The Dataflow Time and Space Complexity of FFTs

Böhm, Alexander; Hiromoto, Robert E.

doi:10.1006/jpdc.1993.1066

Cited by 6 publications

(3 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These multiplications can be eliminated, leading to better code than inlining the general case function would achieve, as this function would access the roots of unity from an array and would not eliminate the simple multiplications. Moreover, the bottom level of k = 1 merely returns the input array and not going to this level avoids a problem in deallocating intermediate arrays in Id, as a one-dimensional FFT function now always creates a new result array (Böhm and Hiromoto, 1993).…”

Section: Problem Specificationmentioning

confidence: 99%

See 1 more Smart Citation

On the effectiveness of functional language features: NAS benchmark FT

1997

View full text Add to dashboard Cite

In this paper we investigate the effectiveness of functional language features when writing scientific codes. Our programs are written in the purely functional subset of Id and executed on a one node Motorola Monsoon machine, and in Haskell and executed on a Sparc 2. In the application we study – the NAS FT benchmark, a three-dimensional heat equation solver – it is necessary to target and select one-dimensional sub-arrays in three-dimensional arrays. Furthermore, it is important to be able to share computation in array definitions. We compare first order and higher order implementations of this benchmark. The higher order version uses functions to select one-dimensional sub-arrays, or slices, from a three-dimensional object, whereas the first order version creates copies to achieve the same result. We compare various representations of a three-dimensional object, and study the effect of strictness in Haskell. We also study the performance of our codes when employing recursive and iterative implementations of the one-dimensional FFT, which forms the kernel of this benchmark. It turns out that these languages still have quite inefficient implementations, with respect to both space and time. For the largest problem we could run (323), Haskell is 15 times slower than Fortran and uses three times more space than is absolutely necessary, whereas Id on Monsoon uses nine times more cycles than Fortran on the MIPS R3000, and uses five times more space than is absolutely necessary. This code, and others like it, should inspire compiler writers to improve the performance of functional language implementations.

show abstract

Section: Problem Specificationmentioning

confidence: 99%

“…In the base case it returns the old object; otherwise it recursively creates a new object, meaning it is safe to release the old object. This problem is discussed in more detail in Böhm and Hiromoto (1993).…”

Section: Storage Usementioning

confidence: 99%

On the effectiveness of functional language features: NAS benchmark FT

1997

View full text Add to dashboard Cite

show abstract

“…Thus, iteratively tearing at the the top, done across all the elements, gives the same bottom case as the recursive half and half tearing. So we start with a tridiagonal matrix given in 1 and partition it by a rank one tearing about the rst o -diagonal element b 1 . W e get, The same updating is then done as given by equation 4 and Schur decomposition of 4x4 matrices are obtained.…”

mentioning

confidence: 99%

Analysis of non-strict functional implementations of the Dongarra-Sorensen eigensolver

Sur

Bohm

1994

Proceedings of the 8th International Conference on Supercomputing - ICS '94

View full text Add to dashboard Cite

We study the producer-consumer parallelism of Eigensolvers composed of a tridiagonalization function, a tridiagonal solver, and a matrix multiplication, written in the non-strict functional programming language Id. We v erify the claim that non-strict functional languages allow the natural exploitation of this type of parallelism, in the framework of realistic numerical codes. We compare the standard top-down Dongarra-Sorensen solver with a new, bottom-up version. We show that this bottom-up implementation is much more space e cient than the top-down version. Also, we compare both versions of the Dongarra-Sorensen solver with the more traditional QL algorithm, and verify that the Dongarra-Sorensen solver is much more e cient, even when run in a serial mode. We show that in a non-strict functional execution model, the Dongarra-Sorensen algorithm can run completely in parallel with the Householder function. Moreover, this can be achieved without any c hange in the code components. We also indicate how the critical path of the complete Eigensolver can be improved.

show abstract

On the Comparative Evaluation of Parallel Languages and Systems: A Functional Note

Hiromoto

1994

Workshops in Computing

View full text Add to dashboard Cite

The Dataflow Time and Space Complexity of FFTs

Cited by 6 publications

References 1 publication

On the effectiveness of functional language features: NAS benchmark FT

On the effectiveness of functional language features: NAS benchmark FT

Analysis of non-strict functional implementations of the Dongarra-Sorensen eigensolver

On the Comparative Evaluation of Parallel Languages and Systems: A Functional Note

Contact Info

Product

Resources

About