Designing garbage-free reversible implementations of the integer cosine transform

Alexis De Vos*, Stephane Burignat, Robert Gluck, Torben Agidius Mogensen, Holger Bock Axelsen, Michael K. Thomsen, Eva Rotenberg, Tetsuo Yokoyama

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


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 integer cosine transformations on n input integers. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. The detailed structure of such a reversible design strongly depends on the odd prime factors of the determinant of the transform: whether those are of the form 2k ± 1 or of the form 2k ± 2l ± 1 or neither of these forms.

Original languageEnglish
Article number11
JournalACM Journal on Emerging Technologies in Computing Systems
Issue number2
Publication statusPublished - 1 Oct 2014


  • Garbage-free multiplication
  • Integer cosine transform
  • Reversible computation


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