diff --git a/ran b/ran old mode 100644 new mode 100755 index 5ef8071..c70b621 --- a/ran +++ b/ran @@ -22,33 +22,55 @@ : $((n+=${#PWD})); : $((n+=${#0})) seed="${n:-100}" } +[ "$1" ] && seed="$1" # allow a seed to be set via $1 # $seed should now contain a number -for i in 1 2 3 4 5; do # 5 times - [ ! "$((seed*seed))" -gt "$seed" ] && break # break if we have reached a max length num - seed=$((seed*seed)) - seed="${seed#?}"; seed="${seed%?}" # use the middle-square method to generate a new seed +# the idea here is the $seed should be /slightly/ random or at least dicated by the contents of the current systen +# now we must remove all possible leading 0's +until [ ${seed#0} = $seed ]; do + seed=${seed#0} done +# echo "being LCG" # LCG imp follows # generate a modulus (m) from the length of $seed and then detemine if its a prime -m="${#seed}"; [ "$((m%2))" -eq 0 -o "$((m%3))" -eq 0 ] || : $((m+=1)) # if prime -# ^ if not a multiple of 2 or 3 expect the number to be prime and increase it by 1 +m="$(( ${#seed} * 10))"; [ "$((m%2))" -eq 0 -o "$((m%3))" -eq 0 -a "$m" -gt 2 -a "$m" -gt 3 ] || : $((m+=1)) # if prime +# ^ if not a multiple of 2 or 3 expect the number to be prime and increase it by 1 p=0 # $p is the next prime and can be determined using a while loop that adds 1 to it until it becomes a prime -if [ "$((m%2))" -eq 0 ]; then # now determine the prime factors of $m +#echo "determine modulus and its factors" +if [ $((m%2)) -eq 0 ]; then # now determine the prime factors of $m f=$((m/2)) # next prime is 3; 5 - p=3 # we know the next prime - until [ ! "$((f%2))" -eq 0 -a ! "$((f%3))" -eq 0 ]; do - f=$((f/p)) - : $((p+=1)); until [ ! "$((p%2))" -eq 0 -a ! "$((p%3))" -eq 0 ]; do - : $((P+=1)) - done - done -elif [ "$((m%3))" -eq 0 ]; then - f=$((m/3)) # next prime is 5; 7 - p=5 - until [ ! "$((f%2))" -eq 0 -a ! "$((f%3))" -eq 0 ]; do - f=$((f/p)) - : $((p+=1)); until [ ! "$((p%2))" -eq 0 -a ! "$((p%3))" -eq 0 ]; do + p=2 + until [ $((f % 2)) -gt 0 -a $(( f % 3)) -gt 0 ]; do + [ $((f%p)) -eq 0 ] && { + f=$((f/p)) + } || { : $((p+=1)) - done + until [ $((p%2)) -gt 0 -a $((p%3)) -gt 0 ] || [ "$p" -eq 2 -o "$p" -eq 3 ]; do + : $((p+=1)) + done + } + done +elif [ $((m%3)) -eq 0 ]; then + f=$((m/3)) # next prime is 5; 7 + p=3 + until [ $((f % 2)) -gt 0 -a $((f % 3)) -gt 0 ]; do + [ $((f%p)) -eq 0 ] && { + f=$((f/p)) + } || { + : $((p+=1)); until [ $((p%2)) -gt 0 -a $((p%3)) -gt 0 ] || [ "$p" -eq 2 -o "$p" -eq 3 ]; do + : $((p+=1)) + done + } done # until $f is prime do the above -fi # $f is the prime factor of $m \ No newline at end of file +fi # $f is the prime factor of $m; $f*2 = $m +if [ "$seed" -gt 75 ]; then + a="$((seed-75))" # here the multiplier (a) is seed (z) - 75 # the 75 here is taken from the ZX81's multiplier (a) from its own LCG +elif [ "$seed" -gt 6 ]; then # the 6 here for fallback is literally random + a="$((seed-6))" +fi +until [ "$(( (a-1)%f ))" -eq 0 ]; do # the multiplier (a) -1 MUST be a multiple of $f + : $((a+=1)) # add to a until a-1 is a multiple of $f +done +# increment (c) and the modulus (m) must be co-prime; and two random primes should be co-prime therefore set $c to $p; see above +# the final digit used by LCG will be the seed (z) # z & c will not be defined to save on memory +seed=$(( ((a*seed)+p)%m )) # finally calculate a need seed via the formula: (a*z + c)%m and return it +echo "$seed"