Ok I think I understand now. C1 will be smaller if the chip needs less current to work and thus the coefficient ratio will be higher for chip that uses less power at the same performance level. Question: do C0 and C1 indeed remain constant across the entire voltage range? And how is all of this related to the fact that increasing voltage has diminishing returns on frequency increases? Is there also a formula for that?
C0 is constant as long as we assume that the work, which is done per cycle is in average constant. C1 is constant as long as we assume that the number of gates switching per cycle is in average constant. I believe both are very reasonable assumptions - and as you may observe are only dependent on architecture and the benchmark in question.
The interesting observation is, that the frequency cancels out. This means if you keep the voltage constant, any change in frequency has no impact on efficiency. With other words, when increasing the voltage, you are getting the quadratic efficiency hit, if you increase the frequency or not.
As disclaimer I want to add, i am considering the most important contributor - namely dynamic power. There is also static power for instance, which I neglected on purpose to simplify the model.
Back to reality however it doesn’t seem like we have a practical way to get M1 voltages. There surely is a sensor for those but it doesn’t seem like Apple exposes it. And finally, I still don’t get why this formula is ultimately useful to me as an interested user since the voltages these chips operate at are fixed anyway. For M1, I care about performance/power at maximal voltage as this is where the chip is doing demanding work. It’s a different story of course for other systems where these things are adjustable.
Depends, what conclusion you want to draw. If you want to reason about the inherent architectural efficiency of Zen vs M1, you really want to know C0/C1. Everything else does not tell you anything about architecture but rather about the ability to reduce voltage.
There is also the misconception, that the big increase in efficiency in ECO mode is somehow a feature of the Zen4 architecture - it is not - it is only voltage scaling of the technology - M1s efficiency will scale the same assuming same technology.
For additional motivation I give following example:
We have following voltages: Veco64 = 0.866V Veco105=1.038V Vnormal=1.183V.
Now based on the kitguru review we do know that the efficiency of the 7950X in normal mode is 179pts/W. Based on the given formula the estimated efficiency for eco105 is 235.4pts/W and eco65 is 338pts/W. The measured values are 249pts/w and 335pts/W - quite close to the estimate.