inexact computing jordi cortadella universitat politècnica de catalunya barcelona academia europaea...
TRANSCRIPT
![Page 1: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/1.jpg)
Inexact Computing
Jordi CortadellaUniversitat Politècnica de Catalunya
Barcelona
Academia Europaea Annual ConfereceJuly 18th, 2014
![Page 2: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/2.jpg)
Inexact Computing Jordi Cortadella 2
![Page 3: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/3.jpg)
Inexact Computing Jordi Cortadella 3
![Page 4: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/4.jpg)
Inexact Computing Jordi Cortadella 4
Power consumption: 150W
Energy:
2 weeks desktop 1 year Ethiopian person
![Page 5: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/5.jpg)
Inexact Computing Jordi Cortadella 5
Tchip = Tambient + Power • Rthermal
Power V2
Speed Power
Transistors
Thermal limit
V
![Page 6: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/6.jpg)
Technology and voltage scaling
250nm 180nm 130nm 90nm 65nm 32nm 14nm0
0.5
1
1.5
2
2.5
Volts
Inexact Computing Jordi Cortadella 6
Transistor size
![Page 7: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/7.jpg)
Energy for computing
Inexact Computing Jordi Cortadella 7
0 1
Energy
![Page 8: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/8.jpg)
Energy for computing
Inexact Computing Jordi Cortadella 8
0 1Voltage
![Page 9: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/9.jpg)
Energy for computing
Inexact Computing Jordi Cortadella 9
0 1Voltage
![Page 10: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/10.jpg)
Exa
ctC
om
pu
tin
g
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Energy and errors
Inexact Computing Jordi Cortadella 10
Source: Kumar, Rabaey, Ramchandran, Dept. EECS, UC BerkeleySRAM Supply Voltage Scaling: a Reliability Perspective, ISQED 2009.
Energy
InexactComputing
Voltage
![Page 11: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/11.jpg)
What does error mean?
Inexact Computing Jordi Cortadella 11
1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0
0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1
0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0
1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0
0 0 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1
1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 1 0
0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0
1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1
0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0
1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1
0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1
1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0
![Page 12: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/12.jpg)
What does error mean?
Inexact Computing Jordi Cortadella 12
1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0
0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1
0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0
1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0
0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1
1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 1 0
0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0
1 1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1
0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0
1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1
0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1
1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0
![Page 13: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/13.jpg)
What does error mean?
Inexact Computing Jordi Cortadella 13
1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0
0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1
0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0
1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0
0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1
1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 1 0
0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0
1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1
0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0
1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1
0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 1 0 1 1
1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0
![Page 14: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/14.jpg)
What does error mean?
Inexact Computing Jordi Cortadella 14
1 1 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 0 1 0
0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1
0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0
1 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0
0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1
1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 0 0 1 0
0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 0 0 0
1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1
0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0
1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 1
0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1
1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 1 0 0
![Page 15: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/15.jpg)
Inexact computing
Inexact Computing Jordi Cortadella 15
+2
2
4
4.00000013
3.14159265
![Page 16: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/16.jpg)
Is inexact computing acceptable?
Inexact Computing Jordi Cortadella 16
![Page 17: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/17.jpg)
What is good enough?
• It depends on– the type of computation– the application domain– subjective perceptions
Inexact Computing Jordi Cortadella 17
![Page 18: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/18.jpg)
Energy vs. error rate
Inexact Computing Jordi Cortadella 18
time
Computation
Energy (Voltage)
Errors
![Page 19: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/19.jpg)
Computing with errors
Inexact Computing Jordi Cortadella 19
Comput. 1CP C CP Comput. 2 C R Comput. 2 C
good enough(go ahead)
checkpoint check
wrong(go back)
correct(go ahead)
Checkpoint
Recoverweak memory(low energy)
strong memory(mostly sleeping)
Comput. 3CP
![Page 20: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/20.jpg)
How to check: Certifying algorithms
Inexact Computing Jordi Cortadella 20
Source: R.M. McConnell, K. Mehlhorn, S. Näher, P. Schweitzer,Certifying Algorithms. Computer Science Review 5(2): 119-161 (2011)
![Page 21: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/21.jpg)
Example: sorting
Inexact Computing Jordi Cortadella 21
1 3 4 7 8 9 13 14 22 23 29 36 38 43 47 52
43 3 14 36 52 23 13 4 22 9 29 7 38 1 47 8
Sorting: O(n log n)
Check:• V’ is sorted: O(n)• V’ is a permutation of V: O(n),
using hashing
V:
V’:
![Page 22: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/22.jpg)
Example: SAT
Inexact Computing Jordi Cortadella 22
Is it satisfiable? (NP)Is is unsatisfiable? (co-NP)
Check: O(n)
UNSAT
How to check?
• Run reliable SAT (high energy), or
• Re-run unreliable SAT(increase probability of correct answer)
![Page 23: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/23.jpg)
Conclusions• Energy should be a first-class citizen in
algorithm design and analysis
• Modern computing should be energy-aware:
Accuracy vs. Sustainability
• New programming paradigms are requiredto live with inexact computations:
<Algorithm, Certificate, Check>Inexact Computing Jordi Cortadella 23
![Page 24: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/24.jpg)
Some bibliography• Krishna V. Palem, Lingamneni Avinash. Ten Years of Building Broken
Chips: The Physics and Engineering of Inexact Computing. ACM Trans. Embedded Comput. Syst. 12(2s): 87 (2013)
• Gary Anthes. Inexact design: beyond fault-tolerance. Commun. ACM 56, 4 (April 2013), 18-20.
• Jaeyoon Kim and Sandip Tiwari. Inexact computing using probabilistic circuits: Ultra low-power digital processing. J. Emerg. Technol. Comput. Syst. 10, 2, Article 16 (March 2014).
• R.M. McConnell, K. Mehlhorn, S. Näher, P. Schweitzer, Certifying Algorithms. Computer Science Review 5(2): 119-161 (2011).
• Computing device using inexact computing architecture processor,Patent US 20110321067 A1
Inexact Computing Jordi Cortadella 24
![Page 25: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/25.jpg)
Inexact Computing Jordi Cortadella 25
![Page 26: Inexact Computing Jordi Cortadella Universitat Politècnica de Catalunya Barcelona Academia Europaea Annual Conferece July 18 th, 2014](https://reader030.vdocument.in/reader030/viewer/2022012908/5697bfbe1a28abf838ca2b99/html5/thumbnails/26.jpg)
Inexact Computing Jordi Cortadella 26