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computational-lithography

mask synthesis by OPC/ILT, lithography and resist simulation (Hopkins imaging), mask rule check and data prep on GPUs

Siemens Calibre, Synopsys Proteus, ASML Brion, NVIDIA cuLitho

SystemTechniques · 14Primitives · 52 computational-lithograp… DAG workflow executiondistributed · medium: Run a graph of dependent tasks by releasing each one when its inputs are done, longest chain first, and skip any task whose input hashes are unchanged.›Halo exchangedistributed · 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.›Polygon clippinggeometry · medium: Polygon intersection/union/difference (Weiler-Atherton, Martinez) for spatial predicatesPolygon tessellationgeometry · medium: Triangulate polygons with holes (ear clipping, earcut, monotone sweep)Tiled image pipelinegraphics · medium: Demand-driven tiled image processing with bounded memory (libvips-style)Graph partitioninggraphs · 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.›Design rule check edge querieshardware-os · medium: Edge-based width/space/enclosure checks on layout polygons with hierarchical scanline queriesGPU compute shadersml-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.›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.›Zstandard (zstd)compression · low: LZ77 plus Huffman and FSE entropy coding, with levels from LZ4-like speed to xz-like ratio, all decoding at about 1-2 GB/s.›Interval treedata-structures · low: Index of ranges that answers "which intervals overlap this point or range?" in O(log n + k); static sorted-array form is the compact, cache-friendly choice.›Quadtree octreegeometry · low: Adaptive spatial subdivision trees for queries and level of detail; loose and linear variantsR-treegeometry · low: A balanced tree of nested bounding boxes that indexes rectangles and points, answering window and nearest-neighbour queries by pruning whole subtrees.›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.›Finite differencesnumerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.›L-BFGSnumerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.›Layout stream formats gdsii oasisstorage · low: GDSII/OASIS hierarchical polygon stream formats for mask and chip layout dataTopological 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.›Content-addressed storagestorage · low: Store each blob under the hash of its bytes: immutable, deduplicated by construction, self-verifying on every read, and composable into Merkle trees.›Exponential backoff with jittersystems · low: Retry after delays that grow geometrically and are randomized, so failed clients spread out instead of hammering a recovering service in synchronized waves.›Eager rendezvous protocoldistributed · low: MPI point-to-point: eager sends for small messages, rendezvous handshake for large onesRdmanetworking · low: RDMA verbs over InfiniBand/RoCE: queue pairs, memory registration, one-sided opsZero-copy I/Onetworking · low: Move bytes between files, sockets and NICs by passing page references instead of copying through user space: sendfile, splice, MSG_ZEROCOPY, kTLS.›+ 7 more techniques+ 36 more primitives

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