Performance Analysis and Optimization

Performance: Time Space Power (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 algorithms Hierarchy of time complexity: increment / decrement addition / subtraction multiplication division / square root other operations can usually trade off time for space Example: addition of 2 16-bit numbers carry-ripple adder: time - 31 gate delays space - 16 full adders carry lookahead adder (4-bit units): time – 8 gate delays space – 4 4-bit CLA units—more gates, routing

fig_14_00 Example: summing array elements— linear in size of array

table_14_00 How to analyze performance and Do optimizations

fig_14_01 Rates of growth for commonly encountered complexity: Asymptotic complexity

fig_14_02 Time complexity: loop

fig_14_03 How does this differ from previous example?

fig_14_04 While loop

fig_14_05 Nested loops—example:

fig_14_06 Time complexity of conditional statements:

fig_14_07 Linear search:

fig_14_08 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 middle Access at middle Access at end (or O(1) if extra pointer)

fig_14_09 Flow of control: sequential

fig_14_10 Loops/conditionals

fig_14_11 Example: loop

fig_14_12 Example: function call

fig_14_13 Code: C level

fig_14_14 Code: machine instruction set level

fig_14_16 If—2 levels

fig_14_18 While-2 levels

fig_14_19 Function call—machine level

fig_14_20 Function—C level

fig_14_21 What happens at machine level

fig_14_22 Function body– c level

fig_14_23 Function body—machine level

fig_14_24 Co-routines

fig_14_25 interrupts

fig_14_26 Response time—2 systems

fig_14_27 Best and worst case times

fig_14_28 Asynchronous events

fig_14_29 Memory: hierarchy / response times

table_14_03 Power usage for some common operations

fig_14_30 Power—sophisticated management possible

fig_14_31 Using a power manager

fig_14_32 Power management schemes

fig_14_33 Standard power modes

table_14_02 Ways to analyze performance during development