Approximate Computing Is Dead; Long Live Approximate Computing - - PowerPoint PPT Presentation

Approximate Computing Is Dead; Long Live Approximate Computing

Adrian Sampson Cornell

Hardware Programming Quality Domains

Hardware Programming Quality Domains No more approximate functional units.

# 0.2 0.4 0.6 0.8 1

MSSIM

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

PDP (pJ)

#10 -3

ACA ETAIV RCAapx Type 1 RCAapx Type 2 RCAapx Type 3 Fixed-Point trunc. Fixed-Point round.

better accuracy better efficiency

Narrower bit widths are
 just as good or better

[Barrois et al., DATE 2017]

approximate adders from the literature just varying the adder width

Hardware Programming Quality Domains No more approximate functional units. No more voltage overscaling.

Dual-voltage approximate CPU

[ASPLOS 2012]

Fetch Decode Reg Read Execute Memory WB

• Br. Predictor

Instruction Cache ITLB Decoder Register File Integer FU FP FU Data Cache DTLB Register File

replicated functional units dual-voltage SRAM arrays

fft imagefill jmeint lu mc raytracer smm sor zxing ALU cache FPU multiplier registers together

(a)

Hardware Programming Quality Domains No more approximate functional units. No more voltage overscaling. In general, no more fine-grained approximate operations.

• 70pJ

25pJ 6pJ Control I-Cache Access Register File Access Add

The Horowitz imbalance

a name I made up for this talk [ISSCC 2014]

• Graph H for hardware of
• y

routers (R) nodes (N) links (L)

Constraint-based programming
 for spatial architectures

[Nowatzki et al., PLDI 2013]

• +
• x

y z

Hardware Programming Quality Domains No more approximate functional units. No more voltage overscaling. In general, no more fine-grained approximate operations. No more automatic approximability analysis.

✓ ✗

int a = ...; int p = ...; @Approx p = a; a = p;

EnerJ type qualifiers

[PLDI 2011]

int a = ...; int p = ...; @Approx

EnerJ type qualifiers

[PLDI 2011]

Let’s insert these automatically!

Hardware Programming Quality Domains No more approximate functional units. No more voltage overscaling. In general, no more fine-grained approximate operations. No more automatic approximability analysis. No more generic unsound compiler transformations.

Loop perforation

[Sidiroglou-Douskos et al., FSE 2011]

for (int i = 0; i < max; i++) { // whatever } i += 2

Hardware Programming Quality Domains No more approximate functional units. No more voltage overscaling. In general, no more fine-grained approximate operations. No more automatic approximability analysis. No more generic unsound compiler transformations. No more weak statistical guarantees.

∀x f(x) is good

Traditional guarantee

Statistical guarantee

Pr [f(x) is good] ≥ T

Statistical guarantee, in reality

Prx∼D [f(x) is good] ≥ T

anticipated input distribution

x probability

x probability

high quality low quality

x probability

x probability

Adversarial distribution

Hardware Programming Quality Domains No more approximate functional units. No more voltage overscaling. In general, no more fine-grained approximate operations. No more automatic approximability analysis. No more generic unsound compiler transformations. No more weak statistical guarantees. No more sadness about the imperfection of quality metrics.

Application Description Error metric FFT Scientific kernels from the SciMark2 benchmark Mean entry difference SOR Mean entry difference MonteCarlo Normalized difference SparseMatMult Mean normalized difference LU Mean entry difference ZXing Smartphone bar code decoder 1 if incorrect, 0 if correct jMonkeyEngine Mobile/desktop game engine Fraction of correct decisions normalized to 0.5 ImageJ Raster image manipulation Mean pixel difference Raytracer 3D image renderer Mean pixel difference

Hardware Programming Quality Domains No more approximate functional units. No more voltage overscaling. In general, no more fine-grained approximate operations. No more automatic approximability analysis. No more generic unsound compiler transformations. No more weak statistical guarantees. No more sadness about the imperfection of quality metrics. No more benchmark-oriented research?

Application Description Error metric FFT Scientific kernels from the SciMark2 benchmark Mean entry difference SOR Mean entry difference MonteCarlo Normalized difference SparseMatMult Mean normalized difference LU Mean entry difference ZXing Smartphone bar code decoder 1 if incorrect, 0 if correct jMonkeyEngine Mobile/desktop game engine Fraction of correct decisions normalized to 0.5 ImageJ Raster image manipulation Mean pixel difference Raytracer 3D image renderer Mean pixel difference

https://arxiv.org/abs/1409.0575

Winning Classification Top-1 Error 0% 5% 10% 15% 20% 25% 30% 2010 2011 2012 2013 2014 2015 2016

ImageNet annual competition

https://youtu.be/-gQMulb6T2o

Real-time graphics

Hardware Programming Quality Domains No more approximate functional units. No more voltage overscaling. In general, no more fine-grained approximate operations. No more automatic approximability analysis. No more generic unsound compiler transformations. No more weak statistical guarantees. No more sadness about the imperfection of quality metrics. No more benchmark-oriented research?

Notes and links: http://www.cs.cornell.edu/~asampson/blog/closedproblems.html