Science and Mathematics

Introduction

C++ is a language well suited for scientific and mathematical programming, due to its flexibility, expressivity, and efficiency. One of the biggest advantages of C++ for numerical processing code is that it can help you avoid redundancy.

Historically, numerical code in many programming languages would repeat algorithms over and over for different kinds of numerical types (e.g., short, long, single, double, custom numerical types, etc.). C++ provides a solution to this problem of redundancy through templates. Templates enable you to write algorithms independantly of the data representation, a technique known commonly as generic programming.

C++ is not without its shortcomings with regards to numerical processing code. The biggest drawback with C++in contrast to specialized mathematical and scientific programming languagesis that the standard library is limited in terms of support of algorithms and data-types relevant to numerical programming. The biggest oversights in the standard library are arguably the lack of matrix types and arbitrary precision integers.

In this chapter, I will provide you with solutions to common numerical programming problems and demonstrate how to use generic programming techniques to write numerical code effectively. Where appropriate, I will recommend widely used open-source libraries with commercially friendly licenses and a proven track record. This chapter introduces the basic techniques of generic programming gradually from recipe to recipe.

Many programmers using C++ still distrust templates and generic programming due to their apparent complexity. When templates were first introduced into the language they were neither well implemented nor well understood by programmers and compiler implementers alike. As a result, many programmers, including yours truly, avoided generic programming in C++ for several years while the technology matured.

Today, generic programming is widely accepted as a powerful and useful programming paradigm, and is supported by the most popular programming languages. Furthermore, C++ compiler technology has improved by leaps and bounds, and modern compilers deal with templates in a much more standardized and efficient manner. As a result, modern C++ is a particularly powerful language for scientific and numerical applications.