BEGIN                                                          CMNT0001
COMMENT       NEWTON FORWARD AND BACKWARD INTERPOLATION PROCEDURE       CMNT0002

              J. K. KONDO                                               CMNT0003
              (PROFESSIONAL SERVICES, BURROUGHS CORPORATION).           CMNT0004

              PROCEDURE CARD SEQUENCE STARTS WITH NFBI0001.             CMNT0005
              FIRST RELEASE 06-28-1963  ;                               CMNT0006


PROCEDURE     INTERP(XO,XF,H,Y,X,BETA,EPSILON,M,INW,LLABEL)  ;          NFBI0001
VALUE         XO,XF,H,X,BETA,EPSILON,M  ;                               NFBI0002
INTEGER       M  ;                                                      NFBI0003
REAL          XO,XF,H,X,EPSILON,INW  ;                                  NFBI0004
BOOLEAN       BETA  ;                                                   NFBI0005
ARRAY         Y[0]  ;                                                   NFBI0006
         BEGIN                                                          NFBI0008
LABEL         LLABEL  ;                                                 NFBI0007
INTEGER       N,I,J,K  ;                                                NFBI0009
REAL          U1,U,TEMP  ;                                              NFBI0010
LABEL         NFOR,L1,NBAK,L2,EOP  ;                                    NFBI0011
              IF (X < (XO - 2|H)) OR (X > (XF + 2|H)) THEN GO TO LLABEL;NFBI0012
              N ~ ABS((XF - XO)/H)  ;  IF M > N THEN M ~ N  ;           NFBI0013
              U1 ~ (XF + XO)/2.0  ;  K ~ 1  ;                           NFBI0014
              IF X < (U1 - 5 | H) THEN GO TO NFOR ELSE                  NFBI0015
              IF (X > U1 + 5 | H) OR BETA THEN GO TO NBAK  ;            NFBI0016
NFOR:         J ~ M - 1  ;  U ~ (X - XO)/H  ;                           NFBI0017
              INW ~ Y[0]  ;  U1 ~ 1.0  ;                                NFBI0018
L1:           Y[0] ~ Y[1] - Y[0]  ;                                     NFBI0019
              IF ABS(Y[0]) < EPSILON THEN GO TO EOP  ;                  NFBI0020
              U1 ~ U1|(U-K+1.0)/K  ;                                    NFBI0021
              INW ~ INW + U1 | Y[0]  ;                                  NFBI0022
              IF K = M THEN GO TO EOP  ;                                NFBI0023
              FOR I ~ 1 STEP 1 UNTIL J DO Y[I] ~ Y[I+1] - Y[I]  ;       NFBI0024
              J ~ J - 1  ;  K ~ K + 1  ;                                NFBI0025
              GO TO L1  ;                                               NFBI0026
NBAK:         U ~ (X - XF)/H  ;   J ~ N - M + 1  ;                      NFBI0027
              INW ~ Y[N]  ;  U1 ~ 1.0  ;                                NFBI0028
L2:           Y[N] ~ Y[N] - Y[N-1]  ;                                   NFBI0029
              IF ABS(Y[N]) < EPSILON THEN GO TO EOP  ;                  NFBI0030
              U1 ~ U1 | (U + K - 1.0) / K  ;                            NFBI0031
              INW ~ INW + Y[N] | U1  ;                                  NFBI0032
              IF K = M THEN GO TO EOP  ;                                NFBI0033
              FOR I ~ N-1 STEP -1 UNTIL J DO  Y[I] ~ Y[I] - Y[I-1]  ;   NFBI0034
              J ~ J + 1  ;  K ~ K + 1  ;                                NFBI0035
              GO TO L2  ;                                               NFBI0036
EOP:          END  ;                                                    NFBI0037
         END  .                                                         CMNT0007


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