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ICECS 2010

The 17th IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010, Athens, Greece. ICECS 2010. RNS multi-voltage low-power multiply-add unit. I. Kouretas and V. Paliouras Electrical and Computer Engineering Dept., University of Patras, GREECE. Outline.

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ICECS 2010

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  1. The 17th IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010, Athens, Greece ICECS 2010 RNS multi-voltage low-power multiply-add unit I. Kouretas and V. Paliouras Electrical and Computer Engineering Dept., University of Patras, GREECE

  2. Outline • Review of RNS basics • Architecture of RNS-based systems • Multi-Vdd RNS architecture • Structure of processing units • Relevance to RNS • Results • Conclusions ICECS 2010, Athens, Greece

  3. Low-power through alternative number representations • Sign-magnitude versus two’s-complement • Depends on data (signal) statistics • Logarithmic number system • Choice of representation parameters • V. Paliouras, T. Stouraitis, “Low-power properties of logarithmic number system,” IEEE Symposium on Computer Arithmetic, 2001. • Residue representations • Numerical properties of RNS • Inherently parallel structure T. Stouraitis, V. Paliouras, “Considering the alternatives in low power design,” IEEE Circuits and Devices, 2001. ICECS 2010, Athens, Greece

  4. RNS basics • RNS maps an integer X to a N-tuple of residues xi. xi =Xmodmiandxiis called thei-th residue. • miis a member of a set of pair-wise co-prime integers called base. • mi is called modulo. • Dynamic range: ICECS 2010, Athens, Greece

  5. RNS architecture vs binary architecture operands results operands results • Data is processed in L parallel independent channels • Benefit: ni << n ICECS 2010, Athens, Greece

  6. Remarks on RNS architecture operands results • The conversion issue • Forward and inverse • Implementation of moduli channels is not identical • There are fast channels and slow channels ICECS 2010, Athens, Greece

  7. RNS advantages / disadvantages • Advantages • Parallel multiplication or addition • Fault tolerance • Reduced power dissipation in filters • Disadvantages • Difficult comparisons • Overflow detection • Sign detection • Division • Scaling / Rounding / Truncation ICECS 2010, Athens, Greece

  8. RNS multi-VDD architecture results operands • p is the number of moduli channels • Power is quadratically related to voltage • Distiguished moduli channels with Vdd(H) and Vdd(L) • Benefit: Easy to implement ICECS 2010, Athens, Greece

  9. Employed RNS base Base used in this study: 30-bits dynamic range • Cases of common choices in the literature ICECS 2010, Athens, Greece

  10. Employed RNS architecture ICECS 2010, Athens, Greece

  11. Architectures of multiply adders ICECS 2010, Athens, Greece

  12. Multi-voltage areas ICECS 2010, Athens, Greece

  13. Synthesis tool • Synopsys dc_shell –topographical mode • Universal Power Format (UPF) mode is used • Net complexity is included • Level shifters complexity is icluded • Vdd(H)=1.2V • Vdd)L)=1.0V ICECS 2010, Athens, Greece

  14. Configuration script • Synopsys UPF generator tool set domain TOP set primary_power {TOP} HIGH_VDD 1.2 set level_shifter_strategy{TOP} fir_rns5_ls_strategy1 set level_shifter{fir_rns5_ls_strategy1} - - self lappend domain LOW set elements {LOW} channel_modulo_2nm1/mac1 channel_modulo_2nm1/mac2 channel_modulo_2np1 channel_modulo_2n flip1 flip2 flip3 flip4 flip5 flip6 set primary_power {LOW} LOW_VDD 1.0 lappend domain HIGH set elements {HIGH} channel_modulo_2nm1/mac3 f_convp1X f_convp1A f_convm1X31 f_convm1A31 f_convm1X63 f_convm1A63 f_convm1X127 back_converter f_convm1A127 set primary_power {HIGH} HIGH_VDD 1.2 set create_pst true ICECS 2010, Athens, Greece

  15. UPF map ICECS 2010, Athens, Greece

  16. Synthesis result ICECS 2010, Athens, Greece

  17. Results 20.5% and 17.8% power savings ICECS 2010, Athens, Greece

  18. Conclusions • Multi-Vdd low power technique is suitable for RNS systems. • Application of multi-Vdd further reduces power dissipation in RNS systems. • High and low Vdd channels can be easily determined. • Further investigation on multi-Vdd RNS systems is required ICECS 2010, Athens, Greece

  19. The End Thank you for your attention! ICECS 2010, Athens, Greece

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