Based from what I read, it seems like the cost might be 0 cycles. Is it really 0 cycles? If the cost is 0 cycles, does this include the jump instruction itself instead of just the possible flush in the CPU instruction cache? I appreciate answers on any CPU architecture.
In general, when someone says that a correctly predicted conditional branch is "free", they don't mean that it magically happens instantaneously, they mean that it has the same cost as an unconditional jump, i.e. that the "conditional" is free, not the whole branch.
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Calculating the solution to an optimization problem takes a 2 GHz CPU one hour. During this process there are no background processes, no RAM is being used and the CPU is at 100% capacity.
Based on this information, can it be derived that a 1 GHz CPU will take two hours to solve the same problem?
A quick search of IPC, frequence, and chip architecture will show you this topic has been breached many times. There are many things that can determine the execution speed of a program (without even going into threading at all) the main ones that pop to mind:
Instruction set - If one chip has an instruction for multiplication, than a*b is atomic. If not, you will need a lot of atomic instructions to perform such an action - big difference in speed, which can prove to make even higher frequency chips slower.
Cycles per second - this is the frequency of the chip.
Instructions per cycle (IPC) - what you are really interested is IPC*frequency, not just frequency. How many atomic actions can you can perform in a second. After the amount of atomic actions (see 1), on a single threaded application this might act as you expect (x2 this => x2 faster program), though no guarantees.
and there are a ton of other nuance technologies that can affect this, like branch prediction which hit the news big time recently. For a complete understanding a book/course might be a better resource.
So, in general, no. If you are comparing two single core, same architecture chips (unlikely), then maybe yes.
Assume I have a CPU running at a constant rate, pulling an equal amount of energy per instruction. I also have two functionally identical programs, which result in the same output, except one has been optimized to execute only 100 instructions, while the other program executes 200 instructions. Is the 100 instruction program necessarily faster than the 200 instruction program? Does a program with fewer instructions draw less power than a program with more instructions?
Things are much more complex than this.
For example execution speed is in many cases dominated by memory. As a practical example some code could process the pixels of an image first in rows and then in columns... a different code instead could be more complex but processing rows and columns at the same time.
The second version could execute more instructions because of more complex housekeeping of the data but I wouldn't be surprised if it was faster because of how memory is organized: reading an image one column at a time is going to "trash the cache" and it's very possible that despite being simple the code working that way could be a LOT slower than the more complex one doing the processing in a memory-friendly way. The simpler code may end up being "stalled" a lot waiting for the cache lines to be filled or flushed to the external memory.
This is just an example, but in reality what happens inside a CPU when code is executed is for many powerful processors today a very very complex process: instructions are exploded in micro-instructions, registers are renamed, there is speculative execution of parts of code depending on what branch predictors guess even before the program counter really reaches a certain instruction and so on. Today the only way to know for sure if something is faster or slower is in many cases just trying with real data and measure.
Is the 100 instruction program necessarily faster than the 200 instruction program?
No. Firstly, on some architectures (such as x86) different instructions can take a different number of cycles. Secondly, there are effects — such cache misses, page faults and branch mispreditictions — that complicate the picture further.
From this it follows that the answer to your headline question is "not necessarily".
Further reading.
I found a paper from 2017 comparing the energy usage, speed, and memory consumption of various programming languages. There is an obvious positive correlation between faster languages also using less energy.
Just reading a bit about what the advantage of GPU is, and I want to verify I understand on a practical level. Lets say I have 10,000 arrays each containing a billion simple equations to run. On a cpu it would need to go through every single equation, 1 at a time, but with a GPU I could run all 10,000 arrays as as 10,000 different threads, all at the same time, so it would finish a ton faster...is this example spot on or have I misunderstood something?
I wouldn't call it spot on, but I think you're headed in the right direction. Mainly, a GPU is optimized for graphics-related calculations. This does not, however, mean that's all it is capable of.
Without knowing how much detail you want me to go into here, I can say at the very least the concept of running things in parallel is relevant. The GPU is very good at performing many tasks simultaneously in one go (known as running in parallel). CPUs can do this too, but the GPU is specifically optimized to handle much larger numbers of specific calculations with preset data.
For example, to render every pixel on your screen requires a calculation, and the GPU will attempt to do as many of these calculations as it can all at the same time. The more powerful the GPU, the more of these it can handle at once and the faster its clock speed. The end result is a higher-end GPU can run your OS and games in 4k resolution, whereas other cards (or integrated graphics) might only be able to handle 1080p or less.
There's a lot more to this as well, but I figured you weren't looking for the insanely technical explanation.
The bottom line is this: For running a single task on one piece of data, the CPU will normally be faster. A single CPU core is generally much faster than a single GPU core. However, they typically have many cores and for running a single task on many pieces of data (so you have to run it once for each), the GPU will usually be faster. But these are data-driven situations, and as such each situation should be assessed on an individual basis to determine which to use and how to use it.
I was told that running programs generate probability data used to optimize repeated instructions.
For example, if an "if-then-else" control structure has been evaluated TRUE 8/10 times, then the next time the "if-then-else" statement is being evaluated, there is an 80% chance the condition will be TRUE. This statistic is used to prompt hardware to load the appropriate data into the registers assuming the outcome will be TRUE. The intent is to speed up the process. If the statement does evaluate to TRUE, data is already loaded to the appropriate registers. If the statement evaluates to FALSE, then the other data is loaded in and simply written over what was decided "more likely".
I have a hard time understanding how the probability calculations don't out-weigh the performance cost of decisions it's trying to improve. Is this something that really happens? Does it happen at a hardware level? Is there a name for this?
I can seem to find any information about the topic.
This is done. It's called branch prediction. The cost is non-trivial, but it's handled by dedicated hardware, so the cost is almost entirely in terms of extra circuitry -- it doesn't affect the time taken to execute the code.
That means the real cost would be one of lost opportunity -- i.e., if there was some other way of designing a CPU that used that amount of circuitry for some other purpose and gained more from doing so. My immediate guess is that the answer is usually no -- branch prediction is generally quite effective in terms of return on investment.
In a GPU implementation we need to estimate its performance in terms of GLOPS. The code is very basic, but my problem is how many FLOPS should I give to the operations "sqrt" or "mad", whether 1 or more.
Besides, I obtain 50 GFLOPS for my code if 1 say 1 FLOP for these operations, while the theoretical maximum for this GPU is 500GFLOPS. If I express it in precentages I get 10 %. In terms of speedup I get 100 times. So I think it is great, but 10% seems to be a bit low yield, what do you think?
Thanks
The right answer is probably "it depends".
For pure comparative performance between code run on different platforms, I usually count transcendentals, sqrt, mads, as one operation. In that sort of situation, the key performance metric is how long the code takes to run. It is almost impossible to do the comparison any other way - how would you go about comparing the "FLOP" count of a hardware instruction for a transcendental which takes 25 cycles to retire, versus a math library generated stanza of fmad instructions which also takes 25 cycles to complete? Counting instructions or FLOPs becomes meaningless in such a case, both performed the desired operation in the same amount of clock cycles, despite a different apparent FLOP count.
On the other hand, for profiling and performance tuning of a piece of code on given hardware, the FLOP count might be a useful metric to have. In GPUs, it is normal to look at FLOP or IOP count and memory bandwidth utilization to determine where the performance bottleneck of a given code lies. Having those numbers might point you in the direction of useful optimizations.