Encyclopedia of Big Data Technologies

2019 Edition
| Editors: Sherif Sakr, Albert Y. Zomaya

Tabular Computation

  • Behrooz ParhamiEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-3-319-77525-8_169

Synonyms

Definitions

Big data necessitates the use of very large memories that can bring about other uses of such units, say, for storing precomputed values of functions of interest, to improve speed and energy efficiency.

Overview

Until the 1970s, when compact and affordable digital scientific calculators became available, we relied on pre-calculated tables of important functions that were published in book form (e.g., Zwillinger 2011). For example, base-10 logarithm of values in [1, 10], at increments of 0.01, might have been given in a 900-entry table, allowing direct readout of values if low precision was acceptable or use of linear interpolation to obtain greater precision. To compute log 35.419, say, one would note that it is 1 + log 3.5419 = 1 + log 3.54 + ε, where log 3.54 is read out from the said table and ε is derived based on the small residual 0.0019 using some sort of approximation or interpolation. Once...

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References

  1. Chen CLP, Zhang C-Y (2014) Data-intensive applications, challenges, techniques and technologies: a survey on big data. Inf Sci 275:314–347CrossRefGoogle Scholar
  2. Chugh M, Parhami B (2013) Logarithmic arithmetic as an alternative to floating-point: a review. In: Proceedings of 47th Asilomar conference on signals, systems, and computers, Pacific Grove, pp 1139–1143Google Scholar
  3. Cray Research (1989) Cray 2 computer system functional description manual, Cray documentationGoogle Scholar
  4. Das Sarma D, Matula DW (1995) Faithful Bipartite ROM reciprocal tables. In: Proceedings of 12th symposium on computer arithmetic, Bath, pp 17–28Google Scholar
  5. De Dinechin F, Tisserand A (2005) Multipartite table methods. IEEE Trans Comput 54(3):319–330CrossRefGoogle Scholar
  6. Gabbay F, Mendelson A (1998) Using value prediction to increase the power of speculative execution hardware. ACM Trans Comput Syst 16(3):234–270CrossRefGoogle Scholar
  7. Gustafsson O, Johanson K (2006) Multiplierless piecewise linear approximation of elementary functions. In: Proceedings of 40th Asilomar conference on signals, systems, and computers, Pacific Grove, pp 1678–1681Google Scholar
  8. Hilbert M, Gomez P (2011) The world’s technological capacity to store, communicate, and compute information. Science 332:60–65CrossRefGoogle Scholar
  9. Jacobson R (2013) 2.5 quintillion bytes of data created every day: how does CPG & retail manage it? IBM Industry Insights, http://www.ibm.com/blogs/insights-on-business/consumer-products/2-5-quintillion-bytes-of-data-created-every-day-how-does-cpg-retail-manage-it/
  10. Kornerup P, Matula DW (2005) Single precision reciprocals by multipartite table lookup. In: Proceedings of 17th IEEE symposium on computer arithmetic. Cape Cod, pp 240–248Google Scholar
  11. Lee DU, Luk W, Villasenor J, Cheung PYK (2003) Non-uniform segmentation for hardware function evaluation. In: Proceedings of 13th international conference on field-programmable logic and applications, Lisbon. LNCS, vol 2778. Springer, pp 796–807Google Scholar
  12. McCallum JC (2017) Graph of memory prices decreasing with time (1957–2017). http://www.jcmit.net/mem2015.htm
  13. Mittal S (2016) A survey of techniques for approximate computing. ACM Comput Surv 48(4):62Google Scholar
  14. Muller J-M (1999) A few results on table-based method. Reliab Comput 5:279–288MathSciNetzbMATHCrossRefGoogle Scholar
  15. Noetzel AS (1989) An interpolating memory unit for function evaluation: analysis and design. IEEE Trans Comput 38(3):377–384MathSciNetzbMATHCrossRefGoogle Scholar
  16. Owens JD et al (2008) GPU computing. Proc IEEE 96(5):879–899CrossRefGoogle Scholar
  17. Parhami B (1997) Modular reduction by multi-level table lookup. Proc 40th Midwest Symp Circuits Syst 1:381–384Google Scholar
  18. Parhami B (2005) Computer architecture: from microprocessors to supercomputers. Oxford University Press, New YorkGoogle Scholar
  19. Parhami B (2010) Computer arithmetic: algorithms and hardware designs, 2nd edn. Oxford University Press, New YorkGoogle Scholar
  20. Parhami B, Hung CY (1994) Optimal table lookup schemes for VLSI implementation of input/output conversions and other residue number operations. In: Proceedings of IEEE workshop on VLSI signal processing VII, La Jolla, pp 470–481Google Scholar
  21. Schulte MJ, Stine JE (1999) Approximating elementary functions with symmetric Bipartite tables. IEEE Trans Comput 48(8):842–847CrossRefGoogle Scholar
  22. Smith AJ (1982) Cache memories. ACM Comput Surv 14(8):473–530CrossRefGoogle Scholar
  23. Stine JE, Schulte MJ (1999) The symmetric table addition method for accurate function approximation. J VLSI Signal Process 21:167–177CrossRefGoogle Scholar
  24. Storer J (1988) Data compression. Computer Science Press, RockvilleGoogle Scholar
  25. Tang PTP (1991) Table-lookup algorithms for elementary functions and their error analysis. In: Proceedings of symposium on computer arithmetic, Bath, pp 232–236Google Scholar
  26. Vinnakota B (1995) Implementing multiplication with split read-only memory. IEEE Trans Comput 44(11):1352–1356zbMATHCrossRefGoogle Scholar
  27. White SA (1989) Application of distributed arithmetic to digital signal processing: a tutorial review. IEEE Trans Acoustics Speech Signal Process 6(3):4–19Google Scholar
  28. Zwillinger D (2011) CRC standard mathematical tables and formulae, 32nd edn. CRC Press, Boca RatonzbMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of CaliforniaSanta BarbaraUSA

Section editors and affiliations

  • Bingsheng He
  • Behrooz Parhami
    • 1
  1. 1.Dept. of Electrical and Computer EngineeringUniversity of California, Santa BarbaraSanta BarbaraUSA