9.6. $RANDOM: generate random integer

#!/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

#!/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

#!/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 -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
  }


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?

#!/bin/bash
# random-between.sh
# Random number between two specified values. 
# Script by Bill Gradwohl, with minor modifications by the document author.
# 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 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+displacement]} -eq 0 ] \
   && echo "We never got an answer of $i." \
   || echo "${i} occurred ${answer[i+displacement]} times."
done


exit 0

#!/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         # Throw count.

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) let "ones += 1";;   # Since die has no "zero", this corresponds to 1.
  1) let "twos += 1";;   # And this to 2, etc.
  2) let "threes += 1";;
  3) let "fours += 1";;
  4) let "fives += 1";;
  5) let "sixes += 1";;
esac
}

echo


while [ "$throw" -lt "$MAXTHROWS" ]
do
  let "die1 = RANDOM % $PIPS"
  update_count $die1
  let "throw += 1"
done  

print_result

exit 0

#  The scores should distribute fairly evenly, assuming RANDOM is fairly 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".

#!/bin/bash
# seeding-random.sh: Seeding the RANDOM variable.

MAXCOUNT=25       # How many numbers to generate.

random_numbers ()
{
count=0
while [ "$count" -lt "$MAXCOUNT" ]
do
  number=$RANDOM
  echo -n "$number "
  let "count += 1"
done  
}

echo; echo

RANDOM=1          # Setting RANDOM seeds the random number generator.
random_numbers

echo; echo

RANDOM=1          # Same seed for RANDOM...
random_numbers    # ...reproduces the exact same number series.
                  #
                  # When is it useful to duplicate a "random" number series?

echo; echo

RANDOM=2          # Trying again, but with a different 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 $2 }')
#  Pseudo-random output fetched
#+ from /dev/urandom (system pseudo-random device-file),
#+ then converted to line of printable (octal) numbers by "od",
#+ finally "awk" retrieves just one number for SEED.
RANDOM=$SEED
random_numbers

echo; echo

exit 0