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CILK/CILK++ AND REDUCERS YUNMING ZHANG

RICE UNIVERSITY

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OUTLINE •  CILK and CILK++ Language Features and

Usages •  Work stealing runtime •  CILK++ Reducers •  Conclusions

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IDEALIZED SHARED MEMORY ARCHITECTURE

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•  Hardware model •  Processors •  Shared global

memory •  Software model

•  Threads •  Shared variables •  Communication •  Synchronization

Slide from Comp 422 Rice University Lecture 4

CILK AND CILK++ DESIGN GOALS •  Programmer friendly

•  Dynamic tasking •  Parallel extension to C

•  Scalable performance •  Efficient runtime system •  Minimum program overhead

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CILK KEYWORDS •  Cilk: a Cilk function •  Spawn: call can execute asynchronously

in a concurrent thread •  Sync: current thread waits for all locally-

spawned functions

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CILK EXAMPLE cilk int fib(n) {

if (n < 2) return n; else { int n1, n2; n1 = spawn fib(n-1); n2 = spawn fib(n-2); sync; return (n1 + n2); }

}

6 Borrowed from Comp 422 Rice University Lecture 4

CILK++ EXAMPLE int fib(n) {

if (n < 2) return n; else { int n1, n2; n1 = cilk_spawn fib(n-1); n2 = fib(n-2); cilk_sync; return (n1 + n2); }

}

7 Borrowed from Comp 422 Rice University Lecture 4

CILK++ EXAMPLE WITH DAG

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Pictures from “Reducers and Other CILK+ HyperObjects” Talk by Matteo Frigo (Intel). Pablo Halpern ( Intel). Charles E. Leiserson (MIT). Stephen Lewin-Berlin (Intel).



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WORK FIRST PRINCIPLE •  Work: T1 •  Critical path length: T∞ •  Number of processor: P •  Expected time

•  Tp = T1/P + O(T∞) •  Parallel slackness assumption

•  T1/P >> C∞T∞

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WORK FIRST PRINCIPLE •  Minimize scheduling overhead borne by

work at the expense of increasing critical path •  Tp ≤ C1Ts/P + C∞T∞ ≈ C1Ts/P Minimize C1 even at the expense of a larger C∞

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WORK STEALING DESIGN GOALS •  Minimizing contentions

•  Decentralized task deque •  Doubly linked deque

•  Minimize communication •  Steal work rather than push work

•  Load balance across cores •  Lazy task creation •  Steal from the top of the deque

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CILK WORK STEALING SCHEDULER

13 Pictures from “Reducers and Other CILK+ HyperObjects” Talk by Matteo Frigo (Intel). Pablo Halpern ( Intel). Charles E. Leiserson (MIT). Stephen Lewin-Berlin (Intel).


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TWO CLONE STRATEGY •  Fast clone

•  Identical in most respects to the C elision of the Cilk program

•  Very little execution overhead •  Sync statements compile to no op •  Allocates an continuation

•  Program variables and instruction pointer •  Slow clone

•  Convert a spawn schedule to slow clone only when it is stolen

•  Restores program state from activation frame that contains local variables, program counter and other parts of the procedure instance

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FAST CLONE

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SLOW CLONE Slow_fib(frame * _cilk_frame){

switch (_cilk_frame->header.entry) { fast_fib(_cilk_frame->n - 1 ); case 1: goto _cilk_sync1; fast_fib(_cilk_frame->n - 2 ); case 2: goto _cilk_sync2; sync (not a no op) case 3: goto _cilk_sync3; }

}

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FRAMES •  C++ Main Frame

•  Local variables of the procedure instance •  Temporary variables •  Linkage information for return values

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FRAMES •  CILK++ Stack Frame

•  Everything in C++ Main Frame •  Continuation •  Parent pointer •  Have exactly one child •  Used by Fast Clone •  A worker can have multiple Stack Frames

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FRAMES •  CILK++ Full Frame (used by slow clone)

•  Everything in CILK++ Stack Frame •  Lock •  Join counter •  List of children (has more than one

children) •  A worker has at most one Full Frame

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EXTENDED DEQUE WITH CALL STACKS

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Stack frame

Full frame

Extended Deque

Call stack

FUNCTION CALL

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Stack frame

Full frame

Extended Deque (Before Function Call) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

FUNCTION CALL

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Stack frame

Full frame

Extended Deque (After Function Call) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

New stack frame

SPAWN

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Stack frame

Full frame

Extended Deque (Before Spawn Call) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

SPAWN

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Stack frame

Full frame

Extended Deque (After Spawn Call) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

Set continuation in last stack frame

RESUME FULL FRAME

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Stack frame

Full frame

Extended Deque Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

Set the full frame to be the only frame in the call stack, resume execution on the continuation

RANDOMLY STEAL

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Stack frame

Full frame


Steal this call stack

RANDOMLY STEAL

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Stack frame

Full frame


Steal this call stack 1 1 1

RANDOMLY STEAL

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Stack frame

Full frame


1

1 1

PROVABLY GOOD STEAL

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Stack frame

Full frame


0

UNCONDITIONALLY STEAL

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Stack frame

Full frame


2

FUNCTION CALL RETURN

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Stack frame

Full frame

Extended Deque (Before Return from a Call Case1) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame


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Stack frame

Full frame

Extended Deque (Return from a Call Case 1) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame


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Stack frame

Full frame

Extended Deque (Return from a Call Case2) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

Worker executes an unconditional steal

SPAWN RETURN

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Stack frame

Full frame

Extended Deque (Before Spawn return Case 1) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

SPAWN RETURN

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Stack frame

Full frame

Extended Deque (After Spawn return Case 1) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

SPAWN RETURN

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Stack frame

Full frame

Extended Deque (Return from a SpawnCase2) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

Worker executes an provably good steal

SYNC

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Stack frame

Full frame

Extended Deque (Sync Case 1) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

Do nothing if it is a stack frame (No Op)

SYNC

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Stack frame

Full frame

Extended Deque (Sync Case 2) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

Pop the frame, provably good steal



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PROBLEMS WITH NON-LOCAL VARIABLES bool has_property(Node *) List<Node *> output_list; void walk(Node *x) {

if (x) { if (has_property(x)) output_list.push_back(x); cilk_spawn walk(x->left); walk(x->right); cilk_sync;

}

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REDUCER DESIGN GOALS •  Support parallelization of programs

containing global variables •  Enable efficient parallel scaling by

avoiding a single point of contention •  Provide deterministic result for

associative reduce operations •  Operate independently of any control

constructs

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REDUCER EXAMPLE bool has_property(Node *) List_append_reducer<Node *> output_list; void walk(Node *x) {

if (x) { if (has_property(x)) output_list.push_back(x); cilk_spawn walk(x->left); walk(x->right); cilk_sync;

}

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HYPER OBJECTS

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REDUCER

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SEMANTICS OF REDUCERS •  The child strand owns the view owned by

parent function before cilk_spawn •  The parent strand owns a new view,

initialized to identity view e, •  A special optimization ensures that if a

view is unchanged when combined with the identity view 3

•  Parent strand P own the view from completed child strands

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REDUCING OVER LIST CONCATENATION

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REDUCING OVER LIST CONCATENATION

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IMPLEMENTATION OF REDUCER •  Each worker maintains a hypermap •  Hypermap

•  Maps reducers to the views •  User

•  The view of the current procedure •  Children

•  The view of the children procedures •  Right

•  The view of right sibling •  Identity

•  The default value of a view

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UNDERSTANDING HYPERMAPS bool has_property(Node *) List_append_reducer<Node *> output_list; void walk(Node *x) ß------------ Proc A {

if (x) { if (has_property(x)) output_list.push_back(x); cilk_spawn walk(x->left); ß---------proc B cilk_spawn walk(x->right); ß-------- proc C cilk_sync;

}

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LAZY CREATION •  A new view will only be created

•  after a steal •  On demand

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HYPERMAP CREATION

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HYPERMAP CREATION

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HYPERMAP CREATION

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HYPERMAP CREATION

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HYPERMAP CREATION

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LOOK UP FAILURE •  Inserts a view containing an identity

element for the reducer into the hypermap. •  Following the lazy principle

•  Look up returns the newly inserted identity view

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RANDOM WORK STEALING A random steal operation steals a full frame P and replaces it with a new full frame C in the victim.

USERC ← USERP; U S E R P ← 0/ ; CHILDRENP←0/; RIGHTP←0/.

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RANDOM WORK STEALING

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RETURN FROM A CALL Let C be a child frame of the parent frame P that originally called C, and suppose that C returns.

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RETURN FROM A CALL

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Stack frame

Full frame

Extended Deque (Before Return from a Call Case1) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

RETURN FROM A CALL

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Stack frame

Full frame

Extended Deque (Return from a Call Case 1) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame


• If C is a stack frame, do nothing,

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Stack frame

Full frame

Extended Deque (Return from a Call Case2) Function call Spawn Call return Spawn return Sync Randomly steal Provably good steal Unconditionally steal Resume full frame

Worker executes an unconditional steal


• If C is a stack frame, do nothing, • If C is a full frame.

• Transfer ownership of view • Children and Right are empty • USERP ← USERC

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RETURN FROM A SPAWN Let C be a child frame of the parent frame P that originally spawned C, and suppose that C returns. •  Always do USERC ← REDUCE(USERC,RIGHTC) •  If C is a stack frame, do nothing •  If C is a full frame

•  If C has siblings, •  RIGHTL ← REDUCE(RIGHTL,USERC)

•  C is the leftmost child •  CHILDRENP ←

REDUCE(CHILDRENP,USERC)

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RETURN FROM A SPAWN EXAMPLE bool has_property(Node *) List_append_reducer<Node *> output_list; void walk(Node *x) ß------------ Proc A {


}

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}

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}

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SYNC A cilk_sync statement waits until all children have completed. When frame P executes a cilk_sync, one of following two cases applies: •  If P is a stack frame, do nothing. •  If P is a full frame,

•  USERP ← REDUCE(CHILDRENP,USERP).

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BENEFITS OF REDUCERS

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CONCLUSIONS •  CILK and CILK++ provide a programmer

friendly programming model •  Extension to C •  Incremental parallelism •  Scaling on future machines

•  Non-compromising performance •  Work stealing runtime •  Minimizing overheads •  Reducers

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FINAL NOTES •  Designed for an idealized shared memory

model •  Today’s architectures are typically NUMA

•  Task creation can be lazier •  http://ieeexplore.ieee.org/xpls/abs_all.jsp?

arnumber=6012915&tag=1 •  Cilk_for

•  Divide and conquer parallelization

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