Grosch's Law

A number of postulates were introduced by some well-known computer architects expressing about the usefulness of parallel architectures.

Figure 3.2: Power-cost relationship according to Grosch's law.

• It was as early as the late 1940s that H. Grosch studied the relationship between the power of a computer system, $P$, and its cost, $C$.
• He postulated that $P=K*C^s$, where $s$ and $K$ are positive constants. Grosch postulated further that the value of $s$ would be close to 2.

• Simply stated, Grosch's law implies that the power of a computer system increases in proportion to the square of its cost (see Fig. 3.6).
• Alternatively, one can express the cost of a system as $C=sqrt(P/K)$ assuming that $s= 2$.
• According to Grosch's law, in order to sell a computer for twice as much, it must be four times as fast.
• Alternatively, to do a computation twice as cheaply, one has to do it four times slower.
• With the advances in computing, it is easy to see that Grosch's law is overturned, and it is possible to build faster and less expensive computers over time.