Quote from: ir.hn on December 19, 2017, 04:30:40 AM

So would I Wink

. I would like to apologize to haltingprobability, I have been a bit harsh on him. Some people like seeing proof, I for one am someone who will go out and search for myself. But different strokes for different folks.

No hard feelings.

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I am not the kind of meticulous person to work on proofs. I don't have a degree in mathematics or computer science and I tend to get interested in developing concepts and ideas and implementing them.

I am a computer engineer. I have a degree in computer engineering. I'm trying to inform you that your intuitive notions about the difference between GPUs and CPUs - while good enough for basic comprehension - are not rigorous and that, in this case, that matters.

There is a theorem in computational complexity (the field of mathematics that studies how fast any given kind of formal problem can be solved), called the speed-up theorem. Basically, this theorem says that any particular solution to a problem (an "algorithm") can be sped up by a linear factor. So, suppose that you find an algorithm A that solves problem Z in time n², where n is the size of a problem in Z. This is called quadratic complexity - as n increases, the time required to solve the problem grows as the square of n. The speed-up theorem tells us that it is always possible to find some fixed factor, k, such that we can construct a new algorithm A' from A that solves a problem in Z in time n² / k. Note that this does not change the complexity class - A still solves problems in Z in quadratic time. Intuitively, this makes sense - if I can solve a problem in time n² with one computer, then I should always be able to solve it in nearly n² / 2 with two computers. There are some very intractable problems where this becomes difficult (due to network complexity) but such problems tend to be academic, i.e. specially constructed to make parallelization difficult.

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CPU's are adaptable, GPU's are not. CPU's are fast and think on their feet whereas GPU's are slow and methodical and share their work well.

This is mostly not true anymore. GPGPUs (General-Purpose GPU) can, in principle, do anything that CPUs can do and the latest GPU cards are being released with GPGPU cores in them. GPU clock speeds are in the same class as CPUs, so they are not slow. GPUs are designed around "data parallelism" or "data flow architecture" and this is why they are well-suited to graphics applications or any application where you can easily parallelize the work by simply dividing up the work surface and handing out more or less identical instructions to each work unit (rendering pipeline).

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So it would be very shortsighted to think that GPU's can accelerate any given task and be better than a CPU.

For any large search problem (and any non-trivial PoW must be a large search problem), GPUs will be superior. If I have to try 2⁶⁰ possibilities (about a billion billion possibilities) in order to solve a given PoW problem, I can try these one-by-one on a CPU or I can parallelize the problem and have multiple CPUs or GPUs work on it in parallel. Suppose I have 128 GPUs available to me. Instead of having to search 2⁶⁰ possibilities, each GPU now only has to solve 2⁵³ possibilities, resulting in a 128x reduction in search time. Factoring is just a large search problem.