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<title>C++ Units</title>
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<p><b><font face="Arial"><font size="4">C++ Units</font><br>
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</font></b><font face="Arial" size="2">by <a href="../index.html">Calum Grant</a></font></p>
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<p><font face="Arial" size="2">Units home page: <a href="index.html">
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http://calumgrant.net/units</a></font></p>
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<p><b><font face="Arial">Introduction</font></b></p>
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<blockquote>
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<p><font face="Arial" size="2">This library is for engineers and scientists
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who deal with physical quantities. Units provide a safety net that check
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the validity of formulae at compile-time and ensure that different units are
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converted where necessary. A large number of physical quantities are
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provided by the library, including all SI units.</font></p>
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<p><font face="Arial" size="2">This library is for software engineers.
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By giving a quantity a unit, it prevents the wrong value being assigned to the
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wrong thing, or passing the wrong value to the wrong argument of a function.
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Units documentation a program - <i>int</i> is not descriptive, but <i>apples</i> is.</font></p>
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<p><font face="Arial" size="2">The library uses templates and generative
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programming techniques to handle units at compile time, so there is no
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run-time overhead. Many units are predefined and it is straightforward
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to add your own.</font></p>
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<p><font face="Arial" size="2">The library is installed by copying the file
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<a href="units.hpp">units.hpp</a> into your include directory. To use the library</font></p>
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<blockquote>
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<pre>#include "units.hpp"</pre>
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</blockquote>
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</blockquote>
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<p><b><font face="Arial">Using built in units</font></b></p>
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<blockquote>
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<p><font face="Arial" size="2">The built in physical quantities are in the
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namespace <i>units::values</i>, so for the purposes of this tutorial, assume
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that</font></p>
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<blockquote>
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<pre>using namespace units::values;</pre>
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</blockquote>
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<p><font face="Arial" size="2">has been written somewhere near the top of the
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file. This namespace gives you access to the following physical
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quantities:</font></p>
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<ul>
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<li><font face="Arial" size="2">No unit: <i>unit, percent, dozen,
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bakers_dozen</i></font></li>
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<li><font face="Arial" size="2">Mass: <i>kg, g, mg, lb, oz, tonne</i></font></li>
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<li><font face="Arial" size="2">Time: <i>s, ms, minute, hour, day, week</i></font></li>
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<li><font face="Arial" size="2">Calendar: <i>month, year, century,
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millennium</i></font></li>
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<li><font face="Arial" size="2">Distance: <i>m, cm, mm, km, inch, foot,
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yard, mile, nautical_mile</i></font></li>
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<li><font face="Arial" size="2">Temperature: <i>K, Celsius, Fahrenheit</i></font></li>
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<li><font face="Arial" size="2">Force: <i>N</i></font></li>
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<li><font face="Arial" size="2">Pressure: <i>Pa, kPa, psi, millibar</i></font></li>
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<li><font face="Arial" size="2">Energy: <i>J</i></font></li>
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<li><font face="Arial" size="2">Power: <i>W</i></font></li>
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<li><font face="Arial" size="2">Area: <i>m2, hectare, are, inch2, acre</i></font></li>
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<li><font face="Arial" size="2">Volume: <i>cm3, ml, cl, liter, dl, m3</i></font></li>
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<li><font face="Arial" size="2">Velocity: <i>mph, kph, meters_per_second,
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knot, mach</i></font></li>
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<li><font face="Arial" size="2">Angle: <i>rad, degree, grad, degree_minute,
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degree_second</i></font></li>
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<li><font face="Arial" size="2">Other units: <i>A, mol, cd, rad, sr, Hz, C,
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V, F, Ohm, S, Wb, T, H, lm, lx, Bq, Gy, Sv, kat, rpm</i></font></li>
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</ul>
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<p><font size="2" face="Arial">The naming convention is to use the symbol of
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the SI unit. For other units, the name is used since there are no
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standard symbols.</font></p>
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<p><font face="Arial" size="2">The built-in values are all doubles, however
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you can change this (see next section). The physical quantities behave
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exactly as normal doubles, except that they check the units and perform
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conversion where necessary.</font></p>
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<p><font face="Arial" size="2">A value can be constructed from a number,
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another value, or the default constructor which initializes the value to zero.
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When constructing from another value, the other value must be compatible or
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you will get a compile-time error:</font></p>
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<blockquote>
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<pre>m x; // x = 0
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m y(10); // y = 10
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m z(cm(250)); // z = 2.5
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m w(s(3)); // Compile-time error: incompatible units
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kph(mph(70)) // Convert miles per hour to km per hour</pre>
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</blockquote>
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<p><font face="Arial" size="2">Assignment is only possible from another value,
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and the value must be compatible:</font></p>
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<blockquote>
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<pre>x = 10; // Compile-time error: 10 of what?
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x = cm(200); // Ok: x = 2.0
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x = s(3) // Compile-time error: incompatible units</pre>
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</blockquote>
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<p><font face="Arial" size="2">The number in the value can be obtained using
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the <i>get() </i>method:</font></p>
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<blockquote>
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<pre>x.get(); // Get current value of x
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cm(m(5)).get() // 500</pre>
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</blockquote>
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<p><font face="Arial" size="2">The normal arithmetic operators are supported:
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<i>+, -, *, /, /=, *=, ++, --</i>. There are some restrictions however.
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You can only add or subtract compatible values. You can multiply or
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divide by any other value, which returns a value with a unit with the correct
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type (multiplied or divided). The <i>*=</i> and <i>/=</i> operators can
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only take a number (in general if you multiply by another unit the type will
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be different). e.g.</font></p>
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<blockquote>
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<pre>miles x = m(1) + cm(10); // Add two distances
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m2 area = foot(10) * yard(3); // Converts to meters squared
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s timer;
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timer += 10; // Compile-time error: add 10 of what
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timer += s(10); // Ok: add 10 seconds to timer
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liter v = hectare(1) * mm(1); // Ok
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H h( m(4)*m(8)*kg(2)/s(2)/s(4)/A(1)/A(2) ); // A complex (but valid) formula
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s(10) + m(4); // Compile-time error: Can't add time and distance</pre>
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</blockquote>
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<p><font face="Arial" size="2">The comparison operators (<i>==, !=, <, <=, >,
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>=</i>) also convert between units implicitly:</font></p>
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<blockquote>
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<pre>minutes(2) > s(70) // true</pre>
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</blockquote>
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<p><font face="Arial" size="2">Writing a value to a stream (using <i>operator
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<<</i>) displays the unit after the value. Many of the built in units
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have names, otherwise the text is generated, as in the following example:</font></p>
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<pre> std::cout << "Flow rate is " << m3(mile(1)*inch(80)*foot(9))/s(minute(5));
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// Output: Flow rate is 29.9026 (m)^3.(s)^-1</pre>
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<p><font face="Arial" size="2">The <i>units::sqrt</i> function provides a
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square root - which also takes the root of the unit of course.</font></p>
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<blockquote>
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<pre>m a, b, c;
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c = units::sqrt( a*a + b*b );</pre>
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</blockquote>
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<p><font face="Arial" size="2">You can take an arbitrary rational
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power of a number using the <i>units::raise</i> template, however you must
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specify the power at compile time so that the compiler knows the unit of the return
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value. e.g.</font></p>
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<blockquote>
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<pre>units::raise<3,1>(m(2)) == m(2)*m(2)*m(2)</pre>
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</blockquote>
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<p><font face="Arial" size="2">There are some trigonometric functions (<i>units::sin</i>,
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<i>units::cos</i> and <i>units::tan</i>) which take an angle. You can
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supply any unit of angle to the function and the function will convert to
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radians. e.g.</font></p>
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<blockquote>
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<pre>units::tan( degree(45) );</pre>
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</blockquote>
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<p><font face="Arial" size="2">There are a number of constants available in
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the <i>units::constants</i> namespace. These are</font></p>
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<ul>
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<li><i><font face="Arial" size="2">k, mu, NA, G0, e0, me, eV, e, F, alpha,
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inv_alpha, u0, phi0, R, G, h, h_bar, mp, Rinf, c, rho, pi, lightyear, g</font></i></li>
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</ul>
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<p><font face="Arial" size="2">Example:</font></p>
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<blockquote>
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<pre>N attractive_force = units::constants::G * kg(1) * kg(2) / m(3) / m(5);</pre>
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</blockquote>
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</blockquote>
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<p><b><font face="Arial">Creating new units</font></b></p>
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<blockquote>
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<pre><font face="sans-serif" size="2">Values with units are provided by the <i>units::value<></i> class template, declared as follows:</font> </pre>
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<blockquote>
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<pre>template<typename Value, typename Unit>
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class value; </pre>
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</blockquote>
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<p><font face="sans-serif" size="2">The predefined units (as used in the
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previous section) are declared in the <i>units::units</i> namespace. So
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you can reuse any of these units but provide a different type, e.g.</font></p>
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<blockquote>
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<pre>units::value<float, units::units::m> length;</pre>
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</blockquote>
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<p><font face="sans-serif" size="2">The unit can be any type, so to create a
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new unit, just create a new type:</font> </p>
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<blockquote>
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<pre>struct apples;
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struct oranges;
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typedef units::value<int, apples> apples_t;
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typedef units::value<int, oranges> oranges_t; </pre>
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</blockquote>
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<pre><font face="sans-serif" size="2">The new value will be protected from interoperating with naked numbers or other types of unit:</font></pre>
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<blockquote>
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<pre>apples_t n(5);
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n = oranges_t(3); // Compile-time error
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n = apples_t(10); // Ok </pre>
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</blockquote>
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</blockquote>
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<p><b><font face="sans-serif">Displaying units</font> </b></p>
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<blockquote>
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<p><font face="sans-serif" size="2">When a value is output (using <i>
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operator<<</i>), it appends the unit to the stream. By default the unit will
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display the text <i>"units"</i>. You can change this by declaring the name of the
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unit with the <i>UNITS_DISPLAY_NAME</i> macro, which takes the unit as its
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first parameter, and its name as its second parameter. e.g.</font> </p>
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<blockquote>
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<pre>UNITS_DISPLAY_NAME( apples, "apples" );
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UNITS_DISPLAY_NAME( oranges, "oranges" ); </pre>
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<pre>std::cout << oranges_t(2); // Output: 2 oranges</pre>
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</blockquote>
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</blockquote>
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<p><b><font face="sans-serif">Converting between units</font> </b></p>
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<blockquote>
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<p><font face="sans-serif" size="2">A unit can be defined in terms of other
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units. The templates <i>units::scale, units::translate, units::pow</i> and <i>
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units::compose</i> provide a means of constructing new units which can be
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converted from and to another unit.</font></p>
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<p><font face="sans-serif" size="2">The <i>units::scale<></i> template
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constructs a unit which is a multiple of another:</font></p>
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<blockquote>
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<pre>struct penny;
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typedef units::scale<penny, 4> farthing; // Multiply penny * 4 to get farthings
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typedef units::scale<penny, 1, 12> shilling; // Multiply penny by 1/12 to get shillings
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typedef units::scale<shilling, 1, 20> pound;
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typedef units::scale<penny, 1, 30> half_crown;
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typedef units::scale<half_crown, 1, 2> crown;</pre>
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<pre>std::cout << "There are " << penny(pound(1)).get() << " old pence in the pound\n";</pre>
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</blockquote>
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<p><font face="Arial" size="2">The <i>units::translate<></i> template
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constructs a unit which is offset from another:</font></p>
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<blockquote>
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<pre>typedef units::translate<units::units::K, -27315, 100> Celcius;
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// Celcius = K - 27315/100</pre>
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</blockquote>
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<p><font face="Arial" size="2">The <i>units::pow<></i> template constructs a unit
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which is a power of another unit:</font></p>
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<blockquote>
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<pre>typedef units::pow<units::units::m, 3> m3; // One cubic meter</pre>
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</blockquote>
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<p><font face="Arial" size="2">Finally the <i>units::compose<></i> template
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creates a unit which multiplies two other units:</font></p>
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<blockquote>
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<pre>typedef units::compose<power, time> energy;
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typedef units::compose< units::units::m, units::pow<units::units::s, -1> > meters_per_second;</pre>
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</blockquote>
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<p><font face="Arial" size="2">The conversion operators are able to analyse
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the type of the unit and generate a conversion function automatically!</font></p>
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</blockquote>
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