Efficient Stream Reduction on the GPU Efficient Stream Reduction on - - PowerPoint PPT Presentation
Efficient Stream Reduction on the GPU Efficient Stream Reduction on the GPU David Roger, Ulf Assarsson, Nicolas Holzschuch Grenoble Chalmers University Cornell University of Technology University Stream Reduction Removing unwanted elements
Grenoble University Chalmers University
Cornell University
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Input stream Reduced stream
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– Ray tracing – Collision detection
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if x[j] is valid then
x[i]=x[j] i=i+1
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– We will speak about scatter later
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Input stream Reduced stream
1 1 1 1 2 3 3 4 4 5 5 5 6 6
Dichotomic search:
performs the displacements
Prefix sum Prefix sum scan:
computes the displacements
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– Hillis and Steele, Horn: O(n log n) – Blelloch, Sengupta et al., Harris et al.: O(n) – Sengupta et al. Hybrid: O(n)
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– NV_transform_feedback – Input stream: vertices in a VBO – Geometry shader discards NULL elements – Output stream: vertices in a VBO
– Slow
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Input stream, split in blocks Reduced stream Reduction of the blocks Concatenation
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– Prefix sum scan – Dichotomic search
– s: size of a block – One block: O(s log s) – n/s blocks: O(n log s)
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– Computes displacements of
the blocks in parallel
– Segments extremities moved
by scattering (vertex engine)
– Other elements linearly
interpolated (rasterization)
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Reduced stream Reduced blocks
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Reduced stream Reduced blocks
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Reduced stream Reduced blocks
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– s is the size of the blocks – s is a constant !
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Input stream, split in blocks Reduced stream Prefix sum scan + Dichotomic search Prefix sum scan + Line drawing
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– Dichotomic search is avoided – Vertex engine: scatter ... but lesser efficiency
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Input stream, split in blocks Reduced stream Prefix sum scan + Dichotomic search Prefix sum scan + Line drawing
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Input stream, split in blocks Reduced stream Prefix sum scan + Dichotomic search Prefix sum scan + Line drawing
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Input block Reduced block
1 1 1 1 2 3 4 4 5 5 5 6 6
Prefix sum
sum[j] = 3
Gather: At output position i Search j in input such as: i = j – sum[j] Search bounds: i+sum[i] ≤ j ≤ i+sum[15] Example: i = 5 6 ≤ j ≤ 11 Search result j = 8
3 ? 0 1 2 3 4 5 6 7 j=8 j=8 9 10 11 12 13 14 15 0 1 2 3 4 i=5 =5 6 7 8 9 10 11 12 13 14 15
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while(found ≠ 0) { if (found < 0) lowBound = j else upBound = j j = (lowBound + upBound) / 2 found = j-sum[j]-i }
lowBound = i + sum[i] upBound = i + sum[n-1] if(upBound > n-1) discard j = (lowBound + upBound)/2 found = j-sum[j]-i
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while(found ≠ 0) { if (found < 0) lowBound = j - found else upBound = j - found j = (lowBound + upBound) / 2 found = j-sum[j]-i }
lowBound = i + sum[i] upBound = i + sum[n-1] if(upBound > n-1) discard j = (lowBound + upBound)/2 found = j-sum[j]-i
Because j – sum[j] is contracting!
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Input stream, split in blocks Reduced stream Prefix sum scan + Dichotomic search Prefix sum scan + Line drawing
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Input stream, split in blocks Reduced stream Prefix sum scan + Dichotomic search Prefix sum scan + Line drawing
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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– Split all segments in two
– Use geometry engine to split only when necessary
Concatenation
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Input stream, split in blocks Reduced stream Reduction of the blocks:
sum scan + search O(n log s)
sequential algo (loop over the block) O(n)
Concatenation:
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– Sum scan (Harris et al. or Sengupta et al.) + scatter
– Expected speed up ≥ 2.5
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– We don't compete with them, we use them !
– O(n) Vs O(n log n)
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