3. evaluation — Evaluation of mathematical expressions

This module defines a class template evaluator which can be used to evaluate mathematical expressions, and exposes as well many of the details of the implementation, which may be reused for other purposes, even though evaluator is the main component of the module. Every feature of this module lives in the namespace polder::evaluation. While most of the internals can be included separately, the whole module can also be included at once with the following line of code:

#include <POLDER/evaluation.h>

The class template evaluator, the main component of this module, is also available directly from the polder namespace. Since there are many things to be said about this simple class, let’s start with a simple example:

#include <cstdlib>
#include <iostream>
#include <POLDER/evaluation.h>

int main()
{
    polder::evaluator<int> eval;

    std::cout << eval("2 + 5 * 3") << '\n'; // 17
    std::cout << eval("(4 + 2) * (2 ** 3)") << '\n'; // 48
    std::cout << eval("5!") << '\n'; // 120

    // Connect the absolute value function
    eval.connect("abs", [](int n) {
        return std::abs(n);
    });

    std::cout << eval("2 * abs(2 - 8) + 4") << '\n'; // 16
}

3.1. The class template evaluator

As said above, the most important class in the module is evaluator and it is the only one most people should care about.

class evaluator<Number>

Engine for evaluating mathematical expressions. It handles by default a set of built-in operators and can be extended by connecting functions to it. The template parameter corresponds to the type of the operations performed by the engine and to the return type of an evaluation.

Number evaluator<Number>::evaluate(const std::string & expression) const

Evaluates the expression string with the current rules of evaluation and returns the result of the evaluation.

Number evaluator<Number>::operator()(const std::string & expression) const

Alias for the method evaluate. The aim is to give a function object feeling to the evaluator class.

void evaluator<Number>::connect(const std::string & name, Func & & function)

Connects the given function to the evaluator. When evaluating an expression, if name is found in the expression string, it is considered as a function and the evaluator will try to call function on the arguments. In order for things to work properly, function has to be callable which takes any number of Number parameters and returns an instance of Number.

In its current form, the evaluator does not handle functions that have more than 16 parameters and does not handle functions with a variable number of parameters either. Overloaded functions are not supported either, a name represents one and only one function, not an overload set.

void evaluator<Number>::disconnect(const std::string & name)

Disconnects the function corresponding to name from the the evaluator if such a function exists.

3.2. Built-in operators

The evaluation module supports a wide range of infix operators out of the box as well as some prefix and postfix operators. The following infix operators are supported:

Infix operator	Meaning
a + b	\(a + b\)
a - b	\(a - b\)
a * b	\(a * b\)
a / b	\(\frac{a}{b}\)
a // b	\(\frac{a}{b}\) (integer division)
a % b	\(a \bmod b\)
a ** b	\(a^b\)
a = b	\(a = b\)
a != b	\(a \neq b\)
a <=> b	\(sign(a - b)\)
a < b	\(a < b\)
a > b	\(a > b\)
a <= b	\(a \le b\)
a >= b	\(a \ge b\)
a && b	\(a \wedge b\)
a || b	\(a \vee b\)
a ^^ b	\(a \oplus b\)
a & b	Bitwise AND
a | b	Bitwise OR
a ^ b	Bitwise XOR
a << b	Left shift
a >> b	Right shift

The following prefix operators are supported:

Prefix operator	Meaning
-n	\(-n\)
!n	\(\neg n\)
~n	Bitwise NOT

The following postfix operators are supported:

Postfix operator	Meaning
n!	\(n!\)