RunMat Runtime Builtin Library

This matrix tracks the public builtin surface implemented by runmat-runtime.

Legend

Column	Meaning
`Status`	`done` means implemented in the runtime; `planned` means documented as expected but not complete in the current library table.
`GPU`	`yes` means provider hooks or device offload exist; `host` means host only; `N/A` means acceleration does not apply.
`Fusion`	`E` elementwise, `R` reduction, `S` stencil/convolution, `M` matrix multiply, `T` transpose/permutation, `P` pipeline/fuse-friendly, `-` not applicable.
`Backend`	External numerical backend category: BLAS, LAPACK, FFT, or `-` when not applicable.

For GPU execution details, see GPU Acceleration & Fusion Engine. For JIT interaction with builtin and semantic calls, see JIT Compilation Pipeline.

Acceleration / GPU

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`acceleration/gpu`	`gpuArray`, `gather`, `gpuDevice`, `gpuInfo`	yes	P	-	Moves values to and from device memory and queries device state.
done	`acceleration/gpu`	`arrayfun`	yes	E	-	Elementwise GPU map through provider hooks and fusion inline constants.
done	`acceleration/gpu`	`pagefun`	yes	P	-	Batched page-wise operations, mapped to batched BLAS/FFT when available.

Arrays

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`array/creation`	`zeros`, `ones`, `eye`, `diag`, `linspace`, `logspace`, `randi`, `rand`, `randn`, `randperm`, `fill`, `range`, `colon`	yes	E	-	Constructors, ranges, and RNG-backed array creation.
done	`array/creation`	`meshgrid`	yes	T	-	Grid generation with device index kernels.
done	`array/shape`	`reshape`, `squeeze`, `permute`, `ipermute`, `repmat`, `repelem`, `kron`, `cat`, `horzcat`, `vertcat`, `flip`, `fliplr`, `flipud`, `rot90`, `circshift`, `tril`, `triu`, `diag`	yes	T	BLAS	Layout transforms; `kron` can use GEMM blocks.
done	`array/indexing`	`sub2ind`, `ind2sub`, `find`	yes	P	-	Index conversions and mask queries.
done	`array/sorting-sets`	`sort`, `sortrows`, `argsort`, `unique`, `union`, `intersect`, `setdiff`, `ismember`, `issorted`	yes	P	-	Ordering and set operations.
done	`array/introspection`	`size`, `length`, `numel`, `ndims`, `isempty`, `isscalar`, `isvector`, `ismatrix`	N/A	-	-	Shape and metadata queries.

Math

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`math/elementwise`	`abs`, `sign`, `real`, `imag`, `conj`, `angle`	yes	E	-	Complex helpers.
done	`math/elementwise`	`exp`, `expm1`, `log`, `log1p`, `log10`, `log2`, `sqrt`, `hypot`, `pow2`	yes	E	-	Exponentials and roots.
done	`math/elementwise`	`single`, `double`, `uint16`	yes	E	-	Numeric casting for scalars and arrays.
done	`math/elementwise`	`plus`, `minus`, `times`, `rdivide`, `ldivide`, `power`, `gamma`, `factorial`	yes	E	-	Elementwise arithmetic and specials.
done	`math/trigonometry`	`sin`, `cos`, `tan`, `asin`, `acos`, `atan`, `atan2`, `sinh`, `cosh`, `tanh`, `asinh`, `acosh`, `atanh`	yes	E	-	Trigonometric and hyperbolic functions.
done	`math/rounding`	`round`, `floor`, `ceil`, `fix`, `mod`, `rem`	yes	E	-	MATLAB-style rounding and modulo behavior.
done	`math/reduction`	`sum`, `prod`, `mean`, `median`, `min`, `max`, `any`, `all`, `std`, `var`, `cumsum`, `cumprod`, `cummin`, `cummax`, `diff`, `nnz`	yes	R	-	Reductions and cumulative operations.

Linear Algebra

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`math/linalg/ops`	`mtimes`, `mrdivide`, `mldivide`, `transpose`, `ctranspose`, `trace`	yes	M/T	BLAS	Core matrix operations.
done	`math/linalg/ops`	`dot`, `mpower`	yes	M	BLAS	Dot product and matrix power.
done	`math/linalg/factor`	`lu`, `qr`, `chol`, `svd`, `eig`	yes	-	LAPACK	Factorizations and eigensolvers.
done	`math/linalg/solve`	`linsolve`, `pinv`, `inv`, `det`, `rank`, `null`, `rref`, `rcond`, `cond`, `norm`	yes	-	LAPACK/BLAS/-	Solves, null spaces, row reduction, and matrix metrics.
done	`math/linalg/structure`	`bandwidth`, `issymmetric`, `ishermitian`, `symrcm`	host	-	-	Structure queries and diagnostics.

FFT, Signal, and Image Processing

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`math/fft`	`fft`, `ifft`, `fft2`, `ifft2`, `fftshift`, `ifftshift`	yes	P	FFT	Fourier transforms through host or device FFT providers.
done	`math/signal`	`conv`, `conv2`, `deconv`, `filter`, `filtfilt`, `butter`, `fir1`, `freqz`, `envelope`	yes	S	FFT	Convolution, filter design/analysis, causal and zero-phase filtering, and signal envelopes; large convolution may use FFT paths.
done	`image/filters`	`fspecial`	host	-	-	Filter kernel generation.
done	`image/filters`	`imfilter`, `filter2`	yes	S	-	Linear image filters and padding modes.
done	`image/color`	`rgb2gray`, `gray2rgb`, `ind2rgb`, `im2double`, `im2uint8`, `im2uint16`, `rgb2hsv`, `hsv2rgb`, `rgb2lab`, `lab2rgb`	host	-	-	Image color and class conversions.

Communications

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`comms/modulation`	`qammod`, `pskmod`	yes	-	-	Integer-symbol gpuArray inputs produce complex-interleaved GPU constellations through provider hooks; bit-symbol paths validate on host and re-upload when GPU residency is requested.

Polynomials and Fitting

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`math/poly`	`polyval`, `polyfit`, `roots`, `polyder`, `polyint`	host	P	LAPACK	Polynomial utilities; `polyfit` uses least squares.

Control Systems

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`control`	`tf`, `feedback`	host	-	-	Transfer-function construction, variable shorthand, arithmetic, and closed-loop interconnection.
done	`control`	`step`, `impulse`, `nyquist`, `stepinfo`, `dcgain`, `pole`, `isstable`	host	-	-	Time response, frequency response, and SISO model analysis.

Statistics

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`stats/summary`	`corrcoef`, `cov`	yes	R	BLAS	Correlation and covariance.
done	`stats/hist`	`histcounts`, `histcounts2`	yes	P	-	Binning and histogram counts.
done	`stats/random`	`rng`	N/A	-	-	Host and device RNG state.

Dates and Times

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`datetime`	`datetime`, `dateshift`, `year`, `month`, `day`, `hour`, `minute`, `second`	host	-	-	Date/time construction, formatting, component extraction, arithmetic, and calendar boundary shifting.
done	`duration`	`duration`, `seconds`, `minutes`, `hours`, `days`, `milliseconds`	host	-	-	Duration construction, display, arithmetic, and datetime interop.

Logical and Comparisons

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`logical/rel`	`eq`, `ne`, `gt`, `ge`, `lt`, `le`	yes	E	-	Relational operations for scalars, tensors, and strings.
done	`logical/bit`	`and`, `or`, `xor`, `not`	yes	E	-	Elementwise logical operations.
done	`logical/tests`	`isnan`, `isinf`, `isfinite`, `isreal`, `islogical`, `isnumeric`	yes	E	-	Predicates and mask generation.
done	`logical`	`logical`	yes	E	-	Logical conversion.

Strings and Text

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`strings/core`	`string`, `char`, `strlength`, `num2str`, `str2double`, `compose`, `sprintf`	host	-	-	Conversion and formatting.
done	`strings/core`	`strcmp`, `strcmpi`, `strncmp`, `strings`, `string.empty`	host	-	-	String comparisons and constructors.
done	`strings/search`	`contains`, `startsWith`, `endsWith`, `strfind`	host	-	-	Search operations.
done	`strings/transform`	`lower`, `upper`, `strip`, `strtrim`, `replace`, `split`, `join`	host	-	-	Basic transformations.
done	`strings/transform`	`strrep`, `strcat`, `extractBetween`, `erase`, `eraseBetween`, `pad`	host	-	-	Additional string transformations.
done	`strings/regex`	`regexp`, `regexpi`, `regexprep`	host	-	-	Regex-backed operations.

Structs, Cells, and Containers

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`structs/core`	`struct`, `fieldnames`, `isfield`, `getfield`, `setfield`, `rmfield`, `orderfields`	host	-	-	Struct manipulation.
done	`cells/core`	`cell`, `cell2mat`, `mat2cell`, `cellfun`	host	P	-	Cell arrays and mapping helpers.
done	`cells/core`	`cellstr`	host	-	-	Cell/string conversion.
done	`containers/map`	`containers.Map`	host	-	-	String-to-value map support.
done	`table`	`table`, `height`, `width`, `groupsummary`	host	-	-	Table containers, properties, dot/paren/brace indexing, grouping summaries, display, and row sorting through `sortrows`.

Introspection, Environment, and Diagnostics

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`introspection`	`class`, `isa`, `which`, `whos`, `who`	N/A	-	-	Type and workspace queries.
done	`introspection`	`ischar`, `isstring`	N/A	-	-	Type predicates.
done	`diagnostics`	`error`, `warning`, `assert`	N/A	-	-	Runtime diagnostics.
done	`timing`	`tic`, `toc`, `timeit`, `pause`	N/A	-	-	Timing and benchmarking helpers.

I/O - Filesystem and Files

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`io/repl-fs`	`cd`, `pwd`, `ls`, `dir`, `mkdir`, `rmdir`, `movefile`, `copyfile`, `delete`, `exist`, `which`, `path`, `addpath`, `rmpath`, `run`, `genpath`, `savepath`, `tempdir`, `tempname`, `getenv`, `setenv`	host	-	-	REPL filesystem and environment helpers; MATLAB command syntax accepts literal path words such as `cd ..`, `addpath ./src`, and `copyfile ./a.m ./b.m`.
done	`io/filetext`	`fileread`, `filewrite`, `fopen`, `fclose`, `fread`, `fwrite`, `feof`, `fgetl`, `fgets`, `fprintf`	host	-	-	Text and binary file I/O.
done	`io/core`	`disp`	host	-	-	Display output sink.
done	`io/interactive`	`input`	host	-	-	Prompted input, including text mode.
done	`io/import`	`importdata`, `textscan`	host	-	-	Legacy text import with delimiter detection, formatted parsing, header text, column headers, and row labels.
done	`io/audio`	`audioinfo`	host	-	-	Audio metadata inspection for WAV/RF64, FLAC, AIFF/AIFC, Ogg/Vorbis, and MP3 frame headers.
done	`io/tabular`	`readtable`, `detectImportOptions`, `spreadsheetImportOptions`, `readmatrix`, `writematrix`, `writecell`, `csvread`, `csvwrite`, `dlmread`, `dlmwrite`	host	-	-	Tabular I/O; `readtable` imports delimited text and spreadsheet files as table variables with sheet/range/name/type options, and `writecell` exports heterogeneous cells to text or spreadsheets.
done	`io/mat`	`save`, `load`	host	-	-	MAT-like persistence.

I/O - JSON, Networking, and Images

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`io/json`	`jsonencode`, `jsondecode`	host	-	-	UTF-8 JSON serialization and parsing.
done	`io/net`	`tcpserver`, `accept`, `tcpclient`, `read`, `readline`, `write`, `close`	host	-	-	TCP client/server operations, TLS, and Unix sockets.
done	`io/http`	`webread`, `webwrite`, `weboptions`	host	-	-	HTTP client operations.
done	`io/image`	`imread`, `imwrite`, `imfinfo`	host	-	-	Image file I/O.
done	`image`	`imhist`	host	-	-	Grayscale and indexed-image intensity histograms, with statement-form plotting.
done	`plot/images`	`image`, `imshow`, `imagesc`	host	-	-	Image display through plotting features.

Plotting and Visualization

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`plot/core`	`plot`, `scatter`, `scatterplot`, `semilogx`, `semilogy`, `loglog`, `bar`, `area`, `histogram`, `hist`, `stairs`, `stem`, `errorbar`, `quiver`, `patch`, `pie`, `subplot`, `figure`, `gcf`, `gca`, `hold`, `clf`, `cla`, `drawnow`, `print`, `get`, `set`, `isgraphics`, `ishandle`, `title`, `sgtitle`, `suptitle`, `xlabel`, `ylabel`, `zlabel`, `legend`, `xlim`, `ylim`, `zlim`, `axis`, `caxis`, `clim`, `xline`, `yline`, `text`, `grid`, `box`, `colormap`, `shading`, `colorbar`	host	-	-	Feature-gated through `plot-core` and backed by `runmat-plot`.
done	`plot/3d`	`plot3`, `scatter3`, `surf`, `surfc`, `mesh`, `meshc`, `contour`, `contour3`, `contourf`, `fill3`, `heatmap`, `view`	host	-	-	Surface, contour, 3D, and heatmap plotting through `plot-core`.

Constants

Status	Path	Names	GPU	Fusion	Backend	Notes
done	`constants`	`pi`, `e`, `eps`, `inf`, `Inf`, `nan`, `NaN`, `true`, `false`	N/A	-	-	Fundamental constants.
done	`constants`	`i`, `j`	N/A	-	-	Imaginary units.