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Reduction of a vector to a scalar

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[99], b[99], 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.