Table-based division by small integer constants

Florent De Dinechin 1, 2 Laurent-Stéphane Didier 3
2 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
3 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : Computing cores to be implemented on FPGAs may involve divisions by small integer constants in fixed or floating point. This article presents a family of architectures addressing this need. They are derived from a simple recurrence whose body can be implemented very efficiently as a look-up table that matches the hardware resources of the target FPGA. For instance, division of a 32-bit integer by the constant 3 may be implemented by a combinatorial circuit of 48 LUT6 on a Virtex-5. Other options are studied, including iterative implementations, and architectures based on embedded memory blocks. This technique also computes the remainder. An efficient implementation of the correctly rounded division of a floating-point constant by such a small integer is also presented.
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Conference papers
8th International Symposium on Applied Reconfigurable Computing (ARC), Mar 2012, Hong Kong, Hong Kong SAR China. Springer, 7199, pp.53-63, 2012, Lecture Notes in Computer Science. 〈10.1007/978-3-642-28365-9_5〉
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Florent De Dinechin, Laurent-Stéphane Didier. Table-based division by small integer constants. 8th International Symposium on Applied Reconfigurable Computing (ARC), Mar 2012, Hong Kong, Hong Kong SAR China. Springer, 7199, pp.53-63, 2012, Lecture Notes in Computer Science. 〈10.1007/978-3-642-28365-9_5〉. 〈ensl-00642145〉

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