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Numerical and mathematical computing
fft-library
FFT library
FFTW, cuFFT
System
Techniques · 3
Primitives · 19
fft-library
Instruction scheduling
compilers · medium: List scheduling over dependence DAGs with latency models; software pipelining of loops
Kernel autotuning
ml-training · medium: Searching tile sizes and launch parameters per shape/hardware, caching the best configs
Fft convolution
signal-processing · medium: Overlap-add and uniformly partitioned convolution for long FIR filters and reverb
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.
›
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.
›
Fast Fourier transform
numerics · 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.
›
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.
›
Gpu memory coalescing banking
hardware-os · low: Coalesced global loads, shared memory bank conflicts, L2 and HBM bandwidth on GPUs
Numa aware allocation
hardware-os · low: Allocate memory and pin threads on the local NUMA node; first-touch and interleave policies
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.
›
Tensor layout transforms
ml-training · low: Choosing and converting tensor layouts (NCHW/NHWC, blocked, tiled) for kernel efficiency
Discrete cosine transform
numerics · low: Fast integer DCT/DST block transforms used by image and video codecs
Floating-point error
numerics · 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.
›
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.
›
Topological sort
graphs · 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.
›
Instruction pipelining
hardware-os · low: Pipeline stages, hazards, forwarding and stalls in CPU cores
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.
›
+ 3 more primitives
System
Techniques · 3
Primitives · 19
fft-library
Instruction scheduling
compilers · medium: List scheduling over dependence DAGs with latency models; software pipelining of loops
Kernel autotuning
ml-training · medium: Searching tile sizes and launch parameters per shape/hardware, caching the best configs
Fft convolution
signal-processing · medium: Overlap-add and uniformly partitioned convolution for long FIR filters and reverb
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.
›
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.
›
Fast Fourier transform
numerics · 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.
›
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.
›
Gpu memory coalescing banking
hardware-os · low: Coalesced global loads, shared memory bank conflicts, L2 and HBM bandwidth on GPUs
Numa aware allocation
hardware-os · low: Allocate memory and pin threads on the local NUMA node; first-touch and interleave policies
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.
›
Tensor layout transforms
ml-training · low: Choosing and converting tensor layouts (NCHW/NHWC, blocked, tiled) for kernel efficiency
Discrete cosine transform
numerics · low: Fast integer DCT/DST block transforms used by image and video codecs
Floating-point error
numerics · 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.
›
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.
›
Topological sort
graphs · 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.
›
Instruction pipelining
hardware-os · low: Pipeline stages, hazards, forwarding and stalls in CPU cores
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.
›
BFS and DFS
graphs · low: The two basic graph traversals; BFS gives hop distances and levels, DFS gives discovery/finish order for cycles, components and topological order.
›
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.
›
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