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Numerical and mathematical computing
statistics-environment
statistical computing environment
R, Stata
System
Techniques · 11
Primitives · 44
statistics-environment
Dependency version resolution
compilers · medium: Pick package versions that satisfy semver constraints (PubGrub, SAT) with readable conflict errors
FFI bindings generation
compilers · medium: Describe a library's C-ABI surface once (header, attributes or IDL) and generate the declarations, converters and wrappers for each caller language.
›
Markdown parsing
graphics · medium: CommonMark two-phase parsing: block structure, then inline delimiter runs
Generalized linear models (GLMs)
machine-learning · medium: Linear model for counts, rates, positive amounts and proportions: a linear score pushed through a link, fitted by iteratively reweighted least squares.
›
Markov chain monte carlo
numerics · medium: Metropolis-Hastings and Gibbs sampling: proposals, burn-in, thinning, convergence
Arima
statistics · medium: ARIMA/SARIMA forecasting: differencing, AR and MA terms, order selection, maximum-likelihood fit
Hypothesis testing
statistics · medium: Pick a test statistic, compare it to its distribution under "no effect", read off a p-value, and control error rates across one test or many.
›
Linear and logistic regression
machine-learning · low: Fit a weighted sum of features to a number (least squares) or a probability (logistic); the baseline every model must beat.
›
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).
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
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L-BFGS
numerics · 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.
›
Bootstrap confidence intervals
statistics · low: Resampling-based confidence intervals for arbitrary statistics
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.
›
Bytecode compilation
compilers · low: Flatten an AST into compact linear instructions with a constant pool, backpatched jumps and slot-numbered locals, so a small loop can execute it.
›
Bytecode interpreter
compilers · low: Register/stack VM dispatch loop for executing compiled plans or rules (SQLite VDBE, nftables)
Closures and upvalues
compilers · low: How interpreters and compilers let a function keep using its enclosing variables after they return: flat closures, open and closed upvalues, closure conversion, capture by value or reference.
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Mark-sweep garbage collection
compilers · low: Find everything reachable from the roots, free the rest in place; handles cycles, never moves objects, and is the base of most production collectors.
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Dictionary encoding
compression · low: Map values to small integer codes via a dictionary for compact, comparable columns
PCA and SVD
machine-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.
›
Quantile regression
machine-learning · low: Predicting quantiles with the pinball loss for probabilistic forecasts and prediction intervals
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.
›
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Columnar memory format
storage · low: In-memory column buffers with validity bitmaps and offsets (Arrow style) for zero-copy exchange
+ 4 more techniques
+ 28 more primitives
System
Techniques · 11
Primitives · 44
statistics-environment
Dependency version resolution
compilers · medium: Pick package versions that satisfy semver constraints (PubGrub, SAT) with readable conflict errors
FFI bindings generation
compilers · medium: Describe a library's C-ABI surface once (header, attributes or IDL) and generate the declarations, converters and wrappers for each caller language.
›
Markdown parsing
graphics · medium: CommonMark two-phase parsing: block structure, then inline delimiter runs
Generalized linear models (GLMs)
machine-learning · medium: Linear model for counts, rates, positive amounts and proportions: a linear score pushed through a link, fitted by iteratively reweighted least squares.
›
Markov chain monte carlo
numerics · medium: Metropolis-Hastings and Gibbs sampling: proposals, burn-in, thinning, convergence
Arima
statistics · medium: ARIMA/SARIMA forecasting: differencing, AR and MA terms, order selection, maximum-likelihood fit
Hypothesis testing
statistics · medium: Pick a test statistic, compare it to its distribution under "no effect", read off a p-value, and control error rates across one test or many.
›
Survey weighting raking
statistics · medium: Raking (iterative proportional fitting) of survey weights to population margins
Idl code generation
compilers · medium: Generate typed client/server stubs and codecs from an interface definition
CDCL SAT solving
optimization · medium: Search for a satisfying assignment, learn a new constraint from every dead end, and jump back past irrelevant choices; handles industrial formulas with millions of clauses.
›
Template engines
compilers · medium: Compile templates with loops, partials and auto-escaping into render functions
Linear and logistic regression
machine-learning · low: Fit a weighted sum of features to a number (least squares) or a probability (logistic); the baseline every model must beat.
›
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).
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
L-BFGS
numerics · 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.
›
Bootstrap confidence intervals
statistics · low: Resampling-based confidence intervals for arbitrary statistics
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.
›
Bytecode compilation
compilers · low: Flatten an AST into compact linear instructions with a constant pool, backpatched jumps and slot-numbered locals, so a small loop can execute it.
›
Bytecode interpreter
compilers · low: Register/stack VM dispatch loop for executing compiled plans or rules (SQLite VDBE, nftables)
Closures and upvalues
compilers · low: How interpreters and compilers let a function keep using its enclosing variables after they return: flat closures, open and closed upvalues, closure conversion, capture by value or reference.
›
Mark-sweep garbage collection
compilers · low: Find everything reachable from the roots, free the rest in place; handles cycles, never moves objects, and is the base of most production collectors.
›
Dictionary encoding
compression · low: Map values to small integer codes via a dictionary for compact, comparable columns
PCA and SVD
machine-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.
›
Quantile regression
machine-learning · low: Predicting quantiles with the pinball loss for probabilistic forecasts and prediction intervals
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.
›
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Columnar memory format
storage · low: In-memory column buffers with validity bitmaps and offsets (Arrow style) for zero-copy exchange
Semver range matching
compilers · low: Semantic version parsing, ordering and range matching
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.
›
Calling conventions abi
compilers · low: System V, Windows x64 and AAPCS64 ABIs: argument registers, stack frames, struct passing, FFI
Reference counting
compilers · 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.
›
Recursive-descent parsing
compilers · low: Hand-written top-down parser with one function per grammar rule; simple, fast, with full control over error messages and recovery.
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Unicode text tokenization for search
search-sort · low: Turn multilingual text into index terms: segment words (UAX 29 style, CJK bigrams), normalize, case-fold and accent-fold, identically at index and query time.
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Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Constrained parameter transforms
numerics · low: Map constrained parameters to unconstrained space (log, logit, simplex, Cholesky) with Jacobian corrections
Mcmc convergence diagnostics
numerics · low: R-hat, effective sample size and divergence checks for MCMC runs
Finite differences
numerics · 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.
›
Kalman filter
robotics · low: Optimal recursive estimator for a linear system with Gaussian noise: fuses a motion model with noisy measurements into a state estimate plus its covariance.
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Wilson score interval
statistics · low: Wilson lower bound for ranking by up/down votes and proportions with few samples
Hash aggregation
storage · low: GROUP BY via hash tables with partitioning and spill to disk
Protobuf wire format
networking · low: Protocol Buffers wire format: tags, varints, length-delimited fields and schema evolution
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.
›
Drat proof certificates
optimization · low: DRAT and LRAT proofs emitted by SAT solvers and checked independently
Two watched literals
optimization · low: Unit propagation for SAT that watches just two literals per clause, so backtracking costs nothing and long clauses are rarely touched.
›
Arena allocator
systems · low: Allocate by bumping a pointer through big chunks and free everything at once: a few instructions per allocation for objects sharing a lifetime.
›
Name resolution
compilers · low: Bind every use of a name to its declaration with a scope stack, handling shadowing, hoisting and closure capture in one AST walk.
›
Html sanitization
security · low: Allowlist-based HTML sanitizing of untrusted markup
Peephole optimization
compilers · low: Local pattern rewrites on short instruction windows or IR
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.
›
Loss functions
machine-learning · low: The scalar a model minimizes: cross-entropy for classes and tokens, MSE or Huber for values, each with a stable form and simple gradient.
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Text normalization
machine-learning · low: Rewrite messy text into one canonical form for matchers and models, or into spoken words for speech output (and back), keeping a map to the original offsets.
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Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
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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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Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
Slab allocator
systems · low: Pre-carve pages into equal-size slots per size class with an in-place free list: O(1) alloc and free, no external fragmentation, cache-warm reuse.
›
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