HAXX (Hamilton's Quaternion Algebra for CXX) is a C++ software infrastructure for the development of efficient scalar and tensorial quaternion algorithms. HAXX can be thought of as two interdependent C++ software libraries:

• The HAXX scalar quaternion class which handles the scalar operations (+,-,etc) over the quaternion numbers
• HBLAS for quaternion and mixed-type linear algebra

HBLAS (Hamilton's Quaternion Basic Linear Algebra Subroutines) provides a BLAS-like interface for matricies and vectors over the quaternion numbers. As HBLAS depends solely on the HAXX scalar quaternion infrastructure, there is no plan currently to release them separately. The HBLAS implementaion of Level 1, 2, and 3 BLAS operations are currently based on the original FORTRAN BLAS implementaions, with serveral extensions and generalizations that account for the loss of scalar commutivity in the quaternion numbers. A primary goal of HBLAS is not only to provide a convienient and efficient interface for quaternion-quaternion linear algebra, but also to efficiently handle mixed-type (quaternion-real, quaternion-complex) linear algebra through their natural embeddings into the quaternion algebra.

HAXX is actively being developed with little focus on backwards compatibility with previous versions. The HAXX and HBLAS interfaces are constantly evolving and can (will) change on a regular basis as new, exciting functionality is added.

• A high-level, modern C++ API for scalar quaternion algebra (addition, subtraction, multiplication, division)
• Access to low level optimization and vectorization of the real arithmetic underlying quaternion operations
• Extension of BLAS functionality to quaternion algebra and mixed-type expressions (HBLAS)
• A reusable software framework to enable future scalar and tensorial algorithmic development using the quaternion algebra

David Williams-Young (Li Research Group / University of Washington)
E-Mail: dbwy at uw dot edu