Transcript Slide 1

Arithmetic Operators Robust to
Multiple Simultaneous Upsets
Carlos Arthur Lang Lisbôa, Luigi Carro
Future technologies, bellow 90nm, will
present transistors so small that they will be
heavily influenced by electromagnetic noise and
SEU induced errors. Since many soft errors might
appear at the same time, a different design
approach must be taken.
• The Robust Multiplier
Introduction
Who cares about multiple
simultaneous transient faults ?
Module 1 (faulty)
wrong
output
Module 2 (no fault)
correct
output
Module 3 (faulty)
wrong
output
V
O
wrong
T output
E
R
Users of TMR-based devices should !
Table 1. Simultaneous Faults x Quantity of Errors Using TMR
Fig. 3 – Sample 2 x 2 bits Multiplier Circuit (w/o redundancy)
(6,400 multiplications - 100 x all possible inputs combinations - w/o voter/counter failures)
Operators and Experiments
• The Robust Adder
S11
01100010101
010111011001
sum
sum
0010100110101
S33
S
S22
Fig. 4 – Adding redundancy to obtain fault tolerance
01010101101
Table 3. Redundant Bits x Fault Tolerance
Fig. 1 – Adder Circuit
111111111111111111111111111111111110000000...0000 (35 1s)
111111111111111111111010101010101010000000...0000 (28 1s)
111111111111111111110000000000000000000000...0000 (21 1s)
2 x count of 1s in the output = 56
Fig. 2 – Adder Operation with pS3 = 0.5
Table 2. % Errors in 1,000 additions
f
2
2
2
2
3
3
3
3
4
4
4
4
r
1
2
3
4
1
2
3
4
1
2
3
4
flips +
balance
flips balance
0
1
3
7
0
1
3
7
0
1
3
7
1
2
4
8
1
2
4
8
1
2
4
8
Notes:
• “r” may be an odd number
• fault tolerance does not
depend on the factors’
width (f); it depends on “r”
• the total quantity of bits
that can change to 1 (w/o
matching complementary
flips) is 2r-1-1
• the total quantity of bits
that can change to 0 (w/o
matching complementary
flips) is 2r-1
Conclusions and Future Work
 Fault tolerance already confirmed by experiments
 Design space to be explored, stressing parallelism
 Reduction of multipliers’ area and time requirements
 Implementation of a digital filter with the operators
Porto Alegre - RS
BRAZIL
Universidade Federal do Rio Grande do Sul - UFRGS
Pós-Graduação em Ciência da Computação
Grupo de Microeletrônica (GME)
Laboratório de Sistemas Embarcados (LSE)
http://www.inf.ufrgs.br/gme, http://www.inf.ufrgs.br/~lse
Phone
+55 51 33166155
e-mail
[email protected]
[email protected]