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array-computing

array language and runtime

NumPy, Julia, MATLAB

SystemTechniques · 17Primitives · 42 array-computing Auto vectorizationcompilers · medium: Loop and SLP vectorization: dependence tests, cost model, turning scalar code into SIMDDataflow analysiscompilers · medium: Compute a fact per program point (live variables, reaching definitions, available expressions) by iterating transfer functions over the CFG to a fixed point.›FFI bindings generationcompilers · medium: Describe a library's C-ABI surface once (header, attributes or IDL) and generate the declarations, converters and wrappers for each caller language.›Generational garbage collectioncompilers · medium: Split the heap by age, collect the small young region often and cheaply, and rarely touch old data; wins whenever most objects die young.›JIT compilationcompilers · medium: Run cold code in a cheap tier, count executions, and compile only what gets hot, trading warm-up time and memory for peak speed.›Alias analysiscompilers · medium: Decide whether two pointers may refer to the same memory (Andersen, Steensgaard, type-based) to enable optimizationsCopying gccompilers · medium: Cheney semispace copying collection: bump allocation, forwarding pointers, compaction for freeSIMD programminghardware-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.›Reference countingcompilers · low: Keep a count of owners in each object, free it when the count hits zero; deterministic and local, but pays on every copy and leaks cycles.›Bytecode interpretercompilers · low: Register/stack VM dispatch loop for executing compiled plans or rules (SQLite VDBE, nftables)mmap and the page cachehardware-os · low: How read() and mmap reach file data through the kernel page cache, what readahead and madvise do, and why databases use their own buffer pool instead.›Pythonlanguages · low: The fastest language to write and the home of ML and data science; slow as an interpreter, fast when C/CUDA libraries do the work.›PCA and SVDmachine-learning · low: Find orthogonal directions of maximum variance by an SVD of the centred data; randomized SVD gets the top k components in a few passes.›Kernel fusionml-training · low: Merge chains of memory-bound GPU ops into one kernel, so intermediates stay in registers instead of round-tripping through HBM.›Tiled matrix multiplicationml-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.›Fast Fourier transformnumerics · low: Computes the DFT in O(n log n) by recursively splitting into even and odd halves; the basis of fast convolution and spectral methods.›Floating-point errornumerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.›LU and Cholesky factorizationnumerics · 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).›PRNGs (PCG, xoshiro)numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.›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.›SSA formcompilers · low: Give every variable exactly one definition, merging at joins with phi functions; def-use becomes explicit and optimizations turn sparse and cheap.›Control-flow graphcompilers · low: Split a linear instruction list into basic blocks and connect them by jumps; the graph every optimizer, SSA builder and dataflow pass walks.›Topological sortgraphs · low: Order the vertices of a DAG so every edge points forward; the core of build systems, schedulers and dependency resolution, with cycle detection for free.›+ 10 more techniques+ 26 more primitives

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