Pipelined Mixed Precision Algorithms on FPGAs for Fast and Accurate PDE Solvers from Low Precision Components

@inproceedings{citeulike:2207869, abstract = {FPGAs are becoming more and more attractive for high precision scientific computations. One of the main problems in efficient resource utilization is the quadratically growing resource usage of multipliers depending on the operand size. Many research efforts have been devoted to the optimization of individual arithmetic and linear algebra operations. In this paper the authors take a higher level approach and seek to reduce the intermediate computational precision on the algorithmic level by optimizing the accuracy towards the final result of an algorithm. In our case this is the accurate solution of partial differential equations (PDEs). Using the Poisson problem as a typical PDE example the authors show that most intermediate operations can be computed with floats or even smaller formats and only very few operations (e.g. 1\%) must be performed in double precision to obtain the same accuracy as a full double precision solver. Thus the FPGA can be configured with many parallel float rather than few resource hungry double operations. To achieve this, the authors adapt the general concept of mixed precision iterative refinement methods to FPGAs and develop a fully pipelined version of the conjugate gradient solver. The authors combine this solver with different iterative refinement schemes and precision combinations to obtain resource efficient mappings of the pipelined algorithm core onto the FPGA}, author = {Strzodka, Robert and Goddeke, Dominik }, booktitle = {Field-Programmable Custom Computing Machines, 2006. FCCM '06. 14th Annual IEEE Symposium on}, citeulike-article-id = {2207869}, doi = {10.1109/FCCM.2006.57}, journal = {Field-Programmable Custom Computing Machines, 2006. FCCM '06. 14th Annual IEEE Symposium on}, keywords = {floating\_point, fpga, mixed\_precision}, pages = {259--270}, posted-at = {2008-03-11 11:15:02}, priority = {2}, title = {Pipelined Mixed Precision Algorithms on FPGAs for Fast and Accurate PDE Solvers from Low Precision Components}, url = {http://dx.doi.org/10.1109/FCCM.2006.57}, year = {2006} }

TY - CONF ID - citeulike:2207869 L3 - citeulike-article-id:2207869 TI - Pipelined Mixed Precision Algorithms on FPGAs for Fast and Accurate PDE Solvers from Low Precision Components T2 - Field-Programmable Custom Computing Machines, 2006. FCCM '06. 14th Annual IEEE Symposium on JF - Field-Programmable Custom Computing Machines, 2006. FCCM '06. 14th Annual IEEE Symposium on SP - 259 EP - 270 N2 - FPGAs are becoming more and more attractive for high precision scientific computations. One of the main problems in efficient resource utilization is the quadratically growing resource usage of multipliers depending on the operand size. Many research efforts have been devoted to the optimization of individual arithmetic and linear algebra operations. In this paper the authors take a higher level approach and seek to reduce the intermediate computational precision on the algorithmic level by optimizing the accuracy towards the final result of an algorithm. In our case this is the accurate solution of partial differential equations (PDEs). Using the Poisson problem as a typical PDE example the authors show that most intermediate operations can be computed with floats or even smaller formats and only very few operations (e.g. 1%) must be performed in double precision to obtain the same accuracy as a full double precision solver. Thus the FPGA can be configured with many parallel float rather than few resource hungry double operations. To achieve this, the authors adapt the general concept of mixed precision iterative refinement methods to FPGAs and develop a fully pipelined version of the conjugate gradient solver. The authors combine this solver with different iterative refinement schemes and precision combinations to obtain resource efficient mappings of the pipelined algorithm core onto the FPGA KW - floating_point KW - fpga KW - mixed_precision AU - Strzodka, Robert AU - Goddeke, Dominik PY - 2006/// UR - http://dx.doi.org/10.1109/FCCM.2006.57 ER -