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New Major Features in Core

  • New support for bfloat16

The 16-bit Brain floating point format[1] is now available as Eigen::bfloat16. The constructor must be called explicitly, but it can otherwise be used as any other scalar type. To convert back-and-forth between uint16_t to extract the bit representation, use Eigen::numext::bit_cast.

  bfloat16 s(0.25);                                 // explicit construction
  uint16_t s_bits = numext::bit_cast<uint16_t>(s);  // bit representation
  using MatrixBf16 = Matrix<bfloat16, Dynamic, Dynamic>;
  MatrixBf16 X = s * MatrixBf16::Random(3, 3);

New backends

    • Unified with CUDA to create a generic GPU backend for NVIDIA/AMD.

Improvements/Cleanups to Core modules

  • Dense matrix decompositions and solvers
    • SVD implementations now have an info() method for checking convergence.
  MatrixXf m = MatrixXf::Random(3,2);
  JacobiSVD<MatrixXf> svd(m, ComputeThinU | ComputeThinV);
  if ( == ComputationInfo::Success) {
    // SVD computation was successful.
    VectorXf x = svd.solve(b);
    • Decompositions now fail quickly for detected invalid inputs.
    • Fixed aliasing issues with in-place small matrix inversions.
    • Fixed several edge-cases with empty or zero inputs.
  • Sparse matrix support, decompositions and solvers
    • Enable assignment and addition with diagonal matrices.
  SparseMatrix<float> A(10, 10);
  VectorXf x = VectorXf::Random(10);
  A = x.asDiagonal();
  A += x.asDiagonal();
    • Added new IRDS iterative linear solver.
  A.makeCompressed();   // Recommendation is to compress input before calling sparse solvers.
  IDRS<SparseMatrix<float>, DiagonalPreconditioner<float> > idrs(A);
  if ( == ComputationInfo::Success) {
    VectorXf x = idrs.solve(b);
    • Support added for SuiteSparse KLU routines.
  A.makeCompressed();   // Recommendation is to compress input before calling sparse solvers.
  KLU<SparseMatrix<T> > klu(A);
  if ( == ComputationInfo::Success) {
    VectorXf x = klu.solve(b);
    • SparseCholesky now works with row-major matrices.
    • Various bug fixes and performance improvements.
  • Improved support for half
    • Native support for ARM __fp16, CUDA/HIP __half, Clang F16C.
    • Better vectorization support across backends.
  • Improved bool support
    • Partial vectorization support for boolean operations.
    • Significantly improved performance (x25) for logical operations with Matrix or Tensor of bool.
  • Improved support for custom types
    • More custom types work out-of-the-box (see #2201[2]).
  • Improved Geometry Module
    • Transform::computeRotationScaling() and Transform::computeScalingRotation() are now more continuous across degeneracies (see !349[3]).
    • New minimal vectorization support.

Backend-specific improvements

  • SSE/AVX/AVX512
    • Enable AVX512 instructions by default if available.
    • New std::complex, half, bfloat16 vectorization support.
    • Better accuracy for several vectorized math functions including exp, log, pow, sqrt.
    • Many missing packet functions added.
  • GPU (CUDA and HIP)
    • Several optimized math functions added, better support for std::complex.
    • Option to disable CUDA entirely by defining EIGEN_NO_CUDA.
    • Many more functions can now be used in device code (e.g. comparisons, matrix inversion).
  • ZVector
    • Vectorized float and std::complex<float> support.
    • Added z14 support.
  • SYCL
    • Redesigned SYCL implementation for use with the Tensor[4] module, which can be enabled by defining EIGEN_USE_SYCL.
    • New generic memory model used by TensorDeviceSycl.
    • Better integration with OpenCL devices.
    • Added many math function specializations.