9.6. $RANDOM: generate random integer

$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 9-26. 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 9-27. 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 9-28. 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 -n " "
  52 for i in $( seq $NUMSLOTS )   # Pretty-print array elements.
  53 do
  54   printf "%3d" ${Slots[$i]}   # Allot three spaces per result.
  55 done
  56 
  57 echo # Row of slots:
  58 echo " |__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|"
  59 echo "                                ^^"
  60 echo #  Note that if the count within any particular slot exceeds 99,
  61      #+ it messes up the display.
  62      #  Running only(!) 500 passes usually avoids this.
  63   }
  64 
  65 
  66 Move () {              # Move one unit right / left, or stay put.
  67   Move=$RANDOM         # How random is $RANDOM? Well, let's see ...
  68   let "Move %= RANGE"  # Normalize into range of 0 - 2.
  69   case "$Move" in
  70     0 ) ;;                   # Do nothing, i.e., stay in place.
  71     1 ) ((POS--));;          # Left.
  72     2 ) ((POS++));;          # Right.
  73     * ) echo -n "Error ";;   # Anomaly! (Should never occur.)
  74   esac
  75   }
  76 
  77 
  78 Play () {                    # Single pass (inner loop).
  79 i=0
  80 while [ "$i" -lt "$ROWS" ]   # One event per row.
  81 do
  82   Move
  83   ((i++));
  84 done
  85 
  86 SHIFT=11                     # Why 11, and not 10?
  87 let "POS += $SHIFT"          # Shift "zero position" to center.
  88 (( Slots[$POS]++ ))          # DEBUG: echo $POS
  89   }
  90 
  91 
  92 Run () {                     # Outer loop.
  93 p=0
  94 while [ "$p" -lt "$PASSES" ]
  95 do
  96   Play
  97   (( p++ ))
  98   POS=0                      # Reset to zero. Why?
  99 done
 100   }
 101 
 102 
 103 # --------------
 104 # main ()
 105 Initialize_Slots
 106 Run
 107 Show_Slots
 108 # --------------
 109 
 110 exit $?
 111 
 112 #  Exercises:
 113 #  ---------
 114 #  1) Show the results in a vertical bar graph, or as an alternative,
 115 #+    a scattergram.
 116 #  2) Alter the script to use /dev/urandom instead of $RANDOM.
 117 #     Will this make the results more random?

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 9-29. 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 # Used with permission.
   6 
   7 
   8 randomBetween() {
   9    #  Generates a positive or negative random number
  10    #+ between $min and $max
  11    #+ and divisible by $divisibleBy.
  12    #  Gives a "reasonably random" distribution of return values.
  13    #
  14    #  Bill Gradwohl - Oct 1, 2003
  15 
  16    syntax() {
  17    # Function embedded within function.
  18       echo
  19       echo    "Syntax: randomBetween [min] [max] [multiple]"
  20       echo
  21       echo -n "Expects up to 3 passed parameters, "
  22       echo    "but all are completely optional."
  23       echo    "min is the minimum value"
  24       echo    "max is the maximum value"
  25       echo -n "multiple specifies that the answer must be "
  26       echo     "a multiple of this value."
  27       echo    "    i.e. answer must be evenly divisible by this number."
  28       echo    
  29       echo    "If any value is missing, defaults area supplied as: 0 32767 1"
  30       echo -n "Successful completion returns 0, "
  31       echo     "unsuccessful completion returns"
  32       echo    "function syntax and 1."
  33       echo -n "The answer is returned in the global variable "
  34       echo    "randomBetweenAnswer"
  35       echo -n "Negative values for any passed parameter are "
  36       echo    "handled correctly."
  37    }
  38 
  39    local min=${1:-0}
  40    local max=${2:-32767}
  41    local divisibleBy=${3:-1}
  42    # Default values assigned, in case parameters not passed to function.
  43 
  44    local x
  45    local spread
  46 
  47    # Let's make sure the divisibleBy value is positive.
  48    [ ${divisibleBy} -lt 0 ] && divisibleBy=$((0-divisibleBy))
  49 
  50    # Sanity check.
  51    if [ $# -gt 3 -o ${divisibleBy} -eq 0 -o  ${min} -eq ${max} ]; then 
  52       syntax
  53       return 1
  54    fi
  55 
  56    # See if the min and max are reversed.
  57    if [ ${min} -gt ${max} ]; then
  58       # Swap them.
  59       x=${min}
  60       min=${max}
  61       max=${x}
  62    fi
  63 
  64    #  If min is itself not evenly divisible by $divisibleBy,
  65    #+ then fix the min to be within range.
  66    if [ $((min/divisibleBy*divisibleBy)) -ne ${min} ]; then 
  67       if [ ${min} -lt 0 ]; then
  68          min=$((min/divisibleBy*divisibleBy))
  69       else
  70          min=$((((min/divisibleBy)+1)*divisibleBy))
  71       fi
  72    fi
  73 
  74    #  If max is itself not evenly divisible by $divisibleBy,
  75    #+ then fix the max to be within range.
  76    if [ $((max/divisibleBy*divisibleBy)) -ne ${max} ]; then 
  77       if [ ${max} -lt 0 ]; then
  78          max=$((((max/divisibleBy)-1)*divisibleBy))
  79       else
  80          max=$((max/divisibleBy*divisibleBy))
  81       fi
  82    fi
  83 
  84    #  ---------------------------------------------------------------------
  85    #  Now, to do the real work.
  86 
  87    #  Note that to get a proper distribution for the end points,
  88    #+ the range of random values has to be allowed to go between
  89    #+ 0 and abs(max-min)+divisibleBy, not just abs(max-min)+1.
  90 
  91    #  The slight increase will produce the proper distribution for the
  92    #+ end points.
  93 
  94    #  Changing the formula to use abs(max-min)+1 will still produce
  95    #+ correct answers, but the randomness of those answers is faulty in
  96    #+ that the number of times the end points ($min and $max) are returned
  97    #+ is considerably lower than when the correct formula is used.
  98    #  ---------------------------------------------------------------------
  99 
 100    spread=$((max-min))
 101    #  Omair Eshkenazi points out that this test is unnecessary,
 102    #+ since max and min have already been switched around.
 103    [ ${spread} -lt 0 ] && spread=$((0-spread))
 104    let spread+=divisibleBy
 105    randomBetweenAnswer=$(((RANDOM%spread)/divisibleBy*divisibleBy+min))   
 106 
 107    return 0
 108 
 109    #  However, Paulo Marcel Coelho Aragao points out that
 110    #+ when $max and $min are not divisible by $divisibleBy,
 111    #+ the formula fails.
 112    #
 113    #  He suggests instead the following formula:
 114    #    rnumber = $(((RANDOM%(max-min+1)+min)/divisibleBy*divisibleBy))
 115 
 116 }
 117 
 118 # Let's test the function.
 119 min=-14
 120 max=20
 121 divisibleBy=3
 122 
 123 
 124 #  Generate an array of expected answers and check to make sure we get
 125 #+ at least one of each answer if we loop long enough.
 126 
 127 declare -a answer
 128 minimum=${min}
 129 maximum=${max}
 130    if [ $((minimum/divisibleBy*divisibleBy)) -ne ${minimum} ]; then 
 131       if [ ${minimum} -lt 0 ]; then
 132          minimum=$((minimum/divisibleBy*divisibleBy))
 133       else
 134          minimum=$((((minimum/divisibleBy)+1)*divisibleBy))
 135       fi
 136    fi
 137 
 138 
 139    #  If max is itself not evenly divisible by $divisibleBy,
 140    #+ then fix the max to be within range.
 141 
 142    if [ $((maximum/divisibleBy*divisibleBy)) -ne ${maximum} ]; then 
 143       if [ ${maximum} -lt 0 ]; then
 144          maximum=$((((maximum/divisibleBy)-1)*divisibleBy))
 145       else
 146          maximum=$((maximum/divisibleBy*divisibleBy))
 147       fi
 148    fi
 149 
 150 
 151 #  We need to generate only positive array subscripts,
 152 #+ so we need a displacement that that will guarantee
 153 #+ positive results.
 154 
 155 disp=$((0-minimum))
 156 for ((i=${minimum}; i<=${maximum}; i+=divisibleBy)); do
 157    answer[i+disp]=0
 158 done
 159 
 160 
 161 # Now loop a large number of times to see what we get.
 162 loopIt=1000   #  The script author suggests 100000,
 163               #+ but that takes a good long while.
 164 
 165 for ((i=0; i<${loopIt}; ++i)); do
 166 
 167    #  Note that we are specifying min and max in reversed order here to
 168    #+ make the function correct for this case.
 169 
 170    randomBetween ${max} ${min} ${divisibleBy}
 171 
 172    # Report an error if an answer is unexpected.
 173    [ ${randomBetweenAnswer} -lt ${min} -o ${randomBetweenAnswer} -gt ${max} ] \
 174    && echo MIN or MAX error - ${randomBetweenAnswer}!
 175    [ $((randomBetweenAnswer%${divisibleBy})) -ne 0 ] \
 176    && echo DIVISIBLE BY error - ${randomBetweenAnswer}!
 177 
 178    # Store the answer away statistically.
 179    answer[randomBetweenAnswer+disp]=$((answer[randomBetweenAnswer+disp]+1))
 180 done
 181 
 182 
 183 
 184 # Let's check the results
 185 
 186 for ((i=${minimum}; i<=${maximum}; i+=divisibleBy)); do
 187    [ ${answer[i+displacement]} -eq 0 ] \
 188    && echo "We never got an answer of $i." \
 189    || echo "${i} occurred ${answer[i+displacement]} times."
 190 done
 191 
 192 
 193 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 9-30. 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         # Throw count.
   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 "$1" in
  32   0) let "ones += 1";;   # Since die has no "zero", this corresponds to 1.
  33   1) let "twos += 1";;   # And this to 2, etc.
  34   2) let "threes += 1";;
  35   3) let "fours += 1";;
  36   4) let "fives += 1";;
  37   5) let "sixes += 1";;
  38 esac
  39 }
  40 
  41 echo
  42 
  43 
  44 while [ "$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 0
  54 
  55 #  The scores should distribute fairly evenly, assuming RANDOM is fairly random.
  56 #  With $MAXTHROWS at 600, all should cluster around 100, plus-or-minus 20 or so.
  57 #
  58 #  Keep in mind that RANDOM is a pseudorandom generator,
  59 #+ and not a spectacularly good one at that.
  60 
  61 #  Randomness is a deep and complex subject.
  62 #  Sufficiently long "random" sequences may exhibit
  63 #+ chaotic and other "non-random" behavior.
  64 
  65 # Exercise (easy):
  66 # ---------------
  67 # Rewrite this script to flip a coin 1000 times.
  68 # 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 9-31. Reseeding RANDOM

   1 #!/bin/bash
   2 # seeding-random.sh: Seeding the RANDOM variable.
   3 
   4 MAXCOUNT=25       # How many numbers to generate.
   5 
   6 random_numbers ()
   7 {
   8 count=0
   9 while [ "$count" -lt "$MAXCOUNT" ]
  10 do
  11   number=$RANDOM
  12   echo -n "$number "
  13   let "count += 1"
  14 done  
  15 }
  16 
  17 echo; echo
  18 
  19 RANDOM=1          # Setting RANDOM seeds the random number generator.
  20 random_numbers
  21 
  22 echo; echo
  23 
  24 RANDOM=1          # Same seed for RANDOM...
  25 random_numbers    # ...reproduces the exact same number series.
  26                   #
  27                   # When is it useful to duplicate a "random" number series?
  28 
  29 echo; echo
  30 
  31 RANDOM=2          # Trying again, but with a different seed...
  32 random_numbers    # gives a different number series.
  33 
  34 echo; echo
  35 
  36 # RANDOM=$$  seeds RANDOM from process id of script.
  37 # It is also possible to seed RANDOM from 'time' or 'date' commands.
  38 
  39 # Getting fancy...
  40 SEED=$(head -1 /dev/urandom | od -N 1 | awk '{ print $2 }')
  41 #  Pseudo-random output fetched
  42 #+ from /dev/urandom (system pseudo-random device-file),
  43 #+ then converted to line of printable (octal) numbers by "od",
  44 #+ finally "awk" retrieves just one number for SEED.
  45 RANDOM=$SEED
  46 random_numbers
  47 
  48 echo; echo
  49 
  50 exit 0

Note

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 15-14, and Example A-38), or even piping to md5sum (see Example 33-14).

There are also other ways to generate pseudorandom numbers in a script. Awk provides a convenient means of doing this.


Example 9-32. Pseudorandom numbers, using awk

   1 #!/bin/bash
   2 # random2.sh: Returns a pseudorandom number in the range 0 - 1.
   3 # Uses the awk rand() function.
   4 
   5 AWKSCRIPT=' { srand(); print rand() } '
   6 #            Command(s) / parameters passed to awk
   7 # Note that srand() reseeds awk's random number generator.
   8 
   9 
  10 echo -n "Random number between 0 and 1 = "
  11 
  12 echo | awk "$AWKSCRIPT"
  13 # What happens if you leave out the 'echo'?
  14 
  15 exit 0
  16 
  17 
  18 # Exercises:
  19 # ---------
  20 
  21 # 1) Using a loop construct, print out 10 different random numbers.
  22 #      (Hint: you must reseed the "srand()" function with a different seed
  23 #+     in each pass through the loop. What happens if you fail to do this?)
  24 
  25 # 2) Using an integer multiplier as a scaling factor, generate random numbers 
  26 #+   in the range between 10 and 100.
  27 
  28 # 3) Same as exercise #2, above, but generate random integers this time.

The date command also lends itself to generating pseudorandom integer sequences.

Notes

[1]

True "randomness," insofar as it exists at all, can only be found in certain incompletely understood natural phenomena, such as radioactive decay. Computers only simulate randomness, and computer-generated sequences of "random" numbers are therefore referred to as pseudorandom.

[2]

The seed of a computer-generated pseudorandom number series can be considered an identification label. For example, think of the pseudorandom series with a seed of 23 as Series #23.

A property of a pseurandom number series is the length of the cycle before it starts repeating itself. A good pseurandom generator will produce series with very long cycles.