[PPT] - L o w - C o s t D u p l i c a t e M u l t i p PowerPoint Presentation

SLIDE 1

L

w
C
s

t D u p l i c a t e M u l t i p l i c a t i

n

M i c h a e l S u l l i v a n a n d E a r l E . S w a r t z l a n d e r , J r .

U n i v e r s i t y

f

T e x a s a t A u s t i n 2 1 5

SLIDE 2

2 / 3

P r

b

l e m S t a t e m e n t

L

w
c
s

t d u p l i c a t i

n

L

w
c
s

t d u p l i c a t i

n

i s a n u n

b

t r u s i v e , d r

p
i

n r e p l a c e m e n t f

r

d u p l i c a t i

n

t h a t m a i n t a i n s i t s s t r e n g t h s w i t h

u

t i t s p r

h

i b i t i v e

v

e r h e a d s .

SLIDE 3

3 / 3

W h a t c a n g

w

r

n

g ?

T r a n s i e n t F a u l t s E n v i r

n

m e n t a l T i m i n g F a u l t s F a b r i c a t i

n

F a u l t s P e r m a n e n t F a u l t s D e s i g n F a u l t s

T ransient Faults

R a t e s ? I m p

r

t a n c e ? … I n t h e f u t u r e ?

? ?

SLIDE 4

4 / 3

E r r

r

D e t e c t i

n

D e s i g n G

a

l s

S t r

n

g a n d F a u l t

A

g n

s

t i c C

n

c u r r e n t a n d L

w
L

a t e n c y F u l l y S e p a r a b l e M a n a g e a b l e C

s

t

1 3 2 4

SLIDE 5

5 / 3

T y p i c a l S e p a r a b l e A p p r

a

c h e s

? S t r

n

g

i

s h + C

n

c u r r e n t / L

w

L a t e n c y

E

x p e n s i v e

SLIDE 6

6 / 3

T y p i c a l S e p a r a b l e A p p r

a

c h e s

+ S t r

n

g ? M e d i u m L a t e n c y ? E x p e n s i v e

i

s h

? S t r

n

g

i

s h + C

n

c u r r e n t / L

w

L a t e n c y

E

x p e n s i v e

SLIDE 7

7 / 3

T y p i c a l S e p a r a b l e A p p r

a

c h e s

C
v

e r a g e h

l

e s ? M e d i u m L a t e n c y + I n e x p e n s i v e

+ S t r

n

g ? M e d i u m L a t e n c y ? E x p e n s i v e

i

s h ? S t r

n

g

i

s h + C

n

c u r r e n t / L

w

L a t e n c y

E

x p e n s i v e

SLIDE 8

8 / 3

F i x e d

P
i

n t M u l t i p l i c a t i

n

( 1 ) P a r t i a l P r

d

u c t G e n e r a t i

n

( 2 ) M u l t i O p e r a n d A d d ( 3 ) C a r r y P r

p

a g a t e A d d i t i

n

SLIDE 9

9 / 3

D u p l i c a t e M u l t i p l i c a t i

n

C a r r y

P

r

p

. A d d i t i

n

P P G e n P P G e n Mu l t i

O

p e r a n d A d d i t i

n

Mu l t i

O

p e r a n d A d d i t i

n

C a r r y

P

r

p

. A d d i t i

n

E q u a l i t y C h e c k e r C a r r y

P

r

p

. A d d i t i

n

P P G e n P P G e n Mu l t i

O

p e r a n d A d d i t i

n

Mu l t i

O

p e r a n d A d d i t i

n

E q u a l i t y C h e c k e r C a r r y

P

r

p

. A d d i t i

n

S t r i c t D u p l i c a t i

n

“ L a z y ”

r

“ D e f e r r e d ” D u p l i c a t i

n

O r i g i n a l M u l t i p l i c a t i

n

O r i g i n a l M u l t i p l i c a t i

n

S t r i c t D u p l i c a t e L a z y D u p l i c a t e

SLIDE 10

1 / 3

L

w
C
s

t D u p l i c a t i

n

+ S t r

n

g + L

w
L

a t e n c y + I n e x p e n s i v e

r

m

d

e r a t e l y e x p e n s i v e

SLIDE 11

1 1 / 3

L

w
C
s

t D u p l i c a t i

n

+ S t r

n

g + L

w
L

a t e n c y + I n e x p e n s i v e

r

m

d

e r a t e l y e x p e n s i v e

A L T E R N A T E N U M B E R S Y S T E M S 1 . C a r r y

S

a v e A r i t h m e t i c 2 . T h e R e s i d u e N u m b e r S y s t e m

SLIDE 12

1 2 / 3

# 1 L a z y C a r r y

S

a v e D u p l i c a t i

n

C a r r y

P

r

p

. A d d i t i

n

P P G e n P P G e n Mu l t i

O

p e r a n d A d d i t i

n

Mu l t i

O

p e r a n d A d d i t i

n

E q u a l i t y C h e c k e r C a r r y

P

r

p

. A d d i t i

n

L a z y D u p l i c a t i

n

C a r r y

P

r

p

. A d d i t i

n

P P G e n P P G e n Mu l t i

O

p e r a n d A d d i t i

n

Mo d i fj e d C h e c k e r Mu l t i

O

p e r a n d A d d i t i

n

L a z y C a r r y

S

a v e D u p l i c a t i

n

O r i g i n a l M u l t i p l i c a t i

n

L a z y D u p l i c a t e O r i g i n a l M u l t i p l i c a t i

n

L a z y C S D u p l i c a t e

SLIDE 13

1 3 / 3

# 1 L a z y C a r r y

S

a v e D u p l i c a t i

n

C a r r y

S

a v e E q u a l i t y C h e c k e r A B i t s l i c e

SLIDE 14

1 4 / 3

# 2 R N S D u p l i c a t i

n

U s e s t h e R e s i d u e N u mb e r S y s t e m ( R N S )

SLIDE 15

1 5 / 3

# 2 R N S D u p l i c a t i

n

U s e s t h e R e s i d u e N u mb e r S y s t e m ( R N S )

C a r r y

P

r

p

. A d d i t i

n

P P G e n P P G e n Mu l t i

O

p e r a n d A d d i t i

n

P P G e n P P G e n Mo d i fj e d C h e c k e r R N S G e n Mu l t i

O

p e r a n d Mo d u l a r A d d i t i

n

Mu l t i

O

p e r a n d Mo d u l a r A d d i t i

n

Mu l t i

O

p e r a n d Mo d u l a r A d d i t i

n

Mo d i fj e d C h e c k e r R N S G e n

O r i g i n a l M u l t i p l i c a t i

n

E v e n B a s e ( 2

a

) R N S M u l t i p l i c a t i

n

M e r s e n n e O d d B a s e ( 2

b

1

) R N S M u l t i p l i c a t i

n

F e r m a t O d d B a s e ( 2

b

+ 1 ) R N S M u l t i p l i c a t i

n

SLIDE 16

1 6 / 3

L

w
C
s

t M u l t i p l i c a t i

n

E v a l u a t i

n

SLIDE 17

1 7 / 3

L

w
C
s

t M u l t i p l i c a t i

n

E v a l u a t i

n

SLIDE 18

1 8 / 3

L

w
C
s

t D u p l i c a t i

n

R e d u c e

v

e r h e a d s

f

d u p l i c a t i

n

f

r

h i g h

r

e l i a b i l i t y p r

c

e s s

r

s . M

r

e a g g r e s s i v e b a s e l i n e f

r

D M R

r

g a n i z a t i

n

s . O p e n s u p n e w r e s e a r c h

p

p

r

t u n i t i e s .

SLIDE 19

1 9 / 3

F u t u r e R e s e a r c h ?

 D

i fg e r e n t

r

g a n i z a t i

n

s a n d n u m b e r s y s t e m s

 O

p t i m i z e d l

w
s

p e e d c h e c k i n g m u l t i p l i e r

 I

m p r

v

i n g t h e p

w

e r

f

t h e c h e c k e r

 M

u l t i

V

t h s y n t h e s i s a n d mu l t i p l e s u p p l y v

l

t a g e s

 R

e l i a b i l i t y f

r

s p e e d / p

w

e r

 T

i mi n g / p

w

e r s p e c u l a t i

n
r

s t

c

h a s t i c l

g

i c

 O

t h e r a p p l i c a t i

n

d

m

a i n s ? S e c u r i t y ?

SLIDE 20

2 / 3

B a c k u p S l i d e s

SLIDE 21

2 1 / 3

A r i t h m e t i c R e l i a b i l i t y

Low-Level Correction No Semantic Information Data Types Matter Low-Level Detection Data Storage Data Transform Rates High Rates Low-to-???

M E M O R Y A R I T H M E T I C

SLIDE 22

2 2 / 3

A r i t h m e t i c R e l i a b i l i t y

Low-Level Correction No Semantic Information Data Types Matter Low-Level Detection Data Storage Data Transform Rates High Rates Low-to-???

M E M O R Y A R I T H M E T I C

SLIDE 23

2 3 / 3

A r i t h m e t i c R e l i a b i l i t y

Low-Level Correction No Semantic Information Data Types Matter Low-Level Detection Data Storage Data Transform Rates High Rates Low-to-???

M E M O R Y A R I T H M E T I C

SLIDE 24

2 4 / 3

B a c k g r

u

n d # 2 : F u l l y S e p a r a b l e

I n s e p a r a b l e S e p a r a b l e

SLIDE 25

2 5 / 3

B a c k g r

u

n d # 3 & # 4

Simplifjes higher-level recovery mechanisms.

T arget: Synchronous, 1-2 cycle latency.

L

w
L

a t e n c y , C

n

c u r r e n t D e t e c t i

n

F u l l d u p l i c a t i

n

> 1 % l

g

i c

v

e r h e a d s ( a r e a a n d p

w

e r ) .

L

w
c
s

t d u p l i c a t i

n

3

5

%

v

e r h e a d s .

M a n a g e a b l e C

s

t s

SLIDE 26

2 6 / 3

B a c k g r

u

n d # 2 : F u l l y S e p a r a b l e

I n c r e a s i n g S e p a r a b i l i t y

SLIDE 27

2 7 / 3

B a c k g r

u

n d # 2 : F u l l y S e p a r a b l e

I n c r e a s i n g S e p a r a b i l i t y

SLIDE 28

2 8 / 3

B a c k g r

u

n d # 2 : F u l l y S e p a r a b l e

I n c r e a s i n g S e p a r a b i l i t y

SLIDE 29

2 9 / 3

B a c k g r

u

n d # 2 : F u l l y S e p a r a b l e

I n c r e a s i n g S e p a r a b i l i t y

SLIDE 30

3 / 3

B a c k g r

u