Register-Transfer (RT) Synthesis

Greg Stitt

ECE Department

University of Florida

Introduction Register-transfer (RT) synthesis

Definition: Synthesis from register transfer level (RTL) descriptions

VHDL, Verilog typically describe circuits as connections of RTL components

What are register-transfer level components? Muxes, ALUs, registers, multipliers, etc. One abstraction level above gates

Basically, components you use in most structural descriptions What are other levels?

Transistor level Gate level Register transfer level High level System level Etc.

RT Synthesis Main Steps

Lex/Parsing Analyzes HDL, converts into intermediate representation

Resource Allocation Maps intermediate representation into RT components

Optimizations Logic minimization State minimization State encoding Etc.

Technology Mapping Placement + Routing

Technology Mapping Converts circuit from one technology

(e.g. gates) onto technology used by physical device (e.g. LUTs, CLBs, etc)

CLB CLB CLB CLB

CLBCLB

Placement Input: Technology-mapped circuit

For simplicity, just consider CLBs Technology-mapped circuit consists of “virtual” CLBs and

“virtual” connections FPGA fabric consists of physical CLBs

Simplified Placement Definition: Map “virtual” CLBs onto physical CLBs

I.e. Decide on a location in the FPGA for each virtual CLB

1 2 3 4

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CLB CLB CLB CLB CLB

CLB CLB CLB CLB CLB

CLB CLB CLB CLB CLB

1 2 3 4 CLB

5 CLB 6 CLB CLB

CLB CLB CLB CLB CLB

Technology Mapped Circuit

FPGA Fabric Possible Placement

Routing Input: A set of placed components, and a list of

“virtual” connections Simplified Routing Definition:

Determine how to configure routing resources to implement “virtual” connections

1 2 3 4 CLB

5 CLB 6 CLB CLB

CLB CLB CLB CLB CLB

1 2 3 4

65

Physical CLBs not connected – must configure routing resources to implement these connections:

Placement+Routing (PAR) Placement and routing highly dependent

Placement affects how well circuit can be routed Example:

1 2 3 4

65

1 2 3 4 CLB

5 CLB 6 CLB CLB

CLB CLB CLB CLB CLB

6 3 CLB 1 CLB

CLB CLB 4 CLB CLB

2 CLB CLB CLB 5

Placement 1 Placement 2

Clearly, placement 1 is easier to route

Placement+Routing (PAR) Goals:

1) Make sure circuit can be implemented on fabric Trivial for placement, difficult for routing Bad placement may make circuit unroutable

2) Minimize delay of critical path Critical path is the longest register to register delay Important - Determines clock speed of circuit

Why is placement and routing important? Bad PAR = slow circuit

Even worse, BAD PAR = no circuit

1 2 3 4 CLB

5 CLB 6 CLB CLB

CLB CLB CLB CLB CLB

6 3 CLB 1 CLB

CLB CLB 4 CLB CLB

2 CLB CLB CLB 5

Even if routing is possible, placement 2 likely to have longer wires – slower clock

Placement 2Placement 1

Placement Problem: Find a placement for each CLB, such that

routing can maximize clock speed Challenges:

1) Huge solution space! Tiny Example: Fabric = 100 physical CLBs, Circuit = 10 “virtual”

CLBs Possibilities = 100! / 90! = 6.2 * 1019 And, that is for a tiny fabric and tiny circuit!!!!!!!!!!! Guess what … placement is NP-Complete

2) How to know how good the routing will be? One (im)possibility - perform routing for each possible placement

Tiny example, cont. - assume same number of routing possibilities as placement possibilities

6.2 * 1019 * 6.2 * 1019 = A BIG NUMBER! Routing is also NP-complete

Cleary, placement needs to estimate quality of routing Estimate known as a cost function

Cost Function Examples Example: average wire length

Motivation: short wires faster than long wires

Not perfect - many short wires not on critical path may lead to inaccuracy

i.e. critical path may still be long despite short average wire length

How to determine wire length? Without routing, don’t know length Possibilities:

1) Euclidian distance - measure straight line distance between CLBs

Ignores how wire would be routed (can’t route diagonals)

2) Manhattan distance - shortest “zig-zag” distance

Includes bends between CLBs

CLB CLB CLB

CLB CLB CLB

CLB CLB CLB

CLB CLB CLB

CLB CLB CLB

CLB CLB CLB

Euclidian Distance

Manhattan Distance

Placement Techniques Placement is an NP-complete optimization problem

Many possible placements, we want the best one What does this suggest for a solution? Remember last lecture!

1) Branch and bound Likely not feasible

2) Map to other NP-complete problem - use heuristic for that problem

3) Use general optimization heuristics Simulated annealing (very common) Hill climbing

How to use general optimization heuristics? Cost function represents quality of placement Neighboring solution – try new location for a “virtual” CLB, swap 2

CLBs, etc.

Placement Techniques Also common to map placement to other NP-

complete problems Example: Min-cut problem

Background: Given a graph, a cut is a set of edges that divides the graph into two (or more) groups

Min-cut problem definition: Find the minimum cut size for a given graph

Similar to graph bipartitioning problemCutsize = 5 Cutsize = 3

Placement Techniques How can graph bipartitioning/min-cut be used

for placement? Graph: Nodes are CLBs, Edges are wires Partition divides FPGA into sections

Goal: minimize communication between sections

Bipartitioning attempts to reduce routing “congestion” i.e. Cost function is cut size

We can use common heuristic for graph bipartitioning Kernighan-Lin (KL) Heuristic

Placement Techniques KLFM Heuristic (Kernighan-Lin Fiduccia-Mattheyses) Basic Idea:

Start with initial partition Iteratively improves cutsize

Cutsize is number of edges between partitions Moves one node at a time

Node that gives greatest reduction or least degradation Lock node after moving Continue moving nodes until all locked or size constraints

are violated Find best partitioning, unlock all nodes Repeat until no improvement found

KLFM Algorithm

Initial Partition

Cutsize = 5

Size = 3 Size = 3Maximum Size = 4

KLFM Algorithm

Cutsize = 3

Size = 4 Size = 2Maximum Size = 4

KLFM Algorithm

Cutsize = 2

Size = 3 Size = 3Maximum Size = 4

KLFM Algorithm

Cutsize = 2

Size = 2 Size = 4Maximum Size = 4

KLFM Algorithm

Cutsize = 4

Size = 3 Size = 3Maximum Size = 4

KLFM Algorithm

Cutsize = 4

Size = 2 Size = 4Maximum Size = 4

KLFM Algorithm

Cutsize = 5

Size = 3 Size = 3Maximum Size = 4

KLFM Algorithm

Cutsize = 2

Size = 3 Size = 3

Backtrack to minimum cut size, unlock nodes, and repeat

Circuit Partitioning How does a partition help us place CLBs?

Apply bipartitioning hierarchically – circuit partitioning

Basic idea 1) Initially divide FPGA into 2 sections

Execute bipartitioning to determine which section “virtual” CLBs get mapped into

2) Divide each section into 2 subsections Execute bipartitioning to determine which subsection

“virtual” CLBs get mapped into 3) Divided each subsection into 2 subsubsections And so on

Placement Summary Definition: Map “virtual” CLB onto physical CLBs,

such that routing can maximize clock frequency Need way of estimating routing quality – cost function

Wire length Typically leads to shorter wires, but may cause congestion

Cutsize Helps with congestion, but may result in long wires

Existing approaches are typically a combination NP-Complete Optimization Problem

Can use many existing heuristics Simulated annealing, KL are common

Routing Definition: Given a placement and a set of “virtual” connections,

implement connections using routing resources such that clock speed is maximized

i.e Figure out how to configure connection boxes and switch boxes in most efficient way

Clearly another optimization problem Huge number of possible routing solutions, we want the best one

Routing is NP-Complete What does this suggest?

1) Branch and bound Likely not feasible

2) Map to other NP-complete problem - use heuristic for that problem 3) Use general optimization heuristics

Simulated annealing Hill climbing Genetic algorithms Etc.

Routing: Background Routing algorithms sometimes performed in 2 stages

Global and detail routing Global routing determines channels to be used for each

connection (“net”) Ignores low-level details of C/S boxes Focuses on finding a short paths that minimize congestion

Detail routing determines low-level connections used by each C/S box

Uses coarse route provided by global router Analogy: Driving directions

Global routing: Take 34th to Archer to 13th, etc. Detailed routing: Get in the right lane, wait at the light, turn left,

change into the right lane, etc.

Maze Routing Input:

Grid structure representing routing resources Each box represents a terminal or a routing resource

Set of source and destination terminals Defines end points of each connection

Problem definition: Find the shortest route for each pair of source and destination terminals

Each box is either a terminal or a routing resource

Maze Routing Heuristic:

1) Expansion – find shortest path from src to dest that avoids used resources

Done using breadth first search Essentially determines shortest distance of each box

from the source, until the dest is found

Terminals

1

1

1

12

2

2

2

2

2

Maze Routing Heuristic, Cont.:

2) Traceback – Follow path from dest with decreasing labels (shortest path to src)

May be multiple paths 3) Repeat 1+2 for each net

Really good animation at: http://foghorn.cadlab.lafayette.edu/MazeRouter.html

Maze Routing Another example Main Weakness:

Quality of routing depends on ordering of nets How to determine best ordering?

Too many possibilities, generally not feasible

Routing blue before purple gives shorter wire length

Pathfinder

1

1

1

1

1

1

11

1

Pathfinder [Ebeling, et al., 1995] Introduced negotiated congestion

Ordering independent During each routing iteration, route nets

using shortest path Allows overuse (congestion) of routing

resources If congestion exists (illegal routing)

Update cost of congested resources based on the amount of overuse

Rip-up all routes and reroute all nets

2

congestion

2

Versatile Place&Route (VPR) Versatile Place&Route (VPR) [Betz] takes as input a

description of the fabric Describe routing resources, etc. Could potentially be used for many FPGAs – “versatile”

2 variations of VPR Routability driven – find an implementation that uses the

fewest routing resources Timing driven – maximize clock speed

Placement/routing technique Modified version of Pathfinder Uses cost function based on fabric description Details: http://www.eecg.toronto.edu/~vaughn/vpr/vpr.html

Summary

RT Synthesis creates circuit from RT-level description 3 important steps – Technology mapping, Placement, Routing

Technology mapping converts gate-level (or other level) representation to CLBs, DSPs, etc.

Placement finds a physical CLB for each mapped CLB Routing configures routing resources to connect CLBs Placement and Routing are NP-Complete

Need heuristics Placement – Simulated annealing, KL, etc. Routing – Maze, Pathfinder, VPR