Abstract-This paper examines the mapping of algorithms encountered when solving dense linear systems and linear leastsquares problems to a custom Linear Algebra Processor. Specifically, the focus is on Cholesky, LU (with partial pivoting), and QR factorizations. As part of the study, we expose the benefits of redesigning floating point units and their surrounding datapaths to support these complicated operations. We show how adding moderate complexity to the architecture greatly alleviates complexities in the algorithm. We study design trade-offs and the effectiveness of architectural modifications to demonstrate that we can improve power and performance efficiency to a level that can otherwise only be expected of full-custom ASIC designs. A feasibility study shows that our extensions to the MAC units can double the speed of required vector-norm operations while reducing energy by 60%. Similarly, up to 20% speedup with 15% savings in energy can be achieved for LU factorization. We show how such efficiency is maintained even in the complex inner kernels of these operations.
In REF , authors have presented several floating point unit architecture extensions to accelerate matrix factorizations.
Floating Point Architecture Extensions for Optimized Matrix Factorization
2013 IEEE 21st Symposium on Computer Arithmetic
2013 IEEE 21st Symposium on Computer Arithmetic
Computer Science