The DOI matches its Crossref record.
Subexpression sharing in filters using canonic signed digit multipliers
Abstract
A common way of implementing constant multiplication is by a series of shift and add operations. As is well known, if the multiplier is represented in Canonical Signed Digit (CSD) form, then the number of additions (or subtractions) used will be a minimum. This paper examines methods for optimizing the design of CSD multipliers, and in particular the gains that can be made by sharing subexpressions. In the case where several multipliers are present in a network of operators, for instance in an FIR filter, the savings achieved by identifying common subexpressions can be as much as 50% of the total number of operators. The asymptotic frequency of the most common subexpression is analyzed mathematically, and it is shown that sharing the two most common subexpressions can be expected to lead to a 33% saving of the number of additions.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
50 Years of CORDIC: Algorithms, Architectures, and Applications
Meher, P. K., Valls, J., Juang, T.-B., Sridharan, K., & Maharatna, K. (2009) · IEEE Transactions on Circuits and Systems I: Regular Papers · doi:10.1109/tcsi.2009.2025803 · Cited by 580
AddNet: Deep Neural Networks Using FPGA-Optimized Multipliers
Faraone, J., Kumm, M., Hardieck, M., Zipf, P., Liu, X., Boland, D., & Leong, P. H. W. (2020) · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · doi:10.1109/tvlsi.2019.2939429 · Cited by 66
Metadata
- Authors
- Hartley, R. I.
- Venue
- IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing
- Published
- 1996
- Volume
- 43
- Issue
- 10
- Pages
- 677-688
- ISSN
- 1057-7130 (ISSN-L)
- OpenAlex
- W2154656381
- Cited by
- 591
- References
- 0
- FWCI
- 7.64
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Subexpression sharing in filters using canonic signed digit multipliers. https://app.cochat.ai/papers/10.1109/82.539000
- The paper
- Hartley, R. I. (1996). Subexpression sharing in filters using canonic signed digit multipliers. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing. https://doi.org/10.1109/82.539000
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
