High-Level Synthesis-II
Virendra Singh
Indian Institute of Science
Bangalore
[email protected]
IEP on Digital System Synthesis @ IIT Kanpur
Architectural Synthesis
Architectural Level Abstraction
Datapath
Controller
Architectural Synthesis
• Constructing the macroscopic structure of a
digital circuit starting from behavioural models
that can be captured from Data flow or
Sequencing Graph
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Architectural Synthesis
Objective
• Area
• Cycle time
• Latency
• Throughput
Worst case bound
Evaluation
Architectural Exploration
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Architectural Synthesis
Architectural synthesis tool can select an appropriate
design point according to some user specific criterion
and construct corresponding user specific Datapath
and Controller
Circuit Specification for Architectural Synthesis
• Behavioural circuit model
• Details about resources being used and constraints
•Capture by Sequencing Graph
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Architectural Synthesis
Resources
• Functional Resources
• Primitive Resources
• Application Specific Resources
• Memory Resources
• Interface Resources
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Architectural Synthesis
Circuit Specification
• Sequencing Graph
• A set of functional resources, fully characterized in
terms of area and execution delay
• A set of constraints
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Architectural Synthesis
Computation: Differential Equation Solver
xl = x + dx
ul = u – (3*x*u*dx) – (3*y*dx)
c = xl < a
Data Flow Graph (DFG): represent operation and data
dependencies
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Data Flow Graph
x
u
y
3
dx
u
3
1
2
*
*
3
6
*
dx
*
7
*
*
yl
5
10
a
xl
+
-
dx
+
8
y
u
4
x
dx
9
<
11
c
ul
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Sequencing Graph
NOP
1
2
*
*
3
*
4
7
*
*
*
8
+
10
+
9
<
11
5
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6
-
NOP
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Hierarchical Sequencing
Graph
NOP
a.0
a.1
*
+
a.2
b.0
a.4
a.3
NOP
CALL
*
NOP
a.n
+
b.1
NOP
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b.2
*
b.n
10
Architectural Synthesis
Architectural Synthesis and optimization
consistes of two stages
1. Placing the operation in time and in space,
i.e., determining their time interval of
execution and binding to resources
2. Determining detailed interconnection of the
datapath and the logic-level specifications of
the control unit
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Temporal Domain:
Scheduling
Delay D = {di; i = 0,1, 2, ….. n}
Start time T ={ti; i= 0, 1, …., n)
Scheduling: Task of determining the start timing,
subject to preceding constraints specified by
sequencing graph
Latency λ = tn – t0
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Temporal Domain:
Scheduling
A scheduled sequencing graph is a vertex-weighted
sequencing graph, where each vertex is labeled by its
start time
Operation
Start time
V1,V2, v6,v8, v10
1
V3, v7, v9,v11
2
V4
3
V5
4
 Chaining
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Temporal Domain:
Scheduling
NOP
1
TIME 1
TIME 2
2
*
*
3
*
4
TIME 3
7
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*
*
*
8
+
10
+
9
<
11
5
TIME 4
6
-
NOP
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Temporal Domain:
Scheduling
NOP
TIME 1
TIME 2
TIME 3
TIME 4
TIME 5
TIME 6
*1
* 2
*
*
+
10
<
11
-
4
3
6
* 7
*
-
8
+
TIME 7
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NOP
5
9
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Spatial Domain: Binding
A fundamental concept that relates operation to
resources is binding
• Resource types
• Resource sharing
Simple case of binding is a dedicated resources
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Spatial Domain: Binding
β(v1) = (1,1)
β(v2) = (1,2)
β(v3) = (1,3)
β(v4) = (2,1)
β(v5) = (2,2)
..
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Spatial Domain: Binding
NOP
1
TIME 1
TIME 2
2
*
*
3
*
4
TIME 3
7
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*
*
*
8
+
10
+
9
<
11
5
TIME 4
6
-
NOP
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Spatial Domain: Binding
A necessary condition for resource binding to produce
a valid circuit implementation is that operation
corresponding to the shared resource do not execute
concurrently
A resource binding can be represented by a labeled
hyper-graph, where the vertex set V represents
operations and the edge set Eβ represents the binding
of the operation to the resources
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Spatial Domain: Binding
NOP
(1,1)
1
TIME 1
TIME 2
TIME 3
(1,2)
(1,3)
2
*
*
3
(2,1)
*
4
7
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*
*
*
8
+
10
+
9
<
11
5
TIME 4
6
(2,2)
(1,4)
-
NOP
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Spatial Domain: Binding
NOP
1
TIME 1
TIME 2
2
*
*
3
*
4
TIME 3
7
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*
*
5
TIME 4
6
0
-
*
8
+
9
+
10
<
11
NOP n
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Sequencing Graph
NOP
1
2
*
*
3
*
4
7
*
*
*
8
+
10
+
9
<
11
5
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6
-
NOP
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Hierarchical Sequencing
Graph
NOP
a.0
(1,1)
a.1
*
+
(2,1)
a.2
b.0
a.4
a.3
(1,2)
NOP
CALL
*
NOP
a.n
+
b.1
NOP
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*
b.n
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Synchronization
0
NOP
a
1
*
SYN
3
2
+
+
NOP n
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Synchronization
0
NOP
NOP
0
a
1
*
a
SYN
SYN
1
*
3
2
+
3
2
+
+
+
NOP n
NOP n
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Synchronization
0
NOP
1
*
a
SYN
+
2
+
3
NOP n
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Area/Performance
Estimation
Accurate area and performance estimation is not an
easy task
Schedule: provides latency
Binding: provides information about the area
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Retiming
+
+
+
Host
δ
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Retiming
7
0
0
Vg
0
7
0
Vf
7
Ve
0
Vh
0
1
0
3
1
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0
Vb
Vc
3
3
1
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Vd
3
1
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Retiming
7
0
0
Vg
0
7
0
Vf
7
Ve
0
Vh
0
1
0
1
3
0
Vb
3
Vc
1
3
Vd
3
1
Delay = 24
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Retiming
1
7
0
0
Vg
0
7
7
Vf
Ve
0
Vh
0
1
0
3
1
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0
Vb
Vc
3
3
0
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3
1
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ASAP Scheduling
NOP
1
TIME 1
TIME 2
2
*
*
3
*
4
TIME 3
7
*
*
*
8
+
10
+
9
<
11
5
TIME 4
6
NOP
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ASAP Scheduling
ASAP(Gs(V,E)){
Schedule v0 by setting t0s = 1;
repeat{
select vertex vi whose predecessors are
all scheduled;
schedule vi by setting tis = max{tjs+ dj}
} untill (vn is scheduled)
return ts
}
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ALAP Scheduling
NOP
1
TIME 1
TIME 2
2
*
*
3
*
4
TIME 3
5
TIME 4
6
*
7
*
-
*
8
+
10
+
9
<
11
NOP
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Scheduling under Timing
Constraints
Scheduling under latency constraints
Absolute constraints on start time
Relative constraints
Relative timing constraints are positive integers
specified for some operation pair vi, vj
A minimum timing constraint lij ≥ 0 requires tj ≥ ti+lij
A maximum timing constraint uij ≤ 0 requires tj ≤ ti+uij
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Constraint Graph
0
NOP
3
Max
1
*
*
Time
4
Time
3
Min
4
2
+
+
NOP n
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Constraint Graph
0
NOP
3
Max
*
*
1
Time
3
2
+
+
0
4
0
Min
3
4
1
*
Time
4
0
NOP
-3
*
2
2
2
4
2
+
NOP n
+
1
1
NOP n
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Relative Scheduling
Scheduling under unbounded delay
The anchors of a constraint graph G(V,E)
consists of the source vertex v0and all vertices
with unbounded delay
Redundant anchor
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Sequencing Graph
0
NOP
a
1
*
SYN
3
2
+
+
NOP n
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Scheduling with Resource
Constraint
Scheduling under resource constraints
• computing area/latency trade-off points
Problems
• Intractable problem
•Area-performance trade-off points are affected
by the other factors - non-resource dominated
circuits
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Scheduling with Resource
Constraint
ILP Formulation
Binary decision variable X = {xil}
1. Start time of each operation is unique
Σl xil = 1
2. Sequencing relations represented by Gs(V,E) must be
satisfied
Σl xil ≥ Σl xjl + dj
3. Resource bound must be met at every schedule step
Σk Σm xim ≤ ak
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ILP Formulation
All operation must
start only once
x0,1 = 1
x1,1 = 1
x2,1 = 1
x3,2 = 1
x4,3 = 1
x5,4 = 1
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x6,1 + x6,2 = 1
x7,2 + x7,3 = 1
x8,1 + x8,2+x8,3 = 1
x9,2 + x9,3+x9,4 = 1
x10,1 + x10,2+x10,3 = 1
x11,2 + x11,3+x11,4 = 1
xn,5 = 1
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ILP Formulation
Constraints – based on sequencing
(more than one starting time for at least one operation)
2 x7,2 + 3 x7,3 – x6,1 – 2 x6,2 – 1 ≥ 0
2 x9,2 + 3 x9,3 + 4 x9,4 – x8,1 – 2 x8,2 – 3 x8,3 – 1 ≥ 0
2 x11,2 + 3 x11,3 + 4 x11,4 – x10,1 – 2 x10,2 – 3 x10,3 – 1 ≥ 0
4 x5,4 – 2 x7,2 – 3 x7,3 – 1 ≥ 0
5 xn,5 – 2 x9,2 – 3 x9,3 – 4 x9,4 – 1 ≥ 0
5 xn,5 – 2 x11,2 – 3 x11,3 – 4 x11,4 – 1 ≥ 0
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ILP Formulation
Resource Constraints
x1,1 + x2,2 + x6,1 + x8,1 ≤ 2
x3,2 + x6,2 + x7,2 + x8,2 ≤ 2
x7,3 + x8,3 ≤ 2
x10,1 ≤ 2
x9,2 + x10,2 + x11,2 ≤ 2
x4,3 + x9,3 + x10,3 + x11,3 ≤ 2
x5,4 + x9,4 +x11,4 ≤ 2
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ILP Formulation
Optimize ΣiΣl l.xil
x6,1 + 2 x6,2 + 3 x7,2 + 3 x7,3 + x8,1 + 2 x8,2 + 3 x8,3
+ 2 x9,2 + 3 x9,3 + 4 x9,4 + x10,1 + 2 x10,2 + 3 x10,3
+ 2 x11,2 + 3 x11,3 + 4 x11,4
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Resource Sharing
Resource sharing: Assignment of resource to
more than one operation
Goal: Reduce area
Resource binding: explicit definition of mapping
between resources and operation
Binding may imply some resources are shared
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Optimum Scheduling
under Resource Constraint
NOP
1
TIME 1
TIME 2
2
*
*
3
*
4
TIME 3
5
TIME 4
6
*
7
*
-
*
8
+
9
+
10
<
11
NOP
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Scheduled Sequencing
Graph
NOP
1
TIME 1
TIME 2
2
*
*
3
*
4
TIME 3
5
TIME 4
6
*
7
*
-
*
8
+
9
+
10
<
11
NOP
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Compatibility Graph
9
3
1
8
4
10
7
6
2
5
11
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Conflict Graph
9
3
1
8
4
10
7
6
2
5
11
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Transitive orientation of
Compatibility Graph
9
3
1
8
4
10
7
6
2
5
11
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Resource Sharing in NonHierarchical Seq. Graph
Searching for binding compatible
Σr bir = a
Σbir Σ xim ≤ 1
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Scheduled and Bound
Sequencing Graph
(1,2)
(1,1)
1
TIME 1
TIME 2
NOP
(2,1)
2
*
*
3
*
4
TIME 3
5
TIME 4
-
6
*
7
*
(2,2)
*
8
+
9
+
10
<
11
NOP
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