How does random number generated in C++?

HelloWorld · #1 (**permalink**) 07-26-2007, 10:16 PM

Below is the code that I'm playing around, I'm just trying to figure out on how does the Random number generator works in C++ it's really weird...

PHP Code:

  #include "stdafx.h"
#include <iostream>
using std::cout;
using std::cin;

#include <string>
using std::endl;
using std::string;

#include <iomanip>
using std::setw;

#include <cstdlib>
using std::rand;

int main() {
    for (int i = 0; i < 10; i++) {
        cout << setw(10) << ( 1 + rand() % 6 ) << endl;
    }
    return 0;
}

More precisely this part:

PHP Code:

  ( 1 + rand() % 6 )

I tried to remove the 1, however I think it gives me from 0 to 5, why do we have to do modulus 6? How does it works?

rpgfan3233 · #2 (**permalink**) 07-26-2007, 10:38 PM

I have one thing to say first of all: the rand() function is not a member of the std namespace. It is a C function, so it is not technically a member of any named namespace. I've seen some code do things such as using ::printf; to use the printf() function, but as far as I know, it isn't actually necessary.

Here is the algorithm that you are using:
min_value + rand() % (max_value - min_value + 1)

That is, min_value would be 1 and max_value would be 6. To see the math behind it:
1 + rand() % (6 - 1 + 1)

The reason why you use modulo 6 is because rand() returns a value between 0 and the constant RAND_MAX (RAND_MAX is a constant defined in stdlib.h (cstdlib in C++), and the minimum value for RAND_MAX is supposed to be 32767). Obviously, you don't want to test the entire range of possible random numbers, just a limited range. That is why modulus is there.

In case you don't know, modulo 6 refers to the remainder in C++. That means that if you have 6 / 6 = 1, there is no remainder. However, if you do 5 / 6 = 0, the remainder is 5. Likewise, 1234 / 6 = 205 with a remainder of 4. In other words, 5 % 6 = 5 and 1234 % 6 = 4. Modulo operations return a value in the range of 0 to (second_operand - 1), where 6 would be the second_operand in the above example. That means that it would render a value in the range of 0 to 5 inclusive. Adding 1 to the result of that makes the range 1 to 6. I'm assuming that it is a dice rolling program since traditional dice have 6 sides.

Also, if that generates different values for you, I'm shocked since the random number generator hasn't even been seeded using the srand() function, which is also found in the same header as rand() and RAND_MAX.

Edit: As for how it works, I have no clue about the internals, especially since the implementation is compiler-specific. The general idea is that a value is selected from an internal table of numbers using a complex algorithm that operates on the seed value.

HelloWorld · #3 (**permalink**) 07-26-2007, 10:55 PM

Quote below is directly from Deitel's book:

Quote:

For GNU C++, the value of RAND_MAX is 214748647; for Visual Studio, the value of RAND_MAX is 32767

Thanx a lot rpgfan3233 for the detail explanation, the equation helps a lot

Edit:

Quote:

min_value + rand() % (max_value - min_value + 1)

This equation right here, why there is "- min_value + 1" ??? I think it's kind of weird, so for example if I use min value of 2 then my maximum would be 6-1 = 5 !!!??? XD that will require me to do:

Code:

2 + rand() % 6 + 1

to keep the same maximum of "6" ??? I think that's kind of weird..

rpgfan3233 · #4 (**permalink**) 07-27-2007, 12:13 AM

That's why I just memorize the expression and use that.

In old-fashioned QuickBASIC (MS-DOS days), the keyword RND returned a float (a SINGLE, as in single-precision floating-point type) between 0 and 1. To change the values, you actually had to multiply rather than use the modulus operator:

Code:

CLS 'clear the screen
DIM Rand AS INTEGER
Rand = 1 + FIX(RND * 6)
PRINT Random 'print the value to the screen
END 'end the program

Note that the same idea that is used in C (MAXVALUE - MINVALUE + 1) works in QuickBASIC, right down to the addition of the MINVALUE to balance things out. Of course, FIX () in QuickBASIC is needed because otherwise Rand would hold a float/SINGLE when we would want an INTEGER.

As for why the "- min_value + 1" thing is there, consider this:
You want to generate some random data between 50 and 100 to test a grade program. Look at what could happen if we used just 50 for min_value and 100 for max_value, with no "- min_value + 1" added on:
50 + (rand() % 100)
50 + (98) //98 is less than 100...
148

But your range is supposed to be 50 to 100!! Now if you try with the "- min_value + 1" added back in:
50 + (rand() % (100 - 50 + 1))
50 + (rand() % 51)
50 + (49) //49 is less than 51...
99

See? If rand() generates a multiple of 51, including 0, it will result in the lowest value (50).

Edit: The part about GNU C++ and Visual Studio, it is actually more platform specific in that instance. GNU C++ on Windows uses Windows libraries at this time. This means that RAND_MAX on Windows is 32767 (0x7FFF). RAND_MAX on Linux is 2147483647 (0x7FFFFFFF).

HelloWorld · #5 (**permalink**) 07-27-2007, 08:24 AM

Quote:

In old-fashioned QuickBASIC (MS-DOS days), the keyword RND returned a float (a SINGLE, as in single-precision floating-point type) between 0 and 1. To change the values, you actually had to multiply rather than use the modulus operator:

LOL! We use the same thing in Java to generates double random value!

Here's how Java generates double random value:

Code:

Random r = new Random();
r.nextDouble(); // Generates double between 0.0 and 1.0
r.nextDouble() * 10; // then generates random number between 0.0 and 10.0

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