Accuracy-Aware Program

Transformations

Sasa Misailovic

MIT CSAIL

Collaborators

Martin Rinard, Michael Carbin, Stelios Sidiroglou, Henry Hoffmann,

Deokhwan Kim, Fan Long, Daniel Roy, Zeyuan Allen Zhu, Michael Kling, Jonathan Kelner, Anant Agarwal

Trade Accuracyfor Energy and Performance

[Rinard ICS’06, OOPSLA’07; Misailovic, Sidiroglou, Hoffmann, Rinard ICSE’10; Carbin, Rinard, ISSTA’10; Hoffmann, Sidiroglou, Carbin, Misailovic, Agarwal, Rinard ASPLOS’11; Sidiroglou, Misailovic, Hoffmann, Rinard FSE’11; Misailovic, Roy, Rinard, SAS‘11; Zhu, Misailovic, Kelner, Rinard POPL’12; Carbin, Kim, Misailovic, Rinard PLDI’12; Misailovic, Sidiroglou, Rinard, RACES‘12; Misailovic, Kim, Rinard TECS PEC’13; Carbin, Kim, Misailovic, Rinard PEPM’13; Carbin, Misailovic, Rinard, OOPSLA ‘13; …]

Harness Approximate Computing

How to systematically generate approximate programs?

How to predict accuracy of the results ofapproximate programs?

How to find the most profitable approximate programs?

Automated Transformations

Probabilistic Reasoning

Explicit Search and Mathematical Optimization

Transformations

Do less work• Loop perforation• Sampling, Task skipping

for (i = 0; i < n; i += 2) { … }

r = var +. 2;

r = f_0(x) f_1(x);

Do different kind of work• Randomized substitution

Exploit Execution Environment• Unreliable operation placement• Unreliable memory regions, Lock elision

Where and when should we apply the transformations?

What are the benefits and costs?

Optimization Framework

• Find Candidates for Transformation

• Analyze Effects of the Transformations

• Navigate Tradeoff Space

for (i = 0; i < n; i++) { … }

for (i = 0; i < n; i += 2) { … }

ccc

Find Transformation Candidates:• Profile program to find time-consuming for

loopsAnalyze the Effects of Transformation:• Performance: Compare execution times• Accuracy: Compare the quality of the results• Safety: memory safety, well formed outputNavigate Tradeoff Space:• Combine multiple perforatable loops

Prioritize loops by their individual performance and accuracy

Greedy or Exhaustive Search with Pruning

Explicit Search Algorithm for Perforation

[Misailovic, Sidiroglou, Hoffmann, Rinard ICSE’10; Hoffmann, Sidiroglou, Carbin, Misailovic, Agarwal, Rinard ASPLOS’11; Sidiroglou, Misailovic,

Hoffmann, Rinard FSE’11]

x264 Cumulative Loop Scores

M

ean

Nor

mal

ized

Tim

e

Accuracy loss (%)

Computational Kernels: Several perforatable computations execute for the majority of the time

Computational patterns:• Distance metrics• Data Statistics• Iteration steps• Monte-Carlo

Benchmark

# Perforatable

Loops

% Time

X264 14 > 60%

Bodytrack 8 > 75%

Swaptions 4 > 99%

Ferret 2 > 40%

Blackscholes

1 > 98%

Canneal 1 > 5%

Streamcluster

1 > 98%

Next Step: Analyses with Guarantees

Accuracy analysis: Results valid for a whole range of inputs, not just those used in testing

Navigation: Explore the space of transformed programs to find those with optimal tradeoffs

Accuracy Analysis: Probabilistic Reasoning

𝐏𝐫 [|𝐑𝐞𝐬−𝐑𝐞𝐬 ′ (𝐪)|>𝐁 ]<𝜺

[Misailovic, Roy, Rinard SAS ’11; Zhu, Misailovic, Kelner, Rinard POPL ’12; Misailovic, Sidiroglou, Rinard, RACES ‘12, Misailovic, Kim, Rinard

TECS PEC ’13, Carbin, Misailovic, Rinard, OOPSLA ’13, Misailovic, Rinard WACAS ‘14,

Misailovic, Carbin, Achour, Qi, Rinard MIT-TR ‘14]

For approximate program configuration

Optimization of Map-Fold Computations

outList = Map ( Func(x),

inputList

)

Func0: (0,T0) Func1: (1,T1)Func2: (2,T2)

[Zhu, Misailovic, Kelner, Rinard POPL 2012; Misailovic, Rinard WACAS 2014]

Accuracy Requirement:

Optimization of Map-Fold Computations

Configuration: Probability to execute each version of Func Range: , Sum:

Accuracy Loss Constraint:

Goal:

Linear + Dynamic programming

outList = Map(

Func0(x)

Func1(x)

Func2(x) ,

inputList)

Func0: (0,T0) Func1: (1,T1) Func2: (2,T2)

[Zhu, Misailovic, Kelner, Rinard POPL 2012; Misailovic, Rinard WACAS 2014]

float<0.99*R(x)>

f(float in unrel x) { y = g(x) +. h(x);

return y *. y; }

Developer’s reliability specification

Chisel: Automatic Generation of Approximate Rely Programs

[Misailovic, Carbin, Achour, Qi, Rinard MIT-TR 14]

Variable and Operation Annotations

Chisel: Automatic Generation of Approximate Rely Programs

Configuration: Unreliable variable or unreliable operationRange:

Reliability Constraint:

Goal:

Integer Linear Programming

float<0.99*R(x)>

f(float x) { y = g(x) + h(x);

return y * y; }

Developer’s specification

[Misailovic, Carbin, Achour, Qi, Rinard MIT-TR 14]

Navigate Search Space: Mathematical Optimization

Find configuration s. t.

[Zhu, Misailovic, Kelner, Rinard POPL ’12; Misailovic, Rinard WACAS ‘14

Misailovic, Carbin, Achour, Qi, Rinard, MIT-TR ‘14]

Looking Forward

Fully Exploit Optimization Opportunities: both application- and hardware-level transformations

Reasoning About Uncertainty: • logic-based techniques• probabilistic techniques• empirical techniques

Practical Aspects: provide intuition and control for developers and domain experts

Takeaway

Accuracy-aware transformations• Improve performance• Reduce energy consumption• Facilitate dynamic adaptation

and software specialization

Program analysis and search can help find profitable, safe, and predictable tradeoffs

Takeaway

Accuracy-aware transformations• Improve performance• Reduce energy consumption• Facilitate dynamic adaptation

and software specialization

Program analysis and search can help find profitable, safe, and predictable tradeoffs