Soleron said:
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No, a single core does not operate at the same cycles per minute, however a single core on the Xbox One's processor can do more work per cycle than one core of the Xbox 360's Xenon processor. A single core of the Xbox 360's CPU does 38.3 GFLOPs. A single core of the Xbox One's processor does 152.5 GFLOPs. So, in the same amount of time, the Xbox One processor can do more than 3 times what the Xbox 360's CPU can do.
Programming on Windows means using Microsoft's C/C++ libraries if you're not coding in .NET. You're not coding to the hardware directly. You might get closer to it than .NET permits, but you're still using libraries provided by Microsoft. Which means, as long as Microsoft updates the libraries to be code compatible with or update the code in the games to be compatible with the new libraries and recompiled with them, it'll work.
As far as memory goes, if you're addressing memory specifically (i.e. reserving blocks and moving data in and out of those blocks manually rather than letting the APIs do it, then you're still addressing a known block of memory. As long as those blocks of memory line up with what is available, cool. If they don't, then you have some work to do but still not a unfathomable task.
The Xenox GPU was the basis for the R600. As long as Microsoft's libraries were used, then those library files can be updated and the game can be recompiled.
Tesellation is a great example. While supported on the Xbox 360, it wasn't fully implemented until DirectX 11. An Xbox 360 game that used tesellation could be improved by utilizing the updated capabilities of both the newer GPU (AMD provides hardware support for tesellation) and API.
Bottom line, it is extremely possible that Microsoft could do this. The question is, would they do it for free?