\def\date{05 Nov 2011}\def\source{V1F1, p.\ 47}\def\author{Udo Wermuth}\input mmix =-3 !!\clearline{\tenbf Farey series}\smallskip t IS $255 LOC Data_Segment _x GREG @ LOC Data_Segment+4*10000 _y GREG @ LOC #100 !!\gts Computation of Farey series !!\gts Calling sequence: \mb{SET \$1,$n$; PUSHJ \$0,:Farey} !!\gts Entry conditions:$n$in \mb{\$1} is the order of the series, $1 < n < 182$ !!\gts \qquad \mb{\l\_x} and \mb{\l\_y} are arrays, each for at least 10000 tetras !!\gts Exit conditions: \mb{\$0} is number of$x/y$pairs, i.e., entries generated in \mb{\l\_x} and \mb{\l\_y} PREFIX :FAREY: !! \startnumbering n IS$1 !! Parameter: order of the Farey series kk IS $2 !!$\mb{kk} \gets 4*k$yk IS$3 !! $y_k$ yk1 IS $4 !!$y_{k+1}$xk IS$5 !! $x_k$ xk1 IS $6 !!$x_{k+1}$flr IS$7 yk2 IS $8 !!$y_{k+2}$xk2 IS$9 !! $x_{k+2}$ :Farey SET n,$0 !1! Get the parameter. SET xk,0 !1! Init for$k=0$. STTU xk,:_x,4*0 !1! SET yk,1 !1! STTU yk,:_y,4*0 !1! SET xk1,1 !1! Init for$k=1$. STTU xk1,:_x,4*1 !1! SET yk1,n !1! STTU yk1,:_y,4*1 !1! SET kk,4 !1!$k\gets1$. nextval ADDU flr,yk,n !A! Calculate the next values \mb{xk2} and \mb{yk2}. DIVU flr,flr,yk1 !A!$\mb{flr} \gets \lfloor(\mb{yk}+n)/\mb{yk1}\rfloor$. MULU xk2,flr,xk1 !A! SUBU xk2,xk2,xk !A!$\mmm xk2 \gets \mmm flr*\mmm xk1 - \mm xk$. MULU yk2,flr,yk1 !A! SUBU yk2,yk2,yk !A!$\mmm yk2 \gets \mmm flr*\mmm yk1 - \mm yk$. INCL kk,4 !A!$k \gets k + 1$. STTU xk2,:_x,kk !A! STTU yk2,:_y,kk !A! SET xk,xk1 !A! Shuffle the registers. SET xk1,xk2 !A! SET yk,yk1 !A! SET yk1,yk2 !A! CMPU flr,xk2,yk2 !A! The computation stops when PBNZ flr,nextval !A!\bad1\bad \quad$1 = 1/1$is computed. INCL kk,4 !1! SR kk,kk,2 !1! Remove factor for tetra. SET$0,kk !1! The number of elements POP 1,0 !1! \quad is returned.\eop !!\endwAoA\bye PREFIX : !!\gts Output the Farey series to StdOut !!\gts Calling sequence: \mb{SET \$1,$x$; PUSHJ \$0,:Output} !!\gts Entry condition: $x$ is the number of quotients to output, the data is in \mb{\l\_x} and \mb{\l\_y} !!\gts Exit condition: PREFIX :Output: LOC (@+7)&-8 GREG @ Buf BYTE " / ",#a,0 !! Template for output NoPairs BYTE "000 pairs x/y have been generated",#a,0 _template GREG #202020202F202020 !! This is \vs\vs\vs\vs/\vs\vs\vs'' items IS $1 !! Parameter: number of array entries asc IS$2 !! An ASCII char idx IS $3 !! Index to {\tt\l\_x} and {\tt\l\_y} acc IS$4 !! The accumulator pos IS $5 !! Position in Buf :Output SET items,$0 !! Get parameter. SL items,items,2 !! Work with tetras. SET idx,0 !! Init index for data. SET acc,$0 !! Print parameter. LDA :t,NoPairs SET pos,2 0H DIV acc,acc,10 GET asc,:rR INCL asc,'0' !! Get an ASCII digit STBU asc,:t,pos !! \quad and store it into \mb{NoPairs}. SUB pos,pos,1 PBNZ acc,0B PBN pos,2F !! Fill leading zeros with blanks. SET asc,' ' 1H STBU asc,:t,pos SUB pos,pos,1 PBNN pos,1B 2H TRAP 0,:Fputs,:StdOut 7H STOU _template,Buf !! Clear buffer. LDA pos,Buf+2 LDTU acc,:_x,idx !! Get value from array \mb{\l\_x}. 0H DIV acc,acc,10 GET asc,:rR INCL asc,'0' !! Convert to ASCII digit STBU asc,pos,0 !! \quad and store it into \mb{Buf}. SUB pos,pos,1 PBNZ acc,0B !! Continue if$\mb{acc} > 0$. LDA pos,Buf+7 !! Now output the \mb{\l\_y} value. LDTU acc,:_y,idx 0H DIV acc,acc,10 GET asc,:rR INCL asc,'0' STBU asc,pos,0 SUB pos,pos,1 PBNZ acc,0B LDA :t,Buf TRAP 0,:Fputs,:StdOut !! Output \mb{Buf} and newline. INCL idx,4 !! Next entries from the data arrays. CMP :t,items,idx !! Done? PBNZ :t,7B !! No, go back. POP 0,0 !! Yes, return. PREFIX : !!\gts ord IS$1 !! parameter to Farey: order of the series pairs IS ord !! parameter to Output: number of pairs GREG @ Banner BYTE "Farey series of order " Order BYTE "00",#a,0 Main SET ord,#2037 !! First set the order to 7. STWU ord,:Order LDA t,Banner TRAP 0,Fputs,StdOut !! Print Banner. SET ord,7 PUSHJ $0,:Farey !! Call Farey. SET pairs,$0 !! Get number of pairs PUSHJ $0,:Output !! \quad and output the pairs. SET ord,#3133 !! Next set the order to 13. STWU ord,:Order LDA t,Banner TRAP 0,Fputs,StdOut SET ord,13 PUSHJ$0,:Farey SET pairs,$0 PUSHJ$0,:Output SET ord,#3339 !! Last test with order 39. STWU ord,:Order LDA t,Banner TRAP 0,Fputs,StdOut SET ord,39 PUSHJ $0,:Farey SET pairs,$0 PUSHJ \$0,:Output TRAP 0,Halt,0 !! \eop