The C++ library has several headers that support numerical programming. The most basic header is <cmath>, which declares transcendental and other mathematical functions. This C header is expanded in C++ to declare overloaded versions of every function. For example, whereas C declares only exp(double), C++ also declares exp(float) and exp(long double).

The <complex> header declares a class template for complex numbers, with the specializations you would probably expect for float, double, and long double. Transcendental and I/O functions are also declared for complex numbers.

The <numeric> header declares a few algorithms (that use standard iterators) for numerical sequences.

The most interesting numerical functions are in <valarray> . A valarray is like an ordinary numerical array, but the compiler is free to make some simplifying assumptions to improve optimization. A valarray is not a container, so it cannot be used with standard algorithms or the standard numeric algorithms.

You can use the complex template as an example of how to define custom numeric types. For example, suppose you want to define a type to represent rational numbers (fractions). To use rational objects in a valarray, you must define the class so it behaves the same as ordinary values, such as ints. In other words, a custom numeric type should have the following:

  • A public default constructor (e.g., rational( ))

  • A public copy constructor (e.g., rational(const rational&))

  • A public destructor

  • A public assignment ...

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