Philox

What it is

Philox (Salmon et al., Parallel Random Numbers: As Easy as 1, 2, 3) is a counter-based generator: each output block is a keyed bijection of an incrementing counter. There is no sequential state to advance — output N is computed directly from counter N — which makes Philox stateless and trivially parallel. simdrng provides the four standard shapes 2x32, 4x32, 2x64 and 4x64 (counter words × word width), each with the reference 10 rounds.

When to use it

Choose Philox when work items must each produce an independent, reproducible sub-stream with no coordination — GPU-style kernels, embarrassingly parallel Monte Carlo, or any case where you want to seek to an arbitrary stream position in O(1). If you instead want the fastest single sequential stream, prefer Xoshiro256++.

Scalar, SIMD dispatch, and native

Type	Header	Use when
Philox<N,W,R> / Philox4x32 …	<simdrng/philox.hpp>	Portable, dependency-free, constexpr-friendly scalar core.
PhiloxSIMD<…> / Philox4x32SIMD …	<simdrng/philox_simd.hpp>	Runtime SIMD dispatch across CPUs from one binary.
PhiloxNative<…> / Philox4x64Native …	<simdrng/philox_simd.hpp>	Built with -march=native for the widest width with no dispatch.

#include <simdrng/philox_simd.hpp>

simdrng::Philox4x32SIMD rng(seed, counter);   // (seed, starting counter)
std::uint64_t x = rng();
double u = rng.uniform();

The 64-bit seed is expanded into the Philox key via SplitMix64 (see SplitMix64); the counter selects the starting stream position.

Periods and streams

A Philox<N,W> block spans a counter space of 2^W·N, so distinct counters give independent, non-overlapping streams with no setup. The common pattern is to fix the seed and assign each work item a disjoint counter range:

simdrng::Philox4x64SIMD rng(seed, /*counter=*/ work_item_id);

See Generator properties for the full period table.

References

Philox is the counter-based design of J. K. Salmon, M. A. Moraes, R. O. Dror and D. E. Shaw, Parallel Random Numbers: As Easy as 1, 2, 3 (SC ‘11). See References.