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https://github.com/pkimpel/retro-220.git
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83a0b62faf
1. Correct missing relocation pseudo-op in MONIT Library routine. 2. Rebuild Generator and Compiler tapes. 3. Recompile and generate corrected listings for example programs. 4. Add Simpson's Rule example from Algol-58 Preliminary Report.
76 lines
6.7 KiB
Plaintext
76 lines
6.7 KiB
Plaintext
BEGIN 00000100
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COMMENT SIMPSON-S RULE INTEGRATION PROCEDURE, TRANSLATED TO BALGOL 00000200
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FROM THE EXAMPLE IN THE PRELIMINARY IAL REPORT; 00000300
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00000400
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COMMENT 00000500
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EXAMPLE.. INTEGRATION OF A FUNCTION F(X) BY SIMPSON-S RULE. THE 00000600
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VALUES OF F(X) ARE SUPPLIED BY AN ASSUMED EXISTENT FUNCTION 00000700
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ROUTINE. THE MESH SIZE IS HALVED UNTIL TWO SUCCESSIVE SIMPSON 00000800
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SUMS AGREE WITHIN A PRESCRIBED ERROR. DURING THE MESH REDUCTION 00000900
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F(X) IS EVALUATED AT MOST ONCE FOR ANY X. A VALUE V GREATER THAN 00001000
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THE MAXIMUM ABSOLUTE VALUE ATTAINED BY THE FUNCTION ON THE 00001100
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INTERVAL IS REQUIRED FOR INITIALZING; 00001200
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00110000
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FILE LINE(KIND=PRINTER, MAXRECSIZE=132, FRAMESIZE=8, FILEUSE=OUT); 00110100
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FORMAT F1("SUM = ",F12.5); 00110200
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REAL SUM; 00110300
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LIST RESULT (SUM); 00110400
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00200000
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REAL PROCEDURE SIMPS(A, B, DELTA, V, F); 00200100
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VALUE A, B, DELTA, V; 00200200
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REAL A, B, DELTA, V; 00200300
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REAL PROCEDURE F(X); VALUE X; REAL X; FORMAL; 00200400
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COMMENT A, B ARE THE MIN AND MAX, RESP. OF THE POINTS DEF. 00200500
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INTERVAL OF INTEG. F() IS THE FUNCTION TO INTEGRATED. 00200600
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DELTA IS THE PERMISSIBLE DIFFERENCE BETWEEN TO SUCCESSIVE SIMPSON 00200700
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SUMS. V IS GREATER THAN THE MAXIMUM ABSOLUTE VALUE OF F ON A, B; 00200800
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BEGIN 00200900
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INTEGER K, N; 00201000
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REAL H, I, IBAR, J, S; 00201100
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LABEL J1; 00201200
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MONITOR LINE (IBAR, N, H, J, S K, I); 00201300
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00201400
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IBAR:= V*(B-A); 00201500
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N:= 1; 00201600
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H:= (B-A)/2; 00201700
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J:= H*(F(A) + F(B)); 00201800
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00201900
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J1: 00202000
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S:= 0; 00202100
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FOR K:= 1 STEP 1 UNTIL N DO 00202200
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S:= S + F(A + (2*K-1)*H); 00202300
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00202400
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I:= J + 4*H*S; 00202500
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IF DELTA < ABS(I-IBAR) THEN 00202600
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BEGIN 00202700
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IBAR:= I; 00202800
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J:= (I+J)/4; 00202900
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N:= 2*N; 00203000
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H:= H/2; 00203100
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GO TO J1 00203200
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END; 00203300
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00203400
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SIMPS:= I/3; 00203500
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END SIMPS; 00203600
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00210000
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REAL PROCEDURE TORADS(X); VALUE X; REAL X; TORADS:= 3.1415926*X/180; 00210100
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00210200
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REAL PROCEDURE SINE(X); VALUE X; REAL X; SINE:= SIN(X); 00210300
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00210400
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REAL PROCEDURE DARCTAN(X); VALUE X; REAL X; DARCTAN:= 1/(X**2 + 1); 00210500
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00210600
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REAL PROCEDURE LOGISTICSIGMOID(X); 00210700
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VALUE X; 00210800
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REAL X; 00210900
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BEGIN 00211000
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LOGISTICSIGMOID:= 1/(1 + EXP(-X)); 00211100
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END LOGISTICSIGMOID; 00211200
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00900000
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SUM:= SIMPS(TORADS(30), TORADS(90), 0.00001, 2.0, SINE); 00900600
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WRITE(LINE, F1, RESULT); 00900700
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SUM:= SIMPS(0, 1, 1@-5, 2.0, DARCTAN); 00900800
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WRITE(LINE, F1, RESULT); 00900900
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SUM:= SIMPS(0.5, 3, 1@-5, 2.0, LOGISTICSIGMOID); 00901000
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WRITE(LINE, F1, RESULT); 00901100
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END. 00999900
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