L. Auslander, J. Johnson, and R. W. Johnson. Automatic implementation of FFT algorithms. Technical Report DU-MCS-96-01, Dept. of Math. and Computer Science, Drexel University, Philadelphia, PA, 1996. Presented at the DARPA ACMP PI meeting.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....real time applications. However, the transformation matrices can be factored, allowing for faster implementations. These factorizations can be represented by mathematical formulas and a single signal processing algorithm can be represented by many different, but mathematically equivalent, formulas [Auslander et al. 1996] . Interestingly, when these formulas are implemented in code and executed, they often have very different running times. While many of the factorizations may produce the exact same number of operations, the different orderings of the operations that the factorizations produce can greatly impact ....

L. Auslander, J. Johnson, and R. Johnson. Automatic implementation of FFT algorithms. Technical Report 96-01, Drexel University, 1996.

....However, these matrices often have a particular form that allows them to be factored into a product of sparse, structured matrices. These factorizations allow for faster implementations of signal processing algorithms. Further, these factorizations can be represented by mathematical formulas [1]. A single signal processing algorithm can be represented by many different but mathematically equivalent formulas. When these formulas are implemented in actual code, they often have very different running times. Thus, an important problem is finding a formula that implements the signal ....

L. Auslander, Jeremy R. Johnson, and R. W. Johnson. Automatic im- plementation of FFT algorithms. Technical Report 96-01, Department of Mathematics and Computer Science, Drexel University, Philadelphia, PA, June 1996.

....allow for fast implementations, the transformation matrices often can be factored into a product of structured matrices. Further, these factorizations can be represented by mathematical 2 formulas and a single transform can be represented by many different, but mathematically equivalent, formulas [1]. As an example of the number of different formulas, we consider 51,819 formulas for a Walsh Hadamard transform of size 2 l and 31,242 formulas for a discrete cosine transform of size 24. Interestingly, when these formulas are implemented in code and executed, they have very different running ....

L. Auslander, Jeremy R. Johnson, and R. W. Johnson, "Automatic implementation of FFT algorithms," Tech. Rep. 96-01, Department of Mathematics and Computer Science, Drexel University, Philadelphia, PA, June 1996.

....real time applications. However, the transformation matrices can be factored, allowing for faster implementations. These factorizations can be represented by mathematicalformulas and a single signal processing algorithm can be represented by many different, but mathematically equivalent, formulas (Auslander et al. 1996). Interestingly, when these formulas are implemented in code and executed, they often have very different running times. The complexity of modern processors makes it difficult to analytically predict or model by hand the performance of formulas. Further, the differences between current processors ....

L. Auslander, J. Johnson, and R. Johnson. Automatic implementation of FFT algorithms. Technical Report 96-01, Drexel University, 1996.

....product of structured matrices, allowing for faster implementations of signal processing algorithms. Furthermore, these factorizations can be represented by mathematical formulas and a single signal processing algorithm can be represented by many different, but mathematically equivalent, formulas (Auslander et al. 1996; Singer Veloso, 2000) Interestingly, when these formulas are implemented in actual code and executed, they often have very different running times. Thus, a crucial problem is finding the formula that implements the signal processing algorithm as efficiently as possible (Moura et al. 1998) ....

Auslander, L., Johnson, J. R., & Johnson, R. W. (1996). Automatic implementation of FFT algorithms (Technical Report 96-01). Department of Mathematics and Computer Science, Drexel University, Philadelphia, PA.

....these rules to other SP transforms in order to obtain ecient implementations. This thesis is part of the SPIRAL project, 1] a recent e ort to create a self adapted library of optimized implementations of SP algorithms. It uses a specialized signal processing language, SPL, an extension of TPL, [2], to formulate signal processing applications in a high level mathematical language, and utilizes optimization rules to automatically generate implementations that are ecient in the given computational platform. SPIRAL is described in the following section. SPIRAL SPIRAL (Signal Processing ....

....of an abstract programming language speci cally designed for SP algorithms is desirable. It allows programmers to design and implement the SP algorithms at a high level, avoiding low level implementation details, and to make their code portable. SPIRAL s SPL is an example of such a language, [2]. SPIRAL s SPL In the framework of SPIRAL, 1] see Chapter 1) classes of fast SP algorithms are represented as mathematical expressions (formulas) using general mathematical constructs. For these purposes, a speci cally designed high level SP programming language, SPL, is being developed. ....

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L. Auslander, J. R. Johnson, and R. W. Johnson, \Automatic Implementation of FFT Algorithms," Technical Report, Department of MCS, Drexel University, Philadelphia, PA, 1996.

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L. Auslander, J. Johnson, and R. W. Johnson. Automatic implementation of FFT algorithms. Technical Report DU-MCS-96-01, Dept. of Math. and Computer Science, Drexel University, Philadelphia, PA, 1996. Presented at the DARPA ACMP PI meeting.

No context found.

L. Auslander, J. Johnson, and R. W. Johnson. Automatic implementation of FFT algorithms. Technical Report DU-MCS-96-01, Dept. of Math. and Computer Science, Drexel University, Philadelphia, PA, 1996. Presented at the DARPA ACMP PI meeting.

No context found.

L. Auslander, J. R. Johnson, and R. W. Johnson. Automatic implementation of FFT algorithms. Technical Report 96-01, Dept. of Math. and Computer Science, Drexel University, Philadelphia, PA, June 1996. Presented at the DARPA ACMP PI meeting.

No context found.

L. Auslander, J. Johnson, and R. W. Johnson. Automatic implementation of FFT algorithms. Technical Report DU-MCS-96-01, Dept. of Math. and Computer Science, Drexel University, Philadelphia, PA, 1996. Presented at the DARPA ACMP PI meeting.

.... # 1 # 2 DFT2 #12 ) 5, 6) 8] DFT2# 13 ) # 12 ) 2, 5, 3, 6, 4) 7, 8) 1, 1, # 2, # 2, # 2, # 2, 1, 1) 16 # DFT2 ) 2, 5, 8, 7, 3, 4) 8] Haar transform The Haar transform HT 2 k is defined recursively by: HT2 = # 1 1 1 1 # , HT 2 k 1 = # HT 2 k# [1 1] 2 k 2 1 2 k# [1 1] # , for k # 1. A fast algorithm for the Haar transform follows directly from the definition. For k = 3 we build the corresponding matrix and input it into the factorization algorithm. HT8 = 1, 8, 6, 4, 2, 7, 5, 3) 8] diag( # 2, # 2) # 14 # DFT2 ) 1, 5, ....

.... [ 5, 6) 8] DFT2# 13 ) # 12 ) 2, 5, 3, 6, 4) 7, 8) 1, 1, # 2, # 2, # 2, # 2, 1, 1) 16 # DFT2 ) 2, 5, 8, 7, 3, 4) 8] Haar transform The Haar transform HT 2 k is defined recursively by: HT2 = # 1 1 1 1 # , HT 2 k 1 = # HT 2 k# [1 1] 2 k 2 1 2 k# [1 1] # , for k # 1. A fast algorithm for the Haar transform follows directly from the definition. For k = 3 we build the corresponding matrix and input it into the factorization algorithm. HT8 = 1, 8, 6, 4, 2, 7, 5, 3) 8] diag( # 2, # 2) # 14 # DFT2 ) 1, 5, 4, 8, 6, 3, 7, 2) 8] ....

[Article contains additional citation context not shown here]

Auslander, L., Johnson, J. R., and Johnson, R. W. Automatic implementation of FFT algorithms. Tech. Rep. 96-01, Dept. of Math. and Computer Science, Drexel University, Philadelphia, PA, June 1996. Presented at the DARPA ACMP PI meeting.

....looks for the fastest implementation out of the set of choices produced by the formula generator and SPL compiler. Due to the exponential size of the search space, intelligent search strategies are required to make this process feasible. SPL is a descendent of the TPL (Tensor Product Language) [1] that was developed for the automatic generation of FFT algorithms. SPL programs are essentially mathematical formulas describing matrix factorizations. As such, they are built using operators from linear algebra and families of parameterized matrices. Such formulas naturally arise when describing ....

L. Auslander, J. Johnson, and R. W. Johnson. Automatic implementation of FFT algorithms. Technical Report DU-MCS-96-01, Dept. of Math. and Computer Science, Drexel University, Philadelphia, PA, June 1996. Presented at the DARPA ACMP PI meeting.

....of Contracting. methodology to the implementation and optimization of the FFT. Various techniques are presented that allow us to find nearly optimal SPL programs while only searching through a small subspace of the allowed programs. The approach presented in this paper was first outlined in [1] and further discussed in [7] Our work is part of a larger e#ort, called SPIRAL [11] for automatically implementing and optimizing signal processing algorithms. This paper presents the first e#cient implementation of the SPL compiler and hence this first true test of the methodology. Our ....

....is the identity matrix, T a diagonal matrix, and L a permutation matrix both depending on r and s. SPL [6] is a domain specific programming language for expressing and implementing matrix factorizations. It was originally developed to investigate and automate the implementation of FFT algorithms, [1]. As such, some of the builtin matrices are biased towards the expression of FFT algorithms, however, it is important to note that SPL is not restricted to the FFT. It contains features that allow the user to introduce notation suitable to any class of matrix expressions. This section reviews some ....

L. Auslander, J. R. Johnson, and R. W. Johnson. Automatic implementation of FFT algorithms. Technical Report 96-01, Dept. of Math. and Computer Science, Drexel University, Philadelphia, PA, June 1996. Presented at the DARPA ACMP PI meeting.

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