ra-ra

ra-ra

ra-ra is a C++20 header-only library for handling multidimensional dense arrays. These are objects that can be indexed in 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 (~5k 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 some arrays, do operations on them, and print the result.

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

  int main()
  {
    // run time rank
    ra::Big<float> A = { {1, 2, 3, 4}, {5, 6, 7, 8} };
    // static rank, run time dimensions
    ra::Big<float, 2> B = { {1, 2, 3, 4}, {5, 6, 7, 8} };
    // static dimensions
    ra::Small<float, 2, 4> C = { {1, 2, 3, 4}, {5, 6, 7, 8} };
    // rank-extending op with STL object
    B += A + C + std::vector {100., 200.};
    // negate right half
    B(ra::all, ra::iota(ra::len/2, ra::len/2)) *= -1;
    // shape is dynamic, so will be printed
    std::cout << "B: " << B << std::endl;
  }

⇒

B: 2 4
103 106 -109 -112
215 218 -221 -224

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 };
  static_assert(6==ra::sum(a));

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 optimization level. The test suite should pass with -O0, but that can take a long time.

Notes

• 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.

Motivation

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

• Blitz++
• Eigen
• Boost.MultiArray
• xtensor
• Adept

Links

• Towards a standard for a C++ multi-dimensional array library for scientific applications Reviews C++ array libraries, including ra-ra (2020-08)
• libsimdpp C++ SIMD library
• J for C programmers Array programming concepts
• GNU APL
• Fortran wiki
• Numpy
• Octave