Performance Analysis and Optimization

Performance:TimeSpacePower(cost)(weight){development time, ease of maintenance,

extensibility}

Note: 1. “big-O” analysis not sufficient here, we are dealing with specific physical sizes

2. notation “big-O” often really means Θ

Arithmetic—basic algorithmsHierarchy of time complexity:

increment / decrementaddition / subtraction

multiplicationdivision / square root

other operations

can usually trade off time for spaceExample: addition of 2 16-bit numbers

carry-ripple adder: time - 31 gate delays space - 16 full adderscarry lookahead adder (4-bit units): time – 8 gate delays space – 4 4-bit CLA units—more gates, routing

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Example: summing array elements—linear in size of array

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How to analyze performance and Do optimizations

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Rates of growth for commonly encountered complexity:Asymptotic complexity

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Time complexity: loop

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How does this differ from previous example?

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While loop

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Nested loops—example:

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Time complexity of conditional statements:

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Linear search:

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Selection sort:

Common data structures (not dynamic):

Array:

O(n) [move]:

Insert / delete at beginning

Insert / delete at end

Insert / delete in middle

O(1):

Access at beginning

Access at middle

Access at end

Common data structures (not dynamic):Linked list:O(1):

Insert / delete at beginning access at beginning

O(n):insert / delete at end (or O(1) if extra pointer)insert / delete in middleAccess at middleAccess at end (or O(1) if extra pointer)

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Flow of control:sequential

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Loops/conditionals

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Example: loop

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Example: function call

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Code: C level

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Code: machine instruction set level

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If—2 levels

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While-2 levels

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Function call—machine level

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Function—C level

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What happens at machine level

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Function body– c level

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Function body—machine level

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Co-routines

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interrupts

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Response time—2 systems

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Best and worst case times

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Asynchronous events

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Memory: hierarchy / response times

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Power usage for some common operations

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Power—sophisticated management possible

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Using a power manager

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Power management schemes

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Standard power modes

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Ways to analyze performance during development