For most common value types, the result type of arithmetic operators is the same as the value type itself. For example, the sum of two double precision floating point numbers is another double precision floating point number. However, there are instances where this is not the case. A simple example is given by the natural numbers where the operator arithmetic obeys the following rules (using the standard notation for number systems):

This library is designed to support arbitrary value type algebra for addition, subtraction, multiplication, division, and rational powers and roots. It uses Boost.Typeof to deduce the result of these operators. For compilers that support typeof, the appropriate value type will be automatically deduced. For compilers that do not provide language support for typeof it is necessary to register all the types used. For the case of natural numbers, this would amount to something like the following:

BOOST_TYPEOF_REGISTER_TYPE(natural);
BOOST_TYPEOF_REGISTER_TYPE(integer);
BOOST_TYPEOF_REGISTER_TYPE(rational);

Conversion is only meaningful for quantities as it implies the presence of at least a multiplicative scale factor and, possibly, and affine linear offset. Macros for simplifying the definition of conversions between units can be found in boost/units/conversion.hpp and boost/units/absolute.hpp (for affine conversions with offsets).

The macro BOOST_UNITS_DEFINE_CONVERSION_FACTOR specifies a scale factor for conversion from the first unit type to the second. The first argument must be a base_unit. The second argument can be either a base_unit or a unit.

Let's declare a simple base unit:

struct foot_base_unit : base_unit<foot_base_unit, length_dimension, 10> { };

Now, we want to be able to convert feet to meters and vice versa. The foot is defined as exactly 0.3048 meters, so we can write the following

BOOST_UNITS_DEFINE_CONVERSION_FACTOR(foot_base_unit, meter_base_unit, double, 0.3048);

Alternately, we could use the SI length typedef:

BOOST_UNITS_DEFINE_CONVERSION_FACTOR(foot_base_unit, SI::length, double, 0.3048);

Since the SI unit of length is the meter, these two definitions are equivalent. If these conversions have been defined, then converting between scaled forms of these units will also automatically work.

The macro BOOST_UNITS_DEFAULT_CONVERSION specifies a conversion that will be applied to a base unit when no direct conversion is possible. This can be used to make arbitrary conversions work with a single specialization:

struct my_unit_tag : boost::units::base_unit<my_unit_tag, boost::units::force_type, 1> {};
// define the conversion factor
BOOST_UNITS_DEFINE_CONVERSION_FACTOR(my_unit_tag, SI::force, double, 3.14159265358979323846);
// make conversion to SI the default.
BOOST_UNITS_DEFAULT_CONVERSION(my_unit_tag, SI::force);

This library is designed to emphasize safety above convenience when performing operations with dimensioned quantities. Specifically, construction of quantities is required to fully specify both value and unit. Direct construction from a scalar value is prohibited (though the static member function from_value is provided to enable this functionality where it is necessary. In addition, a quantity_cast to a reference allows direct access to the underlying value of a quantity variable. An explicit constructor is provided to enable conversion between dimensionally compatible quantities in different unit systems. Implicit conversions between unit systems are allowed only when the reduced units are identical, allowing, for example, trivial conversions between equivalent units in different systems (such as SI seconds and CGS seconds) while simultaneously enabling unintentional unit system mismatches to be caught at compile time and preventing potential loss of precision and performance overhead from unintended conversions. Assignment follows the same rules. An exception is made for quantities for which the unit reduces to dimensionless; in this case, implicit conversion to the underlying value type is allowed via class template specialization. Quantities of different value types are implicitly convertible only if the value types are themselves implicitly convertible. The quantity class also defines a value() member for directly accessing the underlying value.

To summarize, conversions are allowed under the following conditions :

Of course, any time implicit conversion is allowed, an explicit conversion is also legal.

Because dimensionless quantities have no associated units, they behave as normal scalars, and allow implicit conversion to and from the underlying value type or types that are convertible to/from that value type.