"CODE" 33040;
"PROCEDURE" MODIFIED TAYLOR(T,TE,M0,M,U,SIGMA,TAUMIN,I,DERIVATIVE,K,
                  DATA,ALFA,NORM,AETA,RETA,ETA,RHO,OUT);
"INTEGER" M0,M,I,K,NORM;
"REAL" T,TE,SIGMA,TAUMIN,ALFA,AETA,RETA,ETA,RHO;
"ARRAY" U,DATA;
"PROCEDURE" DERIVATIVE,OUT;

"BEGIN" I:=0;
    "BEGIN" "INTEGER" N,P,Q;
        "OWN" "REAL" EC0,EC1,EC2,TAU0,TAU1,TAU2,TAUS,T2;
        "REAL" T0,TAU,TAUI,TAUEC,ECL,BETAN,GAMMA;
        "REAL" "ARRAY" C[M0:M],BETA,BETHA[1:DATA[-2]];
        "BOOLEAN" START,STEP1,LAST;

        "PROCEDURE" COEFFICIENT;
        "BEGIN" "INTEGER" J;"REAL" IFAC;
            IFAC:=1; GAMMA:=.5; N:=DATA[-2]; P:=DATA[-1];
            BETAN:=DATA[0]; Q:= "IF" P<N "THEN" P+1 "ELSE" N;
            "FOR" J:=1 "STEP" 1 "UNTIL" N "DO"
            "BEGIN" BETA[J]:=DATA[J]; IFAC:=IFAC/J;
                BETHA[J]:=IFAC-BETA[J]
            "END";
            "IF" P=N "THEN" BETHA[N]:=IFAC
        "REAL" "PROCEDURE" NORMFUNCTION(NORM,W);
        "INTEGER" NORM; "ARRAY" W;
        "BEGIN" "INTEGER" J; "REAL" S,X;
            S:=0;
            "IF" NORM=1 "THEN"
            "BEGIN" "FOR" J:=M0 "STEP" 1 "UNTIL" M "DO"
                "BEGIN"  X:=ABS(W[J]); "IF" X>S "THEN" S:=X "END"
            "END" "ELSE"
            S:=SQRT(VECVEC(M0,M,0,W,W));
            NORMFUNCTION:=S
        "END";

        "PROCEDURE" LOCAL ERROR BOUND;
        ETA:=AETA+RETA * NORMFUNCTION(NORM,U);

        "PROCEDURE" LOCAL ERROR CONSTRUCTION(I);"INTEGER" I;
        "BEGIN" "IF" I=P "THEN" "BEGIN" ECL:=0;TAUEC:=1 "END";
            "IF" I>P+1 "THEN" TAUEC:=TAUEC*TAU;
            ECL:=ECL+ABS(BETHA[I])*TAUEC*NORMFUNCTION(NORM,C);
            "IF" I=N "THEN"
            "BEGIN" EC0:=EC1;EC1:=EC2;EC2:=ECL;
                RHO:=ECL*TAU**Q
            "END"
        "END";

        "PROCEDURE" STEPSIZE;
        "BEGIN" "REAL" TAUACC,TAUSTAB,AA,BB,CC,EC;
            LOCAL ERROR BOUND;
            "IF" ETA>0 "THEN"
            "BEGIN" "IF" START "THEN"
                "BEGIN" "IF" K=0 "THEN"
                    "BEGIN" "INTEGER" J;
                        "FOR" J:=M0 "STEP" 1 "UNTIL" M "DO" C[J]:=U[J];
                        I:=1; DERIVATIVE(I,C);
                        TAUACC:=ETA/NORMFUNCTION(NORM,C);
                        STEP1:="TRUE"
                    "END" "ELSE"
                    "IF" STEP1 "THEN"
                    "BEGIN" TAUACC:=(ETA/RHO)**(1/Q)*TAU2;
                        "IF" TAUACC>10*TAU2 "THEN"
                        TAUACC:=10*TAU2 "ELSE" STEP1:="FALSE"
                    "END" "ELSE"
                    "BEGIN" BB:=(EC2-EC1)/TAU1; CC:=EC2-BB*T2;
                        EC:=BB*T+CC;
                        TAUACC:="IF" EC<0 "THEN" TAU2 "ELSE"
                        (ETA/EC)**(1/Q);
                        START:="FALSE"
                    "END"

                "END" "ELSE"
                "BEGIN" AA:=((EC0-EC1)/TAU0+(EC2-EC1)/TAU1)/
                            (TAU1+TAU0);
                    BB:=(EC2-EC1)/TAU1-AA*(2*T2-TAU1);
                    CC:=EC2-T2*(BB+AA*T2); EC:=CC+T*(BB+T*AA);
                    TAUACC:="IF" EC<0 "THEN" TAUS
                            "ELSE" (ETA/EC)**(1/Q);
                    "IF" TAUACC>ALFA*TAUS "THEN" TAUACC:=ALFA*TAUS;
                    "IF" TAUACC<GAMMA*TAUS "THEN" TAUACC:=GAMMA*TAUS;
                "END"
            "END" "ELSE" TAUACC:=TE-T;
            "IF" TAUACC<TAUMIN "THEN" TAUACC:=TAUMIN;
            TAUSTAB:=BETAN/SIGMA;
            "IF" TAUSTAB<"-12 * (T-T0) "THEN"
            "BEGIN" OUT;"GOTO" END OF MODIFIED TAYLOR "END";
            TAU:="IF" TAUACC>TAUSTAB "THEN" TAUSTAB "ELSE" TAUACC;
            TAUS:=TAU; "IF" TAU>=TE-T "THEN"
            "BEGIN" TAU:=TE-T;LAST:= "TRUE" "END";
            TAU0:=TAU1;TAU1:=TAU2;TAU2:=TAU
        "END";

        "PROCEDURE" DIFFERENCE SCHEME;
        "BEGIN" "INTEGER" J; "REAL" B;
            "FOR" J:=M0 "STEP" 1 "UNTIL" M "DO" C[J]:=U[J]; TAUI:=1;
          NEXT TERM:
            I:=I+1; DERIVATIVE(I,C); TAUI:=TAUI*TAU;
            B:=BETA[I]*TAUI;
            "IF" ETA>0 "AND" I>=P "THEN" LOCAL ERROR CONSTRUCTION(I);
            "FOR" J:=M0 "STEP" 1 "UNTIL" M "DO" U[J]:=U[J]+B*C[J];
            "IF" I<N "THEN" "GOTO" NEXT TERM;
            T2:=T; "IF" LAST "THEN"
            "BEGIN" LAST:= "FALSE"; T:= TE "END"
            "ELSE" T:= T + TAU
        "END";

        START:= K=0; T0:=T;
        COEFFICIENT; LAST:= "FALSE";
      NEXT LEVEL:
        STEPSIZE; K:=K+1; I:=0; DIFFERENCE SCHEME; OUT;
        "IF" T ^= TE "THEN" "GOTO" NEXT LEVEL
    "END";
    END OF MODIFIED TAYLOR:
"END" MODIFIED TAYLOR;
        "EOP"