a unified framework for schedule and storage optimization

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A Unified Framework for Schedule and Storage Optimization William - PowerPoint PPT Presentation

Jun 13, 2023 •169 likes •1.51k views

A Unified Framework for Schedule and Storage Optimization William Thies, Frdric Vivien, Jeffrey Sheldon, and Saman Amarasinghe MIT Laboratory for Computer Science ICPS/LSIIT, Universit Louis Pasteur http://compiler.lcs.mit.edu/aov

Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Solution: v = (1, 1) i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? i j
Answering Question #1 • Given θ (i, j) = i + j, what is the shortest valid occupancy vector v ? � Why not v = (0, 1)? ??? i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � θ (i, j) is between: θ (i, j) = 2 ∗ i + j (inclusive) θ (i, j) = i (exclusive) i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #2 • Given v = (0, 1), what is the range of valid schedules θ ? � Lets try θ (i, j) = 2 ∗ i + j i j
Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? i j
Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j
Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j
Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j
Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j
Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j
Answering Question #3 • What is the shortest v that is valid for all legal affine schedules? � Range of legal θ i j

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