Incremental tree height reduction for high level synthesis
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
Algorithms for computer algebra
Algorithms for computer algebra
Integrating program transformations in the memory-based synthesis of image and video algorithms
ICCAD '94 Proceedings of the 1994 IEEE/ACM international conference on Computer-aided design
The Strict Time Lower Bound and Optimal Schedules for Parallel Prefix with Resource Constraints
IEEE Transactions on Computers
Polynomial methods for component matching and verification
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
Polynomial methods for allocating complex components
DATE '99 Proceedings of the conference on Design, automation and test in Europe
Using symbolic algebra in algorithmic level DSP synthesis
Proceedings of the 38th annual Design Automation Conference
Computer Approximations
Synthesis and Optimization of Digital Circuits
Synthesis and Optimization of Digital Circuits
Structure of Computers and Computations
Structure of Computers and Computations
Some properties of Gröbner-bases for polynomial ideals
ACM SIGSAM Bulletin
Complex library mapping for embedded software using symbolic algebra
Proceedings of the 39th annual Design Automation Conference
Specifying and verifying imprecise sequential datapaths by Arithmetic Transforms
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Coordinated parallelizing compiler optimizations and high-level synthesis
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Improved use of the carry-save representation for the synthesis of complex arithmetic circuits
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Integration, the VLSI Journal
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The growing market of multi-media applications has required the development of complex ASICs with significant data-path portions. Unfortunately, most high-level synthesis tools and methods cannot automatically synthesize data paths such that complex arithmetic library blocks are intelligently used. Symbolic computer algebra has been previously used to automate mapping data flow into a minimal set of complex arithmetic components. In this paper, we present extensions to the previous methods in order to find the minimal critical path delay (CPD) mapping. A new algorithm is proposed that incorporates symbolic manipulations such as tree-height-reduction, factorization, expansion, and Horner transformation. Such manipulations are used as guidelines in initial library element selection. Furthermore, we demonstrate how substitution can be used for multi-expression component sharing and critical path delay optimization.