如何在许多条件下向量化循环？

Question

I have the loop below. The goal is to perform an operation between all elements of an array tmp and store it in a scalar b . The operation is equivalent to an addition, so there is no specific execution order. For example if we have a + b + c + d, we can compute this in any order, which means (a+b) + (c+d) is possible as well. The same is applicable to this operation. However, there are some special conditions which lead to the result by different ways.

tmp.e and be are longs , while tmp.x and bx are doubles .

Is there any form to compare all tmp.e , in for example pairs of 2 for SSE, and perform the correct computation of bx accordingly. In all cases, it can be viewed as an addMul, in the first case it's just multiplying by 1, in others by 0 or BOUND. Is it possible to vectorize this? If so, how?

Thanks.

void op(vec& tmp, scalar& b)
{
    for (i = 1; i < n; ++i)
    {
        if (b.e == tmp.e[i])
        {
            b.x += tmp.x[i];
            b.normalize();
            continue;
        }
        else if (b.e > tmp.e[i])
        {
            if (b.e > tmp.e[i]+1)
            {
                continue;
            }
            b.x += tmp.x[i] * BOUND;
            b.normalize();
        }
        else
        {
            if (tmp.e[i] > b.e+1)
            {
                b.x = tmp.x[i]; 
                b.e = tmp.e[i];
                b.normalize();
                continue;
            }
            b.x = b.x * BOUND + tmp.x[i];
            b.e = tmp.e[i];
            b.normalize();
        }
    }
}

Answer 1

Per-element conditionals in SIMD code are usually handled by using a packed-compare instruction to generate a mask of all-zero and all-one elements. You can use this to AND or OR vectors. So eg you can increment only the elements that pass a test by using AND to produce a vector with 1 in elements that should be incremented, and 0 in elements that shouldn't, because 0 is the identity value for addition. (x+0 = x).

You can also compute two results and then blend them together, according to a mask. (using AND and OR, or using vector blend instructions.)

This method of doing SIMD conditionals is like a cmov : you have to compute both sides of the branch, even if all the elements you're processing in a vector take the same side of the branch.

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It looks like your data is in struct-of-arrays format already. So you could generate masks from operations on vectors of e values, for use with vectors of x values. If long is 32bits, you could do a compare of 4 elements, and unpack-low and unpack-high to get two masks with 64bit elements to match your doubles. If the arrays are small (so they'd fit in cache even .e[] taking as much space as .x[] ), having the longs the same as the doubles means less unpacking.

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Anyway, it doesn't look promising. Too many conditions, and I have no idea what the whole thing is really trying to accomplish, and what restrictions there might be on the input data. If I knew more about the problem, maybe I could think of a vectorized way to do some of it.

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Oh, I think another fatal flaw is that each iteration depends on the previous iteration, because it might modify b . So you can't vectorize to do multiple iterations in parallel, unless you can work out a rule for updating b based on the last vector element.