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We should always profile code to find true bottlenecks instead of guessing what might be slow

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Quantifying Performance

• Clock frequency, cycles per instruction cycle, and FLOPS are misleading

• Best metric is wall-clock time (seconds to completion);

  $$ \text{Time = Instruction Count * CPI * Clock Period} $$

Amdahl’s Law: The Law of Diminishing Returns

$$ \text{Speedup: } \frac{1}{(1-f)+(\frac{f}{s})} $$

• f is the fraction of total execution time that the optimized part originally consumed
• s is the speedup factor of the optimized part (i.e., making it 2x faster means s = 2)
• To achieve a large overall speedup, you must optimize the common case
• There is a diminishing return: even making a small part infinitely fast only gives a speedup of $\frac{1}{1-f}$
  • If f is 50%, the maximum speedup is only 2x

Tools for Measurement and Profiling