9.3. $RANDOM: generate random integer
Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin. --John von Neumann |
$RANDOM is an internal Bash function (not a constant) that returns a pseudorandom [1] integer in the range 0 - 32767. It should not be used to generate an encryption key.
Example 9-11. Generating random numbers
1 #!/bin/bash 2 3 # $RANDOM returns a different random integer at each invocation. 4 # Nominal range: 0 - 32767 (signed 16-bit integer). 5 6 MAXCOUNT=10 7 count=1 8 9 echo 10 echo "$MAXCOUNT random numbers:" 11 echo "-----------------" 12 while [ "$count" -le $MAXCOUNT ] # Generate 10 ($MAXCOUNT) random integers. 13 do 14 number=$RANDOM 15 echo $number 16 let "count += 1" # Increment count. 17 done 18 echo "-----------------" 19 20 # If you need a random int within a certain range, use the 'modulo' operator. 21 # This returns the remainder of a division operation. 22 23 RANGE=500 24 25 echo 26 27 number=$RANDOM 28 let "number %= $RANGE" 29 # ^^ 30 echo "Random number less than $RANGE --- $number" 31 32 echo 33 34 35 36 # If you need a random integer greater than a lower bound, 37 #+ then set up a test to discard all numbers below that. 38 39 FLOOR=200 40 41 number=0 #initialize 42 while [ "$number" -le $FLOOR ] 43 do 44 number=$RANDOM 45 done 46 echo "Random number greater than $FLOOR --- $number" 47 echo 48 49 # Let's examine a simple alternative to the above loop, namely 50 # let "number = $RANDOM + $FLOOR" 51 # That would eliminate the while-loop and run faster. 52 # But, there might be a problem with that. What is it? 53 54 55 56 # Combine above two techniques to retrieve random number between two limits. 57 number=0 #initialize 58 while [ "$number" -le $FLOOR ] 59 do 60 number=$RANDOM 61 let "number %= $RANGE" # Scales $number down within $RANGE. 62 done 63 echo "Random number between $FLOOR and $RANGE --- $number" 64 echo 65 66 67 68 # Generate binary choice, that is, "true" or "false" value. 69 BINARY=2 70 T=1 71 number=$RANDOM 72 73 let "number %= $BINARY" 74 # Note that let "number >>= 14" gives a better random distribution 75 #+ (right shifts out everything except last binary digit). 76 if [ "$number" -eq $T ] 77 then 78 echo "TRUE" 79 else 80 echo "FALSE" 81 fi 82 83 echo 84 85 86 # Generate a toss of the dice. 87 SPOTS=6 # Modulo 6 gives range 0 - 5. 88 # Incrementing by 1 gives desired range of 1 - 6. 89 # Thanks, Paulo Marcel Coelho Aragao, for the simplification. 90 die1=0 91 die2=0 92 # Would it be better to just set SPOTS=7 and not add 1? Why or why not? 93 94 # Tosses each die separately, and so gives correct odds. 95 96 let "die1 = $RANDOM % $SPOTS +1" # Roll first one. 97 let "die2 = $RANDOM % $SPOTS +1" # Roll second one. 98 # Which arithmetic operation, above, has greater precedence -- 99 #+ modulo (%) or addition (+)? 100 101 102 let "throw = $die1 + $die2" 103 echo "Throw of the dice = $throw" 104 echo 105 106 107 exit 0 |
Example 9-12. Picking a random card from a deck
1 #!/bin/bash
2 # pick-card.sh
3
4 # This is an example of choosing random elements of an array.
5
6
7 # Pick a card, any card.
8
9 Suites="Clubs
10 Diamonds
11 Hearts
12 Spades"
13
14 Denominations="2
15 3
16 4
17 5
18 6
19 7
20 8
21 9
22 10
23 Jack
24 Queen
25 King
26 Ace"
27
28 # Note variables spread over multiple lines.
29
30
31 suite=($Suites) # Read into array variable.
32 denomination=($Denominations)
33
34 num_suites=${#suite[*]} # Count how many elements.
35 num_denominations=${#denomination[*]}
36
37 echo -n "${denomination[$((RANDOM%num_denominations))]} of "
38 echo ${suite[$((RANDOM%num_suites))]}
39
40
41 # $bozo sh pick-cards.sh
42 # Jack of Clubs
43
44
45 # Thank you, "jipe," for pointing out this use of $RANDOM.
46 exit 0 |
Example 9-13. Brownian Motion Simulation
1 #!/bin/bash
2 # brownian.sh
3 # Author: Mendel Cooper
4 # Reldate: 10/26/07
5 # License: GPL3
6
7 # ----------------------------------------------------------------
8 # This script models Brownian motion:
9 #+ the random wanderings of tiny particles in a fluid,
10 #+ as they are buffeted by random currents and collisions.
11 #+ This is colloquially known as the "Drunkard's Walk."
12
13 # It can also be considered as a stripped-down simulation of a
14 #+ Galton Board, a slanted board with a pattern of pegs,
15 #+ down which rolls a succession of marbles, one at a time.
16 #+ At the bottom is a row of slots or catch basins in which
17 #+ the marbles come to rest at the end of their journey.
18 # Think of it as a kind of bare-bones Pachinko game.
19 # As you see by running the script,
20 #+ most of the marbles cluster around the center slot.
21 #+ This is consistent with the expected binomial distribution.
22 # As a Galton Board simulation, the script
23 #+ disregards such parameters as
24 #+ board tilt-angle, rolling friction of the marbles,
25 #+ angles of impact, and elasticity of the pegs.
26 # To what extent does this affect the accuracy of the simulation?
27 # ----------------------------------------------------------------
28
29 PASSES=500 # Number of particle interactions / marbles.
30 ROWS=10 # Number of "collisions" (or horiz. peg rows).
31 RANGE=3 # 0 - 2 output range from $RANDOM.
32 POS=0 # Left/right position.
33 RANDOM=$$ # Seeds the random number generator from PID
34 #+ of script.
35
36 declare -a Slots # Array holding cumulative results of passes.
37 NUMSLOTS=21 # Number of slots at bottom of board.
38
39
40 Initialize_Slots () { # Zero out all elements of the array.
41 for i in $( seq $NUMSLOTS )
42 do
43 Slots[$i]=0
44 done
45
46 echo # Blank line at beginning of run.
47 }
48
49
50 Show_Slots () {
51 echo; echo
52 echo -n " "
53 for i in $( seq $NUMSLOTS ) # Pretty-print array elements.
54 do
55 printf "%3d" ${Slots[$i]} # Allot three spaces per result.
56 done
57
58 echo # Row of slots:
59 echo " |__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|"
60 echo " ||"
61 echo # Note that if the count within any particular slot exceeds 99,
62 #+ it messes up the display.
63 # Running only(!) 500 passes usually avoids this.
64 }
65
66
67 Move () { # Move one unit right / left, or stay put.
68 Move=$RANDOM # How random is $RANDOM? Well, let's see ...
69 let "Move %= RANGE" # Normalize into range of 0 - 2.
70 case "$Move" in
71 0 ) ;; # Do nothing, i.e., stay in place.
72 1 ) ((POS--));; # Left.
73 2 ) ((POS++));; # Right.
74 * ) echo -n "Error ";; # Anomaly! (Should never occur.)
75 esac
76 }
77
78
79 Play () { # Single pass (inner loop).
80 i=0
81 while [ "$i" -lt "$ROWS" ] # One event per row.
82 do
83 Move
84 ((i++));
85 done
86
87 SHIFT=11 # Why 11, and not 10?
88 let "POS += $SHIFT" # Shift "zero position" to center.
89 (( Slots[$POS]++ )) # DEBUG: echo $POS
90
91 # echo -n "$POS "
92
93 }
94
95
96 Run () { # Outer loop.
97 p=0
98 while [ "$p" -lt "$PASSES" ]
99 do
100 Play
101 (( p++ ))
102 POS=0 # Reset to zero. Why?
103 done
104 }
105
106
107 # --------------
108 # main ()
109 Initialize_Slots
110 Run
111 Show_Slots
112 # --------------
113
114 exit $?
115
116 # Exercises:
117 # ---------
118 # 1) Show the results in a vertical bar graph, or as an alternative,
119 #+ a scattergram.
120 # 2) Alter the script to use /dev/urandom instead of $RANDOM.
121 # Will this make the results more random?
122 # 3) Provide some sort of "animation" or graphic output
123 # for each marble played. |
Jipe points out a set of techniques for generating random numbers within a range.
1 # Generate random number between 6 and 30. 2 rnumber=$((RANDOM%25+6)) 3 4 # Generate random number in the same 6 - 30 range, 5 #+ but the number must be evenly divisible by 3. 6 rnumber=$(((RANDOM%30/3+1)*3)) 7 8 # Note that this will not work all the time. 9 # It fails if $RANDOM%30 returns 0. 10 11 # Frank Wang suggests the following alternative: 12 rnumber=$(( RANDOM%27/3*3+6 )) |
Bill Gradwohl came up with an improved formula that works for positive numbers.
1 rnumber=$(((RANDOM%(max-min+divisibleBy))/divisibleBy*divisibleBy+min)) |
Here Bill presents a versatile function that returns a random number between two specified values.
Example 9-14. Random between values
1 #!/bin/bash
2 # random-between.sh
3 # Random number between two specified values.
4 # Script by Bill Gradwohl, with minor modifications by the document author.
5 # Corrections in lines 187 and 189 by Anthony Le Clezio.
6 # Used with permission.
7
8
9 randomBetween() {
10 # Generates a positive or negative random number
11 #+ between $min and $max
12 #+ and divisible by $divisibleBy.
13 # Gives a "reasonably random" distribution of return values.
14 #
15 # Bill Gradwohl - Oct 1, 2003
16
17 syntax() {
18 # Function embedded within function.
19 echo
20 echo "Syntax: randomBetween [min] [max] [multiple]"
21 echo
22 echo -n "Expects up to 3 passed parameters, "
23 echo "but all are completely optional."
24 echo "min is the minimum value"
25 echo "max is the maximum value"
26 echo -n "multiple specifies that the answer must be "
27 echo "a multiple of this value."
28 echo " i.e. answer must be evenly divisible by this number."
29 echo
30 echo "If any value is missing, defaults area supplied as: 0 32767 1"
31 echo -n "Successful completion returns 0, "
32 echo "unsuccessful completion returns"
33 echo "function syntax and 1."
34 echo -n "The answer is returned in the global variable "
35 echo "randomBetweenAnswer"
36 echo -n "Negative values for any passed parameter are "
37 echo "handled correctly."
38 }
39
40 local min=${1:-0}
41 local max=${2:-32767}
42 local divisibleBy=${3:-1}
43 # Default values assigned, in case parameters not passed to function.
44
45 local x
46 local spread
47
48 # Let's make sure the divisibleBy value is positive.
49 [ ${divisibleBy} -lt 0 ] && divisibleBy=$((0-divisibleBy))
50
51 # Sanity check.
52 if [ $# -gt 3 -o ${divisibleBy} -eq 0 -o ${min} -eq ${max} ]; then
53 syntax
54 return 1
55 fi
56
57 # See if the min and max are reversed.
58 if [ ${min} -gt ${max} ]; then
59 # Swap them.
60 x=${min}
61 min=${max}
62 max=${x}
63 fi
64
65 # If min is itself not evenly divisible by $divisibleBy,
66 #+ then fix the min to be within range.
67 if [ $((min/divisibleBy*divisibleBy)) -ne ${min} ]; then
68 if [ ${min} -lt 0 ]; then
69 min=$((min/divisibleBy*divisibleBy))
70 else
71 min=$((((min/divisibleBy)+1)*divisibleBy))
72 fi
73 fi
74
75 # If max is itself not evenly divisible by $divisibleBy,
76 #+ then fix the max to be within range.
77 if [ $((max/divisibleBy*divisibleBy)) -ne ${max} ]; then
78 if [ ${max} -lt 0 ]; then
79 max=$((((max/divisibleBy)-1)*divisibleBy))
80 else
81 max=$((max/divisibleBy*divisibleBy))
82 fi
83 fi
84
85 # ---------------------------------------------------------------------
86 # Now, to do the real work.
87
88 # Note that to get a proper distribution for the end points,
89 #+ the range of random values has to be allowed to go between
90 #+ 0 and abs(max-min)+divisibleBy, not just abs(max-min)+1.
91
92 # The slight increase will produce the proper distribution for the
93 #+ end points.
94
95 # Changing the formula to use abs(max-min)+1 will still produce
96 #+ correct answers, but the randomness of those answers is faulty in
97 #+ that the number of times the end points ($min and $max) are returned
98 #+ is considerably lower than when the correct formula is used.
99 # ---------------------------------------------------------------------
100
101 spread=$((max-min))
102 # Omair Eshkenazi points out that this test is unnecessary,
103 #+ since max and min have already been switched around.
104 [ ${spread} -lt 0 ] && spread=$((0-spread))
105 let spread+=divisibleBy
106 randomBetweenAnswer=$(((RANDOM%spread)/divisibleBy*divisibleBy+min))
107
108 return 0
109
110 # However, Paulo Marcel Coelho Aragao points out that
111 #+ when $max and $min are not divisible by $divisibleBy,
112 #+ the formula fails.
113 #
114 # He suggests instead the following formula:
115 # rnumber = $(((RANDOM%(max-min+1)+min)/divisibleBy*divisibleBy))
116
117 }
118
119 # Let's test the function.
120 min=-14
121 max=20
122 divisibleBy=3
123
124
125 # Generate an array of expected answers and check to make sure we get
126 #+ at least one of each answer if we loop long enough.
127
128 declare -a answer
129 minimum=${min}
130 maximum=${max}
131 if [ $((minimum/divisibleBy*divisibleBy)) -ne ${minimum} ]; then
132 if [ ${minimum} -lt 0 ]; then
133 minimum=$((minimum/divisibleBy*divisibleBy))
134 else
135 minimum=$((((minimum/divisibleBy)+1)*divisibleBy))
136 fi
137 fi
138
139
140 # If max is itself not evenly divisible by $divisibleBy,
141 #+ then fix the max to be within range.
142
143 if [ $((maximum/divisibleBy*divisibleBy)) -ne ${maximum} ]; then
144 if [ ${maximum} -lt 0 ]; then
145 maximum=$((((maximum/divisibleBy)-1)*divisibleBy))
146 else
147 maximum=$((maximum/divisibleBy*divisibleBy))
148 fi
149 fi
150
151
152 # We need to generate only positive array subscripts,
153 #+ so we need a displacement that that will guarantee
154 #+ positive results.
155
156 disp=$((0-minimum))
157 for ((i=${minimum}; i<=${maximum}; i+=divisibleBy)); do
158 answer[i+disp]=0
159 done
160
161
162 # Now loop a large number of times to see what we get.
163 loopIt=1000 # The script author suggests 100000,
164 #+ but that takes a good long while.
165
166 for ((i=0; i<${loopIt}; ++i)); do
167
168 # Note that we are specifying min and max in reversed order here to
169 #+ make the function correct for this case.
170
171 randomBetween ${max} ${min} ${divisibleBy}
172
173 # Report an error if an answer is unexpected.
174 [ ${randomBetweenAnswer} -lt ${min} -o ${randomBetweenAnswer} -gt ${max} ] \
175 && echo MIN or MAX error - ${randomBetweenAnswer}!
176 [ $((randomBetweenAnswer%${divisibleBy})) -ne 0 ] \
177 && echo DIVISIBLE BY error - ${randomBetweenAnswer}!
178
179 # Store the answer away statistically.
180 answer[randomBetweenAnswer+disp]=$((answer[randomBetweenAnswer+disp]+1))
181 done
182
183
184
185 # Let's check the results
186
187 for ((i=${minimum}; i<=${maximum}; i+=divisibleBy)); do
188 [ ${answer[i+disp]} -eq 0 ] \
189 && echo "We never got an answer of $i." \
190 || echo "${i} occurred ${answer[i+disp]} times."
191 done
192
193
194 exit 0 |
Just how random is $RANDOM? The best way to test this is to write a script that tracks the distribution of "random" numbers generated by $RANDOM. Let's roll a $RANDOM die a few times . . .
Example 9-15. Rolling a single die with RANDOM
1 #!/bin/bash
2 # How random is RANDOM?
3
4 RANDOM=$$ # Reseed the random number generator using script process ID.
5
6 PIPS=6 # A die has 6 pips.
7 MAXTHROWS=600 # Increase this if you have nothing better to do with your time.
8 throw=0 # Number of times the dice have been cast.
9
10 ones=0 # Must initialize counts to zero,
11 twos=0 #+ since an uninitialized variable is null, NOT zero.
12 threes=0
13 fours=0
14 fives=0
15 sixes=0
16
17 print_result ()
18 {
19 echo
20 echo "ones = $ones"
21 echo "twos = $twos"
22 echo "threes = $threes"
23 echo "fours = $fours"
24 echo "fives = $fives"
25 echo "sixes = $sixes"
26 echo
27 }
28
29 update_count()
30 {
31 case "$1" in
32 0) ((ones++));; # Since a die has no "zero", this corresponds to 1.
33 1) ((twos++));; # And this to 2.
34 2) ((threes++));; # And so forth.
35 3) ((fours++));;
36 4) ((fives++));;
37 5) ((sixes++));;
38 esac
39 }
40
41 echo
42
43
44 while [ "$throw" -lt "$MAXTHROWS" ]
45 do
46 let "die1 = RANDOM % $PIPS"
47 update_count $die1
48 let "throw += 1"
49 done
50
51 print_result
52
53 exit $?
54
55 # The scores should distribute evenly, assuming RANDOM is random.
56 # With $MAXTHROWS at 600, all should cluster around 100,
57 #+ plus-or-minus 20 or so.
58 #
59 # Keep in mind that RANDOM is a ***pseudorandom*** generator,
60 #+ and not a spectacularly good one at that.
61
62 # Randomness is a deep and complex subject.
63 # Sufficiently long "random" sequences may exhibit
64 #+ chaotic and other "non-random" behavior.
65
66 # Exercise (easy):
67 # ---------------
68 # Rewrite this script to flip a coin 1000 times.
69 # Choices are "HEADS" and "TAILS." |
As we have seen in the last example, it is best to reseed the RANDOM generator each time it is invoked. Using the same seed for RANDOM repeats the same series of numbers. [2] (This mirrors the behavior of the random() function in C.)
Example 9-16. Reseeding RANDOM
1 #!/bin/bash
2 # seeding-random.sh: Seeding the RANDOM variable.
3 # v 1.1, reldate 09 Feb 2013
4
5 MAXCOUNT=25 # How many numbers to generate.
6 SEED=
7
8 random_numbers ()
9 {
10 local count=0
11 local number
12
13 while [ "$count" -lt "$MAXCOUNT" ]
14 do
15 number=$RANDOM
16 echo -n "$number "
17 let "count++"
18 done
19 }
20
21 echo; echo
22
23 SEED=1
24 RANDOM=$SEED # Setting RANDOM seeds the random number generator.
25 echo "Random seed = $SEED"
26 random_numbers
27
28
29 RANDOM=$SEED # Same seed for RANDOM . . .
30 echo; echo "Again, with same random seed ..."
31 echo "Random seed = $SEED"
32 random_numbers # . . . reproduces the exact same number series.
33 #
34 # When is it useful to duplicate a "random" series?
35
36 echo; echo
37
38 SEED=2
39 RANDOM=$SEED # Trying again, but with a different seed . . .
40 echo "Random seed = $SEED"
41 random_numbers # . . . gives a different number series.
42
43 echo; echo
44
45 # RANDOM=$$ seeds RANDOM from process id of script.
46 # It is also possible to seed RANDOM from 'time' or 'date' commands.
47
48 # Getting fancy...
49 SEED=$(head -1 /dev/urandom | od -N 1 | awk '{ print $2 }'| sed s/^0*//)
50 # Pseudo-random output fetched
51 #+ from /dev/urandom (system pseudo-random device-file),
52 #+ then converted to line of printable (octal) numbers by "od",
53 #+ then "awk" retrieves just one number for SEED,
54 #+ finally "sed" removes any leading zeros.
55 RANDOM=$SEED
56 echo "Random seed = $SEED"
57 random_numbers
58
59 echo; echo
60
61 exit 0 |
 | The /dev/urandom pseudo-device file provides a method of generating much more "random" pseudorandom numbers than the $RANDOM variable. dd if=/dev/urandom of=targetfile bs=1 count=XX creates a file of well-scattered pseudorandom numbers. However, assigning these numbers to a variable in a script requires a workaround, such as filtering through od (as in above example, Example 16-14, and Example A-36), or even piping to md5sum (see Example 36-16). There are also other ways to generate pseudorandom numbers in a script. Awk provides a convenient means of doing this. Example 9-17. Pseudorandom numbers, using awk
The date command also lends itself to generating pseudorandom integer sequences. |