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Semantics Consistent Parallelism. Li-Yi Wei Microsoft Research. Parallelism. parallel. parallel. parallel. Traditional parallelization. Sequential consistency [Lampert] parallel algorithms do NOT change result sorting, FFT, matrix, etc. sort. New parallelization (cheating). - PowerPoint PPT Presentation
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Semantics Consistent ParallelismSemantics Consistent Parallelism
Li-Yi Wei
Microsoft Research
ParallelismParallelism
Algorithm
API
Hardware parallel
?
CUDA, BSGP
CPU, GPU
parallel
parallel
Traditional parallelizationTraditional parallelization
Sequential consistency [Lampert]
parallel algorithms do NOT change result
sorting, FFT, matrix, etc.
1 2 3 4 5 6 7 8
3 8 7 1 6 5 2 4
sort
New parallelization (cheating)New parallelization (cheating)
Not all algorithms need to be seq-consistent
perception (graphics/vision/image/video), statistics
approximate solutions might suffice → more parallel
Semantic consistency
Pseudo Random Number GeneratorPseudo Random Number Generator
The main source of randomness in programs
e.g. rand() in c/c++
Desirable properties
white noise statistics
repeatable, fast computation
Traditional sequential method
e.g. xn = (a xn-1 + b) mod c
Parallel PRNGParallel PRNG
1. input trivially prepared in parallel, e.g. linear ramp
2. feed input value into hash, independently & in parallel
3. output white noise
key idea:
borrow cryptographic hash!
[Tzeng and Wei I3D 2008]
hash
input
output
How to start a bar flightHow to start a bar flight
How to stop the bar flightHow to stop the bar flight
Parallel GPU run time (slow motion)
4M Poisson disk samples / secin parallel!
Poisson disk samplingPoisson disk sampling
A set of samples that are
as random as possible
remain a minimum distance r away from each other
Why pick this problem?
important algorithm
- sampling, graphics, statistics
seemly non-parallelizable
Dart throwing [Cook 1986]Dart throwing [Cook 1986]
Loop:
random sample from the entire domain
accept sample if not in conflict with existing ones
O High quality
ground truth
X Slow speed
inherently sequential
Parallel Poisson disk sampling[Wei SIGGRAPH 2008]Parallel Poisson disk sampling[Wei SIGGRAPH 2008]
Samples from a grid
1 sample per grid cell
Sample grid cells far apart in parallel
Watch out for bias!
Tricks to avoid bias
Image cloningImage cloning
http://www.freewebs.com/cheesesandwiches/cloning.jpghttp://mahboubian.googlepages.com/dog-bird.jpg
Poisson image editing[Perez et al. SIGGRAPH 2003]Poisson image editing[Perez et al. SIGGRAPH 2003]
State-of-art for image cloning + other stuff
Solving Poisson equation
interior detail (source)
boundary condition (target)
Heavy computation
[Farbman et al. SIGGRAPH 2009]
p = ∑ wi bi
Easy computation
Run parallel on a GPU
Coordinate interpolationCoordinate interpolation
SummarySummary
Conclusion
sequential consistency too strict
semantic consistency (perceptual, statistical, etc)
Future work
parallelism via semantic consistency
individual algorithms / applications
general methodology?