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Understanding Common Subexpression Elimination
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Today, we'll explore Common Subexpression Elimination, or CSE. Can anyone tell me why eliminating redundant computations is important in programming?
It helps improve the efficiency of the program, right?
Exactly! By avoiding unnecessary calculations, we save time and resources. So, how does CSE actually work?
Does it identify repeated expressions?
Correct! It keeps track of computations in a map. Can anyone think of an example where we calculate the same result multiple times?
Like if I'm calculating the same value in a loop?
Good point! In such cases, CSE can greatly optimize our code. Let's summarize: CSE identifies redundant computations and reuses results to enhance performance.
Detailed Working of CSE
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Now, letβs discuss how CSE operates in detail. When the optimizer processes instructions, what do you think it checks for?
It checks if the same expression has been calculated before?
Exactly! It checks for 'expression signatures'. If two computations have the same signature and their operands aren't redefined, what happens?
The redundant computation is removed!
Right! The optimizer replaces all subsequent uses of the removed computation with the original result. Can anyone give me an example of how the redefinition of an operand affects CSE?
If an operand has a new value assigned, the previous computation isn't valid anymore.
Excellent! We must invalidate previous expressions if operands are redefined. This process is vital for maintaining accurate computations!
Practical Example of CSE
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Let's look at a practical example together. Imagine we have some code that calculates the same sum multiple times. What would be our first step?
We'd check the code to identify candidates for CSE.
Exactly! For example, if we compute `t1 = a + b`, and later calculate `t2 = a + b`, what's next?
We can remove the calculation of `t2` and just use `t1`, right?
Precisely! By reusing `t1`, we enhance our code's efficiency. Remember, CSE significantly reduces redundant CPU cycles!
Could this also reduce the size of the code?
Absolutely! Fewer calculations lead to a more concise program. Great insights, everyone!
Introduction & Overview
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Quick Overview
Standard
This section explains the concept and workings of Common Subexpression Elimination (CSE), which identifies and eliminates repetitive calculations within a single basic block. By maintaining a map of already computed expressions, CSE reduces redundant CPU cycles and improves execution speed.
Detailed
Common Subexpression Elimination (CSE)
Common Subexpression Elimination (CSE) is a powerful optimization that identifies and removes redundant computations of the same expression occurring multiple times within a single basic block. When an identical expression is computed, and its operands have not changed between computations, the CSE optimization allows for reusing the result of the first computation instead of recalculating it. The optimizer processes each instruction sequentially, maintaining a temporary map of available expressions that have already been computed. If it finds that the same expression signature already exists in the map, the optimizer eliminates the redundant calculation and replaces all subsequent references to the computed result with the original one.
The significance of CSE lies in its ability to enhance execution speed by avoiding unnecessary computations, thus conserving CPU cycles and reducing overall code size, contributing to more efficient execution. This section provides a step-by-step example to illustrate how common subexpressions are identified and eliminated, showcasing the direct benefits of implementing this optimization technique.
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Concept of Common Subexpression Elimination
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This optimization identifies and eliminates redundant computations. If the same expression (meaning the same operator applied to operands with the same values) is computed multiple times within a basic block, and none of its operands have been redefined between the first computation and the subsequent ones, then the redundant computations can be removed. The result of the first computation is simply reused.
Detailed Explanation
In CSE, the goal is to avoid recalculating the same expression multiple times. When the compiler sees an expression that has already been calculated within a basic block, and the variables in that expression have not changed, it can substitute the new calculation with the previously computed result. This reduces unnecessary work, making the program faster and more efficient.
Examples & Analogies
Think of CSE like cooking: if you need to make multiple dishes that require boiling water, instead of boiling water for each dish separately, you boil it once and use that same pot of water for all dishes. This saves time and energy, just like CSE saves computational resources.
Detailed Working of CSE
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The optimizer processes instructions within a basic block sequentially. It maintains a temporary 'map' or 'set' of expressions that have already been computed and whose results are currently 'available' (meaning their input operands haven't changed). When an instruction result = operand1 operator operand2 is encountered, the optimizer forms an 'expression signature' (e.g., (operand1, operator, operand2)). It then checks if this exact expression signature already exists in its map of available expressions. If it does exist, and the current values of operand1 and operand2 are the same as they were when the original computation occurred (i.e., neither operand1 nor operand2 have been redefined by an instruction between the original computation and the current one), then the current instruction is removed, and all subsequent uses of its result are replaced with the variable that held the original result.
Detailed Explanation
The CSE process involves scanning through each instruction one by one. If an expression is encountered that has already been calculated before, we can replace the new calculation with the saved result from the first computation. This can be visualized as a shopping list where if you've already written down 'milk' once and bought it, you donβt need to keep repeating 'milk' on your list again; you just check off the first one when you buy.
Examples & Analogies
Imagine you are doing math homework, and you repeatedly compute the value of 5 + 3. Instead of always calculating it, you could just remember the answer (8) and use it each time. This saving of repeated calculations is what CSE accomplishes in programming.
Redefinition Handling in CSE
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If any instruction redefines an operand (e.g., operand1 = new_value), then any previously computed expressions that used operand1 are no longer 'available' for CSE. They must be removed from the map because their value might now be different.
Detailed Explanation
In CSE, keeping track of when variables are redefined is crucial. If a variable that was used in a previously calculated expression is changed later on, then any instances of that previous expression stored for reuse are invalidated because their outcome can no longer be certain.
Examples & Analogies
Consider a situation where you save a file with a draft of a report. If you later make significant changes to the content and save it again, the old draft is no longer accurate. In programming, once a variable is changed, any previous calculations involving it are similarly outdated, requiring us to discard the old computations.
Example of CSE in Action
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Original Three-Address Code:
1. t1 = a + b
2. x = t1 * c
3. t2 = a + b // Candidate for CSE with t1
4. y = t2 + d
5. a = 10 // 'a' is redefined here
6. t3 = a + b // Candidate for CSE (but 'a' changed!)
7. z = t3 * e
After Common Subexpression Elimination:
1. t1 = a + b
2. x = t1 * c
3. y = t1 + d // 't2' replaced by 't1'
4. a = 10
5. t3 = a + b
6. z = t3 * e
Detailed Explanation
In this example, the expression 'a + b' is computed in line 1 and saved in 't1'. Later in line 3, it appears again with 't2', which allows us to replace 't2' with 't1'. This means that instead of recalculating 'a + b', we can just use the value stored in 't1', saving computational time.
Examples & Analogies
Think of a teacher who has already calculated students' average scores for a quiz. Later, she needs to reference that score for various reports; instead of recalculating it each time, she uses the average score she already has. This approach streamlines her work just like CSE streamlines computational tasks.
Benefits of CSE
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Directly reduces redundant CPU cycles by avoiding re-computation. This is one of the most effective local optimizations for improving execution speed. It also slightly reduces code size.
Detailed Explanation
By eliminating unnecessary calculations, CSE not only speeds up the process but also helps reduce the overall program size since fewer instructions may be needed. This makes the program more efficient and allows it to run faster, which is essential in performance-sensitive applications.
Examples & Analogies
Just like taking shortcuts while driving can reduce the time of a journey, avoiding repeated calculations makes executing a program faster, similar to completing a task more quickly by not redundantly doing the same work.
Definitions & Key Concepts
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Key Concepts
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Redundant Computation: Unnecessary repetitions of calculations within a block.
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Expression Signature: A unique representation used to quickly identify identical computations.
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Operand Redefinition: The impact of variables changing value affecting optimization.
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Code Size Reduction: The benefit of optimizations that keep the code concise.
Examples & Real-Life Applications
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Examples
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Calculating the result of 'a + b' multiple times within a single block without changes to 'a' or 'b'.
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Example Three-Address Code demonstrating CSE for 't1 = a + b' and 't2 = a + b', leading to the elimination of 't2' and replacement with 't1'.
Memory Aids
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π΅ Rhymes Time
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CSE's a key to cutting time, use it well to save a dime!
π Fascinating Stories
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Once a programmer doubled their efforts, recalculating sums of variables until CSE showed up, saving them from wasted cycles, leading to faster code!
π§ Other Memory Gems
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CSE: Check, Save, Eliminate β always check for duplicates, save the first computation, eliminate the rest!
π― Super Acronyms
CSE = Common Signatures Evicted β a reminder to evict redundant expressions!
Flash Cards
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Glossary of Terms
Review the Definitions for terms.
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Term: Common Subexpression Elimination (CSE)
Definition:
An optimization technique that identifies and removes redundant computations of the same expression within a basic block.
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Term: Intermediate Representation (IR)
Definition:
A data structure or code used internally by a compiler to represent source code during optimization.
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Term: Basic Block
Definition:
A straight-line sequence of code with no branches except at the end.
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Term: Expression Signature
Definition:
A representation of an expression consisting of its operands and operator, used to identify previously computed expressions.
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Term: Redefinition Handling
Definition:
Managing the state of expressions based on changes to their operands within the block.