The document introduces data-flow analysis, which derives information about a program's dynamic behavior by examining its static code. It discusses liveness analysis, which determines whether a variable is live (will be used in the future) or dead at a given point. The concepts of control flow graphs, uses/defs, and solving the data-flow equations through iterative analysis are explained. An example liveness analysis is worked through to demonstrate the process.
High Speed Decoding of Non-Binary Irregular LDPC Codes Using GPUs (Paper)Enrique Monzo Solves
Implementation of a high speed decoding of non-binary irregular LDPC codes using CUDA GPUs.
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Novel Tree Structure Based Conservative Reversible Binary Coded Decimal Adder...VIT-AP University
Reversible logic has been recognized as one of the most promising technique for the realization of the quantum circuit. In this paper, a cost effective conservative, reversible binary coded decimal
(BCD) adder is proposed for the quantum logic circuit. Towards the realization of BCD adder, few novel gates, such as Half-Adder/Subtraction (HAS-PP), Full-Adder/Subtraction (FAS-PP) and Overflow-detection (OD-PP) based on parity preserving logic are synthesized which incurs 7, 10 and
13 quantum cost respectively. Coupling these gates a novel tree-based methodology is proposed to
implement the required BCD Adder. Also, the BCD adder design has been optimized to achieve the optimum value of quantum cost. In addition, the proposed BCD circuit is extended to n-bit adder using replica based techniques. Experimental result establishes the novelty of the proposed logic,
which outperforms the conventional circuits in terms of logic synthesis and testability. The limitation
of detecting the missing gate and missing control point of the quantum circuit of overflow detection
is finally tackled this work by the proposed OD-PP with the application of the minimum test vector. In addition, reversible circuits of control inputs based testable master-slave D-FF is intended. The noted work on the testable sequential circuit presented here is to develop circuit using minimum test vectors and can find diverse application in the testing paradigm
A parallel 'for' loop memory template for a high level synthesis compilerCraig Moore
We propose a parametrized memory template for applications with parallel 'for' loops. The template's parameters reflect important trade-offs made during system design. The template is incorporated in our high level synthesis (HLS) compiler, where the template's parameters are adjusted to the application. The template fits parallel 'for' loops with no loop dependencies and sequential bodies. We found two alternative template implementations using our compiler. In the future, we will develop templates for other types of 'for' loops. These will be added to the compiler and it will identify the template that works best for the application it is compiling. Once a template is selected, the compiler will use design space exploration to select the best combination of template parameters for the targeted hardware and application.
High Speed Decoding of Non-Binary Irregular LDPC Codes Using GPUs (Paper)Enrique Monzo Solves
Implementation of a high speed decoding of non-binary irregular LDPC codes using CUDA GPUs.
Moritz Beermann, Enrique Monzó, Laurent Schmalen, Peter Vary
IEEE SiPS, Oct. 2013, Taipei, Taiwan
Program Derivation of Operations in Finite Fields of Prime OrderCharles Southerland
The higher-quality version of my undergraduate research presentation (still some typos and missing formulas, but better explanations, more pleasing layout, more coherent analysis, etc.). Presented at Oklahoma Computing Consortium 2011.
Novel Tree Structure Based Conservative Reversible Binary Coded Decimal Adder...VIT-AP University
Reversible logic has been recognized as one of the most promising technique for the realization of the quantum circuit. In this paper, a cost effective conservative, reversible binary coded decimal
(BCD) adder is proposed for the quantum logic circuit. Towards the realization of BCD adder, few novel gates, such as Half-Adder/Subtraction (HAS-PP), Full-Adder/Subtraction (FAS-PP) and Overflow-detection (OD-PP) based on parity preserving logic are synthesized which incurs 7, 10 and
13 quantum cost respectively. Coupling these gates a novel tree-based methodology is proposed to
implement the required BCD Adder. Also, the BCD adder design has been optimized to achieve the optimum value of quantum cost. In addition, the proposed BCD circuit is extended to n-bit adder using replica based techniques. Experimental result establishes the novelty of the proposed logic,
which outperforms the conventional circuits in terms of logic synthesis and testability. The limitation
of detecting the missing gate and missing control point of the quantum circuit of overflow detection
is finally tackled this work by the proposed OD-PP with the application of the minimum test vector. In addition, reversible circuits of control inputs based testable master-slave D-FF is intended. The noted work on the testable sequential circuit presented here is to develop circuit using minimum test vectors and can find diverse application in the testing paradigm
A parallel 'for' loop memory template for a high level synthesis compilerCraig Moore
We propose a parametrized memory template for applications with parallel 'for' loops. The template's parameters reflect important trade-offs made during system design. The template is incorporated in our high level synthesis (HLS) compiler, where the template's parameters are adjusted to the application. The template fits parallel 'for' loops with no loop dependencies and sequential bodies. We found two alternative template implementations using our compiler. In the future, we will develop templates for other types of 'for' loops. These will be added to the compiler and it will identify the template that works best for the application it is compiling. Once a template is selected, the compiler will use design space exploration to select the best combination of template parameters for the targeted hardware and application.
Unix and Shell Programming,
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Our team is responsible for storage at Xiaomi and we provide storage services for dozens of businesses, such as personal cloud storage for smart phones and user profile data. So we will share some practices and improvements of HBase at Xiaomi:
1: We upgraded most of our cluster from 0.94 to 0.98 in the last year and will share some experience about upgrading.
2: We encountered some problems and made some improvements on replication.
3: We fixed or still fixing some confusing behavior from client side.
4: We introduced some improvements on scan to make users easy to use and reduce the time of RPC requests.
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A Novel Solution Of Linear CongruencesJeffrey Gold
Proceedings - NCUR IX. (1995), Vol. II, pp. 708-712
Jeffrey F. Gold
Department of Mathematics, Department of Physics
University of Utah
Salt Lake City, Utah 84112
Don H. Tucker
Department of Mathematics
University of Utah
Salt Lake City, Utah 84112
Introduction
Although the solutions of linear congruences have been of interest for a very long time, they still remain somewhat pedagogically di cult. Because of the importance of linear congruences in fields such as public-key cryptosystems, new and innovative approaches are needed both to attract interest and to make them more accessible. While the potential for new ideas used in future research
is difficult to assess, some use may be found here. In this paper, the authors make use of the remodulization method developed in [1] as a vehicle to characterize the conditions under which solutions exist and then determine the solution space. The method is more efficient than those cited in the standard references. This novel approach relates the solution space of cx = a mod b to the Euler totient function for c rather than that of b, which allows one to develop an alternative and somewhat more efficient
approach to the problem of creating enciphering and deciphering keys in public-key cryptosystems.
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http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
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1. Introduction to Data-flow Analysis
Last Time
– Control flow analysis
– BT discussion
Today
– Introduce iterative data-flow analysis
– Liveness analysis
– Introduce other useful concepts
CIS570 Lecture 4 Introduction to Data-flow Analysis 2
Data-flow Analysis
Idea
– Data-flow analysis derives information about the dynamic
behavior of a program by only examining the static code
Example
– How many registers do we need
1 a := 0
for the program on the right?
2 L1: b := a + 1
– Easy bound: the number of
variables used (3) 3 c := c + b
– Better answer is found by 4 a := b * 2
considering the dynamic 5 if a < 9 goto L1
requirements of the program 6 return c
CIS570 Lecture 4 Introduction to Data-flow Analysis 3
1
2. Liveness Analysis
Definition
– A variable is live at a particular point in the program if its value at that
point will be used in the future (dead, otherwise).
∴ To compute liveness at a given point, we need to look into the future
Motivation: Register Allocation
– A program contains an unbounded number of variables
– Must execute on a machine with a bounded number of registers
– Two variables can use the same register if they are never in use at the same
time (i.e, never simultaneously live).
∴ Register allocation uses liveness information
CIS570 Lecture 4 Introduction to Data-flow Analysis 4
Control Flow Graphs (CFGs)
Simplification
– For now, we will use CFG’s in which nodes represent program
statements rather than basic blocks
Example 1 a = 0
1 a := 0 2 b = a + 1
2 L1: b := a + 1
3 c := c + b 3 c = c + b
4 a := b * 2
5 if a < 9 goto L1 4 a = b * 2
6 return c
5 a<9
No Yes
6 return c
CIS570 Lecture 4 Introduction to Data-flow Analysis 5
2
3. Liveness by Example
What is the live range of b?
– Variable b is read in statement 4, 1 a = 0
so b is live on the (3 → 4) edge
– Since statement 3 does not assign 2 b = a + 1
into b, b is also live on the (2→
3) edge 3 c = c + b
– Statement 2 assigns b, so any
value of b on the (1→2) and (5→ 4 a = b * 2
2) edges are not needed, so b is
dead along these edges 5 a<9
No Yes
b’s live range is (2→3→4) 6 return c
CIS570 Lecture 4 Introduction to Data-flow Analysis 6
Liveness by Example (cont)
Live range of a
– a is live from (1→2) and again from 1 a = 0
(4→5→2)
– a is dead from (2→3→4) 2 b = a + 1
Live range of b 3 c = c + b
– b is live from (2→3→4)
4 a = b * 2
Live range of c
– c is live from 5 a<9
(entry→1→2→3→4→5→2, 5→6) No Yes
6 return c
Variables a and b are never simultaneously live, so they can share a register
CIS570 Lecture 4 Introduction to Data-flow Analysis 7
3
4. Terminology
Flow Graph Terms
– A CFG node has out-edges that lead to successor nodes and in-edges that
come from predecessor nodes
– pred[n] is the set of all predecessors of node n 1 a = 0
succ[n] is the set of all successors of node n
2 b = a + 1
Examples
– Out-edges of node 5: (5→6) and (5→2) 3 c = c + b
– succ[5] = {2,6}
– pred[5] = {4} 4 a = b * 2
– pred[2] = {1,5}
5 a<9
No Yes
6 return c
CIS570 Lecture 4 Introduction to Data-flow Analysis 8
Uses and Defs
Def (or definition) a = 0
– An assignment of a value to a variable
– def[v] = set of CFG nodes that define variable v
– def[n] = set of variables that are defined at node n
a < 9?
Use
– A read of a variable’s value
v live
– use[v] = set of CFG nodes that use variable v
– use[n] = set of variables that are used at node n
∉ def[v]
More precise definition of liveness
– A variable v is live on a CFG edge if ∈ use[v]
(1) ∃ a directed path from that edge to a use of v (node in use[v]), and
(2) that path does not go through any def of v (no nodes in def[v])
CIS570 Lecture 4 Introduction to Data-flow Analysis 9
4
5. The Flow of Liveness
Data-flow
– Liveness of variables is a property that flows
through the edges of the CFG
1 a := 0
Direction of Flow
– Liveness flows backwards through the CFG,
2 b := a + 1
because the behavior at future nodes
3 c := c + b
determines liveness at a given node
4 a := b * 2
– Consider a
– Consider b 5 a < 9?
– Later, we’ll see other properties No Yes
that flow forward 6 return c
CIS570 Lecture 4 Introduction to Data-flow Analysis 10
program points
Liveness at Nodes
edges
We have liveness on edges just before computation
– How do we talk about a = 0
just after computation
liveness at nodes?
1 a := 0
Two More Definitions
– A variable is live-out at a node if it is live on anyb := a + 1 out-
2 of that node’s
edges
n 3 c := c + b
live-out
out-edges
4 a := b * 2
– A variable is live-in at a node if it is live on any of that < 9? in-edges
5 a node’s
No Yes
in-edges
6 return c
live-in
n
CIS570 Lecture 4 Introduction to Data-flow Analysis 11
5
6. Computing Liveness
Rules for computing liveness
(1) Generate liveness: live-in
If a variable is in use[n], n use
it is live-in at node n
(2) Push liveness across edges: pred[n]
live-out live-out live-out
If a variable is live-in at a node n
then it is live-out at all nodes in pred[n] n live-in
(3) Push liveness across nodes:
If a variable is live-out at node n and not in def[n] live-in
n
then the variable is also live-in at n live-out
Data-flow equations
(1) in[n] = use[n] ∪ (out[n] – def[n]) (3)
out[n] = ∪ in[s]
(2)
s ∈ succ[n]
CIS570 Lecture 4 Introduction to Data-flow Analysis 12
Solving the Data-flow Equations
Algorithm
for each node n in CFG
in[n] = ∅; out[n] = ∅ initialize solutions
repeat
for each node n in CFG
in’[n] = in[n] save current results
out’[n] = out[n]
in[n] = use[n] ∪ (out[n] – def[n])
solve data-flow equations
out[n] = ∪ in[s]
s ∈ succ[n]
until in’[n]=in[n] and out’[n]=out[n] for all n test for convergence
This is iterative data-flow analysis (for liveness analysis)
CIS570 Lecture 4 Introduction to Data-flow Analysis 13
6
7. Example
1st 2nd 3rd 4th 5th 6th 7th
node use def in out in out in out in out in out in out in out
# 1 a := 0
1 a a a ac c ac c ac c ac
2 a b a a bc ac bc ac bc ac bc ac bc ac bc 2 b := a + 1
3 bc c bc bc b bc b bc b bc b bc bc bc bc
4 b a b b a b a b ac bc ac bc ac bc ac 3 c := c + b
5 a a a a ac ac ac ac ac ac ac ac ac ac ac
6 c c c c c c c c 4 a := b * 2
Data-flow Equations for Liveness 5 a < 9?
No Yes
in[n] = use[n] ∪ (out[n] – def[n])
6 return c
out[n] = ∪ in[s]
s ∈ succ[n]
CIS570 Lecture 4 Introduction to Data-flow Analysis 14
Example (cont)
Data-flow Equations for Liveness
in[n] = use[n] ∪ (out[n] – def[n]) 1 a := 0
out[n] = ∪ in[s] 2 b := a + 1
s ∈ succ[n]
3 c := c + b
Improving Performance out[3]
Consider the (3→4) edge in the graph: in[4]
4 a := b * 2
out[4]
out[4] is used to compute in[4]
in[4] is used to compute out[3] . . . 5 a < 9?
So we should compute the sets in the No Yes
order: out[4], in[4], out[3], in[3], . . . 6 return c
The order of computation should follow the direction of flow
CIS570 Lecture 4 Introduction to Data-flow Analysis 15
7
8. Iterating Through the Flow Graph Backwards
1st 2nd 3rd
node use def out in out in out in 1 a := 0
#
6 c c c c
2 b := a + 1
5 a c ac ac ac ac ac
4 b a ac bc ac bc ac bc 3 c := c + b
3 bc c bc bc bc bc bc bc
2 a b bc ac bc ac bc ac 4 a := b * 2
1 a ac c ac c ac c
5 a < 9?
Converges much faster!
No Yes
6 return c
CIS570 Lecture 4 Introduction to Data-flow Analysis 16
Solving the Data-flow Equations (reprise)
Algorithm
for each node n in CFG
in[n] = ∅; out[n] = ∅ Initialize solutions
repeat
for each node n in CFG in reverse topsort order
in’[n] = in[n] Save current results
out’[n] = out[n]
out[n] = s ∈ succ[n] in[s]
∪
Solve data-flow equations
in[n] = use[n] ∪ (out[n] – def[n])
until in’[n]=in[n] and out’[n]=out[n] for all n Test for convergence
CIS570 Lecture 4 Introduction to Data-flow Analysis 17
8
9. Time Complexity
Consider a program of size N
– Has N nodes in the flow graph (and at most N variables)
– Each live-in or live-out set has at most N elements
– Each set-union operation takes O(N) time
– The for loop body
– constant # of set operations per node
– O(N) nodes ⇒ O(N2) time for the loop
– Each iteration of the repeat loop can only make the set larger
– Each set can contain at most N variables ⇒ 2N2 iterations
Worst case: O(N4)
Typical case: 2 to 3 iterations with good ordering & sparse sets
⇒ O(N) to O(N2)
CIS570 Lecture 4 Introduction to Data-flow Analysis 18
More Performance Considerations
Basic blocks
– Decrease the size of the CFG by merging nodes 1 a := 0
that have a single predecessor and a single
successor into basic blocks b := a + 2 1
(requires local analysis before and after global c := c + 1
analysis) 3 a := b *
c c + 2
b
a > 9?
One variable at a time 4 No := b *
a 2
Yes
– Instead of computing data-flow information return c
3
for all variables at once using sets, 5 a < 9?
compute a (simplified) analysis for No Yes
each variable separately 6 return c
Representation of sets
– For dense sets, use a bit vector representation
– For sparse sets, use a sorted list (e.g., linked list)
CIS570 Lecture 4 Introduction to Data-flow Analysis 19
9
10. Conservative Approximation
X Y Z
node use def in out in out in out
#
1 a := 0
1 a c ac cd acd c ac
2 a b ac bc acd bcd ac b
2 b := a + 1
3 bc c bc bc bcd bcd b b
4 b a bc ac bcd acd b ac
3 c := c + b
5 a ac ac acd acd ac ac
6 c c c c 4 a := b * 2
Solution X 5 a < 9?
– Our solution as computed on
No Yes
previous slides
6 return c
CIS570 Lecture 4 Introduction to Data-flow Analysis 20
Conservative Approximation (cont)
X Y Z
node use def in out in out in out
#
1 a := 0
1 a c ac cd acd c ac
2 a b ac bc acd bcd ac b
2 b := a + 1
3 bc c bc bc bcd bcd b b
4 b a bc ac bcd acd b ac
3 c := c + b
5 a ac ac acd acd ac ac
6 c c c c 4 a := b * 2
Solution Y 5 a < 9?
– Carries variable d uselessly around the
No Yes
loop
6 return c
– Does Y solve the equations?
– Is d live?
– Does Y lead to a correct program?
Imprecise conservative solutions ⇒ sub-optimal but correct programs
CIS570 Lecture 4 Introduction to Data-flow Analysis 21
10
11. Conservative Approximation (cont)
X Y Z
node use def in out in out in out
#
1 a := 0
1 a c ac cd acd c ac
2 a b ac bc acd bcd ac b
2 b := a + 1
3 bc c bc bc bcd bcd b b
4 b a bc ac bcd acd b ac
3 c := c + b
5 a ac ac acd acd ac ac
6 c c c c 4 a := b * 2
Solution Z 5 a < 9?
– Does not identify c as live in all cases
No Yes
– Does Z solve the equations? 6 return c
– Does Z lead to a correct program?
Non-conservative solutions ⇒ incorrect programs
CIS570 Lecture 4 Introduction to Data-flow Analysis 22
The Need for Approximations
Static vs. Dynamic Liveness
– In the following graph, b*b is always non-negative, so c >= b is always
true and a’s value will never be used after node 2
1 a := b * b Rule (2) for computing liveness
– Since a is live-in at node 4, it is live-out
2 c := a + b at nodes 3 and 2
– This rule ignores actual control flow
3 c >= b?
No Yes
4 return a 5 return c
No compiler can statically know all a program’s dynamic properties!
CIS570 Lecture 4 Introduction to Data-flow Analysis 23
11
12. Concepts
Liveness
– Use in register allocation
– Generating liveness
– Flow and direction
– Data-flow equations and analysis
– Complexity
– Improving performance (basic blocks, single variable, bit sets)
Control flow graphs
– Predecessors and successors
Defs and uses
Conservative approximation
– Static versus dynamic liveness
CIS570 Lecture 4 Introduction to Data-flow Analysis 24
Next Time
Lecture
– Generalizing data-flow analysis
CIS570 Lecture 4 Introduction to Data-flow Analysis 25
12