Garbageless reversible implementation of integer linear transformations

Stéphane Burignat; Kenneth Vermeirsch; Alexis De Vos; Michael Kirkedal Thomsen

doi:10.1007/978-3-642-36315-3_13

Garbageless reversible implementation of integer linear transformations

Stéphane Burignat^*, Kenneth Vermeirsch, Alexis De Vos, Michael Kirkedal Thomsen

^*Corresponding author for this work

Department of Computer Science

5 Citations (Scopus)

Abstract

Discrete linear transformations are important tools in information processing. Many such transforms are injective and therefore prime candidates for a physically reversible implementation into hardware. We present here reversible digital implementations of different integer transformations on four inputs. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. Which of the two computations that actually is performed, simply depends on the orientation of the circuit when it is inserted in a computer board (if one takes care to provide the encapsulation of symmetrical power supplies). Our analysis indicates that the detailed structure of such a reversible design strongly depends on the prime factors of the determinant of the transform: a determinant equal to a power of 2 leads to an efficient garbage-free design.

Original language	English
Title of host publication	Reversible Computation : 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers
Editors	Robert Glück, Tetsuo Yokoyama
Number of pages	11
Publisher	Springer
Publication date	2013
Pages	160-170
ISBN (Print)	978-3-642-36314-6
ISBN (Electronic)	978-3-642-36315-3
DOIs	https://doi.org/10.1007/978-3-642-36315-3_13
Publication status	Published - 2013
Event	4th International Workshop on Reversible Computation - København, Denmark Duration: 2 Jul 2012 → 3 Jul 2012 Conference number: 4

Conference

Conference	4th International Workshop on Reversible Computation
Number	4
Country/Territory	Denmark
City	København
Period	02/07/2012 → 03/07/2012

Series	Lecture notes in computer science
Volume	7581
ISSN	0302-9743

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10.1007/978-3-642-36315-3_13

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Burignat, S., Vermeirsch, K., De Vos, A., & Thomsen, M. K. (2013). Garbageless reversible implementation of integer linear transformations. In R. Glück, & T. Yokoyama (Eds.), Reversible Computation: 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers (pp. 160-170). Springer. Lecture notes in computer science Vol. 7581 https://doi.org/10.1007/978-3-642-36315-3_13

Garbageless reversible implementation of integer linear transformations. / Burignat, Stéphane; Vermeirsch, Kenneth; De Vos, Alexis et al.

Reversible Computation: 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers. ed. / Robert Glück; Tetsuo Yokoyama. Springer, 2013. p. 160-170 (Lecture notes in computer science, Vol. 7581).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Burignat, S, Vermeirsch, K, De Vos, A & Thomsen, MK 2013, Garbageless reversible implementation of integer linear transformations. in R Glück & T Yokoyama (eds), Reversible Computation: 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers. Springer, Lecture notes in computer science, vol. 7581, pp. 160-170, 4th International Workshop on Reversible Computation, København, Denmark, 02/07/2012. https://doi.org/10.1007/978-3-642-36315-3_13

Burignat S, Vermeirsch K, De Vos A, Thomsen MK. Garbageless reversible implementation of integer linear transformations. In Glück R, Yokoyama T, editors, Reversible Computation: 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers. Springer. 2013. p. 160-170. (Lecture notes in computer science, Vol. 7581). doi: 10.1007/978-3-642-36315-3_13

Burignat, Stéphane ; Vermeirsch, Kenneth ; De Vos, Alexis et al. / Garbageless reversible implementation of integer linear transformations. Reversible Computation: 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers. editor / Robert Glück ; Tetsuo Yokoyama. Springer, 2013. pp. 160-170 (Lecture notes in computer science, Vol. 7581).

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AB - Discrete linear transformations are important tools in information processing. Many such transforms are injective and therefore prime candidates for a physically reversible implementation into hardware. We present here reversible digital implementations of different integer transformations on four inputs. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. Which of the two computations that actually is performed, simply depends on the orientation of the circuit when it is inserted in a computer board (if one takes care to provide the encapsulation of symmetrical power supplies). Our analysis indicates that the detailed structure of such a reversible design strongly depends on the prime factors of the determinant of the transform: a determinant equal to a power of 2 leads to an efficient garbage-free design.

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Garbageless reversible implementation of integer linear transformations

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