Chapter 18. Expression Templates

Ru-Brd

In this chapter we explore a template programming technique called expression templates . It was originally invented in support of numeric array classes, and that is also the context in which we introduce it here.

A numeric array class supports numeric operations on whole array objects. For example, it is possible to add two arrays, and the result contains elements that are the sums of the corresponding values in the argument arrays. Similarly, a whole array can be multiplied by a scalar, meaning that each element of the array is scaled. Naturally, it is desirable to keep the operator notation that is so familiar for built-in scalar types:

 Array<double> x(1000), y(1000);   x = 1.2*x + x*y; 

For the serious number cruncher it is crucial that such expressions be evaluated as efficiently as can be expected from the platform on which the code is run. Achieving this with the compact operator notation of this example is no trivial task, but expression templates will come to our rescue.

Expression templates are reminiscent of template metaprogramming. In part this is due to the fact that expression templates rely on sometimes deeply nested template instantiations, which are not unlike the recursive instantiations encountered in template metaprograms. The fact that both techniques were originally developed to support high-performance (see our example using templates to unroll loops on page 314) array operations probably also contributes to a sense that they are related . Certainly the techniques are complementary. For example, metaprogramming is convenient for small, fixed-size array whereas expression templates are very effective for operations on medium-to-large arrays sized at run time.

Ru-Brd