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Revision 3 as of 2004-01-25 18:27:27
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Revision 19 as of 2005-06-27 22:26:31
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Editor: yakko
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Deletions are marked like this. Additions are marked like this.
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{{{
           Performance for entire task using the enhancement when possible
Speedup = -----------------------------------------------------------------
              Performance for entire taks without using the enhancement
{{{#!latex2
$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$
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[[latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1)

{{{#!latex2
$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$
}}}
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                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time
or
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                                                                    FractionEnhanced
New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ )
                                                                    SpeedupEnhanced
                       Execution Time affected by Improvement
New Execution Time = -------------------------------------- + Execution Time unaffected
                            Amount of Improvement (x times)
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--> So we have

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$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$

See SpeedUp

Notice that we are talking about the entire task here and that performance (speedup) is defined in terms of execution time! So we have to define the following:

latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$) (1)

$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$

or

                       Execution Time affected by Improvement
New Execution Time =   --------------------------------------  + Execution Time unaffected
                            Amount of Improvement (x times) 

So we have
                                     1
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced

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AmdahlsLaw (last edited 2020-01-23 23:15:20 by scot)