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A special category of scalar use within loops is reduction operations. This category involves the reduction of a vector of values down to a scalar result.
The most common reduction is the summation of all elements of a vector. Other reductions include:
The dot product of two vectors.
The maximum value in a vector.
The minimum value in a vector.
The product of all vector elements.
The index of the maximum or minimum element of a vector.
The following example shows a dot
product reduction where
x is a reduction scalar.
float a, b, x; int i, n; ... for (i = 0; i < n; i++) x += a[i] * b[i];
Reduction operations are worth vectorizing because they occur so often. In general, reduction operations are vectorized by creating a vector of partial reductions that is then reduced into the final resulting scalar.