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I want to generate random numbers manually. I know that every language have the rand or random function, but I'm curious to know how this is working. Does anyone have code for that?
Have a look at the following:
Random Number Generation
Linear Congruential Generator - a popular approach also used in Java
List of Random Number Generators
And here's another link which elaborates on the use of LCG in Java's Random class
POSIX.1-2001 gives the following example of an implementation of rand() and srand(), possibly useful when one needs the same sequence on two different machines.
static unsigned long next = 1;
/* RAND_MAX assumed to be 32767 */
int myrand(void) {
next = next * 1103515245 + 12345;
return((unsigned)(next/65536) % 32768);
}
void mysrand(unsigned seed) {
next = seed;
}
I assume you mean pseudo-random numbers. The simplest one I know (from writing videogames games back on old machines) worked like this:
seed=seed*5+1;
You do that every time random is called and then you use however many low bits you want. *5+1 has the nice property (IIRC) of hitting every possibility before repeating, no matter how many bits you are looking at.
The downside, of course, is its predictability. But that didn't matter in the games. We were grabbing random numbers like crazy for all sorts of things, and you'd never know what number was coming next.
Do a couple things like this in parallel, and combine the results. This is a linear congruential generator.
http://en.wikipedia.org/wiki/Random_number_generator
Describes the different types of random number generators and how they are created.
Aloha!
By manually do you mean "not using computer" or "write my own code"?
IF it is not using computer you can use things like dice, numbers in a bag and all those methods seen on telly when they select teams, winning Bingo series etc. Las Vegas is filled with these kinds of method used in processes (games) aimed at giving you bad odds and ROI. You can also get the great RAND book and turn to a randomly selected page:
http://www.amazon.com/Million-Random-Digits-Normal-Deviates/dp/0833030477
(Also, for some amusement, read the reviews)
For writing your own code you need to consider why not using the system provided RNG is not good enough. If you are using a modern OS it will have a RNG available for user programs that should be good enough for your application.
If you really need to implement your own there are a huge bunch of generators available. For non security usage you can look at LFSR chains, Congruential generators etc. Whatever the distribution you need (uniform, normal, exponential etc) you should be able to find algorithm descriptions and libraries with implementations.
For security usage you should look at things like Yarrow/Fortuna the NIST SP 800-89 specified PRNGs and RFC 4086 for good entropy sources needed to feed the PRNG. Or even better, use the one in the OS that should meet security RNG requirements.
Implementation of RNGs can be a fun exercise, but is very rarely needed. And don't invent your own algorithm unless it is for toy applications. Do NOT, repeat NOT invent RNGs for security applications (generating cryptographic keys for example), at least unless you do some seripus reading and investigation. You will thank me for it (I hope).
static void Main()
{
DateTime currentTime = DateTime.Now;
int maxValue = 100;
int hour = currentTime.Hour;
int minute = currentTime.Minute;
int second = currentTime.Second;
int milisecond = currentTime.Millisecond;
int randNum = (((hour + 1) * (minute + 1) * (second + 1) * milisecond) % maxValue);
Console.WriteLine(randNum);
Console.ReadLine();
}
Above shows a very simple piece of code to generate random numbers. It is a console program written in C#. If you know any kind of basic programming this should be understandable and easy to convert to any other language desired.
The DateTime simply takes in a current date and time, most programming languages have a facility to do this.
The hour, minute, second and milisecond variables break the date time value it up into its component parts. We are only interested in these parts so can ignore day. Again, in most languages dates and times are usually presented as strings. In .Net we have facilities that allow us to parse this information easily. But in most other languages where times are presented as strings, its is not overly difficult to parse the string for the parts that you want and convert them to their numbers. These facilities are usually provided even in the oldest of languages.
The seed essentially gives us a starting number which always changes. Traditionally you would just multiply this number by a decimal value between 0 and 1 this cuts out that step.
The upperRange defines the maximum value. So the number generated will never be above this value. Also it will never be below 0. So no ngeatives. But if you want negatives you could just negate it manually. (by multiplying it by -1)
The actual variable randNumis what holds the random value you are interested in.
The trick is to get the remainder (the modulus) after dividing the seed by the upper range. The remainder will always be smaller than the divisor which in this case is 100. Simple maths tells you that you cant have a remainder greater than the divisor. So if you divide by 10 you cant have a remainder greater than 10. It is this simple law that gets us our random number between 0 and 100 in this case.
The console.writeline simply outputs it to the screen.
The console.readline simply pauses the program so you can see it.
This is a very simple piece of code to generate random numbers. If you ran this program at the exact same intervil every day (but you would have to do it at the same hour, minute, second and milisecond) for more than 1 day you would begin to generate the same set of numbers again and again each additional day. This is because it is tied to the time. That is the resolution of the generator. So if you know the code of this program, and the time it is run at, you can predict the number generated, but it wont be easy. That is why I used miliseconds. Use seconds or minutes only to see what I mean. So you could write a table showing when 1 goes in, 0 comes out, when 2 goes in 0 comes out and so on. You could then predict the output for every second, and the range of numbers generated. The more you increase the resolution (by increasing the numbers that change) the harder it is and the longer it takes to get a predictable pattern. This method is good enough for most peoples use.
That is the old school way of doing random number generation for basic games. It needed to be fast, and simple. It is. This also highlights exactly why, random numbers genaerators are not really random but psudo random.
I hope this is a reasonable answer to your question.
hopefuly im not redundant because i havent read all the links, but i believe you can get pretty close to true random generator. nowadays systems are often so complex that even the best geeks around need a lot of time to understand whats happening inside :)
just open your mind and think if you can monitor some global system property, use it to seed to ... pick a network packet (not intended for you?) and compute "something" out of its content and use it to seed to ... etc.
you can design the best for your needs with all those hints around ;)
The Mersenne twister has a very long period (2^19937-1).
Here's a very basic implementation in C++:
struct MT{
unsigned int *mt, k, g;
~MT(){ delete mt; }
MT(unsigned int seed) : mt(new unsigned int[624]), k(0), g(0){
for (int i=0; i<624; i++)
mt[i]=!i?seed:(1812433253U*(mt[i-1]^(mt[i-1]>>30))+i);
}
unsigned int operator()(){
unsigned int q=(mt[k]&0x80000000U)|(mt[(k+1)%624]&0x7fffffffU);
mt[k]=mt[(k+397)%624]^(q>>1)^((q&1)?0x9908b0dfU:0);
unsigned int y = mt[k];
y ^= (y >> 11);
y ^= (y << 7) & 0x9d2c5680U;
y ^= (y << 15) & 0xefc60000U;
y ^= (y >> 18);
k = (k+1)%624;
return y;
}
};
One good way to get random numbers is to monitor the ambient level of noise coming through your computer's microphone. If you can get a driver (or language that supports mic input) and convert this to a number, you're well on your way!
It has also been researched in how to get "true randomness" - since computers are nothing more than binary machines, they can't give us "true randomness". After a while, the sequence will begin to repeat itself. The quest for better random number generation is still going, but they say monitoring ambient noise levels in a room is one good way to prevent pattern forming in your random generation.
You can look up this wiki article for more information on the science behind random number generation.
If you are looking for a theoretical treatment on random numbers, probably you can have a look at Volume 2 of the The art of computer programming. It has a chapter dedicated to random numbers. See if it helps you out.
If you are wanting to manually, hard code, your own random generator I can't give you efficiency, however, I can give you reliability. I actually decided to write some code using time to test a computer's processing speed by counting in time and that turned into me writing my own random number generator using the counting algorithm for modulo (the count is random). Please, try it for yourselves and test on number distributions within a large test-set. By the way, this is written in python.
def count_in_time(n):
import time
count = 0
start_time = time.clock()
end_time = start_time + n
while start_time < end_time:
count += 1
start_time += (time.clock() - start_time)
return count
def generate_random(time_to_count, range_nums, rand_lst_size):
randoms = []
iterables = range(range_nums)
count = 0
for i in range(rand_lst_size):
count += count_in_time(time_to_count)
randoms.append(iterables[count%len(iterables)])
return randoms
This document is a very nice write up of pseudo-random number generation and has a number of routines included (in C). It also discusses the need for appropriate seeding of the random number generators (see rule 3). Particularly useful for this is the use of /dev/randon/ (if you are on a linux machine).
Note: the routines included in this document are alot simpler to code up than the Mersenne Twister. See also the WELLRNG generator, which is supposed to have better theoretical properties, as an alternative to the MT.
Read the rands book of random numbers (monte carlo book of random numbers) the numbers in it are randomly generated for you!!! My grandfather worked for rand.
Most RNGs(random number generators) will require a small bit of initialization. This is usually to perform a seeding operation and store the results of the seeded values for later use. Here is an example of a seeding method from a randomizer I wrote for a game engine:
/// <summary>
/// Initializes the number array from a seed provided by <paramref name="seed">seed</paramref>.
/// </summary>
/// <param name="seed">Unsigned integer value used to seed the number array.</param>
private void Initialize(uint seed)
{
this.randBuf[0] = seed;
for (uint i = 1; i < 100; i++)
{
this.randBuf[i] = (uint)(this.randBuf[i - 1] >> 1) + i;
}
}
This is called from the constructor of the randomizing class. Now the real random numbers can be rolled/calculated using the aforementioned seeded values. This is usually where the actual randomizing algorithm is applied. Here is another example:
/// <summary>
/// Refreshes the list of values in the random number array.
/// </summary>
private void Roll()
{
for (uint i = 0; i < 99; i++)
{
uint y = this.randBuf[i + 1] * 3794U;
this.randBuf[i] = (((y >> 10) + this.randBuf[i]) ^ this.randBuf[(i + 399) % 100]) + i;
if ((this.randBuf[i] % 2) == 1)
{
this.randBuf[i] = (this.randBuf[i + 1] << 21) ^ (this.randBuf[i + 1] * (this.randBuf[i + 1] & 30));
}
}
}
Now the rolled values are stored for later use in this example, but those numbers can also be calculated on the fly. The upside to precalculating is a slight performance increase. Depending on the algorithm used, the rolled values could be directly returned or go through some last minute calculations when requested by the code. Here is an example that takes from the prerolled values and spits out a very good looking pseudo random number:
/// <summary>
/// Retrieves a value from the random number array.
/// </summary>
/// <returns>A randomly generated unsigned integer</returns>
private uint Random()
{
if (this.index == 0)
{
this.Roll();
}
uint y = this.randBuf[this.index];
y = y ^ (y >> 11);
y = y ^ ((y << 7) + 3794);
y = y ^ ((y << 15) + 815);
y = y ^ (y >> 18);
this.index = (this.index + 1) % 100;
return y;
}
