Introduction to VLSI Programming Lecture 6:

Resource sharing

(course 2IN30)

Prof. dr. ir.Kees van Berkel

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Time table 2005date class | lab subject

Aug. 30 2 | 0 hours intro; VLSI

Sep. 6 3 | 0 hours handshake circuits

Sep. 13 3 | 0 hours handshake circuits assignment

Sep. 20 3 | 0 hours Tangram

Sep. 27 no lecture

Oct. 4 no lecture

Oct. 11 1 | 2 hours demo, fifos, registers | deadline assignment

Oct. 18 1 | 2 hours design cases;

Oct. 25 1 | 2 hours DLX introduction

Nov. 1 1 | 2 hours low-cost DLX

Nov. 8 1 | 2 hours high-speed DLX

Nov. 29 deadline final report

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Lecture 6

Outline:• Recapitulation of Lecture 5• Sharing of sequentially-used resources:

– commands – auxiliary variables – expressions and operators

• Lab work: assignment GCD

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Tangram• Purpose: programming language for asynchronous

VLSI circuits.

• Creator: Tangram team @ Philips Research Labs (proto-Tangram 1986; release 2 in 1998).

• Inspiration: Hoare’s CSP, Dijkstra’s GCL.

• Lectures: no formal introduction; manual hand-out (learn by example, learn by doing).

• Main tools: compiler, analyzer, simulator, viewer.

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VLSI programming of asynchronous circuits

expander

Tangram program

Handshake circuit

Asynchronous circuit(netlist of gates)

compilersimulator

feedback

behavior,

area, time, energy,

test coverage

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VLSI programming for …

• Low costs: – introduce resource sharing.

• Low delay (high throughput): – introduce parallelism.

• Low energy (low power):– reduce activity; …

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VLSI programming for low costs

• Keep it simple!!

• Introduce resource sharing: commands, auxiliary variables, expressions, operators.

• Enable resource sharing, by:– reducing parallelism– making similar commands equal

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Command sharing

S ; … ; SP : proc(). S

P() ; … ; P()

S

0

S

1

|

S

0 1

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Command sharing: example

a?x ; … ; a?xax : proc(). a?x

ax() ; … ; ax()

1|

0

|

a xw

|

0 1

a xw

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Two-place wagging buffer

ba

byte = type [0..255]

& wag2: main proc(a?chan byte & b!chan byte).begin x,y: var byte& ax : proc(). a?x | ax() ; forever do (a?y || b!x) ; (ax() || b!y) odend

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Procedure definition vs declaration

Procedure definition: P = proc (). S– provides a textual shorthand (expansion)– each call generates copy of resource, i.e. no sharing

Procedure declaration: P : proc (). S– defines a sharable resource– each call generates access to this resource

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Command sharing

• Applies only to sequentially used commands.• Saves resources, almost always

(i.e. when command is more costly than a mixer).• Impact on delay and energy often favorable.• Introduced by means of procedure declaration.• Makes Tangram program less well readable.

Therefore, apply after program is correct & sound.

• Should really be applied by compiler.

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Sharing of auxiliary variables

• x:=E is an auto assignment when E depends on x. This is compiled as aux:=E; x:= aux , where aux is a “fresh” auxiliary variable.

• With multiple auto assignments to x, as in:

x:=E; ... ; x:=F

auxiliary variables can be shared, as in:

aux:=E; aux2x(); ... ; aux:=F; aux2x() with aux2x(): proc(). x:=aux

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Expression sharing

x:=E ; … ; a!Ef : func(). E

x:=f() ; … ; a!f()

|

E

e0

e1

Ee0

Ee1

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Expression sharing

• Applies only to sequentially used expressions.• Often saves resources, (i.e. when expression is more

costly than the demultiplexer).• Introduced by means of function declarations.• Makes Tangram program less well readable.

Therefore apply after program is correct & sound.

• Should really be applied by compiler.

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Operator sharing

• Consider x0 := y0+z0 ; … ; x1 := y1+z1 .

• Operator + can be shared by introducing

add : func(a,b? var T): T. a+b

and applying it as in x0 := add(y0, z0) ; … ; x1 := add(y1,z1) .

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Operator sharing: the costs

• Operator sharing may introduce multiplexers to (all) inputs of the operator and a demultiplexer to its output.

• This form of sharing only reduces costs when:– operator is expensive,– some input(s) and/or output are common.

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Operator sharing: example

• Consider x := y+z0 ; … ; x := y+z1 .

• Operator + can be shared by introducingadd2y : proc(b? var T). x:=y+b

and applying it as inadd2y(z0) ; … ; add2y(z1) .

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Making similar equal: example

Consider: x := y+z ; … ; x := y-z .

Use : y-z = y + bitwise_complement(z) +1

condinv: func (f:bool & x:int8): int8. {f x | f bwc(x)}

begin y=val x cast bool8

| <<f#y.0,f#y.1,f#y.2,f#y.3,f#y.4,f#y.5,f#y.6,f#y.7>> cast int8

end

addsub: func (f:bool & x:int8 & y:int8): int9. {f x+y | f x-y }

(<<f,x>> cast int9 + <<f,condinv(f, y)>> cast int9) cast <<bool,int9>>.1

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Greatest Common Divisor

gcd: main proc (ab?chan <<byte,byte>> & c!chan byte).begin x,y: var byte| forever do

ab?<<x,y>>; do x<y then y:= y-x or x>y then x:= x-y

od; c!xod

end GCDab c

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Assigment 3: make GCD smaller

• Both assignments (y:= y-x and x:= x-y) are auto assignments and hence require an auxiliary variable.

• Program requires 4 arithmetic resources (twice < and –) .

• Reduce costs of GCD by saving on auxiliary variables and arithmetic resources. (Beware the costs of multiplexing!)

• Use of ff variables not allowed for this exercise.

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Lab-work and report

• You are allowed to team up with a colleague.

• Report:

more than listing of functional Tangram programs:– analyze the specifications and requirements;– present design options, alternatives, trade-offs;– motivate your design choices;– explain functional correctness of your Tangram programs;

– analyze & explain {area, time, energy} of your programs.

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Next week: lecture 7

Outline:• Introduction to the DLX processor.

• Introduction to Tangram version of a sub-set DLX (executing a software GCD).

• Lab work: extend instruction set of Tangram DLX and reduce its costs.