Amdahl's Law

By: NYTrojan



Amdahl's law is a formula that tells you how much you can expect to speed up a CPU by improving a particular stage of execution (Hang with me, I swear this is relevant)

{\displaystyle S_{\text{latency}}(s)={\frac {1}{(1-p)+{\frac {p}{s}}}}}

Slatency is the expected speedup

s is how much you sped up a partuclar stage

p is the amount of time you spend in that stage.

 

For example, let's say you spend 30% of your time in a partular stage, and you can make that stage twice as fast.  You will get 

{\displaystyle S_{\text{latency}}={\frac {1}{1-p+{\frac {p}{s}}}}={\frac {1}{1-0.3+{\frac {0.3}{2}}}}=1.18.}

which is to say you'll run 1.18 times faster.  Not a lot.

But if you spend 75% of your time in a stage and make it run twice as fast you'll get

{\displaystyle S_{\text{latency}}={\frac {1}{1-0.75+{\frac {0.75}{2}}}}=1.60.}

Which is a lot better.

 

This is a fancy math way of saying "Focus on what you aren't already good at".  If you improve something that you suck at, that you're spending a lot of time doing, you'll see a lot more overall improvement.  But if you're constantly focused on improving something that is already pretty well maximized then you are wasting your effort.

Keeping Tee around to protect recruiting is incredibly stupid.  We're good at recruiting without him.  We're better with him, but only 1.18 times better.  Instead of multiplying by 1.18, we should focus on a better play caller... something we AREN'T good at... for the 1.6 multiplier.

USC is constantly focused on recruiting and the impact things will have on recruiting.  I don't understand why.  Paul Hackett recruited well.  We can afford to take a small hit there for large gains elsewhere.  Otherwise we're just getting miniscule gains at the expense of much larger ones.

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