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3.6 Performance Models for Vector and Parallel Machines

Hockney and Jesshope [13] introduced two parameters to describe the performance of vector processors. The first parameter is the theoretical peak performance, or asymptotic performance, denoted . It is the maximum possible rate of computation, expressed as a number of floating point operations per second. The parameter may be applied to a single vector pipeline or to an entire system. Thus for a single pipe of the Cray Y-MP is 167 MFLOPS (6ns cycle, one result per cycle), and approximately 2.6 GFLOPS for an 8-processor system with the add and multiply units in operation simultaneously. The other parameter, designated and known as the half performance length, is the length of the vector for which a system attains half of its peak performance, i.e. . is a function of vector startup time and pipeline depth. As these values increase it becomes harder and harder to achieve near peak performance for the system because it requires algorithms with longer and longer vectors. As we saw in section 2.2, the startup times for the CDC vector computers were an order of magnitude greater than those from Cray Research. This is reflected in for the two systems differing also by an order of magnitude. Even though was higher for the CDC machines, the systems from Cray proved more popular than those from CDC, so users seem to find lower more important.