Multipartite table methods
F. de Dinechin,Arnaud Tisserand +1 more
TL;DR: A unified view of most previous table-lookup-and-addition methods (bipartite tables, SBTM, STAM, and multipartite methods) is presented, allowing a more accurate computation of the error entailed by these methods, leading to tables smaller than the best previously published ones by up to 50 percent.
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Abstract: A unified view of most previous table-lookup-and-addition methods (bipartite tables, SBTM, STAM, and multipartite methods) is presented. This unified view allows a more accurate computation of the error entailed by these methods, which enables a wider design space exploration, leading to tables smaller than the best previously published ones by up to 50 percent. The synthesis of these multipartite architectures on Virtex FPGAs is also discussed. Compared to other methods involving multipliers, the multipartite approach offers the best speed/area tradeoff for precisions up to 16 bits. A reference implementation is available at http://www.ens-lyon.fr/LIP/Arenaire/.
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Jean-Michel Muller
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Faithful bipartite ROM reciprocal tables
D. Das Sarma,David W. Matula +1 more
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TL;DR: B bipartite reciprocal tables are described that employ separate table lookup of the positive and negative portions of a borrow-save reciprocal value, and typically provide a round-to-nearest reciprocal for over 90% of input arguments.
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Approximating elementary functions with symmetric bipartite tables
TL;DR: In this paper, a high-speed method for function approximation that employs symmetric bipartite tables is presented, which uses less memory by taking advantage of symmetry and leading zeros in one of the two tables.
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The Symmetric Table Addition Method for Accurate Function Approximation
James E. Stine,Michael J. Schulte +1 more
- 01 Jun 1999
TL;DR: This method has a closed-form solution for the table entries and can be applied to any differentiable function and requires two to three orders of magnitude less memory than conventional table lookups.
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Function evaluation by table look-up and addition
H. Hassler,Naofumi Takagi +1 more
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TL;DR: A general approach decomposing a function into a sum of functions, each with a smaller input site than the original, which can be mapped with essentially the same precision using small ROM tables and adders.
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