General RNGs
These RNGs are good all-rounders, and should be the first to be considered. They are not reproducible and cannot be seeded, but are automatically seeded with a cryptographic RNG upon creation.
Standard
StandardRng is the go-to RNG that works well for anything that doesn't require reproducibility. It's cryptographically secure, so it's safe to use for any application, has good statistical properties, and performs fairly well.
The underlying algorithm is currently ChaCha8, but is subject to change and cannot be relied upon.
var rng = StandardRng.Create();
Small
If you're limited in memory or need a faster RNG than StandardRng, but don't need cryptographic security, SmallRng is the RNG to use. It uses an algorithm that requires a small amount of state while maintaining good statistical properties and high performance.
The underlying algorithm is currently PCG32, but is subject to change and cannot be relied upon.
var rng = SmallRng.Create();
ThreadLocalRng
ThreadLocalRng is thread-safe, cryptographically secure, has good statistical properties, and performs fairly well. It stores the underlying algorithm in thread-local storage to be thread-safe.
The underlying algorithm is currently ChaCha8, but is subject to change and cannot be relied upon.
var rng = ThreadLocalRng.Instance;
Reproducible RNGs
If reproducibile sequences are needed, then a specific algorithm must be selected. The user is responsible for seeding these RNGs correctly.
ChaCha
ChaCha is a seekable, cryptographically secure* RNG.
var seed = new ChaCha.Seed(new UInt32[8]); // All zero seed
var rng = ChaCha.Create(seed);
rng.Position = new ChaCha.Counter(9001, 0); // Seek to an arbitrary position
* 8 rounds and above are unbroken.
Mersenne Twister
Mersenne Twister doesn't offer any noticeable advantages over PCG32, and may later be moved out of the main RandN package.
var seed1 = 5489ul;
var rng1 = Mt1993764.Create(seed1);
// Mersenne Twister can be seeded with an array as well
var seed2 = new UInt64[16]; // All zero seed
var rng2 = Mt1993764.Create(seed2);
PCG 32
A Permuted Congruential Generator with 64-bit state and 32-bit output. The seed is 127 bits, as the highest bit of the stream id is ignored.
var seed = new Pcg32.Seed(578437695752307201ul, 1157159078456920585ul);
var rng = Pcg32.Create(seed);
XorShift
XorShift doesn't offer any noticeable advantages over PCG32, and may later be moved out of the main RandN package.
var seed = (1u, 2u, 3u, 4u);
var rng = XorShift.Create(seed);
OS RNG - SystemCryptoRng
SystemCryptoRng uses the generated returned by System.Security.Cryptography.RandomNumberGenerator.Create(), which is the closest we get to an OS level RNG through .NET. It's cryptographically secure, but not reproducible. The underlying algorithm is provided by .NET, and can vary by runtime version and the platform.
using var rng = SystemCryptoRng.Create();
SystemCryptoRng on Microsoft Docs
CryptoServiceProvider
This RNG is obsolete. Use SystemCryptoRng instead.
CryptoServiceProvider uses System.Security.Cryptography.RNGCryptoServiceProvider, which is the closest we get to an OS level RNG through .NET. It's cryptographically secure, but not reproducible. The underlying algorithm is provided by the cryptographic service provider.
using var rng = CryptoServiceProvider.Create();