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Simulation and scientific computing
lattice-qcd
lattice QCD
MILC, Grid
System
Techniques · 10
Primitives · 36
lattice-qcd
Batch checkpoint restart
distributed · medium: Large batch jobs (end-of-day, settlement, payroll runs) that checkpoint and restart idempotently
Halo exchange
distributed · medium: Each rank stores its block plus a border copy of its neighbours' edge cells, refreshed by small messages every step; communication scales with block surface, not volume.
›
Parallel file system striping
distributed · medium: Striping files across object storage targets (Lustre, GPFS); collective I/O and metadata servers
Kernel autotuning
ml-training · medium: Searching tile sizes and launch parameters per shape/hardware, caching the best configs
Gmres
numerics · medium: GMRES with restarts: Arnoldi, Givens rotations, for nonsymmetric sparse systems
Hamiltonian monte carlo nuts
numerics · medium: HMC with leapfrog integration and the No-U-Turn sampler; step size and mass-matrix adaptation
Markov chain monte carlo
numerics · medium: Metropolis-Hastings and Gibbs sampling: proposals, burn-in, thinning, convergence
Mcmc convergence diagnostics
numerics · low: R-hat, effective sample size and divergence checks for MCMC runs
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Verlet / leapfrog
numerics · low: Half-kick, drift, half-kick: a second-order, time-reversible, symplectic integrator with one force evaluation per step whose energy error stays bounded for millions of steps.
›
Structure of arrays and hot/cold sp…
hardware-os · low: Store each field in its own array and keep rarely used fields apart, so a loop reads only the bytes it needs and the compiler can vectorize it.
›
Gpu memory coalescing banking
hardware-os · low: Coalesced global loads, shared memory bank conflicts, L2 and HBM bandwidth on GPUs
SIMD programming
hardware-os · low: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.
›
CUDA and GPU languages
languages · low: Programming GPUs: thousands of lockstep threads, bound by memory bandwidth; libraries first, Triton for fused kernels, CUDA C++ for peak speed.
›
Collective communication
ml-training · low: The family of group exchanges (broadcast, reduce, all-gather, reduce-scatter, all-to-all) and the latency-plus-bytes cost model that picks ring, tree or direct algorithms by message size and topology.
›
Conjugate gradient
numerics · low: Krylov iteration for symmetric positive definite Ax = b using one matrix-vector product and two dot products per step; converges in about √κ iterations.
›
Low precision number formats
numerics · low: Bf16, fp16, fp8 (E4M3, E5M2), MX block formats and int4: ranges, rounding, scaling
Multigrid
numerics · low: Smooths high-frequency error on the fine grid and solves the smooth remainder on coarser grids; O(n) elliptic solves at any resolution.
›
Reproducible reduction
numerics · low: Order-independent floating-point sums (fixed order, Kahan, binned) for bit-for-bit reproducibility
Bootstrap confidence intervals
statistics · low: Resampling-based confidence intervals for arbitrary statistics
Idempotency keys
finance · low: Client-chosen unique key per logical operation, stored with a request fingerprint and the final response, so retries replay the first result instead of acting twice.
›
Write-ahead log
storage · low: Append each change to a checksummed sequential log and fsync it before touching data pages; the basis of crash durability in nearly every database.
›
Cron scheduling
systems · low: Cron expression parsing and next-fire-time computation, with catch-up and time-zone rules
+ 3 more techniques
+ 20 more primitives
System
Techniques · 10
Primitives · 36
lattice-qcd
Batch checkpoint restart
distributed · medium: Large batch jobs (end-of-day, settlement, payroll runs) that checkpoint and restart idempotently
Halo exchange
distributed · medium: Each rank stores its block plus a border copy of its neighbours' edge cells, refreshed by small messages every step; communication scales with block surface, not volume.
›
Parallel file system striping
distributed · medium: Striping files across object storage targets (Lustre, GPFS); collective I/O and metadata servers
Kernel autotuning
ml-training · medium: Searching tile sizes and launch parameters per shape/hardware, caching the best configs
Gmres
numerics · medium: GMRES with restarts: Arnoldi, Givens rotations, for nonsymmetric sparse systems
Hamiltonian monte carlo nuts
numerics · medium: HMC with leapfrog integration and the No-U-Turn sampler; step size and mass-matrix adaptation
Markov chain monte carlo
numerics · medium: Metropolis-Hastings and Gibbs sampling: proposals, burn-in, thinning, convergence
Incomplete factorization preconditi…
numerics · medium: Sparse approximate LU or Cholesky factors (ILU, IC) that precondition Krylov solvers: fewer iterations than Jacobi, less memory than a direct solve.
›
Fill-reducing ordering
numerics · medium: Permute a sparse symmetric matrix before Cholesky/LU so the factor has few new nonzeros; minimum degree, nested dissection and RCM trade quality, speed and parallelism.
›
Graph partitioning
graphs · medium: Split a graph into k balanced parts with few edges between them; multilevel coarsen-partition-refine (METIS, KaHIP) for quality, streaming heuristics (LDG, Fennel) for one-pass scale.
›
Mcmc convergence diagnostics
numerics · low: R-hat, effective sample size and divergence checks for MCMC runs
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Verlet / leapfrog
numerics · low: Half-kick, drift, half-kick: a second-order, time-reversible, symplectic integrator with one force evaluation per step whose energy error stays bounded for millions of steps.
›
Structure of arrays and hot/cold sp…
hardware-os · low: Store each field in its own array and keep rarely used fields apart, so a loop reads only the bytes it needs and the compiler can vectorize it.
›
Gpu memory coalescing banking
hardware-os · low: Coalesced global loads, shared memory bank conflicts, L2 and HBM bandwidth on GPUs
SIMD programming
hardware-os · low: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.
›
CUDA and GPU languages
languages · low: Programming GPUs: thousands of lockstep threads, bound by memory bandwidth; libraries first, Triton for fused kernels, CUDA C++ for peak speed.
›
Collective communication
ml-training · low: The family of group exchanges (broadcast, reduce, all-gather, reduce-scatter, all-to-all) and the latency-plus-bytes cost model that picks ring, tree or direct algorithms by message size and topology.
›
Conjugate gradient
numerics · low: Krylov iteration for symmetric positive definite Ax = b using one matrix-vector product and two dot products per step; converges in about √κ iterations.
›
Low precision number formats
numerics · low: Bf16, fp16, fp8 (E4M3, E5M2), MX block formats and int4: ranges, rounding, scaling
Multigrid
numerics · low: Smooths high-frequency error on the fine grid and solves the smooth remainder on coarser grids; O(n) elliptic solves at any resolution.
›
Reproducible reduction
numerics · low: Order-independent floating-point sums (fixed order, Kahan, binned) for bit-for-bit reproducibility
Bootstrap confidence intervals
statistics · low: Resampling-based confidence intervals for arbitrary statistics
Idempotency keys
finance · low: Client-chosen unique key per logical operation, stored with a request fingerprint and the final response, so retries replay the first result instead of acting twice.
›
Write-ahead log
storage · low: Append each change to a checksummed sequential log and fsync it before touching data pages; the basis of crash durability in nearly every database.
›
Cron scheduling
systems · low: Cron expression parsing and next-fire-time computation, with catch-up and time-zone rules
Eager rendezvous protocol
distributed · low: MPI point-to-point: eager sends for small messages, rendezvous handshake for large ones
Rdma
networking · low: RDMA verbs over InfiniBand/RoCE: queue pairs, memory registration, one-sided ops
Zero-copy I/O
networking · low: Move bytes between files, sockets and NICs by passing page references instead of copying through user space: sendfile, splice, MSG_ZEROCOPY, kTLS.
›
Leases
distributed · low: A lock that expires on its own: bounded-time ownership that survives crashes and partitions, given bounded clock drift and fencing tokens on writes.
›
Range partitioning
distributed · low: Cut the sorted key space into contiguous half-open ranges kept in a boundary map; split hot or big ranges, merge small ones, move ranges between nodes.
›
Roofline model
hardware-os · low: Bound a kernel's speed by min(peak FLOP/s, arithmetic intensity × memory bandwidth) to know whether to optimize compute or data movement.
›
GPU compute shaders
ml-training · low: The vendor-neutral GPU launch model of Metal, Vulkan and WebGPU: a grid of workgroups, shared memory, barriers and subgroups, driven by recorded command buffers.
›
Tiled matrix multiplication
ml-training · low: Block GEMM into tiles held in shared memory and registers, so each byte loaded from DRAM feeds many FMAs; the core of fast GEMM.
›
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Reverse-mode automatic differentiat…
ml-training · low: Record the forward computation on a tape, then sweep it backwards once to get the gradient of a scalar loss for all inputs.
›
Constrained parameter transforms
numerics · low: Map constrained parameters to unconstrained space (log, logit, simplex, Cholesky) with Jacobian corrections
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
Fencing tokens
distributed · low: A number that grows with every lock grant and is checked by the protected resource, so a paused ex-holder's late write is rejected.
›
CPU caches and the memory hierarchy
hardware-os · low: Sizes, line widths and latencies of L1/L2/L3/DRAM on modern x86 and Apple M-series, and the data-layout rules that follow from them.
›
CRC32C checksums
hardware-os · low: The Castagnoli CRC-32 with dedicated instructions on x86 (SSE4.2) and ARMv8. It is the standard fast integrity check for storage blocks, logs and network frames.
›
fsync, O_DSYNC and O_DIRECT
hardware-os · low: What fsync, fdatasync, O_DSYNC, O_DIRECT and F_FULLFSYNC really guarantee on Linux and macOS, and the exact call sequences for crash-safe files.
›
Cryptographic hashes (SHA-2, BLAKE3)
security · low: Collision-resistant fingerprints of data; SHA-256 for interoperability, BLAKE3 for speed, HMAC/HKDF for keyed uses.
›
Exponential backoff with jitter
systems · low: Retry after delays that grow geometrically and are randomized, so failed clients spread out instead of hammering a recovering service in synchronized waves.
›
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