L12 : Lower Power High Level Synthesis(3)

1999. 8

성균관대학교 조 준 동 교수 http://vada.skku.ac.kr

Matrix-vector product algorithm

Retiming

Flip- flop insertion to minimize hazard activity moving a flip- flop in a circuit

Exploiting spatial locality for interconnect power reduction

Global

Local

Adder1

Adder2

Balancing maximal time-sharing and fully-parallel implementation

A fourth-order parallel-form

IIR filter

(a) Local assignment

(2 global transfers), (b) Non-local assignment

(20 global transfers)

Retiming/pipelining for Critical path

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Minimal Area Time-multiplexed Solution

(meeting the throughput constraint)

Retiming and pipelining

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"Fastest" Solution

Supply voltage can be reduced keeping throughput fixed.

Effective Resource Utilization

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Can reducd interconnect capacitance.

Hazard propagation elimination by clocked sampling

By sampling a steady state signal at a register input, no more glitches are propagated through the nextcombinational logics.

Regularity

• Common patterns enable the design of less complex architecture and therefore simpler interconnect structure (muxes, buffers, and buses). Regular designs often have less control hardware.

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MUX

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Module Selection

• Select the clock period, choose proper hardware modules for all operations(e.g., Wallace or Booth Multiplier), determine where to pipeline (or where to put registers), such that a minimal hardware cost is obtained under given timing and throughput constraints.

• Full pipelining: ineffective clock period mismatches between the execution times of the operators. performing operations in sequence without immediate buffering can result in a reduction of the critical path.

• Clustering operations into non-pipelining hardware modules, the reusability of these modules over the complete computational graph be maximized.

• During clustering, more expensive but faster hardware may be swapped in for operations on the critical path if the clustering violates timing constraints

Estimation• Estimate min and max bounds on the required resources to

– delimit the design space min bounds to serve as an initial solution

– serve as entries in a resource utilization table which guides the transformation, assignment and scheduling operations

• Max bound on execution time is tmax: topological ordering of DFG using ASAP and ALAP

• Minimum bounds on the number of resources for each resource class

Where NRi: the number of resources of class Ri

dRi : the duration of a single operation

ORi : the number of operations

Exploring the Design Space

• Find the minimal area solution constrained to the timing constraints

• By checking the critical paths, it determine if the proposed graph violates the timing constraints. If so, retiming, pipelining and tree height reduction can be applied.

• After acceptable graph is obtained, the resource allocation process is

• initiated.

– change the available hardware (FU's, registers, busses)

– redistribute the time allocation over the sub-graphs

– transform the graph to reduce the hardware requirements.

• Use a rejectionless probabilistic iterative search technique (a variant of Simulated Annealing), where moves are always accepted. This approach reduces computational complexity and gives faster convergence.

Data path Synthesis

Scheduling and Binding• The scheduling task selects the control step, in which a given operation

will happen, i.e., assign each operation to an execution cycle

• Sharing: Bind a resource to more than one operation.– Operations must not execute concurrently.

• Graph scheduled hierachically in a bottom-up fashion

• Power tradeoffs– Shorter schedules enable supply voltage (Vdd) scaling– Schedule directly impacts resource sharing– Energy consumption depends what the previous instruction was– Reordering to minimize the switching on the control path

• Clock selection – Eliminate slacks– Choose optimal system clock period

ASAP Scheduling

• Algorithm • HAL Example

• Algorithm

ALAP Scheduling

• HAL Example

Force Directed Scheduling

Used as priority function. Force is related to concurrency. Sort operations for least force. Mechanical analogy:

Force = constant displacement. constant = operation-type distribution. displacement = change in probability.

Force Directed Scheduling

Example : Operation V6

Force-Directed Scheduling• Algorithm (Paulin)

Force-Directed Scheduling Example• Probability of scheduling operations

into control steps

• Probability of scheduling operations into control steps after operation o3 is scheduled to step s2

• Operator cost for multiplications in a

• Operator cost for multiplications in c

List Scheduling• The scheduled DFG• DFG with mobility labeling (inside <>)

• ready operation list/resource constraint

Static-List Scheduling• DFG

• Partial schedule of five nodes

• Priority list

The final schedule

Divide-and-Conquer to minimize the power consumption

• Decompose a computation into strongly connected components• Any adjacent trivial SCCs are merged into a sub part;• Use pipelining to isolate the sub parts;• For each sub part

– Minimize the number of delays using retiming;

– If (the sub part is linear)• Apply optimal unfolding;

– Else• Apply unfolding after the isolation of nonlinear operations;

• Merge linear sub parts to further optimize;• Schedule merged sub parts to minimize memory usage

Choosing Optimal Clock Period

SCC decomposition stepUsing the standard depth-first search-based algorithm [Tarjan,1972] which has a low order polynomial-time complexity. For any pair of operations A and B within an SCC, there exist both a path from A to B and a path from B to A. The graph formed by all the SCCs is acyclic. Thus, the SCCs can be isolated from each other using pipeline delays, which enables us to optimize each SCC separately.

Idetifying SCC

• The first step of the approach is to identify the computation's strongly connected components,.

Choosing Optimal Clock Period

Supply Voltage Scaling

Lowering Vdd reduces energy, but increase delays

Multiple Supply VoltagesFilter Example

Shut-down 을 이용한 Scheduling: |a-b|

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Loop Scheduling

• Sequential Execution

• Partial loop unrolling

• Loop folding

Loop folding

• Reduce execution delay of a loop.• Pipeline operations inside a loop.

• Overlap execution of operations.• Need a prologue and epilogue.

• Use pipeline scheduling for loop graph model.

DFG Restructuring• DFG2 • DFG2 after redundant operation

insertion

Minimizing the bit transitions for constants during Scheduling

Control Synthesis

•Synthesize circuit that:•Executes scheduled operations.•Provides synchronization.•Supports:

• Iteration.• Branching.• Hierarchy.• Interfaces.

Allocation ◆Bind a resource to more than one operation.

Optimum binding

Example