[#index]
= Global namespace
:mrdocs:

== Namespaces

[cols="1,4"]
|===
| Name| Description
| xref:mp_units.adoc[`mp_units`] 
| The Measurement Library
|===


== xref:mp_units.adoc[mp_units] namespace

The Measurement Library

=== Namespaces

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/utility.adoc[`utility`] 
| Public authoring vocabulary shared by the library's own customization points and by higher‐level tools.
|===


=== Types

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/absolute_point_origin.adoc[`absolute_point_origin`] 
| A point origin located at the zero point of a quantity specification
| xref:mp_units/base_dimension.adoc[`base_dimension`] 
| A dimension of a base quantity
| xref:mp_units/basic_fixed_string-08.adoc[`basic_fixed_string`] 
| A compile‐time fixed string
| xref:mp_units/check_in_range.adoc[`check_in_range`] 
| Policy that checks the value is within [min, max]and reports violations.
| xref:mp_units/check_non_negative.adoc[`check_non_negative`] 
| Policy that checks the value is ≥ 0 and reports violations.
| xref:mp_units/clamp_non_negative.adoc[`clamp_non_negative`] 
| Policy that clamps the value to [0, ∞).]
| xref:mp_units/clamp_to_range.adoc[`clamp_to_range`] 
| Policy that clamps the value to [min, max].
| xref:mp_units/common_unit.adoc[`common_unit`] 
| Measurement unit for an accumulation of two quantities of different units
| xref:mp_units/constraint_violation_handler.adoc[`constraint_violation_handler`] 
| Customization point for handling domain constraint violations.
| xref:mp_units/derived_dimension.adoc[`derived_dimension`] 
| A dimension of a derived quantity
| xref:mp_units/derived_quantity_spec.adoc[`derived_quantity_spec`] 
| A specification of a derived quantity
| xref:mp_units/derived_unit.adoc[`derived_unit`] 
| Measurement unit for a derived quantity
| xref:mp_units/dimension_one-063.adoc[`dimension_one`] 
| Dimension one
| xref:mp_units/dimension_symbol_formatting.adoc[`dimension_symbol_formatting`] 
| Formatting options for `dimension_symbol` and `dimension_symbol_to`.
| xref:mp_units/dimensionless-0f.adoc[`dimensionless`] 
| Quantity of dimension one
| xref:mp_units/is_kind-06.adoc[`is_kind`] 
| Tag property marking a `quantity_spec` as the start of a new hierarchy tree of a kind
| xref:mp_units/kind_of_-00.adoc[`kind_of_`] 
| The type of a quantity kind for the quantity specification `Q`
| xref:mp_units/mag_constant.adoc[`mag_constant`] 
| A named Magnitude constant identified by its symbol and, where supported, its value
| xref:mp_units/named_constant-03.adoc[`named_constant`] 
| A constant defined in terms of a unit
| xref:mp_units/named_unit-0ec.adoc[`named_unit`] 
| A named unit
| xref:mp_units/natural_point_origin_.adoc[`natural_point_origin_`] 
| Implementation type of `natural_point_origin`
| xref:mp_units/non_negative-05.adoc[`non_negative`] 
| Tag property marking a `quantity_spec` as never holding a negative value
| xref:mp_units/one-0f.adoc[`one`] 
| Unit one
| xref:mp_units/parts_per_million-0f.adoc[`parts_per_million`] 
| The "ppm" (parts per million) unit, equal to 1/1,000,000
| xref:mp_units/per.adoc[`per`] 
| Type list type storing the list of components with negative exponents
| xref:mp_units/per_mille-01.adoc[`per_mille`] 
| The "‰" (per mille) unit, equal to 1/1000
| xref:mp_units/percent-02.adoc[`percent`] 
| The "%" (percent) unit, equal to 1/100
| xref:mp_units/pi-0c.adoc[`pi`] 
| The mathematical constant π, exposed as a dimensionless named constant
| xref:mp_units/pi_c-0b.adoc[`pi_c`] 
| A convenient Magnitude constant for pi, which we can manipulate like a regular number.
| xref:mp_units/possibly_negative-09.adoc[`possibly_negative`] 
| Tag property canceling an inherited `non_negative` for a `quantity_spec`
| xref:mp_units/power.adoc[`power`] 
| Type container for exponents with ratio different than `1`
| xref:mp_units/prefixed_unit.adoc[`prefixed_unit`] 
| A prefixed unit
| xref:mp_units/quantity-01.adoc[`quantity`] 
| A quantity
| xref:mp_units/quantity_character.adoc[`quantity_character`] 
| Quantity character
| xref:mp_units/quantity_like_traits.adoc[`quantity_like_traits`] 
| Provides support for external quantity‐like types
| xref:mp_units/quantity_point-08.adoc[`quantity_point`] 
| A quantity point
| xref:mp_units/quantity_point_like_traits.adoc[`quantity_point_like_traits`] 
| Provides support for external quantity point‐like types
| xref:mp_units/quantity_spec-09.adoc[`quantity_spec`] 
| A specification of a quantity used to define its kind, dimension, and character
| xref:mp_units/reference-0b2.adoc[`reference`] 
| Quantity reference type
| xref:mp_units/reflect_in_range.adoc[`reflect_in_range`] 
| Policy that reflects (folds) the value at both boundaries.
| xref:mp_units/relative_point_origin.adoc[`relative_point_origin`] 
| A point origin defined relative to another quantity point
| xref:mp_units/relative_standard_uncertainty.adoc[`relative_standard_uncertainty`] 
| Relative standard uncertainty of a measured constant
| xref:mp_units/representation_canonical_type-0b.adoc[`representation_canonical_type`] 
| Maps a representation value type to the concrete type a quantity should store.
| xref:mp_units/representation_underlying_type-03a.adoc[`representation_underlying_type`] 
| Describes the underlying arithmetic/element type of a representation type.
| xref:mp_units/representation_values.adoc[`representation_values`] 
| A type trait that defines zero, one, min, and max for a representation type
| xref:mp_units/rounded_down_t.adoc[`rounded_down_t`] 
| Tag type for the `rounded_down` rounding policy
| xref:mp_units/rounded_t.adoc[`rounded_t`] 
| Tag type for the `rounded` rounding policy
| xref:mp_units/rounded_up_t.adoc[`rounded_up_t`] 
| Tag type for the `rounded_up` rounding policy
| xref:mp_units/scaled_unit.adoc[`scaled_unit`] 
| Unit being a scaled version of another unit
| xref:mp_units/standard_uncertainty.adoc[`standard_uncertainty`] 
| Absolute standard uncertainty of a measured constant
| xref:mp_units/symbol_text-032.adoc[`symbol_text`] 
| A symbol text representation
| xref:mp_units/truncated_t.adoc[`truncated_t`] 
| Tag type for the `truncated` rounding policy
| xref:mp_units/unit_symbol_formatting.adoc[`unit_symbol_formatting`] 
| Specifies the options used to format a unit symbol
| xref:mp_units/vector_axes.adoc[`vector_axes`] 
| Ordered list of the 1D‐vector component axes a vector quantity decomposes into
| xref:mp_units/vector_components.adoc[`vector_components`] 
| Opts a vector quantity into decomposition into named 1D‐vector components
| xref:mp_units/wrap_to_range.adoc[`wrap_to_range`] 
| Policy that wraps the value into the half‐open range [min, max).]
|===


=== Type Aliases

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/conditional.adoc[`conditional`] 
| Alias for `T` if `B` is `true`, otherwise `F` (equivalent to `std::conditional_t<B, T, F>`)
| xref:mp_units/expr_type.adoc[`expr_type`] 
| The underlying symbolic expression factor type, unwrapping `power` if present
| xref:mp_units/fixed_string.adoc[`fixed_string`] 
| `basic_fixed_string` specialized for `char`
| xref:mp_units/fixed_u16string.adoc[`fixed_u16string`] 
| `basic_fixed_string` specialized for `char16_t`
| xref:mp_units/fixed_u32string.adoc[`fixed_u32string`] 
| `basic_fixed_string` specialized for `char32_t`
| xref:mp_units/fixed_u8string.adoc[`fixed_u8string`] 
| `basic_fixed_string` specialized for `char8_t`
| xref:mp_units/fixed_wstring.adoc[`fixed_wstring`] 
| `basic_fixed_string` specialized for `wchar_t`
| xref:mp_units/quantity_values.adoc[`quantity_values`]  [.small]#[deprecated]#
| Deprecated alias for `representation_values`.
| xref:mp_units/rep_for.adoc[`rep_for`] 
| Public alias that yields the representation type of a quantity‐like type.
| xref:mp_units/representation_canonical_type_t.adoc[`representation_canonical_type_t`] 
| Convenience alias for `representation_canonical_type<T>::type`.
| xref:mp_units/representation_underlying_type_t.adoc[`representation_underlying_type_t`] 
| Convenience alias for `representation_underlying_type<T>::type`.
| xref:mp_units/text_encoding.adoc[`text_encoding`]  [.small]#[deprecated]#
| Deprecated alias for `character_set`
| xref:mp_units/zeroth_point_origin_.adoc[`zeroth_point_origin_`]  [.small]#[deprecated]#
| Deprecated alias for `natural_point_origin_`
|===


=== Enums

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/character_set.adoc[`character_set`] 
| Character set used to render a `symbol_text`
| xref:mp_units/quantity_character_legacy.adoc[`quantity_character_legacy`]  [.small]#[deprecated]#
| The pre‐2.6.0 flat quantity character enumeration
| xref:mp_units/quantity_field.adoc[`quantity_field`] 
| The numeric field axis of a quantity's character
| xref:mp_units/quantity_tensor_order.adoc[`quantity_tensor_order`] 
| The tensor order axis of a quantity's character
| xref:mp_units/unit_symbol_separator.adoc[`unit_symbol_separator`] 
| Specifies the separator placed between the symbols of a unit symbol's factors
| xref:mp_units/unit_symbol_solidus.adoc[`unit_symbol_solidus`] 
| Specifies how the solidus (`/`) is used when formatting a unit symbol's denominator
|===


=== Functions

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/abs.adoc[`abs`] 
| Computes the absolute value of a quantity
| xref:mp_units/absolute.adoc[`absolute`] 
| Constructs a `quantity_point` of reference `R` from a raw representation value
| xref:mp_units/castable.adoc[`castable`] 
| Checks whether a quantity of quantity spec `From` can be cast to quantity spec `To`
| xref:mp_units/cbrt-07.adoc[`cbrt`] 
| `cbrt` overloads
| xref:mp_units/ceil-09.adoc[`ceil`] 
| `ceil` overloads
| xref:mp_units/contains-01b.adoc[`contains`] 
| `contains` overloads
| xref:mp_units/default_point_origin.adoc[`default_point_origin`] 
| Returns the default point origin for a reference
| xref:mp_units/delta.adoc[`delta`] 
| Constructs a `quantity` of reference `R` from a raw representation value
| xref:mp_units/dimension_symbol.adoc[`dimension_symbol`] 
| Returns the textual symbol of a dimension as a `std::basic_string_view`.
| xref:mp_units/dimension_symbol_to.adoc[`dimension_symbol_to`] 
| Writes the textual symbol of a dimension to an output iterator.
| xref:mp_units/epsilon.adoc[`epsilon`]  [.small]#[deprecated]#
| Returns the epsilon of the quantity
| xref:mp_units/exp.adoc[`exp`] 
| Computes Euler's raised to the given power
| xref:mp_units/explicitly_convertible.adoc[`explicitly_convertible`] 
| Checks whether a quantity of quantity spec `From` can be explicitly converted to quantity spec `To`
| xref:mp_units/floor-04.adoc[`floor`] 
| `floor` overloads
| xref:mp_units/fma-0c.adoc[`fma`] 
| `fma` overloads
| xref:mp_units/fmod.adoc[`fmod`] 
| Computes the floating‐point remainder of the division operation x / y.
| xref:mp_units/get-0a.adoc[`get`] 
| `get` overloads
| xref:mp_units/get_canonical_unit.adoc[`get_canonical_unit`] 
| Computes the canonical form of a unit
| xref:mp_units/get_common_quantity_spec-08.adoc[`get_common_quantity_spec`] 
| `get_common_quantity_spec` overloads
| xref:mp_units/get_common_reference.adoc[`get_common_reference`] 
| Returns the common unit of two or more units usable as a reference
| xref:mp_units/get_common_unit-08f.adoc[`get_common_unit`] 
| `get_common_unit` overloads
| xref:mp_units/get_kind.adoc[`get_kind`] 
| Returns the kind of a quantity specification
| xref:mp_units/get_quantity_spec-03.adoc[`get_quantity_spec`] 
| `get_quantity_spec` overloads
| xref:mp_units/get_relative_standard_uncertainty.adoc[`get_relative_standard_uncertainty`] 
| Returns the relative standard uncertainty of a measured constant
| xref:mp_units/get_standard_uncertainty.adoc[`get_standard_uncertainty`] 
| Returns the standard uncertainty of a measured constant
| xref:mp_units/get_unit.adoc[`get_unit`] 
| Returns the unit of a reference
| xref:mp_units/hypot-00.adoc[`hypot`] 
| `hypot` overloads
| xref:mp_units/implicitly_convertible.adoc[`implicitly_convertible`] 
| Checks whether a quantity of quantity spec `From` can be implicitly converted to quantity spec `To`
| xref:mp_units/interconvertible.adoc[`interconvertible`] 
| Checks whether two quantity specifications are convertible to each other in both directions
| xref:mp_units/inverse-0e.adoc[`inverse`] 
| `inverse` overloads
| xref:mp_units/is_eq_zero.adoc[`is_eq_zero`]  [.small]#[deprecated]#
| Checks whether `v` compares equal to `T::zero()`
| xref:mp_units/is_gt_zero.adoc[`is_gt_zero`]  [.small]#[deprecated]#
| Checks whether `v` compares greater than `T::zero()`
| xref:mp_units/is_gteq_zero.adoc[`is_gteq_zero`]  [.small]#[deprecated]#
| Checks whether `v` compares greater than or equal to `T::zero()`
| xref:mp_units/is_integral_scaling.adoc[`is_integral_scaling`] 
| Returns `true` if the scaling factor from `from` to `to` is an exact positive integer.
| xref:mp_units/is_lt_zero.adoc[`is_lt_zero`]  [.small]#[deprecated]#
| Checks whether `v` compares less than `T::zero()`
| xref:mp_units/is_lteq_zero.adoc[`is_lteq_zero`]  [.small]#[deprecated]#
| Checks whether `v` compares less than or equal to `T::zero()`
| xref:mp_units/is_neq_zero.adoc[`is_neq_zero`]  [.small]#[deprecated]#
| Checks whether `v` compares not equal to `T::zero()`
| xref:mp_units/is_non_negative.adoc[`is_non_negative`] 
| Checks whether a quantity specification is tagged as non‐negative
| xref:mp_units/isfinite-01.adoc[`isfinite`] 
| `isfinite` overloads
| xref:mp_units/isinf-0c.adoc[`isinf`] 
| `isinf` overloads
| xref:mp_units/isnan-08.adoc[`isnan`] 
| `isnan` overloads
| xref:mp_units/lerp.adoc[`lerp`] 
| Linear interpolation or extrapolation
| xref:mp_units/midpoint.adoc[`midpoint`] 
| Computes the midpoint of two points
| xref:mp_units/operator_star-00.adoc[`operator*`] 
| Multiplication operators
| xref:mp_units/operator_slash-0a.adoc[`operator/`] 
| Division operators
| xref:mp_units/point.adoc[`point`] 
| Constructs a `quantity_point` of reference `R` from a raw representation value
| xref:mp_units/pow-00.adoc[`pow`] 
| `pow` overloads
| xref:mp_units/quantity_cast-0f.adoc[`quantity_cast`] 
| `quantity_cast` overloads
| xref:mp_units/remainder.adoc[`remainder`] 
| Computes the IEEE remainder of the floating point division operation x / y.
| xref:mp_units/round-01.adoc[`round`] 
| `round` overloads
| xref:mp_units/scale-05.adoc[`scale`] 
| `scale` overloads
| xref:mp_units/sqrt-0c.adoc[`sqrt`] 
| `sqrt` overloads
| xref:mp_units/unit_symbol.adoc[`unit_symbol`] 
| Returns the textual symbol of a unit
| xref:mp_units/unit_symbol_to.adoc[`unit_symbol_to`] 
| Writes the textual symbol of a unit to an output iterator
| xref:mp_units/value_cast-03d.adoc[`value_cast`] 
| `value_cast` overloads
| xref:mp_units/operator_lshift.adoc[`operator<<`] 
| Streams the textual symbol of a dimension to a `std::basic_ostream`.
| xref:mp_units/operator_eq-0a.adoc[`operator==`] 
| Equality operators
| xref:mp_units/operator_3way.adoc[`operator<=>`] 
| Compares two quantity characters lexicographically on (order, field)
|===


=== Variables

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/dimension_one-060.adoc[`dimension_one`] 
| The unique instance of the dimension one.
| xref:mp_units/dimensionless-03.adoc[`dimensionless`] 
| Quantity of dimension one
| xref:mp_units/disable_representation-091.adoc[`disable_representation`] 
| A specializable opt‐out: when `true`, `T` is not accepted as a quantity representation.
| xref:mp_units/disable_representation-09a.adoc[`disable_representation`] 
| Opts `bool` out of being a valid quantity representation.
| xref:mp_units/disable_representation-05.adoc[`disable_representation`] 
| Opts stateless symbolic‐constant tag types out of being a valid quantity representation.
| xref:mp_units/frame_projection.adoc[`frame_projection`] 
| User‐specializable variable template for runtime coordinate frame transformations.
| xref:mp_units/imag.adoc[`imag`] 
| Customization point object returning the imaginary part of a complex‐like value.
| xref:mp_units/implicitly_scalable.adoc[`implicitly_scalable`] 
| Controls whether conversion from `quantity<FromUnit, FromRep>` to `quantity<ToUnit, ToRep>` is implicit or explicit.
| xref:mp_units/is_complex.adoc[`is_complex`]  [.small]#[deprecated]#
| Deprecated, no longer necessary; kept only for backward compatibility.
| xref:mp_units/is_derived_from_specialization_of.adoc[`is_derived_from_specialization_of`] 
| Whether `T` is derived from some specialization of the class template `Type`, which takes type parameters
| xref:mp_units/is_derived_from_specialization_of_v.adoc[`is_derived_from_specialization_of_v`] 
| Whether `T` is derived from some specialization of the class template `Type`, which takes non‐type (`auto`) parameters
| xref:mp_units/is_kind-0b.adoc[`is_kind`] 
| The unique instance of the `is_kind` tag property.
| xref:mp_units/is_scalar.adoc[`is_scalar`]  [.small]#[deprecated]#
| Deprecated, no longer necessary; kept only for backward compatibility.
| xref:mp_units/is_scoped_enum_v.adoc[`is_scoped_enum_v`] 
| Whether `T` is a scoped enumeration type
| xref:mp_units/is_specialization_of-06.adoc[`is_specialization_of`] 
| Whether `T` is a specialization of the class template `Type`, which takes a pack of type parameters
| xref:mp_units/is_specialization_of-0b.adoc[`is_specialization_of`] 
| Specialization confirming that `Type<Params...>` is a specialization of `Type`
| xref:mp_units/is_specialization_of_v-01.adoc[`is_specialization_of_v`] 
| Whether `T` is a specialization of the class template `Type`, which takes a pack of non‐type (`auto`) parameters
| xref:mp_units/is_specialization_of_v-08.adoc[`is_specialization_of_v`] 
| Specialization confirming that `Type<Params...>` is a specialization of `Type`
| xref:mp_units/is_tensor.adoc[`is_tensor`]  [.small]#[deprecated]#
| Deprecated, no longer necessary; kept only for backward compatibility.
| xref:mp_units/is_value_preserving.adoc[`is_value_preserving`]  [.small]#[deprecated]#
| Specifies if a specific conversion between two types is representable without data loss
| xref:mp_units/is_vector.adoc[`is_vector`]  [.small]#[deprecated]#
| Deprecated, no longer necessary; kept only for backward compatibility.
| xref:mp_units/kind_of.adoc[`kind_of`] 
| The quantity kind of the hierarchy tree rooted at the quantity specification `Q`
| xref:mp_units/known_first_factor.adoc[`known_first_factor`]  [.small]#[deprecated]#
| Deprecated placeholder retained for source compatibility
| xref:mp_units/mag-03.adoc[`mag`] 
| A Magnitude constant equal to the value `V`
| xref:mp_units/mag-08.adoc[`mag`] 
| A Magnitude constant equal to the value `V`
| xref:mp_units/mag_pi.adoc[`mag_pi`]  [.small]#[deprecated]#
| Deprecated alias for the pi Magnitude constant
| xref:mp_units/mag_power.adoc[`mag_power`] 
| Create a Magnitude which is some rational number raised to a rational power.
| xref:mp_units/mag_ratio.adoc[`mag_ratio`] 
| A Magnitude constant equal to the rational number `N` / `D`
| xref:mp_units/magnitude.adoc[`magnitude`] 
| Customization point object computing the magnitude of a representation value
| xref:mp_units/modulus.adoc[`modulus`] 
| Customization point object returning the modulus (absolute value) of a complex‐like value.
| xref:mp_units/natural_point_origin.adoc[`natural_point_origin`] 
| The point origin located at the zero point of a quantity specification
| xref:mp_units/non_negative-0d.adoc[`non_negative`] 
| The unique instance of the `non_negative` tag property.
| xref:mp_units/numeric_field-06.adoc[`numeric_field`] 
| The numeric field of a representation type: real or complex.
| xref:mp_units/numeric_field-08.adoc[`numeric_field`] 
| Detects `numeric_field` for a type whose tensor order is known and whose field is consistent.
| xref:mp_units/one-07.adoc[`one`] 
| The unique instance of the unit one.
| xref:mp_units/parts_per_million-0a.adoc[`parts_per_million`] 
| The unique instance of the parts‐per‐million unit.
| xref:mp_units/per_mille-08.adoc[`per_mille`] 
| The unique instance of the per mille unit.
| xref:mp_units/percent-0a.adoc[`percent`] 
| The unique instance of the percent unit.
| xref:mp_units/pi-0f.adoc[`pi`] 
| The unique instance of the π constant.
| xref:mp_units/pi_c-0e.adoc[`pi_c`] 
| The unique instance of the pi magnitude constant.
| xref:mp_units/possibly_negative-01.adoc[`possibly_negative`] 
| The unique instance of the `possibly_negative` tag property.
| xref:mp_units/ppm.adoc[`ppm`] 
| Alias for `parts_per_million`
| xref:mp_units/real.adoc[`real`] 
| Customization point object returning the real part of a complex‐like value.
| xref:mp_units/reference_for.adoc[`reference_for`] 
| Public helper that yields the reference (unit + quantity spec) associated with a quantity‐like type.
| xref:mp_units/rounded.adoc[`rounded`] 
| Rounding policy that rounds to the nearest representable value, to even in halfway cases
| xref:mp_units/rounded_down.adoc[`rounded_down`] 
| Rounding policy that rounds towards negative infinity
| xref:mp_units/rounded_up.adoc[`rounded_up`] 
| Rounding policy that rounds towards positive infinity
| xref:mp_units/space_before_unit_symbol.adoc[`space_before_unit_symbol`] 
| Puts a space ' ' sign before a unit symbol
| xref:mp_units/tensor_order-04.adoc[`tensor_order`] 
| The intrinsic tensor order of a representation type: 0 for scalar, 1 for vector, 2 for tensor.
| xref:mp_units/tensor_order-0b.adoc[`tensor_order`] 
| Structural detection of `tensor_order` for a type exposing exactly one indexing shape.
| xref:mp_units/treat_as_floating_point.adoc[`treat_as_floating_point`] 
| Specifies if a value of a type should be treated as a floating‐point value
| xref:mp_units/truncated.adoc[`truncated`] 
| Rounding policy that rounds towards zero for an integral destination
| xref:mp_units/unit_for.adoc[`unit_for`] 
| Public helper that yields the unit associated with a quantity‐like type.
| xref:mp_units/zeroth_point_origin.adoc[`zeroth_point_origin`]  [.small]#[deprecated]#
| Deprecated alias for `natural_point_origin`
| xref:mp_units/π.adoc[`π`] 
| Alias for `pi`
|===


=== Concepts

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/Dimension.adoc[`Dimension`] 
| A concept matching all dimensions in the library.
| xref:mp_units/DimensionOf.adoc[`DimensionOf`] 
| A concept checking if the argument is of the same dimension.
| xref:mp_units/MeasuredConstant.adoc[`MeasuredConstant`] 
| A concept matching constants that are measured rather than exact by definition
| xref:mp_units/PointOrigin.adoc[`PointOrigin`] 
| A concept matching all quantity point origins in the library
| xref:mp_units/PointOriginFor.adoc[`PointOriginFor`] 
| A concept matching all quantity point origins for a specified quantity type in the library
| xref:mp_units/PrefixableUnit.adoc[`PrefixableUnit`] 
| A concept to be used to define prefixes for a unit
| xref:mp_units/Quantity-0c.adoc[`Quantity`] 
| A concept matching all quantities in the library
| xref:mp_units/QuantityLike.adoc[`QuantityLike`] 
| A concept matching all external quantities like types
| xref:mp_units/QuantityOf.adoc[`QuantityOf`] 
| A concept matching all quantities of the provided quantity spec
| xref:mp_units/QuantityPoint.adoc[`QuantityPoint`] 
| A concept matching all quantity points in the library
| xref:mp_units/QuantityPointLike.adoc[`QuantityPointLike`] 
| A concept matching all external quantity point like types
| xref:mp_units/QuantityPointOf.adoc[`QuantityPointOf`] 
| A concept matching all quantity points of the provided property
| xref:mp_units/QuantitySpec.adoc[`QuantitySpec`] 
| A concept matching all quantity specifications in the library
| xref:mp_units/QuantitySpecOf.adoc[`QuantitySpecOf`] 
| A concept matching all quantity specifications of a provided quantity spec value
| xref:mp_units/Reference-0ba.adoc[`Reference`] 
| A concept matching all references in the library.
| xref:mp_units/ReferenceOf.adoc[`ReferenceOf`] 
| A concept matching all references of the provided quantity spec
| xref:mp_units/RepresentationOf.adoc[`RepresentationOf`] 
| Concept matching a representation type suitable for a quantity specification or character
| xref:mp_units/RoundingPolicy.adoc[`RoundingPolicy`] 
| A concept matching all rounding policies
| xref:mp_units/Unit.adoc[`Unit`] 
| A concept matching all unit types in the library
| xref:mp_units/UnitMagnitude.adoc[`UnitMagnitude`] 
| Concept to detect whether T is a valid UnitMagnitude.
| xref:mp_units/UnitOf.adoc[`UnitOf`] 
| A concept matching all units associated with the provided quantity spec
|===


== xref:mp_units/utility.adoc[mp_units::utility] namespace

Public authoring vocabulary shared by the library's own customization points and by higher‐level tools.

=== Types

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/utility/constrained.adoc[`constrained`] 
| A transparent wrapper that carries an error policy for domain constraint enforcement.
| xref:mp_units/utility/fill_align_width_format_specs.adoc[`fill_align_width_format_specs`] 
| The fill/align/width part of a `std‐format‐spec`, as parsed by xref:mp_units/utility/parse_fill_align_width.adoc[`parse_fill_align_width`].
| xref:mp_units/utility/fill_t.adoc[`fill_t`] 
| The fill character(s) of a `std‐format‐spec`, storing at most one Unicode code point.
| xref:mp_units/utility/fmt_arg_ref.adoc[`fmt_arg_ref`] 
| A reference to a format argument, by index or (when using fmtlib) by name.
| xref:mp_units/utility/safe_int-07.adoc[`safe_int`] 
| Wraps an integral type with overflow detection.
| xref:mp_units/utility/safe_int_terminate_policy.adoc[`safe_int_terminate_policy`] 
| Error policy that terminates the program on overflow (always available, freestanding‐safe).
| xref:mp_units/utility/safe_int_throw_policy.adoc[`safe_int_throw_policy`] 
| Error policy that throws std::overflow_error on overflow (hosted only).
| xref:mp_units/utility/terminate_policy.adoc[`terminate_policy`] 
| Error policy that terminates the program on constraint violation (freestanding‐safe).
| xref:mp_units/utility/throw_policy.adoc[`throw_policy`] 
| Error policy that throws std::domain_error on constraint violation (hosted only).
| xref:mp_units/utility/unspecified_t.adoc[`unspecified_t`] 
| Sentinel type for a specializable variable‐template customization point with no usable default.
| xref:mp_units/utility/width_checker.adoc[`width_checker`] 
| A `Handler` for xref:mp_units/utility/handle_dynamic_spec.adoc[`handle_dynamic_spec`] that validates and extracts a `width` argument.
|===


=== Type Aliases

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/utility/safe_i16.adoc[`safe_i16`] 
| `safe_int` wrapping `std::int16_t`.
| xref:mp_units/utility/safe_i32.adoc[`safe_i32`] 
| `safe_int` wrapping `std::int32_t`.
| xref:mp_units/utility/safe_i64.adoc[`safe_i64`] 
| `safe_int` wrapping `std::int64_t`.
| xref:mp_units/utility/safe_i8.adoc[`safe_i8`] 
| `safe_int` wrapping `std::int8_t`.
| xref:mp_units/utility/safe_u16.adoc[`safe_u16`] 
| `safe_int` wrapping `std::uint16_t`.
| xref:mp_units/utility/safe_u32.adoc[`safe_u32`] 
| `safe_int` wrapping `std::uint32_t`.
| xref:mp_units/utility/safe_u64.adoc[`safe_u64`] 
| `safe_int` wrapping `std::uint64_t`.
| xref:mp_units/utility/safe_u8.adoc[`safe_u8`] 
| `safe_int` wrapping `std::uint8_t`.
|===


=== Enums

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/utility/fmt_align.adoc[`fmt_align`] 
| The alignment option of a `std‐format‐spec`'s fill/align part.
| xref:mp_units/utility/fmt_arg_id_kind.adoc[`fmt_arg_id_kind`] 
| Which alternative of xref:mp_units/utility/fmt_arg_ref/value.adoc[`fmt_arg_ref::value`] is active.
|===


=== Functions

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/utility/at_most_one_of.adoc[`at_most_one_of`] 
| Finds the single modifier from `modifiers` present in [begin, end).]
| xref:mp_units/utility/handle_dynamic_spec.adoc[`handle_dynamic_spec`] 
| Resolves a dynamic (`{}`‐style) spec against the format arguments.
| xref:mp_units/utility/operator_mod-0f.adoc[`operator%`] 
| Modulus operators
| xref:mp_units/utility/operator_star-04b.adoc[`operator*`] 
| Multiplication operators
| xref:mp_units/utility/operator_plus-07.adoc[`operator+`] 
| Unary plus operators
| xref:mp_units/utility/operator_minus-06.adoc[`operator‐`] 
| Unary minus operators
| xref:mp_units/utility/operator_slash-0a.adoc[`operator/`] 
| Division operators
| xref:mp_units/utility/parse_align.adoc[`parse_align`] 
| Parses the fill and alignment part of a `std‐format‐spec` into `specs.`
| xref:mp_units/utility/parse_dynamic_spec.adoc[`parse_dynamic_spec`] 
| Parses a spec value that may be a literal integer or a `{}`‐style dynamic argument reference.
| xref:mp_units/utility/parse_fill_align_width.adoc[`parse_fill_align_width`] 
| Parses the fill/align/width part of a `std‐format‐spec` into `specs.`
| xref:mp_units/utility/parse_nonnegative_int.adoc[`parse_nonnegative_int`] 
| Parses the range [begin, end) as an unsigned integer.]
| xref:mp_units/utility/write_padded.adoc[`write_padded`] 
| Writes a string to an output iterator with fill/align/width padding.
| xref:mp_units/utility/operator_lshift.adoc[`operator<<`] 
| Streams a safe_int's wrapped value to an output stream
| xref:mp_units/utility/operator_eq-0a.adoc[`operator==`] 
| Equality operators
| xref:mp_units/utility/operator_3way-029.adoc[`operator<=>`] 
| Three‐way comparison operators
|===


=== Variables

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/utility/unspecified.adoc[`unspecified`] 
| The default value of a customization point that has not yet been specialized.
|===


=== Concepts

[cols="1,4"]
|===
| Name| Description
| xref:mp_units/utility/Complex.adoc[`Complex`] 
| A complex‐field representation type.
| xref:mp_units/utility/ComplexScalar.adoc[`ComplexScalar`] 
| A complex scalar: complex field with `real()`/`imag()`/`modulus()`.
| xref:mp_units/utility/ConstraintPolicy.adoc[`ConstraintPolicy`] 
| Concept satisfied by error policy types usable with xref:mp_units/utility/constrained.adoc[`constrained`].
| xref:mp_units/utility/OverflowPolicy.adoc[`OverflowPolicy`] 
| Concept satisfied by overflow error policies usable with `safe_int`.
| xref:mp_units/utility/Real.adoc[`Real`] 
| A real‐field representation type.
| xref:mp_units/utility/RealScalar.adoc[`RealScalar`] 
| A real scalar (tensor order 0): real field, totally ordered, self‐scalable.
| xref:mp_units/utility/Scalar.adoc[`Scalar`] 
| A scalar (real or complex, tensor order 0) ‐ the element type a vector/tensor is built from.
| xref:mp_units/utility/Tensor.adoc[`Tensor`] 
| A second‐order tensor (or a lower‐order type filling its slot).
| xref:mp_units/utility/Vector.adoc[`Vector`] 
| A vector (a scalar, or a magnitude‐bearing tensor‐order‐1 type).
| xref:mp_units/utility/specified.adoc[`specified`] 
| Satisfied when a customization point has been given a value (i.e. is not `unspecified`).
|===



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