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 af dette arbejde

Datalogisk Institut

5 Citationer (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.

Originalsprog	Engelsk
Titel	Reversible Computation : 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers
Redaktører	Robert Glück, Tetsuo Yokoyama
Antal sider	11
Forlag	Springer
Publikationsdato	2013
Sider	160-170
ISBN (Trykt)	978-3-642-36314-6
ISBN (Elektronisk)	978-3-642-36315-3
DOI	https://doi.org/10.1007/978-3-642-36315-3_13
Status	Udgivet - 2013
Begivenhed	4th International Workshop on Reversible Computation - København, Danmark Varighed: 2 jul. 2012 → 3 jul. 2012 Konferencens nummer: 4

Konference

Konference	4th International Workshop on Reversible Computation
Nummer	4
Land/Område	Danmark
By	København
Periode	02/07/2012 → 03/07/2012

Navn	Lecture notes in computer science
Vol/bind	7581
ISSN	0302-9743

Adgang til dokumentet

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

Citationsformater

Burignat, S., Vermeirsch, K., De Vos, A., & Thomsen, M. K. (2013). Garbageless reversible implementation of integer linear transformations. I R. Glück, & T. Yokoyama (red.), Reversible Computation: 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers (s. 160-170). Springer. Lecture notes in computer science Bind 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. red. / Robert Glück; Tetsuo Yokoyama. Springer, 2013. s. 160-170 (Lecture notes in computer science, Bind 7581).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › peer review

Burignat, S, Vermeirsch, K, De Vos, A & Thomsen, MK 2013, Garbageless reversible implementation of integer linear transformations. i R Glück & T Yokoyama (red), Reversible Computation: 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers. Springer, Lecture notes in computer science, bind 7581, s. 160-170, 4th International Workshop on Reversible Computation, København, Danmark, 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. I Glück R, Yokoyama T, red., Reversible Computation: 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012. Revised Papers. Springer. 2013. s. 160-170. (Lecture notes in computer science, Bind 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. red. / Robert Glück ; Tetsuo Yokoyama. Springer, 2013. s. 160-170 (Lecture notes in computer science, Bind 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

Abstract

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