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## Quick Start

Before discussing the basics of the library, we first define a few terms that will be used frequently in the following :

- Base dimension : A base dimension is loosely defined as a measurable entity of interest; in conventional dimensional analysis, base dimensions include length ([L]), mass ([M]), time ([T]), etc... but there is no specific restriction on what base dimensions can be used. Base dimensions are essentially a tag type and provide no dimensional analysis functionality themselves.
- Dimension : A collection of zero or more base dimensions, each potentially raised to a different rational power. For example, length = [L]^1, area = [L]^2, velocity = [L]^1/[T]^1, and energy = [M]^1 [L]^2/[T]^2 are all dimensions.
- Base unit : A base unit represents a specific measure of a dimension. For example, while length is an abstract measure of distance, the meter is a concrete base unit of distance. Conversions are defined using base units. Much like base dimensions, base units are a tag type used solely to define units and do not support dimensional analysis algebra.
- Unit : A set of base units raised to rational exponents, e.g. m^1, kg^1, m^1/s^2.
- System : A unit system is a collection of base units representing all the measurable entities of interest for a specific problem. For example, the SI unit system defines seven base units : length ([L]) in meters, mass ([M]) in kilograms, time ([T]) in seconds, current ([I]) in amperes, temperature ([theta]) in kelvin, amount ([N]) in moles, and luminous intensity ([J]) in candelas. All measurable entities within the SI system can be represented as products of various integer or rational powers of these seven base units.
- Quantity : A quantity represents a concrete amount of a unit. Thus, while the meter is the base unit of length in the SI system, 5.5 meters is a quantity of length in that system.

To begin, we present two short tutorials. Tutorial1 demonstrates the use of SI units. After including the appropriate system headers and the headers for the various SI units we will need (all SI units can be included with `boost/units/systems/si.hpp`) and for quantity I/O (`boost/units/io.hpp`), we define a function that computes the work, in joules, done by exerting a force in newtons over a specified distance in meters and outputs the result to `std::cout`. The `quantity` class accepts a second template parameter as its value type; this parameter defaults to `double` if not otherwise specified. To demonstrate the ease of using user-defined types in dimensional calculations, we also present code for computing the complex impedance using `std::complex<double>` as the value type :

    #include <complex>
    #include <iostream>

    #include <boost/typeof/std/complex.hpp>

    #include <boost/units/systems/si/energy.hpp>
    #include <boost/units/systems/si/force.hpp>
    #include <boost/units/systems/si/length.hpp>
    #include <boost/units/systems/si/electric_potential.hpp>
    #include <boost/units/systems/si/current.hpp>
    #include <boost/units/systems/si/resistance.hpp>
    #include <boost/units/systems/si/io.hpp>

    using namespace boost::units;
    using namespace boost::units::si;

    constexpr
    quantity<energy>
    work(const quantity<force>& F, const quantity<length>& dx)
    {
        return F * dx; // Defines the relation: work = force * distance.
    }

    int main()
    {
        /// Test calculation of work.
        quantity<force>     F(2.0 * newton); // Define a quantity of force.
        quantity<length>    dx(2.0 * meter); // and a distance,
        quantity<energy>    E(work(F,dx));  // and calculate the work done.

        std::cout << "F  = " << F << std::endl
                  << "dx = " << dx << std::endl
                  << "E  = " << E << std::endl
                  << std::endl;

        /// Test and check complex quantities.
        typedef std::complex<double> complex_type; // double real and imaginary parts.

        // Define some complex electrical quantities.
        quantity<electric_potential, complex_type> v = complex_type(12.5, 0.0) * volts;
        quantity<current, complex_type>            i = complex_type(3.0, 4.0) * amperes;
        quantity<resistance, complex_type>         z = complex_type(1.5, -2.0) * ohms;

        std::cout << "V   = " << v << std::endl
                  << "I   = " << i << std::endl
                  << "Z   = " << z << std::endl
                  // Calculate from Ohm's law voltage = current * resistance.
                  << "I * Z = " << i * z << std::endl
                  // Check defined V is equal to calculated.
                  << "I * Z == V? " << std::boolalpha << (i * z == v) << std::endl
                  << std::endl;
        return 0;
    }

The intent and function of the above code should be obvious; the output produced is :

    F  = 2 N
    dx = 2 m
    E  = 4 J

    V   = (12.5,0) V
    I   = (3,4) A
    Z   = (1.5,-2) Ohm
    I*Z = (12.5,0) V
    I*Z == V? true

While this library attempts to make simple dimensional computations easy to code, it is in no way tied to any particular unit system (SI or otherwise). Instead, it provides a highly flexible compile-time system for dimensional analysis, supporting arbitrary collections of base dimensions, rational powers of units, and explicit quantity conversions. It accomplishes all of this via template metaprogramming techniques. With modern optimizing compilers, this results in zero runtime overhead for quantity computations relative to the same code without unit checking.