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Chapter 5 ½ Function and Performance 61

associated with the base packaging, power, and interface. The electronic selection follows a square law; a doubling of the selection circuitry provides access to a core stack that is 4 times larger. All other costs are roughly linear, although the manufacturing cost for larger stacks would probably follow some economy of scale due to the high setup cost of threading core memories.

Another point is that Grosch's law, derived from the definition of performance, is itself a definition. Consider Knight's model:

Performance = processing rate X memory size X word length If we ignore word length (assuming word length is constant for members of a computer class or family), then performance does increase as the square of memory price, since the factors of rate and size are each a function of memory price. To derive this result we proceed as follows.

Let P equal the price of the memory on the system. Assume the use of a 2k x 1 memory chip and a memory system n bits wide, and further assume that the processor can use 100 percent of the memory data rate. To supply concrete cost and performance parameters we will use a 4-kiobit chip, which in 1978 cost about $25 and had a cycle time (at the processor) of about 500 ns. Then,

Thus, according to this performance model, Grosch's law holds by definition because

1 Memory price and processor price are linearly related (predictably, since they use the same semiconductor technology).

2 Processor performance is usually matched to memory size, as suggested by Amdahl (see page 46).


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