"CODE" 33033;
   "PROCEDURE" RKE (X, XE, N, Y, DER, DATA, FI, OUT);
   "VALUE"  FI, N; "INTEGER" N; "REAL" X, XE;
   "BOOLEAN" FI; "ARRAY" Y, DATA;
   "PROCEDURE" DER, OUT;
   "BEGIN" "INTEGER" J;
      "REAL" XT, H, HMIN, INT, HL, HT, ABSH, FHM, DISCR, TOL, MU,
      MU1, FH, E1, E2;
      "BOOLEAN" LAST, FIRST, REJECT;
      "ARRAY" K0, K1, K2, K3, K4[1:N];
      "IF" FI "THEN"
      "BEGIN" DATA[3]:= XE - X; DATA[4]:= DATA[5]:= DATA[6]:= 0 "END";
      ABSH:= H:= ABS(DATA[3]);
      "IF" XE < X "THEN" H:= - H; INT:= ABS(XE - X);
      HMIN:= INT * DATA[1] + DATA[2];
      E1:= 12 * DATA[1] / INT; E2:= 12 * DATA[2] / INT;
      FIRST:= "TRUE"; REJECT:= "FALSE"; "IF" FI "THEN"
      "BEGIN" LAST:= "TRUE"; "GOTO" STEP "END";
   TEST: ABSH:= ABS(H); "IF" ABSH < HMIN "THEN"
      "BEGIN" H:= SIGN (XE - X) * HMIN; ABSH:= HMIN "END";
      "IF" H >= XE - X "EQV" H >= 0 "THEN"
      "BEGIN" LAST:= "TRUE"; H:= XE - X; ABSH:= ABS(H) "END"
      "ELSE" LAST:= "FALSE";
   STEP: "IF" ^ REJECT "THEN"
      "BEGIN" "FOR" J:= 1 "STEP" 1 "UNTIL" N "DO" K0[J]:= Y[J];
          DER(X, K0)
      "END";
      HT:= .184262134833347 * H; XT:= X + HT;
      "FOR" J:= 1 "STEP" 1 "UNTIL" N "DO" K1[J]:= K0[J] * HT + Y[J];
      DER(XT, K1);
      HT:= .690983005625053"-1 * H; XT:= 4 * HT + X;
      "FOR" J:= 1 "STEP" 1 "UNTIL" N "DO" K2[J]:=
      (3 * K1[J] + K0[J]) * HT + Y[J];
      DER(XT, K2);
      XT:= .5 * H + X; HT:= .1875 * H;
      "FOR" J:= 1 "STEP" 1 "UNTIL" N "DO" K3[J]:=((1.74535599249993
      * K2[J] - K1[J]) * 2.23606797749979 + K0[J]) * HT + Y[J];
      DER(XT, K3);
      XT:= .723606797749979 * H + X; HT:= .4 * H;
      "FOR" J:= 1 "STEP" 1 "UNTIL" N "DO" K4[J]:= (((.517595468166681
      * K0[J] - K1[J]) * .927050983124840 + K2[J]) * 1.46352549156242
      + K3[J]) * HT + Y[J];
      DER(XT, K4);
      XT:= "IF" LAST "THEN" XE "ELSE" X + H; HT:= 2 * H;
      "FOR" J:= 1 "STEP" 1 "UNTIL" N "DO" K1[J]:= ((((2 * K4[J] +
      K2[J]) * .412022659166595 + K1[J]) * 2.23606797749979 -
      K0[J]) * .375 - K3[J]) * HT + Y[J];
      DER(XT, K1);
      REJECT:= "FALSE"; FHM:= 0;
      "FOR" J:= 1 "STEP" 1 "UNTIL" N "DO"
      "BEGIN" DISCR:= ABS((1.6 * K3[J] - K2[J] - K4[J]) * 5 +
          K0[J] + K1[J]);
         TOL:= ABS(K0[J]) * E1 + E2;
         REJECT:= DISCR > TOL "OR" REJECT;
         FH:= DISCR / TOL; "IF" FH > FHM "THEN" FHM:= FH
      "END";
      MU:= 1 / (1 + FHM) + .45; "IF" REJECT "THEN"
      "BEGIN" DATA[5]:= DATA[5] + 1; "IF" ABSH <= HMIN "THEN"
         "BEGIN" DATA[6]:= DATA[6] + 1; HL:= H; REJECT:= "FALSE";
            FIRST:= "TRUE"; "GOTO" NEXT
         "END";
         H:= MU * H; "GOTO" TEST
      "END";
      "IF" FIRST "THEN"
      "BEGIN" FIRST:= "FALSE"; HL:= H; H:= MU * H; "GOTO" ACC
      "END";
      FH:= MU * H / HL + MU - MU1; HL:= H; H:= FH * H;
   ACC: MU1:= MU; HT:= HL / 12;
      "FOR" J:= 1 "STEP" 1 "UNTIL" N "DO" Y[J]:=
      ((K2[J] + K4[J]) * 5 + K0[J] + K1[J]) * HT + Y[J];
   NEXT: DATA[3]:= HL; DATA[4]:= DATA[4] + 1; X:= XT; OUT;
      "IF" X ^= XE "THEN" "GOTO" TEST
   "END" RKE;
        "EOP"