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+# Faster than Lightspeed Constants
+
+In most libraries, physical constants are implemented as constant (possibly `constexpr`)
+quantity values. Such an approach has some disadvantages, often resulting in longer
+compilation times and a loss of precision.
+
+
+## Simplifying constants in an equation
+
+When dealing with equations involving physical constants, they often occur more than once
+in an expression. Such a constant may appear both in a numerator and denominator of
+a quantity equation. As we know from fundamental physics, we can simplify such an expression
+by striking a constant out of the equation. Supporting such behavior allows a faster runtime
+performance and often a better precision of the resulting value.
+
+
+## Physical constants as units
+
+The **mp-units** library allows and encourages implementing physical constants as
+regular units. With that, the constant's value is handled at compile-time, and under
+favorable circumstances, it can be simplified in the same way as all other repeated
+units do. If it is not simplified, the value is stored in a type, and the expensive
+multiplication or division operations can be delayed in time until a user selects
+a specific unit to represent/print the data.
+
+Such a feature often also allows using simpler or faster representation types in the equation.
+For example, instead of always having to multiply a small integral value with a big
+floating-point constant number, we can just use the integral type all the way. Only
+in case a constant will not simplify in the equation, and the user will require a specific
+unit, such a multiplication will be lazily invoked, and the representation type will
+need to be expanded to facilitate that. With that, addition, subtractions, multiplications,
+and divisions will always be the fastest - compiled away or done in out-of-order execution.
+
+To benefit from all of the above, in the **mp-units** library, SI defining and other constants
+are implemented as units in the following way:
+
+```cpp
+namespace si {
+
+namespace si2019 {
+
+inline constexpr struct speed_of_light_in_vacuum :
+  named_unit<"c", mag<299'792'458> * metre / second> {} speed_of_light_in_vacuum;
+
+}  // namespace si2019
+
+inline constexpr struct magnetic_constant :
+  named_unit<basic_symbol_text{"μ₀", "u_0"}, mag<4> * mag_pi * mag_power<10, -7> * henry / metre> {} magnetic_constant;
+
+}  // namespace mp_units::si
+```
+
+
+## Usage examples
+
+With the above definitions, we can calculate vacuum permittivity as:
+
+```cpp
+constexpr auto permeability_of_vacuum = 1. * si::magnetic_constant;
+constexpr auto speed_of_light_in_vacuum = 1 * si::si2019::speed_of_light_in_vacuum;
+
+QuantityOf<isq::permittivity_of_vacuum> auto q = 1 / (permeability_of_vacuum * pow<2>(speed_of_light_in_vacuum));
+
+std::cout << "permittivity of vacuum = " << q << " = " << q[F / m] << "\n";
+```
+
+The above first prints the following:
+
+```text
+permittivity of vacuum = 1  μ₀⁻¹ c⁻² = 8.85419e-12 F/m
+```
+
+As we can clearly see, all the calculations above were just about multiplying and dividing
+the number `1` with the rest of the information provided as a compile-time type. Only when
+a user wants a specific SI unit as a result the unit ratios are lazily resolved.
+
+Another similar example can be an equation for total energy:
+
+```cpp
+QuantityOf<isq::mechanical_energy> auto total_energy(QuantityOf<isq::momentum> auto p,
+                                                     QuantityOf<isq::mass> auto m,
+                                                     QuantityOf<isq::speed> auto c)
+{
+  return isq::mechanical_energy(sqrt(pow<2>(p * c) + pow<2>(m * pow<2>(c))));
+}
+```
+
+```cpp
+constexpr auto GeV = si::giga<si::electronvolt>;
+constexpr QuantityOf<isq::speed> auto c = 1. * si::si2019::speed_of_light_in_vacuum;
+constexpr auto c2 = pow<2>(c);
+
+const auto p1 = isq::momentum(4. * GeV / c);
+const QuantityOf<isq::mass> auto m1 = 3. * GeV / c2;
+const auto E = total_energy(p1, m1, c);
+
+std::cout << "in `GeV` and `c`:\n"
+          << "p = " << p1 << "\n"
+          << "m = " << m1 << "\n"
+          << "E = " << E << "\n";
+
+const auto p2 = p1[GeV / (m / s)];
+const auto m2 = m1[GeV / pow<2>(m / s)];
+const auto E2 = total_energy(p2, m2, c)[GeV];
+
+std::cout << "\nin `GeV`:\n"
+          << "p = " << p2 << "\n"
+          << "m = " << m2 << "\n"
+          << "E = " << E2 << "\n";
+
+const auto p3 = p1[kg * m / s];
+const auto m3 = m1[kg];
+const auto E3 = total_energy(p3, m3, c)[J];
+
+std::cout << "\nin SI base units:\n"
+          << "p = " << p3 << "\n"
+          << "m = " << m3 << "\n"
+          << "E = " << E3 << "\n";
+```
+
+The above prints the following:
+
+```text
+in `GeV` and `c`:
+p = 4 GeV/c
+m = 3 GeV/c²
+E = 5 GeV
+
+in `GeV`:
+p = 1.33426e-08 GeV s/m
+m = 3.33795e-17 GeV s²/m²
+E = 5 GeV
+
+in SI base units:
+p = 2.13771e-18 kg m/s
+m = 5.34799e-27 kg
+E = 8.01088e-10 J
+```