Chapter 7 - Question 3
Develop a recurrence relation that can be used as the basis for a pseudo-random number-generator that, from a given initial 'seed', produces real values R: 0 <= R < 1.
Solution 1
PHP:
<? // random number generator // returns the specified amount of random numbers based on the seed function random_numbers($seed, $amount) { // loop for each amount for (; $amount > 0; $amount--) { // get the current microseconds $microseconds = explode(' ', microtime()); // get the last two digits of the microseconds $random = substr($microseconds[0]*1, -2, 2); // add that to the seed $seed += $random; // mod the result by 100 to get a two digit number $seed %= 100; // add this number to the array $generated[] = $seed / 100; } // return all the random numbers return $generated; } // generate a random seed value // any number can be used to start $seed = mt_rand(1, 500); // generate a random amount of random numbers to return $amount = mt_rand(5, 15); // show the seed and amount echo 'From the seed ' . $seed . ', the first ' . $amount . ' random numbers are:<br/>'; // show the random numbers generated echo implode(', ', random_numbers($seed, $amount));?>Which produces:
From the seed 343, the first 9 random numbers are:
0.38, 0.62, 0.03, 0.59, 0.3, 0.16, 0.18, 0.35, 0.67
I wanted to see how random my random number generator is. So I ran the script three times outputting 500,000 values each time and added up the frequency each number appeared. The average frequency should be around 15,000. Here's a chart showing the frequency of all the numbers:
The faded-salmon line shows that all the numbers appear around the amount they are expected to appear, so my random number generator can be considered random!
Log
- November 7, 2005 - Added solution 1.