Diff for "AmdahlsLaw" - Dr. A's Wiki

Differences between revisions 22 and 30 (spanning 8 versions)

<<latex($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)>>

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:

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

This gives a new Execution time of

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

So we have

latex($$SpeedupOverall=\left(\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}}\right)$$)

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-  ⇤ ← Revision 22 as of 2005-06-27 22:28:09 → 
  Size: 1129
  Editor: yakko
  Comment:
+   ← Revision 30 as of 2008-10-24 02:23:46 → ⇥
  Size: 720
  Editor: 209-142-131-35
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 3:
-{{{#!latex2
$$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$
}}}
+<<latex($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)>>
-Line 11:
+Line 9:
-[[latex2($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1) and more stuff over here.
+[[latex($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1)
-Line 13:
+Line 11:
-{{{#!latex2
$$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$
}}}
+This gives a new Execution time of
-Line 17:
+Line 13:
-{{{
or

                       Execution Time affected by Improvement
New Execution Time =   --------------------------------------  + Execution Time unaffected
                            Amount of Improvement (x times)
+[[latex($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)]]
-Line 25:
+Line 16:
-
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced
-Line 31:
+Line 17:
-}}}
+[[latex($$SpeedupOverall=\left(\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}}\right)$$)]]