Overview
SplitMix64 is a randomness and sampling method that generates samples, estimates, or pseudorandom values while controlling distribution and variance. It is most useful when repeatable sample behavior matters as much as raw randomness.
CoreSource checked
SplitMix64
SplitMix64 generates deterministic pseudorandom sequences from a seed.
Quick Facts
Compact metadata for implementation and discovery.
- Category
- Randomness & Sampling
- Difficulty
- Intermediate
- Family
- Randomness and Sampling
- Tier
- Core
- Status
- Verified
- Review
- Source Checked
- Sources
- 1
- Formulas
- 0
- Relationships
- 3
- Code example
- Ready
- Visualization
- Ready
Core Concepts
probability distributionrandom variatevariance controlrandom drawdistributionestimate
Quick facts
Complexity
Runtime and memory behavior at a glance.
Best
O(n)
Average
O(n)
Worst
O(n^2)
Space
O(n)
When to Use
- Use SplitMix64 when sample quality, reproducibility, or distribution shape affects the result.
- Use it when deterministic seeds and distribution checks can be part of testing.
When Not to Use
- Avoid when the target distribution is poorly defined.
- Avoid when independence, burn-in, or seeding assumptions cannot be tested.
What It Does
- Draws or transforms random values
- Controls bias, variance, or coverage
- Returns samples for simulation or estimation
Use Cases
- Monte Carlo estimation
- Simulation
- Randomized testing
Inputs
- Target distribution or population
- Random seed or random source
- Sample count
Outputs
- Random samples
- Estimated statistic
- Generated sequence
Pseudocode
- 1.Initialize the random source and sampling parameters
- 2.Draw or transform candidate values
- 3.Accept, weight, or store samples according to the method
- 4.Repeat until the requested sample count is reached
- 5.Return the sample set or estimate
Canonical Example
- Input
- target = small distribution, samples = 5, seed = 7
- Output
- five repeatable samples or an estimate
- Explanation
- SplitMix64 uses the seed and sampling rule to produce values with the intended distribution or coverage.
Implementation Notes
- Expose the seed and record enough parameters to reproduce samples.
- Test distribution behavior with small deterministic checks before large simulations.
Common Pitfalls
- Using an untracked seed makes results hard to reproduce.
- Confusing distribution quality with visual randomness can hide bias.
Interactive Mechanism Walkthrough
Iterative Convergence & State TrajectoryShow samples accumulating over the target distribution or sample space.
Step 1 of 5: Initialize the random source and sampling parameters
samplingNotes
SplitMix64 operates in O(n) time and O(n) space within the Randomness and Sampling family. Often compared with Rejection Sampling and Importance Sampling.
Sources (1)
What each reference supports for this entry.
Fast Splittable Pseudorandom Number Generators
PaperReference for SplitMix-style splittable generators, mixing functions, and 64-bit state progression.
Open sourceExplore Next
Good next jumps from the relationship graph, ranked for useful discovery.
Relationships
View full relationship pageAlternative toLinear Congruential Generator
SplitMix64 advances a 64-bit state with a Weyl increment and applies a strong mixing function.
Often paired withXoshiro Random Number Generator
SplitMix64 is commonly used to initialize xoshiro-family states.
Related Algorithms
Tags
Randomness & SamplingSampling