5.5 (Scaled speedup) Scaled speedup is defined as the speedup obtained when the problem size is increased linearly with the number of processing elements; that is, if W is chosen as a base problem size for a single processing element, then

Equation 5.37

graphics/05fig70.gif

For the problem of adding n numbers on p processing elements (Example 5.1), plot the speedup curves, assuming that the base problem for p = 1 is that of adding 256 numbers. Use p = 1, 4, 16, 64, and 256. Assume that it takes 10 time units to communicate a number between two processing elements, and that it takes one unit of time to add two numbers. Now plot the standard speedup curve for the base problem size and compare it with the scaled speedup curve.

Hint: The parallel runtime is (n/p - 1) + 11 log p.

Equation 5.37

graphics/05fig70.gif

For the problem of adding n numbers on p processing elements (Example 5.1), plot the speedup curves, assuming that the base problem for p = 1 is that of adding 256 numbers. Use p = 1, 4, 16, 64, and 256. Assume that it takes 10 time units to communicate a number between two processing elements, and that it takes one unit of time to add two numbers. Now plot the standard speedup curve for the base problem size and compare it with the scaled speedup curve.

Hint: The parallel runtime is (n/p - 1) + 11 log p.

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