Re: [eigen] matrix::linspace

[Hauke Heibel <hauke.heibel@xxxxxxxxxxxxxx>]

I am still getting results as bad as this here:

vec: 2141.66 ms
lin: 1950.84 ms

MSVC seems to fail to optimize properly. I will try to look at the assembly..

- Hauke

On Sun, Jan 24, 2010 at 6:17 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:
> Hi Hauke,
>
> You've been trapped in a subtlety of gael's BenchTimer: when you use a
> single BenchTimer object more than 1 time, it returns the best time.
>
> I'd propose to rename it to something more explicit, and letting the
> BenchTimer name refer to something much simpler.
>
> That is why, when I ran your program, I got twice the same time.
>
> Now I edited main.cpp as attached, and I get:
>
> vec: 893.094 ms
> lin: 6745.94 ms
>
> Cheers,
> Benoit
>
> 2010/1/24 Hauke Heibel <hauke.heibel@xxxxxxxxxxxxxx>:
>> I tried using sequential packet access. Unfortunately, it did not
>> help. Maybe I am still missing something. The required patch (indexed
>> packet access) is attached to this mail as well as my test code.
>>
>> - Hauke
>>
>> On Sat, Jan 23, 2010 at 4:03 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:
>>> 2010/1/23 Hauke Heibel <hauke.heibel@xxxxxxxxxxxxxx>:
>>>> Hi there,
>>>>
>>>> I am working on some functionality which would allow something like this:
>>>>
>>>>  VectorXd a = VectorXd::linspace(low,high,num_steps)
>>>>
>>>> which should be corresponding to:
>>>>
>>>>  const double step_size = (high-low)/(num_steps-1);
>>>>  VectorXd a(num_steps);
>>>>  for (int i=0; i<num_steps; ++i)
>>>>   a(i) = low+i*step_size;
>>>>
>>>> In Eigen, this is best implemented based on NullaryExpressions, i.e.
>>>> Matrices, where each element can be computed based on some functor.
>>>
>>> I agree!
>>>
>>>> In
>>>> theory, this should not only be nice from a usability point of view
>>>> but I also hoped of gaining from vectorization. It tuns out, that this
>>>> is not that easy - it maybe due to MSVC but maybe also due to my lack
>>>> of SSE skills. For the most simple example
>>>>
>>>>  for (int i=0; i<num_steps; ++i) a(i) = i;
>>>>
>>>> I managed to implement the functor's method ei_linspace_op::packetOp
>>>> such that we do actually gain from vectorization as (note that I added
>>>> integer parameters to it):
>>>>
>>>>  // for doubles only
>>>>  ei_linspace_op::packetOp(int i, int = 0)
>>>>  {
>>>>    return ei_padd(ei_pset1<Scalar>(i),ei_pset<Scalar>(0,1));
>>>>  }
>>>>
>>>> For me the first surprise was that this performs way better than just
>>>> returning ei_pset<Scalar>(i,i+1).
>>>
>>> Notice that reading from memory is costly, and ei_pset1 is costly
>>> because it needs a SHUFPD instruction, so naively I would think that
>>> the best that can happen is that you make once and for all a packet
>>> (0,1) and a packet (1,1) and at each step you only add the latter into
>>> the former. Perhaps your code is fast because it allowed the compiler
>>> to do that optimization?
>>>
>>>> Next, I looked into the case:
>>>>
>>>>  for (int i=0; i<num_steps; ++i) a(i) = low+i
>>>>
>>>> and here, I totally failed. Returning
>>>>
>>>>  return ei_pset<Scalar>(m_low+i,m_low+i+1);
>>>>
>>>> resulted in no statistically meaningful gain (~0.06%) speedup. The
>>>> same holds for
>>>>
>>>>  return ei_padd(ei_pset1<Scalar>(i),ei_padd(ei_pset1(m_low),ei_pset<Scalar>(0,1)));
>>>>
>>>> which is even sometimes slower and permuting the operators did not help either.
>>>>
>>>> So, I am sort of puzzled about what I could improve. Any ideas? Any
>>>> SSE operation, I am not aware of for creating (a, a+1, a+2, ...)
>>>
>>> Same remark as above. I would initially store the packet (low,low+1)
>>> in a SSE register, store (1,1) into another SSE register, and only do
>>> a ei_padd at each iteration. Naively I would think that that is much
>>> faster?
>>>
>>>> Finally, note that ei_pset is not yet in PacketMath. Over here, I
>>>> added forward delarations into GenericPacketMath and the actual SSE
>>>> implementation in the corresponding PacketMath header (no Altivec
>>>> yet). They GenericPacketMath declarations (as the name says) have no
>>>> implementations since I don't see any meaningful way of providing them
>>>> nor do I think they are useful.
>>>
>>> Indeed I think they're only used in the matrix product code, which
>>> doesn't use your new ei_pset function.
>>>
>>>> The second change in the lib was
>>>> mentioned above - I added indices to the packetOp functions.
>>>
>>> Oh right, you need to fit your stuff with our packetOp infrastructure.
>>> Hm, not easy indeed, as I was assuming sequential, not random access.
>>>
>>>>
>>>> If everything regarding the vectorization fails, we could still
>>>> provide the functionality (with a specialization for the trivial case
>>>> where we gain from vectorizing) because at least, I think it is nifty.
>>>
>>> We might fail to vectorize random access efficiently. But 95% of use
>>> cases will be sequential access. This could then be a use case for a
>>> ReturnByValue function. When nesting this into a larger expression,
>>> this would have the drawback of introducing a temporary, and the
>>> advantage of enabling full vectorization instead of preventing
>>> vectorization of the larger expression.
>>>
>>> Benoit
>>>
>>>
>>>
>>
>