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1. Commit library tape images, directories, and extracted text files. 2. Commit additional utilities under Unisys-Emode-Tools.
89 lines
7.0 KiB
Plaintext
89 lines
7.0 KiB
Plaintext
BEGIN 00000100
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COMMENT PROGRAM - SIMPSONS RULE, 00000200
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CUBE LIBRARY NUMBER IS D100001. 00000300
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THIS VERSION DATED 6/19/67; 00000400
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COMMENT 00000500
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"SIMPSON-S RULE"** 00000600
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00000700
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DISCLAIMER: THE AUTHORS OF THIS PROGRAM, THE CUBE ORGANIZATION, 00000800
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AND THE BURROUGHS CORPORATION, BELIEVE THIS PROGRAM MATERIAL 00000900
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TO BE CORRECT, HOWEVER, THEY BEAR NO RESPONSIBILITY, 00001000
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FINANCIAL OR OTHERWISE, FOR ERROR RESULTING FROM ITS USE, NOR 00001100
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ACCEPT ANY RESPONSIBILITY FOR ITS MAINTENANCE. 00001200
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00001300
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AUTHOR 00001400
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TRANSLITERATED BY PAUL DAVIS UNIVERSITY OF VIRGINIA 00001500
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00001600
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ABSTRACT 00001700
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SIMPSON-S RULE INTEGRATION OF SINGLE OR MULTIPLE INTEGRALS 00001800
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00001900
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SYSTEM 00002000
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MINIMUM B5000 00002100
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00002200
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00002300
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00002400
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SIMPS IS A TYPE REAL PROCEDURE WHICH CALCULATES THE VALUE OF A 00002500
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SINGLE INTEGRAL BY SIMPSON"S RULE. THE PROCEDURE IS WRITTEN IN SUCH A 00002600
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WAY THAT IT CAN BE CALLED RECURSIVELY FOR THE EVALUATION OF AN ITERATED 00002700
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INTEGRAL. 00002800
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00002900
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THE PROCEDURE CALL IS 00003000
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SIMPS (X,X1,X2,DELTA,F) 00003100
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WHERE THE INTEGRATION OF THE REAL EXPRESSION F IS TO BE TAKEN OVER THE 00003200
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REAL VARIABLE X BETWEEN THE LIMITS X1 AND X2, WHERE X1 AND X2 MAY BE 00003300
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EXPRESSIONS, AND WITHIN A RELATIVE TOLERANCE DELTA. 00003400
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FOR EXAMPLE THE CALL 00003500
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M~SIMPS(X,0,1,@-8,SIMPS(Y,0,SQRT(1-X*2),@-10,X*2+Y*2)) 00003600
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WAS USED TO EVALUATE THE DOUBLE INTEGRAL OF 00003700
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F(X)=X*2+Y*2 00003800
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FOR Y=0 TO Y=SQRT(1-X*2) AND X=0 TO X=1. ANALYTICALLY ONE OBTAINS 00003900
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M=.392699. THE PROCEDURE SIMPS PRODUCED M=.3926978 IN 9.35 SECONDS. 00004000
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00004100
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** TRANSLITERATED FROM THE ALGORITHM SECTION OF THE "COMMUNICATIONS OF00004200
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THE ACM", VOL.7, NUMBER 6,JUNE 1964. 00004300
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00004400
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************************************************************************00004500
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00004600
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00004700
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00004800
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;00004900
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FILE OUT LP 1(1,15); 00005000
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FORMAT F(F12.7); 00005100
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REAL X,Y,Z; 00005200
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REAL PROCEDURE SIMPS(X,X1,X2,DELTA,F); 00005300
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VALUE X1,X2,DELTA; REAL X,X1,X2,DELTA,F; 00005400
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BEGIN 00005500
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BOOLEAN TURNING; LABEL BOX,BOX2; 00005600
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REAL Z1,Z2,Z3,H,K; 00005700
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TURNING~FALSE; 00005800
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IF X1=X2 THEN 00005900
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BEGIN 00006000
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Z1~0; 00006100
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GO TO BOX2 00006200
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END; 00006300
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IF X1>X2 THEN 00006400
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BEGIN 00006500
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H~X1; 00006600
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X1~X2; 00006700
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X2~H; 00006800
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TURNING~TRUE; 00006900
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END; 00007000
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X~X1; Z1~F; X~X2; Z3~Z1~Z1+F; 00007100
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K~X2-X1; 00007200
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BOX: 00007300
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Z2~0; H~K/2; 00007400
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FOR X~X1+H STEP K UNTIL X2 DO Z2~Z2+F; 00007500
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Z1~Z1+4|Z2; 00007600
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IF H|ABS((Z1-2|Z3)/(IF Z1=0 THEN 1.0 ELSE Z1))<DELTA 00007700
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THEN GO TO BOX2 ELSE Z3~Z1; 00007800
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Z1~Z1-2|Z2; 00007900
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K~H; 00008000
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GO TO BOX; 00008100
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BOX2: 00008200
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IF TURNING THEN H~-H; 00008300
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SIMPS~H|Z1/3 00008400
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END OF SIMPS; 00008500
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WRITE(LP,F, 00008600
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SIMPS(X,0,1,@-8,SIMPS(Y,0,SQRT(1-X*2),@-10,X*2+Y*2)) ); 00008700
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END. 00008800
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