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Generation of Optimal Bit-Width Topology of Fast Hybrid Adder in a Parallel Multiplier. Sabyasachi Das Synplicity Inc. Sunil P. Khatri Texas A&M University (sunilkhatri@tamu.edu). Presented by David Pan, UT Austin. What is a Multiplier?. IC block that perform multiplication operation

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generation of optimal bit width topology of fast hybrid adder in a parallel multiplier

Generation of Optimal Bit-Width Topology of Fast Hybrid Adder in a Parallel Multiplier

Sabyasachi Das

Synplicity Inc.

Sunil P. Khatri

Texas A&M University

(sunilkhatri@tamu.edu)

Presented by

David Pan, UT Austin

what is a multiplier
What is a Multiplier?
  • IC block that perform multiplication operation
  • Well-known logic architectures
  • Computationally-intensive
  • Wide usage in DSP, Graphics, Microprocessors
structure of multiplier
Structure of Multiplier

Inputs

  • Multiplier block consists of 3 parts (written in the order of data-flow)
    • Partial Product Generator (PPGen)
    • Partial Product Reduction Tree (PPRT)
    • Final Carry-Propagation Adder (CPA)

Partial Product

Generator (PPGen)

Partial Product

Reduction Tree

(PPRT)

Final Carry

Propagation

Adder (CPA)

Output

final adder in a multiplier
Final Adder in a Multiplier
  • Frequently used adder architectures
    • Ripple-Carry
      • Area-efficient, but slow
      • Timing-efficient if inputs have skewed arrival time
    • Parallel-Prefix architecture (Brent-Kung, Kogge-Stone)
      • Faster architecture
      • Requires more area
    • Carry-Select
      • Large area overhead (often >100%)
      • Better delay if Cin signal arrives late.
3 stage hybrid adder
3-stage Hybrid Adder
  • Multipliers exhibit a typical arrival time pattern (in the input of the CPA)
  • Hybrid adder produces best result for Multipliers
  • This outperforms all stand-alone architectures

Stelling et al., “Design Strategies for optimal hybrid final adders in a parallel

multiplier”, In The Journal of VLSI Signal Processing, 1996

3 stage hybrid adder6

wrpl

wbk

wcs

wrpl

wbk

wcs

SubAdder1

(Ripple)

SubAdder2

(Brent-Kung)

SubAdder3

(Carry-Select)

wrpl

wbk

wcs

3-Stage Hybrid Adder

There are many possible configurations (w1, w2and w3).

Exhaustive exploration is not feasible (huge runtime)

How to identify the best configuration?

identification of optimal topology
Identification of Optimal Topology
  • Width of the Ripple adder
    • At every bit (i), compute T(Ci+1) and check if
      • T(Ci+1) ≤ T(ai+1) or
      • T(Ci+1) ≤ T(bi+1)
    • If check passes, wrpl = i+1
    • Else continue checking until 3 consecutive bits fail the check (Hill Climbing)
    • Return the value i as the Ripple Adder width
delay of the hybrid adder
Delay of the Hybrid Adder

wrpl

wbk

wcs

wrpl

wbk

wcs

SubAdder1

(Ripple)

SubAdder2

(Brent-Kung)

SubAdder3

(Carry-Select)

wrpl

wbk

wcs

Ts3 + Dmx

Tco2 + Dmx

Ts2

Thybrid =Max (Ts2, (Tco2+Dmx), (Ts3+Dmx))

identification of optimal topology9
Identification of Optimal Topology
  • Width of the BK and Carry-Select Adders
    • Initial Configuration
      • wbk = 2p, where p= log2 (n – wrpl)
      • wcs = n – wbk – wrpl
      • Example: If n=32 and wrpl=7 then wbk=16 and wcs=9
    • Iterative approach
    • Estimate delay of a configuration and explore in the appropriate direction (similar to Binary Search)
results
Results
  • For different adder widths, our approach always found best configuration in very short runtime.
  • Runtime example: for a 32-bit Adder,
    • Trying all possible configurations (561) takes 16-23 hours of runtime
    • Our approach takes 4-18 minutes of runtime and always computes the best configuration.
results11
Results
  • Now, it is feasible to use this powerful hybrid-adder architecture during synthesis (~12% faster adder).