All these libraries under the hood delegate to the same things for the actual computation, so the only advantage of one over the other would be this type of stuff.
That NumPy/CuPy coerce to a float64 under the hood, and gives us no way to force it not to do so, is a disadvantage that they have in my opinion.
In any case, like the article says, the performance of NumPy/CuPy is still good enough, and maybe NumPy thinks it knows better then it's users that they should be using higher precision always.
Edit: I know I'll face the brigade of NumPy users. But I invite people to engage in the discussion unbiased. With a switch from CPU to GPU you'd expect more than 29% performance boost. If CuPy went with a float32 proc, it would give you a 96% performance increase! So ya, I think we can start to argue CuPy isn't doing the right thing here.
This is just getting tiring.
Numpy and Cupy are perfectly capable of doing float32 computation - their only "fault" is that they coerce data to float64 in this one fairly unimportant function (which you can implement to your liking in 3-4 LOC). Hell, PFNs entire deep learning system, Chainer (which mind you, both predated and inspired PyTorch, and is still quite competitive with it), is built entirely on top of Cupy!
Benchmarks make sense only when the outputs are the same - in this case, they certainly are not. It's the responsibility of the author to make sure that the outputs are the same (a real benchmark), or to argue that Numpy/Cupy are wasting time by using float64 in xp.cov (an issue of implementation). He does neither.
You're arguing that they would perfectly be capable of an implementation which would use float32, ya sure, if you change their source code you can have them be faster, that's an obvious to me? The question is, what kind of performance can you expect as a user using them as a library, and this benchmark is revealing of that in this case. What is wrong with it?
It's like saying that you can change the implementation of Python and it will make Python code run faster, like sure you can, but you don't benchmark hypothetical future versions, the current version of CuPy uses float64 for this function, and that makes it that it barely runs faster then the CPU version. Point in case, I don't know what else you're trying to disagree about here.
> their only fault is that they coerce data to float64 in this one fairly unimportant function
I don't know that, all I know is when picking one function and benchmarking it, we found a flaw which result in performance gains from CPU to GPU to be extremely underwhelming. How many more if we started to benchmark the rest?
You don't need to change the numpy or cupy source code, just write your own version of the function in a few lines of code using other primitives that numpy/cupy provides.
Note that is exactly what is done for the neanderthal version.
You could get away using a double to only accumulate the sum, but it's a pain to write such mixed-precision (slow) function in C and then wrap it in Python, esp. for something like this.
(See, https://github.com/numpy/numpy/blob/v1.17.0/numpy/lib/functi...)
BTW did you check that your corr function gives the correct result? It looks to me that you forgot a few steps.
The part that is flawed is that you're comparing this to Numpy (CPU)/ Cupy (GPU) both of which coerce the input array to float64 (for precision reasons) before computing the covariance and correlation. You only need to check the output type of the result to verify this (if the pointer to the code is not sufficient).
The reason for that is that CuPy is poorly implemented. And CuPy is poorly implemented because it is constrained by what NumPy does, which, in turn, does stuff that is OK on the CPU, and often translates poorly to the GPU.
You're comparing float32 vs float64 computation. I don't need to tell you how much slower DGEMM is vs SGEMM esp. on the GPU (you mention this in the post yourself!).
Numpy does this for precision reasons, and CuPy simply follows its behavior. This is precisely why I noted that the float32 version runs 3x faster on the CPU.
> The reason for that is that CuPy is poorly implemented.
It's a cheap shot to call something 'poorly implemented' when you don't understand what you're benchmarking.
It would be interesting to compare it against a float64 version in Neanderthal as well I agree with that.
That said, a flawed benchmark would mean to me that it isn't indicative of the performance one can expect when actually using the library on real world use case, but for now this benchmark for NumPy/CuPy does seem to be indicative of what you'd expect.
Now, the next question is, for model accuracy vs scale, is going with float64 coercion always the ideal trade off? What if you still needed to squeeze more performance? Is it really a bad idea to do so by going down to float32? Especially considering how much faster GPU can accelerate that?
>> Nope, we work with float32.
>It seems that is not true.
Well, it is true. We work with float32. I explicitly checked that and NumPy/CuPy answered that the array is indeed float32. The fact, which I didn't know then, is that NumPy/CuPy internally decides on its own to use float64 without warning or possibility for us to order it not to do that. But, it is not I (or "us") that work with float64.
I would say that your comment would stand if I mistakenly ordered NumPy/CuPy to use float64 while claiming that I work with float32 (which could happen hypothetically if there was a non-obvious, but documented option to use float32 that I missed).
I never claimed that my library aims for being a replacement for CuPy, or to have any compatibility with NumPy.
It would be more valuable to CuPy developers if I debugged CuPy to discover why that problem exists, but why should I be obligated to? I was writing this for a perspective of a user of these libraries.
I agree with both of you, you’re both looking at this thing from a different perspective. It’s perhaps just better to gather timing measurements on a few variants with the trade-offs that each library has made, and how that affects implementation / speed.
> Nope, we work with float32.
It seems that is not true. The blog should make clear that it isn't straightforward or possible to get cupy to do this.
And even if your argument stands, that does not change the fact that CuPy does not accelerate NumPy (in this particular case, but I'd say often).
If you look at the article, it is not even using Python anywhere, it uses NumPy/CuPy directly from Clojure. So it really is comparing Neanderthal vs NumPy/CuPy, and uses Clojure in both cases.
You should state that the reason the neanderthal version runs faster is that it is doing the computation in lower precision than numpy / cupy.
The article walks through an investigation of why cupy's result is underwhelming (is the input data accidentally fp64? is the input data on the cpu? is the computation happening on the cpu?), so you should finish it by explaining that numpy and cupy do the computation in fp64.
https://github.com/cupy/cupy/blob/b19577199d3f75c76e23c75194...
The following function in PyTorch completes the float32 computation in 27 ms (1080 Ti). I'm fairly sure that a similar function in Cupy would achieve very similar results.
The heart of the computation SGEMM is in anycase provided by CUBLAS, and the only areas in which PyT and Cupy differ are in the tricks used to unroll the loop for the broadcasting & L1 op. The performance difference b/w PyT, Cupy and others should be negligible IMO.Note: np.corrcoef takes about 1.12 s and the above float32 version takes 325ms on the CPU.