Optimizing C++ vector expressions

Recently, I´ve been entertaining myself by studying all the nifty new programming techniques that have been invented since I was in school. I started with C++ and object-oriented programming. I´m now progressing through generic programming, aspect-oriented programming, partial evaluation and generative programming. What I´m really interested in is whether all these tricks work in the real world of graphics programming. My answer so far is “Yes, but...”. To see “but what?”, I define one of the problems I want to solve in in this article. I wanted to have a programming language that defined vectors and the arithmetic operations between them. C++ allows me to do this, but there are various pitfalls in doing this well. This article addresses one of these pitfalls: the speed of execution of vector arithmetic. The conventional approach turns out to be somewhat slow, but there´s a very tricky technique that can make vector arithmetic very fast. It´s based on the work of T. Veldhuizen (1998) and uses the C++ template mechanism in bizarre and unexpected ways