# 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  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.  (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

 ``` 1 #!/bin/bash 2 # random2.sh: Returns a pseudorandom number in the range 0 - 1, 3 #+ to 6 decimal places. For example: 0.822725 4 # Uses the awk rand() function. 5  6 AWKSCRIPT=' { srand(); print rand() } ' 7 # Command(s)/parameters passed to awk 8 # Note that srand() reseeds awk's random number generator. 9  10  11 echo -n "Random number between 0 and 1 = " 12  13 echo | awk "\$AWKSCRIPT" 14 # What happens if you leave out the 'echo'? 15  16 exit 0 17  18  19 # Exercises: 20 # --------- 21  22 # 1) Using a loop construct, print out 10 different random numbers. 23 # (Hint: you must reseed the srand() function with a different seed 24 #+ in each pass through the loop. What happens if you omit this?) 25  26 # 2) Using an integer multiplier as a scaling factor, generate random numbers 27 #+ in the range of 10 to 100. 28  29 # 3) Same as exercise #2, above, but generate random integers this time.```

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

### Notes

  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.  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.