Download presentation

Presentation is loading. Please wait.

Published byDerek Parks Modified over 2 years ago

1
SIAM Parallel Processing’2006 - Feb 22 Mini Symposium Adaptive Algorithms for Scientific computing 9h45 Adaptive algorithms - Theory and applications Jean-Louis Roch &al. AHA Team INRIA-CNRS Grenoble, France 10h15Hybrids in exact linear algebra Dave Saunders U. Delaware, USA 10h45Adaptive programming with hierarchical multiprocessor tasks Thomas Rauber, Gudula Runger, U. Bayreuth, Germany 11h15 Cache-Oblivious algorithms Michael Bender, Stony Brook U., USA Adaptive, hybrids, oblivious : what do those terms mean ? Taxonomy of autonomic computing [Ganek & Corbi 2003] : – Self-configuring / self-healing / self-optimising / self-protecting Objective: towards an analysis based on the algorithm performance

2
Adaptive algorithms Theory and applications Van Dat Cung, Jean-Guillaume Dumas, Thierry Gautier, Guillaume Huard, Bruno Raffin, Jean-Louis Roch, Denis Trystram IMAG-INRIA Workgroup on “Adaptive and Hybrid Algorithms” Grenoble, France Contents I. Some criteria to analyze adaptive algorithms II. Work-stealing and adaptive parallel algorithms III.Adaptive parallel prefix computation

3
Why adaptive algorithms and how? Input data vary Resources availability is versatile Adaptation to improve performances Scheduling partitioning load-balancing work-stealing Measures on resources Measures on data Calibration tuning parameters block size/ cache choice of instructions, … priority managing Choices in the algorithm sequential / parallel(s) approximated / exact in memory / out of core … An algorithm is « hybrid » iff there is a choice at a high level between at least two algorithms, each of them could solve the same problem

4
Modeling an hybrid algorithm Several algorithms to solve a same problem f : –Eg : algo_f 1, algo_f 2 (block size), … algo_f k : –each algo_f k being recursive Adaptation to choose algo_f j for each call to f algo_f i ( n, … ) { …. f ( n - 1, … ) ; …. f ( n / 2, … ) ; … }. E.g. “practical” hybrids: Atlas, Goto, FFPack FFTW cache-oblivious B-tree any parallel program with scheduling support: Cilk, Athapascan/Kaapi, Nesl,TLib…

5
How to manage overhead due to choices ? Classification 1/2 : –Simple hybrid iff O(1) choices [eg block size in Atlas, …] –Baroque hybrid iff an unbounded number of choices [eg recursive splitting factors in FFTW] choices are either dynamic or pre-computed based on input properties.

6
Choices may or may not be based on architecture parameters. Classification 2/2. : an hybrid is –Oblivious: control flow does not depend neither on static properties of the resources nor on the input [eg cache-oblivious algorithm [ Bender ] –Tuned : strategic choices are based on static parameters [eg block size w.r.t cache, granularity, ] Engineered tuned orself tuned [eg ATLAS and GOTO libraries, FFTW, …] [eg [LinBox/FFLAS] [ Saunders&al] –Adaptive : self-configuration of the algorithm, dynamlc Based on input properties or resource circumstances discovered at run-time [eg : idle processors, data properties, …] [eg TLib Rauber&Rünger]

7
Examples BLAS libraries –Atlas: simple tuned (self-tuned) –Goto : simple engineered (engineered tuned) –LinBox / FFLAS : simple self-tuned,adaptive [Saunders&al] FFTW –Halving factor : baroque tuned –Stopping criterion : simple tuned Parallel algorithm and scheduling : –Choice of parallel degree : eg Tlib [Rauber&Rünger] –Work-stealing schedile : baroque hybrid

8
Adaptive algorithms Theory and applications Van Dat Cung, Jean-Guillaume Dumas, Thierry Gautier,Guillaume Huard, Bruno Raffin, Jean-Louis Roch, Denis Trystram INRIA-CNRS Project on“Adaptive and Hybrid Algorithms” Grenoble, France Contents I. Some criteria to analyze for adaptive algorithms II. Work-stealing and adaptive parallel algorithms III.Adaptive parallel prefix computation

9
Work-stealing (1/2) «Depth » W = #ops on a critical path (parallel time on resources) Workstealing = “ greedy ” schedule but distributed and randomized Each processor manages locally the tasks it creates When idle, a processor steals the oldest ready task on a remote -non idle- victim processor (randomly chosen) « Work » W 1 = #total operations performed

10
Work-stealing (2/2) «Depth » W = #ops on a critical path (parallel time on resources) « Work » W 1 = #total operations performed Interests : -> suited to heterogeneous architectures with slight modification [Bender-Rabin02] -> with good probability, near-optimal schedule on p processors with average speeds ave T p < W 1 /(p ave ) + O ( W / ave ) NB : #succeeded steals = #task migrations < p W [Blumofe 98, Narlikar 01, Bender 02] Implementation: work-first principle [Cilk, Kaapi] Local parallelism is implemented by sequential function call Restrictions to ensure validity of the default sequential schedule - serie-parallel/Cilk - reference order/Kaapi

11
Work-stealing and adaptability Work-stealing ensures allocation of processors to tasks transparently to the application with provable performances Support to addition of new resources Support to resilience of resources and fault-tolerance (crash faults, network, … ) Checkpoint/restart mechanisms with provable performances [Porch, Kaapi, … ] “ Baroque hybrid ” adaptation: there is an -implicit- dynamic choice between two algorithms a sequential (local) algorithm : depth-first (default choice) A parallel algorithm : breadth-first Choice is performed at runtime, depending on resource idleness Well suited to applications where a fine grain parallel algorithm is also a good sequential algorithm [Cilk]: Parallel Divide&Conquer computations Tree searching, Branch&X … -> suited when both sequential and parallel algorithms perform (almost) the same number of operations

12
Solution: to mix both a sequential and a parallel algorithm Basic technique : Parallel algorithm until a certain « grain »; then use the sequential one Problem : W increases also, the number of migration … and the inefficiency ;o( Work-preserving speed-up [Bini-Pan 94] = cascading [Jaja92] Careful interplay of both algorithms to build one with both W small and W 1 = O( W seq ) Divide the sequential algorithm into block Each block is computed with the (non-optimal) parallel algorithm Drawback : sequential at coarse grain and parallel at fine grain ;o( Adaptive granularity : dual approach : Parallelism is extracted at run-time from any sequential task But often parallelism has a cost !

13
Self-adaptive grain algorithm Based on the Work-first principle : Executes always a sequential algorithm to reduce parallelism overhead => use parallel algorithm only if a processor becomes idle by extracting parallelism from a sequential computation Hypothesis : two algorithms : - 1 sequential : SeqCompute - 1 parallel : LastPartComputation : at any time, it is possible to extract parallelism from the remaining computations of the sequential algorithm –Examples : - iterated product [Vernizzi 05]- gzip / compression [Kerfali 04] - MPEG-4 / H264 [Bernard 06]- prefix computation [Traore 06] SeqCompute Extract_par LastPartComputation SeqCompute

14
Adaptive algorithms Theory and applications Van Dat Cung, Jean-Guillaume Dumas, Thierry Gautier,Guillaume Huard, Bruno Raffin, Jean-Louis Roch, Denis Trystram INRIA-CNRS Project on“Adaptive and Hybrid Algorithms” Grenoble, France Contents I. Some criteria to analyze for adaptive algorithms II. Work-stealing and adaptive parallel algorithms III.Adaptive parallel prefix computation

15
Sequential algorithm : for (i= 0 ; i <= n; i++ ) [ i ] = [ i – 1 ] * a [ i ] ; Parallel algorithm [Ladner-Fischer] : Prefix computation : an example where parallelism always costs 1 = a 0 * a 1 2 =a 0 * a 1 * a 2 … n =a 0 * a 1 * … * a n W =2. log n but W 1 = 2.n Twice more expensive than the sequential … a 0 a 1 a 2 a 3 a 4 … a n-1 a n **** Prefix of size n/2 1 3 … n 2 4 … n-1 *** W 1 = W = n

16
Adaptive prefix computation – Any (parallel) prefix performs at least W 1 2.n - W ops – Strict-lower bound on p identical processors: T p 2n/(p+1) block algorithm + pipeline [Nicolau&al. 2000] Application of adaptive scheme : – One process performs the main “sequential” computation – Other work-stealer processes computes parallel « segmented » prefix –Near-optimal performance on processors with changing speeds : T p < 2n/((p+1). ave ) + O ( log n / ave ) lower bound

17
0 a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 a 10 a 11 a 12 Work- stealer 1 Main Seq. Work- stealer 2 Adaptive Prefix on 3 processors 11 Steal request

18
Adaptive Prefix on 3 processors 0 a 1 a 2 a 3 a 4 Work- stealer 1 Main Seq. 11 Work- stealer 2 a 5 a 6 a 7 a 8 a 9 a 10 a 11 a 12 77 33 Steal request 22 66 i =a 5 *…*a i

19
Adaptive Prefix on 3 processors 0 a 1 a 2 a 3 a 4 Work- stealer 1 Main Seq. 11 Work- stealer 2 a 5 a 6 a 7 a 8 77 33 44 22 66 i =a 5 *…*a i a 9 a 10 a 11 a 12 88 44 Preempt 10 i =a 9 *…*a i 88 88

20
Adaptive Prefix on 3 processors 0 a 1 a 2 a 3 a 4 8 Work- stealer 1 Main Seq. 11 Work- stealer 2 a 5 a 6 a 7 a 8 77 33 44 22 66 i =a 5 *…*a i a 9 a 10 a 11 a 12 88 55 10 i =a 9 *…*a i 99 66 11 88 Preempt 11 88

21
Adaptive Prefix on 3 processors 0 a 1 a 2 a 3 a 4 8 11 a 12 Work- stealer 1 Main Seq. 11 Work- stealer 2 a 5 a 6 a 7 a 8 77 33 44 22 66 i =a 5 *…*a i a 9 a 10 a 11 a 12 88 55 10 i =a 9 *…*a i 99 66 11 12 10 77 11 88

22
Adaptive Prefix on 3 processors 0 a 1 a 2 a 3 a 4 8 11 a 12 Work- stealer 1 Main Seq. 11 Work- stealer 2 a 5 a 6 a 7 a 8 77 33 44 22 66 i =a 5 *…*a i a 9 a 10 a 11 a 12 88 55 10 i =a 9 *…*a i 99 66 11 12 10 77 11 88 Implicit critical path on the sequential process

23
Adaptive prefix : some experiments Single user context Adaptive is equivalent to : - sequential on 1 proc - optimal parallel-2 proc. on 2 processors - … - optimal parallel-8 proc. on 8 processors Multi-user context Adaptive is the fastest 15% benefit over a static grain algorithm Multi-user context Adaptive is the fastest 15% benefit over a static grain algorithm External charge Parallel Adaptive Parallel Adaptive Prefix of 10000 elements on a SMP 8 procs (IA64 / linux) #processors Time (s) #processors Join work with Daouda Traore

24
The Prefix race: sequential/parallel fixed/ adaptive Adaptative 8 proc. Parallel 8 proc. Parallel 7 proc. Parallel 6 proc. Parallel 5 proc. Parallel 4 proc. Parallel 3 proc. Parallel 2 proc. Sequential On each of the 10 executions, adaptive completes first

25
Conclusion Adaptive : what choices and how to choose ? Illustration : Adaptive parallel prefix based on work-stealing - self-tuned baroque hybrid : O(p log n ) choices - achieves near-optimal performance processor oblivious Generic adaptive scheme to implement parallel algorithms with provable performance

26
Mini Symposium Adaptive Algorithms for Scientific computing 9h45 Adaptive algorithms - Theory and applications Jean-Louis Roch &al. AHA Team INRIA-CNRS Grenoble, France 10h15Hybrids in exact linear algebra Dave Saunders, U. Delaware, USA 10h45 Adaptive programming with hierarchical multiprocessor tasks Thomas Rauber, U. Bayreuth, Germany 11h15 Cache-Obloivious algorithms Michael Bender, Stony Brook U., USA Adaptive, hybrids, oblivious : what do those terms mean ? Taxonomy of autonomic computing [Ganek & Corbi 2003] : – Self-configuring / self-healing / self-optimising / self-protecting Objective: towards an analysis based on the algorithm performance

27
Questions ?

Similar presentations

OK

21/03/2006 Cryptologie, Sécurité des systèmes & Espionnage industriel 1 Calculs sécurisés adaptatifs sur infrastructure de calcul global Calculs sécurisés.

21/03/2006 Cryptologie, Sécurité des systèmes & Espionnage industriel 1 Calculs sécurisés adaptatifs sur infrastructure de calcul global Calculs sécurisés.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on waves tides and ocean currents of the world Ppt on water transport in india Conceptual architecture view ppt on mac Ppt on staff motivation Broken text ppt on file Ppt on bluetooth based smart sensor networks inc Ppt on review writing software Ppt on spices of india Ppt on nitrogen cycle and nitrogen fixation meaning Ppt on relations and functions for class 11th chemistry