Small Multiplier-based Multiplication and Division Operators for PDF

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ISSN 0249-6399 ISRN INRIA/RR--4494--FR+ENG

apport de recherche

SmallMultiplier-basedMultiplicationand

DivisionOperatorsforVirtex-IIDevices

Jean-LucBeuchat,ArnaudTisserand

No4494

July2002

TH`EME2

Unit´ederechercheINRIARhˆone-Alpes

LUT LUT 11 0 01 LUT 0 LUT

101LUT

LUT10 1 0 LUT 0 LUT 10 FF FF FF FF FF FF FF FF FF FF

MULT18x18

MULT18x18S

pipeline stage(c) Embedded multiplier with an internal FF FF FF FF FF FF

Slice 0Slice 1

Slice 2Slice 3

CLB

First carry chain

Second carry chain

(a) Virtex-II CLB(b) Embedded multiplier netnet net

TmultckTioockTmultTiockiq TioockCritical path

Critical path

library virtex2; use virtex2.components.all mult: MULT18x18S port map (

P => XY,

A => X,

B => Y,

C => Clk,

CE => Ce,

R => Clr);. . .

m X0

X=X0+2nX1=n1X

i=0x i2i+2nmn1X i=0x n+i2i; XY X0 ?????Y0 X ?????Y X0 ?X1 ?Y0 ???????Y1 X0 Y0 X1 Y1 X0 Y1 X1

Y0concatenation5:03:0

7:4

X0 * Y0

X1 * Y0 * k

X0 * Y1 * k

X1 * Y1 * k * k

X1X0 Y1Y0

Optional pipeline leveln bits

?(X1+X0)(Y1+Y0) ???????X0Y0 (X1+X0) ?????(Y1+Y0) ???X1X0 X0 X1 Y1Y0 X0 Y0 X1

Y113:43:0

X0X1Y1Y0

X0 * Y0

X1 * Y1 * k * k-X1 * Y1 * kSign extension

(X0+X1) * (Y0+Y1) * k -X0 * Y0 * k m X ?????Y X1Y0 xiyj m17 i i (2mi1) i=m1iX j=0x iyj2i+j+m1X j=i+1x jym1i2j+mi1: max( i)=m1iX j=02 i+j+m1X j=i+12 j+mi1 m1iX j=02 i+j+2m2i2X j=mi2 i+j=2i22m2i11: max( i+ i+1)=22mi1+22mi22i+12i =101111|{z}

2m2i40100|{z}

i i+ i+1 ?????(2mi) 0+ 1)+( 2+ 3) max( 0+

1)|{z}

42
2+

3)|{z}

40
=101111| {z}

3801+101111|{z}

340100:

i m ?????n n = 17 X0 Y0 X1 Y1 n = 17 PP3

PP2PP0PP1

0 00000 00 00 0 0000 0

PP0PP1PP2PP3

n = 17 n = 17 (a) Proposed multiplierm bits

MULT18x18

m-n partial products PP0 PP1 PP2 PP3 (c) Adding the partial products(b) Adding the partial products (tree structure) m=18 ?????m=19 m m=23 50
182
=8 n n=17 n n n=m=2 n=17 n 0 50
100
150
200
250
300
350
400
450
500
550

1820222426283032

slicenumber operandsize

33333333rrrrrrrreeeeeeee

13 14 15 16 17 18 19 20 21
22

1820222426283032

[ns] operandsize rrr rrrrr eeeeeeee

33333333

3 ??X0 ?????Y0 20 25
30
35
40
45
50
55

182022242628303234

slicenumber operandsize

333333333

rrrrrrrrr 10 11 12 13 14 15 16 17 18 19

182022242628303234

[ns] operandsize

333333333

rrrrrrrrr eeeeeeeee ?n=17 ?n=m=2 ?n=17 n<<17 r t=dn=ke x=d qj x rwj ?????d ?nr ?????nd qj+1 qj+1d wjwj+1 q j+1rwj d shift

Qsel table

r=2k k qj+1d 2k nr ?????nd f;+1;:::;0;:::;1;g k f2;1;0;1;2g ?=2 f3;2;1;0;1;2;3g ?=3 nr+nd qj+1d wj wj nr;nd 2700
50
100
150
200
250
300
350

16243240

123
area [slice number]

MULT18x18 block number

operand size std r2 r4/2 r4/3 r8/5 r8/6 #MULT 200
250
300
350
400
450
500
550
600
650
700

16243240

121416182022242628

division time [ns] iteration delay [ns] operand size std r2 r4/2 r4/3 r8/5 r8/6 n qj+1d qj+1d

´Editeur

http://www.inria.fr

ISSN0249-6399

quotesdbs_dbs47.pdfusesText_47

[PDF] Small Multiplier-based Multiplication and Division Operators for

ISSN 0249-6399 ISRN INRIA/RR--4494--FR+ENG

SmallMultiplier-basedMultiplicationand

DivisionOperatorsforVirtex-IIDevices

Jean-LucBeuchat,ArnaudTisserand

No4494

July2002

TH`EME2

Unit´ederechercheINRIARhˆone-Alpes

101LUT

MULT18x18

MULT18x18S

Slice 0Slice 1

Slice 2Slice 3

First carry chain

Second carry chain

TmultckTioockTmultTiockiq TioockCritical path

Critical path

P => XY,

A => X,

B => Y,

C => Clk,

CE => Ce,

R => Clr);. . .

X=X0+2nX1=n1X

Y0concatenation5:03:0

X0 * Y0

X1 * Y0 * k

X0 * Y1 * k

X1 * Y1 * k * k

Optional pipeline leveln bits

Y113:43:0

X0X1Y1Y0

X0 * Y0

X1 * Y1 * k * k-X1 * Y1 * kSign extension

2m2i40100|{z}

1)|{z}

3)|{z}

3801+101111|{z}

340100:

PP2PP0PP1

PP0PP1PP2PP3

MULT18x18

1820222426283032

33333333rrrrrrrreeeeeeee

1820222426283032

33333333

182022242628303234

333333333

182022242628303234

333333333

Qsel table

16243240

MULT18x18 block number

16243240

121416182022242628

´Editeur

ISSN0249-6399