Title: On Metrics for Comparing Routability Estimation Methods for FPGAs
1On Metrics for Comparing Routability Estimation
Methods for FPGAs
- Parivallal Kannan, Shankar Balachandran, Dinesh
Bhatia - Center for Integrated Circuits and Systems
- The University of Texas at Dallas
- http//www.cics.utdallas.edu/
Speaker
2Outline
- Introduction
- Routability Estimation
- fGREP and enhancements to fGREP (FPL 2001)
- RISA (ICCAD 94)
- Lous Method and enhancements (ISPD 2001)
- Rents Rule based method (TCAD 2002)
- Proposed Estimation Quality Metric
- Experimentation and Results
- Conclusion
3Introduction
- Interconnect Estimation
- Estimate the routing resource requirement of
adesign before actually routing it - FPGA device size is ever increasing gtgt1 mil gates
- Design Cycles are lengthy
- Multiple iterations of Placement and Routing
- Prediction of wiring requirements duringphysical
design is essential for - Fast design closure
- Performance
- Maximum Area utilization
4Introduction (contd.)
- FPGA design flow
- Routing resources are fixed
- Routability Estimation is more appropriate term
- If device has enough routing resources to
satisfy an estimate, then the design is routable - Useful Parameters
- Peak Routing Demand (Global)
- Routing Demand Distribution (Local)
5Estimation Methods
- Rents Rule
- Empirical relationship between gates and pins
- RISA (ICCAD 94)
- empirical method based on a wiring distribution
map - fGREP (FPL 2001)
- based on the concept of routing flexibility
- Lous Method (ISPD 2001)
- based on the ratio of number paths using a
routing elementto total number of paths - Other Methods
- Stochastic models (Brown et.al.), BDD based
method(Wood et.al.)
6Estimation methods for FPGAs
- fGREP
- Designed for FPGAs
- Yang et.al (TCAD 2002)
- Rents rule based method for ASIC design flows
- Easily adaptable to FPGAs for estimating
peakrouting demand - Regional Estimation model may not be
applicableto FPGAs - RISA
- Easily adaptable to FPGAs. VPR has an
implementation - Lous method
- Easily adaptable to FPGAs (VLSI 2002)
7Requirements of a Good Routability Estimation
Method
- Accurate
- Estimates should conform to standard routers
- Reliable
- Should produce comparable errors over a large set
of benchmarks - Fast
- to be used inside other PD Methods
- Usable
- Global and Local results
- Generic
- Architecture Independence
8Preliminaries
- Generic island style FPGA architecture (VPR
style) - Logic blocks (L), Connection Boxes (C), Switch
Boxes (S) - Routing Graph of FPGA G(V,E)
- V is the set of routing channels
- E is the set of switch boxes
9fGREP
- New formulation for estimating routing demand for
aplaced circuit. - Based on the concept of routing flexibility
- Flexibility is the number of alternatives
available to reacha nets terminal - Directly operates on multi-terminal nets
- Estimates match very closely the actual routes
produced by a detailed router (VPR, Pathfinder) - Very Fast implementation is possible. Easy
deployment. - Generic - can be adapted for any FPGA
architectureand ASIC design flows
10fGREP - Definitions
- A net nk?N, is a set of terminals, Tk?V
- Every terminal tik?Tk, exacts a routing demand
called terminal demand on all elements in the
net bounding box - Terminal Demand on a routing element at a
distance lq from a terminal tik vi, is
proportional to the total number of routing
elements at the same distance - Distance is measured on the breadth-first search
tree from a terminal - The set of such equidistant elements form a
level-set,
11fGREP Definitions (cont.)
- The terminal demand due to vi on vj is then,
- All the terminals of a net collectively produce a
Net Demand. This is the terminal demand due
to the terminal with the lowest distance from the
routing element vj, - Final routing demand on an element due to all the
nets in the netlist is,
12fGREP Illustration
Level-Set Illustration
Terminal and Net Demand Illustration
13fGREP Enhancements
- fGREP runtimes are high for large high fanout
nets - fGREP runtime is proportional to E x T, where
Eis the set of routing elements in the net
bounding box and T, the set of terminals of the
net - Major speed-up possible by limiting the search to
within the Zones of Influence of each terminal - Within a zone, the net-demands are due to a
single terminal - The zones are the Voronoi regions of the
terminals, within the net-bounding box
14fGREP Enhancements (contd.)
- Problems with zoning
- fGREP needs the cardinality of the level-set, to
calculate the demands - Zoning will result in clipping and fragmenting of
the search wave-front - Terminal T1, wave-front is fragmented to W1, W2,
W3, W4 - Simple Solution
- Maintain complete wave-front as long as at-least
one routing-element is within the terminals zone
of influence - Perform search in parallel from all terminals of
a net
- Up-to 30X speedup over fGREP was obtained by
this method.
15RISA Chang (ICCAD 94)
- Empirically determined net-weights q are
applied to all routing elements in a nets
bounding box - For a M pin net, the net-weight q is calculated
froma Wiring Distribution Map (WDM) - WDM is obtained by adding up and normalizing the
demands due to optimal Steiner trees generated
over K sets ofM random points (K very large) - Mean value of the WDM is the net-weight q of a
M terminal net - Authors provide the values for the net-weights
for 1 ? M ? 50. Values for larger M can be found
by a linear regression process.
16RISA (contd.)
- Expression for the routing demand on a region Ri
(W,L), due toa net nk (net b-box X,Y) with an
overlap of (w,l) is, - For the FPGA architecture, WLwl1. Hence the
demands are, - Total routing demand on a routing-element is then
the sum of each nets routing demand
17Lous Method Lou et.al.(ISPD 2001)
- For a 2-terminal net, analytically calculate the
total number of paths and the number of paths
using a particular routing element - Routing demand on a routing element is the ratio
of the number of paths incident on the element to
the total number of paths - A M terminal net (M gt 2) has to be decomposed
into 2-terminal segments - Authors propose MST or RST decomposition
- Authors dont know how to handle segment
overlaps. They suggest a simple addition of the
demands, where the bounding boxes overlap.
18Lous Method Enhancements
- Most of the error is produced in the regions
where the bounding boxes of the 2-terminal
segments overlap
- We propose a simple solution
- use the Maximum of the demands due to
theoverlapping regions - Up-to 103 better estimates compared to the
original method (compared with a detailed router)
19Rents Rule Yang et.al (TCAD 2002)
- Empirical relationship between number of blocks B
and the number of pins P, - r is the rents exponent
- Tb is the avg number of interconnections per
block - Recursively partition a circuit to get the
cutsets. Find out rents exponent as the slope of
the log-log plot of number of cells and nets in
the partitions. - The Peak Routing Demand is then given by,
20Estimation Quality Metric
- No uniform reporting methods for interconnect
estimation research - RISA reports the method being used in a
placementmethod and reports the congestion
obtained with andwithout using RISA - Yang et.al (TCAD2002) compare peak estimates with
aL-shaped Global router, which is but an
approximationto a router - Lou et.al. (ISPD2001) just report the congestion
map obtained by using Lous method - No comparison with well known detailed/global
routers - Impossible to ascertain the relative merits of
estimation methods - For CAD deployment, the accuracy, reliability and
runtime requirements of estimation methods MUST
be known.
21Est. Quality Metric (contd.)
- Quality Metric should be based on well
knownstate-of-the-art detailed routers and be
easily reproduced - PathFinder (FPGA95), available with VPR
- Free for research and source code available
- Or at-least use a standard commercial router
- Four parameters as adequate quality metrics
- Peak Demand Error (W)
- Mean of regional errors (?)
- Standard deviation of the regional errors (?)
- Runtimes on standard benchmarks (t)
22Est. Quality Metric (contd.)
- Peak Estimation Error
- quick Figure of Merit for the global estimation
quality - Mean of Regional Estimation Errors
- Correlation of local estimates
- Standard Deviation of Regional Estimation Errors
- quick Figure of Merit for the distribution of
local estimation errors - Runtimes
- duh !
23Results - Peak Demand Runtime
24Results Mean and Std Deviation of Errors
25Results - Illustration
- fGREP2 is the most reliable
- RISA is the fastest, followed by fGREP2
26Conclusion
- Implemented all the routability estimation
methods - Proposed enhancements to fGREP andLous method,
resulting in significantlybetter results - Proposed a simple yet effective Estimation
Quality Metric - Showed that RISA is the fastest while fGREP is
the most accurate and reliable.
27Thank You !