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

Differences between revisions 3 and 23 (spanning 20 versions)

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

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:

Start with stuff and latex2( $S p e e d u p O v e r a l l = \frac{O l d E x e c u t i o n T i m e}{N e w E x e c u t i o n T i m e}$ ) (1) and more stuff over here.

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

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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-  ⇤ ← Revision 3 as of 2004-01-25 18:27:27 → 
  Size: 1150
  Editor: yakko
  Comment:
+   ← Revision 23 as of 2005-06-27 22:28:22 → ⇥
  Size: 1150
  Editor: yakko
  Comment:
-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
 $S p e e d u p = \frac{P e r f o r m a n c e u s i n g e n h a n c e m e n t w h e n p o s s i b l e}{P e r f o r m a n c e w i t h o u t e n h a n c e m e n t}$
-Line 13:
+Line 11:
+Start with stuff and [[latex2( $S p e e d u p O v e r a l l = \frac{O l d E x e c u t i o n T i m e}{N e w E x e c u t i o n T i m e}$ )]] (1) and more stuff over here.

{{{#!latex2
 $N e w E x e c T i m e = O l d E x e c T i m e (1 - F r a c t i o n E n h a n c e d + \frac{F r a c t i o n E n h a n c e d}{S p e e d u p E n h a n c e d})$ 
}}}
-Line 14:
+Line 18:
-                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time
+or
-Line 18:
+Line 20:
-                                                                    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)
-Line 22:
+Line 24:
--->
+So we have