Random Numbers

Random numbers—too important to be left to chance!

Random Number Generation

A true random number generator has three important properties:

It is unbiased.
All values of whatever sample size is collected are equiprobable.
It is unpredictable.
It is impossible to predict what the next output will be, given all the previous outputs, but not the internal “hidden” state.
It is unreproducible.
Two of the same generators, given the same starting conditions, will produce different outputs.

Random Number Generation

Other Descriptions:

A “good” random number generator is unbiased.
A “cryptographically strong” random number generator is unpredictable.
A “true” random number generator, is unreproducible.

Very rarely is a random number generator all of: “good”, “cryptographically strong”, and “true”. This isn't necessarily a bad thing, but it's worth remembering when evaluating claims that one random number generator is “better” than another.

Random Number Generation

<stdlib.h> provides us with two random number generator functions:

rand()
srand()

Random Number Generation

`rand()`

This function generates a number between 0 and RAND_MAX.
RAND_MAX is a symbolic constant, defined in <stdlib.h>
Every number between 0 and RAND_MAX has an equal chance of being chosen each time rand() is called.
```
int number = rand();
printf("%d\n", number);
```
```
1804289383
```

Why is the number so big? Shouldn’t we randomly get a small number every once in a while?

Seeding the generator

`srand()`

This function is used to produce a truer sequence of random numbers, which is achieved by seeding srand() with a different seed every time it is called.
This function is called only once in a particular program. Once!
After that, call rand() to get random numbers.

Random Number Generation

A popular method for seeding is to use the system clock.
time(NULL) returns the number of seconds since the start of 1970.
Really—the year 1970.
As of Wednesday 11:55ᴘᴍ, there were 1741845357 seconds since the start of 1970.
```
srand(time(NULL));
printf("%d\n", rand());
```
```
998249311
```

Scaling

Numbers generated by the random number generators may not necessarily be in the desired range.
Scaling allows us to restrict the output values to what is needed.

Scaling

To use rand() and srand() to produce values in a particular range, we may generalize:
```
int number = a + rand() % b;
```
- a is the shifting value (the first number in the desired range of consecutive integers)
- b is the scaling factor (the width of the desired range of consecutive integers).
That is, it returns b different numbers, starting at a.
In other words, it produces b…b+a−1, inclusive.
- Note that b+a is not a possibility.

Example

srand(time(NULL));

for (int row = 0; row < 7; row++) {
    for (int i = 0; i < 20; i++)
        printf(" %d", 18 + rand() % 8);
    printf("\n");
}

 25 19 22 20 22 18 18 25 25 25 19 24 20 23 25 22 18 23 24 22
 22 23 21 22 19 18 21 24 23 21 23 22 22 19 24 19 20 25 18 19
 24 19 25 19 25 24 23 25 21 22 21 18 19 24 22 20 25 25 18 22
 20 24 18 24 25 25 25 19 24 18 20 22 19 20 23 18 18 21 25 22
 25 20 22 18 19 18 20 18 25 21 22 19 19 22 25 18 21 25 20 19
 25 22 24 18 24 21 19 25 24 18 21 23 21 25 23 22 25 18 22 24
 21 18 25 22 22 24 22 18 23 24 19 22 21 25 23 19 21 24 18 19

CS157: Intro to C, Part II

Spring 2018

Random

Random Numbers

Random numbers—too important to be left to chance!

Random Number Generation

Random Number Generation

Other Descriptions:

Random Number Generation

Random Number Generation

`rand()`

Seeding the generator

`srand()`

Random Number Generation

Scaling

Scaling

Example