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17th IEEE Symposium on Computer Arithmetic (ARITH'05)
NBit Unsigned Division via NBit MultiplyAdd
Cape Cod, Massachusetts, USA
June 27June 29
ISBN: 0769523668
ASCII Text  x  
Arch D. Robison, "NBit Unsigned Division via NBit MultiplyAdd," Computer Arithmetic, IEEE Symposium on, pp. 131139, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), 2005.  
BibTex  x  
@article{ 10.1109/ARITH.2005.31, author = {Arch D. Robison}, title = {NBit Unsigned Division via NBit MultiplyAdd}, journal ={Computer Arithmetic, IEEE Symposium on}, volume = {0}, year = {2005}, issn = {10636889}, pages = {131139}, doi = {http://doi.ieeecomputersociety.org/10.1109/ARITH.2005.31}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  Computer Arithmetic, IEEE Symposium on TI  NBit Unsigned Division via NBit MultiplyAdd SN  10636889 SP131 EP139 A1  Arch D. Robison, PY  2005 KW  null VL  0 JA  Computer Arithmetic, IEEE Symposium on ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/ARITH.2005.31
Integer division on modern processors is expensive compared to multiplication. Previous algorithms for performing unsigned division by an invariant divisor, via reciprocal approximation, suffer in the worst case from a common requirement for n + 1 bit multiplication, which typically must be synthesized from nbit multiplication and extra arithmetic operations. This paper presents, and proves, a hybrid of previous algorithms that replaces n + 1 bit multiplication with a single fused multiplyadd operation on nbit operands, thus reducing any nbit unsigned division to the upper n bits of a multiplyadd, followed by a single right shift. An additional benefit is that the prerequisite calculations are simple and fast. On the Itanium® 2 processor, the technique is advantageous for as few as two quotients that share a common runtime divisor.
Citation:
Arch D. Robison, "NBit Unsigned Division via NBit MultiplyAdd," arith, pp.131139, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), 2005
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