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1. Commit library tape images, directories, and extracted text files. 2. Commit additional utilities under Unisys-Emode-Tools.
134 lines
10 KiB
Plaintext
134 lines
10 KiB
Plaintext
BEGIN 00000100
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COMMENT PROCEDURE - RANDOM, 00000200
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CUBE LIBRARY NUMBER IS V100001. 00000300
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THIS VERSION DATED 6/20/67; 00000400
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COMMENT 00000500
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"RANDOM" 00000600
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00000700
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DISCLAIMER 00000800
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DISCLAIMER: THE AUTHORS OF THIS PROGRAM, THE CUBE ORGANIZATION, 00000900
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AND THE BURROUGHS CORPORATION, BELIEVE THIS PROGRAM MATERIAL 00001000
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TO BE CORRECT, HOWEVER, THEY BEAR NO RESPONSIBILITY, 00001100
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FINANCIAL OR OTHERWISE, FOR ERROR RESULTING FROM ITS USE, NOR 00001200
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ACCEPT ANY RESPONSIBILITY FOR ITS MAINTENANCE. 00001300
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00001400
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AUTHOR 00001500
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WM. A. WULF UNIVERSITY OF VIRGINIA 00001600
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00001700
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ABSTRACT 00001800
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THE PROGRAM GENERATES A PSEUDO-RANDOM SEQUENCE OVER AN INTERVAL C{X{D 00001900
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WHERE C AND D ARE SPECIFIED IN THE CALL. 00002000
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00002100
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SYSTEM 00002200
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MINIMUM B5000. 00002300
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00002400
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00002500
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MATHEMATICAL DISCUSSION 00002600
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00002700
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THE SEQUENCE OF PSEUDO-RANDOM NUMBERS IS GENERATED BY NORMALIZING 00002800
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00002900
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X[I+1] = P|(X[I] MOD 2*A) 00003000
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00003100
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TO THE INTERVAL (C,D),WHERE A IS CHOSEN SUCH THAT 00003200
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00003300
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(P|2) < 2*39 < (P|2*(A+1)) 00003400
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00003500
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AND P IS CHOSEN FROM 00003600
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00003700
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P=8T-3 T=1,2,... 00003800
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00003900
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00004000
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IN PARTICULAR FOR THIS PROCEDURE THE FOLLOWING CHOICES WERE MADE: 00004100
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00004200
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T=2 00004300
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00004400
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THUS P=13 00004500
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AND A=35 00004600
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00004700
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THE VALUE OF X[0] IS AN INPUT PARAMETER. THE THEORETICAL BASIS FOR THESE00004800
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CHOICES IS GIVEN IN "NUMERICAL METHODS FOR SCIENTISTS AND ENGINEERS", 00004900
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BY HAMMING. 00005000
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00005100
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THE FOLLOWING TABLE SHOWS THE VALUES OF 00005200
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X-BAR 00005300
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AND (X*2)-BAR 00005400
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FOR VARIOUS VALUES OF N AND X[0]. THE THEORETICAL 00005500
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VALUES FOR THESE SHOULD BE .5 AND .3333... . 00005600
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00005700
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00005800
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STARTING 00005900
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CONSTANT N X-BAR (X*2)-BAR 00006000
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-------- ----- ----------- -----------00006100
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00006200
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500 0.497882202 0.33285615200006300
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13543288579 1000 0.494498538 0.32704795500006400
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5000 0.499812258 0.33301384300006500
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00006600
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500 0.477618983 0.31145862200006700
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24376589411 1000 0.488730932 0.32355101700006800
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5000 0.501847597 0.33571464900006900
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00007000
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00007100
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500 0.502539971 0.34503988500007200
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34359738367 1000 0.503262243 0.34043405800007300
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5000 0.507513557 0.34213742000007400
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00007500
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500 0.483932789 0.31383800200007600
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11324679915 1000 0.494948306 0.32851833800007700
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5000 0.498790265 0.33225082400007800
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00007900
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00008000
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00008100
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00008200
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INSTRUCTIONS FOR USING "RANDOM" 00008300
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00008400
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00008500
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THE REAL PROCEDURE RANDOM IS ENTERED WITH THREE PARAMETERS 00008600
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FOR EXAMPLE: 00008700
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R~RANDOM(A,B,C); 00008800
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COMMENT 00008900
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A AND B DEFINE THE UPPER AND LOWER BOUNDS OF THE INTERVAL. C SHOULD 00009000
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EITHER BE ZERO OR AN ELEVEN DIGIT ODD INTEGER. WHEN C!0, THEN C IS 00009100
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TAKEN TO BE X[0], AND THE VALUE OF RANDOM WILL BE P|(X[0]MOD 2*35) 00009200
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NORMALIZED TO THE PROPER INTERVAL. WHEN C=0, THEN THE VALUE OF RANDOM 00009300
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IS COMPUTED FROM P(X[I]MOD 2*35). 00009400
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THUS WHEN RANDOM IS CALLED THE FIRST TIME IN A PROGRAM, C SHOULD 00009500
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BE AN ELEVEN DIGIT ODD INTEGER. ON SUBSEQUENT CALLS C WILL PROBABLY 00009600
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BE ZERO. 00009700
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00009800
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************************************************************************00009900
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00010000
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00010100
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; 00010200
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FILE OUT LP 1(1,15); 00010300
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INTEGER I,J,N; 00010400
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REAL SUM,SUMSQ,R; 00010500
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FORMAT F(I13,X4,I5,2(X4,F8.3)); 00010600
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00010700
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00010800
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REAL PROCEDURE RANDOM(A,B,START); 00010900
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VALUE A,B,START; 00011000
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REAL A,B; 00011100
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INTEGER START; 00011200
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BEGIN 00011300
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OWN INTEGER X; 00011400
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IF START!0 THEN X~START; 00011500
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X~X.[13:35]; 00011600
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X~X|13; 00011700
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RANDOM~X/446676598784|(B-A)+A 00011800
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END OF RANDOM; 00011900
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FOR J~13543288579,24376589411,34359738367,11324679915 DO 00012000
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FOR N~500,1000,5000 DO 00012100
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BEGIN 00012200
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SUM~SUMSQ~0; 00012300
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00012400
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R~RANDOM(0,1,J); 00012500
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FOR I~1 STEP 1 UNTIL N DO 00012600
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BEGIN 00012700
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R~RANDOM(0,1,0); 00012800
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SUM~SUM+R;SUMSQ~SUMSQ+R|R; 00012900
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END SUM LOOP; 00013000
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WRITE(LP,F,J,N,SUM/N,SUMSQ/N); 00013100
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END OF N LOOP; 00013200
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END. 00013300
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