New Alta Slide Template

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STatic Analysis of Reactive Systems
S T A R S

Felice Balarin Cadence Berkeley Labs
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Discrete System Example
Voice Mail Pager
play
tick
network
request
sample
control
buffer
message
frame

• For a given processor, can I process all workload
  between two ticks?
• How much bus traffic will I generate?
• How much energy will I use?

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Solutions

• Prototyping
• expensive, comes very late in the design cycle
• Simulation
• limited number of test vectors
• need estimates on timing, energy, bus traffic,
  ...
• STARS STatic Analysis of Reactive Systems
• valid upper bound for any input

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STARS

• A methodology for worst-case analysis of discrete
  systems that can be used to find a conservative
  bound on response time.
• and power
• and bus utilization

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VM pager Timing Analysis
play
tick
network
request
sample
control
buffer
message
frame

• STARS gives an upper bound on processor busy
  period for ANY input sequence

buffer control Idle
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Outline

• STARS theory
• simple
• timing
• VCC implementation
• Automatic abstraction

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STARS overview
play
tick
network
request
sample
control
buffer
message
frame

• given T find s that is worse than signature of
  any execution window of length T
• let T be time required to process inputs with
  signature s

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Signatures

• in practice, counting events
• state transitions may be considered events
• combinations of events may have separate counters
• may need linear constraints over counters
• less events is better than (?) more events

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Signature Abstractions

• Estimate output signature based on input
  signature and length
• must be conservative (ideally, not more than
  necessary)

?
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Signature Abstraction Practice

• Different approaches for
• environment
• mostly manual
• useful for simulation test-benches, formal
  verification, ...
• depends mostly on time
• system
• need to analyze code
• could be automated for restricted class of
  systems
• mostly depends on signatures

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Signature Abstractions Environment
play
tick
network
request
sample
control
buffer
message
frame

• at least 625?s between messages
• Fms (s, T) T/625 1
• tick has 125?s period
• Ftk (s, T) T/125 1
• at most 1 play a second
• Fpl (s, T) T/1,000,000 1

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Signature Abstraction Buffer
play
tick
network
request
sample
control
buffer
message
frame

• BUFFER
• if ( present ( frame )
• samples frame last 50
• if ( present ( tick ) last gt 0)
• emit sample ( samples last -- )
• if ( last 20 ) emit request()

Frq (s, T) min( fr, tk/30) Fsm (s, T) min(
tk, 50fr )
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Fix-point Theorem

• If
• s F(s, T),
• s is worse than signature of initial state,
• then s is worse than signature of any execution
  segment of length T

? s
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Solving Fix-Point Equations

• Simple iteration
• let s be the signature of initial state
• repeat
• s F (s, T)
• until convergence
• works because F is monotone, so s either
  converges,
• or grows beyond any reasonable bounds

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Workload Function

• Estimates required processor time from signatures
• must be conservative

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Workload Function VM pager
play
tick
network
request
sample
control
buffer
message
frame

• BUFFER
• if ( present ( frame )
• samples frame
• last 50
• if ( present ( tick ) last gt 0)
• emit sample ( samples last -- )
• if ( last 20 )
• emit request()

1 line 10 time units
W (s) 20fr 20sm ...
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STARS

• Pick a signature
• Chose a signature abstraction F and workload
  function W and verify they and conservative
• Solve
• s F(s,T)
• T W(s)
• T is a bound on response time
• the processor cannot be continuously busy for
  more than T time units

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(More) Realistic Voice Mail Pager

• 16 modules
• 4000 lines of C code annotated with timing
  estimates
• build signature abstractions manually
• 150 lines of C code

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VMP First experiment

• model environment so that a single message is
  received and then played
• same as DES test-bench
• max busy period
• DES 82 ?s (simulating 8s took 30 s)
• STARS 83 ?s (took 16 ms to compute)

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VMP second experiment

• same as first except
• dont limit the environment to a single message
• max busy period
• STARS 148 ?s (more than 125 ?s between two ticks)
• DES can find input that has 146 ?s

66?s wide window in a 6250 ?s period
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Outline

• STARS theory
• simple
• timing
• VCC implementation
• Automatic abstraction

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VCC

• FUNCTION
• a network of communicating processes
• ARCHITECTURE
• processors, ASICs, buses, memories
• MAPPING
• allows performance estimation
• Functional simulation, Performance analysis
• Export to implementation, STatic Analys

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VCC Function Specification

• Black Box C
• can emit events on output ports
• can detect events on input ports
• Init() function executed once at the beginning
• Run() function can be executed if there are some
  input events
• can be simulated
• cannot be estimated

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VCC Function Specification

• White Box C
• point_entry_init() instead of Init()
• point_entry_run() instead of Run()
• can be converted to Black Box and simulated
• can be estimated, converted to Black Box
  annotated with performance estimates and
  simulated

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Extended Black Box for STARS

• there is a counter counting the number of events
  on each port
• the user can define additional counters
• add starsAbstraction() to Init() and Run()
• starsAbstraction() is used by STARS
• starsAbstraction() can be verified by executing
  it during the simulation using monitors

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How it fits in VCC (black.h)

• include "black_interface.h" // generated by
  "fabricate"
• ifndef _black_h_
• define _black_h_
• class CPP_MODEL_IMPLEMENTATION public
  CPP_MODEL_INTERFACE
• public
• CPP_MODEL_IMPLEMENTATION(const ModuleProto ,
  InstanceInit )
• void Run()
• void Init()
• ...
• starsCounter incount
• void starsAbstraction()
• endif
• ...

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How it fits in VCC (black.cpp)

• include "black.h"
• include ltassert.hgt
• CPP_MODEL_IMPLEMENTATIONCPP_MODEL_IMPLEMENTATION
  (const ModuleProto proto, InstanceInit inst)
• CPP_MODEL_INTERFACE(proto, inst),
  queueStore_(0)
• void CPP_MODEL_IMPLEMENTATIONInit()
• incount.Initialize("incount",this)
• starsMonitor m monitor()
• cts_ ((int)InitialCTS.Value().value() 0) ?
  false true
• queueSize_ (int)MaximumQueueSize.Value().value
  ()
• ...

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How it fits in VCC (black.cpp)

• ...
• void CPP_MODEL_IMPLEMENTATIONRun()
• if (CleartoSend.Enabled())
• incount
• if (incount.total() 1000)
  incount.mgr()-gtrunStars()
• ...
• void CPP_MODEL_IMPLEMENTATIONstarsAbstraction()
• QueueInput.count.setBound(25590)
• QueueOutput.count.setBound(QueueInput.count)
• incount.setBound(QueueInput.count/210)
• ...

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S T A R S