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
[47]
integer in the range 0 - 32767. It should
not be used to generate an encryption
key.
Example 9.11. Generating random numbers
#!/bin/bash
# $RANDOM returns a different random integer at each invocation.
# Nominal range: 0 - 32767 (signed 16-bit integer).
MAXCOUNT=10
count=1
echo
echo "$MAXCOUNT random numbers:"
echo "-----------------"
while [ "$count" -le $MAXCOUNT ] # Generate 10 ($MAXCOUNT) random integers.
do
number=$RANDOM
echo $number
let "count += 1" # Increment count.
done
echo "-----------------"
# If you need a random int within a certain range, use the 'modulo' operator.
# This returns the remainder of a division operation.
RANGE=500
echo
number=$RANDOM
let "number %= $RANGE"
# ^^
echo "Random number less than $RANGE --- $number"
echo
# If you need a random integer greater than a lower bound,
#+ then set up a test to discard all numbers below that.
FLOOR=200
number=0 #initialize
while [ "$number" -le $FLOOR ]
do
number=$RANDOM
done
echo "Random number greater than $FLOOR --- $number"
echo
# Let's examine a simple alternative to the above loop, namely
# let "number = $RANDOM + $FLOOR"
# That would eliminate the while-loop and run faster.
# But, there might be a problem with that. What is it?
# Combine above two techniques to retrieve random number between two limits.
number=0 #initialize
while [ "$number" -le $FLOOR ]
do
number=$RANDOM
let "number %= $RANGE" # Scales $number down within $RANGE.
done
echo "Random number between $FLOOR and $RANGE --- $number"
echo
# Generate binary choice, that is, "true" or "false" value.
BINARY=2
T=1
number=$RANDOM
let "number %= $BINARY"
# Note that let "number >>= 14" gives a better random distribution
#+ (right shifts out everything except last binary digit).
if [ "$number" -eq $T ]
then
echo "TRUE"
else
echo "FALSE"
fi
echo
# Generate a toss of the dice.
SPOTS=6 # Modulo 6 gives range 0 - 5.
# Incrementing by 1 gives desired range of 1 - 6.
# Thanks, Paulo Marcel Coelho Aragao, for the simplification.
die1=0
die2=0
# Would it be better to just set SPOTS=7 and not add 1? Why or why not?
# Tosses each die separately, and so gives correct odds.
let "die1 = $RANDOM % $SPOTS +1" # Roll first one.
let "die2 = $RANDOM % $SPOTS +1" # Roll second one.
# Which arithmetic operation, above, has greater precedence --
#+ modulo (%) or addition (+)?
let "throw = $die1 + $die2"
echo "Throw of the dice = $throw"
echo
exit 0
Example 9.12. Picking a random card from a deck
#!/bin/bash
# pick-card.sh
# This is an example of choosing random elements of an array.
# Pick a card, any card.
Suites="Clubs
Diamonds
Hearts
Spades"
Denominations="2
3
4
5
6
7
8
9
10
Jack
Queen
King
Ace"
# Note variables spread over multiple lines.
suite=($Suites) # Read into array variable.
denomination=($Denominations)
num_suites=${#suite[*]} # Count how many elements.
num_denominations=${#denomination[*]}
echo -n "${denomination[$((RANDOM%num_denominations))]} of "
echo ${suite[$((RANDOM%num_suites))]}
# $bozo sh pick-cards.sh
# Jack of Clubs
# Thank you, "jipe," for pointing out this use of $RANDOM.
exit 0
Example 9.13. Brownian Motion Simulation
#!/bin/bash
# brownian.sh
# Author: Mendel Cooper
# Reldate: 10/26/07
# License: GPL3
# ----------------------------------------------------------------
# This script models Brownian motion:
#+ the random wanderings of tiny particles in a fluid,
#+ as they are buffeted by random currents and collisions.
#+ This is colloquially known as the "Drunkard's Walk."
# It can also be considered as a stripped-down simulation of a
#+ Galton Board, a slanted board with a pattern of pegs,
#+ down which rolls a succession of marbles, one at a time.
#+ At the bottom is a row of slots or catch basins in which
#+ the marbles come to rest at the end of their journey.
# Think of it as a kind of bare-bones Pachinko game.
# As you see by running the script,
#+ most of the marbles cluster around the center slot.
#+ This is consistent with the expected binomial distribution.
# As a Galton Board simulation, the script
#+ disregards such parameters as
#+ board tilt-angle, rolling friction of the marbles,
#+ angles of impact, and elasticity of the pegs.
# To what extent does this affect the accuracy of the simulation?
# ----------------------------------------------------------------
PASSES=500 # Number of particle interactions / marbles.
ROWS=10 # Number of "collisions" (or horiz. peg rows).
RANGE=3 # 0 - 2 output range from $RANDOM.
POS=0 # Left/right position.
RANDOM=$$ # Seeds the random number generator from PID
#+ of script.
declare -a Slots # Array holding cumulative results of passes.
NUMSLOTS=21 # Number of slots at bottom of board.
Initialize_Slots () { # Zero out all elements of the array.
for i in $( seq $NUMSLOTS )
do
Slots[$i]=0
done
echo # Blank line at beginning of run.
}
Show_Slots () {
echo; echo
echo -n " "
for i in $( seq $NUMSLOTS ) # Pretty-print array elements.
do
printf "%3d" ${Slots[$i]} # Allot three spaces per result.
done
echo # Row of slots:
echo " |__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|"
echo " ||"
echo # Note that if the count within any particular slot exceeds 99,
#+ it messes up the display.
# Running only(!) 500 passes usually avoids this.
}
Move () { # Move one unit right / left, or stay put.
Move=$RANDOM # How random is $RANDOM? Well, let's see ...
let "Move %= RANGE" # Normalize into range of 0 - 2.
case "$Move" in
0 ) ;; # Do nothing, i.e., stay in place.
1 ) ((POS--));; # Left.
2 ) ((POS++));; # Right.
* ) echo -n "Error ";; # Anomaly! (Should never occur.)
esac
}
Play () { # Single pass (inner loop).
i=0
while [ "$i" -lt "$ROWS" ] # One event per row.
do
Move
((i++));
done
SHIFT=11 # Why 11, and not 10?
let "POS += $SHIFT" # Shift "zero position" to center.
(( Slots[$POS]++ )) # DEBUG: echo $POS
# echo -n "$POS "
}
Run () { # Outer loop.
p=0
while [ "$p" -lt "$PASSES" ]
do
Play
(( p++ ))
POS=0 # Reset to zero. Why?
done
}
# --------------
# main ()
Initialize_Slots
Run
Show_Slots
# --------------
exit $?
# Exercises:
# ---------
# 1) Show the results in a vertical bar graph, or as an alternative,
#+ a scattergram.
# 2) Alter the script to use /dev/urandom instead of $RANDOM.
# Will this make the results more random?
# 3) Provide some sort of "animation" or graphic output
# for each marble played.
Jipe points out a set of techniques for generating random numbers within a range.
# Generate random number between 6 and 30. rnumber=$((RANDOM%25+6)) # Generate random number in the same 6 - 30 range, #+ but the number must be evenly divisible by 3. rnumber=$(((RANDOM%30/3+1)*3)) # Note that this will not work all the time. # It fails if $RANDOM%30 returns 0. # Frank Wang suggests the following alternative: rnumber=$(( RANDOM%27/3*3+6 ))
Bill Gradwohl came up with an improved formula that works for positive numbers.
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
#!/bin/bash
# random-between.sh
# Random number between two specified values.
# Script by Bill Gradwohl, with minor modifications by the document author.
# Corrections in lines 187 and 189 by Anthony Le Clezio.
# Used with permission.
randomBetween() {
# Generates a positive or negative random number
#+ between $min and $max
#+ and divisible by $divisibleBy.
# Gives a "reasonably random" distribution of return values.
#
# Bill Gradwohl - Oct 1, 2003
syntax() {
# Function embedded within function.
echo
echo "Syntax: randomBetween [min] [max] [multiple]"
echo
echo -n "Expects up to 3 passed parameters, "
echo "but all are completely optional."
echo "min is the minimum value"
echo "max is the maximum value"
echo -n "multiple specifies that the answer must be "
echo "a multiple of this value."
echo " i.e. answer must be evenly divisible by this number."
echo
echo "If any value is missing, defaults area supplied as: 0 32767 1"
echo -n "Successful completion returns 0, "
echo "unsuccessful completion returns"
echo "function syntax and 1."
echo -n "The answer is returned in the global variable "
echo "randomBetweenAnswer"
echo -n "Negative values for any passed parameter are "
echo "handled correctly."
}
local min=${1:-0}
local max=${2:-32767}
local divisibleBy=${3:-1}
# Default values assigned, in case parameters not passed to function.
local x
local spread
# Let's make sure the divisibleBy value is positive.
[ ${divisibleBy} -lt 0 ] && divisibleBy=$((0-divisibleBy))
# Sanity check.
if [ $# -gt 3 -o ${divisibleBy} -eq 0 -o ${min} -eq ${max} ]; then
syntax
return 1
fi
# See if the min and max are reversed.
if [ ${min} -gt ${max} ]; then
# Swap them.
x=${min}
min=${max}
max=${x}
fi
# If min is itself not evenly divisible by $divisibleBy,
#+ then fix the min to be within range.
if [ $((min/divisibleBy*divisibleBy)) -ne ${min} ]; then
if [ ${min} -lt 0 ]; then
min=$((min/divisibleBy*divisibleBy))
else
min=$((((min/divisibleBy)+1)*divisibleBy))
fi
fi
# If max is itself not evenly divisible by $divisibleBy,
#+ then fix the max to be within range.
if [ $((max/divisibleBy*divisibleBy)) -ne ${max} ]; then
if [ ${max} -lt 0 ]; then
max=$((((max/divisibleBy)-1)*divisibleBy))
else
max=$((max/divisibleBy*divisibleBy))
fi
fi
# ---------------------------------------------------------------------
# Now, to do the real work.
# Note that to get a proper distribution for the end points,
#+ the range of random values has to be allowed to go between
#+ 0 and abs(max-min)+divisibleBy, not just abs(max-min)+1.
# The slight increase will produce the proper distribution for the
#+ end points.
# Changing the formula to use abs(max-min)+1 will still produce
#+ correct answers, but the randomness of those answers is faulty in
#+ that the number of times the end points ($min and $max) are returned
#+ is considerably lower than when the correct formula is used.
# ---------------------------------------------------------------------
spread=$((max-min))
# Omair Eshkenazi points out that this test is unnecessary,
#+ since max and min have already been switched around.
[ ${spread} -lt 0 ] && spread=$((0-spread))
let spread+=divisibleBy
randomBetweenAnswer=$(((RANDOM%spread)/divisibleBy*divisibleBy+min))
return 0
# However, Paulo Marcel Coelho Aragao points out that
#+ when $max and $min are not divisible by $divisibleBy,
#+ the formula fails.
#
# He suggests instead the following formula:
# rnumber = $(((RANDOM%(max-min+1)+min)/divisibleBy*divisibleBy))
}
# Let's test the function.
min=-14
max=20
divisibleBy=3
# Generate an array of expected answers and check to make sure we get
#+ at least one of each answer if we loop long enough.
declare -a answer
minimum=${min}
maximum=${max}
if [ $((minimum/divisibleBy*divisibleBy)) -ne ${minimum} ]; then
if [ ${minimum} -lt 0 ]; then
minimum=$((minimum/divisibleBy*divisibleBy))
else
minimum=$((((minimum/divisibleBy)+1)*divisibleBy))
fi
fi
# If max is itself not evenly divisible by $divisibleBy,
#+ then fix the max to be within range.
if [ $((maximum/divisibleBy*divisibleBy)) -ne ${maximum} ]; then
if [ ${maximum} -lt 0 ]; then
maximum=$((((maximum/divisibleBy)-1)*divisibleBy))
else
maximum=$((maximum/divisibleBy*divisibleBy))
fi
fi
# We need to generate only positive array subscripts,
#+ so we need a displacement that will guarantee
#+ positive results.
disp=$((0-minimum))
for ((i=${minimum}; i<=${maximum}; i+=divisibleBy)); do
answer[i+disp]=0
done
# Now loop a large number of times to see what we get.
loopIt=1000 # The script author suggests 100000,
#+ but that takes a good long while.
for ((i=0; i<${loopIt}; ++i)); do
# Note that we are specifying min and max in reversed order here to
#+ make the function correct for this case.
randomBetween ${max} ${min} ${divisibleBy}
# Report an error if an answer is unexpected.
[ ${randomBetweenAnswer} -lt ${min} -o ${randomBetweenAnswer} -gt ${max} ] \
&& echo MIN or MAX error - ${randomBetweenAnswer}!
[ $((randomBetweenAnswer%${divisibleBy})) -ne 0 ] \
&& echo DIVISIBLE BY error - ${randomBetweenAnswer}!
# Store the answer away statistically.
answer[randomBetweenAnswer+disp]=$((answer[randomBetweenAnswer+disp]+1))
done
# Let's check the results
for ((i=${minimum}; i<=${maximum}; i+=divisibleBy)); do
[ ${answer[i+disp]} -eq 0 ] \
&& echo "We never got an answer of $i." \
|| echo "${i} occurred ${answer[i+disp]} times."
done
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
#!/bin/bash
# How random is RANDOM?
RANDOM=$$ # Reseed the random number generator using script process ID.
PIPS=6 # A die has 6 pips.
MAXTHROWS=600 # Increase this if you have nothing better to do with your time.
throw=0 # Number of times the dice have been cast.
ones=0 # Must initialize counts to zero,
twos=0 #+ since an uninitialized variable is null, NOT zero.
threes=0
fours=0
fives=0
sixes=0
print_result ()
{
echo
echo "ones = $ones"
echo "twos = $twos"
echo "threes = $threes"
echo "fours = $fours"
echo "fives = $fives"
echo "sixes = $sixes"
echo
}
update_count()
{
case "$1" in
0) ((ones++));; # Since a die has no "zero", this corresponds to 1.
1) ((twos++));; # And this to 2.
2) ((threes++));; # And so forth.
3) ((fours++));;
4) ((fives++));;
5) ((sixes++));;
esac
}
echo
while [ "$throw" -lt "$MAXTHROWS" ]
do
let "die1 = RANDOM % $PIPS"
update_count $die1
let "throw += 1"
done
print_result
exit $?
# The scores should distribute evenly, assuming RANDOM is random.
# With $MAXTHROWS at 600, all should cluster around 100,
#+ plus-or-minus 20 or so.
#
# Keep in mind that RANDOM is a ***pseudorandom*** generator,
#+ and not a spectacularly good one at that.
# Randomness is a deep and complex subject.
# Sufficiently long "random" sequences may exhibit
#+ chaotic and other "non-random" behavior.
# Exercise (easy):
# ---------------
# Rewrite this script to flip a coin 1000 times.
# Choices are "HEADS" and "TAILS."
As we have seen in the last example, it is best to
reseed the RANDOM
generator each time it is invoked. Using the same seed
for RANDOM repeats the same series
of numbers.
[48]
(This mirrors the behavior of the
random() function in
C.)
Example 9.16. Reseeding RANDOM
#!/bin/bash
# seeding-random.sh: Seeding the RANDOM variable.
# v 1.1, reldate 09 Feb 2013
MAXCOUNT=25 # How many numbers to generate.
SEED=
random_numbers ()
{
local count=0
local number
while [ "$count" -lt "$MAXCOUNT" ]
do
number=$RANDOM
echo -n "$number "
let "count++"
done
}
echo; echo
SEED=1
RANDOM=$SEED # Setting RANDOM seeds the random number generator.
echo "Random seed = $SEED"
random_numbers
RANDOM=$SEED # Same seed for RANDOM . . .
echo; echo "Again, with same random seed ..."
echo "Random seed = $SEED"
random_numbers # . . . reproduces the exact same number series.
#
# When is it useful to duplicate a "random" series?
echo; echo
SEED=2
RANDOM=$SEED # Trying again, but with a different seed . . .
echo "Random seed = $SEED"
random_numbers # . . . gives a different number series.
echo; echo
# RANDOM=$$ seeds RANDOM from process id of script.
# It is also possible to seed RANDOM from 'time' or 'date' commands.
# Getting fancy...
SEED=$(head -1 /dev/urandom | od -N 1 | awk '{ print $2 }'| sed s/^0*//)
# Pseudo-random output fetched
#+ from /dev/urandom (system pseudo-random device-file),
#+ then converted to line of printable (octal) numbers by "od",
#+ then "awk" retrieves just one number for SEED,
#+ finally "sed" removes any leading zeros.
RANDOM=$SEED
echo "Random seed = $SEED"
random_numbers
echo; echo
exit 0
The /dev/urandom pseudo-device file
provides a method of generating much more “random”
pseudorandom numbers than the $RANDOM
variable. dd if=/dev/urandom of=targetfile
bs=1 count=XX creates a file of well-scattered
pseudorandom numbers. However, assigning these numbers
to a variable in a script requires a workaround, such
as filtering through od
(as in above example, Example 16.14, “Generating 10-digit random numbers”, and
Example A.36, “Insertion sort”), or even piping to
md5sum (see Example 36.16, “A “horserace” game”).
There are also other ways to generate pseudorandom numbers in a script. Awk provides a convenient means of doing this.
Example 9.17. Pseudorandom numbers, using awk
#!/bin/bash
# random2.sh: Returns a pseudorandom number in the range 0 - 1,
#+ to 6 decimal places. For example: 0.822725
# Uses the awk rand() function.
AWKSCRIPT=' { srand(); print rand() } '
# Command(s)/parameters passed to awk
# Note that srand() reseeds awk's random number generator.
echo -n "Random number between 0 and 1 = "
echo | awk "$AWKSCRIPT"
# What happens if you leave out the 'echo'?
exit 0
# Exercises:
# ---------
# 1) Using a loop construct, print out 10 different random numbers.
# (Hint: you must reseed the srand() function with a different seed
#+ in each pass through the loop. What happens if you omit this?)
# 2) Using an integer multiplier as a scaling factor, generate random numbers
#+ in the range of 10 to 100.
# 3) Same as exercise #2, above, but generate random integers this time.
The date command also lends itself to generating pseudorandom integer sequences.
[47] 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.
[48] 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.