall ???    ??? | ||
|  | !   3        MyCall DxCall ??? | ||
|  | !   4        MyCall DxCall RRR | ||
|  | !   5        MyCall DxCall 73 | ||
|  | !   6        MyCall DxCall RR73 | ||
|  | !   7        ???    DxCall ??? | ||
|  | 
 | ||
|  |      naptypes(0,1:4)=(/1,2,0,0/) | ||
|  |      naptypes(1,1:4)=(/2,3,0,0/) | ||
|  |      naptypes(2,1:4)=(/2,3,0,0/) | ||
|  |      naptypes(3,1:4)=(/3,4,5,6/) | ||
|  |      naptypes(4,1:4)=(/3,4,5,6/) | ||
|  |      naptypes(5,1:4)=(/3,1,2,0/)  !? | ||
|  |      first=.false. | ||
|  |   endif | ||
|  | 
 | ||
|  |   max_iterations=30 | ||
|  |   nharderrors=-1 | ||
|  |   fs2=12000.0/NDOWN | ||
|  |   dt2=1.0/fs2 | ||
|  |   twopi=8.0*atan(1.0) | ||
|  |   delfbest=0. | ||
|  |   ibest=0 | ||
|  | 
 | ||
|  |   call timer('ft8_down',0) | ||
|  |   call ft8_downsample(dd0,newdat,f1,cd0)   !Mix f1 to baseband and downsample | ||
|  |   call timer('ft8_down',1) | ||
|  | 
 | ||
|  |   i0=nint((xdt+0.5)*fs2)                   !Initial guess for start of signal | ||
|  |   smax=0.0 | ||
|  |   do idt=i0-8,i0+8                         !Search over +/- one quarter symbol | ||
|  |      call sync8d(cd0,idt,ctwk,0,sync) | ||
|  |      if(sync.gt.smax) then | ||
|  |         smax=sync | ||
|  |         ibest=idt | ||
|  |      endif | ||
|  |   enddo | ||
|  |   xdt2=ibest*dt2                           !Improved estimate for DT | ||
|  | 
 | ||
|  | ! Now peak up in frequency | ||
|  |   i0=nint(xdt2*fs2) | ||
|  |   smax=0.0 | ||
|  |   do ifr=-5,5                              !Search over +/- 2.5 Hz | ||
|  |     delf=ifr*0.5 | ||
|  |     dphi=twopi*delf*dt2 | ||
|  |     phi=0.0 | ||
|  |     do i=1,32 | ||
|  |       ctwk(i)=cmplx(cos(phi),sin(phi)) | ||
|  |       phi=mod(phi+dphi,twopi) | ||
|  |     enddo | ||
|  |    call sync8d(cd0,i0,ctwk,1,sync) | ||
|  |     if( sync .gt. smax ) then | ||
|  |       smax=sync | ||
|  |       delfbest=delf | ||
|  |     endif | ||
|  |   enddo | ||
|  |   a=0.0 | ||
|  |   a(1)=-delfbest | ||
|  |   call twkfreq1(cd0,NP2,fs2,a,cd0) | ||
|  |   xdt=xdt2 | ||
|  |   f1=f1+delfbest                           !Improved estimate of DF | ||
|  | 
 | ||
|  |   call sync8d(cd0,i0,ctwk,2,sync) | ||
|  | 
 | ||
|  |   j=0 | ||
|  |   do k=1,NN | ||
|  |     i1=ibest+(k-1)*32 | ||
|  |     csymb=cmplx(0.0,0.0) | ||
|  |     if( i1.ge.1 .and. i1+31 .le. NP2 ) csymb=cd0(i1:i1+31) | ||
|  |     call four2a(csymb,32,1,-1,1) | ||
|  |     s2(0:7,k)=abs(csymb(1:8))/1e3 | ||
|  |   enddo   | ||
|  | 
 | ||
|  | ! sync quality check | ||
|  |   is1=0 | ||
|  |   is2=0 | ||
|  |   is3=0 | ||
|  |   do k=1,7 | ||
|  |     ip=maxloc(s2(:,k)) | ||
|  |     if(icos7(k-1).eq.(ip(1)-1)) is1=is1+1 | ||
|  |     ip=maxloc(s2(:,k+36)) | ||
|  |     if(icos7(k-1).eq.(ip(1)-1)) is2=is2+1 | ||
|  |     ip=maxloc(s2(:,k+72)) | ||
|  |     if(icos7(k-1).eq.(ip(1)-1)) is3=is3+1 | ||
|  |   enddo | ||
|  | ! hard sync sum - max is 21 | ||
|  |   nsync=is1+is2+is3 | ||
|  |   if(nsync .le. 6) then ! bail out | ||
|  |     nbadcrc=1 | ||
|  |     return | ||
|  |   endif | ||
|  | 
 | ||
|  |   j=0 | ||
|  |   do k=1,NN | ||
|  |      if(k.le.7) cycle | ||
|  |      if(k.ge.37 .and. k.le.43) cycle | ||
|  |      if(k.gt.72) cycle | ||
|  |      j=j+1 | ||
|  |      s1(0:7,j)=s2(0:7,k) | ||
|  |   enddo   | ||
|  | 
 | ||
|  |   call indexx(s1sort,8*ND,indxs1) | ||
|  |   xmeds1=s1sort(indxs1(nint(0.5*8*ND))) | ||
|  |   s1=s1/xmeds1 | ||
|  | 
 | ||
|  |   do j=1,ND | ||
|  |      i4=3*j-2 | ||
|  |      i2=3*j-1 | ||
|  |      i1=3*j | ||
|  | ! Max amplitude | ||
|  |      ps=s1(0:7,j) | ||
|  |      r1=max(ps(1),ps(3),ps(5),ps(7))-max(ps(0),ps(2),ps(4),ps(6)) | ||
|  |      r2=max(ps(2),ps(3),ps(6),ps(7))-max(ps(0),ps(1),ps(4),ps(5)) | ||
|  |      r4=max(ps(4),ps(5),ps(6),ps(7))-max(ps(0),ps(1),ps(2),ps(3)) | ||
|  |      bmeta(i4)=r4 | ||
|  |      bmeta(i2)=r2 | ||
|  |      bmeta(i1)=r1 | ||
|  |      bmetap(i4)=r4 | ||
|  |      bmetap(i2)=r2 | ||
|  |      bmetap(i1)=r1 | ||
|  | ! Max log metric | ||
|  |      psl=log(ps) | ||
|  |      r1=max(psl(1),psl(3),psl(5),psl(7))-max(psl(0),psl(2),psl(4),psl(6)) | ||
|  |      r2=max(psl(2),psl(3),psl(6),psl(7))-max(psl(0),psl(1),psl(4),psl(5)) | ||
|  |      r4=max(psl(4),psl(5),psl(6),psl(7))-max(psl(0),psl(1),psl(2),psl(3)) | ||
|  |      bmetb(i4)=r4 | ||
|  |      bmetb(i2)=r2 | ||
|  |      bmetb(i1)=r1 | ||
|  | 
 | ||
|  | ! Metric for Cauchy noise | ||
|  | !     r1=log(ps(1)**3+ps(3)**3+ps(5)**3+ps(7)**3)- & | ||
|  | !        log(ps(0)**3+ps(2)**3+ps(4)**3+ps(6)**3) | ||
|  | !     r2=log(ps(2)**3+ps(3)**3+ps(6)**3+ps(7)**3)- & | ||
|  | !        log(ps(0)**3+ps(1)**3+ps(4)**3+ps(5)**3) | ||
|  | !     r4=log(ps(4)**3+ps(5)**3+ps(6)**3+ps(7)**3)- & | ||
|  | !        log(ps(0)**3+ps(1)**3+ps(2)**3+ps(3)**3) | ||
|  | ! Metric for AWGN, no fading | ||
|  | !     bscale=2.5 | ||
|  | !     b0=bessi0(bscale*ps(0)) | ||
|  | !     b1=bessi0(bscale*ps(1)) | ||
|  | !     b2=bessi0(bscale*ps(2)) | ||
|  | !     b3=bessi0(bscale*ps(3)) | ||
|  | !     b4=bessi0(bscale*ps(4)) | ||
|  | !     b5=bessi0(bscale*ps(5)) | ||
|  | !     b6=bessi0(bscale*ps(6)) | ||
|  | !     b7=bessi0(bscale*ps(7)) | ||
|  | !     r1=log(b1+b3+b5+b7)-log(b0+b2+b4+b6) | ||
|  | !     r2=log(b2+b3+b6+b7)-log(b0+b1+b4+b5) | ||
|  | !     r4=log(b4+b5+b6+b7)-log(b0+b1+b2+b3) | ||
|  | 
 | ||
|  |      if(nQSOProgress .eq. 0 .or. nQSOProgress .eq. 5) then | ||
|  | ! When bits 88:115 are set as ap bits, bit 115 lives in symbol 39 along | ||
|  | ! with no-ap bits 116 and 117. Take care of metrics for bits 116 and 117. | ||
|  |         if(j.eq.39) then  ! take care of bits that live in symbol 39 | ||
|  |            if(apsym(28).lt.0) then | ||
|  |               bmetap(i2)=max(ps(2),ps(3))-max(ps(0),ps(1)) | ||
|  |               bmetap(i1)=max(ps(1),ps(3))-max(ps(0),ps(2)) | ||
|  |            else  | ||
|  |               bmetap(i2)=max(ps(6),ps(7))-max(ps(4),ps(5)) | ||
|  |               bmetap(i1)=max(ps(5),ps(7))-max(ps(4),ps(6)) | ||
|  |            endif | ||
|  |         endif | ||
|  |      endif | ||
|  | 
 | ||
|  | ! When bits 116:143 are set as ap bits, bit 115 lives in symbol 39 along | ||
|  | ! with ap bits 116 and 117. Take care of metric for bit 115. | ||
|  | !        if(j.eq.39) then  ! take care of bit 115 | ||
|  | !           iii=2*(apsym(29)+1)/2 + (apsym(30)+1)/2  ! known values of bits 116 & 117 | ||
|  | !           if(iii.eq.0) bmetap(i4)=ps(4)-ps(0) | ||
|  | !           if(iii.eq.1) bmetap(i4)=ps(5)-ps(1) | ||
|  | !           if(iii.eq.2) bmetap(i4)=ps(6)-ps(2) | ||
|  | !           if(iii.eq.3) bmetap(i4)=ps(7)-ps(3) | ||
|  | !        endif | ||
|  | 
 | ||
|  | ! bit 144 lives in symbol 48 and will be 1 if it is set as an ap bit. | ||
|  | ! take care of metrics for bits 142 and 143 | ||
|  |      if(j.eq.48) then  ! bit 144 is always 1 | ||
|  |        bmetap(i4)=max(ps(5),ps(7))-max(ps(1),ps(3)) | ||
|  |        bmetap(i2)=max(ps(3),ps(7))-max(ps(1),ps(5)) | ||
|  |      endif  | ||
|  | 
 | ||
|  | ! bit 154 lives in symbol 52 and will be 0 if it is set as an ap bit | ||
|  | ! take care of metrics for bits 155 and 156 | ||
|  |      if(j.eq.52) then  ! bit 154 will be 0 if it is set as an ap bit. | ||
|  |         bmetap(i2)=max(ps(2),ps(3))-max(ps(0),ps(1)) | ||
|  |         bmetap(i1)=max(ps(1),ps(3))-max(ps(0),ps(2)) | ||
|  |      endif   | ||
|  | 
 | ||
|  |   enddo | ||
|  | 
 | ||
|  |   call normalizebmet(bmeta,3*ND) | ||
|  |   call normalizebmet(bmetb,3*ND) | ||
|  |   call normalizebmet(bmetap,3*ND) | ||
|  | 
 | ||
|  |   scalefac=2.83 | ||
|  |   llr0=scalefac*bmeta | ||
|  |   llr1=scalefac*bmetb | ||
|  |   llra=scalefac*bmetap  ! llr's for use with ap | ||
|  |   apmag=scalefac*(maxval(abs(bmetap))*1.01) | ||
|  | 
 | ||
|  | ! pass # | ||
|  | !------------------------------ | ||
|  | !   1        regular decoding | ||
|  | !   2        erase 24 | ||
|  | !   3        erase 48 | ||
|  | !   4        ap pass 1 | ||
|  | !   5        ap pass 2 | ||
|  | !   6        ap pass 3 | ||
|  | !   7        ap pass 4, etc. | ||
|  | 
 | ||
|  |   if(lapon) then  | ||
|  |      npasses=4+nappasses(nQSOProgress) | ||
|  |   else | ||
|  |      npasses=4 | ||
|  |   endif | ||
|  | 
 | ||
|  |   do ipass=1,npasses  | ||
|  |                 | ||
|  |      llr=llr0 | ||
|  |      if(ipass.eq.2) llr=llr1 | ||
|  |      if(ipass.eq.3) llr(1:24)=0.  | ||
|  |      if(ipass.eq.4) llr(1:48)=0.  | ||
|  |      if(ipass.le.4) then | ||
|  |         apmask=0 | ||
|  |         llrap=llr | ||
|  |         iaptype=0 | ||
|  |      endif | ||
|  |          | ||
|  |      if(ipass .gt. 4) then | ||
|  |         iaptype=naptypes(nQSOProgress,ipass-4) | ||
|  |         if(iaptype.ge.3 .and. (abs(f1-nfqso).gt.napwid .and. abs(f1-nftx).gt.napwid) ) cycle  | ||
|  |         if(iaptype.eq.1 .or. iaptype.eq.2 ) then ! AP,???,???  | ||
|  |            apmask=0 | ||
|  |            apmask(88:115)=1    ! first 28 bits are AP | ||
|  |            apmask(144)=1       ! not free text | ||
|  |            llrap=llr | ||
|  |            if(iaptype.eq.1) llrap(88:115)=apmag*mcq | ||
|  |            if(iaptype.eq.2) llrap(88:115)=apmag*apsym(1:28) | ||
|  |            llrap(116:117)=llra(116:117)   | ||
|  |            llrap(142:143)=llra(142:143) | ||
|  |            llrap(144)=-apmag | ||
|  |         endif | ||
|  |         if(iaptype.eq.3) then   ! mycall, dxcall, ??? | ||
|  |            apmask=0 | ||
|  |            apmask(88:115)=1   ! mycall | ||
|  |            apmask(116:143)=1  ! hiscall | ||
|  |            apmask(144)=1      ! not free text | ||
|  |            llrap=llr | ||
|  |            llrap(88:143)=apmag*apsym(1:56) | ||
|  |            llrap(144)=-apmag | ||
|  |         endif | ||
|  |         if(iaptype.eq.4 .or. iaptype.eq.5 .or. iaptype.eq.6) then   | ||
|  |            apmask=0 | ||
|  |            apmask(88:115)=1   ! mycall | ||
|  |            apmask(116:143)=1  ! hiscall | ||
|  |            apmask(144:159)=1  ! RRR or 73 or RR73 | ||
|  |            llrap=llr | ||
|  |            llrap(88:143)=apmag*apsym(1:56) | ||
|  |            if(iaptype.eq.4) llrap(144:159)=apmag*mrrr  | ||
|  |            if(iaptype.eq.5) llrap(144:159)=apmag*m73  | ||
|  |            if(iaptype.eq.6) llrap(144:159)=apmag*mrr73  | ||
|  |         endif | ||
|  |         if(iaptype.eq.7) then   ! ???, dxcall, ??? | ||
|  |            apmask=0 | ||
|  |            apmask(116:143)=1  ! hiscall | ||
|  |            apmask(144)=1      ! not free text | ||
|  |            llrap=llr | ||
|  |            llrap(115)=llra(115) | ||
|  |            llrap(116:143)=apmag*apsym(29:56) | ||
|  |            llrap(144)=-apmag | ||
|  |         endif | ||
|  |      endif | ||
|  | 
 | ||
|  |      cw=0 | ||
|  |      call timer('bpd174  ',0) | ||
|  |      call bpdecode174(llrap,apmask,max_iterations,decoded,cw,nharderrors,  & | ||
|  |           niterations) | ||
|  |      call timer('bpd174  ',1) | ||
|  |      dmin=0.0 | ||
|  |      if(ndepth.eq.3 .and. nharderrors.lt.0) then | ||
|  |         ndeep=3 | ||
|  |         if(abs(nfqso-f1).le.napwid .or. abs(nftx-f1).le.napwid) then | ||
|  |           if((ipass.eq.3 .or. ipass.eq.4) .and. .not.nagain) then | ||
|  |             ndeep=3  | ||
|  |           else    | ||
|  |             ndeep=4   | ||
|  |           endif | ||
|  |         endif | ||
|  |         if(nagain) ndeep=5 | ||
|  |         call timer('osd174  ',0) | ||
|  |         call osd174(llrap,apmask,ndeep,decoded,cw,nharderrors,dmin) | ||
|  |         call timer('osd174  ',1) | ||
|  |      endif | ||
|  |      nbadcrc=1 | ||
|  |      message='                      ' | ||
|  |      xsnr=-99.0 | ||
|  |      if(count(cw.eq.0).eq.174) cycle           !Reject the all-zero codeword | ||
|  | !###     if(any(decoded(73:75).ne.0)) cycle        !Reject if any of the 3 extra bits is nonzero | ||
|  |      if(nharderrors.ge.0 .and. nharderrors+dmin.lt.60.0 .and. &         | ||
|  |         .not.(sync.lt.2.0 .and. nharderrors.gt.35)      .and. & | ||
|  |         .not.(ipass.gt.2 .and. nharderrors.gt.39)       .and. & | ||
|  |         .not.(ipass.eq.4 .and. nharderrors.gt.30)             & | ||
|  |        ) then | ||
|  |         call chkcrc12a(decoded,nbadcrc) | ||
|  |      else | ||
|  |         nharderrors=-1 | ||
|  |         cycle  | ||
|  |      endif | ||
|  | !### | ||
|  |      i3bit=4*decoded(73) + 2*decoded(74) + decoded(75) | ||
|  |      iFreeText=decoded(57) | ||
|  | !     if(nbadcrc.eq.0) write(*,3001) nharderrors,nbadcrc,i3bit | ||
|  | !3001 format('A',3i5) | ||
|  | !###      | ||
|  |      if(nbadcrc.eq.0) then | ||
|  |         call extractmessage174(decoded,message,ncrcflag,recent_calls,nrecent) | ||
|  |         call genft8(message,mygrid6,bcontest,i3bit,msgsent,msgbits,itone) | ||
|  |         if(i3bit.eq.1 .and. iFreeText.eq.0) message(21:21)='1' | ||
|  |         if(i3bit.eq.2 .and. iFreeText.eq.0) message(21:21)='2' | ||
|  |         if(lsubtract) call subtractft8(dd0,itone,f1,xdt2) | ||
|  |         xsig=0.0 | ||
|  |         xnoi=0.0 | ||
|  |         do i=1,79 | ||
|  |            xsig=xsig+s2(itone(i),i)**2 | ||
|  |            ios=mod(itone(i)+4,7) | ||
|  |            xnoi=xnoi+s2(ios,i)**2 | ||
|  |         enddo | ||
|  |         xsnr=0.001 | ||
|  |         if(xnoi.gt.0 .and. xnoi.lt.xsig) xsnr=xsig/xnoi-1.0 | ||
|  |         xsnr=10.0*log10(xsnr)-27.0 | ||
|  |         xsnr2=db(xsig/xbase - 1.0) - 32.0 | ||
|  | !        write(52,3052) f1,xdt,xsig,xnoi,xbase,xsnr,xsnr2 | ||
|  | !3052    format(7f10.2) | ||
|  |         if(.not.nagain) xsnr=xsnr2 | ||
|  |         if(xsnr .lt. -24.0) xsnr=-24.0 | ||
|  |         return | ||
|  |      endif | ||
|  |   enddo | ||
|  |   | ||
|  |   return | ||
|  | end subroutine ft8b | ||
|  | 
 | ||
|  | subroutine normalizebmet(bmet,n) | ||
|  |   real bmet(n) | ||
|  | 
 | ||
|  |   bmetav=sum(bmet)/real(n) | ||
|  |   bmet2av=sum(bmet*bmet)/real(n) | ||
|  |   var=bmet2av-bmetav*bmetav | ||
|  |   if( var .gt. 0.0 ) then | ||
|  |      bmetsig=sqrt(var) | ||
|  |   else | ||
|  |      bmetsig=sqrt(bmet2av) | ||
|  |   endif | ||
|  |   bmet=bmet/bmetsig | ||
|  |   return | ||
|  | end subroutine normalizebmet | ||
|  | 
 | ||
|  | 
 | ||
|  | function bessi0(x)  | ||
|  | ! From Numerical Recipes | ||
|  |    real bessi0,x | ||
|  |    double precision p1,p2,p3,p4,p5,p6,p7,q1,q2,q3,q4,q5,q6,q7,q8,q9,y | ||
|  |    save p1,p2,p3,p4,p5,p6,p7,q1,q2,q3,q4,q5,q6,q7,q8,q9 | ||
|  |    data p1,p2,p3,p4,p5,p6,p7/1.0d0,3.5156229d0,3.0899424d0,1.2067492d0, & | ||
|  |       0.2659732d0,0.360768d-1,0.45813d-2/ | ||
|  |    data q1,q2,q3,q4,q5,q6,q7,q8,q9/0.39894228d0,0.1328592d-1,           & | ||
|  |       0.225319d-2,-0.157565d-2,0.916281d-2,-0.2057706d-1,               & | ||
|  |       0.2635537d-1,-0.1647633d-1,0.392377d-2/ | ||
|  | 
 | ||
|  |    if (abs(x).lt.3.75) then  | ||
|  |       y=(x/3.75)**2 | ||
|  |       bessi0=p1+y*(p2+y*(p3+y*(p4+y*(p5+y*(p6+y*p7)))))  | ||
|  |    else | ||
|  |       ax=abs(x) | ||
|  |       y=3.75/ax  | ||
|  |       bessi0=(exp(ax)/sqrt(ax))*(q1+y*(q2+y*(q3+y*(q4         & | ||
|  |            +y*(q5+y*(q6+y*(q7+y*(q8+y*q9)))))))) | ||
|  |    endif | ||
|  |    return | ||
|  | end function bessi0 | ||
|  | 
 |