# 5.9 — Random number generation

The ability to generate random numbers can be useful in certain kinds of programs, particularly in games, statistics modeling programs, and scientific simulations that need to model random events. Take games for example -- without random events, monsters would always attack you the same way, you’d always find the same treasure, the dungeon layout would never change, etc… and that would not make for a very good game.

So how do we generate random numbers? In real life, we often generate random results by doing things like flipping a coin, rolling a dice, or shuffling a deck of cards. These events involve so many physical variables (e.g. gravity, friction, air resistance, momentum, etc…) that they become almost impossible to predict or control, and produce results that are for all intents and purposes random.

However, computers aren’t designed to take advantage of physical variables -- your computer can’t toss a coin, throw a dice, or shuffle real cards. Computers live in a controlled electrical world where everything is binary (false or true) and there is no in-between. By their very nature, computers are designed to produce results that are as predictable as possible. When you tell the computer to calculate 2 + 2, you always want the answer to be 4. Not 3 or 5 on occasion.

Consequently, computers are generally incapable of generating random numbers. Instead, they must simulate randomness, which is most often done using pseudo-random number generators.

A pseudo-random number generator (PRNG) is a program that takes a starting number (called a seed), and performs mathematical operations on it to transform it into some other number that appears to be unrelated to the seed. It then takes that generated number and performs the same mathematical operation on it to transform it into a new number that appears unrelated to the number it was generated from. By continually applying the algorithm to the last generated number, it can generate a series of new numbers that will appear to be random if the algorithm is complex enough.

Rule: You should only seed your random number generators once. Seeding them more than once will cause the results to be less random or non-random.

It’s actually fairly easy to write a PRNG. Here’s a short program that generates 100 pseudo-random numbers:

The result of this program is:

```23070   27857   22756   10839   27946
11613   30448   21987   22070   1001
27388   5999    5442    28789   13576
28411   10830   29441   21780   23687
5466    2957    19232   24595   22118
14873   5932    31135   28018   32421
14648   10539   23166   22833   12612
28343   7562    18877   32592   19011
13974   20553   9052    15311   9634
27861   7528    17243   27310   8033
28020   24807   1466    26605   4992
5235    30406   18041   3980    24063
15826   15109   24984   15755   23262
17809   2468    13079   19946   26141
1968    16035   5878    7337    23484
24623   13826   26933   1480    6075
11022   19393   1492    25927   30234
17485   23520   18643   5926    21209
2028    16991   3634    30565   2552
20971   23358   12785   25092   30583
```

Each number appears to be pretty random with respect to the previous one. As it turns out, our algorithm actually isn’t very good, for reasons we will discuss later. But it does effectively illustrate the principle of PRNG number generation.

Generating random numbers in C++

C (and by extension C++) comes with a built-in pseudo-random number generator. It is implemented as two separate functions that live in the cstdlib header:

`std::srand()` sets the initial seed value to a value that is passed in by the caller. srand() should only be called once at the beginning of your program. This is usually done at the top of main().

`std::rand()` generates the next random number in the sequence. That number will be a pseudo-random integer between 0 and RAND_MAX, a constant in cstdlib that is typically set to 32767.

Here’s a sample program using these functions:

Here’s the output of this program:

```17421	8558	19487	1344	26934
7796	28102	15201	17869	6911
4981	417	12650	28759	20778
31890	23714	29127	15819	29971
1069	25403	24427	9087	24392
15886	11466	15140	19801	14365
18458	18935	1746	16672	22281
16517	21847	27194	7163	13869
5923	27598	13463	15757	4520
15765	8582	23866	22389	29933
31607	180	17757	23924	31079
30105	23254	32726	11295	18712
29087	2787	4862	6569	6310
21221	28152	12539	5672	23344
28895	31278	21786	7674	15329
10307	16840	1645	15699	8401
22972	20731	24749	32505	29409
17906	11989	17051	32232	592
17312	32714	18411	17112	15510
8830	32592	25957	1269	6793
```

PRNG sequences and seeding

If you run the std::rand() sample program above multiple times, you will note that it prints the same result every time! This means that while each number in the sequence is seemingly random with regards to the previous ones, the entire sequence is not random at all! And that means our program ends up totally predictable (the same inputs lead to the same outputs every time). There are cases where this can be useful or even desired (e.g. you want a scientific simulation to be repeatable, or you’re trying to debug why your random dungeon generator crashes).

But often, this is not what is desired. If you’re writing a game of hi-lo (where the user has 10 tries to guess a number, and the computer tells them whether their guess is too high or too low), you don’t want the program picking the same numbers each time. So let’s take a deeper look at why this is happening, and how we can fix it.

Remember that each number in a PRNG sequence is generated from the previous number, in a deterministic way. Thus, given any starting seed number, PRNGs will always generate the same sequence of numbers from that seed as a result! We are getting the same sequence because our starting seed number is always 5323.

In order to make our entire sequence randomized, we need some way to pick a seed that’s not a fixed number. The first answer that probably comes to mind is that we need a random number! That’s a good thought, but if we need a random number to generate random numbers, then we’re in a catch-22. It turns out, we really don’t need our seed to be a random number -- we just need to pick something that changes each time the program is run. Then we can use our PRNG to generate a unique sequence of pseudo-random numbers from that seed.

The commonly accepted method for doing this is to enlist the system clock. Each time the user runs the program, the time will be different. If we use this time value as our seed, then our program will generate a different sequence of numbers each time it is run!

C comes with a function called time() that returns the number of seconds since midnight on Jan 1, 1970. To use it, we merely need to include the ctime header, and then initialize srand() with a call to std::time(nullptr) (or std::time(0) if your compiler is pre-C++11). We haven’t covered nullptr yet, but it’s essentially the equivalent of 0 in this context.

Here’s the same program as above, using a call to time() as the seed:

Now our program will generate a different sequence of random numbers every time! Run it a couple of times and see for yourself.

Generating random numbers between two arbitrary values

Generally, we do not want random numbers between 0 and RAND_MAX -- we want numbers between two other values, which we’ll call min and max. For example, if we’re trying to simulate the user rolling a die, we want random numbers between 1 and 6 (pedantic grammar note: yes, die is the singular of dice).

Here’s a short function that converts the result of rand() into the range we want:

To simulate the roll of a die, we’d call getRandomNumber(1, 6). To pick a randomized digit, we’d call getRandomNumber(0, 9).

Optional reading: How does the previous function work?

The getRandomNumber() function may seem a little complicated, but it’s not too bad.

Let’s revisit our goal. The function rand() returns a number between 0 and RAND_MAX (inclusive). We want to somehow transform the result of rand() into a number between min and max (inclusive). This means that when we do our transformation, 0 should become min, and RAND_MAX should become max, with a uniform distribution of numbers in between.

We do that in five parts:

1. We multiply our result from std::rand() by fraction. This converts the result of rand() to a floating point number between 0 (inclusive), and 1 (exclusive).

If rand() returns a 0, then 0 * fraction is still 0. If rand() returns RAND_MAX, then RAND_MAX * fraction is RAND_MAX / (RAND_MAX + 1), which is slightly less than 1. Any other number returned by rand() will be evenly distributed between these two points.

2. Next, we need to know how many numbers we can possibly return. In other words, how many numbers are between min (inclusive) and max (inclusive)?

This is simply (max - min + 1). For example, if max = 8 and min = 5, (max - min + 1) = (8 - 5 + 1) = 4. There are 4 numbers between 5 and 8 (that is, 5, 6, 7, and 8).

3. We multiply the prior two results together. If we had a floating point number between 0 (inclusive) and 1 (exclusive), and then we multiply by (min - max + 1), we now have a floating point number between 0 (inclusive) and (max - min + 1) (exclusive).
4. We cast the previous result to an integer. This removes any fractional component, leaving us with an integer result between 0 (inclusive) and (max - min) (inclusive).
5. Finally, we add min, which shifts our result to an integer between min (inclusive) and max (inclusive).

Optional reading: Why don’t we use the modulus operator (%) in the previous function?

One of the most common questions readers have submitted is why we use division in the above function instead of modulus (%). The short answer is that the modulus method tends to be biased in favor of low numbers.

Let’s consider what would happen if the above function looked like this instead:

Seems similar, right? Let’s explore where this goes wrong. To simplify the example, let’s say that rand() always returns a random number between 0 and 9 (inclusive). For our sample case, we’ll pick min = 0, and max = 6. Thus, max - min + 1 is 7.

Now let’s calculate all possible outcomes:

```0 + (0 % 7) = 0
0 + (1 % 7) = 1
0 + (2 % 7) = 2
0 + (3 % 7) = 3
0 + (4 % 7) = 4
0 + (5 % 7) = 5
0 + (6 % 7) = 6

0 + (7 % 7) = 0
0 + (8 % 7) = 1
0 + (9 % 7) = 2
```

Look at the distribution of results. The results 0 through 2 come up twice, whereas 3 through 6 come up only once. This method has a clear bias towards low results. By extension, most cases involving this algorithm will behave similarly.

Now lets take a look at the result of the getRandomNumber() function above, using the same parameters as above (rand() returns a number between 0 and 9 (inclusive), min = 0 and max = 6). In this case, fraction = 1 / (9 + 1) = 0.1. max - min + 1 is still 7.

Calculating all possible outcomes:

```0 + static_cast(7 * (0 * 0.1))) = 0 + static_cast(0) = 0
0 + static_cast(7 * (1 * 0.1))) = 0 + static_cast(0.7) = 0
0 + static_cast(7 * (2 * 0.1))) = 0 + static_cast(1.4) = 1
0 + static_cast(7 * (3 * 0.1))) = 0 + static_cast(2.1) = 2
0 + static_cast(7 * (4 * 0.1))) = 0 + static_cast(2.8) = 2
0 + static_cast(7 * (5 * 0.1))) = 0 + static_cast(3.5) = 3
0 + static_cast(7 * (6 * 0.1))) = 0 + static_cast(4.2) = 4
0 + static_cast(7 * (7 * 0.1))) = 0 + static_cast(4.9) = 4
0 + static_cast(7 * (8 * 0.1))) = 0 + static_cast(5.6) = 5
0 + static_cast(7 * (9 * 0.1))) = 0 + static_cast(6.3) = 6
```

The bias here is still slightly towards lower numbers (0, 2, and 4 appear twice, whereas 1, 3, 5, and 6 appear once), but it’s much more uniformly distributed.

Even though getRandomNumber() is a little more complicated to understand than the modulus alternative, we advocate for the division method because it produces a less biased result.

What is a good PRNG?

As I mentioned above, the PRNG we wrote isn’t a very good one. This section will discuss the reasons why. It is optional reading because it’s not strictly related to C or C++, but if you like programming you will probably find it interesting anyway.

In order to be a good PRNG, the PRNG needs to exhibit a number of properties:

First, the PRNG should generate each number with approximately the same probability. This is called distribution uniformity. If some numbers are generated more often than others, the result of the program that uses the PRNG will be biased!

For example, let’s say you’re trying to write a random item generator for a game. You’ll pick a random number between 1 and 10, and if the result is a 10, the monster will drop a powerful item instead of a common one. You would expect a 1 in 10 chance of this happening. But if the underlying PRNG is not uniform, and generates a lot more 10s than it should, your players will end up getting more rare items than you’d intended, possibly trivializing the difficulty of your game.

Generating PRNGs that produce uniform results is difficult, and it’s one of the main reasons the PRNG we wrote at the top of this lesson isn’t a very good PRNG.

Second, the method by which the next number in the sequence is generated shouldn’t be obvious or predictable. For example, consider the following PRNG algorithm: `num = num + 1`. This PRNG is perfectly uniform, but it’s not very useful as a sequence of random numbers!

Third, the PRNG should have a good dimensional distribution of numbers. This means it should return low numbers, middle numbers, and high numbers seemingly at random. A PRNG that returned all low numbers, then all high numbers may be uniform and non-predictable, but it’s still going to lead to biased results, particularly if the number of random numbers you actually use is small.

Fourth, all PRNGs are periodic, which means that at some point the sequence of numbers generated will eventually begin to repeat itself. As mentioned before, PRNGs are deterministic, and given an input number, a PRNG will produce the same output number every time. Consider what happens when a PRNG generates a number it has previously generated. From that point forward, it will begin to duplicate the sequence between the first occurrence of that number and the next occurrence of that number over and over. The length of this sequence is known as the period.

For example, here are the first 100 numbers generated from a PRNG with poor periodicity:

```112	9	130	97	64
31	152	119	86	53
20	141	108	75	42
9	130	97	64	31
152	119	86	53	20
141	108	75	42	9
130	97	64	31	152
119	86	53	20	141
108	75	42	9	130
97	64	31	152	119
86	53	20	141	108
75	42	9	130	97
64	31	152	119	86
53	20	141	108	75
42	9	130	97	64
31	152	119	86	53
20	141	108	75	42
9	130	97	64	31
152	119	86	53	20
141	108	75	42	9
```

You will note that it generated 9 as the second number, and 9 again as the 16th number. The PRNG gets stuck generating the sequence in-between these two 9’s repeatedly: 9-130-97-64-31-152-119-86-53-20-141-108-75-42-(repeat).

A good PRNG should have a long period for all seed numbers. Designing an algorithm that meets this property can be extremely difficult -- most PRNGs will have long periods for some seeds and short periods for others. If the user happens to pick a seed that has a short period, then the PRNG won’t be doing a good job.

Despite the difficulty in designing algorithms that meet all of these criteria, a lot of research has been done in this area because of its importance to scientific computing.

std::rand() is a mediocre PRNG

The algorithm used to implement std::rand() can vary from compiler to compiler, leading to results that may not be consistent across compilers. Most implementations of rand() use a method called a Linear Congruential Generator (LCG). If you have a look at the first example in this lesson, you’ll note that it’s actually a LCG, though one with intentionally picked poor constants. LCGs tend to have shortcomings that make them not good choices for most kinds of problems.

One of the main shortcomings of rand() is that RAND_MAX is usually set to 32767 (essentially 15-bits). This means if you want to generate numbers over a larger range (e.g. 32-bit integers), rand() is not suitable. Also, rand() isn’t good if you want to generate random floating point numbers (e.g. between 0.0 and 1.0), which is often useful when doing statistical modelling. Finally, rand() tends to have a relatively short period compared to other algorithms.

That said, rand() is perfectly suitable for learning how to program, and for programs in which a high-quality PRNG is not a necessity.

For applications where a high-quality PRNG is useful, I would recommend Mersenne Twister (or one of its variants), which produces great results and is relatively easy to use. Mersenne Twister was adopted into C++11, and we’ll show how to use it later in this lesson.

Debugging programs that use random numbers

Programs that use random numbers can be difficult to debug because the program may exhibit different behaviors each time it is run. Sometimes it may work, and sometimes it may not. When debugging, it’s helpful to ensure your program executes the same (incorrect) way each time. That way, you can run the program as many times as needed to isolate where the error is.

For this reason, when debugging, it’s a useful technique to set the random seed (via `std::srand`) to a specific value (e.g. 0) that causes the erroneous behavior to occur. This will ensure your program generates the same results each time, making debugging easier. Once you’ve found the error, you can seed using the system clock again to start generating randomized results again.

Random numbers in C++11

C++11 added a ton of random number generation functionality to the C++ standard library, including the Mersenne Twister algorithm, as well as generators for different kinds of random distributions (uniform, normal, Poisson, etc…). This is accessed via the <random> header.

Here’s a short example showing how to generate random numbers in C++11 using Mersenne Twister (h/t to user Fernando):

Author's note

Before C++17, you need to use add empty brackets to create `die` after the type
`std::uniform_int_distribution<> die{ 1, 6 }`

You’ll note that Mersenne Twister generates random 32-bit unsigned integers (not 15-bit integers like std::rand()), giving a lot more range. There’s also a version (std::mt19937_64) for generating 64-bit unsigned integers.

C++11 style random numbers across multiple functions

The above example create a random generator for use within a single function. What happens if we want to use a random number generator in multiple functions?

Although you can create a static local std::mt19937 variable in each function that needs it (static so that it only gets seeded once), it’s a little overkill to have every function that needs a random number generator seed and maintain its own local generator. A better option in most cases is to create a global random number generator (inside a namespace!). Remember how we told you to avoid non-const global variables? This is an exception (also note: std::rand() and std::srand() access a global object, so there’s precedent for this).

Using a random library

A perhaps better solution is to use a 3rd party library that handles all of this stuff for you, such as the header-only Effolkronium’s random library. You simply add the header to your project, #include it, and then you can start generating random numbers via `Random::get(min, max)`.

Here’s the above program using Effolkronium’s library:

Help! My random number generator is generating the same sequence of random numbers!

If your random number generator is generating the same sequence of random numbers every time your program is run, you probably didn’t seed it properly. Make sure you’re seeding it with a value that changes each time the program is run (like `std::time(nullptr)`).

Help! My random number generator always generates the same first number!

The implementation of rand() in Visual Studio and a few other compilers has a flaw -- the first random number generated doesn’t change much for similar seed values. This means that when using std::time(nullptr) to seed your random number generator, the first result from rand() won’t change much in successive runs. However, the results of successive calls to rand() aren’t impacted, and will be sufficiently randomized.

The solution here, and a good rule of thumb in general, is to discard the first random number generated from the random number generator.

Help! My random number generator isn’t generating random numbers at all!

If your random number generator is generating the same number every time you ask it for a random number, then you are probably either reseeding the random number generator before generating a random number, or you’re creating a new random generator for each random number.

Here’s are two functions that exhibit the issue:

In both cases, the random number generator is being seeded each time before a random number is generated. This will cause a similar number to be generated each time.

In the top case, `std::srand()` is reseeding the built-in random number generator before rand() is called (by `getRandomNumber()`).

In the bottom case, we’re creating a new Mersenne Twister, seeding it, generating a single random number, and then destroying it.

For best results, you should only seed a random number generator once (generally at program initialization for `std::srand()`, or the point of creation for other random number generators), and then use that same random number generator for each successive random number generated.

### 436 comments to 5.9 — Random number generation

• Elis

As part of a "Hi-lo game" I used the following randomization process. Just using the randomize function would always yield the same result in lower ranges. E.g. loNumber == 3 and hiNumber == 9 would always yield 7 e.t.c.
With this I managed to get pretty good results.
Since this runs the randomize function many times in a row is it a necessity to place the seed elsewhere than in the function itself (as below)?

As always thanks for the great tutorials!

• nascardriver

Yes. Never seed more than once. Seeding again with the same seed will reset the sequence, so you'll get the same "random" number again.

• Ged

I don't understand these lines fully. Would appreciate if you could explain a bit more.

• nascardriver

You won't be able to understand them fully until you get to classes and templates.
`std::my19937` wants a `std::mt19937::result_type`, but `std::time` returns an unspecified type, so we need to cast it.

> how does uniform_int_distribution even work
There's no general answer, as the standard only says _what_ `std::uniform_int_distribution` does, but not _how_. If you want to understand how it works, you'll have to read up on discrete probability, finish learning C++, and then try to read a standard implementation.

> why do we have <>
They're not necessary since C++17, you can write `std::uniform_int_distribution die{ 1, 6 };`. Inside the <>, you can specify the integer type you want to have as a result, eg.
`std::uniform_int_distribution die{ 1, 6 };`

> how does die(1,6)
You'll need to know about classes and constructors. Basically, `die` stores the numbers you give it (min and max) and uses them later when it generates a number.

• Tushar

Output:

990     3213    1565    28503   21640
5362    29035   4686    32618   27599
7500    3776    13427   15361   8288
30298   17693   11683   32746   9669
10489   9238    19735   17318   20090
18670   12737   24603   871     13768
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541   22541
22541   22541   22541   22541

Why are the numbers being repeated?

• Luiz

It's going to take someone more experienced than me to explain but I managed to fix it by doing the following:
snip

I assigned seed to it's module by 34567 everytime

It's probably got to do with undefined behaviour via overflow

• Tushar

Okay so this has reduced repetition of a single number though its producing repeated pattern

Output:

3381    2929    3321    745     1801
2633    1993    3401    2505    1737
1225    2889    713     1097    73
3401    2505    1737    1225    2889
713     1097    73      3401    2505
1737    1225    2889    713     1097
73      3401    2505    1737    1225
2889    713     1097    73      3401
2505    1737    1225    2889    713
1097    73      3401    2505    1737
1225    2889    713     1097    73
3401    2505    1737    1225    2889
713     1097    73      3401    2505
1737    1225    2889    713     1097
73      3401    2505    1737    1225
2889    713     1097    73      3401
2505    1737    1225    2889    713
1097    73      3401    2505    1737
1225    2889    713     1097    73
3401    2505    1737    1225    2889
You can see the pattern starting with 713 1097 73... 2889.

• Luiz

There's no error within the code, it is all caused by the math and overflowing of the unsigned int. The operations your number go through in your pseudo random generator have created a pattern. If you want to try to create one that's less predictable you could try adding more operations of different sorts or such. I reckon this is also true for the reason as to why 22541 was being repeated on the first version of your code.

• Luiz

Also as it is said in this lesson: The PRNG is perfectly uniform, so you're better off using a different method to generate random numbers

• Tushar

Doesn't generate repeated number nor a pattern!
Is it correct?

• nascardriver

`end` and `std::time(nullptr)` are constant, you're basically doing

just more expensive. The modulus that you removed is now performed by the wrap-around of `seed`.

Take your original code and change the constant factor to an odd number, that should get rid of the repetition.

I don't know why this works, Mike observed something similar here https://www.learncpp.com/cpp-tutorial/59-random-number-generation/comment-page-6/#comment-427692

• Mike

"Consider what happens when a PRNG generates a number it has previously generated. From that point forward, it will begin to duplicate the sequence between the first occurrence of that number and the next occurrence of that number over and over. The length of this sequence is known as the period."

Is this behavior only with large ranges? Because when I do it with a range of 1-6 (roll of die) or other similar low ranges, the numbers often get repeated many times, yet I haven't noticed a pattern from any of them. Based on what Alex stated above, shouldn't a pattern start right after the first number is repeated?

Other than the much larger range, how are these different than the example that Alex provided?

• nascardriver

When you generate a number from 1 to 6, you're using a way larger number and scale it down. When you see two 1s, they're probably not both based on the same number.
Consider a simple `std::rand` generator

`die` is 1 for 1, 7, 13, 19, etc.

• Mike

Thanks for the feedback!
So if I understood you correctly, scaling down from a larger number, like maybe the RAND_MAX of 32767, to a significantly smaller range of numbers, like the roll of a die, will likely contribute to a longer or better period?

• nascardriver

Scaling down the number doesn't affect the period. The period is caused by the implementation of the PRNG, which you're not changing.

• hellmet

I have a few questions with the examples here.

What is 'mersenne' here? I think it's the uniform initialization of
What is the type of 'die' here? It looks like a variable but later used as a function?

• nascardriver

`mersenne` is an `std::mt19937`, a mersenne twister. It's a random number generator, seeded with the current time.
`die`'s type is `std::uniform_int_distribution`, you don't need the `<>`. It's a variable, but its `operator()` has been overloaded so it can be used as if it was a function (Covered later).
`die` uses `mersenne` to generate a random number. Then it turns the random number into a number in the range of 1 to 6 with all numbers being equally likely to occur.

• hellmet

Ahh I see, variable with () is an overloaded operator, cool I'll get back to this page once that is covered; and the Mersenne is a variable that's being uniform initialized with time that's being static cast to a std::mt199...::result type. Got it, Thanks a lot!

• nascardriver

> the Mersenne is a variable that's being uniform initialized
It's not uniform initialized. Uniform initialization (Brace initialization) uses curly braces

Brace initialization is a form of direct initialization, but with higher type safety and it can be used to initialize lists.

• hellmet

My bad! Got the names mixed up. So kind of you point that out too! Thank you!

• Jon

I hope you don't mind a couple of comments related to pedagogy...

I wonder if it's worth mentioning, at least in passing, cryptographically strong random and why you shouldn't use that for anything but crypto.

My take is that this lesson, while quite good, is a big jump from the last one where we just learned about the for loop. We still haven't been taught about angle brackets and such. Personally, I'm not bothered by the pacing here but I've been programming for decades and I'm just brushing up on modern C++.

Thank you so much for the lessons and please don't take this as criticism, it's just food for thought.

• Alex

I never mind feedback, criticism or otherwise. It's part of how we learn and grow.

> I wonder if it's worth mentioning, at least in passing, cryptographically strong random and why you shouldn't use that for anything but crypto.

Curious why this is relevant to the lesson.

> My take is that this lesson, while quite good, is a big jump from the last one where we just learned about the for loop

What parts do you find to be big jumps? The heavy algorithmic focus, or something more language-syntax specific?

> We still haven't been taught about angle brackets and such

Somewhere prior to this point I mention that angle brackets are how we parameterize types. I'll see if I can find and reinforce that, because it's an important point prior to being able to describe how they actually function (covered in the lessons on templates).

• Mike

When debugging, how do you watch or monitor a value that keeps changing, yet doesn't have a variable assigned to it, like this PRNG statement that I took from a For Loop? Obviously, the value is there and it keeps changing, but even hovering your mouse over it while debugging will not display any results.

std::cout << std::rand() << '\t';

• Alex

One thing that works sometimes is placing a breakpoint on the entry point to wherever the intermediate value (e.g. the result of std::rand) is being sent. In this case, that would be to operator<<, which is likely going to hit everything.

Probably the easiest thing to do is assign the value you're interested in to a variable so it persists beyond the life of the expression, and examine it immediately after.

Anybody else have any better tips here?

• nascardriver

I didn't reply because this depends on the debugger and IDE and I suppose Mike doesn't use gdb.
In gdb, you can "b"reak on the `std::cout ...` line, "step" into `std::rand`, then "finish" and it prints the return value.
I've seen an integrated debugger that shows return values, but I don't think it was for cpp. Though I'm sure one exist for cpp as well.

If the source code can be modified, the line can be split

then break on the `\t` line and "p"rint \$rax if the architecture uses rax for return values and it's an integer.

Personally I do

• Mike

I notice that if I alter the following line in the first code snippet from Ch5.9, that after 13 results, the remaining 87 results are always 32767. At first, I was confused by this, but then I realized, it must be because during each iteration of @PRNG(), the @seed value is always increasing. So at some point, the @seed value is greater than 32768, and so the difference is wrapped. But at some point the amount that is now wrapped is even larger than the 32768, which apparently it can't wrap around again, and thus keeps displaying 32768. So does this mean values can only wrap around once, or is something else at play here?

My primary question is though, why when using the seed values Alex provided in the code snippet, this behavior does not happen? And his numbers are much larger than the one's I used. I even changed the count to 1000, yet the 32768 never repeats. Is he using some special magic numbers to make this happen?

original code from Ch5.9, first snippet:
seed = 8253729 * seed + 2396403;

my alteration:
seed = 2 * seed + 1;

• nascardriver

The multiplication by 2 is the problem. Once you generate `seed - 1`, you'll always get `seed - 1` as the result, because

You'll observe the same behavior when you replace 2 with any even number (I didn't prove that, but seems to work out).

> using the seed values Alex provided in the code snippet, this behavior does not happen
He uses an odd number for the multiplication. Add or subtract one and it'll get stuck too.

• Mike

Interesting, it makes since now. It's also good to know the additional wrapping was not the issue, though for a nascent learner like myself, it seemed logical.

• SullenSecret

I'm sorry, but I feel like many parts of this lesson need further explanations. I had more trouble with it than usual due to certain details simply not being explained. It's as if this topic is disliked by the author.

• Alex

Can you be more specific about which parts were hard for you to understand? Thanks!

• Raiyan

What's the difference between

and

.

• nascardriver

`std::mt19937::result_type` is an `std::uint_fast32_t`, a 32-bit wide integer.
`unsigned int` is at least 16 bits wide.
By casting to `unsigned int` you're discarding 16 bits, greatly decreasing the number of potential seeds. On top of that, `std::mt19937` doesn't want to have an `unsigned int`, so an implicit cast has to be performed to convert the `unsigned int` to `std::mt19937::result_type`.
Using `unsigned int` here is unfounded.

• alfonso

I do not understand why. If I use CASE 1, the returned "random" number is always the same. But if I use CASE 2 (with global (namespaced) seed) the result is as expected, random.

• nascardriver

See the paragraph "Help! My random number generator isn’t generating random numbers at all!" at the end of this lesson.

• alfonso

"The random number generator is being seeded each time before a random number is generated. This will cause a similar number to be generated each time."

Ok, but why? This is yet another observation not quite an explanation. The answer may reside in the PRNG implementation.

Here because the program runs way below a second, three successive calls to std::time () should return the same timestamp value so seed should (?) have the same value. In the other case,  the global seed has the same value at each randomReal () call.

There are many whys in my head, a lot of confusion too. For example, why reseeding is bad when reseeding should give even more randomness and so on. I will go deep in the mersenne implementation, if not now for sure in the near future. Thank you!

• nascardriver

A random number generator generates a predictable, seemingly random, sequence of numbers. The seed changes what this sequence looks like or where it starts. If you use the same seed twice, you'll get the same sequence twice.

> reseeding should give even more randomness
Random number generators can't be improved by changing the seed.

• alfonso

Yes, I would expect that an unchangeable seed to give me similar results. But here in both cases the seed did not changed between successive randomReal () calls. You can verify this using a code line:

just before line 17 and you will see the same seed value for each randomReal () call.

Though, when using global case it generates random different results. This I want to understand, why Alex MUST use a global variable. Of course, I can see the different output of programs, but I still do not understand why the global variable affects different the final output. Again, in both cases the seed does not change between successive randomReal () calls. The reason must be somewhere else.

• nascardriver

> the seed did not changed between successive randomReal () calls
That's the point. You're creating a new twister and seeding it with the same seed as last time every time you call `randomReal`. This will produce the same sequence and the first call to `realNumber` will give you the same number as it did last time.
With the global variable, the twister is only seeded once.

You might want to have a look at how simple pseudo random number generators are implemented (Don't look at the mersenne twister, unless you're up for some math and bits).

• alfonso

So it depends how the seed is used by mersenne twister. The seed is the same in all cases, but the seed is a sequence of many numbers and how that seed is used makes the difference. Seeding again it will use the same seed (sequence of numbers) in the same way. Seeding once it will use the same seed but in different ways between successive calls. So it looks like just scratching the surface and with your help. I can handle some math and bits but I can't handle class templates yet. Thank you!

• nascardriver

> the seed is a sequence of many numbers
Not quite. The seed only initializes the generator and determines what the sequence will look like. Re-using a seed is like resetting the generator.

> I can handle some math and bits but I can't handle class templates yet.
You don't need to look at the cpp implementation. Mersenne twister is not language-specific.
https://en.wikipedia.org/wiki/Mersenne_Twister#Algorithmic_detail

• Parsa

How do you set the value of RAND_MAX since RANDMAX is a constant and is not modifiable?

• Alex