Hardware/Software Co-Design
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1 1 / 45 Hardware/Software Co-Design Parallel Patterns III Miaoqing Huang University of Arkansas Fall 2011
2 2 / 45 Outline 1 2
3 3 / 45 Outline 1 2
4 What is segmented scan? Scan + Barriers/Flags associated with certain positions in the input arrays Operations do not propagate beyond barriers Value Flag Output / 45
5 What is segmented scan? Scan + Barriers/Flags associated with certain positions in the input arrays Operations do not propagate beyond barriers Value Flag Output How to deal with it? 5 / 45
6 What is segmented scan? Scan + Barriers/Flags associated with certain positions in the input arrays Operations do not propagate beyond barriers Value Flag Output How to deal with it? Deal with the segments one by one 6 / 45
7 What is segmented scan? Scan + Barriers/Flags associated with certain positions in the input arrays Operations do not propagate beyond barriers Value Flag Output How to deal with it? Deal with the segments one by one Do many scans at once, no matter their sizes 7 / 45
8 Example (of the Naive Approach) Value Flag / 45
9 Example (of the Naive Approach) Value Flag Value Flag / 45
10 Example (of the Naive Approach) Value Flag Value Flag Value Flag / 45
11 Example (of the Naive Approach) Value Flag Value Flag Value Flag Value Flag / 45
12 Example (of the Naive Approach) Value Flag Value Flag Value Flag Value Flag Value Flag / 45
13 Pseudo Code (of the Naive Approach) //x[]: value; f[]: flag for d = 0 to log(n) - 1 do forall k in parallel do if k>=2^d then if f[k] is NOT set then x[out][k] = x[in][k-2^d] + x[in][k] f[out][k] = f[in][k-2^d] f[in][k] else x[out][k] = x[in][k] f[out][k] = f[in][k] else x[out][k] = x[in][k] f[out][k] = f[in][k] swap(in,out) 13 / 45
14 Pseudo Code (of the Naive Approach) //x[]: value; f[]: flag for d = 0 to log(n) - 1 do forall k in parallel do if k>=2^d then if f[k] is NOT set then x[out][k] = x[in][k-2^d] + x[in][k] f[out][k] = f[in][k-2^d] f[in][k] else x[out][k] = x[in][k] f[out][k] = f[in][k] else x[out][k] = x[in][k] f[out][k] = f[in][k] swap(in,out) Work-efficient implementation See Scan Primitives for GPU Computing by Sengupta, Harris, Zhang, and Owens 14 / 45
15 15 / 45 Outline 1 2
16 16 / 45 Sort Useful for almost everything Optimized versions for the GPU already exist Two examples Radix sort Quick sort
17 Radix Sort Definition Sort integers by processing individual digits, by comparing individual digits sharing the same significant position Least Significant Digit (LSD) radix sort 1 Take the least significant digit (or group of bits, both being examples of radices) of each key 2 Group the keys based on that digit, but otherwise keep the original order of keys 3 Repeat the grouping process with each more significant digit 17 / 45
18 18 / 45 Radix Sort Example original list
19 19 / 45 Radix Sort Example original list
20 20 / 45 Radix Sort Example original list 1s place
21 21 / 45 Radix Sort Example original list 1s place
22 22 / 45 Radix Sort Example original list 1s place 10s place
23 23 / 45 Radix Sort Example original list 1s place 10s place
24 24 / 45 Radix Sort Example original list 1s place 10s place 100s place
25 25 / 45 Radix Sort on GPU Integers are represented in radix-2 format on computer Split can be used for radix sort
26 26 / 45 Radix Sort on GPU Integers are represented in radix-2 format on computer Split can be used for radix sort
27 27 / 45 Radix Sort on GPU Integers are represented in radix-2 format on computer Split can be used for radix sort
28 28 / 45 Radix Sort on GPU Integers are represented in radix-2 format on computer Split can be used for radix sort
29 29 / 45 Radix Sort on GPU Integers are represented in radix-2 format on computer Split can be used for radix sort
30 30 / 45 Radix Sort on GPU Integers are represented in radix-2 format on computer Split can be used for radix sort
31 31 / 45 Radix Sort on GPU Integers are represented in radix-2 format on computer Split can be used for radix sort
32 32 / 45 Radix Sort on GPU Integers are represented in radix-2 format on computer Split can be used for radix sort
33 33 / 45 Quick Sort Quick sort sorts by employing a divide and conquer strategy to divide a list into two sub-lists Steps 1 Pick an element, called a pivot, from the list 2 Reorder the list so that all elements with values less than the pivot come before the pivot, while all elements with values greater than the pivot come after it (equal values can go either way) After this partitioning, the pivot is in its final position 3 Recursively sort the sub-list of lesser elements and the sub-list of greater elements
34 34 / 45 Quick Sort Quick sort sorts by employing a divide and conquer strategy to divide a list into two sub-lists Steps 1 Pick an element, called a pivot, from the list 2 Reorder the list so that all elements with values less than the pivot come before the pivot, while all elements with values greater than the pivot come after it (equal values can go either way) After this partitioning, the pivot is in its final position 3 Recursively sort the sub-list of lesser elements and the sub-list of greater elements Example is given at the chalkboard
35 35 / 45 Quick Sort on GPU Use segmented scan and split
36 36 / 45 Quick Sort on GPU Use segmented scan and split
37 37 / 45 Quick Sort on GPU Use segmented scan and split
38 38 / 45 Quick Sort on GPU Use segmented scan and split
39 39 / 45 Quick Sort on GPU Use segmented scan and split
40 40 / 45 Quick Sort on GPU Use segmented scan and split
41 41 / 45 Quick Sort on GPU Use segmented scan and split
42 42 / 45 Quick Sort on GPU Use segmented scan and split
43 43 / 45 Quick Sort on GPU Use segmented scan and split
44 44 / 45 Quick Sort on GPU Use segmented scan and split
45 45 / 45 Quick Sort on GPU Use segmented scan and split
46 46 / 45 Lab-6 Preview for (m=0; m<m; m++) { phimag[m] = rphi[m]*rphi[m] + iphi[m]*iphi[m]; for (n=0; n<n; n++) { expq = 2*PI*(kx[m]*x[n]+ky[m]*y[n]+kz[m]*z[n]); } } rq[n] += phimag[m]*cos(expq); iq[n] += phimag[m]*sin(expq);
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