[#mp_units-scaling_traits]
= xref:mp_units.adoc[mp_units]::scaling_traits
:relfileprefix: ../
:mrdocs:

A type trait that defines the behavior of scaling a value using a magnitude

== Synopsis

Declared in `<mp‐units/framework/scaling.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<
    typename From,
    typename To>
struct scaling_traits
    : /* implementation-defined */
----

== Description

Whereas C++ numeric types usually represent a (fixed) subset of the real numbers (or another vector‐space over the field of the real numbers), the magnitude concept fundamentally can represent any real number. Thus, in general, the result of a scaling operation is not exactly representable, and some form of approximation may be needed. That approximation is not part of the semantics of a physical quantity, but of its representation in C++. Therefore, the approximation semantics are dictated by the representation type, which can be customised for user‐types through this type‐trait.

In the following, _{V}_ shall denote the vector‐space represented by all representation types involved in the following discussion.

A specialization `scaling_traits<From,` To> shall provide the following member:

* `template <auto M> static constexpr To scale(const From& value)`: Given an element of _{V}_ represented by `value` and a real number represented by `M,` return a value of type `To` representing `M * value`, another element of _{V}_. The scaling factor `M` encodes the represented real value in its type.

== Base Classes

[cols="1,4"]
|===
|Name|Description

| `/* implementation-defined */`
| 
|===

== Template Parameters

[cols="1,4"]
|===
|Name|Description

| *From*
| a representation type whose value is being scaled
| *To*
| a representation type in which the result shall be represented
|===


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