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This model gives the performance or speedup of a parallel system over that of a nonparallel system Themachine parallelismis measured hyW, the number ofpxocessors_in the machine, and reflects the maximum number of tasks that can be simultaneously performed by the system The parameter/, however, is the vectorizability of the program which reflects the program parallelism The formulation of this model is influenced by traditional supercomputers that contain a scalar unit and a vector unit The vector unit, consisting of N processors, executes the vectorizable portion of the program by performing N tasks at a time The nonvectorizable portion of the program is then executed in the scalar unit in a sequential fashion We have already observed the oppressive tyranny of the nonvectorizable portion of the program on the overall performance that can be obtained through parallel processing The assumption that the nonvectorizable portion of the program must be exe^ cuted sequentially is overly pessimistic and not necessary If some, even low, level of parallelism can be achieved for the nonvectorizable portion of the program, the severe impact of the sequential bottleneck can be significantly moderated figure 18 illustrates this principle This figure, taken from an IBM technical report coauthored

bottom_btnonRollOver = function():Void { hammer_mc_rotation = rotateAmt; nail_mc_y += bashAmt; rotateAmt -= bashAmt / 7; }

The first step uses the CGRectInset function to shrink our bounds rect a bit, giving us a little wiggle room so that we can draw a rounded rect with thick lines without having them clipped by our edges. Then we create a path representing a rounded rect, specifying the basic geometry of the rect as well as two numbers defining the size of the elliptical curves used for the rounded corners. After that, we issue simple commands to set colors, a line width, and do some drawing.

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You may be wondering where the number 7 came from This number actually came from a trial and error process when I initially created the game At the end of this exercise, you can change this number to modify the change in rotation amount for the hammer if you d like to see what a different value would look like

Note that specifying which color to use for a drawing operation is a separate step from the drawing operation itself, as is setting the line width. Also, although setting the line width is done through a method on the path itself, setting the color looks like a sort of free-floating operation. You just send any color the set message, and suddenly it s the current color! What s happening is that NSColor s set method interacts with the underlying graphics context, setting the color that will be used for subsequent drawing operations. One consequence of this is that NSColor s set method will only do something useful while there is a current graphics context, such as within a drawRect: method. Another consequence is that the current color is a property (in a general sense, if not an Objective-C language sense) of the graphics context, so whatever color was set before our method is saved at the beginning of our method when [NSGraphicsContext saveGraphicsState] is called, and restored at the end when [NSGraphicsContext restoreGraphicsState] is called, putting everything back in order again. At this point, if you Build & Run the application, you ll see that it draws a white rect with a black outline (Figure 13 4).

top_btnonRollOver = function():Void { }

Examining the curve for Equation (19) in figure 18, we see that the speedup is equal to 6 i f / i s 100%, that is, perfectly vectorizable A s / d r o p s off from 100%, the speedup drops off very quickly; as / b e c o m e s 0%, the speedup is one; that is, no speedup is obtained With higher values of N, this speedup drop-off rate gets significantly worse, and as/approaches 0%, all the speedups approach one, regardless of the value of N Now assume that the minimum degree of parallelism of 2 can be achieved for the nonvectorizable portion of the program The speedup now becomes S = 1 (1-/)/ 2 6

Now let s continue, and start drawing the head. Add these lines to the drawRect: method, toward the end but still before the [NSGraphicsContext restoreGraphicsState] call:

value of the hammer s rotation to zero This will make the hammer move up when the mouse (or Wii remote) rolls over the top button

NSRect hRect = CGRectInset([self bounds],20,20); NSBezierPath *head = [NSBezierPath bezierPathWithOvalInRect:hRect]; NSGradient *faceGradient = [[NSGradient alloc] initWithStartingColor:[NSColor whiteColor] endingColor:[NSColor lightGrayColor]]; [faceGradient drawInBezierPath:head angle:45]; [head setLineWidth:3]; [head stroke];

top_btnonRollOver = function():Void { hammer_mc_rotation = 0; }

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