high-level synthesis-ii
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High-Level Synthesis-II
Virendra SinghIndian Institute of Science
Bangalorevirendra@computer.org
IEP on Digital System Synthesis @ IIT Kanpur
Dec 18,2007 HLS@iitk 2
Architectural SynthesisArchitectural 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
Dec 18,2007 HLS@iitk 3
Architectural Synthesis
Objective
• Area
• Cycle time
• Latency
• Throughput
Worst case bound
Evaluation
Architectural Exploration
Dec 18,2007 HLS@iitk 4
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
Dec 18,2007 HLS@iitk 5
Architectural Synthesis
Resources
• Functional Resources
• Primitive Resources
• Application Specific Resources
• Memory Resources
• Interface Resources
Dec 18,2007 HLS@iitk 6
Architectural Synthesis
Circuit Specification
• Sequencing Graph
• A set of functional resources, fully characterized in terms of area and execution delay
• A set of constraints
Dec 18,2007 HLS@iitk 7
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
Dec 18,2007 HLS@iitk 8
Data Flow Graph
* * * +
*
*
* + <
--
1 2
3
4
5
6
7
8
9
10
11
x
3
u dx 3 yu
dxx dx
u
dx y a
c
xl
yl
ul
Dec 18,2007 HLS@iitk 9
Sequencing Graph
* * * +
*
*
* + <
--
NOP
NOP
1 2
3
4
5
6
7
8
9
10
11
Dec 18,2007 HLS@iitk 10
Hierarchical Sequencing Graph
NOP
*
CALL
+
*
*+
NOP
NOP
NOP
a.0
a.3
a.2
a.1
a.4
a.n
b.0
b.n
b.2b.1
Dec 18,2007 HLS@iitk 11
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
Dec 18,2007 HLS@iitk 12
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
Dec 18,2007 HLS@iitk 13
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
Dec 18,2007 HLS@iitk 14
Temporal Domain: Scheduling
* * * +
*
*
* + <
--
NOP
NOP
1 2
3
4
5
6
7
8
9
10
11
TIME 1
TIME 2
TIME 3
TIME 4
Dec 18,2007 HLS@iitk 15
Temporal Domain: Scheduling
*
*
*
+
*
*
*
+
<
-
-
NOP
NOP
1
2
3
4
5
6
7
8
9
10
11
TIME 1
TIME 2
TIME 3
TIME 4
TIME 5
TIME 6
TIME 7
Dec 18,2007 HLS@iitk 16
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
Dec 18,2007 HLS@iitk 17
Spatial Domain: Binding
β(v1) = (1,1)
β(v2) = (1,2)
β(v3) = (1,3)
β(v4) = (2,1)
β(v5) = (2,2)
..
Dec 18,2007 HLS@iitk 18
Spatial Domain: Binding
* * * +
*
*
* + <
--
NOP
NOP
1 2
3
4
5
6
7
8
9
10
11
TIME 1
TIME 2
TIME 3
TIME 4
Dec 18,2007 HLS@iitk 19
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
Dec 18,2007 HLS@iitk 20
Spatial Domain: Binding
* * * +
*
*
* + <
--
NOP
NOP
1 2
3
4
5
6
7
8
9
10
11
TIME 1
TIME 2
TIME 3
TIME 4
n
(1,1) (1,2) (1,3) (1,4)(2,2)
(2,1)
Dec 18,2007 HLS@iitk 21
Spatial Domain: Binding
* * * +
* **+
<
--
NOP
NOP
1 2
3
4
5
6
78
9
10
11
TIME 1
TIME 2
TIME 3
TIME 4
0
n
Dec 18,2007 HLS@iitk 22
Sequencing Graph
* * * +
*
*
* + <
--
NOP
NOP
1 2
3
4
5
6
7
8
9
10
11
Dec 18,2007 HLS@iitk 23
Hierarchical Sequencing Graph
NOP
*
CALL
+
*
*+
NOP
NOP
NOP
a.0
a.3
a.2
a.1
a.4
a.n
b.0
b.n
b.2b.1
(1,2)
(1,1)
(2,1)
Dec 18,2007 HLS@iitk 24
Synchronization
* SYN
+ +
NOP
NOP
0
1a
2 3
n
Dec 18,2007 HLS@iitk 25
Synchronization
*SYN
+ +
NOP
NOP
0
1
a
2 3
n
* SYN
+ +
NOP
NOP
0
1a
2 3
n
Dec 18,2007 HLS@iitk 26
Synchronization
*SYN
+
+
NOP
NOP
0
1
a
2
3
n
Dec 18,2007 HLS@iitk 27
Area/Performance Estimation
Accurate area and performance estimation is not an easy task
Schedule: provides latency
Binding: provides information about the area
Dec 18,2007 HLS@iitk 28
Retiming
+
Host
δ
+
δ
+
δ δ
Dec 18,2007 HLS@iitk 29
Retiming
Vg
Vh
Va
Vf
Vb
Ve
Vc Vd
7 7 70
3 3 3
3
00
0 0
0
00
11 1 1
Dec 18,2007 HLS@iitk 30
Retiming
Vg
Vh
Va
Vf
Vb
Ve
Vc Vd
7 7 70
3 3 3
3
00
0 0
0
00
1 11 1
Delay = 24
Dec 18,2007 HLS@iitk 31
Retiming
Vg
Vh
Va
Vf
Vb
Ve
Vc Vd
7 7 70
3 3 3
3
00
0 0
1
00
11 0 1
Dec 18,2007 HLS@iitk 32
ASAP Scheduling
* * * +
*
*
* + <
--
NOP
NOP
1 2
3
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6
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8
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10
11
TIME 1
TIME 2
TIME 3
TIME 4
Dec 18,2007 HLS@iitk 33
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
}
Dec 18,2007 HLS@iitk 34
ALAP Scheduling
* *
*+
*
**+ <
--
NOP
NOP
1 2
3
4
5
6
7 8
9
10
11
TIME 1
TIME 2
TIME 3
TIME 4
Dec 18,2007 HLS@iitk 35
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
Dec 18,2007 HLS@iitk 36
Constraint Graph
* *
+ +
NOP
NOP
0
13
2 4
n
Min
Time
4Max
Time
3
Dec 18,2007 HLS@iitk 37
Constraint Graph0
4
* *
+ +
NOP
NOP
13
2
n
Min
Time
4
Max
Time
3
* *
+ +
NOP
NOP
13
2
n
4
0
0 04
222- 3
11
Dec 18,2007 HLS@iitk 38
Relative SchedulingScheduling 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
Dec 18,2007 HLS@iitk 39
Sequencing Graph
1
3
* SYN
+ +
NOP
NOP
0
a
2
n
Dec 18,2007 HLS@iitk 40
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
Dec 18,2007 HLS@iitk 41
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
Dec 18,2007 HLS@iitk 42
ILP FormulationAll operation must start only once
x0,1 = 1
x1,1 = 1
x2,1 = 1
x3,2 = 1
x4,3 = 1
x5,4 = 1
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
Dec 18,2007 HLS@iitk 43
ILP FormulationConstraints – 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
Dec 18,2007 HLS@iitk 44
ILP FormulationResource 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
Dec 18,2007 HLS@iitk 45
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
Dec 18,2007 HLS@iitk 46
Resource SharingResource 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
Dec 18,2007 HLS@iitk 47
Optimum Schedulingunder Resource Constraint
* *
*
+
*
**+
<
--
NOP
NOP
1 2
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7 8
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11
TIME 1
TIME 2
TIME 3
TIME 4
Dec 18,2007 HLS@iitk 48
Scheduled Sequencing Graph
* *
*
+
*
**+
<
--
NOP
NOP
1 2
3
4
5
6
7 8
9
10
11
TIME 1
TIME 2
TIME 3
TIME 4
Dec 18,2007 HLS@iitk 49
Compatibility Graph
3
6
1 8
7 2
4
9
10
115
Dec 18,2007 HLS@iitk 50
Conflict Graph
3
6
1 8
7 2
4
9
10
115
Dec 18,2007 HLS@iitk 51
Transitive orientation of Compatibility Graph
3
6
1 8
7 2
4
9
10
115
Dec 18,2007 HLS@iitk 52
Resource Sharing in Non-Hierarchical Seq. Graph
Searching for binding compatible
Σr bir = a
Σbir Σ xim ≤ 1
Dec 18,2007 HLS@iitk 53
Scheduled and Bound Sequencing Graph
* *
*
+
*
**+
<
--
NOP
NOP
1 2
3
4
5
6
7 8
9
10
11
TIME 1
TIME 2
TIME 3
TIME 4
(1,1)
(1,2)
(2,1)
(2,2)
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