Not exactly, that is the point of how a processor understands time..... a processor only understands a clock tick.. A signal that goes high then low. The total time for that is irrelevant. You and I perceive time not clock ticks, so in your words this is correct ... point of diminishing returns.
Frequency is cycles per second, or cycles/second. As frequency increases the number of ticks increases within one second. However, calculating Pi in super PI only depends X number of clock ticks that performs x number of instructions. As you increase frequency, you increase the number of clock ticks per unit time, but you are observing unit time.... so the functionality of the observed time it takes to complete a task (lower is better) is inversely proportional to frequency. I.e. F(x) = 1/x, so plot a simple plot of 1/x, it approaches zero asymptotically, a paraboly is afunction of f(x) = x^2 this is different.
Units of a quanity are important, and mathematically, they are treated like any variable or number. Super PI, Pi calculated and reported in time is not directly linear to Frequency because frequency is in 1/Time... to make one a direct finction of the other simply convert Super PI from time domain to frequncy domain and plot... wolla linear. This is the same as you will read around when people discuss how to calcuate % improvement for benches that are 'slower is better', slower is better benchmarks always approach a 'point of diminishing returns'.... go check it out, find any review of a series of processors varying as a function of frequency for the same core where the reported bench is in units of time... and plot time vs frequency, it will always be inversely proportional.... Very simple.
KTE's data is also 'paraboloic' to use your word -- (actually not parabolic, that is a function of a quadratic equation), he just chose 1M on short time scales and over a smaller frequecy range in that he was on a 'flatter' area of the curve... if he did 8M and repeated the same data, assuming he makes no mistakes... he would get what you see in the X6800 data above as the 8M stretches out time to see the inverse proportionality.
Now, how does this relate to K10... well not much, we first have to assume that the one data point is correct (i.e. ~39 second SP1M at 2.0 GHz), what people are arguing is that K10 'turns on' after 2.4-2.6 GHz range such that it scales 'better'.... this is odd way of arguing it, because the digital logic of a CPU is just that, it only knows a clock tick it does not care how long that clock tick is when all the transistors flip on and off to give the computational result for that tick... simply speeding up the ticks does not change the logistical arrangement of bits and the functional blocks that create the logic to actuate those bits.....
From this data point, again assuming it is true, in the absense of extrenal bottlenecks (such as the memory, if that is even important), Super Pi should scale at best linear to frequency ... so, within a few %+/- due to noise (background processes, etc), SP1M for K10 would scale as such:
2.0 Ghz == 39 seconds
2.2 Ghz == 36.4 seconds
2.4 GHz == 34.2 seconds
2.6 GHz == 32.3 seconds
2.8 Ghz == 30.7 seconds
3.0 Ghz == 29.3 seconds
But this is gross based on one data point, I personally have a hard time believing K10 will give this kind of super pi performance, it is barely better than a K8....
Jack
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