Concurrent models of computation for embedded software
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- Marilyn Wiggins
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1 Concurrent models of computaton for embedded software and hardware! Researcher overvew what t looks lke semantcs what t means and how t relates desgnng an actor language actor propertes and how to represent them usng the language workng wth actor descrptons what Xlnx does wth actors
2 smple actors actor ID () In > Out : acton In: [a] > Out: [a] actor ID () In > Out : acton [a] > [a] actor Add () Input1, Input > Output: acton [a], [b] > [a + b] actor AddSeq () Input > Output: acton [a, b] > [a + b] 3 parameters actor Scale (k) Input > Output: acton [a] > [k * a] parametrc actor defntons represent a famly of actors 4
3 actons frng rules + frng functons actor Add () Input1, Input > Output: acton [a], [b] > [a + b] actons lke these descrbe frng rules and frng functon: { ( a),( b) : a, b Z} f : ( a),( b) a ( a + b) 5 multple actons actor NDMerge () Input1, Input > Output: acton Input1: [x] > [x] acton Input: [x] > [x] multple actons result n multple frng rules and functons: 1 {( a), : a Z}, f1 : ( a), a ( a) {,( a) : a Z}, f :,( a) a ( a) such actors may be non-determnstc 6
4 nondetermnsm actor NDMerge () Input1, Input > Output: acton Input1: [x] > [x] acton Input: [x] > [x] 1 { ( a), : a Z}, f1 : ( a), a ( a) {,( a) : a Z}, f :,( a) a ( a)... but t gets even worse... actor NDSplt () Input > Output1, Output: acton [x] > Output1: [x] acton [x] > Output: [x] 1 {( a) : a Z}, f1 :( a) a ( a), {( a) : a Z}, f :( a) a,( a) dfferent actons may result n overlappng (here: dentcal) sets of frng rules, and dfferent frng functons: the combned frng functon sn t (a functon)!!! the resultng process s no longer functonal what could ths possbly be useful for??? 7 guarded actons actor Splt () Input > Y, N: acton [a] > Y: [a] guard P(a) acton [a] > N: [a] guard not P(a) guards may constran the tokens accepted by an acton: 1 {( a) : P( a) }, f1 : ( a) a ( a), {( a) : P( a) }, f : ( a) a,( a) 8
5 guarded actons actor Select () S, A, B > Output: acton S: [sel], A: [v] > [v] guard sel acton S: [sel], B: [v] > [v] guard not sel 1 {(true),( v), : v Z}, f1 : (true),( v), a ( v) {(false),,( v) : v Z}, f : (false),,( v) a ( v) cf Lect. 15, slde 8 9 actors wth state actor Sum () Input > Output: sum : 0; acton [a] > [sum] do sum : sum + a; refers to state at the of the acton executon state requres an extenson of the actor model: the frng rules may dep on the state (wll see ths later) the frng functon takes [state, nput] to [state, output] here, the state space s somorphc to Z---thus: f {[ σ,( a) ]: σ, a Z} :[ σ,( a) ] a [ a + σ,( a + σ )] note: we wll omt sngleton state for stateless actors 10
6 actors wth state: ratonale could state not be realzed by drect feedback? yes, but state s specal n a number of practcal ways... there s but one nstance of t t s always drectly fed back t s not shared wth other actors more fundamentally, state s what allows for actors to be compostonal: a dataflow network cannot n general be represented by a sngle stateless actor (the queues contan state) 11 state-depent guards actor Select () S, A, B > Output: {[ ( ) ] [ ( ) ]} state 0; 1 0, true,,, 0, false,, acton S: [sel] > [ 0, ( true),, ] a [ 1, ] guard state 0 do f1 : f sel then [ 0, ( false ),, ] a [, ] state : 1; else state : ; {[ 1,, ( a), ]: a Z} f : [ 1,, ( a), ] a [ 0, ( a) ] for a Z acton A: [v] > [v] guard state 1 do state : 0; 3 {[,,, ( a) ]: a Z} acton B: [v] > [v] guard state do f3 :[,,, ( a) ] a [ 0, ( a) ] for a Z state : 0; cf Lect. 15, slde 8 1
7 prortes (when order matters) actor ProcessStream () In, Confg > Out: c : ntalconfg(); acton Confg: [newc] > do c : newc; acton In: [data] > [compute(data, c)] ntuton: among the enabled actons, one wth maxmal prorty s fred how to enforce frng of one acton over another? actor ProcessStream () In, Confg > Out: c : ntalconfg(); confg: acton Confg: [newc] > do c : newc; process: acton In: [data] > [compute(data, c)] prorty confg > process; 13 prortes (the harmless case) actor Route () A > X, Y, Z: acton [v] > X: [v] guard P(v) acton [v] > Y: [v] guard Q(v) and not P(v) acton [v] > Z: [v] guard not Q(v) and not P(v) actor Route () A > X, Y, Z: tox: acton [v] > X: [v] guard P(v) toy: acton [v] > Y: [v] guard Q(v) toz: acton [v] > Z: [v] prorty tox > toy > toz; 14
8 prortes (more mergng) actor BasedMerge () Input1, Input > Output: A: acton Input1: [x] > [x] B: acton Input: [x] > [x] prorty A > B actor PrettyFarMerge () Input1, Input > Output: Both: acton [x], [y] > [x, y] Both: acton [x], [y] > [y, x] One: acton Input1: [x] > [x] One: acton Input: [x] > [x] prorty Both > One 15 formal verson of a CAL actor (pre-semantcs) σ 0,, f I I, f set of n acton ndces: I { 1, K, n} state space: Σ ntal state: non-reflexve partal order on I: σ Σ I 0 f I I each acton s defned as: (non-jonable) frng rules: frng functon:, f Σ S m fn f : S n fn Σ allowng for some handwavng about exactly how ths nformaton s derved from the actor source text 16
9 semantcs actor descrptons and actors A L [ ] [ L]? actor Splt () Input > Y, N: acton [a] > Y: [a] guard P(a) acton [a] > N: [a] guard not P(a) 17 semantcs A: actor transton systems (untmed verson) an actor transton system (ATS) n a state space Σ: ntal state transton relaton prorty order σ 0, τ,f σ Σ 0 m τ Σ S fn S f n fn Σ rreflexve partal order on τ exercse for the reader: 1. what could be a sutable fxed-pont semantcs for an ATS? (.e. what process corresponds to an ATS?). what would be a sutable semantcs for a network of ATS? notaton: sas ( σ, s, s, σ ) τ σ σ 18
10 semantcs [ ]: semantc mappng constructng an ATS from a formal CAL actor n state space Σ: I σ Σ I { 1, K, n} f I I Σ S 0 CAL actor σ 0,, f I m fn f : S n fn Σ I, f τ τ I τ t f t ATS σ 0, τ,f {( σ, s, s, σ ):[ σ, s] f ([ σ, s] ) [ σ, s ]} I, j I : f j t τ t τ k I : k f t τ I j k 19 semantcs expressveness [CAL] ATS? example 1: {(, ( a ), ( b), ): a, Z} τ b (nonfnte/unbounded nondetermnsm) example : sa f ( s ) wth s ( a,..., a ), 1 n k such that a Z, n mn k N : k a 1 (prefx length deps on token values) 0
11 semantcs relaton to frng rules/frng functon gven a set of frng rules and a frng functon, f CAL the correspondng ATS s, τ, wth τ {(, s, f () s, ): s } [ ] ATS note: ths constructon s njectve up to somorphsm FR+FF 1 semantcs relaton to frng rules/frng functon sa f ( s) wth s ( a1,..., an ), such that a Z, n mn k N : k k 1 a FR+FF {(,( a ), ( b), ): a, Z} τ b
12 language desgn what CAL actor results n FR+FF? actor C () X > Y: acton [a] > [f(a)] guard P(a) acton [a] > [g(a)] guard Q(a) what does t dep on?? actor B () X > Y: acton [a] > [1] acton [a] > [] actor A () X > Y: acton [a] > [f(a)] actor D () X > Y: acton [a] > [f(a)] guard P(a) acton [a] > [g(a)] guard Q(a) and not P(a)?... (equvalence, somorphsm) actor E () X > Y: A: acton [a] > [f(a)] guard P(a) B: acton [a] > [g(a)] guard Q(a) prorty A > B; 3 language desgn statc propertes A p L [ p [ L ] 1 L [ p [ L ] 1 L p [ L] L [ p ] p exercse: name some p along wth a representatve p CAL 4
13 language desgn redundancy (non-orthogonalty) actor AlmostFarMerge () Input1, Input > Output: s : 0; acton Input1: [x] > [x] guard s 0 do s : 1; acton Input: [x] > [x] guard s 1 do s : 0; property p of ths actor? actor AlmostFarMerge () Input1, Input > Output: A: acton Input1: [x] > [x] B: acton InputB: [x] > [x] schedule fsm s1: s1 (A) --> s; s (B) --> s1; rule of thumb: f p s mportant, and p L s nasty, t may be tme for a new construct. what s the p CAL that represents t? 5 workng wth actor descrptons example: actor projecton (remove outputs) actor AddSub () A, B > Sum, Dff: acton [a], [b] > [a + b], [a - b] say the Dff output s unconnected... remove port and all ts output expressons actor AddSub () A, B > Sum: acton [a], [b] > [a + b] 6
14 workng wth actor descrptons example: actor projecton (remove nputs) actor ProcessStream () In, Confg > Out: c : ntalconfg(); confg: acton Confg: [newc] > do c : newc; assume the Confg nput s not connected... process: acton In: [data] > [compute(data, c)] prorty confg > process; actor ProcessStream () In > Out: remove the port, and any acton that reads from t c : ntalconfg(); process: acton In: [data] > [compute(data, c)] 7 workng wth actor descrptons dscoverng concurrency v 1 v 1 Queue 1 aa bb xx A yy Thread 3 zz Thread 1 a x B b y a b C x y Queue 3 Queue a a b b D x x Thread v a b E x v actor B () a, b > x, y: s : <somethng>; acton a: [v] > x: [f(v, s)] acton b: [v] > y: [g(v)] do s : h(v, s); 8
15 Xlnx actors to (programmable) hardware drver applcaton vdeo encodng and decodng (MPEG4 et al.) challenges fast hardware small hardware hardware & software actor machnes actor-specfc confgurable processor archtectures» ppelned acton frng» resource sharng shameless plug Xlnx does take nterns... 9 The. Thanks! nfo: contact: jorn.janneck@xlnx.com 30
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