SplitMix64

What it is

SplitMix64 (Steele; recommended by Vigna for seeding) is a tiny, fast 64-bit generator built from a Weyl sequence (the state is bumped by the golden-ratio constant each call) followed by an avalanche mix. Its period is 2⁶⁴.

When to use it

SplitMix64 is a seeding helper, not a general-purpose engine. simdrng uses it internally to expand a single 64-bit seed into the larger state of the other generators, so that even low-entropy seeds (0, 1, …) produce well-distributed starting states. Use it directly when you need to derive several independent 64-bit seeds from one master seed; for actual random streams use Xoshiro256++, Philox, or ChaCha.

Scalar only

SplitMix64 has a single scalar implementation — there is no SIMD-dispatch or -march=native variant, because it exists to seed the other engines rather than to produce bulk output.

#include <simdrng/splitmix.hpp>

simdrng::SplitMix sm(seed);
std::uint64_t a = sm();            // a derived seed
std::uint64_t b = sm();            // another, independent of a

Each call advances the state and returns the next mixed value, so successive calls yield independent 64-bit seeds.

Periods and streams

SplitMix64 has a period of 2⁶⁴. simdrng uses it only to expand a 64-bit seed into the larger state of the other engines. See Generator properties for the full period table.

References

Using SplitMix64 to seed the other generators follows S. Vigna’s explicit recommendation (https://prng.di.unimi.it/), quoted under Seeding. See References.