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| N. Yoshida, E. Goto, S. Ichikawa, "Pseudorandom Rounding for Truncated Multipliers," IEEE Transactions on Computers, vol. 40, no. 9, pp. 1065-1067, September, 1991. | |||
| BibTex | x | ||
| @article{ 10.1109/12.83650, author = {N. Yoshida and E. Goto and S. Ichikawa}, title = {Pseudorandom Rounding for Truncated Multipliers}, journal ={IEEE Transactions on Computers}, volume = {40}, number = {9}, issn = {0018-9340}, year = {1991}, pages = {1065-1067}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.83650}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Pseudorandom Rounding for Truncated Multipliers IS - 9 SN - 0018-9340 SP1065 EP1067 EPD - 1065-1067 A1 - N. Yoshida, A1 - E. Goto, A1 - S. Ichikawa, PY - 1991 KW - rounding; truncated multipliers; multiple-precision; floating-point numbers; pseudorandom rounding; multiplications; digital arithmetic. VL - 40 JA - IEEE Transactions on Computers ER - | |||
An economical, unbiased, overflow-free rounding scheme for multiplication of multiple-precision floating-point numbers is proposed. The scheme, called pseudorandom rounding, saves multiplications of lower bits and makes use of statistical properties of bits around the least significant bit of products in order to compensate for truncated parts. The method is deterministic, and inputs are commutable. The validity of the rounding is verified by numerical simulation.
[1] Fairchild Fast Data Book84/85, Portland, Fairchild Camera and Instrument Corp., 1984.
[2] TRW LSI Multipliers Applications Notes, Redondo Beach, TRW LSI Products.
[3] D. E. Knuth,The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Reading, MA: Addison-Wesley, 1981.
[4] J. L. Barlow and E. H. Bareiss, "On roundoff distribution in floating point and logarithmic arithmetic,"Computing, vol. 34, pp. 325-364, 1985.
[5] J. L. Barlow, "Probabilistic error analysis of floating point and CRD arithmetic," Ph.D. dissertation, Northwestern Univ., Evanston, IL, 1981.
[6] D. J. Kuck, D. S. Parker, Jr., and A. H. Sameh, "Analysis of rounding methods in floating-point arithmetic,"IEEE Trans. Comput., vol. C-26, pp. 643-650, July-1977.
[7] J. Bustoz, A. Feldstein, R. Goodman, and S. Linnainmaa, "Improved trailing digits estimates applied to optimal computer arithmetic,"J. ACM, vol. 26, pp. 716-730, Oct. 1979.
[8] A. H. Taub, Ed.John von Neumann Collected Works, Vol. 5. New York: Macmillan, 1963, p. 57.
[9] N. Inada, E. Goto, and T. Soma, "Fortran and Lisp Accelerators--FLATS2," inProc. 2nd RIKEN Symp. Josephson Electron., Wakoshi, Mar. 1985, pp. 120-130.