Timing driven placement for heterogeneous fpga
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Timing-Driven Placement for Heterogeneous FPGA. Bo Hu Velogix Inc. ICCAD 06. Outline. Introduction Problem Multi-layer Density System Timing-Driven Placement Experiments Conclusions. Introduction.

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  • Introduction

  • Problem

  • Multi-layer Density System

  • Timing-Driven Placement

  • Experiments

  • Conclusions


  • Traditional homogeneous FPGA is mainly based on programmable Look-Up tables. Its logic density and performance are usually inferior to ASIC.

  • Nowadays more ASIC-like dedicated functional blocks are integrated in heterogeneous FPGA.

  • The overall density and performance disadvantages are mitigated in modern FPGAs.


  • A simplified example of a heterogeneous FPGA.

It consists of two-dimension array of Basic Process Unit(BPU).

Each BPU contains a two-dimension array of LUTs, a computing unit(CU) and a memory block.


  • Given a netlist of design components, the task of a timing-driven placer is to assign components(single LUT or a complex functional block) into the proper locations on the FPGA chip.

  • The input to an analytical placer are a graph representing the design netlist and a region specifying where the netlist should be placed.

  • Each node in the graph is assigned a geometric shape.

  • Handling non-overlapping requirement is through density D(x,y). Since D(x,y) is a two-dimension function, we call it a single-layer density system.


  • Suppose that the design to be placed consists of only CUs and LUTs.

Large CU geometric shape forms blockage for memory blocks and LUTs.


Small CU geometric shape cause congestion.

A group of CU components might be closely located in some local region where there are not enough CU resources available.


  • In general, Computing Units and Memory Blocks have much more sparse distribution than LUTs.

  • A single density layer cannot satisfy the distribution requirements for different architectural resources simultaneously.

  • Create one density layer for each architectural resource: Multi-layer density system.

Multi layer density system
Multi-layer Density System

  • A computational block(CB) is a pre-designed functional block implemented using the resources available on the chip. The example CB shown below consists of 3 CUs, 3 memory blocks and 12 LUTs relatively placed within a 2x2 BPU region.

Multi layer density system1
Multi-layer Density System

  • Before a node is mapped to a density layer, we need to first determine its geometric shape.

  • Complex shape for CU density layer.

Multi layer density system2
Multi-layer Density System

  • Complex shape for memory block density layer.

Multi layer density system3
Multi-layer Density System

  • Complex shape for LUT density layer.

Multi layer density system4
Multi-layer Density System

  • With the new multi-layer density system, a heterogeneous placement task is translated to a set of homogeneous ones, with each of them being handled at a different density layer.

Timing driven placement
Timing-Driven Placement

  • Expansion Basics

  • Based on fixed-point addition technique.

  • In analytical placement formulation, nodes tend to cluster to each other due to intrinsic attracting forces induced by connections.

  • A connection with larger weight and longer length induces stronger intrinsic force.

  • Fixed-points are used to apply additional attracting forces on nodes and work against intrinsic ones in order to pull the nodes away from high density area.

  • The placer based on expansion consists of a sequence of expansion iterations. It stops when density distribution satisfies preset criteria.

Timing driven placement1
Timing-Driven Placement

  • Density

d(b): density at bin b.

A(b,n): the intersection area between b and node n.

A(b): the area of bin b.

Timing optimization
Timing optimization

Wp[ j ] and Wp[ j-1 ] is the weight for connection p at jth and jth-1 expansion.

f[ j ] is the adjustment factor at jth expansion.

Timing optimization1
Timing optimization

f0[ j ] : the preset maximum adjustment factor at jth iteration. f0[ 0]=1 and gradually approaches to zero.

Sp : timing slack on connection p.

Sworst : the worst slack.

ε : a preset value used to decide whether a connection is critical.

lp : the current length of connection p.

lpmin and lpmax : the minmum and maxmum length of p.


  • Multi-Layer density system for heterogeneous FPGA placement.

  • The timing-driven placement algorithm can handle complex placement requirements inherent in heterogeneous FPGAs.