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## How to randomize bits and integers efficiently in C++

This article will tell you some resources for efficient ways to randomize bits and integers in C++.

### Default fast 64 bit RNG for C++

Here's a default quite efficient one called lehmer64 if you're too lazy to benchmark a lot of them. There might be faster ones if you check the resources, but I haven't done my own benchmarking yet. This one should still be up there in the top contenders though.

I was not sure if you need to seed it using the functions at Lehmer 64 Source Code or just can give any random seed like "1337" below. Reading the article at Wikipedia on Lehmer RNG we can see that the seed must be coprime to the modulus. Well then, it seems that any odd number is coprime to the modulus 2^64, since they are not divisible by 2.

If you need an even faster generator, probably go with one of the Xoroshiro. Both of them can be further optimized though by using 2,3 or 4 generators simultaneously and getting vectorized.

sprkrd: The author of xoshiro also recommends seeding using splitmix64 (which is the same seeding algorithm that lehmer64 used). In the case of xoshiro it's clear why: states with lots of 0s affect negatively the quality of the produced numbers. In case of lehmer, i'm not so sure that splitmix is that much of a requirement, it would seem it'd work with any non-zero seed.

derjack: Is int128 that fast? I just use xorshift. So perhaps that's also a valid alternative. Benchmarking on CG needed :) .

Once you have chosen a fast random integer generator, you can AND together a few of them, to get probabilities of 1/2, 1/4, 1/8 and so on, for each bit to be set.

### Faster than Modulo Reduction to constrain range of random number

sprkrd: regarding rng speed... often the bottleneck is not in the RNG itself it's in the function you use to draw a random sample from an uniform distribution for instance, for drawing a random int between 0 and a-1, you could do a simple rng() % a and the modulo operation can be more costly than, say, an addition or a bitwise operation There are ways to have an uniform number in the (0,a-1) interval that are slightly faster than %.

Here's the solution and here are benchmarks.

Fastest code from last link included here for convenience:

```
uint32_t bounded_rand(rng_t& rng, uint32_t range) {
uint32_t x = rng();
uint64_t m = uint64_t(x) * uint64_t(range);
uint32_t l = uint32_t(m);
if (l < range) {
uint32_t t = -range;
if (t >= range) {
t -= range;
if (t >= range)
t %= range;
}
while (l < t) {
x = rng();
m = uint64_t(x) * uint64_t(range);
l = uint32_t(m);
}
}
return m >> 32;
}
```

### Generating uniform doubles in the unit interval

Quoting https://prng.di.unimi.it/:

A standard double (64-bit) floating-point number in IEEE floating point format has 52 bits of significand, plus an implicit bit at the left of the significand. Thus, the representation can actually store numbers with 53 significant binary digits.

Because of this fact, in C99 a 64-bit unsigned integer x should be converted to a 64-bit double using the expression

```
#include <stdint.h>
(x >> 11) * 0x1.0p-53
```

### Resources

#### Fastest Random Number Generators

- The Fastest Conventional Random Number Generator That Can Pass Big Crush
- StackOverflow: Need a fast random generator for C
- Random number generators for C performance tested
- Testing RNGs
- Hash Function Quality and Speed Tests
- Presenting XXH3

#### Selecting a random bit from a bitset

- StackOverflow: Best C++ way to choose randomly position of set bit in bitset
- StackOverflow: Find nth set bit in an int

#### Suggestions from CodinGame chat

## Advanced usage

If you want a more complex example (external libraries, viewers...), use the Advanced C++ template