automatic vectorization of tree traversals
play

AUTOMATIC VECTORIZATION OF TREE TRAVERSALS Youngjoon Jo, Michael - PowerPoint PPT Presentation

Dec 25, 2022 •240 likes •1.38k views

AUTOMATIC VECTORIZATION OF TREE TRAVERSALS Youngjoon Jo, Michael Goldfarb and Milind Kulkarni PACT, Edinburgh, U.K. September 11 th , 2013 2 Youngjoon Jo Commodity processors and SIMD Commodity processors support SIMD (Single Instruction

  1. 27 Youngjoon Jo An abstract model void main() { � foreach(Point p : points) { � foreach(Node n : p.oracleNodes()) { � update(p, n); � } � } � } � �

  2. 28 Youngjoon Jo Iteration space of traversal void main() { � foreach(Point p : points) { � foreach(Node n : p.oracleNodes()) { � update(p, n); � } � } � Nodes } � � Points

  3. 29 Youngjoon Jo Iteration space of traversal Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  4. 30 Youngjoon Jo Iteration space of traversal Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  5. 31 Youngjoon Jo How to vectorize? Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  6. 32 Youngjoon Jo Outline • Example & Abstract Model • Point Blocking to Enable SIMD • Traversal Splicing to Enhance Utilization • Automatic Transformation • Evaluation and Conclusion

  7. 33 Youngjoon Jo Point blocking [OOPSLA 2011] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  8. 34 Youngjoon Jo Point blocking [OOPSLA 2011] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  9. 35 Youngjoon Jo Point blocked code void recurse(Point *p, Node *n) { � if (truncate(p, n)) return; � if (n->isLeaf()) { � update(p, n); � } else { � recurse(p, n->left); � recurse(p, n->right); � } � } �

  10. 36 Youngjoon Jo Point blocked code void recurse(Block *block, Node *n) { � if (truncate(p, n)) return; � if (n->isLeaf()) { � update(p, n); � } else { � recurse(p, n->left); � recurse(p, n->right); � } � } �

  11. 37 Youngjoon Jo Point blocked code void recurse(Block *block, Node *n) { � if (truncate(p, n)) return; � if (n->isLeaf()) { � Function update(p, n); � body } else { � recurse(p, n->left); � recurse(p, n->right); � } � } �

  12. 38 Youngjoon Jo Point blocked code Loop over points in block void recurse(Block *block, Node *n) { � for (int i = 0; i = block->size; i++) { � Point *p = block->p[i]; � if (truncate(p, n)) continue; � Function if (n->isLeaf()) { � update(p, n); � body } else { � recurse(p, n->left); � recurse(p, n->right); � } � } � } �

  13. 39 Youngjoon Jo Point blocked code Loop over points in block void recurse(Block *block, Node *n) { � for (int i = 0; i = block->size; i++) { � Point *p = block->p[i]; � if (truncate(p, n)) continue; � Function if (n->isLeaf()) { � update(p, n); � body } else { � recurse(p, n->left); � recurse(p, n->right); � } � } � } �

  14. 40 Youngjoon Jo Point blocked code Loop over points in block void recurse(Block *block, Node *n) { � Block *nextBlock = // next level block � for (int i = 0; i = block->size; i++) { � Point *p = block->p[i]; � if (truncate(p, n)) continue; � Function if (n->isLeaf()) { � body update(p, n); � } else { � nextBlock->add(p); � } � } � } �

  15. 41 Youngjoon Jo Point blocked code Loop over points in block void recurse(Block *block, Node *n) { � Block *nextBlock = // next level block � for (int i = 0; i = block->size; i++) { � Point *p = block->p[i]; � if (truncate(p, n)) continue; � Function if (n->isLeaf()) { � body update(p, n); � } else { � nextBlock->add(p); � } � } � if (nextBlock->size > 0) { � Next block recurse(nextBlock, n->left); � recurses children recurse(nextBlock, n->right); � } � } �

  16. 42 Youngjoon Jo Point blocking [OOPSLA 2011] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  17. 43 Youngjoon Jo Point blocking [OOPSLA 2011] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  18. 44 Youngjoon Jo Point blocking [OOPSLA 2011] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  19. 45 Youngjoon Jo Analogous to packet SIMD Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  20. 46 Youngjoon Jo Analogous to packet SIMD Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 e g r e v i d 2 s 3 t n o i p n e h w n w o d s k a e r B 4 5 6 7 8 9 10 11 12 13 14 15

  21. 47 Youngjoon Jo Packet SIMD has poor utilization Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E Partial Full F SIMD SIMD G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  22. 48 Youngjoon Jo Packet SIMD has poor utilization Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 Partial Full SIMD SIMD 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  23. 49 Youngjoon Jo SIMD utilization Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 Partial Full n o i t a z l i i u t D M SIMD I S SIMD 2 3 k r o w l a t o T / D 4 5 6 M 7 S I l u l f n i k r o W = 8 9 10 11 12 13 14 15

  24. 50 Youngjoon Jo SIMD utilization Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G k r o H w l a o t T / D M I S l l u f n i k r o W 1 Partial Full s e l c r i c l a t o T / e SIMD u l SIMD b n 2 i s 3 e l c r i C = 4 5 6 7 2 3 . 0 = 4 7 / 4 2 = 8 9 10 11 12 13 14 15

  25. 51 Youngjoon Jo Use larger block size Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H D M S I n a h t r e 1 g r a Partial l Full e z i s k c o l b e s U SIMD SIMD 2 3 ! s t n i o p t c a p m o c d n a h 4 t 5 6 7 d w i 8 9 10 11 12 13 14 15

  26. 52 Youngjoon Jo Use larger block size Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  27. 53 Youngjoon Jo Better utilization with larger block size Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H Partial SIMD 1 Full SIMD 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  28. 54 Youngjoon Jo Better utilization with larger block size Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H Partial SIMD 1 s e c l Full r c i a l o t T / e u b l n i SIMD s e c l 2 r 3 C i 6 8 . 0 = 4 5 6 7 4 7 / 4 6 = 8 9 10 11 12 13 14 15

  29. 55 Youngjoon Jo SIMD utilization – Block size 1 SIMD Utilization 0.8 Barnes-Hut 0.6 Point Correlation 0.4 Nearest Neighbor 0.2 Vantage Point 0 4 40 400 4000 40000 400000 Photon Mapping Block Size

  30. 56 Youngjoon Jo Ideal utilization Ideal Utilization 1 SIMD Utilization 0.8 Barnes-Hut 0.6 Point Correlation 0.4 Nearest Neighbor 0.2 Vantage Point 0 4 40 400 4000 40000 400000 Photon Mapping Block Size s t n o i p l a t o t o t l a u q e e z s i k c o B l n o t i a z i i l t u D M I S a l e d i s d l e i y

  31. 57 Youngjoon Jo Use max block! Problem solved? 1 SIMD Utilization 0.8 Barnes-Hut 0.6 Point Correlation 0.4 Nearest Neighbor 0.2 Vantage Point 0 4 40 400 4000 40000 400000 Photon Mapping Block Size

  32. 58 Youngjoon Jo Large block has poor locality 1 SIMD Utilization 0.8 Barnes-Hut 0.6 Point Correlation 0.4 Nearest Neighbor 0.2 Vantage Point 0 4 40 400 4000 40000 400000 Photon Mapping Block Size

  33. 59 Youngjoon Jo Large block has poor locality 1 SIMD Utilization 0.8 Barnes-Hut 0.6 Point Correlation 0.4 Nearest Neighbor 0.2 Vantage Point 0 4 40 400 4000 40000 400000 Photon Mapping Block Size n o t i a z i i l t u d o o g h i t w e l u d e h c s d e e N y t i a l c o l d o o g d n a

  34. 60 Youngjoon Jo Outline • Example & Abstract Model • Point Blocking to Enable SIMD • Traversal Splicing to Enhance Utilization • Automatic Transformation • Evaluation and Conclusion

  35. 61 Youngjoon Jo Traversal splicing [OOPSLA 2012] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  36. 62 Youngjoon Jo Traversal splicing [OOPSLA 2012] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1. Designate splice nodes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  37. 63 Youngjoon Jo Traversal splicing [OOPSLA 2012] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  38. 64 Youngjoon Jo Traversal splicing [OOPSLA 2012] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  39. 65 Youngjoon Jo Traversal splicing [OOPSLA 2012] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 3. Resume at next node 4 5 6 7 8 9 10 11 12 13 14 15

  40. 66 Youngjoon Jo Traversal splicing [OOPSLA 2012] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 3. Resume at next node 4 5 6 7 8 9 10 11 12 13 14 15

  41. 67 Youngjoon Jo Traversal splicing [OOPSLA 2012] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 3. Resume at next node 4 5 6 7 4. Repeat 2-3 until finished 8 9 10 11 12 13 14 15

  42. 68 Youngjoon Jo Traversal splicing [OOPSLA 2012] Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 3. Resume at next node 4 5 6 7 4. Repeat 2-3 until finished 8 9 10 11 12 13 14 15

  43. 69 Youngjoon Jo Can change order of points Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H f o r e d r o e h t e g n a 1. Designate splice nodes h c 1 n a c e W 2. Traverse up to splice node ? w 2 o 3 h t u b , s n t i o 3. Resume at next node p d e s u a p 4 5 6 7 4. Repeat 2-3 until finished 8 9 10 11 12 13 14 15

  44. 70 Youngjoon Jo Dynamic sorting Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B e m a s h c a e r h c i h w C s t n o i p : t h g i s n I Points r D a l i m s i e v a h o t y l e k l i e r a E s e d o n e r F u t u f n i s a l s r e v a t r G H y r o t s i h l 1. Designate splice nodes a s r 1 e v a r t n o g n t i r o s c 2. Traverse up to splice node i m a n y D 2 3 3. Resume at next node 4 5 6 7 4. Repeat 2-3 until finished 8 9 10 11 12 13 14 15

  45. 71 Youngjoon Jo Dynamic sorting Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A B C Points D E F G H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  46. 72 Youngjoon Jo Dynamic sorting Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A A B B C C Points D D E E F F G G H H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 3. Reorder points at splice node 4 5 6 7 8 9 10 11 12 13 14 15

  47. 73 Youngjoon Jo Dynamic sorting Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A A B C C E Points D F E H F B G D H G 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 3. Reorder points at splice node 4 5 6 7 8 9 10 11 12 13 14 15

  48. 74 Youngjoon Jo Dynamic sorting Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A A A B C C C E E Points D F F E H H F B B G D D H G G 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 3. Reorder points at splice node 4 5 6 7 4. Resume at next node 8 9 10 11 12 13 14 15

  49. 75 Youngjoon Jo Dynamic sorting Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A A E B C B C E D Points D F G E H A F B C G D F H G H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 3. Reorder points at splice node 4 5 6 7 4. Resume at next node 5. Repeat 2-4 until finished 8 9 10 11 12 13 14 15

  50. 76 Youngjoon Jo Dynamic sorting Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A A E B C B C E D Points D F G E H A F B C G D F H G H 1. Designate splice nodes 1 2. Traverse up to splice node 2 3 3. Reorder points at splice node 4 5 6 7 4. Resume at next node 5. Repeat 2-4 until finished 8 9 10 11 12 13 14 15

  51. 77 Youngjoon Jo Dynamic sorting enhances utilization Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A A E B C B C E D Points D F G E H A Partial F B C SIMD G D F H G H 1 Full SIMD 2 3 4 5 6 7 8 9 10 11 12 13 14 15

  52. 78 Youngjoon Jo Dynamic sorting enhances utilization Nodes 1 2 4 8 9 5 10 11 3 6 12 13 7 14 15 A A E B C B C E D Points D F G E H A Partial F B C SIMD G D F H G H 1 s e c l Full r c i a l o t T / e u b l n i SIMD s e c l 2 r 3 C i 5 6 . 0 = 4 5 6 7 4 7 / 8 4 = 8 9 10 11 12 13 14 15

  53. 79 Youngjoon Jo SIMD utilization – splice depth 1 N/A SIMD Utilization 0.8 2 0.6 4 0.4 6 0.2 8 0 4 40 400 4000 40000 400000 10 Block Size Nearest Neighbor

  54. 80 Youngjoon Jo SIMD utilization – splice depth Block size: 512 Splice depth: 10 1 N/A SIMD Utilization 0.8 2 0.6 4 0.4 Block size: 6 0.2 524288 8 0 4 40 400 4000 40000 400000 10 Block Size Nearest Neighbor

  55. 81 Youngjoon Jo SIMD utilization 1 0.9 0.8 Utilization 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Baseline A Priori Sort Dynamic Sort Ideal

  56. 82 Youngjoon Jo SIMD utilization 1 0.9 0.8 Utilization 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 y l l a c t i a m o u t a n a c g n t i Baseline r A Priori Sort Dynamic Sort Ideal o s c i m a n y D m u m i x a m e h t t s o m l a t c a r t x e n o i a t z i i l t u D M S I f o t n u o m a

  57. 83 Youngjoon Jo Outline • Example & Abstract Model • Point Blocking to Enable SIMD • Traversal Splicing to Enhance Utilization • Automatic Transformation • Evaluation and Conclusion

  58. 84 Youngjoon Jo Automatic transformation • Point blocking Jo and Kulkarni [OOPSLA 2011] • Traversal splicing Jo and Kulkarni [OOPSLA 2012]

  59. 85 Youngjoon Jo Automatic transformation • Our key addition for SIMD: Layout transformation from AoS (array of structures) to SoA (structure of arrays) • + Allows vector load/stores • + Packed data has better spatial locality • - More overhead in moving data AoS (array of structures) x1 y1 z1 x2 y2 z2 x3 y3 z3 x4 y4 z4 SoA (structure of arrays) x1 x2 x3 x4 y1 y2 y3 y4 z1 z2 z3 z4

  60. 86 Youngjoon Jo AoS to SoA layout • Whole program AoS to SoA layout transformation difficult to automate with aliasing • Limit scope to traversal code only • Copy in to SoA before traversal • Copy out to AoS after traversal • Inter-procedural, flow-insensitive analysis • Determine which point fields should be SoA • Conservatively ensure correctness

  61. 87 Youngjoon Jo AoS to SoA layout � � � void recurse(Point *p, Node *n) { � if (truncate(p, n)) return; � if (n->isLeaf()) { � update(p, n); � } else { � recurse(p, n->left); � recurse(p, n->right); � } � } �

  62. 88 Youngjoon Jo AoS to SoA layout struct Point { float f1, f2, f3; } � � � void recurse(Point *p, Node *n) { � if (truncate(p, n)) return; � if (n->isLeaf()) { � update(p, n); � } else { � recurse(p, n->left); � recurse(p, n->right); � } � } � � �

  63. 89 Youngjoon Jo AoS to SoA layout struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � void recurse(Point *p, Node *n) { � if (truncate(p, n)) return; � if (n->isLeaf()) { � update(p, n); � } else { � recurse(p, n->left); � recurse(p, n->right); � } � } � �

  64. 90 Youngjoon Jo AoS to SoA layout struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � void recurse(Point *p, Node *n) { � if (truncate(p, n)) return; � if (n->isLeaf()) { � update(p, n); � } else { � recurse(p, n->left); � recurse(p, n->right); � } � } � � bool truncate(Point *p, Node *n) { � return p->f1 == n->point->f1; � } � � void update(Point *p, Node *n) { � p->f2 += n->point->f3; � } � �

  65. 91 Youngjoon Jo Ensuring correctness struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � void recurse(Point *p, Node *n) { � if (truncate(p, n)) return; � if (n->isLeaf()) { � update(p, n); � } else { � recurse(p, n->left); � recurse(p, n->right); � } � } � � bool truncate(Point *p, Node *n) { � return p->f1 == n->point->f1; � } � � void update(Point *p, Node *n) { � p->f2 += n->point->f3; � } � �

  66. 92 Youngjoon Jo Ensuring correctness struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � � � Point-access Non-point-access � Read Write Read Write � � f1 � f2 � � f3 � � bool truncate(Point *p, Node *n) { � return p->f1 == n->point->f1; � } � � void update(Point *p, Node *n) { � p->f2 += n->point->f3; � } � �

  67. 93 Youngjoon Jo Ensuring correctness struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � � � Point-access Non-point-access � Read Write Read Write � � f1 ✓ � f2 � � f3 � � bool truncate(Point *p, Node *n) { � return p->f1 == n->point->f1; � } � � void update(Point *p, Node *n) { � p->f2 += n->point->f3; � } � �

  68. 94 Youngjoon Jo Ensuring correctness struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � � � Point-access Non-point-access � Read Write Read Write � � f1 ✓ ✓ � f2 � � f3 � � bool truncate(Point *p, Node *n) { � return p->f1 == n->point->f1; � } � � void update(Point *p, Node *n) { � p->f2 += n->point->f3; � } � �

  69. 95 Youngjoon Jo Ensuring correctness struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � � � Point-access Non-point-access � Read Write Read Write � � f1 ✓ ✓ � f2 ✓ ✓ � � f3 � � bool truncate(Point *p, Node *n) { � return p->f1 == n->point->f1; � } � � void update(Point *p, Node *n) { � p->f2 += n->point->f3; � } � �

  70. 96 Youngjoon Jo Ensuring correctness struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � � � Point-access Non-point-access � Read Write Read Write � � f1 ✓ ✓ � f2 ✓ ✓ � � f3 ✓ � � bool truncate(Point *p, Node *n) { � return p->f1 == n->point->f1; � } � � void update(Point *p, Node *n) { � p->f2 += n->point->f3; � } � �

  71. 97 Youngjoon Jo Transforming SoA fields struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � � � Point-access Non-point-access � Read Write Read Write � � f1 ✓ ✓ � f2 ✓ ✓ � � f3 ✓ � � bool truncate(Point *p, Node *n) { � return p->f1 == n->point->f1; � } � � void update(Point *p, Node *n) { � p->f2 += n->point->f3; � } � �

  72. 98 Youngjoon Jo Transforming SoA fields struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � � � Point-access Non-point-access � Read Write Read Write � � f1 ✓ ✓ � f2 ✓ ✓ � � f3 ✓ � � bool truncate(Block *block, int bi, Node *n) { � return block->f1[bi] == n->point->f1; � } � � void update(Block *block, int bi, Node *n) { � block->f2[bi] += n->point->f3; � } � �

  73. 99 Youngjoon Jo Correctness violation example struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � � � Point-access Non-point-access � Read Write Read Write � � f1 ✓ ✓ � f2 ✓ ✓ ✓ � � f3 � � bool truncate(Block *block, int bi, Node *n) { � return block->f1[bi] == n->point->f1; � } � � void update(Block *block, int bi, Node *n) { � block->f2[bi] += n->point->f2; � } � �

  74. 100 Youngjoon Jo Ensuring correctness struct Point { float f1, f2, f3; } � struct Node { Node *left, *right; Point *point; } � � � � Point-access Non-point-access � Read Write Read Write � � f1 ✓ ✓ � f2 ✓ ✓ ✓ � y l e v t i a v r e s n o c s i � s y f3 a l n a d n u o S � t . c e r r o c n o � i a t m r o s f n a r t A o bool truncate(Point *p, Node *n) { � S s e v o r p return p->f1 == n->point->f1; � u r o f o l l a m r o f s n } � a r t o t s e c i f f u S � void update(Point *p, Node *n) { � . s k a r m h c n e b p->f2 += n->point->f3; � p->f3 = 1; � } � �

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

Tree traversals Todays announcements: MT1 Feb 4, 7-9:00p WOOD 2 HW2 out, due Feb 5,

Tree traversals Todays announcements: MT1 Feb 4, 7-9:00p WOOD 2 HW2 out, due Feb 5,

Tree traversals Todays announcements: MT1 Feb 4, 7-9:00p WOOD 2 HW2 out, due Feb 5, 11:59p Todays Plan Trees and their traversals Warm up: What is the number of nodes N ( h ) in a perfect binary tree of height h ? 1 / 8 A

330 views • 8 slides
Tree Properties & Traversals CS16: Introduction to Data Structures & Algorithms Spring

Tree Properties & Traversals CS16: Introduction to Data Structures & Algorithms Spring

Tree Properties & Traversals CS16: Introduction to Data Structures & Algorithms Spring 2020 How does OS calculate size of directories? Outline Tree & Binary Tree ADT Tree Traversals Breadth-First Traversal

1.06k views • 56 slides
TSLP Throttling Automatic Vectorization: When Less is More Vasileios Porpodas and Timothy M.

TSLP Throttling Automatic Vectorization: When Less is More Vasileios Porpodas and Timothy M.

TSLP Throttling Automatic Vectorization: When Less is More Vasileios Porpodas and Timothy M. Jones University of Cambridge LLVM Developers Meeting 2015 www.cl.cam.ac.uk/ vp331/ slide 1 of 16 Why SIMD Vectorization? Scalar Reg. File

1.55k views • 112 slides
overview tree traversals data structures and algorithms binary search 2020 10 01 lecture 10

overview tree traversals data structures and algorithms binary search 2020 10 01 lecture 10

overview tree traversals data structures and algorithms binary search 2020 10 01 lecture 10 binary search trees overview recap definitions binary tree: every node has at most 2 successors (empty tree is also a binary tree) tree traversals

399 views • 10 slides
Using Machine Learning to Improve Automatic Vectorization Kevin Stock Louis-Nol Pouchet P .

Using Machine Learning to Improve Automatic Vectorization Kevin Stock Louis-Nol Pouchet P .

Using Machine Learning to Improve Automatic Vectorization Kevin Stock Louis-Nol Pouchet P . Sadayappan The Ohio State University January 24, 2012 HiPEAC Conference Paris, France Introduction: HiPEAC12 Vectorization Observations

346 views • 22 slides
Q1 Q1-3 More BinaryTree methods Tree Traversals After today, you should be able to

Q1 Q1-3 More BinaryTree methods Tree Traversals After today, you should be able to

Q1 Q1-3 More BinaryTree methods Tree Traversals After today, you should be able to traverse trees on paper & in code } Doublets is next assignment. } Also with a partner meet later during today's class. } Instructor demo later

426 views • 16 slides
Q1-3 Q1-3 More BinaryTree methods Tree Traversals After today, you should be able to

Q1-3 Q1-3 More BinaryTree methods Tree Traversals After today, you should be able to

Q1-3 Q1-3 More BinaryTree methods Tree Traversals After today, you should be able to traverse trees on paper & in code 1 Please complete the Stacks&Queues partner evaluation in Moodle after you submit your final code. Due

717 views • 15 slides
Q1 Q1 More BinaryTree methods Tree Traversals and Iterators After today, you should be able

Q1 Q1 More BinaryTree methods Tree Traversals and Iterators After today, you should be able

Q1 Q1 More BinaryTree methods Tree Traversals and Iterators After today, you should be able to traverse trees on paper & in code implement a simple iterator for trees Why must I use a StringBuilder? Strings are immutable.

408 views • 15 slides
Graph & Tree Search and Traversals Algorithms Mark Redekopp David Kempe Sandra Batista 2

Graph & Tree Search and Traversals Algorithms Mark Redekopp David Kempe Sandra Batista 2

1 CSCI 104 Graph & Tree Search and Traversals Algorithms Mark Redekopp David Kempe Sandra Batista 2 RECURSIVE TREE TRAVERSALS 3 Guiding Recursive Principle f(n) f(n-1) 1 0 1 2 3 4 A useful principle when trying to 50 51

1.08k views • 90 slides
Q1 Q1 More BinaryTree methods Tree Traversals Exam review After today, you should be able

Q1 Q1 More BinaryTree methods Tree Traversals Exam review After today, you should be able

Q1 Q1 More BinaryTree methods Tree Traversals Exam review After today, you should be able to traverse trees on paper & in code } Doublets is next assignment. } Also with a partner well find partner later. } Instructor demo

557 views • 19 slides
General Transformations for GPU Execution of Tree Traversals Michael Goldfarb*, Youngjoon Jo**,

General Transformations for GPU Execution of Tree Traversals Michael Goldfarb*, Youngjoon Jo**,

General Transformations for GPU Execution of Tree Traversals Michael Goldfarb*, Youngjoon Jo**, Milind Kulkarni School of Electrical and Computer Engineering * Now at Qualcomm; ** Now at Google Thursday, November 21, 13 GPU execution of

1.28k views • 92 slides
Trees Linear Vs non-linear data structures Types of binary trees Binary tree traversals

Trees Linear Vs non-linear data structures Types of binary trees Binary tree traversals

Trees Linear Vs non-linear data structures Types of binary trees Binary tree traversals Representations of a binary tree Binary tree ADT Binary search tree EECS 268 Programming II 1 Overview We have discussed linear

1.05k views • 76 slides
Tr Treelogy: : A Benchma mark rk Su Suite for r Tree Traversals Nikhil Hegde, Jianqiao Liu,

Tr Treelogy: : A Benchma mark rk Su Suite for r Tree Traversals Nikhil Hegde, Jianqiao Liu,

Purdue University Programming Languages Group Tr Treelogy: : A Benchma mark rk Su Suite for r Tree Traversals Nikhil Hegde, Jianqiao Liu, Kirshanthan Sundararajah, and Milind Kulkarni School of Electrical and Computer Engineering

391 views • 25 slides
More simple BinaryTree methods Tree Traversals 1 Exam 1 Day 11 in class Coverage:

More simple BinaryTree methods Tree Traversals 1 Exam 1 Day 11 in class Coverage:

More simple BinaryTree methods Tree Traversals 1 Exam 1 Day 11 in class Coverage: Everything from reading and lectures, Sessions 1-9 Programs through Hardy Written assignments 1-3 Allowed resources: Written part:

330 views • 12 slides
PSLP: Padded SLP Automatic Vectorization Vasileios Porpodas , Alberto Magni and Timothy M.

PSLP: Padded SLP Automatic Vectorization Vasileios Porpodas , Alberto Magni and Timothy M.

PSLP: Padded SLP Automatic Vectorization Vasileios Porpodas , Alberto Magni and Timothy M. Jones University of Cambridge University of Edinburgh EuroLLVM APR 2015 slide 1 of 17 www.cl.cam.ac.uk/ vp331/ Why SIMD

1.29k views • 90 slides
Trees 9/21/2007 8:11 AM Outline and Reading Tree ADT (6.1) Preorder and postorder traversals

Trees 9/21/2007 8:11 AM Outline and Reading Tree ADT (6.1) Preorder and postorder traversals

1 Trees Trees 9/21/2007 8:11 AM Outline and Reading Tree ADT (6.1) Preorder and postorder traversals (6.2.3) BinaryTree ADT (6.3.1) Inorder traversal (6.3.4) Euler Tour traversal (6.3.4) Template method pattern (6.3.5) Data

478 views • 18 slides
Protection, DAQ, Splice Resistance Darryl Orris/Mike Tartaglia 25 April 2016 LMQXF Cold Mass

Protection, DAQ, Splice Resistance Darryl Orris/Mike Tartaglia 25 April 2016 LMQXF Cold Mass

CM Testing Equipment: Quench Protection, DAQ, Splice Resistance Darryl Orris/Mike Tartaglia 25 April 2016 LMQXF Cold Mass Requirements and Conceptual Design Review Overview Test Stand Controls Existing Siemens PLC will be upgraded to

885 views • 23 slides
Click to go to website: www.njctl.org Slide 2 / 81 Eukaryotes & Gene Expression Practice

Click to go to website: www.njctl.org Slide 2 / 81 Eukaryotes & Gene Expression Practice

Slide 1 / 81 New Jersey Center for Teaching and Learning Progressive Science Initiative This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be

940 views • 81 slides
Psychoneuroimmunology Scott Carroll, MD Director of Child Psychiatric Consultation Services

Psychoneuroimmunology Scott Carroll, MD Director of Child Psychiatric Consultation Services

Psychoneuroimmunology Scott Carroll, MD Director of Child Psychiatric Consultation Services University of New Mexico Childrens Hospital What is PNI ? Multidisciplinary study of how the emotions, nervous system and the immune system

594 views • 16 slides
Analysis of variance April 16, 2009 Contents Comparison of several groups One-way ANOVA

Analysis of variance April 16, 2009 Contents Comparison of several groups One-way ANOVA

Analysis of variance April 16, 2009 Contents Comparison of several groups One-way ANOVA Two-way ANOVA Interaction Model checking Acknowledgement for use of presentation Julie Lyng Forman, Dept. of Biostatistics (2008),

1.17k views • 63 slides
Personality and Conversation Engagingness for Virtual Assistants Emily Wu and Esther Kim

Personality and Conversation Engagingness for Virtual Assistants Emily Wu and Esther Kim

Personality and Conversation Engagingness for Virtual Assistants Emily Wu and Esther Kim Introduction Deliverables: Gold-standard dialogue consisting of several scenarios Methods: 3 surveys completed by workers on MTurk Methods

477 views • 14 slides
CS6710 Tool Suite Verilog is the Key Tool Verilog Sim Behavioral Verilog is synthesized into

CS6710 Tool Suite Verilog is the Key Tool Verilog Sim Behavioral Verilog is synthesized into

CS6710 Tool Suite Verilog is the Key Tool Verilog Sim Behavioral Verilog is synthesized into Structural Verilog Synopsys Behavioral Synthesis Structural Verilog represents net-lists Verilog Structural From Behavioral Cadence

607 views • 21 slides
What is a database system ? Database: a large, integrated collection of data. Models a real

What is a database system ? Database: a large, integrated collection of data. Models a real

2 What is a database system ? Database: a large, integrated collection of data. Models a real world enterprise Entities (teams, games) Relationships (Orphan Pamuk received the Nobel Prize) Course introduction Constraints (

246 views • 7 slides
Virtual Workshops 101 Virtual Workshops 101 What weve learned facilitating virtually, tips

Virtual Workshops 101 Virtual Workshops 101 What weve learned facilitating virtually, tips

Virtual Workshops 101 Virtual Workshops 101 What weve learned facilitating virtually, tips & tricks for successful virtual workshops, and a chance to try on your activities in a safe environment. What we What we ll cover ll cover

705 views • 21 slides

More recommend