#!/bin/bash
# sieve.sh (ex68.sh)

# Sieve of Eratosthenes
# Ancient algorithm for finding prime numbers.

#  This runs a couple of orders of magnitude slower
#+ than the equivalent program written in C.

LOWER_LIMIT=1       # Starting with 1.
UPPER_LIMIT=1000    # Up to 1000.
# (You may set this higher . . . if you have time on your hands.)

PRIME=1
NON_PRIME=0

let SPLIT=UPPER_LIMIT/2
# Optimization:
# Need to test numbers only halfway to upper limit. Why?


declare -a Primes
# Primes[] is an array.


initialize ()
{
# Initialize the array.

i=$LOWER_LIMIT
until [ "$i" -gt "$UPPER_LIMIT" ]
do
  Primes[i]=$PRIME
  let "i += 1"
done
#  Assume all array members guilty (prime)
#+ until proven innocent.
}

print_primes ()
{
# Print out the members of the Primes[] array tagged as prime.

i=$LOWER_LIMIT

until [ "$i" -gt "$UPPER_LIMIT" ]
do

  if [ "${Primes[i]}" -eq "$PRIME" ]
  then
    printf "%8d" $i
    # 8 spaces per number gives nice, even columns.
  fi
  
  let "i += 1"
  
done

}

sift () # Sift out the non-primes.
{

let i=$LOWER_LIMIT+1
# Let's start with 2.

until [ "$i" -gt "$UPPER_LIMIT" ]
do

if [ "${Primes[i]}" -eq "$PRIME" ]
# Don't bother sieving numbers already sieved (tagged as non-prime).
then

  t=$i

  while [ "$t" -le "$UPPER_LIMIT" ]
  do
    let "t += $i "
    Primes[t]=$NON_PRIME
    # Tag as non-prime all multiples.
  done

fi  

  let "i += 1"
done  


}


# ==============================================
# main ()
# Invoke the functions sequentially.
initialize
sift
print_primes
# This is what they call structured programming.
# ==============================================

echo

exit 0



# -------------------------------------------------------- #
# Code below line will not execute, because of 'exit.'

#  This improved version of the Sieve, by Stephane Chazelas,
#+ executes somewhat faster.

# Must invoke with command-line argument (limit of primes).

UPPER_LIMIT=$1                  # From command-line.
let SPLIT=UPPER_LIMIT/2         # Halfway to max number.

Primes=( '' $(seq $UPPER_LIMIT) )

i=1
until (( ( i += 1 ) > SPLIT ))  # Need check only halfway.
do
  if [[ -n $Primes[i] ]]
  then
    t=$i
    until (( ( t += i ) > UPPER_LIMIT ))
    do
      Primes[t]=
    done
  fi  
done  
echo ${Primes[*]}

exit $?