The Essentials ofComputer(computer) 463

# The Essentials ofComputer(computer) 463 - Memory Memory PE...

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Memory PE Memory PE PE PE PE (a) (b) FIGURE 9.14 a. A Simple Processing Element (PE) b. A Systolic Array Processor A good example of using systolic arrays can be found in polynomial evalua- tion. To evaluate the polynomial y = a 0 + a 1 x + a 2 x 2 + ... + a k x k , we can use Horner’s Rule: y = (((( a n x + a n 1 ) x + a n 2 ) x + a n 3 ) x .... a 1 ) x + a 0 A linear systolic array, in which the processors are arranged in pairs, can be used to evaluate a polynomial using Horner’s Rule, as shown in Figure 9.15. One processor multiplies its input by x and passes the result to the right. The next processor adds a j and passes the result to the right. After an initial latency of 2 n cycles to get started, a polynomial is computed in every cycle. Systolic arrays are typically used for repetitive tasks, including Fourier trans- formations, image processing, data compression, shortest path problems, sorting, signal processing, and various matrix computations (such as inversion and multi-
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