Meanings of Nmax and nhalf in linpack Testing

These two indicators appear in the machine evaluation parameter table of top500. The specific meanings are as follows:

Nmax: the maximum scale of the linpack test to solve the problem. An empirical formula is provided for the value: total content (converted to byte)/8 and then the root number.

Nhalf: This indicator is very interesting. This indicator indicates that when the scale of the problem solved by linpack is nhalf, the test result is exactly half of the theoretical cluster peak (rpeak. Why should we set this indicator? This indicator can reflect the bandwidth and interconnect performance indicators of the entire system. Generally, the smaller the value of nhalf, the better. Generally, the value is below 10 of Nmax. It can be understood as follows: the smaller the problem scale nhalf, the better the machine can run out of the average rpeak flops, which means the bandwidth of this machine is very good, because of small-scale problems, he can also achieve 50% efficiency. Do you understand?