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CS184a: Computer Architecture (Structure and Organization)

CS184a: Computer Architecture (Structure and Organization). Day 10: January 31, 2003 Compute 2:. Last Time. LUTs area structure big LUTs vs. small LUTs with interconnect design space optimization. Today. Cascades ALUs PLAs. Last Time. Larger LUTs Less interconnect delay

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CS184a: Computer Architecture (Structure and Organization)

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  1. CS184a:Computer Architecture(Structure and Organization) Day 10: January 31, 2003 Compute 2:

  2. Last Time • LUTs • area • structure • big LUTs vs. small LUTs with interconnect • design space • optimization

  3. Today • Cascades • ALUs • PLAs

  4. Last Time • Larger LUTs • Less interconnect delay • General: Larger compute blocks • Minimize interconnect • Large LUTs • Not efficient for typical logic structure

  5. Different Structure • How can we have “larger” compute nodes (less general interconnect) without paying huge area penalty of large LUTs?

  6. Small LUTs capture structure What structure does a small-LUT-mapped netlist have? Structure in subgraphs

  7. Structure • LUT sequences ubiquitous

  8. Hardwired Logic Blocks Single Output

  9. Hardwired Logic Blocks Two outputs

  10. Delay Model • Tcascade =T(3LUT) + T(mux)

  11. Options

  12. Chung & Rose Study [Chung & Rose, DAC ’92]

  13. Cascade LUT Mappings [Chung & Rose, DAC ’92]

  14. ALU vs. Cascaded LUT?

  15. 4-LUT Cascade ALU

  16. ALU vs. LUT ? • Compare/contrast • ALU • Only subset of ops available • Denser coding for those ops • Smaller • …but interconnect dominates

  17. Parallel Prefix LUT Cascade? • Can compute LUT cascade in O(log(N)) time? • Can compute mux cascade using parallel prefix? • Can make mux cascade associative?

  18. Parallel Prefix Mux cascade • How can mux transform Smux-out? • A=0, B=0  mux-out=0 • A=1, B=1  mux-out=1 • A=0, B=1  mux-out=S • A=1, B=0  mux-out=/S

  19. Parallel Prefix Mux cascade • How can mux transform Smux-out? • A=0, B=0  mux-out=0 Stop= S • A=1, B=1  mux-out=1 Generate= G • A=0, B=1  mux-out=S Buffer = B • A=1, B=0  mux-out=/S Invert = I

  20. Parallel Prefix Mux cascade • How can 2 muxes transform input? • Can I compute transform from 1 mux transforms?

  21. SSS SGG SBS SIG Two-mux transforms • GSS • GGG • GBG • GIS • BSS • BGG • BBB • BII • ISS • IGG • IBI • IIB

  22. Generalizing mux-cascade • How can N muxes transform the input? • Is mux transform composition associative?

  23. Parallel Prefix Mux-cascade

  24. Commercial Devices

  25. Xilinx XC4000 CLB

  26. Xilinx Virtex-II

  27. Altera Stratix

  28. Programmable Array Logic(PLAs)

  29. PLA • Directly implement flat (two-level) logic • O=a*b*c*d + !a*b*!d + b*!c*d • Exploit substrate properties allow wired-OR

  30. Wired-or • Connect series of inputs to wire • Any of the inputs can drive the wire high

  31. Wired-or • Implementation with Transistors

  32. Programmable Wired-or • Use some memory function to programmable connect (disconnect) wires to OR • Fuse:

  33. Programmable Wired-or • Gate-memory model

  34. Diagram Wired-or

  35. Wired-or array • Build into array • Compute many different or functions from set of inputs

  36. Combined or-arrays to PLA • Combine two or (nor) arrays to produce PLA (and-or array) Programmable Logic Array

  37. PLA • Can implement each and on single line in first array • Can implement each or on single line in second array

  38. PLA • Efficiency questions: • Each and/or is linear in total number of potential inputs (not actual) • How many product terms between arrays?

  39. PLAs • Fast Implementations for large ANDs or Ors • Number of P-terms can be exponential in number of input bits • most complicated functions • not exponential for many functions • Can use arrays of small PLAs • to exploit structure • like we saw arrays of small memories last time

  40. PLA Product Terms • Can be exponential in number of inputs • E.g. n-input xor (parity function) • When flatten to two-level logic, requires exponential product terms • a*!b+!a*b • a*!b*!c+!a*b*!c+!a*!b*c+a*b*c • …and shows up in important functions • Like addition…

  41. PLAs vs. LUTs? • Look at Inputs, Outputs, P-Terms • minimum area (one study, see paper) • K=10, N=12, M=3 • A(PLA 10,12,3) comparable to 4-LUT? • 80-130%? • 300% on ECC (structure LUT can exploit) • Delay? • Claim 40% fewer logic levels (4-LUT) • (general interconnect crossings) [Kouloheris & El Gamal/CICC’92]

  42. PLA

  43. PLA and Memory

  44. PLA and PAL PAL = Programmable Array Logic

  45. Conventional/Commercial FPGA Altera 9K (from databook)

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