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- Yevgen Voronenko, Markus Püschel
- ACM Trans. Algorithms
- 2007

A variable can be multiplied by a given set of fixed-point constants using a multiplier block that consists exclusively of additions, subtractions, and shifts. The generation of a multiplier block from the set of constants is known as the multiple constant multiplication (MCM) problem. Finding the optimal solution, namely, the one with the fewest number of… (More)

- Markus Püschel, José M. F. Moura, +10 authors Nicholas Rizzolo
- Proceedings of the IEEE
- 2005

— Fast changing, increasingly complex, and diverse computing platforms pose central problems in scientific computing: How to achieve, with reasonable effort, portable optimal performance? We present SPIRAL that considers this problem for the performance-critical domain of linear digital signal processing (DSP) transforms. For a specified transform, SPIRAL… (More)

- Jeremy R. Johnson, Markus Püschel
- ICASSP
- 2000

This paper describes an approach to implementing and optimizing fast signal transforms. Algorithms for computing signal transforms are expressed by symbolic expressions , which can be automatically generated and translated into programs. Optimizing an implementation involves searching for the fastest program obtained from one of the possible expressions. In… (More)

- Peter Tummeltshammer, James C. Hoe, Markus Püschel
- IEEE Transactions on Computer-Aided Design of…
- 2007

This paper studies area-efficient arithmetic circuits to multiply a fixed-point input value selectively by one of several preset fixed-point constants. We present an algorithm that generates a class of solutions to this time-multiplexed multiple-constant multiplication problem by ldquofusingrdquo single-constant multiplication circuits for the required… (More)

- Sung-Chul Han, Franz Franchetti, Markus Püschel
- 2006 International Conference on Parallel…
- 2006

A recent trend in computing are domain-specific program generators, designed to alleviate the effort of porting and reoptimizing libraries for fast-changing and increasingly complex computing platforms. Examples include ATLAS, SPIRAL, and the codelet generator in FFTW. Each of these generators produces highly optimized source code directly from a problem… (More)

- Markus Püschel, José M. F. Moura
- IEEE Transactions on Signal Processing
- 2008

This paper introduces a general and axiomatic approach to <i>linear</i> signal processing (SP) that we refer to as the algebraic signal processing theory (ASP). Basic to ASP is the <i>linear</i> <i>signal</i> <i>model</i> defined as a triple (<i>A</i>,<i>M</i>,Phi) where familiar concepts like the filter space and the signal space are cast as an algebra… (More)

- Markus Püschel, José M. F. Moura
- IEEE Trans. Signal Processing
- 2008

— This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives the algorithms by stepwise decomposition of the associated signal models, or polynomial algebras. This decomposition is… (More)

- Markus Püschel
- 2002

SPIRAL is a generator of libraries for fast software implementations of signal processing transforms. These libraries are adapted to the computing platform and can be re-optimized as the hardware is upgraded or replaced. In this overview talk we explain SPIRAL's infrastructure and its main components: the mathematical framework that concisely describes… (More)

- Grace Nordin, Peter A. Milder, James C. Hoe, Markus Püschel
- Proceedings. 42nd Design Automation Conference…
- 2005

This paper presents a parameterized soft core generator for the discrete Fourier transform (DFT). Reusable IPs of digital signal processing (DSP) kernels are important time-saving resources in DSP hardware development. Unfortunately, reusable IPs, however optimized, can introduce inefficiencies because they cannot fit the exact requirements of every… (More)

- Gagandeep Singh, Markus Püschel, Martin T. Vechev
- PLDI
- 2015

Numerical abstract domains are a fundamental component in modern static program analysis and are used in a wide range of scenarios (e.g. computing array bounds, disjointness, etc). However, analysis with these domains can be very expensive, deeply affecting the scalability and practical applicability of the static analysis. Hence, it is critical to ensure… (More)