A C++20 array and expression template library with some J/APL features

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ra-ra is a C++20 header-only library for handling multidimensional dense arrays. These are objects that can be indexed on 0 or more dimensions; the number of dimensions is known as ‘rank’. For example, vectors are arrays of rank 1 and matrices are arrays of rank 2.

ra-ra implements expression templates. This is a C++ technique (pioneered by Blitz++) to delay the execution of expressions involving array operands, and in this way avoid the unnecessary creation of large temporary array objects.

ra-ra is compact (about 6k loc), easy to extend, and generic. There are no arbitrary type restrictions or limits on rank or argument count.

In this example (examples/read-me.cc), we create an array, do some operations on it, and print the result.

  #include "ra/ra.hh"
  #include <iostream>

  int main()
      // compile time rank, 4x2 array
      ra::Big<float, 2> A = { {1, 2, 3, 4}, {5, 6, 7, 8} };
      // rank-extending op with STL object
      A += std::vector {10., 20.};
      // negate right half
      A(ra::all, ra::iota(ra::len/2, ra::len/2)) *= -1;
      // shape is dynamic, so will be printed
      std::cout << "A: " << A << std::endl;

A: 2 4
11 12 -13 -14
25 26 -27 -28

Please check the manual online at lloda.github.io/ra-ra, or have a look at the examples/ folder.

ra-ra offers:

  • Array types with arbitrary compile time or runtime rank, and compile time or runtime shape.
  • Memory owning types as well as views over any piece of memory.
  • Support for builtin arrays and for the standard library, including <ranges>.
  • Interoperability with other libraries and/or languages through transparent memory layout.
  • Slicing with indices of arbitrary rank, linear range indices, axis skipping and elision, and contextual len.
  • Rank extension by prefix matching, as in APL/J, for functions of any number of arguments.
  • Iterators over subarrays of any rank.
  • Axis insertion, e.g. for broadcasting.
  • Outer product operation.
  • Tensor index object.
  • Short-circuiting logical operators.
  • Argument list selection operators (where with bool selector, or pick with integer selector).
  • Reshape, transpose, reverse, collapse/explode, stencils.
  • Arbitrary types as array elements, or as scalar operands.
  • Many predefined array operations. Adding yours is trivial.
  • Rank conjunction as in J (compile time ranks only).
  • Configurable error checking.

constexpr is suported as much as possible. For example:

  constexpr ra::Small<int, 3> a = { 1, 2, 3 };

Performance is competitive with hand written scalar (element by element) loops, but probably not with cache-tuned code such as your platform BLAS, or with code using SIMD. Please have a look at the benchmarks in bench/.

Building the tests and the benchmarks

ra-ra is header-only and has no dependencies other than a C++20 compiler and the standard library. I test regularly with gcc ≥ 11.3. If you can test with Clang, please let me know.

The test suite in test/ runs under either SCons (CXXFLAGS=-O3 scons) or CMake (CXXFLAGS=-O3 cmake . && make && make test). Running the test suite will also build and run the examples and the benchmarks.

  • Some of the benchmarks will try to use BLAS if you have define RA_USE_BLAS=1 in the environment.
  • The test suite is built with -fsanitize=address by default, and this can cause significant slowdown. Disable by adding -fno-sanitize=address to CXXFLAGS at build time.
  • The performance of ra-ra depends heavily on the optimization level. The test suite should pass with -O0, but that can take a long time.


  • Both index and size types are signed. Index base is 0.
  • The default array order is C or row-major (last dimension changes fastest). You can make array views with other orders, but newly created arrays use C order.
  • The subscripting operator is () or [] indistinctly. Multi-argument [] requires __cpp_multidimensional_subscript > 202110L (in gcc 12 with -std=c++2b).
  • Indices are checked by default. This can be disabled with a compilation flag.
  • ra-ra doesn't use exceptions, but it provides a hook so you can throw your own exceptions on ra-ra errors. See ‘Error handling’ in the manual.
  • ra-ra uses zero size arrays and VLAs internally.

Bugs & defects

  • Operations that require allocation, such as concatenation or search, are mostly absent.
  • No good abstraction for reductions. You can write reductions abusing rank extension, but it's awkward.
  • Traversal of arrays is basic, just unrolling of inner dimensions.
  • Handling of nested / ragged arrays is inconsistent.
  • No support for parallel operations or GPU.
  • No SIMD to speak of.

Please see the TODO file for a concrete list of known issues.


I do numerical work in C++, and I need support for array operations. The built-in array types that C++ inherits from C are very insufficient, so at the time of C++11 when I started writing ra-ra, a number of libraries where already available. However, most of these libraries seemed to support only vectors and matrices, or small objects for vector algebra.

Blitz++ was a major inspiration as an early generic library. But it was a heroic feat to write such a library in C++ in the late 90s. Variadic templates, lambdas, perfect forwarding, etc. make things much easier, for the library writer as well as for the user.

From APL and J I've taken the rank extension mechanism, and perhaps an inclination for carrying each feature to its logical end.

ra-ra wants to remain simple. I try not to second-guess the compiler and I don't stress performance as much as Blitz++ did. However, I'm wary of adding features that could become an obstacle if I ever tried to make things fast(er). I believe that implementating new traversal methods, or perhaps optimizing specific expression patterns, should be possible without having to turn the library inside out.

Other C++ array libraries