Analog and mixed-signal circuit simulation often employs the use of the so-called LU decomposition method to solve a set of linear algebraic equations represented as Ax=b, where A is a square matrix. The LU method requires the factorization of A into two tri-diagonal matrices. Factorization is of O(n3) time and dominates the execution time of the LU decomposition method.
A number of approaches have been developed for reducing the execution time of LU factorization. One approach is to unroll the factorization algorithm and, considering each resulting assignment statement to be a machine operation, interpret the instruction stream. If an interpreter is implemented in a special purpose hardware engine there may be efficiencies to be gained by using a uniquely-developed floating-point unit within the hardware interpreter.
This thesis documents the research in exploring alternatives in the design of a special purpose double precision floating point unit for a hardware interpreter to perform LU factorization using unrolled code. Alternatives explored were primarily looking at integer adder and multiplier units of the floating-point unit to determine the speed and area for each integer unit that were considered. A floating-point divider algorithm was also explored and studied. The result of this study for the pipelined floating-point unit gives the best performance with the Block Carry-look-ahead integer adder, Booth-2 integer multiplier and the SRT integer divider units.
One of the interesting aspects of this research was heavy use of rapid prototyping. All models were implemented in VHDL to evaluate system level performance, synthesized by Synopsys to gate level, and analyzed for time and area at the logic level. Finally, chip level area and space characteristics were obtained using Xilinx place and route tools.
|School:||University of Cincinnati|
|School Location:||United States -- Ohio|
|Source:||MAI 57/06M(E), Masters Abstracts International|
|Keywords:||Floating point unit, Lu factorization, Pipelined, Teee-754 format, Virtex fpga|
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