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https://github.com/retro-software/B5500-software.git
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2c72f7fd1d
1. Commit library tape images, directories, and extracted text files. 2. Commit additional utilities under Unisys-Emode-Tools.
93 lines
7.2 KiB
Plaintext
93 lines
7.2 KiB
Plaintext
BEGIN CMNT0001
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COMMENT THIS PROCEDURE DETERMINES ALL THE ZEROS OF A CMNT0002
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POLYNOMIAL P(X) PROVIDED THE ZEROS ARE REAL CMNT0003
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AND UNEQUAL. CMNT0004
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CMNT0005
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JOANNE K. KONDO CMNT0006
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(PROFESSIONAL SERVICES, BURROUGHS CORPORATION). CMNT0007
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CMNT0008
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PROCEDURE CARD SEQUENCE CODE STARTS WITH NWTN0001. CMNT0009
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FIRST RELEASE 07/01/1963 ; CMNT0010
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CMNT0011
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CMNT0012
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PROCEDURE NEWTONMAEHLY (A, N, EPS, Z) ; NWTN0001
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VALUE N, EPS ; NWTN0002
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INTEGER N ; NWTN0003
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REAL EPS ; NWTN0004
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ARRAY A, Z[0] ; NWTN0005
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NWTN0006
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BEGIN NWTN0007
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NWTN0008
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REAL AA, PP, QQ, X0, X1 ; NWTN0009
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INTEGER I, M, S ; NWTN0010
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LABEL ITERATION; NWTN0011
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ARRAY B, Q[0:N-1], P[0:N] ; NWTN0012
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NWTN0013
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PROCEDURE HORNER(P,Q,N,X,PP,QQ) ; NWTN0014
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VALUE N, X ; NWTN0015
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ARRAY P, Q[0] ; NWTN0016
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REAL PP, X, QQ ; NWTN0017
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INTEGER N ; NWTN0018
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NWTN0019
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BEGIN NWTN0020
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NWTN0021
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REAL S, S1 ; NWTN0022
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INTEGER I ; NWTN0023
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NWTN0024
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S ~ S1 ~ 0 ; NWTN0025
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FOR I ~ 0 STEP 1 UNTIL N-1 DO NWTN0026
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BEGIN NWTN0027
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S ~ S | X + P[I] ; NWTN0028
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S1 ~ S1 | X + Q[I] NWTN0029
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END ; NWTN0030
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PP ~ S | X + P[N] ; QQ ~ S1 ; NWTN0031
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END ; NWTN0032
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NWTN0033
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COMMENT THE FIRST APPROXIMATION OF THE LARGEST ZERO IS DETERMINED;NWTN0034
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NWTN0035
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P[0] ~ AA ~ A[0] ; X0 ~ PP ~ 0 ; NWTN0036
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S ~ SIGN(A[0]) ; NWTN0037
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FOR I ~ 1 STEP 1 UNTIL N DO NWTN0038
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IF S | A[I] < 0 THEN NWTN0039
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BEGIN NWTN0040
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IF PP = 0 THEN PP ~ I ; NWTN0041
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IF X0 < ABS(A[I]) THEN X0 ~ ABS(A[I]) NWTN0042
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END ; NWTN0043
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X0 ~ IF PP = 0 THEN 0 ELSE 1 + (X0/AA)*(1/PP) ; NWTN0044
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FOR I ~ 0 STEP 1 UNTIL N-1 DO NWTN0045
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B[I] ~ (N-I) | A[I] ; NWTN0046
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FOR M ~ 1 STEP 1 UNTIL N DO NWTN0047
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BEGIN NWTN0048
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NWTN0049
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COMMENT THE APPROXIMATION IS IMPROVED UNTIL THE ACCEPTANCE NWTN0050
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CRITERION IS MET ; NWTN0051
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NWTN0052
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ITERATION: HORNER(A,B,N,X0,PP,QQ) ; NWTN0053
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X1 ~ X0 - PP/QQ ; NWTN0054
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IF ABS(X1-X0) > EPS | ABS(X1) THEN NWTN0055
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BEGIN NWTN0056
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X0 ~ X1 ; GO TO ITERATION NWTN0057
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END ; NWTN0058
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NWTN0059
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COMMENT Z[M] = X1 IS THE M-TH ZERO OF THE POLYNOMIAL ; NWTN0060
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NWTN0061
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Z[M] ~ X1 ; Q[0] ~ PP ~ B[0] ~ B[0] - AA ; NWTN0062
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IF M < N THEN NWTN0063
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BEGIN NWTN0064
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FOR I ~ 1 STEP 1 UNTIL N-1 DO NWTN0065
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BEGIN NWTN0066
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PP ~ P[I] ~ X1 | P[I-1] + A[I] ; NWTN0067
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PP ~ B[I] ~ B[I] - PP ; NWTN0068
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Q[I] ~ X1 | Q[I-1] + PP NWTN0069
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END ; NWTN0070
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HORNER(P,Q,N-1,X1,PP,QQ) ; NWTN0071
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X0 ~ X1 - PP/QQ NWTN0072
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NWTN0073
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COMMENT XO IS THE FIRST APPROXIMATION FOR THE NEXT ZERO ; NWTN0074
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NWTN0075
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END NWTN0076
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END NWTN0077
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END ; NWTN0078
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END . CMNT0013
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