An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology
ICS '97 Proceedings of the 11th international conference on Supercomputing
A fast Fourier transform compiler
Proceedings of the ACM SIGPLAN 1999 conference on Programming language design and implementation
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
FLAME: Formal Linear Algebra Methods Environment
ACM Transactions on Mathematical Software (TOMS)
Automatically tuned linear algebra software
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
The science of deriving dense linear algebra algorithms
ACM Transactions on Mathematical Software (TOMS)
Formal loop merging for signal transforms
Proceedings of the 2005 ACM SIGPLAN conference on Programming language design and implementation
Auto-vectorization of interleaved data for SIMD
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
Proceedings of the 13th ACM SIGPLAN Symposium on Principles and practice of parallel programming
Anatomy of high-performance matrix multiplication
ACM Transactions on Mathematical Software (TOMS)
Parametric multi-level tiling of imperfectly nested loops
Proceedings of the 23rd international conference on Supercomputing
Computer Generation of General Size Linear Transform Libraries
Proceedings of the 7th annual IEEE/ACM International Symposium on Code Generation and Optimization
Operator Language: A Program Generation Framework for Fast Kernels
DSL '09 Proceedings of the IFIP TC 2 Working Conference on Domain-Specific Languages
Generating SIMD vectorized permutations
CC'08/ETAPS'08 Proceedings of the Joint European Conferences on Theory and Practice of Software 17th international conference on Compiler construction
Vapor SIMD: Auto-vectorize once, run everywhere
CGO '11 Proceedings of the 9th Annual IEEE/ACM International Symposium on Code Generation and Optimization
From relational verification to SIMD loop synthesis
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
When polyhedral transformations meet SIMD code generation
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
| Hi-index | 0.00 |
Many applications in media processing, control, graphics, and other domains require efficient small-scale linear algebra computations. However, most existing high performance libraries for linear algebra, such as ATLAS or Intel MKL are more geared towards large-scale problems (matrix sizes in the hundreds and larger) and towards specific interfaces (e.g., BLAS). In this paper we present LGen: a compiler for small-scale, basic linear algebra computations. The input to LGen is a fixed-size linear algebra expression; the output is a corresponding C function optionally including intrinsics to efficiently use SIMD vector extensions. LGen generates code using two levels of mathematical domain-specific languages (DSLs). The DSLs are used to perform tiling, loop fusion, and vectorization at a high level of abstraction, before the final code is generated. In addition, search is used to select among alternative generated implementations. We show benchmarks of code generated by LGen against Intel MKL and IPP as well as against alternative generators, such as the C++ template-based Eigen and the BTO compiler. The achieved speed-up is typically about a factor of two to three.