Some algorithms for seemingly straightforward and simplemathematical equations are actually extremely difficult to implement. For instance, rounding problems can compromise accuracy, some mathematical equations can cause values to exceed the range of a floating-point value on the system, and some algorithms (notably the classic Fourier Transform) take much too long if done in a brute-force fashion. Furthermore, different sets of data work better with different algorithms. Consequently, beautiful code and beautiful mathematics are not necessarily one and the same.
The programmers who wrote the code for the CERN mathematical library recognized the difference between mathematical equations and computed solutions: the difference between theory and practice. In this chapter, I will explore the beauty in a few of the programming strategies that they used to bridge that gap.
My idea of beautiful code stems from my belief that the ultimate purpose of code is to work. In other words, code should accurately and efficiently perform the task that it was designed to complete, in such a way that there are no ambiguities as to how it will behave.
I find beauty in code that I can trust—code that I am confident will produce results that are correct and applicable to my problem. What I am defining here as my first criterion of beautiful code is code that I can use and reuse without any shred of doubt in the code’s ...