Imprecise Computing

Yavuz Yetim

Overview

• Motivation• Background• Definition and Causes of Imprecision• Solution Approaches• Discussion of Two Methods• Future Work

Motivation

• Precision = Overkill

• Applications inherently imprecision tolerant

• Cosmic Rays

Perfect timing, High Vdd, ECC, CRC, checker circuits

PowerPerformance

Background

• Vulnerability Factor [Mukherjee, Weaver, Emer, Reinhardt, Austin, 2003]– Not all bits are important (Architectural)– The important bits are not always important (Timing)

Evaluation Method

Background

• Algorithmic Noise Tolerance [Hegde, Shanbhag, 1999]– Reduce noise in predictable signals

DSP Applications

Background

• Error Resilient System Architecture

Inflexible, Suboptimal

Definition of Imprecise Data

• Stochastic Process– Probabilistic Issues– Time Issues

Imprecision

Time

PDFGoogle Page RankOr MIS

Memory bit: Reverse time

Causes of Imprecision

• Unit: Hardware Faults• Input: Data From Noisy Channel• Operation: Software Bugs

UnitInput Output

Operation

Solution Approaches

• Decrease imprecision by estimation– ANT approach in software

• Tolerate imprecision by controlling it– ERSA only handles exceptions– Numerical control

• Input: 10-3, Output: 10-2

Software Support

• Information flow– Hardware-Software– Data-Data

• Ease of use• Efficiency• Resource Management

Two Analysis Methods

• Probabilistic Method

• Heuristic Method

Probabilistic Method

int <0.9> b, c;imp int <0.8> a, <0.9, 0.6> d, <0.7> e;.// some code modifying b, ca = b + c;.// some code modifying e.d = a + e; #<0.85a+0.15e, a_def=0, e_def=0>

b c

a e

d

Heuristic Method

• Keep performance metric for variables• Update all with info from hardware• Feedback for adjusting imprecision

Comparison

• Probabilistic

– Probabilistic– Operational Overhead– Both online and offline

optimization

• Heuristic

– Definite– Hardware Overhead– Only online optimization

Future Work

• Combine two methods• Better evaluation for different methods• Compiler, architecture and hardware support• Power and Performance evaluations

Thank you…