= Reference
:mrdocs:

== Namespaces

[cols=1]
|===
| Name
| link:#mp_units[`mp_units`] 
|===

== link:#mp_units[mp_units] namespace

=== Types

[cols=2]
|===
| Name
| Description
| link:#mp_units-absolute_point_origin[`absolute_point_origin`] 
| 
| link:#mp_units-base_dimension[`base_dimension`] 
| A dimension of a base quantity
| link:#mp_units-basic_fixed_string-08[`basic_fixed_string`] 
| A compile‐time fixed string
| link:#mp_units-binomial_distribution[`binomial_distribution`] 
| 
| link:#mp_units-cartesian_vector-08[`cartesian_vector`] 
| 
| link:#mp_units-cauchy_distribution[`cauchy_distribution`] 
| 
| link:#mp_units-chi_squared_distribution[`chi_squared_distribution`] 
| 
| link:#mp_units-common_unit[`common_unit`] 
| Measurement unit for an accumulation of two quantities of different units
| link:#mp_units-delta_[`delta_`] 
| 
| link:#mp_units-derived_dimension[`derived_dimension`] 
| A dimension of a derived quantity
| link:#mp_units-derived_quantity_spec[`derived_quantity_spec`] 
| A specification of a derived quantity
| link:#mp_units-derived_unit[`derived_unit`] 
| Measurement unit for a derived quantity
| link:#mp_units-dimension_one-063[`dimension_one`] 
| Dimension one
| link:#mp_units-dimension_symbol_formatting[`dimension_symbol_formatting`] 
| 
| link:#mp_units-dimensionless-0f[`dimensionless`] 
| Quantity of dimension one
| link:#mp_units-discrete_distribution[`discrete_distribution`] 
| 
| link:#mp_units-exponential_distribution[`exponential_distribution`] 
| 
| link:#mp_units-extreme_value_distribution[`extreme_value_distribution`] 
| 
| link:#mp_units-fisher_f_distribution[`fisher_f_distribution`] 
| 
| link:#mp_units-gamma_distribution[`gamma_distribution`] 
| 
| link:#mp_units-geometric_distribution[`geometric_distribution`] 
| 
| link:#mp_units-is_kind-06[`is_kind`] 
| 
| link:#mp_units-kind_of_-00[`kind_of_`] 
| 
| link:#mp_units-kind_of_-0d[`kind_of_<Q>`] 
| 
| link:#mp_units-lognormal_distribution[`lognormal_distribution`] 
| 
| link:#mp_units-mag_constant[`mag_constant`] 
| 
| link:#mp_units-named_unit-0ec[`named_unit`] 
| A named unit
| link:#mp_units-named_unit-06[`named_unit<Symbol>`] 
| Specialization for a unit that can be reused by several base quantities
| link:#mp_units-named_unit-07[`named_unit<Symbol, U>`] 
| Specialization for unit of a specified base quantity
| link:#mp_units-named_unit-05[`named_unit<Symbol, U, QS>`] 
| Specialization for a unit with special name valid only for a specific quantity
| link:#mp_units-named_unit-0e4[`named_unit<Symbol, U, QS, PO>`] 
| 
| link:#mp_units-negative_binomial_distribution[`negative_binomial_distribution`] 
| 
| link:#mp_units-normal_distribution[`normal_distribution`] 
| 
| link:#mp_units-one-0f[`one`] 
| Unit one
| link:#mp_units-parts_per_million-0f[`parts_per_million`] 
| 
| link:#mp_units-per[`per`] 
| Type list type storing the list of components with negative exponents
| link:#mp_units-per_mille-01[`per_mille`] 
| 
| link:#mp_units-percent-02[`percent`] 
| 
| link:#mp_units-pi-0c[`pi`] 
| 
| link:#mp_units-piecewise_constant_distribution[`piecewise_constant_distribution`] 
| 
| link:#mp_units-piecewise_linear_distribution[`piecewise_linear_distribution`] 
| 
| link:#mp_units-point_[`point_`] 
| 
| link:#mp_units-poisson_distribution[`poisson_distribution`] 
| 
| link:#mp_units-power[`power`] 
| Type container for exponents with ratio different than `1`
| link:#mp_units-prefixed_unit[`prefixed_unit`] 
| A prefixed unit
| link:#mp_units-quantity-01[`quantity`] 
| A quantity
| link:#mp_units-quantity_like_traits[`quantity_like_traits`] 
| Provides support for external quantity‐like types
| link:#mp_units-quantity_point-08[`quantity_point`] 
| A quantity point
| link:#mp_units-quantity_point_like_traits[`quantity_point_like_traits`] 
| Provides support for external quantity point‐like types
| link:#mp_units-quantity_spec-09[`quantity_spec`] 
| 
| link:#mp_units-quantity_spec-0a6[`quantity_spec<QS, Args...>`] 
| 
| link:#mp_units-quantity_spec-0a0[`quantity_spec<QS, Eq, Args...>`] 
| 
| link:#mp_units-reference[`reference`] 
| Quantity reference type
| link:#mp_units-relative_point_origin[`relative_point_origin`] 
| 
| link:#mp_units-representation_values[`representation_values`] 
| A type trait that defines zero, one, min, and max for a representation type
| link:#mp_units-scaled_unit[`scaled_unit`] 
| Unit being a scaled version of another unit
| link:#mp_units-student_t_distribution[`student_t_distribution`] 
| 
| link:#mp_units-symbol_text-032[`symbol_text`] 
| A symbol text representation
| link:#mp_units-system_reference[`system_reference`] 
| System‐specific reference
| link:#mp_units-uniform_int_distribution[`uniform_int_distribution`] 
| 
| link:#mp_units-uniform_real_distribution[`uniform_real_distribution`] 
| 
| link:#mp_units-unit_symbol_formatting[`unit_symbol_formatting`] 
| 
| link:#mp_units-weibull_distribution[`weibull_distribution`] 
| 
| link:#mp_units-zeroth_point_origin_[`zeroth_point_origin_`] 
| 
| link:#mp_units-conditional[`conditional`] 
| 
| link:#mp_units-expr_type[`expr_type`] 
| 
| link:#mp_units-fixed_string[`fixed_string`] 
| 
| link:#mp_units-fixed_u16string[`fixed_u16string`] 
| 
| link:#mp_units-fixed_u32string[`fixed_u32string`] 
| 
| link:#mp_units-fixed_u8string[`fixed_u8string`] 
| 
| link:#mp_units-fixed_wstring[`fixed_wstring`] 
| 
| link:#mp_units-is_same[`is_same`] 
| 
| link:#mp_units-quantity_values[`quantity_values`] 
| 
| link:#mp_units-text_encoding[`text_encoding`] 
| 
| link:#mp_units-value_type_t[`value_type_t`] 
| 
| link:#mp_units-wrapped_type_t[`wrapped_type_t`] 
| 
|===

=== Enums

[cols=2]
|===
| Name
| Description
| link:#mp_units-character_set[`character_set`] 
| 
| link:#mp_units-quantity_character[`quantity_character`] 
| Quantity character
| link:#mp_units-unit_symbol_separator[`unit_symbol_separator`] 
| 
| link:#mp_units-unit_symbol_solidus[`unit_symbol_solidus`] 
| 
|===

=== Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-abs[`abs`] 
| Computes the absolute value of a quantity
| link:#mp_units-castable[`castable`] 
| 
| link:#mp_units-cbrt-07[`cbrt`] 
| `cbrt` overloads
| link:#mp_units-ceil[`ceil`] 
| Computes the smallest quantity with integer representation and unit type To with its number not less than q
| link:#mp_units-contains-01b[`contains`] 
| 
| link:#mp_units-cubic[`cubic`] 
| Computes the cubic power of a unit
| link:#mp_units-default_point_origin[`default_point_origin`] 
| 
| link:#mp_units-dimension_symbol[`dimension_symbol`] 
| 
| link:#mp_units-dimension_symbol_to[`dimension_symbol_to`] 
| 
| link:#mp_units-epsilon[`epsilon`] 
| Returns the epsilon of the quantity
| link:#mp_units-exp[`exp`] 
| Computes Euler's raised to the given power
| link:#mp_units-explicitly_convertible[`explicitly_convertible`] 
| 
| link:#mp_units-floor[`floor`] 
| Computes the largest quantity with integer representation and unit type To with its number not greater than q
| link:#mp_units-fma-0c[`fma`] 
| `fma` overloads
| link:#mp_units-fmod[`fmod`] 
| Computes the floating‐point remainder of the division operation x / y.
| link:#mp_units-get-0a[`get`] 
| 
| link:#mp_units-get_canonical_unit[`get_canonical_unit`] 
| 
| link:#mp_units-get_common_quantity_spec-08[`get_common_quantity_spec`] 
| 
| link:#mp_units-get_common_reference[`get_common_reference`] 
| 
| link:#mp_units-get_common_unit-08f[`get_common_unit`] 
| 
| link:#mp_units-get_kind[`get_kind`] 
| 
| link:#mp_units-get_quantity_spec-021[`get_quantity_spec`] 
| 
| link:#mp_units-get_unit-02[`get_unit`] 
| 
| link:#mp_units-hypot-00[`hypot`] 
| `hypot` overloads
| link:#mp_units-implicitly_convertible[`implicitly_convertible`] 
| 
| link:#mp_units-interconvertible[`interconvertible`] 
| 
| link:#mp_units-inverse-0e[`inverse`] 
| Computes the inverse of a quantity in a provided unit
| link:#mp_units-is_eq_zero[`is_eq_zero`] 
| 
| link:#mp_units-is_gt_zero[`is_gt_zero`] 
| 
| link:#mp_units-is_gteq_zero[`is_gteq_zero`] 
| 
| link:#mp_units-is_lt_zero[`is_lt_zero`] 
| 
| link:#mp_units-is_lteq_zero[`is_lteq_zero`] 
| 
| link:#mp_units-is_neq_zero[`is_neq_zero`] 
| 
| link:#mp_units-isfinite-01[`isfinite`] 
| `isfinite` overloads
| link:#mp_units-isinf-0c[`isinf`] 
| `isinf` overloads
| link:#mp_units-isnan-08c[`isnan`] 
| `isnan` overloads
| link:#mp_units-lerp[`lerp`] 
| Linear interpolation or extrapolation
| link:#mp_units-magnitude-0c[`magnitude`] 
| 
| link:#mp_units-midpoint[`midpoint`] 
| Computes the midpoint of two points
| link:#mp_units-operator_mod-01[`operator%`] 
| Modulus operators
| link:#mp_units-operator_star-000[`operator*`] 
| Multiplication operators
| link:#mp_units-operator_plus-0ad[`operator+`] 
| Addition operators
| link:#mp_units-operator_minus-0c[`operator‐`] 
| Subtraction operators
| link:#mp_units-operator_slash-0a[`operator/`] 
| Division operators
| link:#mp_units-pow-00[`pow`] 
| `pow` overloads
| link:#mp_units-quantity_cast-0f[`quantity_cast`] 
| `quantity_cast` overloads
| link:#mp_units-remainder[`remainder`] 
| Computes the IEEE remainder of the floating point division operation x / y.
| link:#mp_units-round[`round`] 
| Computes the nearest quantity with integer representation and unit type `To` to `q`
| link:#mp_units-sqrt-0c[`sqrt`] 
| `sqrt` overloads
| link:#mp_units-square[`square`] 
| Computes the square power of a unit
| link:#mp_units-swap[`swap`] 
| 
| link:#mp_units-unit_symbol[`unit_symbol`] 
| 
| link:#mp_units-unit_symbol_to[`unit_symbol_to`] 
| 
| link:#mp_units-unit_vector[`unit_vector`] 
| 
| link:#mp_units-value_cast-03d[`value_cast`] 
| `value_cast` overloads
| link:#mp_units-operator_lshift-0e9[`operator<<`] 
| Stream insertion operators
| link:#mp_units-operator_eq-0cb[`operator==`] 
| Equality operators
| link:#mp_units-operator_3way-06[`operator<=>`] 
| Three‐way comparison operators
|===

=== Variables

[cols=2]
|===
| Name
| Description
| link:#mp_units-absolute[`absolute`] 
| 
| link:#mp_units-delta[`delta`] 
| 
| link:#mp_units-dimension_one-060[`dimension_one`] 
| 
| link:#mp_units-dimensionless-03[`dimensionless`] 
| Quantity of dimension one
| link:#mp_units-disable_real-00[`disable_real`] 
| //////////// REAL SCALAR ///////////////
| link:#mp_units-disable_real-0b[`disable_real<bool>`] 
| 
| link:#mp_units-imag[`imag`] 
| 
| link:#mp_units-is_complex[`is_complex`] 
| 
| link:#mp_units-is_derived_from_specialization_of[`is_derived_from_specialization_of`] 
| 
| link:#mp_units-is_derived_from_specialization_of_v[`is_derived_from_specialization_of_v`] 
| 
| link:#mp_units-is_kind-0b[`is_kind`] 
| 
| link:#mp_units-is_same_v-0d[`is_same_v`] 
| 
| link:#mp_units-is_same_v-0e[`is_same_v<T, T>`] 
| 
| link:#mp_units-is_scalar[`is_scalar`] 
| 
| link:#mp_units-is_specialization_of-06[`is_specialization_of`] 
| 
| link:#mp_units-is_specialization_of-0b[`is_specialization_of<Type<Params...>, Type>`] 
| 
| link:#mp_units-is_specialization_of_v-01[`is_specialization_of_v`] 
| 
| link:#mp_units-is_specialization_of_v-08[`is_specialization_of_v<Type<Params...>, Type>`] 
| 
| link:#mp_units-is_tensor[`is_tensor`] 
| 
| link:#mp_units-is_value_preserving[`is_value_preserving`] 
| Specifies if a specific conversion between two types preserves the value
| link:#mp_units-is_vector[`is_vector`] 
| 
| link:#mp_units-kind_of[`kind_of`] 
| 
| link:#mp_units-known_first_factor[`known_first_factor`] 
| /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
| link:#mp_units-mag[`mag`] 
| 
| link:#mp_units-mag_pi[`mag_pi`] 
| 
| link:#mp_units-mag_power[`mag_power`] 
| Create a Magnitude which is some rational number raised to a rational power.
| link:#mp_units-mag_ratio[`mag_ratio`] 
| 
| link:#mp_units-magnitude-04[`magnitude`] 
| 
| link:#mp_units-modulus[`modulus`] 
| 
| link:#mp_units-one-07[`one`] 
| 
| link:#mp_units-parts_per_million-0a[`parts_per_million`] 
| 
| link:#mp_units-per_mille-08[`per_mille`] 
| 
| link:#mp_units-percent-0a[`percent`] 
| 
| link:#mp_units-pi-0f[`pi`] 
| 
| link:#mp_units-point[`point`] 
| 
| link:#mp_units-ppm[`ppm`] 
| 
| link:#mp_units-real[`real`] 
| 
| link:#mp_units-space_before_unit_symbol[`space_before_unit_symbol`] 
| Puts a space ' ' sign before a unit symbol
| link:#mp_units-treat_as_floating_point[`treat_as_floating_point`] 
| Specifies if a value of a type should be treated as a floating‐point value
| link:#mp_units-zeroth_point_origin[`zeroth_point_origin`] 
| 
| link:#mp_units-π[`π`] 
| 
|===

=== Concepts

[cols=2]
|===
| Name
| Description
| link:#mp_units-AssociatedUnit[`AssociatedUnit`] 
| A concept matching all units that can be used as quantity references
| link:#mp_units-Dimension[`Dimension`] 
| A concept matching all dimensions in the library.
| link:#mp_units-DimensionOf[`DimensionOf`] 
| A concept checking if the argument is of the same dimension.
| link:#mp_units-PointOrigin[`PointOrigin`] 
| A concept matching all quantity point origins in the library
| link:#mp_units-PointOriginFor[`PointOriginFor`] 
| A concept matching all quantity point origins for a specified quantity type in the library
| link:#mp_units-PrefixableUnit[`PrefixableUnit`] 
| A concept to be used to define prefixes for a unit
| link:#mp_units-Quantity[`Quantity`] 
| A concept matching all quantities in the library
| link:#mp_units-QuantityLike[`QuantityLike`] 
| A concept matching all external quantities like types
| link:#mp_units-QuantityOf[`QuantityOf`] 
| A concept matching all quantities of the provided quantity spec
| link:#mp_units-QuantityPoint[`QuantityPoint`] 
| A concept matching all quantity points in the library
| link:#mp_units-QuantityPointLike[`QuantityPointLike`] 
| A concept matching all external quantity point like types
| link:#mp_units-QuantityPointOf[`QuantityPointOf`] 
| A concept matching all quantity points of the provided property
| link:#mp_units-QuantitySpec[`QuantitySpec`] 
| 
| link:#mp_units-QuantitySpecOf[`QuantitySpecOf`] 
| A concept matching all quantity specifications of a provided quantity spec value
| link:#mp_units-Reference[`Reference`] 
| A concept matching all references in the library.
| link:#mp_units-ReferenceOf[`ReferenceOf`] 
| A concept matching all references of the provided quantity spec
| link:#mp_units-RepresentationOf[`RepresentationOf`] 
| 
| link:#mp_units-Unit[`Unit`] 
| A concept matching all unit types in the library
| link:#mp_units-UnitMagnitude[`UnitMagnitude`] 
| Concept to detect whether T is a valid UnitMagnitude.
| link:#mp_units-UnitOf[`UnitOf`] 
| A concept matching all units associated with the provided quantity spec
|===

=== Deduction Guides

[cols=1]
|===
| Name
| link:#mp_units-basic_fixed_string-0d[`basic_fixed_string<CharT, N ‐ 1>`] 
| link:#mp_units-basic_fixed_string-0f[`basic_fixed_string<CharT, 1 + sizeof...(Rest)>`] 
| link:#mp_units-basic_fixed_string-0a[`basic_fixed_string<CharT, N>`] 
| link:#mp_units-cartesian_vector-06[`cartesian_vector<std::common_type_t<Arg, Args...>>`] 
| link:#mp_units-quantity-05[`quantity<quantity_like_traits<Q>::reference, quantity_like_traits<Q>::rep>`] 
| link:#mp_units-quantity-02[`quantity<R{}, Value>`] 
| link:#mp_units-quantity_point-04[`quantity_point<Q::reference, default_point_origin(Q::reference), Q::rep>`] 
| link:#mp_units-quantity_point-0cb[`quantity_point<quantity_point_like_traits<QP>::reference, quantity_point_like_traits<QP>::point_origin, quantity_point_like_traits<QP>::rep>`] 
| link:#mp_units-quantity_point-0c5[`quantity_point<Q::reference, PO{}, Q::rep>`] 
| link:#mp_units-symbol_text-06[`symbol_text<1, 1>`] 
| link:#mp_units-symbol_text-07[`symbol_text<N, N>`] 
| link:#mp_units-symbol_text-03f[`symbol_text<N ‐ 1, N ‐ 1>`] 
| link:#mp_units-symbol_text-0f[`symbol_text<N, M>`] 
| link:#mp_units-symbol_text-01[`symbol_text<N ‐ 1, M ‐ 1>`] 
|===

== Types

[cols=2]
|===
| Name
| Description
| link:#mp_units-absolute_point_origin[`absolute_point_origin`] 
| 
| link:#mp_units-base_dimension[`base_dimension`] 
| A dimension of a base quantity
| link:#mp_units-basic_fixed_string-08[`basic_fixed_string`] 
| A compile‐time fixed string
| link:#mp_units-binomial_distribution[`binomial_distribution`] 
| 
| link:#mp_units-cartesian_vector-08[`cartesian_vector`] 
| 
| link:#mp_units-cauchy_distribution[`cauchy_distribution`] 
| 
| link:#mp_units-chi_squared_distribution[`chi_squared_distribution`] 
| 
| link:#mp_units-common_unit[`common_unit`] 
| Measurement unit for an accumulation of two quantities of different units
| link:#mp_units-delta_[`delta_`] 
| 
| link:#mp_units-derived_dimension[`derived_dimension`] 
| A dimension of a derived quantity
| link:#mp_units-derived_quantity_spec[`derived_quantity_spec`] 
| A specification of a derived quantity
| link:#mp_units-derived_unit[`derived_unit`] 
| Measurement unit for a derived quantity
| link:#mp_units-dimension_one-063[`dimension_one`] 
| Dimension one
| link:#mp_units-dimension_symbol_formatting[`dimension_symbol_formatting`] 
| 
| link:#mp_units-dimensionless-0f[`dimensionless`] 
| Quantity of dimension one
| link:#mp_units-discrete_distribution[`discrete_distribution`] 
| 
| link:#mp_units-exponential_distribution[`exponential_distribution`] 
| 
| link:#mp_units-extreme_value_distribution[`extreme_value_distribution`] 
| 
| link:#mp_units-fisher_f_distribution[`fisher_f_distribution`] 
| 
| link:#mp_units-gamma_distribution[`gamma_distribution`] 
| 
| link:#mp_units-geometric_distribution[`geometric_distribution`] 
| 
| link:#mp_units-is_kind-06[`is_kind`] 
| 
| link:#mp_units-kind_of_-00[`kind_of_`] 
| 
| link:#mp_units-kind_of_-0d[`kind_of_<Q>`] 
| 
| link:#mp_units-lognormal_distribution[`lognormal_distribution`] 
| 
| link:#mp_units-mag_constant[`mag_constant`] 
| 
| link:#mp_units-named_unit-0ec[`named_unit`] 
| A named unit
| link:#mp_units-named_unit-06[`named_unit<Symbol>`] 
| Specialization for a unit that can be reused by several base quantities
| link:#mp_units-named_unit-07[`named_unit<Symbol, U>`] 
| Specialization for unit of a specified base quantity
| link:#mp_units-named_unit-05[`named_unit<Symbol, U, QS>`] 
| Specialization for a unit with special name valid only for a specific quantity
| link:#mp_units-named_unit-0e4[`named_unit<Symbol, U, QS, PO>`] 
| 
| link:#mp_units-negative_binomial_distribution[`negative_binomial_distribution`] 
| 
| link:#mp_units-normal_distribution[`normal_distribution`] 
| 
| link:#mp_units-one-0f[`one`] 
| Unit one
| link:#mp_units-parts_per_million-0f[`parts_per_million`] 
| 
| link:#mp_units-per[`per`] 
| Type list type storing the list of components with negative exponents
| link:#mp_units-per_mille-01[`per_mille`] 
| 
| link:#mp_units-percent-02[`percent`] 
| 
| link:#mp_units-pi-0c[`pi`] 
| 
| link:#mp_units-piecewise_constant_distribution[`piecewise_constant_distribution`] 
| 
| link:#mp_units-piecewise_linear_distribution[`piecewise_linear_distribution`] 
| 
| link:#mp_units-point_[`point_`] 
| 
| link:#mp_units-poisson_distribution[`poisson_distribution`] 
| 
| link:#mp_units-power[`power`] 
| Type container for exponents with ratio different than `1`
| link:#mp_units-prefixed_unit[`prefixed_unit`] 
| A prefixed unit
| link:#mp_units-quantity-01[`quantity`] 
| A quantity
| link:#mp_units-quantity_like_traits[`quantity_like_traits`] 
| Provides support for external quantity‐like types
| link:#mp_units-quantity_point-08[`quantity_point`] 
| A quantity point
| link:#mp_units-quantity_point_like_traits[`quantity_point_like_traits`] 
| Provides support for external quantity point‐like types
| link:#mp_units-quantity_spec-09[`quantity_spec`] 
| 
| link:#mp_units-quantity_spec-0a6[`quantity_spec<QS, Args...>`] 
| 
| link:#mp_units-quantity_spec-0a0[`quantity_spec<QS, Eq, Args...>`] 
| 
| link:#mp_units-reference[`reference`] 
| Quantity reference type
| link:#mp_units-relative_point_origin[`relative_point_origin`] 
| 
| link:#mp_units-representation_values[`representation_values`] 
| A type trait that defines zero, one, min, and max for a representation type
| link:#mp_units-scaled_unit[`scaled_unit`] 
| Unit being a scaled version of another unit
| link:#mp_units-student_t_distribution[`student_t_distribution`] 
| 
| link:#mp_units-symbol_text-032[`symbol_text`] 
| A symbol text representation
| link:#mp_units-system_reference[`system_reference`] 
| System‐specific reference
| link:#mp_units-uniform_int_distribution[`uniform_int_distribution`] 
| 
| link:#mp_units-uniform_real_distribution[`uniform_real_distribution`] 
| 
| link:#mp_units-unit_symbol_formatting[`unit_symbol_formatting`] 
| 
| link:#mp_units-weibull_distribution[`weibull_distribution`] 
| 
| link:#mp_units-zeroth_point_origin_[`zeroth_point_origin_`] 
| 
| link:#mp_units-conditional[`conditional`] 
| 
| link:#mp_units-expr_type[`expr_type`] 
| 
| link:#mp_units-fixed_string[`fixed_string`] 
| 
| link:#mp_units-fixed_u16string[`fixed_u16string`] 
| 
| link:#mp_units-fixed_u32string[`fixed_u32string`] 
| 
| link:#mp_units-fixed_u8string[`fixed_u8string`] 
| 
| link:#mp_units-fixed_wstring[`fixed_wstring`] 
| 
| link:#mp_units-is_same[`is_same`] 
| 
| link:#mp_units-quantity_values[`quantity_values`] 
| 
| link:#mp_units-text_encoding[`text_encoding`] 
| 
| link:#mp_units-value_type_t[`value_type_t`] 
| 
| link:#mp_units-wrapped_type_t[`wrapped_type_t`] 
| 
|===

== Enums

[cols=2]
|===
| Name
| Description
| link:#mp_units-character_set[`character_set`] 
| 
| link:#mp_units-quantity_character[`quantity_character`] 
| Quantity character
| link:#mp_units-unit_symbol_separator[`unit_symbol_separator`] 
| 
| link:#mp_units-unit_symbol_solidus[`unit_symbol_solidus`] 
| 
|===

== Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-abs[`abs`] 
| Computes the absolute value of a quantity
| link:#mp_units-castable[`castable`] 
| 
| link:#mp_units-cbrt-07[`cbrt`] 
| `cbrt` overloads
| link:#mp_units-ceil[`ceil`] 
| Computes the smallest quantity with integer representation and unit type To with its number not less than q
| link:#mp_units-contains-01b[`contains`] 
| 
| link:#mp_units-cubic[`cubic`] 
| Computes the cubic power of a unit
| link:#mp_units-default_point_origin[`default_point_origin`] 
| 
| link:#mp_units-dimension_symbol[`dimension_symbol`] 
| 
| link:#mp_units-dimension_symbol_to[`dimension_symbol_to`] 
| 
| link:#mp_units-epsilon[`epsilon`] 
| Returns the epsilon of the quantity
| link:#mp_units-exp[`exp`] 
| Computes Euler's raised to the given power
| link:#mp_units-explicitly_convertible[`explicitly_convertible`] 
| 
| link:#mp_units-floor[`floor`] 
| Computes the largest quantity with integer representation and unit type To with its number not greater than q
| link:#mp_units-fma-0c[`fma`] 
| `fma` overloads
| link:#mp_units-fmod[`fmod`] 
| Computes the floating‐point remainder of the division operation x / y.
| link:#mp_units-get-0a[`get`] 
| 
| link:#mp_units-get_canonical_unit[`get_canonical_unit`] 
| 
| link:#mp_units-get_common_quantity_spec-08[`get_common_quantity_spec`] 
| 
| link:#mp_units-get_common_reference[`get_common_reference`] 
| 
| link:#mp_units-get_common_unit-08f[`get_common_unit`] 
| 
| link:#mp_units-get_kind[`get_kind`] 
| 
| link:#mp_units-get_quantity_spec-021[`get_quantity_spec`] 
| 
| link:#mp_units-get_unit-02[`get_unit`] 
| 
| link:#mp_units-hypot-00[`hypot`] 
| `hypot` overloads
| link:#mp_units-implicitly_convertible[`implicitly_convertible`] 
| 
| link:#mp_units-interconvertible[`interconvertible`] 
| 
| link:#mp_units-inverse-0e[`inverse`] 
| Computes the inverse of a quantity in a provided unit
| link:#mp_units-is_eq_zero[`is_eq_zero`] 
| 
| link:#mp_units-is_gt_zero[`is_gt_zero`] 
| 
| link:#mp_units-is_gteq_zero[`is_gteq_zero`] 
| 
| link:#mp_units-is_lt_zero[`is_lt_zero`] 
| 
| link:#mp_units-is_lteq_zero[`is_lteq_zero`] 
| 
| link:#mp_units-is_neq_zero[`is_neq_zero`] 
| 
| link:#mp_units-isfinite-01[`isfinite`] 
| `isfinite` overloads
| link:#mp_units-isinf-0c[`isinf`] 
| `isinf` overloads
| link:#mp_units-isnan-08c[`isnan`] 
| `isnan` overloads
| link:#mp_units-lerp[`lerp`] 
| Linear interpolation or extrapolation
| link:#mp_units-magnitude-0c[`magnitude`] 
| 
| link:#mp_units-midpoint[`midpoint`] 
| Computes the midpoint of two points
| link:#mp_units-operator_mod-01[`operator%`] 
| Modulus operators
| link:#mp_units-operator_star-000[`operator*`] 
| Multiplication operators
| link:#mp_units-operator_plus-0ad[`operator+`] 
| Addition operators
| link:#mp_units-operator_minus-0c[`operator‐`] 
| Subtraction operators
| link:#mp_units-operator_slash-0a[`operator/`] 
| Division operators
| link:#mp_units-pow-00[`pow`] 
| `pow` overloads
| link:#mp_units-quantity_cast-0f[`quantity_cast`] 
| `quantity_cast` overloads
| link:#mp_units-remainder[`remainder`] 
| Computes the IEEE remainder of the floating point division operation x / y.
| link:#mp_units-round[`round`] 
| Computes the nearest quantity with integer representation and unit type `To` to `q`
| link:#mp_units-sqrt-0c[`sqrt`] 
| `sqrt` overloads
| link:#mp_units-square[`square`] 
| Computes the square power of a unit
| link:#mp_units-swap[`swap`] 
| 
| link:#mp_units-unit_symbol[`unit_symbol`] 
| 
| link:#mp_units-unit_symbol_to[`unit_symbol_to`] 
| 
| link:#mp_units-unit_vector[`unit_vector`] 
| 
| link:#mp_units-value_cast-03d[`value_cast`] 
| `value_cast` overloads
| link:#mp_units-operator_lshift-0e9[`operator<<`] 
| Stream insertion operators
| link:#mp_units-operator_eq-0cb[`operator==`] 
| Equality operators
| link:#mp_units-operator_3way-06[`operator<=>`] 
| Three‐way comparison operators
|===

== Variables

[cols=2]
|===
| Name
| Description
| link:#mp_units-absolute[`absolute`] 
| 
| link:#mp_units-delta[`delta`] 
| 
| link:#mp_units-dimension_one-060[`dimension_one`] 
| 
| link:#mp_units-dimensionless-03[`dimensionless`] 
| Quantity of dimension one
| link:#mp_units-disable_real-00[`disable_real`] 
| //////////// REAL SCALAR ///////////////
| link:#mp_units-disable_real-0b[`disable_real<bool>`] 
| 
| link:#mp_units-imag[`imag`] 
| 
| link:#mp_units-is_complex[`is_complex`] 
| 
| link:#mp_units-is_derived_from_specialization_of[`is_derived_from_specialization_of`] 
| 
| link:#mp_units-is_derived_from_specialization_of_v[`is_derived_from_specialization_of_v`] 
| 
| link:#mp_units-is_kind-0b[`is_kind`] 
| 
| link:#mp_units-is_same_v-0d[`is_same_v`] 
| 
| link:#mp_units-is_same_v-0e[`is_same_v<T, T>`] 
| 
| link:#mp_units-is_scalar[`is_scalar`] 
| 
| link:#mp_units-is_specialization_of-06[`is_specialization_of`] 
| 
| link:#mp_units-is_specialization_of-0b[`is_specialization_of<Type<Params...>, Type>`] 
| 
| link:#mp_units-is_specialization_of_v-01[`is_specialization_of_v`] 
| 
| link:#mp_units-is_specialization_of_v-08[`is_specialization_of_v<Type<Params...>, Type>`] 
| 
| link:#mp_units-is_tensor[`is_tensor`] 
| 
| link:#mp_units-is_value_preserving[`is_value_preserving`] 
| Specifies if a specific conversion between two types preserves the value
| link:#mp_units-is_vector[`is_vector`] 
| 
| link:#mp_units-kind_of[`kind_of`] 
| 
| link:#mp_units-known_first_factor[`known_first_factor`] 
| /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
| link:#mp_units-mag[`mag`] 
| 
| link:#mp_units-mag_pi[`mag_pi`] 
| 
| link:#mp_units-mag_power[`mag_power`] 
| Create a Magnitude which is some rational number raised to a rational power.
| link:#mp_units-mag_ratio[`mag_ratio`] 
| 
| link:#mp_units-magnitude-04[`magnitude`] 
| 
| link:#mp_units-modulus[`modulus`] 
| 
| link:#mp_units-one-07[`one`] 
| 
| link:#mp_units-parts_per_million-0a[`parts_per_million`] 
| 
| link:#mp_units-per_mille-08[`per_mille`] 
| 
| link:#mp_units-percent-0a[`percent`] 
| 
| link:#mp_units-pi-0f[`pi`] 
| 
| link:#mp_units-point[`point`] 
| 
| link:#mp_units-ppm[`ppm`] 
| 
| link:#mp_units-real[`real`] 
| 
| link:#mp_units-space_before_unit_symbol[`space_before_unit_symbol`] 
| Puts a space ' ' sign before a unit symbol
| link:#mp_units-treat_as_floating_point[`treat_as_floating_point`] 
| Specifies if a value of a type should be treated as a floating‐point value
| link:#mp_units-zeroth_point_origin[`zeroth_point_origin`] 
| 
| link:#mp_units-π[`π`] 
| 
|===

== Concepts

[cols=2]
|===
| Name
| Description
| link:#mp_units-AssociatedUnit[`AssociatedUnit`] 
| A concept matching all units that can be used as quantity references
| link:#mp_units-Dimension[`Dimension`] 
| A concept matching all dimensions in the library.
| link:#mp_units-DimensionOf[`DimensionOf`] 
| A concept checking if the argument is of the same dimension.
| link:#mp_units-PointOrigin[`PointOrigin`] 
| A concept matching all quantity point origins in the library
| link:#mp_units-PointOriginFor[`PointOriginFor`] 
| A concept matching all quantity point origins for a specified quantity type in the library
| link:#mp_units-PrefixableUnit[`PrefixableUnit`] 
| A concept to be used to define prefixes for a unit
| link:#mp_units-Quantity[`Quantity`] 
| A concept matching all quantities in the library
| link:#mp_units-QuantityLike[`QuantityLike`] 
| A concept matching all external quantities like types
| link:#mp_units-QuantityOf[`QuantityOf`] 
| A concept matching all quantities of the provided quantity spec
| link:#mp_units-QuantityPoint[`QuantityPoint`] 
| A concept matching all quantity points in the library
| link:#mp_units-QuantityPointLike[`QuantityPointLike`] 
| A concept matching all external quantity point like types
| link:#mp_units-QuantityPointOf[`QuantityPointOf`] 
| A concept matching all quantity points of the provided property
| link:#mp_units-QuantitySpec[`QuantitySpec`] 
| 
| link:#mp_units-QuantitySpecOf[`QuantitySpecOf`] 
| A concept matching all quantity specifications of a provided quantity spec value
| link:#mp_units-Reference[`Reference`] 
| A concept matching all references in the library.
| link:#mp_units-ReferenceOf[`ReferenceOf`] 
| A concept matching all references of the provided quantity spec
| link:#mp_units-RepresentationOf[`RepresentationOf`] 
| 
| link:#mp_units-Unit[`Unit`] 
| A concept matching all unit types in the library
| link:#mp_units-UnitMagnitude[`UnitMagnitude`] 
| Concept to detect whether T is a valid UnitMagnitude.
| link:#mp_units-UnitOf[`UnitOf`] 
| A concept matching all units associated with the provided quantity spec
|===

== Deduction Guides

[cols=1]
|===
| Name
| link:#mp_units-basic_fixed_string-0d[`basic_fixed_string<CharT, N ‐ 1>`] 
| link:#mp_units-basic_fixed_string-0f[`basic_fixed_string<CharT, 1 + sizeof...(Rest)>`] 
| link:#mp_units-basic_fixed_string-0a[`basic_fixed_string<CharT, N>`] 
| link:#mp_units-cartesian_vector-06[`cartesian_vector<std::common_type_t<Arg, Args...>>`] 
| link:#mp_units-quantity-05[`quantity<quantity_like_traits<Q>::reference, quantity_like_traits<Q>::rep>`] 
| link:#mp_units-quantity-02[`quantity<R{}, Value>`] 
| link:#mp_units-quantity_point-04[`quantity_point<Q::reference, default_point_origin(Q::reference), Q::rep>`] 
| link:#mp_units-quantity_point-0cb[`quantity_point<quantity_point_like_traits<QP>::reference, quantity_point_like_traits<QP>::point_origin, quantity_point_like_traits<QP>::rep>`] 
| link:#mp_units-quantity_point-0c5[`quantity_point<Q::reference, PO{}, Q::rep>`] 
| link:#mp_units-symbol_text-06[`symbol_text<1, 1>`] 
| link:#mp_units-symbol_text-07[`symbol_text<N, N>`] 
| link:#mp_units-symbol_text-03f[`symbol_text<N ‐ 1, N ‐ 1>`] 
| link:#mp_units-symbol_text-0f[`symbol_text<N, M>`] 
| link:#mp_units-symbol_text-01[`symbol_text<N ‐ 1, M ‐ 1>`] 
|===

== Synopsis

Declared in `<mp‐units/ext/type_traits.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<
    bool B,
    typename T,
    typename F>
using conditional = /* implementation-defined */::type<T, F>;
----

== Synopsis

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

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<typename T>
using expr_type = /* implementation-defined */::type;
----

== Synopsis

Declared in `<mp‐units/ext/fixed_string.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<std::size_t N>
using fixed_string = link:#mp_units-basic_fixed_string-08[basic_fixed_string<char, N>];
----

== Synopsis

Declared in `<mp‐units/ext/fixed_string.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<std::size_t N>
using fixed_u16string = link:#mp_units-basic_fixed_string-08[basic_fixed_string<char16_t, N>];
----

== Synopsis

Declared in `<mp‐units/ext/fixed_string.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<std::size_t N>
using fixed_u32string = link:#mp_units-basic_fixed_string-08[basic_fixed_string<char32_t, N>];
----

== Synopsis

Declared in `<mp‐units/ext/fixed_string.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<std::size_t N>
using fixed_u8string = link:#mp_units-basic_fixed_string-08[basic_fixed_string<char8_t, N>];
----

== Synopsis

Declared in `<mp‐units/ext/fixed_string.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<std::size_t N>
using fixed_wstring = link:#mp_units-basic_fixed_string-08[basic_fixed_string<wchar_t, N>];
----

== Synopsis

Declared in `<mp‐units/ext/type_traits.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<
    class T,
    class U>
using is_same = std::bool_constant<is_same_v<T, U>>;
----

== Synopsis

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

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<typename Rep>
using quantity_values = link:#mp_units-representation_values[representation_values<Rep>];
----

== Synopsis

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

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using text_encoding = link:#mp_units-character_set[character_set];
----

== Synopsis

Declared in `<mp‐units/ext/type_traits.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<typename T>
requires std::is_object_v<T>
using value_type_t = /* implementation-defined */::type;
----

== Synopsis

Declared in `<mp‐units/ext/type_traits.h>`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<typename T>
requires (!std::is_pointer_v<T> && !std::is_array_v<T>) &&
            requires { typename std::indirectly_readable_traits<T>::value_type; }
using wrapped_type_t = std::indirectly_readable_traits<T>::value_type;
----

== Synopsis

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

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<link:#mp_units-QuantitySpec[QuantitySpec] auto QS>
struct absolute_point_origin
    : /* implementation-defined */
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `/* implementation-defined */`
| 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-absolute_point_origin-_quantity_spec_[`_quantity_spec_`] 
|===

== Derived Classes

[cols=2]
|===
| Name
| Description
| link:#mp_units-zeroth_point_origin_[`zeroth_point_origin_`]
| 
|===

== Synopsis

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

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-QuantitySpec[QuantitySpec] auto _quantity_spec_ = QS;
----

A dimension of a base quantity

== Synopsis

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

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template<link:#mp_units-symbol_text-032[symbol_text] Symbol>
struct base_dimension
    : /* implementation-defined */
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `/* implementation-defined */`
| 
|===

== Static Data Members

[cols=2]
|===
| Name
| Description
| link:#mp_units-base_dimension-_symbol_[`_symbol_`] 
| Unique base dimension identifier
|===

== Description

Base quantity is a quantity in a conventionally chosen subset of a given system of quantities, where no quantity in the subset can be expressed in terms of the other quantities within that subset. They are referred to as being mutually independent since a base quantity cannot be expressed as a product of powers of the other base quantities.

`Symbol` template parameter is an unique identifier of the base dimension. The same identifiers can be multiplied and divided which will result with an adjustment of its factor in an exponent of a `derived_dimension` (in case of zero the dimension will be simplified and removed from further analysis of current expresion).

User should derive a strong type from this class template rather than use it directly in the source code. For example:

[,cpp]
----
{.cpp}
 inline constexpr struct dim_length final : base_dimension<"L"> {} dim_length;
 inline constexpr struct dim_time final : base_dimension<"T"> {} dim_time;
 inline constexpr struct dim_mass final : base_dimension<"M"> {} dim_mass;
----
[NOTE]
A common convention in this library is to assign the same name for a type and an object of this type&period; Besides defining them user never works with the dimension types in the source code&period; All operations are done on the objects&period; Contrarily, the dimension types are the only one visible in the compilation errors&period; Having them of the same names improves user experience and somehow blurs those separate domains&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Symbol*
| an unique identifier of the base dimension used to provide dimensional analysis support
|===

Unique base dimension identifier

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;symbol&lowbar; = Symbol;
----

A compile&hyphen;time fixed string

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT,
    std::size&lowbar;t N&gt;
class basic&lowbar;fixed&lowbar;string;
----

== Types

[cols=1]
|===
| Name
| link:#mp_units-basic_fixed_string-08-const_iterator[`const&lowbar;iterator`] 
| link:#mp_units-basic_fixed_string-08-const_pointer[`const&lowbar;pointer`] 
| link:#mp_units-basic_fixed_string-08-const_reference[`const&lowbar;reference`] 
| link:#mp_units-basic_fixed_string-08-const_reverse_iterator[`const&lowbar;reverse&lowbar;iterator`] 
| link:#mp_units-basic_fixed_string-08-difference_type[`difference&lowbar;type`] 
| link:#mp_units-basic_fixed_string-08-iterator[`iterator`] 
| link:#mp_units-basic_fixed_string-08-pointer[`pointer`] 
| link:#mp_units-basic_fixed_string-08-reference[`reference`] 
| link:#mp_units-basic_fixed_string-08-reverse_iterator[`reverse&lowbar;iterator`] 
| link:#mp_units-basic_fixed_string-08-size_type[`size&lowbar;type`] 
| link:#mp_units-basic_fixed_string-08-value_type[`value&lowbar;type`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-basic_fixed_string-08-2constructor-012[`basic&lowbar;fixed&lowbar;string`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-basic_fixed_string-08-operator_assign[`operator&equals;`] 
| Copy assignment operator
| link:#mp_units-basic_fixed_string-08-at[`at`] 
| 
| link:#mp_units-basic_fixed_string-08-back[`back`] 
| 
| link:#mp_units-basic_fixed_string-08-begin[`begin`] 
| 
| link:#mp_units-basic_fixed_string-08-c_str[`c&lowbar;str`] 
| 
| link:#mp_units-basic_fixed_string-08-cbegin[`cbegin`] 
| 
| link:#mp_units-basic_fixed_string-08-cend[`cend`] 
| 
| link:#mp_units-basic_fixed_string-08-crbegin[`crbegin`] 
| 
| link:#mp_units-basic_fixed_string-08-crend[`crend`] 
| 
| link:#mp_units-basic_fixed_string-08-data[`data`] 
| 
| link:#mp_units-basic_fixed_string-08-end[`end`] 
| 
| link:#mp_units-basic_fixed_string-08-front[`front`] 
| 
| link:#mp_units-basic_fixed_string-08-operator_subs[`operator&lsqb;&rsqb;`] 
| 
| link:#mp_units-basic_fixed_string-08-rbegin[`rbegin`] 
| 
| link:#mp_units-basic_fixed_string-08-rend[`rend`] 
| 
| link:#mp_units-basic_fixed_string-08-swap[`swap`] 
| 
| link:#mp_units-basic_fixed_string-08-view[`view`] 
| 
| link:#mp_units-basic_fixed_string-08-2conversion[`operator std::basic&lowbar;string&lowbar;view&lt;CharT&gt;`] 
| Conversion to `basic&lowbar;string&lowbar;view`
|===

== Data Members

[cols=1]
|===
| Name
| link:#mp_units-basic_fixed_string-08-data_[`data&lowbar;`] 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-basic_fixed_string-08-empty[`empty`] 
| link:#mp_units-basic_fixed_string-08-length[`length`] 
| link:#mp_units-basic_fixed_string-08-max_size[`max&lowbar;size`] 
| link:#mp_units-basic_fixed_string-08-size[`size`] 
|===

== Friends

[cols=2]
|===
| Name
| Description
| `link:#mp_units-operator_lshift-0e6[mp&lowbar;units::operator&lt;&lt;]`
| Stream insertion operator
| `link:#mp_units-operator_3way-05[mp&lowbar;units::operator&lt;&equals;&gt;]`
| Three&hyphen;way comparison operator
| `link:#mp_units-operator_3way-0d[mp&lowbar;units::operator&lt;&equals;&gt;]`
| Three&hyphen;way comparison operator
| `link:#mp_units-operator_eq-03d[mp&lowbar;units::operator&equals;&equals;]`
| Equality operator
| `link:#mp_units-operator_eq-032[mp&lowbar;units::operator&equals;&equals;]`
| Equality operator
| `link:#mp_units-operator_plus-06[mp&lowbar;units::operator&plus;]`
| Addition operator
| `link:#mp_units-operator_plus-0ec[mp&lowbar;units::operator&plus;]`
| Addition operator
| `link:#mp_units-operator_plus-07[mp&lowbar;units::operator&plus;]`
| Addition operator
| `link:#mp_units-operator_plus-0e3[mp&lowbar;units::operator&plus;]`
| Addition operator
| `link:#mp_units-operator_plus-0e6[mp&lowbar;units::operator&plus;]`
| Addition operator
|===

== Template Parameters

[cols=2]
|===
| Name
| Description
| *CharT*
| Character type to be used by the string
| *N*
| The size of the string
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using const&lowbar;iterator = link:#mp_units-basic_fixed_string-08-value_type[value&lowbar;type] const*;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using const&lowbar;pointer = link:#mp_units-basic_fixed_string-08-value_type[value&lowbar;type] const*;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using const&lowbar;reference = link:#mp_units-basic_fixed_string-08-value_type[value&lowbar;type] const&;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using const&lowbar;reverse&lowbar;iterator = std::reverse&lowbar;iterator&lt;const&lowbar;iterator&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using difference&lowbar;type = std::ptrdiff&lowbar;t;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using iterator = link:#mp_units-basic_fixed_string-08-const_iterator[const&lowbar;iterator];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using pointer = link:#mp_units-basic_fixed_string-08-value_type[value&lowbar;type]*;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using reference = link:#mp_units-basic_fixed_string-08-value_type[value&lowbar;type]&;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using reverse&lowbar;iterator = link:#mp_units-basic_fixed_string-08-const_reverse_iterator[const&lowbar;reverse&lowbar;iterator];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using size&lowbar;type = std::size&lowbar;t;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using value&lowbar;type = CharT;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

Copy constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-basic_fixed_string-08-2constructor-08[basic&lowbar;fixed&lowbar;string](link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& other) noexcept = default;
----

[.small]#link:#mp_units-basic_fixed_string-08-2constructor-08[_» more&period;&period;&period;_]#

Construct from `CharT`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
consteval
explicit(false)
link:#mp_units-basic_fixed_string-08-2constructor-0f[basic&lowbar;fixed&lowbar;string](CharT const(& txt)[]) noexcept;
----

[.small]#link:#mp_units-basic_fixed_string-08-2constructor-0f[_» more&period;&period;&period;_]#

Construct from `Chars`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::same&lowbar;as&lt;CharT&gt;&period;&period;&period; Chars&gt;
requires (sizeof&period;&period;&period;(Chars) &equals;&equals; N) &amp;&amp; (&period;&period;&period; &amp;&amp; !std&colon;&colon;is&lowbar;pointer&lowbar;v&lt;Chars&gt;)
constexpr
explicit
link:#mp_units-basic_fixed_string-08-2constructor-030[basic&lowbar;fixed&lowbar;string](Chars&period;&period;&period; chars) noexcept;
----

[.small]#link:#mp_units-basic_fixed_string-08-2constructor-030[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::ranges::input&lowbar;range R&gt;
requires std&colon;&colon;same&lowbar;as&lt;std&colon;&colon;ranges&colon;&colon;range&lowbar;value&lowbar;t&lt;R&gt;, CharT&gt;
constexpr
link:#mp_units-basic_fixed_string-08-2constructor-015[basic&lowbar;fixed&lowbar;string](
    std::from&lowbar;range&lowbar;t,
    R&& r);
----

[.small]#link:#mp_units-basic_fixed_string-08-2constructor-015[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::input&lowbar;iterator It,
    std::sentinel&lowbar;for&lt;It&gt; S&gt;
requires std&colon;&colon;same&lowbar;as&lt;std&colon;&colon;iter&lowbar;value&lowbar;t&lt;It&gt;, CharT&gt;
constexpr
link:#mp_units-basic_fixed_string-08-2constructor-03a[basic&lowbar;fixed&lowbar;string](
    It begin,
    S end);
----

[.small]#link:#mp_units-basic_fixed_string-08-2constructor-03a[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::input&lowbar;iterator It,
    std::sentinel&lowbar;for&lt;It&gt; S&gt;
requires std&colon;&colon;same&lowbar;as&lt;std&colon;&colon;iter&lowbar;value&lowbar;t&lt;It&gt;, CharT&gt;
constexpr
link:#mp_units-basic_fixed_string-08-2constructor-05[basic&lowbar;fixed&lowbar;string](
    It begin,
    S end);
----

[.small]#link:#mp_units-basic_fixed_string-08-2constructor-05[_» more&period;&period;&period;_]#

Copy constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
basic&lowbar;fixed&lowbar;string(link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& other) noexcept = default;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy construct from
|===

Construct from `CharT`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
consteval
explicit(false)
basic&lowbar;fixed&lowbar;string(CharT const(& txt)[]) noexcept;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *txt*
| The object to copy construct from
|===

Construct from `Chars`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::same&lowbar;as&lt;CharT&gt;&period;&period;&period; Chars&gt;
requires (sizeof&period;&period;&period;(Chars) &equals;&equals; N) &amp;&amp; (&period;&period;&period; &amp;&amp; !std&colon;&colon;is&lowbar;pointer&lowbar;v&lt;Chars&gt;)
constexpr
explicit
basic&lowbar;fixed&lowbar;string(Chars&period;&period;&period; chars) noexcept;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *chars*
| The object to construct from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::ranges::input&lowbar;range R&gt;
requires std&colon;&colon;same&lowbar;as&lt;std&colon;&colon;ranges&colon;&colon;range&lowbar;value&lowbar;t&lt;R&gt;, CharT&gt;
constexpr
basic&lowbar;fixed&lowbar;string(
    std::from&lowbar;range&lowbar;t,
    R&& r);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::input&lowbar;iterator It,
    std::sentinel&lowbar;for&lt;It&gt; S&gt;
requires std&colon;&colon;same&lowbar;as&lt;std&colon;&colon;iter&lowbar;value&lowbar;t&lt;It&gt;, CharT&gt;
constexpr
basic&lowbar;fixed&lowbar;string(
    It begin,
    S end);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::input&lowbar;iterator It,
    std::sentinel&lowbar;for&lt;It&gt; S&gt;
requires std&colon;&colon;same&lowbar;as&lt;std&colon;&colon;iter&lowbar;value&lowbar;t&lt;It&gt;, CharT&gt;
constexpr
basic&lowbar;fixed&lowbar;string(
    It begin,
    S end);
----

Copy assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string]&
operator&equals;(link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& other) noexcept = default;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy assign from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_reference[const&lowbar;reference]
at(link:#mp_units-basic_fixed_string-08-size_type[size&lowbar;type] pos) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_reference[const&lowbar;reference]
back() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_iterator[const&lowbar;iterator]
begin() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_pointer[const&lowbar;pointer]
c&lowbar;str() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_iterator[const&lowbar;iterator]
cbegin() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_iterator[const&lowbar;iterator]
cend() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_reverse_iterator[const&lowbar;reverse&lowbar;iterator]
crbegin() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_reverse_iterator[const&lowbar;reverse&lowbar;iterator]
crend() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_pointer[const&lowbar;pointer]
data() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_iterator[const&lowbar;iterator]
end() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_reference[const&lowbar;reference]
front() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_reference[const&lowbar;reference]
operator&lsqb;&rsqb;(link:#mp_units-basic_fixed_string-08-size_type[size&lowbar;type] pos) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_reverse_iterator[const&lowbar;reverse&lowbar;iterator]
rbegin() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08-const_reverse_iterator[const&lowbar;reverse&lowbar;iterator]
rend() const noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
void
swap(link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string]& s) noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
std::basic&lowbar;string&lowbar;view&lt;CharT&gt;
view() const noexcept;
----

Conversion to `basic&lowbar;string&lowbar;view`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
explicit(false)
operator std::basic&lowbar;string&lowbar;view&lt;CharT&gt;() const noexcept;
----

== Return Value

The object converted to `basic&lowbar;string&lowbar;view`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
CharT data&lowbar;[] = &lcub;&rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
std::bool&lowbar;constant&lt;N &equals;&equals; 0&gt; empty = &lcub;&rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
std::integral&lowbar;constant&lt;size&lowbar;type, N&gt; length = &lcub;&rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
std::integral&lowbar;constant&lt;size&lowbar;type, N&gt; max&lowbar;size = &lcub;&rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
std::integral&lowbar;constant&lt;size&lowbar;type, N&gt; size = &lcub;&rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;integral&lt;typename Q&colon;&colon;rep&gt;
struct binomial&lowbar;distribution
    : std::binomial&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::binomial&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-binomial_distribution-base[`base`] 
| link:#mp_units-binomial_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-binomial_distribution-2constructor-08[`binomial&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-binomial_distribution-max[`max`] 
| 
| link:#mp_units-binomial_distribution-min[`min`] 
| 
| link:#mp_units-binomial_distribution-operator_call[`operator()`] 
| 
| link:#mp_units-binomial_distribution-t[`t`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::binomial&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-binomial_distribution-2constructor-0b[binomial&lowbar;distribution]();
----

[.small]#link:#mp_units-binomial_distribution-2constructor-0b[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-binomial_distribution-2constructor-0c[binomial&lowbar;distribution](
    Q const& t,
    double p);
----

[.small]#link:#mp_units-binomial_distribution-2constructor-0c[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
binomial&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
binomial&lowbar;distribution(
    Q const& t,
    double p);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
t() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; T = double&gt;
class cartesian&lowbar;vector
    : public &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-cartesian_vector-08-value_type[`value&lowbar;type`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-cartesian_vector-08-2constructor-0b[`cartesian&lowbar;vector`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-cartesian_vector-08-operator_assign-0b6[`operator&equals;`] 
| Assignment operators
| link:#mp_units-cartesian_vector-08-magnitude[`magnitude`] 
| 
| link:#mp_units-cartesian_vector-08-operator_star_eq[`operator&ast;&equals;`] 
| Multiplication assignment operator
| link:#mp_units-cartesian_vector-08-operator_plus[`operator&plus;`] 
| Unary plus operator
| link:#mp_units-cartesian_vector-08-operator_plus_eq[`operator&plus;&equals;`] 
| Addition assignment operator
| link:#mp_units-cartesian_vector-08-operator_minus[`operator&hyphen;`] 
| Unary minus operator
| link:#mp_units-cartesian_vector-08-operator_minus_eq[`operator&hyphen;&equals;`] 
| Subtraction assignment operator
| link:#mp_units-cartesian_vector-08-operator_slash_eq[`operator&sol;&equals;`] 
| Division assignment operator
| link:#mp_units-cartesian_vector-08-operator_subs-0c[`operator&lsqb;&rsqb;`] 
| Subscript operators
| link:#mp_units-cartesian_vector-08-unit[`unit`] 
| 
|===

== Data Members

[cols=1]
|===
| Name
| link:#mp_units-cartesian_vector-08-_coordinates_[`&lowbar;coordinates&lowbar;`] 
|===

== Friends

[cols=2]
|===
| Name
| Description
| `link:#mp_units-operator_lshift-0b[mp&lowbar;units::operator&lt;&lt;]`
| Stream insertion operator
| `link:#mp_units-unit_vector[mp&lowbar;units::unit&lowbar;vector]`
| 
| `link:#mp_units-magnitude-0c[mp&lowbar;units::magnitude]`
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using value&lowbar;type = T;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

Copy constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-cartesian_vector-08-2constructor-010[cartesian&lowbar;vector](link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector] const& other) = default;
----

[.small]#link:#mp_units-cartesian_vector-08-2constructor-010[_» more&period;&period;&period;_]#

Copy constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename U&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;T, U&gt;
constexpr
explicit(!std&colon;&colon;convertible&lowbar;to&lt;U, T&gt;)
link:#mp_units-cartesian_vector-08-2constructor-0c[cartesian&lowbar;vector](link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;] const& other);
----

[.small]#link:#mp_units-cartesian_vector-08-2constructor-0c[_» more&period;&period;&period;_]#

Move constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-cartesian_vector-08-2constructor-0e[cartesian&lowbar;vector](link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&& other) = default;
----

[.small]#link:#mp_units-cartesian_vector-08-2constructor-0e[_» more&period;&period;&period;_]#

Move constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename U&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;T, U&gt;
constexpr
explicit(!std&colon;&colon;convertible&lowbar;to&lt;U, T&gt;)
link:#mp_units-cartesian_vector-08-2constructor-05[cartesian&lowbar;vector](link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;]&& other);
----

[.small]#link:#mp_units-cartesian_vector-08-2constructor-05[_» more&period;&period;&period;_]#

Construct from `Args`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename&period;&period;&period; Args&gt;
requires (&period;&period;&period; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;T, Args&gt;)
constexpr
explicit(!(&period;&period;&period; &amp;&amp; std&colon;&colon;convertible&lowbar;to&lt;Args, T&gt;))
link:#mp_units-cartesian_vector-08-2constructor-015[cartesian&lowbar;vector](Args&period;&period;&period;&&&period;&period;&period; args);
----

[.small]#link:#mp_units-cartesian_vector-08-2constructor-015[_» more&period;&period;&period;_]#

Copy constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
cartesian&lowbar;vector(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector] const& other) = default;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy construct from
|===

Copy constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename U&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;T, U&gt;
constexpr
explicit(!std&colon;&colon;convertible&lowbar;to&lt;U, T&gt;)
cartesian&lowbar;vector(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;] const& other);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy construct from
|===

Move constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
cartesian&lowbar;vector(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&& other) = default;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to move construct from
|===

Move constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename U&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;T, U&gt;
constexpr
explicit(!std&colon;&colon;convertible&lowbar;to&lt;U, T&gt;)
cartesian&lowbar;vector(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;]&& other);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to move construct from
|===

Construct from `Args`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename&period;&period;&period; Args&gt;
requires (&period;&period;&period; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;T, Args&gt;)
constexpr
explicit(!(&period;&period;&period; &amp;&amp; std&colon;&colon;convertible&lowbar;to&lt;Args, T&gt;))
cartesian&lowbar;vector(Args&period;&period;&period;&&&period;&period;&period; args);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *args*
| The object to move construct from
|===

Assignment operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

Copy assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
link:#mp_units-cartesian_vector-08-operator_assign-05[operator&equals;](link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector] const& other) = default;
----

[.small]#link:#mp_units-cartesian_vector-08-operator_assign-05[_» more&period;&period;&period;_]#

Copy assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::convertible&lowbar;to&lt;T&gt; U&gt;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
link:#mp_units-cartesian_vector-08-operator_assign-07[operator&equals;](link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;] const& other);
----

[.small]#link:#mp_units-cartesian_vector-08-operator_assign-07[_» more&period;&period;&period;_]#

Move assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
link:#mp_units-cartesian_vector-08-operator_assign-0b3[operator&equals;](link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&& other) = default;
----

[.small]#link:#mp_units-cartesian_vector-08-operator_assign-0b3[_» more&period;&period;&period;_]#

Move assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::convertible&lowbar;to&lt;T&gt; U&gt;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
link:#mp_units-cartesian_vector-08-operator_assign-0d[operator&equals;](link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;]&& other);
----

[.small]#link:#mp_units-cartesian_vector-08-operator_assign-0d[_» more&period;&period;&period;_]#

Copy assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
operator&equals;(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector] const& other) = default;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy assign from
|===

Copy assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::convertible&lowbar;to&lt;T&gt; U&gt;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
operator&equals;(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;] const& other);
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy assign from
|===

Move assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
operator&equals;(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&& other) = default;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to move assign from
|===

Move assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::convertible&lowbar;to&lt;T&gt; U&gt;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
operator&equals;(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;]&& other);
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to move assign from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
T
magnitude() const
requires treat&lowbar;as&lowbar;floating&lowbar;point&lt;T&gt;;
----

Multiplication assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename U&gt;
requires requires(T t, U u) &lcub;
      &lcub; t &ast;&equals; u &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;T&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
operator&ast;&equals;(U const& value);
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *value*
| The right operand
|===

Unary plus operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]
operator&plus;() const;
----

== Return Value

Another instance of the object

Addition assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename U&gt;
requires requires(T t, U u) &lcub;
      &lcub; t &plus;&equals; u &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;T&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
operator&plus;&equals;(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;] const& other);
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The right operand
|===

Unary minus operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]
operator&hyphen;() const;
----

== Return Value

Another instance of the object

Subtraction assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename U&gt;
requires requires(T t, U u) &lcub;
      &lcub; t &hyphen;&equals; u &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;T&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
operator&hyphen;&equals;(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;U&gt;] const& other);
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The right operand
|===

Division assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename U&gt;
requires requires(T t, U u) &lcub;
      &lcub; t &sol;&equals; u &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;T&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]&
operator&sol;&equals;(U const& value);
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *value*
| The right operand
|===

Subscript operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
T&
link:#mp_units-cartesian_vector-08-operator_subs-0f[operator&lsqb;&rsqb;](std::size&lowbar;t i);
----

[.small]#link:#mp_units-cartesian_vector-08-operator_subs-0f[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
T const&
link:#mp_units-cartesian_vector-08-operator_subs-01[operator&lsqb;&rsqb;](std::size&lowbar;t i) const;
----

[.small]#link:#mp_units-cartesian_vector-08-operator_subs-01[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
T&
operator&lsqb;&rsqb;(std::size&lowbar;t i);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
T const&
operator&lsqb;&rsqb;(std::size&lowbar;t i) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]
unit() const
requires treat&lowbar;as&lowbar;floating&lowbar;point&lt;T&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
T &lowbar;coordinates&lowbar;[3];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct cauchy&lowbar;distribution
    : std::cauchy&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::cauchy&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-cauchy_distribution-base[`base`] 
| link:#mp_units-cauchy_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-cauchy_distribution-2constructor-08[`cauchy&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-cauchy_distribution-a[`a`] 
| 
| link:#mp_units-cauchy_distribution-b[`b`] 
| 
| link:#mp_units-cauchy_distribution-max[`max`] 
| 
| link:#mp_units-cauchy_distribution-min[`min`] 
| 
| link:#mp_units-cauchy_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::cauchy&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-cauchy_distribution-2constructor-0a[cauchy&lowbar;distribution]();
----

[.small]#link:#mp_units-cauchy_distribution-2constructor-0a[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-cauchy_distribution-2constructor-00[cauchy&lowbar;distribution](
    Q const& a,
    Q const& b);
----

[.small]#link:#mp_units-cauchy_distribution-2constructor-00[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
cauchy&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
cauchy&lowbar;distribution(
    Q const& a,
    Q const& b);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
a() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
b() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct chi&lowbar;squared&lowbar;distribution
    : std::chi&lowbar;squared&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::chi&lowbar;squared&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-chi_squared_distribution-base[`base`] 
| link:#mp_units-chi_squared_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-chi_squared_distribution-2constructor-0b[`chi&lowbar;squared&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-chi_squared_distribution-max[`max`] 
| 
| link:#mp_units-chi_squared_distribution-min[`min`] 
| 
| link:#mp_units-chi_squared_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::chi&lowbar;squared&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-chi_squared_distribution-2constructor-03[chi&lowbar;squared&lowbar;distribution]();
----

[.small]#link:#mp_units-chi_squared_distribution-2constructor-03[_» more&period;&period;&period;_]#

Construct from `rep`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
link:#mp_units-chi_squared_distribution-2constructor-06[chi&lowbar;squared&lowbar;distribution](link:#mp_units-chi_squared_distribution-rep[rep] const& n);
----

[.small]#link:#mp_units-chi_squared_distribution-2constructor-06[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
chi&lowbar;squared&lowbar;distribution();
----

Construct from `rep`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
chi&lowbar;squared&lowbar;distribution(link:#mp_units-chi_squared_distribution-rep[rep] const& n);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *n*
| The object to copy construct from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

Measurement unit for an accumulation of two quantities of different units

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] U1,
    link:#mp_units-Unit[Unit] U2,
    link:#mp_units-Unit[Unit]&period;&period;&period; Rest&gt;
struct common&lowbar;unit final
    : ::&lowbar;base&lowbar;type&lowbar;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `::&lowbar;base&lowbar;type&lowbar;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-common_unit-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-common_unit-_common_unit_[`&lowbar;common&lowbar;unit&lowbar;`] 
|===

== Description

While adding two quantities of different units we can often identify which of those unit should be used to prevent data truncation&period; For example, adding `1 m &plus; 1 `mm&grave; will end up in a quantity expressed in millimeters&period; However, for some cases this is not possible&period; Choosing any of the units from the arguments of the addition would result in a data truncation&period; For example, a common unit for `1 km &plus; 1 `mi&grave; is `&lsqb;8&sol;125&rsqb; m`&period; Instead of returning such a complex unit type the library will return a `common&lowbar;unit&lt;mi, km&gt;`&period; This type is convertible to both `mi` and `km` without risking data truncation, but is not equal to any of them&period;

[NOTE]
User should not instantiate this type! It is not exported from the C&plus;&plus; module&period; The library will instantiate this type automatically based on the unit arithmetic equation provided by the user&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = link:#mp_units-common_unit[common&lowbar;unit];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;common&lowbar;unit&lowbar; = detail&colon;&colon;get&lowbar;common&lowbar;scaled&lowbar;unit(U1&lcub;&rcub;, U2&lcub;&rcub;, Rest&lcub;&rcub;&period;&period;&period;);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;construction&lowbar;helpers&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Reference[Reference] R&gt;
struct delta&lowbar;;
----

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-delta_-operator_call[`operator()`] 
| Function call operator
|===

Function call operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;construction&lowbar;helpers&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;R&lcub;&rcub;, Rep&gt;]
operator()(FwdRep&& lhs) const;
----

== Return Value

A quantity

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The right operand
|===

A dimension of a derived quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol;&period;&period;&period; Expr&gt;
struct derived&lowbar;dimension final
    : &sol;&ast; implementation-defined &ast;&sol;
    , &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Description

Derived dimension is an expression of the dependence of a quantity on the base quantities of a system of quantities as a product of powers of factors corresponding to the base quantities, omitting any numerical factors&period;

Instead of using a raw list of exponents this library decided to use symbolic expression syntax to make types more digestable for the user&period; The positive exponents are ordered first and all negative exponents are put as a list into the `per&lt;&period;&period;&period;&gt;` class template&period; If a power of exponent is different than `1` the dimension type is enclosed in `power&lt;Dim, Num, Den&gt;` class template&period; Otherwise, it is just put directly in the list without any wrapper&period; There is also one special case&period; In case all of the exponents are negative than the `dimension&lowbar;one` being a dimension of a dimensionless quantity is put in the front to increase the readability&period;

For example&colon;

[,cpp]
----
{.cpp}
 using frequency = decltype(inverse(dim_time));
 using speed = decltype(dim_length / dim_time);
 using acceleration = decltype(dim_speed / dim_time);
 using force = decltype(dim_mass * dim_acceleration);
 using energy = decltype(dim_force * dim_length);
 using moment_of_force = decltype(dim_length * dim_force);
 using torque = decltype(dim_moment_of_force);
----
&hyphen; `frequency` will be derived from type `derived&lowbar;dimension&lt;dimension&lowbar;one, per&lt;dim&lowbar;time&gt;&gt;` &hyphen; `speed` will be derived from type `derived&lowbar;dimension&lt;dim&lowbar;length, per&lt;dim&lowbar;time&gt;&gt;` &hyphen; `acceleration` will be derived from type `derived&lowbar;dimension&lt;dim&lowbar;length, per&lt;power&lt;dim&lowbar;time, 2&gt;&gt;&gt;` &hyphen; `force` will be derived from type `derived&lowbar;dimension&lt;dim&lowbar;length, dim&lowbar;mass, per&lt;power&lt;dim&lowbar;time, 2&gt;&gt;&gt;` &hyphen; `energy` will be derived from type `derived&lowbar;dimension&lt;power&lt;dim&lowbar;length, 2&gt;, dim&lowbar;mass, per&lt;power&lt;dim&lowbar;time, 2&gt;&gt;&gt;`

[NOTE]
A common convention in this library is to assign the same name for a type and an object of this type&period; Besides defining them user never works with the dimension types in the source code&period; All operations are done on the objects&period; Contrarily, the dimension types are the only one visible in the compilation errors&period; Having them of the same names improves user experience and somehow blurs those separate domains&period;

[NOTE]
User should not instantiate this type! It is not exported from the C&plus;&plus; module&period; The library will instantiate this type automatically based on the dimensional arithmetic equation provided by the user&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Ds*
| a parameter pack consisting tokens allowed in the dimension specification (base dimensions, `dimension&lowbar;one`, `power&lt;Dim, Num, Den&gt;`, `per&lt;&period;&period;&period;&gt;`)
|===

A specification of a derived quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol;&period;&period;&period; Expr&gt;
struct derived&lowbar;quantity&lowbar;spec final
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Description

Derived quantity is a quantity, in a system of quantities, defined in terms of other quantities of that system&period; Its dimension is an expression of the dependence of a quantity on the base quantities of a system of quantities as a product of powers of factors corresponding to the base quantities, omitting any numerical factors&period;

Instead of using a raw list of exponents this library decided to use symbolic expression syntax to make types more digestable for the user both for quantity specification and its dimension&period; The positive exponents are ordered first and all negative exponents are put as a list into the `per&lt;&period;&period;&period;&gt;` class template&period; If a power of exponent is different than `1` the quantity type is enclosed in `power&lt;Q, Num, Den&gt;` class template&period; Otherwise, it is just put directly in the list without any wrapper&period; In case all of the exponents are negative than the `dimensionless`&sol;`dimension&lowbar;one` is put in the front to increase the readability&period;

The character of those quantities is derived from ingredients or overriden with a template parameter&period;

For example&colon;

[,cpp]
----
{.cpp}
 auto frequency = inverse(period_duration);
 auto area = pow<2>(length);
 auto speed = distance / duration;
 auto velocity = displacement / duration;
 auto acceleration = velocity / duration;
----
&hyphen; the type of `frequency` is `derived&lowbar;quantity&lowbar;spec&lt;dimensionless, per&lt;period&lowbar;duration&gt;&gt;` &hyphen; the dimension type of `frequency` is `derived&lowbar;dimension&lt;dimension&lowbar;one, per&lt;dim&lowbar;time&gt;&gt;` &hyphen; the type of `area` is `derived&lowbar;quantity&lowbar;spec&lt;power&lt;length, 2&gt;&gt;` &hyphen; the dimension type of `area` is `derived&lowbar;dimension&lt;power&lt;dim&lowbar;length, 2&gt;&gt;` &hyphen; the type of `speed` is `derived&lowbar;quantity&lowbar;spec&lt;distance, per&lt;duration&gt;&gt;` &hyphen; the dimension type of `speed` is `derived&lowbar;dimension&lt;dim&lowbar;length, per&lt;dim&lowbar;time&gt;&gt;` &hyphen; the type of `velocity` is `derived&lowbar;quantity&lowbar;spec&lt;displacement, per&lt;duration&gt;&gt;` &hyphen; the dimension type of `velocity` is `derived&lowbar;dimension&lt;dim&lowbar;length, per&lt;dim&lowbar;time&gt;&gt;` &hyphen; the type of `acceleration` is `derived&lowbar;quantity&lowbar;spec&lt;velocity, per&lt;duration&gt;&gt;` &hyphen; the dimension type of `acceleration` is `derived&lowbar;dimension&lt;dim&lowbar;length, per&lt;power&lt;dim&lowbar;time, 2&gt;&gt;&gt;`

[NOTE]
User should not instantiate this type! It is not exported from the C&plus;&plus; module&period; The library will instantiate this type automatically based on the dimensional arithmetic equation provided by the user&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Expr*
| a parameter pack consisting tokens allowed in the quantity specification (named quantity specification, `dimensionless`, `power&lt;Q, Num, Den&gt;`, `per&lt;&period;&period;&period;&gt;`)
|===

Measurement unit for a derived quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol;&period;&period;&period; Expr&gt;
struct derived&lowbar;unit final
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Description

Derived units are defined as products of powers of the base units&period;

Instead of using a raw list of exponents this library decided to use expression template syntax to make types more digestable for the user&period; The positive exponents are ordered first and all negative exponents are put as a list into the `per&lt;&period;&period;&period;&gt;` class template&period; If a power of exponent is different than `1` the unit type is enclosed in `power&lt;Dim, Num, Den&gt;` class template&period; Otherwise, it is just put directly in the list without any wrapper&period; There is also one special case&period; In case all of the exponents are negative then the `one` being a coherent unit of a dimensionless quantity is put in the front to increase the readability&period;

For example&colon;

[,cpp]
----
{.cpp}
 static_assert(is_of_type<inverse(second), derived_unit<one, per<second>>>);
 static_assert(is_of_type<one / inverse(second), second>);
 static_assert(is_of_type<one * second, second>);
 static_assert(is_of_type<metre * metre, derived_unit<power<metre, 2>>>);
 static_assert(is_of_type<metre * second, derived_unit<metre, second>>);
 static_assert(is_of_type<metre / second, derived_unit<metre, per<second>>>);
 static_assert(is_of_type<metre / square(second), derived_unit<metre, per<power<second, 2>>>>);
 static_assert(is_of_type<watt / joule, derived_unit<watt, per<joule>>>);
----
Every unit in the library has its internal canonical representation being the list of exponents of named base units (with the exception of `kilogram` which is represented as `gram` here) and a scaling ratio represented with a magnitude&period;

Two units are deemed convertible if their canonical version has units of the same type&period; Two units are equivalent when they are convertible and their canonical versions have the same scaling ratios&period;

The above means that&colon; &hyphen; `1&sol;s` and `Hz` are both convertible and equal &hyphen; `m` and `km` are convertible but not equal &hyphen; `m` and `m²` ane not convertible and not equal

[NOTE]
This also means that units like `hertz` and `becquerel` are also considered convertible and equal&period;

[NOTE]
User should not instantiate this type! It is not exported from the C&plus;&plus; module&period; The library will instantiate this type automatically based on the unit arithmetic equation provided by the user&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Us*
| a parameter pack consisting tokens allowed in the unit specification (units, `power&lt;U, Num, Den&gt;`, `per&lt;&period;&period;&period;&gt;`)
|===

Dimension one

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct dimension&lowbar;one final
    : &sol;&ast; implementation-defined &ast;&sol;
    , &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Description

Dimension for which all the exponents of the factors corresponding to the base dimensions are zero&period; It is a dimension of a quantity of dimension one also known as &quot;dimensionless&quot;&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct dimension&lowbar;symbol&lowbar;formatting;
----

== Data Members

[cols=1]
|===
| Name
| link:#mp_units-dimension_symbol_formatting-char_set[`char&lowbar;set`] 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-character_set[character&lowbar;set] char&lowbar;set = character&lowbar;set&colon;&colon;default&lowbar;character&lowbar;set;
----

Quantity of dimension one

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct dimensionless final
    : link:#mp_units-quantity_spec-09[mp&lowbar;units::quantity&lowbar;spec&lt;derived&lowbar;quantity&lowbar;spec&lt;&gt;&lcub;&rcub;&gt;]
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `link:#mp_units-quantity_spec-09[mp&lowbar;units::quantity&lowbar;spec&lt;derived&lowbar;quantity&lowbar;spec&lt;&gt;&lcub;&rcub;&gt;]`
| 
|===

== Description

Quantity of dimension one also commonly named as &quot;dimensionless&quot; is a quantity with a dimension for which all the exponents of the factors corresponding to the base dimensions are zero&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;integral&lt;typename Q&colon;&colon;rep&gt;
struct discrete&lowbar;distribution
    : std::discrete&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::discrete&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-discrete_distribution-base[`base`] 
| link:#mp_units-discrete_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-discrete_distribution-2constructor-03[`discrete&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-discrete_distribution-max[`max`] 
| 
| link:#mp_units-discrete_distribution-min[`min`] 
| 
| link:#mp_units-discrete_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::discrete&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-discrete_distribution-2constructor-016[discrete&lowbar;distribution]();
----

[.small]#link:#mp_units-discrete_distribution-2constructor-016[_» more&period;&period;&period;_]#

Construct from `initializer&lowbar;list`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-discrete_distribution-2constructor-0b[discrete&lowbar;distribution](std::initializer&lowbar;list&lt;double&gt; weights);
----

[.small]#link:#mp_units-discrete_distribution-2constructor-0b[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename InputIt&gt;
link:#mp_units-discrete_distribution-2constructor-018[discrete&lowbar;distribution](
    InputIt first,
    InputIt last);
----

[.small]#link:#mp_units-discrete_distribution-2constructor-018[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
link:#mp_units-discrete_distribution-2constructor-07[discrete&lowbar;distribution](
    std::size&lowbar;t count,
    double xmin,
    double xmax,
    UnaryOperation unary&lowbar;op);
----

[.small]#link:#mp_units-discrete_distribution-2constructor-07[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
discrete&lowbar;distribution();
----

Construct from `initializer&lowbar;list`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
discrete&lowbar;distribution(std::initializer&lowbar;list&lt;double&gt; weights);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *weights*
| The object to construct from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename InputIt&gt;
discrete&lowbar;distribution(
    InputIt first,
    InputIt last);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
discrete&lowbar;distribution(
    std::size&lowbar;t count,
    double xmin,
    double xmax,
    UnaryOperation unary&lowbar;op);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct exponential&lowbar;distribution
    : std::exponential&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::exponential&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-exponential_distribution-base[`base`] 
| link:#mp_units-exponential_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-exponential_distribution-2constructor-05[`exponential&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-exponential_distribution-max[`max`] 
| 
| link:#mp_units-exponential_distribution-min[`min`] 
| 
| link:#mp_units-exponential_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::exponential&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-exponential_distribution-2constructor-02[exponential&lowbar;distribution]();
----

[.small]#link:#mp_units-exponential_distribution-2constructor-02[_» more&period;&period;&period;_]#

Construct from `rep`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
link:#mp_units-exponential_distribution-2constructor-08[exponential&lowbar;distribution](link:#mp_units-exponential_distribution-rep[rep] const& lambda);
----

[.small]#link:#mp_units-exponential_distribution-2constructor-08[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
exponential&lowbar;distribution();
----

Construct from `rep`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
exponential&lowbar;distribution(link:#mp_units-exponential_distribution-rep[rep] const& lambda);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *lambda*
| The object to copy construct from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct extreme&lowbar;value&lowbar;distribution
    : std::extreme&lowbar;value&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::extreme&lowbar;value&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-extreme_value_distribution-base[`base`] 
| link:#mp_units-extreme_value_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-extreme_value_distribution-2constructor-04[`extreme&lowbar;value&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-extreme_value_distribution-a[`a`] 
| 
| link:#mp_units-extreme_value_distribution-max[`max`] 
| 
| link:#mp_units-extreme_value_distribution-min[`min`] 
| 
| link:#mp_units-extreme_value_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::extreme&lowbar;value&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-extreme_value_distribution-2constructor-0c[extreme&lowbar;value&lowbar;distribution]();
----

[.small]#link:#mp_units-extreme_value_distribution-2constructor-0c[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-extreme_value_distribution-2constructor-05[extreme&lowbar;value&lowbar;distribution](
    Q const& a,
    link:#mp_units-extreme_value_distribution-rep[rep] const& b);
----

[.small]#link:#mp_units-extreme_value_distribution-2constructor-05[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
extreme&lowbar;value&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
extreme&lowbar;value&lowbar;distribution(
    Q const& a,
    link:#mp_units-extreme_value_distribution-rep[rep] const& b);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
a() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct fisher&lowbar;f&lowbar;distribution
    : std::fisher&lowbar;f&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::fisher&lowbar;f&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-fisher_f_distribution-base[`base`] 
| link:#mp_units-fisher_f_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-fisher_f_distribution-2constructor-0d[`fisher&lowbar;f&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-fisher_f_distribution-max[`max`] 
| 
| link:#mp_units-fisher_f_distribution-min[`min`] 
| 
| link:#mp_units-fisher_f_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::fisher&lowbar;f&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-fisher_f_distribution-2constructor-05[fisher&lowbar;f&lowbar;distribution]();
----

[.small]#link:#mp_units-fisher_f_distribution-2constructor-05[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-fisher_f_distribution-2constructor-09[fisher&lowbar;f&lowbar;distribution](
    link:#mp_units-fisher_f_distribution-rep[rep] const& m,
    link:#mp_units-fisher_f_distribution-rep[rep] const& n);
----

[.small]#link:#mp_units-fisher_f_distribution-2constructor-09[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
fisher&lowbar;f&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
fisher&lowbar;f&lowbar;distribution(
    link:#mp_units-fisher_f_distribution-rep[rep] const& m,
    link:#mp_units-fisher_f_distribution-rep[rep] const& n);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct gamma&lowbar;distribution
    : std::gamma&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::gamma&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-gamma_distribution-base[`base`] 
| link:#mp_units-gamma_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-gamma_distribution-2constructor-06[`gamma&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-gamma_distribution-max[`max`] 
| 
| link:#mp_units-gamma_distribution-min[`min`] 
| 
| link:#mp_units-gamma_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::gamma&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-gamma_distribution-2constructor-09[gamma&lowbar;distribution]();
----

[.small]#link:#mp_units-gamma_distribution-2constructor-09[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-gamma_distribution-2constructor-0b[gamma&lowbar;distribution](
    link:#mp_units-gamma_distribution-rep[rep] const& alpha,
    link:#mp_units-gamma_distribution-rep[rep] const& beta);
----

[.small]#link:#mp_units-gamma_distribution-2constructor-0b[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
gamma&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
gamma&lowbar;distribution(
    link:#mp_units-gamma_distribution-rep[rep] const& alpha,
    link:#mp_units-gamma_distribution-rep[rep] const& beta);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;integral&lt;typename Q&colon;&colon;rep&gt;
struct geometric&lowbar;distribution
    : std::geometric&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::geometric&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-geometric_distribution-base[`base`] 
| link:#mp_units-geometric_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-geometric_distribution-2constructor-07[`geometric&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-geometric_distribution-max[`max`] 
| 
| link:#mp_units-geometric_distribution-min[`min`] 
| 
| link:#mp_units-geometric_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::geometric&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-geometric_distribution-2constructor-02[geometric&lowbar;distribution]();
----

[.small]#link:#mp_units-geometric_distribution-2constructor-02[_» more&period;&period;&period;_]#

Construct from `double`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
link:#mp_units-geometric_distribution-2constructor-0e[geometric&lowbar;distribution](double p);
----

[.small]#link:#mp_units-geometric_distribution-2constructor-0e[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
geometric&lowbar;distribution();
----

Construct from `double`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
geometric&lowbar;distribution(double p);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *p*
| The value to construct from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct is&lowbar;kind;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Q&gt;
struct kind&lowbar;of&lowbar;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantitySpec[QuantitySpec] Q&gt;
requires (!detail&colon;&colon;QuantityKindSpec&lt;Q&gt;) &amp;&amp; (detail&colon;&colon;get&lowbar;kind&lowbar;tree&lowbar;root(Q&lcub;&rcub;) &equals;&equals; Q&lcub;&rcub;)
struct link:#mp_units-kind_of_-00[kind&lowbar;of&lowbar;]&lt;Q&gt; final
    : Q::&lowbar;base&lowbar;type&lowbar;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `Q::&lowbar;base&lowbar;type&lowbar;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-kind_of_-0d-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-kind_of_-0d-_quantity_spec_[`&lowbar;quantity&lowbar;spec&lowbar;`] 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = link:#mp_units-kind_of_-0d[kind&lowbar;of&lowbar;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;quantity&lowbar;spec&lowbar; = Q&lcub;&rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct lognormal&lowbar;distribution
    : std::lognormal&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::lognormal&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-lognormal_distribution-base[`base`] 
| link:#mp_units-lognormal_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-lognormal_distribution-2constructor-02[`lognormal&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-lognormal_distribution-m[`m`] 
| 
| link:#mp_units-lognormal_distribution-max[`max`] 
| 
| link:#mp_units-lognormal_distribution-min[`min`] 
| 
| link:#mp_units-lognormal_distribution-operator_call[`operator()`] 
| 
| link:#mp_units-lognormal_distribution-s[`s`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::lognormal&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-lognormal_distribution-2constructor-04[lognormal&lowbar;distribution]();
----

[.small]#link:#mp_units-lognormal_distribution-2constructor-04[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-lognormal_distribution-2constructor-0b[lognormal&lowbar;distribution](
    Q const& m,
    Q const& s);
----

[.small]#link:#mp_units-lognormal_distribution-2constructor-0b[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
lognormal&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
lognormal&lowbar;distribution(
    Q const& m,
    Q const& s);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
m() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
s() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-symbol_text-032[symbol&lowbar;text] Symbol,
    long double Value&gt;
requires (Value &gt; 0)
struct mag&lowbar;constant;
----

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-mag_constant-_symbol_[`&lowbar;symbol&lowbar;`] 
| link:#mp_units-mag_constant-_value_[`&lowbar;value&lowbar;`] 
|===

== Derived Classes

[cols=2]
|===
| Name
| Description
| link:#mp_units-pi-0c[`pi`]
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;symbol&lowbar; = Symbol;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
long double &lowbar;value&lowbar; = Value;
----

A named unit

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-symbol_text-032[symbol&lowbar;text] Symbol,
    auto&period;&period;&period;&gt;
struct named&lowbar;unit;
----

== Derived Classes

[cols=2]
|===
| Name
| Description
| link:#mp_units-parts_per_million-0f[`parts&lowbar;per&lowbar;million`]
| 
| link:#mp_units-per_mille-01[`per&lowbar;mille`]
| 
| link:#mp_units-percent-02[`percent`]
| 
|===

== Description

Defines a unit with a special name&period; It may be used to provide a base unit in the system of units (e&period;g&period; `metre`) or a name assigned to another scaled or derived unit (e&period;g&period; `hour`, `joule`)&period; Most of the named units may be composed with a prefix to create a `prefixed&lowbar;unit`&period;

For example&colon;

[,cpp]
----
{.cpp}
 inline constexpr struct second final : named_unit<"s", kind_of<time>> {} second;
 inline constexpr struct metre final : named_unit<"m", kind_of<length> {} metre;
 inline constexpr struct hertz final : named_unit<"Hz", inverse(second), kind_of<frequency>> {} hertz;
 inline constexpr struct newton final : named_unit<"N", kilogram * metre / square(second)> {} newton;
 inline constexpr struct degree_Celsius final : named_unit<{u8"℃", "`C"}, kelvin, zeroth_degree_Celsius> {}
 degree_Celsius; inline constexpr struct minute final : named_unit<"min", mag<60> * second> {} minute;
----
[NOTE]
A common convention in this library is to assign the same name for a type and an object of this type&period; Besides defining them user never works with the unit types in the source code&period; All operations are done on the objects&period; Contrarily, the unit types are the only one visible in the compilation errors&period; Having them of the same names improves user experience and somehow blurs those separate domains&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Symbol*
| a short text representation of the unit
|===

Specialization for a unit that can be reused by several base quantities

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-symbol_text-032[symbol&lowbar;text] Symbol&gt;
requires (!Symbol&period;empty())
struct link:#mp_units-named_unit-0ec[named&lowbar;unit]&lt;Symbol&gt;
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-named_unit-06-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Static Data Members

[cols=2]
|===
| Name
| Description
| link:#mp_units-named_unit-06-_symbol_[`&lowbar;symbol&lowbar;`] 
| Unique base unit identifier
|===

== Description

This specialization is used in rare cases where more than one base quantity in a specific system of units uses the same unit&period; For example in a hypothetical system of natural units where constant for speed of light `c &equals; 1`, length and time could be measured in seconds&period; In such cases `system&lowbar;reference` has to be used to explicitly express such a binding&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Symbol*
| a short text representation of the unit
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = link:#mp_units-named_unit-06[named&lowbar;unit];
----

Unique base unit identifier

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;symbol&lowbar; = Symbol;
----

Specialization for unit of a specified base quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-symbol_text-032[symbol&lowbar;text] Symbol,
    link:#mp_units-Unit[Unit] auto QS&gt;
requires (!Symbol&period;empty())
struct link:#mp_units-named_unit-0ec[named&lowbar;unit]&lt;Symbol, U&gt;
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-named_unit-07-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Static Data Members

[cols=2]
|===
| Name
| Description
| link:#mp_units-named_unit-07-_quantity_spec_[`&lowbar;quantity&lowbar;spec&lowbar;`] 
| 
| link:#mp_units-named_unit-07-_symbol_[`&lowbar;symbol&lowbar;`] 
| Unique base unit identifier
|===

== Description

Associates a unit with a specified base quantity&period; For example `si&colon;&colon;metre` is a unit to measure `isq&colon;&colon;length` in the SI system&period;

[NOTE]
This is the preferred way to define a measurement unit for a specific base quantity&period;

[NOTE]
It does not have to (or sometimes even can&apos;t) be a proper system&apos;s base unit&period; For example a base unit of mass in the SI is `si&colon;&colon;kilogram` but here you are about to provide an `si&colon;&colon;gram` and it will work just fine as those two are convertible to each other&period; A similar case would be the `cgs&colon;&colon;centimetre` that is a base unit for `isq&colon;&colon;length` in the CGS system&period;

Allows assigning a special name to another scaled or derived unit (e&period;g&period; `hour`, `joule`)&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Symbol*
| a short text representation of the unit
| *QuantitySpec*
| a specification of a base quantity to be measured with this unit
| *Unit*
| a unit for which we provide a special name
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = link:#mp_units-named_unit-07[named&lowbar;unit];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;quantity&lowbar;spec&lowbar; = QS;
----

Unique base unit identifier

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;symbol&lowbar; = Symbol;
----

== Description

Unique unit identifier

Specialization for a unit with special name valid only for a specific quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-symbol_text-032[symbol&lowbar;text] Symbol,
    link:#mp_units-AssociatedUnit[AssociatedUnit] auto QS,
    &sol;&ast; implementation-defined &ast;&sol; auto PO&gt;
requires (!Symbol&period;empty()) &amp;&amp; (QS&period;dimension &equals;&equals; detail&colon;&colon;get&lowbar;associated&lowbar;quantity(U)&period;dimension)
struct link:#mp_units-named_unit-0ec[named&lowbar;unit]&lt;Symbol, U, QS&gt;
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-named_unit-05-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Static Data Members

[cols=2]
|===
| Name
| Description
| link:#mp_units-named_unit-05-_point_origin_[`&lowbar;point&lowbar;origin&lowbar;`] 
| 
| link:#mp_units-named_unit-05-_quantity_spec_[`&lowbar;quantity&lowbar;spec&lowbar;`] 
| 
| link:#mp_units-named_unit-05-_symbol_[`&lowbar;symbol&lowbar;`] 
| Unique base unit identifier
|===

== Description

The same as the above but additionally limits the usage of this unit to provided quantities&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Symbol*
| a short text representation of the unit
| *Unit*
| a unit for which we provide a special name
| *QuantitySpec*
| a specification of a quantity to be measured with this unit
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = link:#mp_units-named_unit-05[named&lowbar;unit];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;point&lowbar;origin&lowbar; = PO;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;quantity&lowbar;spec&lowbar; = QS;
----

Unique base unit identifier

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;symbol&lowbar; = Symbol;
----

== Description

Unique unit identifier

Unique unit identifier

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-symbol_text-032[symbol&lowbar;text] Symbol,
    link:#mp_units-AssociatedUnit[AssociatedUnit] auto U,
    &sol;&ast; implementation-defined &ast;&sol; auto QS,
    link:#mp_units-PointOrigin[PointOrigin] auto PO&gt;
requires (!Symbol&period;empty()) &amp;&amp; (QS&period;dimension &equals;&equals; detail&colon;&colon;get&lowbar;associated&lowbar;quantity(U)&period;dimension)
struct link:#mp_units-named_unit-0ec[named&lowbar;unit]&lt;Symbol, U, QS, PO&gt;
    : ::&lowbar;base&lowbar;type&lowbar;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `::&lowbar;base&lowbar;type&lowbar;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-named_unit-0e4-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Static Data Members

[cols=2]
|===
| Name
| Description
| link:#mp_units-named_unit-0e4-_point_origin_[`&lowbar;point&lowbar;origin&lowbar;`] 
| 
| link:#mp_units-named_unit-0e4-_quantity_spec_[`&lowbar;quantity&lowbar;spec&lowbar;`] 
| 
| link:#mp_units-named_unit-0e4-_symbol_[`&lowbar;symbol&lowbar;`] 
| Unique unit identifier
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = link:#mp_units-named_unit-0e4[named&lowbar;unit];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;point&lowbar;origin&lowbar; = PO;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;quantity&lowbar;spec&lowbar; = QS;
----

Unique unit identifier

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;symbol&lowbar; = Symbol;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;integral&lt;typename Q&colon;&colon;rep&gt;
struct negative&lowbar;binomial&lowbar;distribution
    : std::negative&lowbar;binomial&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::negative&lowbar;binomial&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-negative_binomial_distribution-base[`base`] 
| link:#mp_units-negative_binomial_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-negative_binomial_distribution-2constructor-03[`negative&lowbar;binomial&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-negative_binomial_distribution-k[`k`] 
| 
| link:#mp_units-negative_binomial_distribution-max[`max`] 
| 
| link:#mp_units-negative_binomial_distribution-min[`min`] 
| 
| link:#mp_units-negative_binomial_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::negative&lowbar;binomial&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-negative_binomial_distribution-2constructor-0d[negative&lowbar;binomial&lowbar;distribution]();
----

[.small]#link:#mp_units-negative_binomial_distribution-2constructor-0d[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-negative_binomial_distribution-2constructor-0f[negative&lowbar;binomial&lowbar;distribution](
    Q const& k,
    double p);
----

[.small]#link:#mp_units-negative_binomial_distribution-2constructor-0f[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
negative&lowbar;binomial&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
negative&lowbar;binomial&lowbar;distribution(
    Q const& k,
    double p);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
k() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct normal&lowbar;distribution
    : std::normal&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::normal&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-normal_distribution-base[`base`] 
| link:#mp_units-normal_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-normal_distribution-2constructor-04[`normal&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-normal_distribution-max[`max`] 
| 
| link:#mp_units-normal_distribution-mean[`mean`] 
| 
| link:#mp_units-normal_distribution-min[`min`] 
| 
| link:#mp_units-normal_distribution-operator_call[`operator()`] 
| 
| link:#mp_units-normal_distribution-stddev[`stddev`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::normal&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-normal_distribution-2constructor-0a0[normal&lowbar;distribution]();
----

[.small]#link:#mp_units-normal_distribution-2constructor-0a0[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-normal_distribution-2constructor-0a8[normal&lowbar;distribution](
    Q const& mean,
    Q const& stddev);
----

[.small]#link:#mp_units-normal_distribution-2constructor-0a8[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
normal&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
normal&lowbar;distribution(
    Q const& mean,
    Q const& stddev);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
mean() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
stddev() const;
----

Unit one

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct one final
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-one-0f-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Description

Unit of a dimensionless quantity&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = &sol;&ast; implementation-defined &ast;&sol;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct parts&lowbar;per&lowbar;million final
    : link:#mp_units-named_unit-0ec[named&lowbar;unit&lt;&quot;ppm&quot;, mag&lowbar;ratio&lt;1, 1000000&gt; &ast; one&gt;]
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `link:#mp_units-named_unit-0ec[named&lowbar;unit&lt;&quot;ppm&quot;, mag&lowbar;ratio&lt;1, 1000000&gt; &ast; one&gt;]`
| A named unit
|===

Type list type storing the list of components with negative exponents

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbolic&lowbar;expression&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    &sol;&ast; implementation-defined &ast;&sol; T,
    &sol;&ast; implementation-defined &ast;&sol;&period;&period;&period; Ts&gt;
struct per final
----

== Description

[NOTE]
Can&apos;t be empty

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct per&lowbar;mille final
    : link:#mp_units-named_unit-0ec[named&lowbar;unit&lt;symbol&lowbar;text&lt;4UL &hyphen; 1, 3UL &hyphen; 1&gt;&lcub;u8&quot;&bsol;342&bsol;200&bsol;260&quot;, &quot;%o&quot;&rcub;, mag&lowbar;ratio&lt;1, 1000&gt; &ast; one&gt;]
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `link:#mp_units-named_unit-0ec[named&lowbar;unit&lt;symbol&lowbar;text&lt;4UL &hyphen; 1, 3UL &hyphen; 1&gt;&lcub;u8&quot;&bsol;342&bsol;200&bsol;260&quot;, &quot;%o&quot;&rcub;, mag&lowbar;ratio&lt;1, 1000&gt; &ast; one&gt;]`
| A named unit
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct percent final
    : link:#mp_units-named_unit-0ec[named&lowbar;unit&lt;&quot;%&quot;, mag&lowbar;ratio&lt;1, 100&gt; &ast; one&gt;]
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `link:#mp_units-named_unit-0ec[named&lowbar;unit&lt;&quot;%&quot;, mag&lowbar;ratio&lt;1, 100&gt; &ast; one&gt;]`
| A named unit
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct pi final
    : link:#mp_units-mag_constant[mag&lowbar;constant&lt;symbol&lowbar;text&lt;3UL &hyphen; 1, 3UL &hyphen; 1&gt;&lcub;u8&quot;&bsol;317&bsol;200&quot;, &quot;pi&quot;&rcub;, std&colon;&colon;numbers&colon;&colon;pi&lowbar;v&lt;long double&gt;&gt;]
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `link:#mp_units-mag_constant[mag&lowbar;constant&lt;symbol&lowbar;text&lt;3UL &hyphen; 1, 3UL &hyphen; 1&gt;&lcub;u8&quot;&bsol;317&bsol;200&quot;, &quot;pi&quot;&rcub;, std&colon;&colon;numbers&colon;&colon;pi&lowbar;v&lt;long double&gt;&gt;]`
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
class piecewise&lowbar;constant&lowbar;distribution
    : public std::piecewise&lowbar;constant&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::piecewise&lowbar;constant&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-piecewise_constant_distribution-2constructor-00[`piecewise&lowbar;constant&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-piecewise_constant_distribution-intervals[`intervals`] 
| 
| link:#mp_units-piecewise_constant_distribution-max[`max`] 
| 
| link:#mp_units-piecewise_constant_distribution-min[`min`] 
| 
| link:#mp_units-piecewise_constant_distribution-operator_call[`operator()`] 
| 
|===

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-piecewise_constant_distribution-2constructor-04[piecewise&lowbar;constant&lowbar;distribution]();
----

[.small]#link:#mp_units-piecewise_constant_distribution-2constructor-04[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
link:#mp_units-piecewise_constant_distribution-2constructor-07[piecewise&lowbar;constant&lowbar;distribution](
    std::initializer&lowbar;list&lt;Q&gt; bl,
    UnaryOperation fw);
----

[.small]#link:#mp_units-piecewise_constant_distribution-2constructor-07[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename InputIt1,
    typename InputIt2&gt;
link:#mp_units-piecewise_constant_distribution-2constructor-0d[piecewise&lowbar;constant&lowbar;distribution](
    InputIt1 first&lowbar;i,
    InputIt1 last&lowbar;i,
    InputIt2 first&lowbar;w);
----

[.small]#link:#mp_units-piecewise_constant_distribution-2constructor-0d[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
link:#mp_units-piecewise_constant_distribution-2constructor-09[piecewise&lowbar;constant&lowbar;distribution](
    std::size&lowbar;t nw,
    Q const& xmin,
    Q const& xmax,
    UnaryOperation fw);
----

[.small]#link:#mp_units-piecewise_constant_distribution-2constructor-09[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
piecewise&lowbar;constant&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
piecewise&lowbar;constant&lowbar;distribution(
    std::initializer&lowbar;list&lt;Q&gt; bl,
    UnaryOperation fw);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename InputIt1,
    typename InputIt2&gt;
piecewise&lowbar;constant&lowbar;distribution(
    InputIt1 first&lowbar;i,
    InputIt1 last&lowbar;i,
    InputIt2 first&lowbar;w);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
piecewise&lowbar;constant&lowbar;distribution(
    std::size&lowbar;t nw,
    Q const& xmin,
    Q const& xmax,
    UnaryOperation fw);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
std::vector&lt;Q&gt;
intervals() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
class piecewise&lowbar;linear&lowbar;distribution
    : public std::piecewise&lowbar;linear&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::piecewise&lowbar;linear&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-piecewise_linear_distribution-2constructor-08[`piecewise&lowbar;linear&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-piecewise_linear_distribution-intervals[`intervals`] 
| 
| link:#mp_units-piecewise_linear_distribution-max[`max`] 
| 
| link:#mp_units-piecewise_linear_distribution-min[`min`] 
| 
| link:#mp_units-piecewise_linear_distribution-operator_call[`operator()`] 
| 
|===

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-piecewise_linear_distribution-2constructor-04[piecewise&lowbar;linear&lowbar;distribution]();
----

[.small]#link:#mp_units-piecewise_linear_distribution-2constructor-04[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
link:#mp_units-piecewise_linear_distribution-2constructor-07[piecewise&lowbar;linear&lowbar;distribution](
    std::initializer&lowbar;list&lt;Q&gt; bl,
    UnaryOperation fw);
----

[.small]#link:#mp_units-piecewise_linear_distribution-2constructor-07[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename InputIt1,
    typename InputIt2&gt;
link:#mp_units-piecewise_linear_distribution-2constructor-0c6[piecewise&lowbar;linear&lowbar;distribution](
    InputIt1 first&lowbar;i,
    InputIt1 last&lowbar;i,
    InputIt2 first&lowbar;w);
----

[.small]#link:#mp_units-piecewise_linear_distribution-2constructor-0c6[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
link:#mp_units-piecewise_linear_distribution-2constructor-0cd[piecewise&lowbar;linear&lowbar;distribution](
    std::size&lowbar;t nw,
    Q const& xmin,
    Q const& xmax,
    UnaryOperation fw);
----

[.small]#link:#mp_units-piecewise_linear_distribution-2constructor-0cd[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
piecewise&lowbar;linear&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
piecewise&lowbar;linear&lowbar;distribution(
    std::initializer&lowbar;list&lt;Q&gt; bl,
    UnaryOperation fw);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename InputIt1,
    typename InputIt2&gt;
piecewise&lowbar;linear&lowbar;distribution(
    InputIt1 first&lowbar;i,
    InputIt1 last&lowbar;i,
    InputIt2 first&lowbar;w);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename UnaryOperation&gt;
piecewise&lowbar;linear&lowbar;distribution(
    std::size&lowbar;t nw,
    Q const& xmin,
    Q const& xmax,
    UnaryOperation fw);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
std::vector&lt;Q&gt;
intervals() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;construction&lowbar;helpers&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Reference[Reference] R&gt;
struct point&lowbar;;
----

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-point_-operator_call[`operator()`] 
| Function call operator
|===

Function call operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;construction&lowbar;helpers&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R&lcub;&rcub;, default&lowbar;point&lowbar;origin(R&lcub;&rcub;), Rep&gt;]
operator()(FwdRep&& lhs) const;
----

== Return Value

A quantity point

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The right operand
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;integral&lt;typename Q&colon;&colon;rep&gt;
struct poisson&lowbar;distribution
    : std::poisson&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::poisson&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-poisson_distribution-base[`base`] 
| link:#mp_units-poisson_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-poisson_distribution-2constructor-09[`poisson&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-poisson_distribution-max[`max`] 
| 
| link:#mp_units-poisson_distribution-min[`min`] 
| 
| link:#mp_units-poisson_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::poisson&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-poisson_distribution-2constructor-0e[poisson&lowbar;distribution]();
----

[.small]#link:#mp_units-poisson_distribution-2constructor-0e[_» more&period;&period;&period;_]#

Construct from `double`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
link:#mp_units-poisson_distribution-2constructor-00[poisson&lowbar;distribution](double p);
----

[.small]#link:#mp_units-poisson_distribution-2constructor-00[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
poisson&lowbar;distribution();
----

Construct from `double`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
poisson&lowbar;distribution(double p);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *p*
| The value to construct from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

Type container for exponents with ratio different than `1`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbolic&lowbar;expression&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    &sol;&ast; implementation-defined &ast;&sol; F,
    int Num,
    int Den&period;&period;&period;&gt;
requires (detail&colon;&colon;valid&lowbar;ratio&lt;Num, Den&period;&period;&period;&gt; &amp;&amp; detail&colon;&colon;positive&lowbar;ratio&lt;Num, Den&period;&period;&period;&gt; &amp;&amp; !detail&colon;&colon;ratio&lowbar;one&lt;Num, Den&period;&period;&period;&gt;)
struct power final
----

== Types

[cols=1]
|===
| Name
| link:#mp_units-power-_factor_[`&lowbar;factor&lowbar;`] 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-power-_exponent_[`&lowbar;exponent&lowbar;`] 
|===

== Description

Ratio must be mathematically valid and non&hyphen;negative&period; Negative exponents are passed to `per&lt;&period;&period;&period;&gt;` with inverted sign (as positive exponents)&period;

[NOTE]
`Den` is an optional parameter to shorten the types presented to the user in the case when `Den` equals `1`&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *F*
| factor to be raised to specified power
| *Num*
| Power ratio numerator
| *Den*
| &lsqb;optional&rsqb; Power ration denominator
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbolic&lowbar;expression&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;factor&lowbar; = F;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbolic&lowbar;expression&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
&sol;&ast; implementation-defined &ast;&sol; &lowbar;exponent&lowbar; = &lcub;Num, Den&period;&period;&period;&rcub;;
----

A prefixed unit

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-symbol_text-032[symbol&lowbar;text] Symbol,
    link:#mp_units-UnitMagnitude[UnitMagnitude] auto M,
    link:#mp_units-PrefixableUnit[PrefixableUnit] auto U&gt;
requires (!Symbol&period;empty())
struct prefixed&lowbar;unit
    : ::&lowbar;base&lowbar;type&lowbar;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `::&lowbar;base&lowbar;type&lowbar;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-prefixed_unit-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-prefixed_unit-_symbol_[`&lowbar;symbol&lowbar;`] 
|===

== Description

Defines a new unit that is a scaled version of another unit with the scaling factor specified by a predefined prefix&period;

For example&colon;

[,cpp]
----
{.cpp}
 template<PrefixableUnit auto U>
 struct kilo_ : prefixed_unit<"k", mag_power<10, 3>, U> {};

 template<PrefixableUnit auto U>
 constexpr kilo_<U> kilo;

 inline constexpr auto kilogram = si::kilo<gram>;
----
== Template Parameters

[cols=2]
|===
| Name
| Description
| *Symbol*
| a prefix text to prepend to a unit symbol
| *M*
| scaling factor of the prefix
| *U*
| a named unit to be prefixed
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = link:#mp_units-prefixed_unit[prefixed&lowbar;unit];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;symbol&lowbar; = Symbol &plus; U&period;&lowbar;symbol&lowbar;;
----

A quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] auto R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R)&gt;] Rep = double&gt;
class quantity;
----

== Types

[cols=1]
|===
| Name
| link:#mp_units-quantity-01-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-quantity-01-2constructor-06a[`quantity`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-quantity-01-2destructor[`&#126;quantity`] [.small]#[destructor]#
| Destructor
| link:#mp_units-quantity-01-operator_assign-0ed[`operator&equals;`] 
| Assignment operators
| link:#mp_units-quantity-01-force_in-022[`force&lowbar;in`] 
| 
| link:#mp_units-quantity-01-force_numerical_value_in[`force&lowbar;numerical&lowbar;value&lowbar;in`] 
| 
| link:#mp_units-quantity-01-in-08[`in`] 
| 
| link:#mp_units-quantity-01-numerical_value_in[`numerical&lowbar;value&lowbar;in`] 
| 
| link:#mp_units-quantity-01-numerical_value_ref_in-0d[`numerical&lowbar;value&lowbar;ref&lowbar;in`]  [.small]#[deleted]#
| 
| link:#mp_units-quantity-01-operator_mod_eq[`operator%&equals;`] 
| Modulus assignment operator
| link:#mp_units-quantity-01-operator_star_eq-01[`operator&ast;&equals;`] 
| Multiplication assignment operators
| link:#mp_units-quantity-01-operator_plus[`operator&plus;`] 
| 
| link:#mp_units-quantity-01-operator_inc-0e[`operator&plus;&plus;`] 
| Increment operators
| link:#mp_units-quantity-01-operator_plus_eq[`operator&plus;&equals;`] 
| Addition assignment operator
| link:#mp_units-quantity-01-operator_minus[`operator&hyphen;`] 
| 
| link:#mp_units-quantity-01-operator_dec-07[`operator&hyphen;&hyphen;`] 
| Decrement operators
| link:#mp_units-quantity-01-operator_minus_eq[`operator&hyphen;&equals;`] 
| Subtraction assignment operator
| link:#mp_units-quantity-01-operator_slash_eq-04[`operator&sol;&equals;`] 
| Division assignment operators
| link:#mp_units-quantity-01-2conversion-0a[`operator `] 
| Conversion operators
|===

== Static Member Functions

[cols=1]
|===
| Name
| link:#mp_units-quantity-01-max[`max`] 
| link:#mp_units-quantity-01-min[`min`] 
| link:#mp_units-quantity-01-zero[`zero`] 
|===

== Data Members

[cols=2]
|===
| Name
| Description
| link:#mp_units-quantity-01-numerical_value_is_an_implementation_detail_[`numerical&lowbar;value&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;`] 
| needs to be public for a structural type
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-quantity-01-dimension[`dimension`] 
| link:#mp_units-quantity-01-quantity_spec[`quantity&lowbar;spec`] 
| link:#mp_units-quantity-01-reference[`reference`] 
| link:#mp_units-quantity-01-unit[`unit`] 
|===

== Friends

[cols=2]
|===
| Name
| Description
| `link:#mp_units-operator_3way-0c3[mp&lowbar;units::operator&lt;&equals;&gt;]`
| Three&hyphen;way comparison operator
| `link:#mp_units-operator_3way-01[mp&lowbar;units::operator&lt;&equals;&gt;]`
| Three&hyphen;way comparison operator
| `link:#mp_units-operator_eq-037[mp&lowbar;units::operator&equals;&equals;]`
| Equality operator
| `link:#mp_units-operator_eq-01[mp&lowbar;units::operator&equals;&equals;]`
| Equality operator
| `link:#mp_units-operator_slash-07[mp&lowbar;units::operator&sol;]`
| 
| `link:#mp_units-operator_slash-03f[mp&lowbar;units::operator&sol;]`
| 
| `link:#mp_units-operator_slash-04[mp&lowbar;units::operator&sol;]`
| 
| `link:#mp_units-operator_star-0a[mp&lowbar;units::operator&ast;]`
| 
| `link:#mp_units-operator_star-002[mp&lowbar;units::operator&ast;]`
| 
| `link:#mp_units-operator_star-04[mp&lowbar;units::operator&ast;]`
| 
| `link:#mp_units-operator_mod-0c9[mp&lowbar;units::operator%]`
| 
| `link:#mp_units-operator_mod-0c5[mp&lowbar;units::operator%]`
| 
| `link:#mp_units-operator_mod-0d[mp&lowbar;units::operator%]`
| 
| `link:#mp_units-operator_minus-0b[mp&lowbar;units::operator&hyphen;]`
| 
| `link:#mp_units-operator_minus-09[mp&lowbar;units::operator&hyphen;]`
| 
| `link:#mp_units-operator_minus-0d[mp&lowbar;units::operator&hyphen;]`
| 
| `link:#mp_units-operator_plus-04[mp&lowbar;units::operator&plus;]`
| 
| `link:#mp_units-operator_plus-0b7[mp&lowbar;units::operator&plus;]`
| 
| `link:#mp_units-operator_plus-0b5[mp&lowbar;units::operator&plus;]`
| 
|===

== Non-Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-abs[`abs`]
| Computes the absolute value of a quantity
| link:#mp_units-cbrt-0d[`cbrt`]
| Computes the cubic root of a quantity
| link:#mp_units-ceil[`ceil`]
| Computes the smallest quantity with integer representation and unit type To with its number not less than q
| link:#mp_units-epsilon[`epsilon`]
| Returns the epsilon of the quantity
| link:#mp_units-exp[`exp`]
| Computes Euler&apos;s raised to the given power
| link:#mp_units-floor[`floor`]
| Computes the largest quantity with integer representation and unit type To with its number not greater than q
| link:#mp_units-fma-09[`fma`]
| Computes the fma of 3 quantities
| link:#mp_units-fma-0a[`fma`]
| Computes the fma of 2 quantities and a quantity point
| link:#mp_units-fmod[`fmod`]
| Computes the floating&hyphen;point remainder of the division operation x &sol; y&period;
| link:#mp_units-hypot-08[`hypot`]
| Computes the square root of the sum of the squares of x, y, and z, without undue overflow or underflow at intermediate stages of the computation
| link:#mp_units-hypot-0e[`hypot`]
| Computes the square root of the sum of the squares of x and y, without undue overflow or underflow at intermediate stages of the computation
| link:#mp_units-inverse-09[`inverse`]
| Computes the inverse of a quantity in a provided unit
| link:#mp_units-isfinite-0d[`isfinite`]
| Determines if a quantity is finite&period;
| link:#mp_units-isinf-0f[`isinf`]
| Determines if a quantity is infinite&period;
| link:#mp_units-isnan-00[`isnan`]
| Determines if a quantity is a nan&period;
| link:#mp_units-pow-05[`pow`]
| Computes the value of a quantity raised to the `Num&sol;Den` power
| link:#mp_units-remainder[`remainder`]
| Computes the IEEE remainder of the floating point division operation x &sol; y&period;
| link:#mp_units-round[`round`]
| Computes the nearest quantity with integer representation and unit type `To` to `q`
| link:#mp_units-sqrt-0b[`sqrt`]
| Computes the square root of a quantity
| link:#mp_units-value_cast-028[`value&lowbar;cast`]
| Explicit cast of a quantity&apos;s representation type
|===

== Description

Property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed by means of a number and a reference&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *R*
| a reference of the quantity providing all information about quantity properties
| *Rep*
| a type to be used to represent values of a quantity
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity-01-2constructor-062[quantity]() = default;
----

[.small]#link:#mp_units-quantity-01-2constructor-062[_» more&period;&period;&period;_]#

Copy constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity-01-2constructor-000[quantity](link:#mp_units-quantity-01[quantity] const& other) = default;
----

[.small]#link:#mp_units-quantity-01-2constructor-000[_» more&period;&period;&period;_]#

Copy constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;QuantityConstructibleFrom&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;
constexpr
explicit(!implicitly&lowbar;convertible(get&lowbar;quantity&lowbar;spec(R2), quantity&lowbar;spec) &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;Rep2, rep&gt;)
link:#mp_units-quantity-01-2constructor-02[quantity](link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& q);
----

[.small]#link:#mp_units-quantity-01-2constructor-02[_» more&period;&period;&period;_]#

Move constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity-01-2constructor-01[quantity](link:#mp_units-quantity-01[quantity]&& other) = default;
----

[.small]#link:#mp_units-quantity-01-2constructor-01[_» more&period;&period;&period;_]#

Construct from `Q`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityLike[QuantityLike] Q&gt;
requires detail&colon;&colon;QuantityConstructibleFrom&lt;quantity, detail&colon;&colon;quantity&lowbar;like&lowbar;type&lt;Q&gt;&gt;
constexpr
explicit(quantity&lowbar;like&lowbar;traits&lt;Q&gt;&colon;&colon;explicit&lowbar;import &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;detail&colon;&colon;quantity&lowbar;like&lowbar;type&lt;Q&gt;, quantity&lt;R, Rep&gt;&gt;)
link:#mp_units-quantity-01-2constructor-07[quantity](Q const& q);
----

[.small]#link:#mp_units-quantity-01-2constructor-07[_» more&period;&period;&period;_]#

Construct from `FwdValue`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename FwdValue&gt;
requires detail&colon;&colon;DimensionlessOne&lt;reference&gt; &amp;&amp; detail&colon;&colon;ValuePreservingConstruction&lt;rep, FwdValue&gt;
constexpr
explicit(!std&colon;&colon;convertible&lowbar;to&lt;FwdValue, rep&gt;)
link:#mp_units-quantity-01-2constructor-0a[quantity](FwdValue&& val);
----

[.small]#link:#mp_units-quantity-01-2constructor-0a[_» more&period;&period;&period;_]#

Constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdValue,
    link:#mp_units-Reference[Reference] R2&gt;
requires (!equivalent(unit, get&lowbar;unit(R2&lcub;&rcub;))) &amp;&amp;
            detail&colon;&colon;QuantityConstructibleFrom&lt;quantity, quantity&lt;R2&lcub;&rcub;, std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;FwdValue&gt;&gt;&gt;
constexpr
link:#mp_units-quantity-01-2constructor-03[quantity](
    FwdValue&& val,
    R2);
----

[.small]#link:#mp_units-quantity-01-2constructor-03[_» more&period;&period;&period;_]#

Constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdValue,
    link:#mp_units-Reference[Reference] R2&gt;
requires (equivalent(unit, get&lowbar;unit(R2&lcub;&rcub;))) &amp;&amp; detail&colon;&colon;ValuePreservingConstruction&lt;rep, FwdValue&gt;
constexpr
link:#mp_units-quantity-01-2constructor-009[quantity](
    FwdValue&& val,
    R2);
----

[.small]#link:#mp_units-quantity-01-2constructor-009[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
quantity() = default;
----

Copy constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
quantity(link:#mp_units-quantity-01[quantity] const& other) = default;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy construct from
|===

Copy constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;QuantityConstructibleFrom&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;
constexpr
explicit(!implicitly&lowbar;convertible(get&lowbar;quantity&lowbar;spec(R2), quantity&lowbar;spec) &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;Rep2, rep&gt;)
quantity(link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& q);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| The object to copy construct from
|===

Move constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
quantity(link:#mp_units-quantity-01[quantity]&& other) = default;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to move construct from
|===

Construct from `Q`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityLike[QuantityLike] Q&gt;
requires detail&colon;&colon;QuantityConstructibleFrom&lt;quantity, detail&colon;&colon;quantity&lowbar;like&lowbar;type&lt;Q&gt;&gt;
constexpr
explicit(quantity&lowbar;like&lowbar;traits&lt;Q&gt;&colon;&colon;explicit&lowbar;import &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;detail&colon;&colon;quantity&lowbar;like&lowbar;type&lt;Q&gt;, quantity&lt;R, Rep&gt;&gt;)
quantity(Q const& q);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| The object to copy construct from
|===

Construct from `FwdValue`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename FwdValue&gt;
requires detail&colon;&colon;DimensionlessOne&lt;reference&gt; &amp;&amp; detail&colon;&colon;ValuePreservingConstruction&lt;rep, FwdValue&gt;
constexpr
explicit(!std&colon;&colon;convertible&lowbar;to&lt;FwdValue, rep&gt;)
quantity(FwdValue&& val);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *val*
| The object to move construct from
|===

Constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdValue,
    link:#mp_units-Reference[Reference] R2&gt;
requires (!equivalent(unit, get&lowbar;unit(R2&lcub;&rcub;))) &amp;&amp;
            detail&colon;&colon;QuantityConstructibleFrom&lt;quantity, quantity&lt;R2&lcub;&rcub;, std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;FwdValue&gt;&gt;&gt;
constexpr
quantity(
    FwdValue&& val,
    R2);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *val*
| The object to move construct from
|===

Constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdValue,
    link:#mp_units-Reference[Reference] R2&gt;
requires (equivalent(unit, get&lowbar;unit(R2&lcub;&rcub;))) &amp;&amp; detail&colon;&colon;ValuePreservingConstruction&lt;rep, FwdValue&gt;
constexpr
quantity(
    FwdValue&& val,
    R2);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *val*
| The object to move construct from
|===

Destructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&#126;quantity() = default;
----

Assignment operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

Copy assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity-01[quantity]&
link:#mp_units-quantity-01-operator_assign-0eb[operator&equals;](link:#mp_units-quantity-01[quantity] const& other) = default;
----

[.small]#link:#mp_units-quantity-01-operator_assign-0eb[_» more&period;&period;&period;_]#

Move assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity-01[quantity]&
link:#mp_units-quantity-01-operator_assign-05[operator&equals;](link:#mp_units-quantity-01[quantity]&& other) = default;
----

[.small]#link:#mp_units-quantity-01-operator_assign-05[_» more&period;&period;&period;_]#

Assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename FwdValue&gt;
requires detail&colon;&colon;DimensionlessOne&lt;reference&gt; &amp;&amp; detail&colon;&colon;ValuePreservingAssignment&lt;rep, FwdValue&gt;
constexpr
link:#mp_units-quantity-01[quantity]&
link:#mp_units-quantity-01-operator_assign-01[operator&equals;](FwdValue&& val);
----

[.small]#link:#mp_units-quantity-01-operator_assign-01[_» more&period;&period;&period;_]#

Copy assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity-01[quantity]&
operator&equals;(link:#mp_units-quantity-01[quantity] const& other) = default;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy assign from
|===

Move assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity-01[quantity]&
operator&equals;(link:#mp_units-quantity-01[quantity]&& other) = default;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to move assign from
|===

Assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename FwdValue&gt;
requires detail&colon;&colon;DimensionlessOne&lt;reference&gt; &amp;&amp; detail&colon;&colon;ValuePreservingAssignment&lt;rep, FwdValue&gt;
constexpr
link:#mp_units-quantity-01[quantity]&
operator&equals;(FwdValue&& val);
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *val*
| The object to move assign from
|===

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;ToRep, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity-01-force_in-020[force&lowbar;in]() const;
----

[.small]#link:#mp_units-quantity-01-force_in-020[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;SaneScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity-01-force_in-0e[force&lowbar;in](ToU) const;
----

[.small]#link:#mp_units-quantity-01-force_in-0e[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep,
    &sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;ToRep, rep&gt; &amp;&amp; detail&colon;&colon;SaneScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity-01-force_in-021[force&lowbar;in](ToU) const;
----

[.small]#link:#mp_units-quantity-01-force_in-021[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;ToRep, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
force&lowbar;in() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;SaneScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
force&lowbar;in(ToU) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep,
    &sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;ToRep, rep&gt; &amp;&amp; detail&colon;&colon;SaneScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
force&lowbar;in(ToU) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; U&gt;
requires detail&colon;&colon;SaneScaling&lt;unit, U&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01-rep[rep]
force&lowbar;numerical&lowbar;value&lowbar;in(U) const noexcept;
----

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep&gt;
requires detail&colon;&colon;ValuePreservingConstruction&lt;ToRep, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity-01-in-0d[in]() const;
----

[.small]#link:#mp_units-quantity-01-in-0d[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;ValuePreservingScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity-01-in-07[in](ToU) const;
----

[.small]#link:#mp_units-quantity-01-in-07[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep,
    &sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;ValuePreservingConstruction&lt;ToRep, rep&gt; &amp;&amp;
             detail&colon;&colon;ValuePreservingConversion&lt;unit, rep, ToU&lcub;&rcub;, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity-01-in-0e[in](ToU) const;
----

[.small]#link:#mp_units-quantity-01-in-0e[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep&gt;
requires detail&colon;&colon;ValuePreservingConstruction&lt;ToRep, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
in() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;ValuePreservingScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
in(ToU) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep,
    &sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;ValuePreservingConstruction&lt;ToRep, rep&gt; &amp;&amp;
             detail&colon;&colon;ValuePreservingConversion&lt;unit, rep, ToU&lcub;&rcub;, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
in(ToU) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; U&gt;
requires detail&colon;&colon;ValuePreservingScaling&lt;unit, U&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01-rep[rep]
numerical&lowbar;value&lowbar;in(U) const noexcept;
----

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Unit[Unit] U&gt;
requires (equivalent(U&lcub;&rcub;, unit))
constexpr
link:#mp_units-quantity-01-rep[rep] const&&
link:#mp_units-quantity-01-numerical_value_ref_in-08[numerical&lowbar;value&lowbar;ref&lowbar;in](U) const &amp;&amp; noexcept = delete;
----

[.small]#link:#mp_units-quantity-01-numerical_value_ref_in-08[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Unit[Unit] U&gt;
requires (equivalent(U&lcub;&rcub;, unit))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01-rep[rep] const&
link:#mp_units-quantity-01-numerical_value_ref_in-06[numerical&lowbar;value&lowbar;ref&lowbar;in](U) const &amp; noexcept;
----

[.small]#link:#mp_units-quantity-01-numerical_value_ref_in-06[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Unit[Unit] U&gt;
requires (equivalent(U&lcub;&rcub;, unit))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01-rep[rep]&
link:#mp_units-quantity-01-numerical_value_ref_in-03[numerical&lowbar;value&lowbar;ref&lowbar;in](U) &amp; noexcept;
----

[.small]#link:#mp_units-quantity-01-numerical_value_ref_in-03[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Unit[Unit] U&gt;
requires (equivalent(U&lcub;&rcub;, unit))
constexpr
link:#mp_units-quantity-01-rep[rep] const&&
numerical&lowbar;value&lowbar;ref&lowbar;in(U) const &amp;&amp; noexcept = delete;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Unit[Unit] U&gt;
requires (equivalent(U&lcub;&rcub;, unit))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01-rep[rep] const&
numerical&lowbar;value&lowbar;ref&lowbar;in(U) const &amp; noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Unit[Unit] U&gt;
requires (equivalent(U&lcub;&rcub;, unit))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01-rep[rep]&
numerical&lowbar;value&lowbar;ref&lowbar;in(U) &amp; noexcept;
----

Modulus assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R2,
    typename Rep2&gt;
requires (!treat&lowbar;as&lowbar;floating&lowbar;point&lt;rep&gt;) &amp;&amp; (implicitly&lowbar;convertible(get&lowbar;quantity&lowbar;spec(R2), quantity&lowbar;spec)) &amp;&amp;
            detail&colon;&colon;ValuePreservingConversion&lt;get&lowbar;unit(R2), Rep2, unit, rep&gt; &amp;&amp; requires(rep&amp; a, const Rep2 b) &lcub;
              &lcub; a %&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
            &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
operator%&equals;(link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& other) &amp;;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The right operand
|===

Multiplication assignment operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

Multiplication assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; Q2&gt;
requires detail&colon;&colon;ScalarValuePreservingTo&lt;typename Q2&colon;&colon;rep, rep&gt; &amp;&amp; requires(rep&amp; a, const Q2&colon;&colon;rep b) &lcub;
      &lcub; a &ast;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
link:#mp_units-quantity-01-operator_star_eq-0c[operator&ast;&equals;](Q2 const& other) &amp;;
----

[.small]#link:#mp_units-quantity-01-operator_star_eq-0c[_» more&period;&period;&period;_]#

Multiplication assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; Value&gt;
requires requires(rep&amp; a, const Value b) &lcub;
      &lcub; a &ast;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
link:#mp_units-quantity-01-operator_star_eq-07[operator&ast;&equals;](Value const& val) &amp;;
----

[.small]#link:#mp_units-quantity-01-operator_star_eq-07[_» more&period;&period;&period;_]#

Multiplication assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; Q2&gt;
requires detail&colon;&colon;ScalarValuePreservingTo&lt;typename Q2&colon;&colon;rep, rep&gt; &amp;&amp; requires(rep&amp; a, const Q2&colon;&colon;rep b) &lcub;
      &lcub; a &ast;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
operator&ast;&equals;(Q2 const& other) &amp;;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The right operand
|===

Multiplication assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; Value&gt;
requires requires(rep&amp; a, const Value b) &lcub;
      &lcub; a &ast;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
operator&ast;&equals;(Value const& val) &amp;;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *val*
| The right operand
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
operator&plus;() const
requires requires(const rep v) &lcub;
      &lcub; &plus;v &rcub; &hyphen;&gt; std&colon;&colon;common&lowbar;with&lt;rep&gt;&semi;
    &rcub;;
----

Increment operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

Increment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-quantity-01[quantity]&
link:#mp_units-quantity-01-operator_inc-02[operator&plus;&plus;]() &amp;
requires requires(rep&amp; v) &lcub;
      &lcub; &plus;&plus;v &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;;
----

[.small]#link:#mp_units-quantity-01-operator_inc-02[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity-01-operator_inc-08[operator&plus;&plus;](int)
requires requires(rep&amp; v) &lcub;
      &lcub; v&plus;&plus; &rcub; &hyphen;&gt; std&colon;&colon;common&lowbar;with&lt;rep&gt;&semi;
    &rcub;;
----

[.small]#link:#mp_units-quantity-01-operator_inc-08[_» more&period;&period;&period;_]#

Increment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-quantity-01[quantity]&
operator&plus;&plus;() &amp;
requires requires(rep&amp; v) &lcub;
      &lcub; &plus;&plus;v &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;;
----

== Return Value

Reference to the current object

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
operator&plus;&plus;(int)
requires requires(rep&amp; v) &lcub;
      &lcub; v&plus;&plus; &rcub; &hyphen;&gt; std&colon;&colon;common&lowbar;with&lt;rep&gt;&semi;
    &rcub;;
----

Addition assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R2,
    typename Rep2&gt;
requires (implicitly&lowbar;convertible(get&lowbar;quantity&lowbar;spec(R2), quantity&lowbar;spec)) &amp;&amp;
            detail&colon;&colon;ValuePreservingConversion&lt;get&lowbar;unit(R2), Rep2, unit, rep&gt; &amp;&amp; requires(rep&amp; a, const Rep2 b) &lcub;
              &lcub; a &plus;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
            &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
operator&plus;&equals;(link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& other) &amp;;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The right operand
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
operator&hyphen;() const
requires requires(const rep v) &lcub;
      &lcub; &hyphen;v &rcub; &hyphen;&gt; std&colon;&colon;common&lowbar;with&lt;rep&gt;&semi;
    &rcub;;
----

Decrement operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

Decrement operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-quantity-01[quantity]&
link:#mp_units-quantity-01-operator_dec-0a[operator&hyphen;&hyphen;]() &amp;
requires requires(rep&amp; v) &lcub;
      &lcub; &hyphen;&hyphen;v &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;;
----

[.small]#link:#mp_units-quantity-01-operator_dec-0a[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity-01-operator_dec-01[operator&hyphen;&hyphen;](int)
requires requires(rep&amp; v) &lcub;
      &lcub; v&hyphen;&hyphen; &rcub; &hyphen;&gt; std&colon;&colon;common&lowbar;with&lt;rep&gt;&semi;
    &rcub;;
----

[.small]#link:#mp_units-quantity-01-operator_dec-01[_» more&period;&period;&period;_]#

Decrement operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-quantity-01[quantity]&
operator&hyphen;&hyphen;() &amp;
requires requires(rep&amp; v) &lcub;
      &lcub; &hyphen;&hyphen;v &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;;
----

== Return Value

Reference to the current object

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
operator&hyphen;&hyphen;(int)
requires requires(rep&amp; v) &lcub;
      &lcub; v&hyphen;&hyphen; &rcub; &hyphen;&gt; std&colon;&colon;common&lowbar;with&lt;rep&gt;&semi;
    &rcub;;
----

Subtraction assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R2,
    typename Rep2&gt;
requires (implicitly&lowbar;convertible(get&lowbar;quantity&lowbar;spec(R2), quantity&lowbar;spec)) &amp;&amp;
            detail&colon;&colon;ValuePreservingConversion&lt;get&lowbar;unit(R2), Rep2, unit, rep&gt; &amp;&amp; requires(rep&amp; a, const Rep2 b) &lcub;
              &lcub; a &hyphen;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
            &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
operator&hyphen;&equals;(link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& other) &amp;;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The right operand
|===

Division assignment operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

Division assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; Q2&gt;
requires detail&colon;&colon;ScalarValuePreservingTo&lt;typename Q2&colon;&colon;rep, rep&gt; &amp;&amp; requires(rep&amp; a, const Q2&colon;&colon;rep b) &lcub;
      &lcub; a &sol;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
link:#mp_units-quantity-01-operator_slash_eq-0a[operator&sol;&equals;](Q2 const& rhs) &amp;;
----

[.small]#link:#mp_units-quantity-01-operator_slash_eq-0a[_» more&period;&period;&period;_]#

Division assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; Value&gt;
requires requires(rep&amp; a, const Value b) &lcub;
      &lcub; a &sol;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
link:#mp_units-quantity-01-operator_slash_eq-0d[operator&sol;&equals;](Value const& val) &amp;;
----

[.small]#link:#mp_units-quantity-01-operator_slash_eq-0d[_» more&period;&period;&period;_]#

Division assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; Q2&gt;
requires detail&colon;&colon;ScalarValuePreservingTo&lt;typename Q2&colon;&colon;rep, rep&gt; &amp;&amp; requires(rep&amp; a, const Q2&colon;&colon;rep b) &lcub;
      &lcub; a &sol;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
operator&sol;&equals;(Q2 const& rhs) &amp;;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *rhs*
| The right operand
|===

Division assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; Value&gt;
requires requires(rep&amp; a, const Value b) &lcub;
      &lcub; a &sol;&equals; b &rcub; &hyphen;&gt; std&colon;&colon;same&lowbar;as&lt;rep&amp;&gt;&semi;
    &rcub;
constexpr
link:#mp_units-quantity-01[quantity]&
operator&sol;&equals;(Value const& val) &amp;;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *val*
| The right operand
|===

Conversion operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

Conversion to `Q&lowbar;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q&lowbar;,
    link:#mp_units-QuantityLike[QuantityLike] Q = std::remove&lowbar;cvref&lowbar;t&lt;Q&lowbar;&gt;&gt;
requires detail&colon;&colon;QuantityConstructibleFrom&lt;detail&colon;&colon;quantity&lowbar;like&lowbar;type&lt;Q&gt;, quantity&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
explicit(quantity&lowbar;like&lowbar;traits&lt;Q&gt;&colon;&colon;explicit&lowbar;export &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;quantity&lt;R, Rep&gt;, detail&colon;&colon;quantity&lowbar;like&lowbar;type&lt;Q&gt;&gt;)
operator Q&lowbar;() const noexcept(noexcept(quantity&lowbar;like&lowbar;traits&lt;Q&gt;&colon;&colon;from&lowbar;numerical&lowbar;value(this&hyphen;&gt;numerical&lowbar;value&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;)) &amp;&amp; std&colon;&colon;is&lowbar;nothrow&lowbar;copy&lowbar;constructible&lowbar;v&lt;rep&gt;);
----

[.small]#link:#mp_units-quantity-01-2conversion-0d[_» more&period;&period;&period;_]#

Conversion to `V&lowbar;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename V&lowbar;,
    std::constructible&lowbar;from&lt;rep&gt; Value = std::remove&lowbar;cvref&lowbar;t&lt;V&lowbar;&gt;&gt;
requires detail&colon;&colon;DimensionlessOne&lt;reference&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
explicit
operator V&lowbar;() const &amp; noexcept;
----

[.small]#link:#mp_units-quantity-01-2conversion-00[_» more&period;&period;&period;_]#

Conversion to `Q&lowbar;`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q&lowbar;,
    link:#mp_units-QuantityLike[QuantityLike] Q = std::remove&lowbar;cvref&lowbar;t&lt;Q&lowbar;&gt;&gt;
requires detail&colon;&colon;QuantityConstructibleFrom&lt;detail&colon;&colon;quantity&lowbar;like&lowbar;type&lt;Q&gt;, quantity&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
explicit(quantity&lowbar;like&lowbar;traits&lt;Q&gt;&colon;&colon;explicit&lowbar;export &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;quantity&lt;R, Rep&gt;, detail&colon;&colon;quantity&lowbar;like&lowbar;type&lt;Q&gt;&gt;)
operator Q&lowbar;() const noexcept(noexcept(quantity&lowbar;like&lowbar;traits&lt;Q&gt;&colon;&colon;from&lowbar;numerical&lowbar;value(this&hyphen;&gt;numerical&lowbar;value&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;)) &amp;&amp; std&colon;&colon;is&lowbar;nothrow&lowbar;copy&lowbar;constructible&lowbar;v&lt;rep&gt;);
----

== Return Value

The object converted to `Q&lowbar;`

Conversion to `V&lowbar;`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename V&lowbar;,
    std::constructible&lowbar;from&lt;rep&gt; Value = std::remove&lowbar;cvref&lowbar;t&lt;V&lowbar;&gt;&gt;
requires detail&colon;&colon;DimensionlessOne&lt;reference&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
explicit
operator V&lowbar;() const &amp; noexcept;
----

== Return Value

The object converted to `V&lowbar;`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
static
link:#mp_units-quantity-01[quantity]
max() noexcept
requires requires &lcub; representation&lowbar;values&lt;rep&gt;&colon;&colon;max()&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
static
link:#mp_units-quantity-01[quantity]
min() noexcept
requires requires &lcub; representation&lowbar;values&lt;rep&gt;&colon;&colon;min()&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
static
link:#mp_units-quantity-01[quantity]
zero() noexcept
requires requires &lcub; representation&lowbar;values&lt;rep&gt;&colon;&colon;zero()&semi; &rcub;;
----

needs to be public for a structural type

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
Rep numerical&lowbar;value&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-Dimension[Dimension] auto dimension = quantity&lowbar;spec&period;dimension;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-QuantitySpec[QuantitySpec] auto quantity&lowbar;spec = get&lowbar;quantity&lowbar;spec(reference);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-Reference[Reference] auto reference = R;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-Unit[Unit] auto unit = get&lowbar;unit(reference);
----

Provides support for external quantity&hyphen;like types

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
struct quantity&lowbar;like&lowbar;traits;
----

== Description

The type trait should provide the `reference` object, a type alias `rep,` and static member functions `to&lowbar;numerical&lowbar;value(T)` that returns the raw value of the quantity and `from&lowbar;numerical&lowbar;value(rep)` that returns `T` from `rep&period;`

If the following expression is `true,` the specified conversion will be explicit&colon; &hyphen; `explicit&lowbar;import` for the conversion from `T` to a `quantity` type, &hyphen; `explicit&lowbar;export` for the conversion from a `quantity` type to `T&period;`

Usage example can be found in `mp&hyphen;units&sol;systems&sol;si&sol;chrono&period;h` header file&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *T*
| the type to provide support for
|===

A quantity point

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] auto R,
    link:#mp_units-PointOriginFor[PointOriginFor&lt;get&lowbar;quantity&lowbar;spec(R)&gt;] auto PO = default&lowbar;point&lowbar;origin(R),
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R)&gt;] Rep = double&gt;
class quantity&lowbar;point;
----

== Types

[cols=1]
|===
| Name
| link:#mp_units-quantity_point-08-quantity_type[`quantity&lowbar;type`] 
| link:#mp_units-quantity_point-08-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-quantity_point-08-2constructor-075[`quantity&lowbar;point`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-quantity_point-08-2destructor[`&#126;quantity&lowbar;point`] [.small]#[destructor]#
| Destructor
| link:#mp_units-quantity_point-08-operator_assign-04[`operator&equals;`] 
| Assignment operators
| link:#mp_units-quantity_point-08-force_in-03[`force&lowbar;in`] 
| 
| link:#mp_units-quantity_point-08-in-0ac[`in`] 
| 
| link:#mp_units-quantity_point-08-operator_inc-0d[`operator&plus;&plus;`] 
| Increment operators
| link:#mp_units-quantity_point-08-operator_plus_eq[`operator&plus;&equals;`] 
| Addition assignment operator
| link:#mp_units-quantity_point-08-operator_dec-0f[`operator&hyphen;&hyphen;`] 
| Decrement operators
| link:#mp_units-quantity_point-08-operator_minus_eq[`operator&hyphen;&equals;`] 
| Subtraction assignment operator
| link:#mp_units-quantity_point-08-point_for[`point&lowbar;for`] 
| 
| link:#mp_units-quantity_point-08-quantity_from-00[`quantity&lowbar;from`] 
| 
| link:#mp_units-quantity_point-08-quantity_from_zero[`quantity&lowbar;from&lowbar;zero`] 
| 
| link:#mp_units-quantity_point-08-quantity_ref_from-05[`quantity&lowbar;ref&lowbar;from`]  [.small]#[deleted]#
| 
| link:#mp_units-quantity_point-08-2conversion-04[`operator `] 
| Conversion operators
|===

== Static Member Functions

[cols=1]
|===
| Name
| link:#mp_units-quantity_point-08-max[`max`] 
| link:#mp_units-quantity_point-08-min[`min`] 
|===

== Data Members

[cols=1]
|===
| Name
| link:#mp_units-quantity_point-08-quantity_from_origin_is_an_implementation_detail_[`quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;`] 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-quantity_point-08-absolute_point_origin[`absolute&lowbar;point&lowbar;origin`] 
| link:#mp_units-quantity_point-08-dimension[`dimension`] 
| link:#mp_units-quantity_point-08-point_origin[`point&lowbar;origin`] 
| link:#mp_units-quantity_point-08-quantity_spec[`quantity&lowbar;spec`] 
| link:#mp_units-quantity_point-08-reference[`reference`] 
| link:#mp_units-quantity_point-08-unit[`unit`] 
|===

== Friends

[cols=2]
|===
| Name
| Description
| `link:#mp_units-operator_3way-0c8[mp&lowbar;units::operator&lt;&equals;&gt;]`
| Three&hyphen;way comparison operator
| `link:#mp_units-operator_eq-0ca[mp&lowbar;units::operator&equals;&equals;]`
| Equality operator
| `link:#mp_units-operator_minus-0e[mp&lowbar;units::operator&hyphen;]`
| 
| `link:#mp_units-operator_minus-01[mp&lowbar;units::operator&hyphen;]`
| 
| `link:#mp_units-operator_minus-06[mp&lowbar;units::operator&hyphen;]`
| 
| `link:#mp_units-operator_minus-05[mp&lowbar;units::operator&hyphen;]`
| 
| `link:#mp_units-operator_plus-00[mp&lowbar;units::operator&plus;]`
| 
| `link:#mp_units-operator_plus-0a5[mp&lowbar;units::operator&plus;]`
| 
|===

== Non-Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-isfinite-0b[`isfinite`]
| Determines if a quantity point is finite&period;
| link:#mp_units-isinf-04[`isinf`]
| Determines if a quantity point is infinite&period;
| link:#mp_units-isnan-082[`isnan`]
| Determines if a quantity point is a nan&period;
| link:#mp_units-lerp[`lerp`]
| Linear interpolation or extrapolation
| link:#mp_units-midpoint[`midpoint`]
| Computes the midpoint of two points
| link:#mp_units-value_cast-021[`value&lowbar;cast`]
| Explicit cast of a quantity point&apos;s representation type
|===

== Description

An absolute quantity measured from an origin&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *R*
| a reference of the quantity point providing all information about quantity properties
| *PO*
| a type that represents the origin point from which the quantity point is measured from
| *Rep*
| a type to be used to represent values of a quantity point
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using quantity&lowbar;type = link:#mp_units-quantity-01[quantity&lt;reference, Rep&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity_point-08-2constructor-07e[quantity&lowbar;point]() = default;
----

[.small]#link:#mp_units-quantity_point-08-2constructor-07e[_» more&period;&period;&period;_]#

Copy constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity_point-08-2constructor-047[quantity&lowbar;point](link:#mp_units-quantity_point-08[quantity&lowbar;point] const& other) = default;
----

[.small]#link:#mp_units-quantity_point-08-2constructor-047[_» more&period;&period;&period;_]#

Move constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity_point-08-2constructor-0d[quantity&lowbar;point](link:#mp_units-quantity_point-08[quantity&lowbar;point]&& other) = default;
----

[.small]#link:#mp_units-quantity_point-08-2constructor-0d[_» more&period;&period;&period;_]#

Construct from `QP`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityPointLike[QuantityPointLike] QP&gt;
requires (quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;point&lowbar;origin &equals;&equals; point&lowbar;origin) &amp;&amp;
            std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference,
                                                            typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;
constexpr
explicit(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;explicit&lowbar;import &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference, typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;, quantity&lowbar;type&gt;)
link:#mp_units-quantity_point-08-2constructor-04c[quantity&lowbar;point](QP const& qp);
----

[.small]#link:#mp_units-quantity_point-08-2constructor-04c[_» more&period;&period;&period;_]#

Construct from `QP`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, typename QP&colon;&colon;quantity&lowbar;type&gt;
constexpr
explicit(!std&colon;&colon;convertible&lowbar;to&lt;typename QP&colon;&colon;quantity&lowbar;type, quantity&lowbar;type&gt;)
link:#mp_units-quantity_point-08-2constructor-0e[quantity&lowbar;point](QP const& qp);
----

[.small]#link:#mp_units-quantity_point-08-2constructor-0e[_» more&period;&period;&period;_]#

Construct from `FwdQ`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, FwdQ&gt; &amp;&amp; (point&lowbar;origin &equals;&equals; default&lowbar;point&lowbar;origin(R))
constexpr
explicit
link:#mp_units-quantity_point-08-2constructor-01[quantity&lowbar;point](FwdQ&& q);
----

[.small]#link:#mp_units-quantity_point-08-2constructor-01[_» more&period;&period;&period;_]#

Constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, FwdQ&gt;
constexpr
link:#mp_units-quantity_point-08-2constructor-09[quantity&lowbar;point](
    FwdQ&& q,
    decltype(PO));
----

[.small]#link:#mp_units-quantity_point-08-2constructor-09[_» more&period;&period;&period;_]#

Constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-PointOrigin[PointOrigin] PO2,
    link:#mp_units-QuantityOf[QuantityOf&lt;PO2&colon;&colon;&lowbar;quantity&lowbar;spec&lowbar;&gt;] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, FwdQ&gt; &amp;&amp; detail&colon;&colon;SameAbsolutePointOriginAs&lt;PO2, PO&gt;
constexpr
link:#mp_units-quantity_point-08-2constructor-02[quantity&lowbar;point](
    FwdQ&& q,
    PO2);
----

[.small]#link:#mp_units-quantity_point-08-2constructor-02[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
quantity&lowbar;point() = default;
----

Copy constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
quantity&lowbar;point(link:#mp_units-quantity_point-08[quantity&lowbar;point] const& other) = default;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy construct from
|===

Move constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
quantity&lowbar;point(link:#mp_units-quantity_point-08[quantity&lowbar;point]&& other) = default;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to move construct from
|===

Construct from `QP`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityPointLike[QuantityPointLike] QP&gt;
requires (quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;point&lowbar;origin &equals;&equals; point&lowbar;origin) &amp;&amp;
            std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference,
                                                            typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;
constexpr
explicit(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;explicit&lowbar;import &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference, typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;, quantity&lowbar;type&gt;)
quantity&lowbar;point(QP const& qp);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *qp*
| The object to copy construct from
|===

Construct from `QP`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, typename QP&colon;&colon;quantity&lowbar;type&gt;
constexpr
explicit(!std&colon;&colon;convertible&lowbar;to&lt;typename QP&colon;&colon;quantity&lowbar;type, quantity&lowbar;type&gt;)
quantity&lowbar;point(QP const& qp);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *qp*
| The object to copy construct from
|===

Construct from `FwdQ`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, FwdQ&gt; &amp;&amp; (point&lowbar;origin &equals;&equals; default&lowbar;point&lowbar;origin(R))
constexpr
explicit
quantity&lowbar;point(FwdQ&& q);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| The object to move construct from
|===

Constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, FwdQ&gt;
constexpr
quantity&lowbar;point(
    FwdQ&& q,
    decltype(PO));
----

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| The object to move construct from
|===

Constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-PointOrigin[PointOrigin] PO2,
    link:#mp_units-QuantityOf[QuantityOf&lt;PO2&colon;&colon;&lowbar;quantity&lowbar;spec&lowbar;&gt;] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;quantity&lowbar;type, FwdQ&gt; &amp;&amp; detail&colon;&colon;SameAbsolutePointOriginAs&lt;PO2, PO&gt;
constexpr
quantity&lowbar;point(
    FwdQ&& q,
    PO2);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| The object to move construct from
|===

Destructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&#126;quantity&lowbar;point() = default;
----

Assignment operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

Copy assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
link:#mp_units-quantity_point-08-operator_assign-03[operator&equals;](link:#mp_units-quantity_point-08[quantity&lowbar;point] const& other) = default;
----

[.small]#link:#mp_units-quantity_point-08-operator_assign-03[_» more&period;&period;&period;_]#

Move assignment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
link:#mp_units-quantity_point-08-operator_assign-08[operator&equals;](link:#mp_units-quantity_point-08[quantity&lowbar;point]&& other) = default;
----

[.small]#link:#mp_units-quantity_point-08-operator_assign-08[_» more&period;&period;&period;_]#

Copy assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
operator&equals;(link:#mp_units-quantity_point-08[quantity&lowbar;point] const& other) = default;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to copy assign from
|===

Move assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
operator&equals;(link:#mp_units-quantity_point-08[quantity&lowbar;point]&& other) = default;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *other*
| The object to move assign from
|===

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;ToRep, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity_point-08-force_in-02[force&lowbar;in]() const;
----

[.small]#link:#mp_units-quantity_point-08-force_in-02[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;SaneScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity_point-08-force_in-09[force&lowbar;in](ToU) const;
----

[.small]#link:#mp_units-quantity_point-08-force_in-09[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep,
    &sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;ToRep, rep&gt; &amp;&amp; detail&colon;&colon;SaneScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity_point-08-force_in-0b[force&lowbar;in](ToU) const;
----

[.small]#link:#mp_units-quantity_point-08-force_in-0b[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;ToRep, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
force&lowbar;in() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;SaneScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
force&lowbar;in(ToU) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep,
    &sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires std&colon;&colon;constructible&lowbar;from&lt;ToRep, rep&gt; &amp;&amp; detail&colon;&colon;SaneScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
force&lowbar;in(ToU) const;
----

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep&gt;
requires detail&colon;&colon;ValuePreservingConstruction&lt;ToRep, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity_point-08-in-01[in]() const;
----

[.small]#link:#mp_units-quantity_point-08-in-01[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;ValuePreservingScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity_point-08-in-07[in](ToU) const;
----

[.small]#link:#mp_units-quantity_point-08-in-07[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep,
    &sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;ValuePreservingConstruction&lt;ToRep, rep&gt; &amp;&amp;
             detail&colon;&colon;ValuePreservingConversion&lt;unit, rep, ToU&lcub;&rcub;, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-quantity_point-08-in-0af[in](ToU) const;
----

[.small]#link:#mp_units-quantity_point-08-in-0af[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep&gt;
requires detail&colon;&colon;ValuePreservingConstruction&lt;ToRep, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
in() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;ValuePreservingScaling&lt;unit, ToU&lcub;&rcub;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
in(ToU) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] ToRep,
    &sol;&ast; implementation-defined &ast;&sol; ToU&gt;
requires detail&colon;&colon;ValuePreservingConstruction&lt;ToRep, rep&gt; &amp;&amp;
             detail&colon;&colon;ValuePreservingConversion&lt;unit, rep, ToU&lcub;&rcub;, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;quantity&lowbar;spec&gt;] auto
in(ToU) const;
----

Increment operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

Increment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
link:#mp_units-quantity_point-08-operator_inc-08[operator&plus;&plus;]() &amp;
requires requires &lcub; &plus;&plus;quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&semi; &rcub;;
----

[.small]#link:#mp_units-quantity_point-08-operator_inc-08[_» more&period;&period;&period;_]#

Increment operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]
link:#mp_units-quantity_point-08-operator_inc-03[operator&plus;&plus;](int)
requires requires &lcub; quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&plus;&plus;&semi; &rcub;;
----

[.small]#link:#mp_units-quantity_point-08-operator_inc-03[_» more&period;&period;&period;_]#

Increment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
operator&plus;&plus;() &amp;
requires requires &lcub; &plus;&plus;quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&semi; &rcub;;
----

== Return Value

Reference to the current object

Increment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]
operator&plus;&plus;(int)
requires requires &lcub; quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&plus;&plus;&semi; &rcub;;
----

== Return Value

Another instance of the object

Addition assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R2,
    typename Rep2&gt;
requires (implicitly&lowbar;convertible(get&lowbar;quantity&lowbar;spec(R2), quantity&lowbar;spec)) &amp;&amp;
            detail&colon;&colon;ValuePreservingConversion&lt;get&lowbar;unit(R2), Rep2, unit, rep&gt; &amp;&amp;
            requires(const quantity&lowbar;type q) &lcub; quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar; &plus;&equals; q&semi; &rcub;
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
operator&plus;&equals;(link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& q) &amp;;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| The right operand
|===

Decrement operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

Decrement operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
link:#mp_units-quantity_point-08-operator_dec-0d[operator&hyphen;&hyphen;]() &amp;
requires requires &lcub; &hyphen;&hyphen;quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&semi; &rcub;;
----

[.small]#link:#mp_units-quantity_point-08-operator_dec-0d[_» more&period;&period;&period;_]#

Decrement operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]
link:#mp_units-quantity_point-08-operator_dec-03[operator&hyphen;&hyphen;](int)
requires requires &lcub; quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&hyphen;&hyphen;&semi; &rcub;;
----

[.small]#link:#mp_units-quantity_point-08-operator_dec-03[_» more&period;&period;&period;_]#

Decrement operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
operator&hyphen;&hyphen;() &amp;
requires requires &lcub; &hyphen;&hyphen;quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&semi; &rcub;;
----

== Return Value

Reference to the current object

Decrement operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]
operator&hyphen;&hyphen;(int)
requires requires &lcub; quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&hyphen;&hyphen;&semi; &rcub;;
----

== Return Value

Another instance of the object

Subtraction assignment operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R2,
    typename Rep2&gt;
requires (implicitly&lowbar;convertible(get&lowbar;quantity&lowbar;spec(R2), quantity&lowbar;spec)) &amp;&amp;
            detail&colon;&colon;ValuePreservingConversion&lt;get&lowbar;unit(R2), Rep2, unit, rep&gt; &amp;&amp;
            requires(const quantity&lowbar;type q) &lcub; quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar; &hyphen;&equals; q&semi; &rcub;
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point]&
operator&hyphen;&equals;(link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& q) &amp;;
----

== Return Value

Reference to the current object

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| The right operand
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; NewPO&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;(NewPO&lcub;&rcub;)&gt;] auto
point&lowbar;for(NewPO new&lowbar;origin) const;
----

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires requires(const quantity&lowbar;point qp) &lcub; qp &hyphen; PO2&lcub;&rcub;&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-quantity_point-08-quantity_from-04[quantity&lowbar;from](PO2) const;
----

[.small]#link:#mp_units-quantity_point-08-quantity_from-04[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-quantity_point-08-quantity_from-0f[quantity&lowbar;from](QP const& qp) const;
----

[.small]#link:#mp_units-quantity_point-08-quantity_from-0f[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires requires(const quantity&lowbar;point qp) &lcub; qp &hyphen; PO2&lcub;&rcub;&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
quantity&lowbar;from(PO2) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
quantity&lowbar;from(QP const& qp) const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
quantity&lowbar;from&lowbar;zero() const;
----

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires (PO2&lcub;&rcub; &equals;&equals; point&lowbar;origin)
constexpr
link:#mp_units-quantity_point-08-quantity_type[quantity&lowbar;type] const&&
link:#mp_units-quantity_point-08-quantity_ref_from-0c[quantity&lowbar;ref&lowbar;from](PO2) const &amp;&amp; noexcept = delete;
----

[.small]#link:#mp_units-quantity_point-08-quantity_ref_from-0c[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires (PO2&lcub;&rcub; &equals;&equals; point&lowbar;origin)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08-quantity_type[quantity&lowbar;type] const&
link:#mp_units-quantity_point-08-quantity_ref_from-01[quantity&lowbar;ref&lowbar;from](PO2) const &amp; noexcept;
----

[.small]#link:#mp_units-quantity_point-08-quantity_ref_from-01[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires (PO2&lcub;&rcub; &equals;&equals; point&lowbar;origin)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08-quantity_type[quantity&lowbar;type]&
link:#mp_units-quantity_point-08-quantity_ref_from-04[quantity&lowbar;ref&lowbar;from](PO2) &amp; noexcept;
----

[.small]#link:#mp_units-quantity_point-08-quantity_ref_from-04[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires (PO2&lcub;&rcub; &equals;&equals; point&lowbar;origin)
constexpr
link:#mp_units-quantity_point-08-quantity_type[quantity&lowbar;type] const&&
quantity&lowbar;ref&lowbar;from(PO2) const &amp;&amp; noexcept = delete;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires (PO2&lcub;&rcub; &equals;&equals; point&lowbar;origin)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08-quantity_type[quantity&lowbar;type] const&
quantity&lowbar;ref&lowbar;from(PO2) const &amp; noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires (PO2&lcub;&rcub; &equals;&equals; point&lowbar;origin)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08-quantity_type[quantity&lowbar;type]&
quantity&lowbar;ref&lowbar;from(PO2) &amp; noexcept;
----

Conversion operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

Conversion to `QP&lowbar;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename QP&lowbar;,
    link:#mp_units-QuantityPointLike[QuantityPointLike] QP = std::remove&lowbar;cvref&lowbar;t&lt;QP&lowbar;&gt;&gt;
requires (point&lowbar;origin &equals;&equals; quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;point&lowbar;origin) &amp;&amp;
            std&colon;&colon;convertible&lowbar;to&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference,
                                                        typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
explicit(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;explicit&lowbar;export &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference, typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;)
operator QP&lowbar;() &amp;&amp; noexcept(noexcept(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;from&lowbar;numerical&lowbar;value(this&hyphen;&gt;quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&period;numerical&lowbar;value&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;)) &amp;&amp; std&colon;&colon;is&lowbar;nothrow&lowbar;move&lowbar;constructible&lowbar;v&lt;rep&gt;);
----

[.small]#link:#mp_units-quantity_point-08-2conversion-08[_» more&period;&period;&period;_]#

Conversion to `QP&lowbar;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename QP&lowbar;,
    link:#mp_units-QuantityPointLike[QuantityPointLike] QP = std::remove&lowbar;cvref&lowbar;t&lt;QP&lowbar;&gt;&gt;
requires (point&lowbar;origin &equals;&equals; quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;point&lowbar;origin) &amp;&amp;
            std&colon;&colon;convertible&lowbar;to&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference,
                                                        typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
explicit(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;explicit&lowbar;export &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference, typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;)
operator QP&lowbar;() const &amp; noexcept(noexcept(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;from&lowbar;numerical&lowbar;value(this&hyphen;&gt;quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&period;numerical&lowbar;value&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;)) &amp;&amp; std&colon;&colon;is&lowbar;nothrow&lowbar;copy&lowbar;constructible&lowbar;v&lt;rep&gt;);
----

[.small]#link:#mp_units-quantity_point-08-2conversion-07[_» more&period;&period;&period;_]#

Conversion to `QP&lowbar;`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename QP&lowbar;,
    link:#mp_units-QuantityPointLike[QuantityPointLike] QP = std::remove&lowbar;cvref&lowbar;t&lt;QP&lowbar;&gt;&gt;
requires (point&lowbar;origin &equals;&equals; quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;point&lowbar;origin) &amp;&amp;
            std&colon;&colon;convertible&lowbar;to&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference,
                                                        typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
explicit(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;explicit&lowbar;export &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference, typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;)
operator QP&lowbar;() &amp;&amp; noexcept(noexcept(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;from&lowbar;numerical&lowbar;value(this&hyphen;&gt;quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&period;numerical&lowbar;value&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;)) &amp;&amp; std&colon;&colon;is&lowbar;nothrow&lowbar;move&lowbar;constructible&lowbar;v&lt;rep&gt;);
----

== Return Value

The object converted to `QP&lowbar;`

Conversion to `QP&lowbar;`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename QP&lowbar;,
    link:#mp_units-QuantityPointLike[QuantityPointLike] QP = std::remove&lowbar;cvref&lowbar;t&lt;QP&lowbar;&gt;&gt;
requires (point&lowbar;origin &equals;&equals; quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;point&lowbar;origin) &amp;&amp;
            std&colon;&colon;convertible&lowbar;to&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference,
                                                        typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
explicit(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;explicit&lowbar;export &verbar;&verbar; !std&colon;&colon;convertible&lowbar;to&lt;quantity&lowbar;type, quantity&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference, typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;rep&gt;&gt;)
operator QP&lowbar;() const &amp; noexcept(noexcept(quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;from&lowbar;numerical&lowbar;value(this&hyphen;&gt;quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;&period;numerical&lowbar;value&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;)) &amp;&amp; std&colon;&colon;is&lowbar;nothrow&lowbar;copy&lowbar;constructible&lowbar;v&lt;rep&gt;);
----

== Return Value

The object converted to `QP&lowbar;`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
static
link:#mp_units-quantity_point-08[quantity&lowbar;point]
max() noexcept
requires requires &lcub; quantity&lowbar;type&colon;&colon;max()&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
static
link:#mp_units-quantity_point-08[quantity&lowbar;point]
min() noexcept
requires requires &lcub; quantity&lowbar;type&colon;&colon;min()&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-quantity_point-08-quantity_type[quantity&lowbar;type] quantity&lowbar;from&lowbar;origin&lowbar;is&lowbar;an&lowbar;implementation&lowbar;detail&lowbar;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-PointOrigin[PointOrigin] auto absolute&lowbar;point&lowbar;origin = detail&colon;&colon;get&lowbar;absolute&lowbar;point&lowbar;origin(PO);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-Dimension[Dimension] auto dimension = quantity&lowbar;spec&period;dimension;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-PointOrigin[PointOrigin] auto point&lowbar;origin = PO;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-QuantitySpec[QuantitySpec] auto quantity&lowbar;spec = get&lowbar;quantity&lowbar;spec(reference);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-Reference[Reference] auto reference = R;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-Unit[Unit] auto unit = get&lowbar;unit(reference);
----

Provides support for external quantity point&hyphen;like types

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
struct quantity&lowbar;point&lowbar;like&lowbar;traits;
----

== Description

The type trait should provide nested `reference` and `origin` objects, a type alias `rep,` and static member functions `to&lowbar;numerical&lowbar;value(T)` that returns the raw value of the the quantity being the offset of the point from the origin and `from&lowbar;numerical&lowbar;value(rep)` that returns `T` formed this raw value&period;

If the following expression is `true,` the specified conversion will be explicit&colon; &hyphen; `explicit&lowbar;import` for the conversion from `T` to a `quantity&lowbar;point` type, &hyphen; `explicit&lowbar;export` for the conversion from a `quantity&lowbar;point` type to `T&period;`

Usage example can be found in `mp&hyphen;units&sol;systems&sol;si&sol;chrono&period;h` header file&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *T*
| the type to provide support for
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;auto&period;&period;&period;&gt;
struct quantity&lowbar;spec;
----

== Derived Classes

[cols=2]
|===
| Name
| Description
| link:#mp_units-dimensionless-0f[`dimensionless`]
| Quantity of dimension one
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    &sol;&ast; implementation-defined &ast;&sol; auto Dim,
    &sol;&ast; implementation-defined &ast;&sol; auto Args&period;&period;&period;&gt;
struct link:#mp_units-quantity_spec-09[quantity&lowbar;spec]&lt;QS, Args&period;&period;&period;&gt;
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-quantity_spec-0a6-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-quantity_spec-0a6-_equation_[`&lowbar;equation&lowbar;`] 
| link:#mp_units-quantity_spec-0a6-_parent_[`&lowbar;parent&lowbar;`] 
| link:#mp_units-quantity_spec-0a6-character[`character`] 
| link:#mp_units-quantity_spec-0a6-dimension[`dimension`] 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = link:#mp_units-quantity_spec-0a6[quantity&lowbar;spec];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;equation&lowbar; = Eq;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;parent&lowbar; = QS;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-quantity_character[quantity&lowbar;character] character = detail&colon;&colon;quantity&lowbar;character&lowbar;init&lt;Args&period;&period;&period;&gt;(QS&period;character);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-Dimension[Dimension] auto dimension = &lowbar;parent&lowbar;&period;dimension;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    &sol;&ast; implementation-defined &ast;&sol; auto QS,
    &sol;&ast; implementation-defined &ast;&sol; auto Eq,
    &sol;&ast; implementation-defined &ast;&sol; auto Args&period;&period;&period;&gt;
requires (explicitly&lowbar;convertible(Eq, QS))
struct link:#mp_units-quantity_spec-09[quantity&lowbar;spec]&lt;QS, Eq, Args&period;&period;&period;&gt;
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-quantity_spec-0a0-_base_type_[`&lowbar;base&lowbar;type&lowbar;`] 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-quantity_spec-0a0-_equation_[`&lowbar;equation&lowbar;`] 
| link:#mp_units-quantity_spec-0a0-_parent_[`&lowbar;parent&lowbar;`] 
| link:#mp_units-quantity_spec-0a0-character[`character`] 
| link:#mp_units-quantity_spec-0a0-dimension[`dimension`] 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using &lowbar;base&lowbar;type&lowbar; = link:#mp_units-quantity_spec-0a0[quantity&lowbar;spec];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;equation&lowbar; = Eq;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto &lowbar;parent&lowbar; = QS;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-quantity_character[quantity&lowbar;character] character = detail&colon;&colon;quantity&lowbar;character&lowbar;init&lt;Args&period;&period;&period;&gt;(Eq&period;character);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-Dimension[Dimension] auto dimension = &lowbar;parent&lowbar;&period;dimension;
----

Quantity reference type

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] Q,
    link:#mp_units-Unit[Unit] U&gt;
struct reference;
----

== Friends

[cols=2]
|===
| Name
| Description
| `link:#mp_units-cbrt-0e[mp&lowbar;units::cbrt]`
| 
| `link:#mp_units-sqrt-0f[mp&lowbar;units::sqrt]`
| 
| `link:#mp_units-pow-07[mp&lowbar;units::pow]`
| Computes the value of a reference raised to the `Num&sol;Den` power
| `link:#mp_units-inverse-0b[mp&lowbar;units::inverse]`
| 
| `link:#mp_units-operator_slash-0d6[mp&lowbar;units::operator&sol;]`
| 
| `link:#mp_units-operator_slash-0e7[mp&lowbar;units::operator&sol;]`
| 
| `link:#mp_units-operator_slash-0d3[mp&lowbar;units::operator&sol;]`
| 
| `link:#mp_units-operator_star-02b[mp&lowbar;units::operator&ast;]`
| 
| `link:#mp_units-operator_star-0f[mp&lowbar;units::operator&ast;]`
| 
| `link:#mp_units-operator_star-05[mp&lowbar;units::operator&ast;]`
| 
| `link:#mp_units-operator_eq-02[mp&lowbar;units::operator&equals;&equals;]`
| Equality operator
| `link:#mp_units-operator_eq-07[mp&lowbar;units::operator&equals;&equals;]`
| Equality operator
|===

== Description

Quantity reference describes all the properties of a quantity besides its representation type&period;

In most cases this class template is not explicitly instantiated by the user&period; It is implicitly instantiated by the library&apos;s framework while binding a quantity specification with a compatible unit&period;

[,cpp]
----
{.cpp}
 Reference auto kmph = isq::speed[km / h];
 QuantityOf<isq::speed[km / h]> auto speed = 90 * kmph;
----
The following syntaxes are not allowed&colon; `2 &sol; kmph`, `kmph 3, &grave;kmph &sol; 4`, `70 isq&colon;&colon;length&lsqb;km&rsqb; &sol; isq&colon;time&lsqb;h&rsqb;`&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityPoint[QuantityPoint] auto QP&gt;
struct relative&lowbar;point&lowbar;origin
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-relative_point_origin-_absolute_point_origin_[`&lowbar;absolute&lowbar;point&lowbar;origin&lowbar;`] 
| link:#mp_units-relative_point_origin-_quantity_point_[`&lowbar;quantity&lowbar;point&lowbar;`] 
| link:#mp_units-relative_point_origin-_quantity_spec_[`&lowbar;quantity&lowbar;spec&lowbar;`] 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-PointOrigin[PointOrigin] auto &lowbar;absolute&lowbar;point&lowbar;origin&lowbar; = QP&period;absolute&lowbar;point&lowbar;origin;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-QuantityPoint[QuantityPoint] auto &lowbar;quantity&lowbar;point&lowbar; = QP;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
link:#mp_units-QuantitySpec[QuantitySpec] auto &lowbar;quantity&lowbar;spec&lowbar; = &lsqb;&rsqb;() &lcub;
    &sol;&sol; select the strongest of specs
    if constexpr (detail&colon;&colon;QuantityKindSpec&lt;MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(QP&period;quantity&lowbar;spec)&gt;)
      return QP&period;point&lowbar;origin&period;&lowbar;quantity&lowbar;spec&lowbar;&semi;
    else
      return QP&period;quantity&lowbar;spec&semi;
  &rcub;();
----

A type trait that defines zero, one, min, and max for a representation type

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Rep&gt;
struct representation&lowbar;values
    : std::chrono::duration&lowbar;values&lt;Rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::chrono::duration&lowbar;values&lt;Rep&gt;`
| 
|===

== Static Member Functions

[cols=1]
|===
| Name
| link:#mp_units-representation_values-one[`one`] 
|===

== Description

The zero, one, min, and max member functions in mp&lowbar;units&colon;&colon;quantity forward their work to these methods&period; This type can be specialized if the representation Rep requires a specific implementation to return these quantity objects&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Rep*
| a representation type for which a type trait is defined
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
static
Rep
one() noexcept
requires std&colon;&colon;constructible&lowbar;from&lt;Rep, int&gt;;
----

Unit being a scaled version of another unit

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-UnitMagnitude[UnitMagnitude] auto M,
    link:#mp_units-Unit[Unit] U&gt;
requires (M !&equals; detail&colon;&colon;unit&lowbar;magnitude&lt;&gt;&lcub;&rcub; &amp;&amp; M !&equals; mag&lt;1&gt;)
struct scaled&lowbar;unit final
    : &sol;&ast; implementation-defined &ast;&sol;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `&sol;&ast; implementation-defined &ast;&sol;`
| 
|===

== Description

[NOTE]
User should not instantiate this type! It is not exported from the C&plus;&plus; module&period; The library will instantiate this type automatically based on the unit arithmetic equation provided by the user&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *M*
| magnitude describing the scale factor
| *U*
| reference unit being scaled
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct student&lowbar;t&lowbar;distribution
    : std::student&lowbar;t&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::student&lowbar;t&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-student_t_distribution-base[`base`] 
| link:#mp_units-student_t_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-student_t_distribution-2constructor-077[`student&lowbar;t&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-student_t_distribution-max[`max`] 
| 
| link:#mp_units-student_t_distribution-min[`min`] 
| 
| link:#mp_units-student_t_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::student&lowbar;t&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-student_t_distribution-2constructor-07f[student&lowbar;t&lowbar;distribution]();
----

[.small]#link:#mp_units-student_t_distribution-2constructor-07f[_» more&period;&period;&period;_]#

Construct from `rep`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
link:#mp_units-student_t_distribution-2constructor-06[student&lowbar;t&lowbar;distribution](link:#mp_units-student_t_distribution-rep[rep] const& n);
----

[.small]#link:#mp_units-student_t_distribution-2constructor-06[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
student&lowbar;t&lowbar;distribution();
----

Construct from `rep`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
explicit
student&lowbar;t&lowbar;distribution(link:#mp_units-student_t_distribution-rep[rep] const& n);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *n*
| The object to copy construct from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

A symbol text representation

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::size&lowbar;t N,
    std::size&lowbar;t M&gt;
class symbol&lowbar;text;
----

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-symbol_text-032-2constructor-01[`symbol&lowbar;text`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-symbol_text-032-ascii[`ascii`] 
| 
| link:#mp_units-symbol_text-032-empty[`empty`] 
| 
| link:#mp_units-symbol_text-032-portable[`portable`] 
| 
| link:#mp_units-symbol_text-032-unicode[`unicode`] 
| 
| link:#mp_units-symbol_text-032-utf8[`utf8`] 
| 
|===

== Data Members

[cols=1]
|===
| Name
| link:#mp_units-symbol_text-032-portable_[`portable&lowbar;`] 
| link:#mp_units-symbol_text-032-utf8_[`utf8&lowbar;`] 
|===

== Friends

[cols=2]
|===
| Name
| Description
| `link:#mp_units-operator_eq-0a[mp&lowbar;units::operator&equals;&equals;]`
| Equality operator
| `link:#mp_units-operator_3way-0b[mp&lowbar;units::operator&lt;&equals;&gt;]`
| Three&hyphen;way comparison operator
| `link:#mp_units-operator_plus-0e1[mp&lowbar;units::operator&plus;]`
| Addition operator
|===

== Description

This class template is responsible for definition and handling of a symbol text representation&period; In the libary it is used to define symbols of units and prefixes&period; Each symbol can have two versions&colon; UTF&hyphen;8 and portable&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *N*
| The size of a UTF&hyphen;8 symbol
| *M*
| The size of the portable symbol
|===

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

Construct from `char`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
explicit(false)
link:#mp_units-symbol_text-032-2constructor-05[symbol&lowbar;text](char ch);
----

[.small]#link:#mp_units-symbol_text-032-2constructor-05[_» more&period;&period;&period;_]#

Construct from `fixed&lowbar;string`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
explicit(false)
link:#mp_units-symbol_text-032-2constructor-0f[symbol&lowbar;text](link:#mp_units-fixed_string[fixed&lowbar;string&lt;N&gt;] const& txt);
----

[.small]#link:#mp_units-symbol_text-032-2constructor-0f[_» more&period;&period;&period;_]#

Construct from `char`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
consteval
explicit(false)
link:#mp_units-symbol_text-032-2constructor-0a[symbol&lowbar;text](char const(& txt)[]);
----

[.small]#link:#mp_units-symbol_text-032-2constructor-0a[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
link:#mp_units-symbol_text-032-2constructor-0c[symbol&lowbar;text](
    link:#mp_units-fixed_u8string[fixed&lowbar;u8string&lt;N&gt;] const& utf8,
    link:#mp_units-fixed_string[fixed&lowbar;string&lt;M&gt;] const& portable);
----

[.small]#link:#mp_units-symbol_text-032-2constructor-0c[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
consteval
link:#mp_units-symbol_text-032-2constructor-04[symbol&lowbar;text](
    char8&lowbar;t const(& u)[],
    char const(& a)[]);
----

[.small]#link:#mp_units-symbol_text-032-2constructor-04[_» more&period;&period;&period;_]#

Construct from `char`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
explicit(false)
symbol&lowbar;text(char ch);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *ch*
| The value to construct from
|===

Construct from `fixed&lowbar;string`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
explicit(false)
symbol&lowbar;text(link:#mp_units-fixed_string[fixed&lowbar;string&lt;N&gt;] const& txt);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *txt*
| The object to copy construct from
|===

Construct from `char`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
consteval
explicit(false)
symbol&lowbar;text(char const(& txt)[]);
----

== Parameters

[cols=2]
|===
| Name
| Description
| *txt*
| The value to construct from
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
symbol&lowbar;text(
    link:#mp_units-fixed_u8string[fixed&lowbar;u8string&lt;N&gt;] const& utf8,
    link:#mp_units-fixed_string[fixed&lowbar;string&lt;M&gt;] const& portable);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
consteval
symbol&lowbar;text(
    char8&lowbar;t const(& u)[],
    char const(& a)[]);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
constexpr
auto const&
ascii() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
empty() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto const&
portable() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
constexpr
auto const&
unicode() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto const&
utf8() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-fixed_string[fixed&lowbar;string&lt;M&gt;] portable&lowbar;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-fixed_u8string[fixed&lowbar;u8string&lt;N&gt;] utf8&lowbar;;
----

System&hyphen;specific reference

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;system&lowbar;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] auto Q,
    link:#mp_units-Unit[Unit] auto CoU&gt;
requires (!MP&lowbar;UNITS&lowbar;ASSOCIATED&lowbar;UNIT&lowbar;T(decltype(CoU))) &verbar;&verbar; (CoU &equals;&equals; one)
struct system&lowbar;reference;
----

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-system_reference-operator_subs[`operator&lsqb;&rsqb;`] 
| Subscript operator
|===

== Static Data Members

[cols=1]
|===
| Name
| link:#mp_units-system_reference-coherent_unit[`coherent&lowbar;unit`] 
| link:#mp_units-system_reference-quantity_spec[`quantity&lowbar;spec`] 
|===

== Description

This type is used in rare cases where more than one base quantity in a specific system of units uses the same unit&period; For example in a hypothetical system of natural units where constant for speed of light `c &equals; 1`, length and time could be measured in seconds&period; In such cases `system&lowbar;reference` has to be used to explicitly express such a binding&period;

For example&colon;

[,cpp]
----
{.cpp}
 // hypothetical natural system of units for c=1

 inline constexpr struct second final : named_unit<"s"> {} second;
 inline constexpr struct minute final : named_unit<"min", mag<60> * second> {} minute;
 inline constexpr struct gram final : named_unit<"g"> {} gram;
 inline constexpr auto kilogram = si::kilo<gram>;

 inline constexpr struct time : system_reference<isq::time, second> {} time;
 inline constexpr struct length : system_reference<isq::length, second> {} length;
 inline constexpr struct speed : system_reference<isq::speed, second / second> {} speed;
 inline constexpr struct force : system_reference<isq::force, kilogram / second> {} force;
----
== Template Parameters

[cols=2]
|===
| Name
| Description
| *Q*
| quantity for which a unit is being assigned
| *CoU*
| coherent unit for a quantity in this system
|===

Subscript operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;system&lowbar;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; U&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-reference[reference&lt;decltype(Q), U&gt;]
operator&lsqb;&rsqb;(U rhs) const;
----

== Return Value

Quantity reference type

== Parameters

[cols=2]
|===
| Name
| Description
| *rhs*
| The right operand
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;system&lowbar;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto coherent&lowbar;unit = CoU;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;system&lowbar;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr static
auto quantity&lowbar;spec = Q;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;integral&lt;typename Q&colon;&colon;rep&gt;
struct uniform&lowbar;int&lowbar;distribution
    : std::uniform&lowbar;int&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::uniform&lowbar;int&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-uniform_int_distribution-base[`base`] 
| link:#mp_units-uniform_int_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-uniform_int_distribution-2constructor-05[`uniform&lowbar;int&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-uniform_int_distribution-a[`a`] 
| 
| link:#mp_units-uniform_int_distribution-b[`b`] 
| 
| link:#mp_units-uniform_int_distribution-max[`max`] 
| 
| link:#mp_units-uniform_int_distribution-min[`min`] 
| 
| link:#mp_units-uniform_int_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::uniform&lowbar;int&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-uniform_int_distribution-2constructor-06[uniform&lowbar;int&lowbar;distribution]();
----

[.small]#link:#mp_units-uniform_int_distribution-2constructor-06[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-uniform_int_distribution-2constructor-07[uniform&lowbar;int&lowbar;distribution](
    Q const& a,
    Q const& b);
----

[.small]#link:#mp_units-uniform_int_distribution-2constructor-07[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
uniform&lowbar;int&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
uniform&lowbar;int&lowbar;distribution(
    Q const& a,
    Q const& b);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
a() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
b() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct uniform&lowbar;real&lowbar;distribution
    : std::uniform&lowbar;real&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::uniform&lowbar;real&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-uniform_real_distribution-base[`base`] 
| link:#mp_units-uniform_real_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-uniform_real_distribution-2constructor-00[`uniform&lowbar;real&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-uniform_real_distribution-a[`a`] 
| 
| link:#mp_units-uniform_real_distribution-b[`b`] 
| 
| link:#mp_units-uniform_real_distribution-max[`max`] 
| 
| link:#mp_units-uniform_real_distribution-min[`min`] 
| 
| link:#mp_units-uniform_real_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::uniform&lowbar;real&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-uniform_real_distribution-2constructor-04[uniform&lowbar;real&lowbar;distribution]();
----

[.small]#link:#mp_units-uniform_real_distribution-2constructor-04[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-uniform_real_distribution-2constructor-02[uniform&lowbar;real&lowbar;distribution](
    Q const& a,
    Q const& b);
----

[.small]#link:#mp_units-uniform_real_distribution-2constructor-02[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
uniform&lowbar;real&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
uniform&lowbar;real&lowbar;distribution(
    Q const& a,
    Q const& b);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
a() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
b() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;symbol&lowbar;formatting&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
struct unit&lowbar;symbol&lowbar;formatting;
----

== Data Members

[cols=1]
|===
| Name
| link:#mp_units-unit_symbol_formatting-char_set[`char&lowbar;set`] 
| link:#mp_units-unit_symbol_formatting-separator[`separator`] 
| link:#mp_units-unit_symbol_formatting-solidus[`solidus`] 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;symbol&lowbar;formatting&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-character_set[character&lowbar;set] char&lowbar;set = character&lowbar;set&colon;&colon;default&lowbar;character&lowbar;set;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;symbol&lowbar;formatting&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-unit_symbol_separator[unit&lowbar;symbol&lowbar;separator] separator = unit&lowbar;symbol&lowbar;separator&colon;&colon;default&lowbar;separator;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;symbol&lowbar;formatting&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-unit_symbol_solidus[unit&lowbar;symbol&lowbar;solidus] solidus = unit&lowbar;symbol&lowbar;solidus&colon;&colon;default&lowbar;denominator;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
requires std&colon;&colon;floating&lowbar;point&lt;typename Q&colon;&colon;rep&gt;
struct weibull&lowbar;distribution
    : std::weibull&lowbar;distribution&lt;Q::rep&gt;
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `std::weibull&lowbar;distribution&lt;Q::rep&gt;`
| 
|===

== Types

[cols=1]
|===
| Name
| link:#mp_units-weibull_distribution-base[`base`] 
| link:#mp_units-weibull_distribution-rep[`rep`] 
|===

== Member Functions

[cols=2]
|===
| Name
| Description
| link:#mp_units-weibull_distribution-2constructor-0b[`weibull&lowbar;distribution`]         [.small]#[constructor]#
| Constructors
| link:#mp_units-weibull_distribution-max[`max`] 
| 
| link:#mp_units-weibull_distribution-min[`min`] 
| 
| link:#mp_units-weibull_distribution-operator_call[`operator()`] 
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using base = std::weibull&lowbar;distribution&lt;rep&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
using rep = Q::rep;
----

Constructors

== Synopses

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

Default constructor


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-weibull_distribution-2constructor-07[weibull&lowbar;distribution]();
----

[.small]#link:#mp_units-weibull_distribution-2constructor-07[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-weibull_distribution-2constructor-06[weibull&lowbar;distribution](
    link:#mp_units-weibull_distribution-rep[rep] const& a,
    link:#mp_units-weibull_distribution-rep[rep] const& b);
----

[.small]#link:#mp_units-weibull_distribution-2constructor-06[_» more&period;&period;&period;_]#

Default constructor

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
weibull&lowbar;distribution();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
weibull&lowbar;distribution(
    link:#mp_units-weibull_distribution-rep[rep] const& a,
    link:#mp_units-weibull_distribution-rep[rep] const& b);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
max() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
Q
min() const;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;random&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Generator&gt;
Q
operator()(Generator& g);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantitySpec[QuantitySpec] auto QS&gt;
struct zeroth&lowbar;point&lowbar;origin&lowbar; final
    : link:#mp_units-absolute_point_origin[absolute&lowbar;point&lowbar;origin&lt;QS&gt;]
----

== Base Classes

[cols=2]
|===
| Name
| Description
| `link:#mp_units-absolute_point_origin[absolute&lowbar;point&lowbar;origin&lt;QS&gt;]`
| 
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
enum class character&lowbar;set : int8&lowbar;t;
----

== Members


[cols=2]
|===
| Name
| Description
|`utf8`
|
|`unicode`
|
|`portable`
|
|`ascii`
|
|`default&lowbar;character&lowbar;set`
|
|`default&lowbar;encoding`
|
|===

Quantity character

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;representation&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
enum class quantity&lowbar;character : int8&lowbar;t;
----

== Members


[cols=2]
|===
| Name
| Description
|`real&lowbar;scalar`
|
|`complex&lowbar;scalar`
|
|`vector`
|
|`tensor`
|
|===

== Description

Scalars, vectors and tensors are mathematical objects that can be used to denote certain physical quantities and their values&period; They are as such independent of the particular choice of a coordinate system, whereas each scalar component of a vector or a tensor and each component vector and component tensor depend on that choice&period;

A scalar is a physical quantity that has magnitude but no direction&period; It might be a real or complex number which affects which operations are allowed on a quantity&period;

Vectors are physical quantities that possess both magnitude and direction and whose operations obey the axioms of a vector space&period;

Tensors can be used to describe more general physical quantities&period; For example, the Cauchy stress tensor possess magnitude, direction, and orientation qualities&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;symbol&lowbar;formatting&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
enum class unit&lowbar;symbol&lowbar;separator : int8&lowbar;t;
----

== Members


[cols=2]
|===
| Name
| Description
|`space`
|
|`half&lowbar;high&lowbar;dot`
|
|`default&lowbar;separator`
|
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;symbol&lowbar;formatting&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
enum class unit&lowbar;symbol&lowbar;solidus : int8&lowbar;t;
----

== Members


[cols=2]
|===
| Name
| Description
|`one&lowbar;denominator`
|
|`always`
|
|`never`
|
|`default&lowbar;denominator`
|
|===

Computes the absolute value of a quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; abs(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;abs(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;]
abs(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept;
----

== Return Value

Quantity The absolute value of a provided quantity

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| Quantity being the base of the operation
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] From,
    link:#mp_units-QuantitySpec[QuantitySpec] To&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
castable(
    From from,
    To to);
----

`cbrt` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

Computes the cubic root of a dimension


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-cbrt-05[cbrt](auto d);
----

[.small]#link:#mp_units-cbrt-05[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-cbrt-0e[cbrt](link:#mp_units-reference[reference]);
----

[.small]#link:#mp_units-cbrt-0e[_» more&period;&period;&period;_]#

Computes the cubic root of a quantity


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; cbrt(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;cbrt(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;cbrt(R), Rep&gt;]
link:#mp_units-cbrt-0d[cbrt](link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept;
----

[.small]#link:#mp_units-cbrt-0d[_» more&period;&period;&period;_]#

== Return Value

* Dimension The result of computation
* QuantitySpec The result of computation
* Unit The result of computation
* Quantity The result of computation

== Parameters

[cols=2]
|===
| Name
| Description
| *d*
| Dimension being the base of the operation
| *q*
| Quantity specification being the base of the operation
| *u*
| Unit being the base of the operation
|===

Computes the cubic root of a dimension

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
cbrt(auto d);
----

== Return Value

* Dimension The result of computation
* QuantitySpec The result of computation
* Unit The result of computation

== Parameters

[cols=2]
|===
| Name
| Description
| *d*
| Dimension being the base of the operation
| *q*
| Quantity specification being the base of the operation
| *u*
| Unit being the base of the operation
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
cbrt(link:#mp_units-reference[reference]);
----

Computes the cubic root of a quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; cbrt(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;cbrt(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;cbrt(R), Rep&gt;]
cbrt(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept;
----

== Description

Both the quantity value and its quantity specification are the base of the operation&period;

== Return Value

Quantity The result of computation

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| Quantity being the base of the operation
|===

Computes the smallest quantity with integer representation and unit type To with its number not less than q

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto To,
    auto R,
    typename Rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;detail&colon;&colon;clone&lowbar;reference&lowbar;with&lt;To&gt;(R), Rep&gt;]
ceil(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept
requires requires &lcub; q&period;force&lowbar;in(To)&semi; &rcub; &amp;&amp;
           ((treat&lowbar;as&lowbar;floating&lowbar;point&lt;Rep&gt; &amp;&amp; (requires(Rep v) &lcub; ceil(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;ceil(v)&semi; &rcub;)) &verbar;&verbar;
            (!treat&lowbar;as&lowbar;floating&lowbar;point&lt;Rep&gt; &amp;&amp; requires &lcub; representation&lowbar;values&lt;Rep&gt;&colon;&colon;one()&semi; &rcub;));
----

== Return Value

Quantity The rounded quantity with unit type To

== Template Parameters

[cols=2]
|===
| Name
| Description
| *q*
| Quantity being the base of the operation
|===

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| A quantity
|===

== Synopses

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    auto Vs&period;&period;&period;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
link:#mp_units-contains-0c8[contains]();
----

[.small]#link:#mp_units-contains-0c8[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;typename&period;&period;&period;&gt; typename T,
    typename&period;&period;&period; Ts&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
link:#mp_units-contains-01e[contains]();
----

[.small]#link:#mp_units-contains-01e[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;auto&period;&period;&period;&gt; typename T,
    typename&period;&period;&period; Ts&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
link:#mp_units-contains-0c1[contains]();
----

[.small]#link:#mp_units-contains-0c1[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    auto Vs&period;&period;&period;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
contains();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;typename&period;&period;&period;&gt; typename T,
    typename&period;&period;&period; Ts&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
contains();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;auto&period;&period;&period;&gt; typename T,
    typename&period;&period;&period; Ts&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
contains();
----

Computes the cubic power of a unit

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
cubic(auto u);
----

== Return Value

Unit The result of computation

== Parameters

[cols=2]
|===
| Name
| Description
| *u*
| Unit being the base of the operation
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Reference[Reference] R&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-PointOriginFor[PointOriginFor&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] auto
default&lowbar;point&lowbar;origin(R);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-dimension_symbol_formatting[dimension&lowbar;symbol&lowbar;formatting] fmt = dimension&lowbar;symbol&lowbar;formatting&lcub;&rcub;,
    typename CharT = char,
    link:#mp_units-Dimension[Dimension] D&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
std::basic&lowbar;string&lowbar;view&lt;CharT&gt;
dimension&lowbar;symbol(D);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT = char,
    std::output&lowbar;iterator&lt;CharT&gt; Out,
    link:#mp_units-Dimension[Dimension] D&gt;
constexpr
Out
dimension&lowbar;symbol&lowbar;to(
    Out out,
    D d,
    link:#mp_units-dimension_symbol_formatting[dimension&lowbar;symbol&lowbar;formatting] const& fmt = dimension&lowbar;symbol&lowbar;formatting&lcub;&rcub;);
----

Returns the epsilon of the quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Rep,
    link:#mp_units-Reference[Reference] R&gt;
requires RepresentationOf&lt;Rep, get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt; &amp;&amp; requires &lcub; std&colon;&colon;numeric&lowbar;limits&lt;Rep&gt;&colon;&colon;epsilon()&semi; &rcub;
&lsqb;&lsqb;deprecated, nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;R&lcub;&rcub;, Rep&gt;]
epsilon(R r) noexcept;
----

== Description

The returned value is defined by a &period;

== Return Value

Quantity The epsilon value for quantity&apos;s representation type

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Q*
| Quantity type being the base of the operation
|===

Computes Euler&apos;s raised to the given power

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-ReferenceOf[ReferenceOf&lt;dimensionless&gt;] auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; exp(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;exp(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;]
exp(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q);
----

== Description

[NOTE]
Such an operation has sense only for a dimensionless quantity&period;

== Return Value

Quantity The value of the same quantity type

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| Quantity being the base of the operation
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] From,
    link:#mp_units-QuantitySpec[QuantitySpec] To&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
explicitly&lowbar;convertible(
    From from,
    To to);
----

Computes the largest quantity with integer representation and unit type To with its number not greater than q

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto To,
    auto R,
    typename Rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;detail&colon;&colon;clone&lowbar;reference&lowbar;with&lt;To&gt;(R), Rep&gt;]
floor(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept
requires requires &lcub; q&period;force&lowbar;in(To)&semi; &rcub; &amp;&amp;
           ((treat&lowbar;as&lowbar;floating&lowbar;point&lt;Rep&gt; &amp;&amp; (requires(Rep v) &lcub; floor(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;floor(v)&semi; &rcub;)) &verbar;&verbar;
            (!treat&lowbar;as&lowbar;floating&lowbar;point&lt;Rep&gt; &amp;&amp; requires &lcub; representation&lowbar;values&lt;Rep&gt;&colon;&colon;one()&semi; &rcub;));
----

== Return Value

Quantity The rounded quantity with unit type To

== Template Parameters

[cols=2]
|===
| Name
| Description
| *q*
| Quantity being the base of the operation
|===

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| A quantity
|===

`fma` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

Computes the fma of 3 quantities


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto S,
    auto T,
    typename Rep1,
    typename Rep2,
    typename Rep3&gt;
requires requires &lcub; get&lowbar;common&lowbar;quantity&lowbar;spec(get&lowbar;quantity&lowbar;spec(R) &ast; get&lowbar;quantity&lowbar;spec(S), get&lowbar;quantity&lowbar;spec(T))&semi; &rcub; &amp;&amp;
           (equivalent(get&lowbar;unit(R) &ast; get&lowbar;unit(S), get&lowbar;unit(T))) &amp;&amp; requires(Rep1 v1, Rep2 v2, Rep3 v3) &lcub;
             requires requires &lcub; fma(v1, v2, v3)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;fma(v1, v2, v3)&semi; &rcub;&semi;
           &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;get&lowbar;common&lowbar;quantity&lowbar;spec(get&lowbar;quantity&lowbar;spec(R) &ast; get&lowbar;quantity&lowbar;spec(S), get&lowbar;quantity&lowbar;spec(T))&gt;] auto
link:#mp_units-fma-09[fma](
    link:#mp_units-quantity-01[quantity&lt;R, Rep1&gt;] const& a,
    link:#mp_units-quantity-01[quantity&lt;S, Rep2&gt;] const& x,
    link:#mp_units-quantity-01[quantity&lt;T, Rep3&gt;] const& b) noexcept;
----

[.small]#link:#mp_units-fma-09[_» more&period;&period;&period;_]#

Computes the fma of 2 quantities and a quantity point


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto S,
    auto T,
    auto Origin,
    typename Rep1,
    typename Rep2,
    typename Rep3&gt;
requires requires &lcub; get&lowbar;common&lowbar;quantity&lowbar;spec(get&lowbar;quantity&lowbar;spec(R) &ast; get&lowbar;quantity&lowbar;spec(S), get&lowbar;quantity&lowbar;spec(T))&semi; &rcub; &amp;&amp;
           (equivalent(get&lowbar;unit(R) &ast; get&lowbar;unit(S), get&lowbar;unit(T))) &amp;&amp; requires(Rep1 v1, Rep2 v2, Rep3 v3) &lcub;
             requires requires &lcub; fma(v1, v2, v3)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;fma(v1, v2, v3)&semi; &rcub;&semi;
           &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;get&lowbar;common&lowbar;quantity&lowbar;spec(get&lowbar;quantity&lowbar;spec(R) &ast; get&lowbar;quantity&lowbar;spec(S), get&lowbar;quantity&lowbar;spec(T))&gt;] auto
link:#mp_units-fma-0a[fma](
    link:#mp_units-quantity-01[quantity&lt;R, Rep1&gt;] const& a,
    link:#mp_units-quantity-01[quantity&lt;S, Rep2&gt;] const& x,
    link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;T, Origin, Rep3&gt;] const& b) noexcept;
----

[.small]#link:#mp_units-fma-0a[_» more&period;&period;&period;_]#

== Return Value

* Quantity&colon; The nearest floating point representable to ax&plus;b
* QuantityPoint&colon; The nearest floating point representable to ax&plus;b

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Multiplicand
| *x&colon;*
| Multiplicand
| *b&colon;*
| Addend
|===

Computes the fma of 3 quantities

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto S,
    auto T,
    typename Rep1,
    typename Rep2,
    typename Rep3&gt;
requires requires &lcub; get&lowbar;common&lowbar;quantity&lowbar;spec(get&lowbar;quantity&lowbar;spec(R) &ast; get&lowbar;quantity&lowbar;spec(S), get&lowbar;quantity&lowbar;spec(T))&semi; &rcub; &amp;&amp;
           (equivalent(get&lowbar;unit(R) &ast; get&lowbar;unit(S), get&lowbar;unit(T))) &amp;&amp; requires(Rep1 v1, Rep2 v2, Rep3 v3) &lcub;
             requires requires &lcub; fma(v1, v2, v3)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;fma(v1, v2, v3)&semi; &rcub;&semi;
           &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;get&lowbar;common&lowbar;quantity&lowbar;spec(get&lowbar;quantity&lowbar;spec(R) &ast; get&lowbar;quantity&lowbar;spec(S), get&lowbar;quantity&lowbar;spec(T))&gt;] auto
fma(
    link:#mp_units-quantity-01[quantity&lt;R, Rep1&gt;] const& a,
    link:#mp_units-quantity-01[quantity&lt;S, Rep2&gt;] const& x,
    link:#mp_units-quantity-01[quantity&lt;T, Rep3&gt;] const& b) noexcept;
----

== Return Value

Quantity&colon; The nearest floating point representable to ax&plus;b

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Multiplicand
| *x&colon;*
| Multiplicand
| *b&colon;*
| Addend
| *a*
| A quantity
| *x*
| A quantity
| *b*
| A quantity
|===

Computes the fma of 2 quantities and a quantity point

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto S,
    auto T,
    auto Origin,
    typename Rep1,
    typename Rep2,
    typename Rep3&gt;
requires requires &lcub; get&lowbar;common&lowbar;quantity&lowbar;spec(get&lowbar;quantity&lowbar;spec(R) &ast; get&lowbar;quantity&lowbar;spec(S), get&lowbar;quantity&lowbar;spec(T))&semi; &rcub; &amp;&amp;
           (equivalent(get&lowbar;unit(R) &ast; get&lowbar;unit(S), get&lowbar;unit(T))) &amp;&amp; requires(Rep1 v1, Rep2 v2, Rep3 v3) &lcub;
             requires requires &lcub; fma(v1, v2, v3)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;fma(v1, v2, v3)&semi; &rcub;&semi;
           &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;get&lowbar;common&lowbar;quantity&lowbar;spec(get&lowbar;quantity&lowbar;spec(R) &ast; get&lowbar;quantity&lowbar;spec(S), get&lowbar;quantity&lowbar;spec(T))&gt;] auto
fma(
    link:#mp_units-quantity-01[quantity&lt;R, Rep1&gt;] const& a,
    link:#mp_units-quantity-01[quantity&lt;S, Rep2&gt;] const& x,
    link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;T, Origin, Rep3&gt;] const& b) noexcept;
----

== Return Value

QuantityPoint&colon; The nearest floating point representable to ax&plus;b

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Multiplicand
| *x&colon;*
| Multiplicand
| *b&colon;*
| Addend
| *a*
| A quantity
| *x*
| A quantity
| *b*
| A quantity point
|===

Computes the floating&hyphen;point remainder of the division operation x &sol; y&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R1,
    typename Rep1,
    auto R2,
    typename Rep2&gt;
requires requires(Rep1 v1, Rep2 v2) &lcub;
    get&lowbar;common&lowbar;reference(R1, R2)&semi;
    requires requires &lcub; fmod(v1, v2)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;fmod(v1, v2)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;get&lowbar;quantity&lowbar;spec(R1)&gt;] auto
fmod(
    link:#mp_units-quantity-01[quantity&lt;R1, Rep1&gt;] const& x,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& y) noexcept;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *x*
| A quantity
| *y*
| A quantity
|===

== Synopses

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    same&lowbar;as&lt;T&gt; auto V&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
link:#mp_units-get-039[get]();
----

[.small]#link:#mp_units-get-039[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;typename&period;&period;&period;&gt; typename T,
    typename T1&gt;
requires is&lowbar;specialization&lowbar;of&lt;T1, T&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
link:#mp_units-get-01[get]();
----

[.small]#link:#mp_units-get-01[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;auto&period;&period;&period;&gt; typename T,
    typename T1&gt;
requires is&lowbar;specialization&lowbar;of&lowbar;v&lt;T1, T&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
link:#mp_units-get-05f[get]();
----

[.small]#link:#mp_units-get-05f[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    auto V1,
    auto V2,
    auto Vs&period;&period;&period;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
link:#mp_units-get-07[get]();
----

[.small]#link:#mp_units-get-07[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;typename&period;&period;&period;&gt; typename T,
    typename T1,
    typename T2,
    typename&period;&period;&period; Ts&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
link:#mp_units-get-03d[get]();
----

[.small]#link:#mp_units-get-03d[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;auto&period;&period;&period;&gt; typename T,
    typename T1,
    typename T2,
    typename&period;&period;&period; Ts&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
link:#mp_units-get-05b[get]();
----

[.small]#link:#mp_units-get-05b[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    same&lowbar;as&lt;T&gt; auto V&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
get();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;typename&period;&period;&period;&gt; typename T,
    typename T1&gt;
requires is&lowbar;specialization&lowbar;of&lt;T1, T&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
get();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;auto&period;&period;&period;&gt; typename T,
    typename T1&gt;
requires is&lowbar;specialization&lowbar;of&lowbar;v&lt;T1, T&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
get();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    auto V1,
    auto V2,
    auto Vs&period;&period;&period;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
get();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;typename&period;&period;&period;&gt; typename T,
    typename T1,
    typename T2,
    typename&period;&period;&period; Ts&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
get();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    template&lt;auto&period;&period;&period;&gt; typename T,
    typename T1,
    typename T2,
    typename&period;&period;&period; Ts&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
get();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
get&lowbar;canonical&lowbar;unit(auto u);
----

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
link:#mp_units-get_common_quantity_spec-04[get&lowbar;common&lowbar;quantity&lowbar;spec](auto q);
----

[.small]#link:#mp_units-get_common_quantity_spec-04[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] Q1,
    link:#mp_units-QuantitySpec[QuantitySpec] Q2&gt;
requires (detail&colon;&colon;have&lowbar;common&lowbar;quantity&lowbar;spec(Q1&lcub;&rcub;, Q2&lcub;&rcub;))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
link:#mp_units-get_common_quantity_spec-01[get&lowbar;common&lowbar;quantity&lowbar;spec](
    Q1,
    Q2);
----

[.small]#link:#mp_units-get_common_quantity_spec-01[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
link:#mp_units-get_common_quantity_spec-0a[get&lowbar;common&lowbar;quantity&lowbar;spec](
    auto q1,
    auto q2,
    auto q3,
    auto&period;&period;&period; rest)
requires requires &lcub; mp&lowbar;units&colon;&colon;get&lowbar;common&lowbar;quantity&lowbar;spec(mp&lowbar;units&colon;&colon;get&lowbar;common&lowbar;quantity&lowbar;spec(q1, q2), q3, rest&period;&period;&period;)&semi; &rcub;;
----

[.small]#link:#mp_units-get_common_quantity_spec-0a[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
get&lowbar;common&lowbar;quantity&lowbar;spec(auto q);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] Q1,
    link:#mp_units-QuantitySpec[QuantitySpec] Q2&gt;
requires (detail&colon;&colon;have&lowbar;common&lowbar;quantity&lowbar;spec(Q1&lcub;&rcub;, Q2&lcub;&rcub;))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
get&lowbar;common&lowbar;quantity&lowbar;spec(
    Q1,
    Q2);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
get&lowbar;common&lowbar;quantity&lowbar;spec(
    auto q1,
    auto q2,
    auto q3,
    auto&period;&period;&period; rest)
requires requires &lcub; mp&lowbar;units&colon;&colon;get&lowbar;common&lowbar;quantity&lowbar;spec(mp&lowbar;units&colon;&colon;get&lowbar;common&lowbar;quantity&lowbar;spec(q1, q2), q3, rest&period;&period;&period;)&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R1,
    link:#mp_units-Reference[Reference] R2,
    link:#mp_units-Reference[Reference]&period;&period;&period; Rest&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Reference[Reference] auto
get&lowbar;common&lowbar;reference(
    auto u1,
    auto u2,
    auto&period;&period;&period; rest)
requires (!(MP&lowbar;UNITS&lowbar;ASSOCIATED&lowbar;UNIT&lowbar;T(R1) &amp;&amp; MP&lowbar;UNITS&lowbar;ASSOCIATED&lowbar;UNIT&lowbar;T(R2) &amp;&amp;
             (&period;&period;&period; &amp;&amp; MP&lowbar;UNITS&lowbar;ASSOCIATED&lowbar;UNIT&lowbar;T(Rest)))) &amp;&amp;
          requires &lcub;
            get&lowbar;common&lowbar;quantity&lowbar;spec(get&lowbar;quantity&lowbar;spec(r1), get&lowbar;quantity&lowbar;spec(r2), get&lowbar;quantity&lowbar;spec(rest)&period;&period;&period;)&semi;
            get&lowbar;common&lowbar;unit(get&lowbar;unit(r1), get&lowbar;unit(r2), get&lowbar;unit(rest)&period;&period;&period;)&semi;
          &rcub;;
----

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-get_common_unit-0e[get&lowbar;common&lowbar;unit](auto u);
----

[.small]#link:#mp_units-get_common_unit-0e[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit]&period;&period;&period; Us,
    &sol;&ast; implementation-defined &ast;&sol; NewUnit&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-get_common_unit-08c[get&lowbar;common&lowbar;unit](
    NewUnit nu,
    link:#mp_units-common_unit[common&lowbar;unit&lt;Us&period;&period;&period;&gt;] cu);
----

[.small]#link:#mp_units-get_common_unit-08c[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] U1,
    &sol;&ast; implementation-defined &ast;&sol; U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-get_common_unit-0d[get&lowbar;common&lowbar;unit](
    U1 u1,
    U2 u2);
----

[.small]#link:#mp_units-get_common_unit-0d[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit]&period;&period;&period; Us,
    &sol;&ast; implementation-defined &ast;&sol; NewUnit&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-get_common_unit-08d[get&lowbar;common&lowbar;unit](
    link:#mp_units-common_unit[common&lowbar;unit&lt;Us&period;&period;&period;&gt;],
    NewUnit);
----

[.small]#link:#mp_units-get_common_unit-08d[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] Front,
    link:#mp_units-Unit[Unit]&period;&period;&period; Rest,
    link:#mp_units-Unit[Unit]&period;&period;&period; Us&gt;
requires (detail&colon;&colon;UnitConvertibleTo&lt;common&lowbar;unit&lt;Front, Rest&period;&period;&period;&gt;, common&lowbar;unit&lt;Us&period;&period;&period;&gt;&lcub;&rcub;&gt;)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-get_common_unit-09[get&lowbar;common&lowbar;unit](
    link:#mp_units-common_unit[common&lowbar;unit&lt;Front, Rest&period;&period;&period;&gt;],
    link:#mp_units-common_unit[common&lowbar;unit&lt;Us&period;&period;&period;&gt;]);
----

[.small]#link:#mp_units-get_common_unit-09[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-get_common_unit-02[get&lowbar;common&lowbar;unit](
    auto u1,
    auto u2,
    auto u3,
    auto&period;&period;&period; rest)
requires requires &lcub; get&lowbar;common&lowbar;unit(get&lowbar;common&lowbar;unit(u1, u2), u3, rest&period;&period;&period;)&semi; &rcub;;
----

[.small]#link:#mp_units-get_common_unit-02[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
get&lowbar;common&lowbar;unit(auto u);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit]&period;&period;&period; Us,
    &sol;&ast; implementation-defined &ast;&sol; NewUnit&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
get&lowbar;common&lowbar;unit(
    NewUnit nu,
    link:#mp_units-common_unit[common&lowbar;unit&lt;Us&period;&period;&period;&gt;] cu);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] U1,
    &sol;&ast; implementation-defined &ast;&sol; U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
get&lowbar;common&lowbar;unit(
    U1 u1,
    U2 u2);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit]&period;&period;&period; Us,
    &sol;&ast; implementation-defined &ast;&sol; NewUnit&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
get&lowbar;common&lowbar;unit(
    link:#mp_units-common_unit[common&lowbar;unit&lt;Us&period;&period;&period;&gt;],
    NewUnit);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] Front,
    link:#mp_units-Unit[Unit]&period;&period;&period; Rest,
    link:#mp_units-Unit[Unit]&period;&period;&period; Us&gt;
requires (detail&colon;&colon;UnitConvertibleTo&lt;common&lowbar;unit&lt;Front, Rest&period;&period;&period;&gt;, common&lowbar;unit&lt;Us&period;&period;&period;&gt;&lcub;&rcub;&gt;)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
get&lowbar;common&lowbar;unit(
    link:#mp_units-common_unit[common&lowbar;unit&lt;Front, Rest&period;&period;&period;&gt;],
    link:#mp_units-common_unit[common&lowbar;unit&lt;Us&period;&period;&period;&gt;]);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
get&lowbar;common&lowbar;unit(
    auto u1,
    auto u2,
    auto u3,
    auto&period;&period;&period; rest)
requires requires &lcub; get&lowbar;common&lowbar;unit(get&lowbar;common&lowbar;unit(u1, u2), u3, rest&period;&period;&period;)&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantitySpec[QuantitySpec] Q&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol; auto
get&lowbar;kind(Q);
----

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&lowbar;concepts&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
link:#mp_units-get_quantity_spec-029[get&lowbar;quantity&lowbar;spec](U);
----

[.small]#link:#mp_units-get_quantity_spec-029[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q,
    typename U&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
link:#mp_units-get_quantity_spec-00[get&lowbar;quantity&lowbar;spec](link:#mp_units-reference[reference&lt;Q, U&gt;]);
----

[.small]#link:#mp_units-get_quantity_spec-00[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
get&lowbar;quantity&lowbar;spec(U);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q,
    typename U&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-QuantitySpec[QuantitySpec] auto
get&lowbar;quantity&lowbar;spec(link:#mp_units-reference[reference&lt;Q, U&gt;]);
----

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&lowbar;concepts&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-get_unit-06[get&lowbar;unit](auto u);
----

[.small]#link:#mp_units-get_unit-06[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q,
    typename U&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-get_unit-09[get&lowbar;unit](link:#mp_units-reference[reference&lt;Q, U&gt;]);
----

[.small]#link:#mp_units-get_unit-09[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
get&lowbar;unit(auto u);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q,
    typename U&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
get&lowbar;unit(link:#mp_units-reference[reference&lt;Q, U&gt;]);
----

`hypot` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

Computes the square root of the sum of the squares of x and y, without undue overflow or underflow at intermediate stages of the computation


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R1,
    typename Rep1,
    auto R2,
    typename Rep2&gt;
requires requires(Rep1 v1, Rep2 v2) &lcub;
    get&lowbar;common&lowbar;reference(R1, R2)&semi;
    requires requires &lcub; hypot(v1, v2)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;hypot(v1, v2)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;get&lowbar;quantity&lowbar;spec(get&lowbar;common&lowbar;reference(R1, R2))&gt;] auto
link:#mp_units-hypot-0e[hypot](
    link:#mp_units-quantity-01[quantity&lt;R1, Rep1&gt;] const& x,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& y) noexcept;
----

[.small]#link:#mp_units-hypot-0e[_» more&period;&period;&period;_]#

Computes the square root of the sum of the squares of x, y, and z, without undue overflow or underflow at intermediate stages of the computation


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R1,
    typename Rep1,
    auto R2,
    typename Rep2,
    auto R3,
    typename Rep3&gt;
requires requires(Rep1 v1, Rep2 v2, Rep3 v3) &lcub;
    get&lowbar;common&lowbar;reference(R1, R2, R3)&semi;
    requires requires &lcub; hypot(v1, v2, v3)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;hypot(v1, v2, v3)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;get&lowbar;quantity&lowbar;spec(get&lowbar;common&lowbar;reference(R1, R2, R3))&gt;] auto
link:#mp_units-hypot-08[hypot](
    link:#mp_units-quantity-01[quantity&lt;R1, Rep1&gt;] const& x,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& y,
    link:#mp_units-quantity-01[quantity&lt;R3, Rep3&gt;] const& z) noexcept;
----

[.small]#link:#mp_units-hypot-08[_» more&period;&period;&period;_]#

Computes the square root of the sum of the squares of x and y, without undue overflow or underflow at intermediate stages of the computation

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R1,
    typename Rep1,
    auto R2,
    typename Rep2&gt;
requires requires(Rep1 v1, Rep2 v2) &lcub;
    get&lowbar;common&lowbar;reference(R1, R2)&semi;
    requires requires &lcub; hypot(v1, v2)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;hypot(v1, v2)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;get&lowbar;quantity&lowbar;spec(get&lowbar;common&lowbar;reference(R1, R2))&gt;] auto
hypot(
    link:#mp_units-quantity-01[quantity&lt;R1, Rep1&gt;] const& x,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& y) noexcept;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *x*
| A quantity
| *y*
| A quantity
|===

Computes the square root of the sum of the squares of x, y, and z, without undue overflow or underflow at intermediate stages of the computation

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R1,
    typename Rep1,
    auto R2,
    typename Rep2,
    auto R3,
    typename Rep3&gt;
requires requires(Rep1 v1, Rep2 v2, Rep3 v3) &lcub;
    get&lowbar;common&lowbar;reference(R1, R2, R3)&semi;
    requires requires &lcub; hypot(v1, v2, v3)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;hypot(v1, v2, v3)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;get&lowbar;quantity&lowbar;spec(get&lowbar;common&lowbar;reference(R1, R2, R3))&gt;] auto
hypot(
    link:#mp_units-quantity-01[quantity&lt;R1, Rep1&gt;] const& x,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& y,
    link:#mp_units-quantity-01[quantity&lt;R3, Rep3&gt;] const& z) noexcept;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *x*
| A quantity
| *y*
| A quantity
| *z*
| A quantity
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] From,
    link:#mp_units-QuantitySpec[QuantitySpec] To&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
implicitly&lowbar;convertible(
    From from,
    To to);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] QS1,
    link:#mp_units-QuantitySpec[QuantitySpec] QS2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
interconvertible(
    QS1 qs1,
    QS2 qs2);
----

Computes the inverse of a quantity in a provided unit

== Synopses

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-inverse-0d[inverse](auto d);
----

[.small]#link:#mp_units-inverse-0d[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-inverse-0b[inverse](link:#mp_units-reference[reference]);
----

[.small]#link:#mp_units-inverse-0b[_» more&period;&period;&period;_]#

Computes the inverse of a quantity in a provided unit


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto To,
    auto R,
    typename Rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-inverse-09[inverse](link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q)
requires (!detail&colon;&colon;scaling&lowbar;overflows&lowbar;non&lowbar;zero&lowbar;values&lt;Rep&gt;(one &sol; get&lowbar;unit(R), To)) &amp;&amp; requires &lcub;
    representation&lowbar;values&lt;Rep&gt;&colon;&colon;one()&semi;
    value&lowbar;cast&lt;To&gt;(representation&lowbar;values&lt;Rep&gt;&colon;&colon;one() &sol; q)&semi;
  &rcub;;
----

[.small]#link:#mp_units-inverse-09[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
inverse(auto d);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
inverse(link:#mp_units-reference[reference]);
----

Computes the inverse of a quantity in a provided unit

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto To,
    auto R,
    typename Rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
inverse(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q)
requires (!detail&colon;&colon;scaling&lowbar;overflows&lowbar;non&lowbar;zero&lowbar;values&lt;Rep&gt;(one &sol; get&lowbar;unit(R), To)) &amp;&amp; requires &lcub;
    representation&lowbar;values&lt;Rep&gt;&colon;&colon;one()&semi;
    value&lowbar;cast&lt;To&gt;(representation&lowbar;values&lt;Rep&gt;&colon;&colon;one() &sol; q)&semi;
  &rcub;;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| A quantity
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;compare&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
requires requires &lcub;
    &lcub; T&colon;&colon;zero() &rcub; &hyphen;&gt; std&colon;&colon;equality&lowbar;comparable&lowbar;with&lt;T&gt;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
is&lowbar;eq&lowbar;zero(T v);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;compare&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
requires requires &lcub;
    &lcub; T&colon;&colon;zero() &rcub; &hyphen;&gt; std&colon;&colon;three&lowbar;way&lowbar;comparable&lowbar;with&lt;T&gt;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
is&lowbar;gt&lowbar;zero(T v);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;compare&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
requires requires &lcub;
    &lcub; T&colon;&colon;zero() &rcub; &hyphen;&gt; std&colon;&colon;three&lowbar;way&lowbar;comparable&lowbar;with&lt;T&gt;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
is&lowbar;gteq&lowbar;zero(T v);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;compare&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
requires requires &lcub;
    &lcub; T&colon;&colon;zero() &rcub; &hyphen;&gt; std&colon;&colon;three&lowbar;way&lowbar;comparable&lowbar;with&lt;T&gt;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
is&lowbar;lt&lowbar;zero(T v);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;compare&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
requires requires &lcub;
    &lcub; T&colon;&colon;zero() &rcub; &hyphen;&gt; std&colon;&colon;three&lowbar;way&lowbar;comparable&lowbar;with&lt;T&gt;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
is&lowbar;lteq&lowbar;zero(T v);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;compare&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
requires requires &lcub;
    &lcub; T&colon;&colon;zero() &rcub; &hyphen;&gt; std&colon;&colon;equality&lowbar;comparable&lowbar;with&lt;T&gt;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
is&lowbar;neq&lowbar;zero(T v);
----

`isfinite` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

Determines if a quantity is finite&period;


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; isfinite(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;isfinite(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-isfinite-0d[isfinite](link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& a) noexcept;
----

[.small]#link:#mp_units-isfinite-0d[_» more&period;&period;&period;_]#

Determines if a quantity point is finite&period;


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto PO,
    typename Rep&gt;
requires requires(quantity&lt;R, Rep&gt; q) &lcub; isfinite(q)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-isfinite-0b[isfinite](link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R, PO, Rep&gt;] const& a) noexcept;
----

[.small]#link:#mp_units-isfinite-0b[_» more&period;&period;&period;_]#

== Return Value

* bool&colon; Whether the quantity is finite or not&period;
* bool&colon; Whether the quantity point is finite or not&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Quantity to analyze&period;
|===

Determines if a quantity is finite&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; isfinite(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;isfinite(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
isfinite(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& a) noexcept;
----

== Return Value

bool&colon; Whether the quantity is finite or not&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Quantity to analyze&period;
| *a*
| A quantity
|===

Determines if a quantity point is finite&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto PO,
    typename Rep&gt;
requires requires(quantity&lt;R, Rep&gt; q) &lcub; isfinite(q)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
isfinite(link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R, PO, Rep&gt;] const& a) noexcept;
----

== Return Value

bool&colon; Whether the quantity point is finite or not&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Quantity point to analyze&period;
| *a*
| A quantity point
|===

`isinf` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

Determines if a quantity is infinite&period;


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; isinf(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;isinf(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-isinf-0f[isinf](link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& a) noexcept;
----

[.small]#link:#mp_units-isinf-0f[_» more&period;&period;&period;_]#

Determines if a quantity point is infinite&period;


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto PO,
    typename Rep&gt;
requires requires(quantity&lt;R, Rep&gt; q) &lcub; isinf(q)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-isinf-04[isinf](link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R, PO, Rep&gt;] const& a) noexcept;
----

[.small]#link:#mp_units-isinf-04[_» more&period;&period;&period;_]#

== Return Value

* bool&colon; Whether the quantity is infinite or not&period;
* bool&colon; Whether the quantity point is infinite or not&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Quantity to analyze&period;
|===

Determines if a quantity is infinite&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; isinf(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;isinf(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
isinf(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& a) noexcept;
----

== Return Value

bool&colon; Whether the quantity is infinite or not&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Quantity to analyze&period;
| *a*
| A quantity
|===

Determines if a quantity point is infinite&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto PO,
    typename Rep&gt;
requires requires(quantity&lt;R, Rep&gt; q) &lcub; isinf(q)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
isinf(link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R, PO, Rep&gt;] const& a) noexcept;
----

== Return Value

bool&colon; Whether the quantity point is infinite or not&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Quantity point to analyze&period;
| *a*
| A quantity point
|===

`isnan` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

Determines if a quantity is a nan&period;


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; isnan(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;isnan(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-isnan-00[isnan](link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& a) noexcept;
----

[.small]#link:#mp_units-isnan-00[_» more&period;&period;&period;_]#

Determines if a quantity point is a nan&period;


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto PO,
    typename Rep&gt;
requires requires(quantity&lt;R, Rep&gt; q) &lcub; isnan(q)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-isnan-082[isnan](link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R, PO, Rep&gt;] const& a) noexcept;
----

[.small]#link:#mp_units-isnan-082[_» more&period;&period;&period;_]#

== Return Value

* bool&colon; Whether the quantity is a NaN or not&period;
* bool&colon; Whether the quantity point is a NaN or not&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Quantity to analyze&period;
|===

Determines if a quantity is a nan&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; isnan(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;isnan(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
isnan(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& a) noexcept;
----

== Return Value

bool&colon; Whether the quantity is a NaN or not&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Quantity to analyze&period;
| *a*
| A quantity
|===

Determines if a quantity point is a nan&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    auto PO,
    typename Rep&gt;
requires requires(quantity&lt;R, Rep&gt; q) &lcub; isnan(q)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
isnan(link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R, PO, Rep&gt;] const& a) noexcept;
----

== Return Value

bool&colon; Whether the quantity point is a NaN or not&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a&colon;*
| Quantity point to analyze&period;
| *a*
| A quantity point
|===

Linear interpolation or extrapolation

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R1,
    auto Origin,
    typename Rep1,
    auto R2,
    typename Rep2,
    typename Factor&gt;
requires requires(Rep1 a, Rep2 b, Factor t) &lcub;
    get&lowbar;common&lowbar;reference(R1, R2)&semi;
    requires requires &lcub; lerp(a, b, t)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;lerp(a, b, t)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;get&lowbar;quantity&lowbar;spec(get&lowbar;common&lowbar;reference(R1, R2))&gt;] auto
lerp(
    link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R1, Origin, Rep1&gt;] const& a,
    link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R2, Origin, Rep2&gt;] const& b,
    Factor const& t) noexcept;
----

== Description

Computes the linear interpolation between `a` and `b`, if the parameter `t` is inside `&lsqb;​0​, 1)` (the linear extrapolation otherwise), i&period;e&period; the result of `a &plus; t(b − a)` with accounting for floating&hyphen;point calculation imprecision&period;

== Parameters

[cols=2]
|===
| Name
| Description
| *a*
| A quantity point
| *b*
| A quantity point
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
T
magnitude(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector] const& vec)
requires treat&lowbar;as&lowbar;floating&lowbar;point&lt;T&gt;;
----

Computes the midpoint of two points

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R1,
    auto Origin,
    typename Rep1,
    auto R2,
    typename Rep2&gt;
requires requires(Rep1 a, Rep2 b) &lcub;
    get&lowbar;common&lowbar;reference(R1, R2)&semi;
    requires requires &lcub; midpoint(a, b)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;midpoint(a, b)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPointOf[QuantityPointOf&lt;get&lowbar;quantity&lowbar;spec(get&lowbar;common&lowbar;reference(R1, R2))&gt;] auto
midpoint(
    link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R1, Origin, Rep1&gt;] const& a,
    link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;R2, Origin, Rep2&gt;] const& b) noexcept;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *a*
| A quantity point
| *b*
| A quantity point
|===

Modulus operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;modulus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_mod-0c5[operator%](
    Q const& lhs,
    Value const& rhs);
----

[.small]#link:#mp_units-operator_mod-0c5[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;modulus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_mod-0c9[operator%](
    Value const& lhs,
    Q const& rhs);
----

[.small]#link:#mp_units-operator_mod-0c9[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires (!treat&lowbar;as&lowbar;floating&lowbar;point&lt;Rep&gt;) &amp;&amp; (!treat&lowbar;as&lowbar;floating&lowbar;point&lt;Rep2&gt;) &amp;&amp;
            detail&colon;&colon;CommonlyInvocableQuantities&lt;std&colon;&colon;modulus&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_mod-0d[operator%](
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_mod-0d[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;modulus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator%(
    Q const& lhs,
    Value const& rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;modulus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator%(
    Value const& lhs,
    Q const& rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires (!treat&lowbar;as&lowbar;floating&lowbar;point&lt;Rep&gt;) &amp;&amp; (!treat&lowbar;as&lowbar;floating&lowbar;point&lt;Rep2&gt;) &amp;&amp;
            detail&colon;&colon;CommonlyInvocableQuantities&lt;std&colon;&colon;modulus&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator%(
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

Multiplication operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U1&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-operator_star-02b[operator&ast;](
    U1 lhs,
    link:#mp_units-reference[reference] rhs);
----

[.small]#link:#mp_units-operator_star-02b[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-operator_star-0f[operator&ast;](
    link:#mp_units-reference[reference] lhs,
    U2 rhs);
----

[.small]#link:#mp_units-operator_star-0f[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R,
    typename Q&gt;
requires Quantity&lt;std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;Q&gt;&gt;
constexpr
auto
link:#mp_units-operator_star-0b[operator&ast;](
    R lhs,
    Q&& q) = delete;
----

[.small]#link:#mp_units-operator_star-0b[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R,
    typename Rep&gt;
requires RepresentationOf&lt;std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;Rep&gt;, get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;
constexpr
auto
link:#mp_units-operator_star-029[operator&ast;](
    R lhs,
    Rep&& rhs) = delete;
----

[.small]#link:#mp_units-operator_star-029[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q2,
    typename U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-operator_star-05[operator&ast;](
    link:#mp_units-reference[reference] lhs,
    link:#mp_units-reference[reference&lt;Q2, U2&gt;] rhs);
----

[.small]#link:#mp_units-operator_star-05[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    typename Value&gt;
requires (!Quantity&lt;Value&gt;) &amp;&amp;
            (!Reference&lt;Value&gt;) &amp;&amp; detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;multiplies&lt;&gt;, rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-operator_star-002[operator&ast;](
    Q const& q,
    Value const& val);
----

[.small]#link:#mp_units-operator_star-002[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Value,
    std::derived&lowbar;from&lt;quantity&gt; Q&gt;
requires (!Quantity&lt;Value&gt;) &amp;&amp;
            (!Reference&lt;Value&gt;) &amp;&amp; detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;multiplies&lt;&gt;, const Value&amp;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-operator_star-0a[operator&ast;](
    Value const& val,
    Q const& q);
----

[.small]#link:#mp_units-operator_star-0a[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;InvocableQuantities&lt;std&colon;&colon;multiplies&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_star-04[operator&ast;](
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_star-04[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_star-022[operator&ast;](
    FwdQ&& q,
    R rhs);
----

[.small]#link:#mp_units-operator_star-022[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
requires detail&colon;&colon;OffsetUnit&lt;decltype(get&lowbar;unit(R&lcub;&rcub;))&gt;
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
constexpr
auto
link:#mp_units-operator_star-09[operator&ast;](
    FwdRep&& lhs,
    R r);
----

[.small]#link:#mp_units-operator_star-09[_» more&period;&period;&period;_]#

Multiplication operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
requires (!detail&colon;&colon;OffsetUnit&lt;decltype(get&lowbar;unit(R&lcub;&rcub;))&gt;)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;R&lcub;&rcub;, Rep&gt;]
link:#mp_units-operator_star-009[operator&ast;](
    FwdRep&& lhs,
    R r);
----

[.small]#link:#mp_units-operator_star-009[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U1&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
operator&ast;(
    U1 lhs,
    link:#mp_units-reference[reference] rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
operator&ast;(
    link:#mp_units-reference[reference] lhs,
    U2 rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R,
    typename Q&gt;
requires Quantity&lt;std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;Q&gt;&gt;
constexpr
auto
operator&ast;(
    R lhs,
    Q&& q) = delete;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R,
    typename Rep&gt;
requires RepresentationOf&lt;std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;Rep&gt;, get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;
constexpr
auto
operator&ast;(
    R lhs,
    Rep&& rhs) = delete;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q2,
    typename U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
operator&ast;(
    link:#mp_units-reference[reference] lhs,
    link:#mp_units-reference[reference&lt;Q2, U2&gt;] rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    typename Value&gt;
requires (!Quantity&lt;Value&gt;) &amp;&amp;
            (!Reference&lt;Value&gt;) &amp;&amp; detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;multiplies&lt;&gt;, rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
operator&ast;(
    Q const& q,
    Value const& val);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Value,
    std::derived&lowbar;from&lt;quantity&gt; Q&gt;
requires (!Quantity&lt;Value&gt;) &amp;&amp;
            (!Reference&lt;Value&gt;) &amp;&amp; detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;multiplies&lt;&gt;, const Value&amp;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
operator&ast;(
    Value const& val,
    Q const& q);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;InvocableQuantities&lt;std&colon;&colon;multiplies&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&ast;(
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&ast;(
    FwdQ&& q,
    R rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
requires detail&colon;&colon;OffsetUnit&lt;decltype(get&lowbar;unit(R&lcub;&rcub;))&gt;
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
constexpr
auto
operator&ast;(
    FwdRep&& lhs,
    R r);
----

Multiplication operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
requires (!detail&colon;&colon;OffsetUnit&lt;decltype(get&lowbar;unit(R&lcub;&rcub;))&gt;)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;R&lcub;&rcub;, Rep&gt;]
operator&ast;(
    FwdRep&& lhs,
    R r);
----

== Return Value

A quantity

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *r*
| The right operand
|===

Addition operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

Addition operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, 1 &plus; N&gt;]
link:#mp_units-operator_plus-07[operator&plus;](
    CharT const lhs,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& rhs) noexcept;
----

[.small]#link:#mp_units-operator_plus-07[_» more&period;&period;&period;_]#

Addition operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N &plus; 1&gt;]
link:#mp_units-operator_plus-0e3[operator&plus;](
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    CharT rhs) noexcept;
----

[.small]#link:#mp_units-operator_plus-0e3[_» more&period;&period;&period;_]#

Addition operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N &plus; N2&gt;]
link:#mp_units-operator_plus-0e6[operator&plus;](
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N2&gt;] const& rhs) noexcept;
----

[.small]#link:#mp_units-operator_plus-0e6[_» more&period;&period;&period;_]#

Addition operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N &plus; N2 &hyphen; 1&gt;]
link:#mp_units-operator_plus-0ec[operator&plus;](
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    CharT const(& rhs)[]) noexcept;
----

[.small]#link:#mp_units-operator_plus-0ec[_» more&period;&period;&period;_]#

Addition operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N1&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N1 &plus; N &hyphen; 1&gt;]
link:#mp_units-operator_plus-06[operator&plus;](
    CharT const(& lhs)[],
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& rhs) noexcept;
----

[.small]#link:#mp_units-operator_plus-06[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;plus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_plus-0b7[operator&plus;](
    Q const& lhs,
    Value const& rhs);
----

[.small]#link:#mp_units-operator_plus-0b7[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;plus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_plus-04[operator&plus;](
    Value const& lhs,
    Q const& rhs);
----

[.small]#link:#mp_units-operator_plus-04[_» more&period;&period;&period;_]#

Addition operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::size&lowbar;t N2,
    std::size&lowbar;t M2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N &plus; N2, M &plus; M2&gt;]
link:#mp_units-operator_plus-0e1[operator&plus;](
    link:#mp_units-symbol_text-032[symbol&lowbar;text] const& lhs,
    link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N2, M2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_plus-0e1[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;CommonlyInvocableQuantities&lt;std&colon;&colon;plus&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_plus-0b5[operator&plus;](
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_plus-0b5[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-ReferenceOf[ReferenceOf&lt;PO&period;&lowbar;quantity&lowbar;spec&lowbar;&gt;] auto R2,
    typename Rep2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
link:#mp_units-operator_plus-0a5[operator&plus;](
    QP const& qp,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& q)
requires requires &lcub; qp&period;quantity&lowbar;ref&lowbar;from(PO) &plus; q&semi; &rcub;;
----

[.small]#link:#mp_units-operator_plus-0a5[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-ReferenceOf[ReferenceOf&lt;PO&period;&lowbar;quantity&lowbar;spec&lowbar;&gt;] auto R1,
    typename Rep1,
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
link:#mp_units-operator_plus-00[operator&plus;](
    link:#mp_units-quantity-01[quantity&lt;R1, Rep1&gt;] const& q,
    QP const& qp)
requires requires &lcub; q &plus; qp&period;quantity&lowbar;ref&lowbar;from(PO)&semi; &rcub;;
----

[.small]#link:#mp_units-operator_plus-00[_» more&period;&period;&period;_]#

Addition operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, 1 &plus; N&gt;]
operator&plus;(
    CharT const lhs,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& rhs) noexcept;
----

== Return Value

A compile&hyphen;time fixed string

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Addition operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N &plus; 1&gt;]
operator&plus;(
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    CharT rhs) noexcept;
----

== Return Value

A compile&hyphen;time fixed string

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Addition operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N &plus; N2&gt;]
operator&plus;(
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N2&gt;] const& rhs) noexcept;
----

== Return Value

A compile&hyphen;time fixed string

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Addition operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N &plus; N2 &hyphen; 1&gt;]
operator&plus;(
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    CharT const(& rhs)[]) noexcept;
----

== Return Value

A compile&hyphen;time fixed string

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Addition operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N1&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N1 &plus; N &hyphen; 1&gt;]
operator&plus;(
    CharT const(& lhs)[],
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& rhs) noexcept;
----

== Return Value

A compile&hyphen;time fixed string

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;plus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&plus;(
    Q const& lhs,
    Value const& rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;plus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&plus;(
    Value const& lhs,
    Q const& rhs);
----

Addition operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::size&lowbar;t N2,
    std::size&lowbar;t M2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N &plus; N2, M &plus; M2&gt;]
operator&plus;(
    link:#mp_units-symbol_text-032[symbol&lowbar;text] const& lhs,
    link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N2, M2&gt;] const& rhs);
----

== Return Value

A symbol text representation

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;CommonlyInvocableQuantities&lt;std&colon;&colon;plus&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&plus;(
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-ReferenceOf[ReferenceOf&lt;PO&period;&lowbar;quantity&lowbar;spec&lowbar;&gt;] auto R2,
    typename Rep2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
operator&plus;(
    QP const& qp,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& q)
requires requires &lcub; qp&period;quantity&lowbar;ref&lowbar;from(PO) &plus; q&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-ReferenceOf[ReferenceOf&lt;PO&period;&lowbar;quantity&lowbar;spec&lowbar;&gt;] auto R1,
    typename Rep1,
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
operator&plus;(
    link:#mp_units-quantity-01[quantity&lt;R1, Rep1&gt;] const& q,
    QP const& qp)
requires requires &lcub; q &plus; qp&period;quantity&lowbar;ref&lowbar;from(PO)&semi; &rcub;;
----

Subtraction operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-PointOrigin[PointOrigin] PO1,
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP&gt;
requires QuantityPointOf&lt;quantity&lowbar;point, PO1&lcub;&rcub;&gt; &amp;&amp;
             ReferenceOf&lt;MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(reference), PO1&colon;&colon;&lowbar;quantity&lowbar;spec&lowbar;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_minus-0e[operator&hyphen;](
    PO1 po,
    QP const& qp);
----

[.small]#link:#mp_units-operator_minus-0e[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;minus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_minus-09[operator&hyphen;](
    Q const& lhs,
    Value const& rhs);
----

[.small]#link:#mp_units-operator_minus-09[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_minus-06[operator&hyphen;](
    QP const& lhs,
    QP2 const& rhs)
requires requires &lcub; lhs&period;quantity&lowbar;ref&lowbar;from(point&lowbar;origin) &hyphen; rhs&period;quantity&lowbar;ref&lowbar;from(QP2&colon;&colon;point&lowbar;origin)&semi; &rcub;;
----

[.small]#link:#mp_units-operator_minus-06[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires QuantityPointOf&lt;quantity&lowbar;point, PO2&lcub;&rcub;&gt; &amp;&amp;
             ReferenceOf&lt;MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(reference), PO2&colon;&colon;&lowbar;quantity&lowbar;spec&lowbar;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_minus-01[operator&hyphen;](
    QP const& qp,
    PO2 po);
----

[.small]#link:#mp_units-operator_minus-01[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;minus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_minus-0b[operator&hyphen;](
    Value const& lhs,
    Q const& rhs);
----

[.small]#link:#mp_units-operator_minus-0b[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;CommonlyInvocableQuantities&lt;std&colon;&colon;minus&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_minus-0d[operator&hyphen;](
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_minus-0d[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-ReferenceOf[ReferenceOf&lt;PO&period;&lowbar;quantity&lowbar;spec&lowbar;&gt;] auto R2,
    typename Rep2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
link:#mp_units-operator_minus-05[operator&hyphen;](
    QP const& qp,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& q)
requires requires &lcub; qp&period;quantity&lowbar;ref&lowbar;from(PO) &hyphen; q&semi; &rcub;;
----

[.small]#link:#mp_units-operator_minus-05[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-PointOrigin[PointOrigin] PO1,
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP&gt;
requires QuantityPointOf&lt;quantity&lowbar;point, PO1&lcub;&rcub;&gt; &amp;&amp;
             ReferenceOf&lt;MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(reference), PO1&colon;&colon;&lowbar;quantity&lowbar;spec&lowbar;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&hyphen;(
    PO1 po,
    QP const& qp);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;minus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&hyphen;(
    Q const& lhs,
    Value const& rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&hyphen;(
    QP const& lhs,
    QP2 const& rhs)
requires requires &lcub; lhs&period;quantity&lowbar;ref&lowbar;from(point&lowbar;origin) &hyphen; rhs&period;quantity&lowbar;ref&lowbar;from(QP2&colon;&colon;point&lowbar;origin)&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-PointOrigin[PointOrigin] PO2&gt;
requires QuantityPointOf&lt;quantity&lowbar;point, PO2&lcub;&rcub;&gt; &amp;&amp;
             ReferenceOf&lt;MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(reference), PO2&colon;&colon;&lowbar;quantity&lowbar;spec&lowbar;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&hyphen;(
    QP const& qp,
    PO2 po);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp;
             detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;minus&lt;&gt;, Rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&hyphen;(
    Value const& lhs,
    Q const& rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;CommonlyInvocableQuantities&lt;std&colon;&colon;minus&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&hyphen;(
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-ReferenceOf[ReferenceOf&lt;PO&period;&lowbar;quantity&lowbar;spec&lowbar;&gt;] auto R2,
    typename Rep2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
operator&hyphen;(
    QP const& qp,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& q)
requires requires &lcub; qp&period;quantity&lowbar;ref&lowbar;from(PO) &hyphen; q&semi; &rcub;;
----

Division operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U1&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-operator_slash-0d6[operator&sol;](
    U1 lhs,
    link:#mp_units-reference[reference] rhs);
----

[.small]#link:#mp_units-operator_slash-0d6[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-operator_slash-0e7[operator&sol;](
    link:#mp_units-reference[reference] lhs,
    U2 rhs);
----

[.small]#link:#mp_units-operator_slash-0e7[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R,
    typename Q&gt;
requires Quantity&lt;std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;Q&gt;&gt;
constexpr
auto
link:#mp_units-operator_slash-035[operator&sol;](
    R lhs,
    Q&& q) = delete;
----

[.small]#link:#mp_units-operator_slash-035[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R,
    typename Rep&gt;
requires RepresentationOf&lt;std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;Rep&gt;, get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;
constexpr
auto
link:#mp_units-operator_slash-02[operator&sol;](
    R lhs,
    Rep&& rhs) = delete;
----

[.small]#link:#mp_units-operator_slash-02[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q2,
    typename U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-operator_slash-0d3[operator&sol;](
    link:#mp_units-reference[reference] lhs,
    link:#mp_units-reference[reference&lt;Q2, U2&gt;] rhs);
----

[.small]#link:#mp_units-operator_slash-0d3[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    typename Value&gt;
requires (!Quantity&lt;Value&gt;) &amp;&amp;
            (!Reference&lt;Value&gt;) &amp;&amp; detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;divides&lt;&gt;, rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
link:#mp_units-operator_slash-03f[operator&sol;](
    Q const& q,
    Value const& val);
----

[.small]#link:#mp_units-operator_slash-03f[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Value,
    std::derived&lowbar;from&lt;quantity&gt; Q&gt;
requires (!Quantity&lt;Value&gt;) &amp;&amp;
            (!Reference&lt;Value&gt;) &amp;&amp; detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;divides&lt;&gt;, const Value&amp;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_slash-07[operator&sol;](
    Value const& val,
    Q const& q);
----

[.small]#link:#mp_units-operator_slash-07[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;InvocableQuantities&lt;std&colon;&colon;divides&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_slash-04[operator&sol;](
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_slash-04[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_slash-08[operator&sol;](
    FwdQ&& q,
    R rhs);
----

[.small]#link:#mp_units-operator_slash-08[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
requires detail&colon;&colon;OffsetUnit&lt;decltype(get&lowbar;unit(R&lcub;&rcub;))&gt;
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
constexpr
auto
link:#mp_units-operator_slash-0e4[operator&sol;](
    FwdRep&& lhs,
    R rhs);
----

[.small]#link:#mp_units-operator_slash-0e4[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
requires (!detail&colon;&colon;OffsetUnit&lt;decltype(get&lowbar;unit(R&lcub;&rcub;))&gt;)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-operator_slash-0f[operator&sol;](
    FwdRep&& lhs,
    R rhs);
----

[.small]#link:#mp_units-operator_slash-0f[_» more&period;&period;&period;_]#

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U1&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
operator&sol;(
    U1 lhs,
    link:#mp_units-reference[reference] rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
operator&sol;(
    link:#mp_units-reference[reference] lhs,
    U2 rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R,
    typename Q&gt;
requires Quantity&lt;std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;Q&gt;&gt;
constexpr
auto
operator&sol;(
    R lhs,
    Q&& q) = delete;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R,
    typename Rep&gt;
requires RepresentationOf&lt;std&colon;&colon;remove&lowbar;cvref&lowbar;t&lt;Rep&gt;, get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;
constexpr
auto
operator&sol;(
    R lhs,
    Rep&& rhs) = delete;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q2,
    typename U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
operator&sol;(
    link:#mp_units-reference[reference] lhs,
    link:#mp_units-reference[reference&lt;Q2, U2&gt;] rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    typename Value&gt;
requires (!Quantity&lt;Value&gt;) &amp;&amp;
            (!Reference&lt;Value&gt;) &amp;&amp; detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;divides&lt;&gt;, rep, const Value&amp;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;quantity&lowbar;spec&gt;] auto
operator&sol;(
    Q const& q,
    Value const& val);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Value,
    std::derived&lowbar;from&lt;quantity&gt; Q&gt;
requires (!Quantity&lt;Value&gt;) &amp;&amp;
            (!Reference&lt;Value&gt;) &amp;&amp; detail&colon;&colon;InvokeResultOf&lt;quantity&lowbar;spec, std&colon;&colon;divides&lt;&gt;, const Value&amp;, rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&sol;(
    Value const& val,
    Q const& q);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires detail&colon;&colon;InvocableQuantities&lt;std&colon;&colon;divides&lt;&gt;, quantity, quantity&lt;R2, Rep2&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&sol;(
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdQ,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&sol;(
    FwdQ&& q,
    R rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
requires detail&colon;&colon;OffsetUnit&lt;decltype(get&lowbar;unit(R&lcub;&rcub;))&gt;
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
constexpr
auto
operator&sol;(
    FwdRep&& lhs,
    R rhs);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename FwdRep,
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Rep = std::remove&lowbar;cvref&lowbar;t&lt;FwdRep&gt;&gt;
requires (!detail&colon;&colon;OffsetUnit&lt;decltype(get&lowbar;unit(R&lcub;&rcub;))&gt;)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
operator&sol;(
    FwdRep&& lhs,
    R rhs);
----

`pow` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

Computes the value of a reference raised to the `Num&sol;Den` power


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    intmax&lowbar;t Num,
    intmax&lowbar;t Den = 1&gt;
requires (Den !&equals; 0)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-pow-07[pow](link:#mp_units-reference[reference]);
----

[.small]#link:#mp_units-pow-07[_» more&period;&period;&period;_]#

Computes the value of a dimension raised to the `Num&sol;Den` power


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    intmax&lowbar;t Num,
    intmax&lowbar;t Den = 1,
    link:#mp_units-Unit[Unit] D&gt;
requires (Den !&equals; 0)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-pow-09[pow](D d);
----

[.small]#link:#mp_units-pow-09[_» more&period;&period;&period;_]#

Computes the value of a quantity raised to the `Num&sol;Den` power


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    intmax&lowbar;t Num,
    intmax&lowbar;t Den = 1,
    auto R,
    typename Rep&gt;
requires (Den !&equals; 0) &amp;&amp; requires(Rep v) &lcub;
    representation&lowbar;values&lt;Rep&gt;&colon;&colon;one()&semi;
    requires requires &lcub; pow(v, 1&period;0)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;pow(v, 1&period;0)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;pow&lt;Num, Den&gt;(R), Rep&gt;]
link:#mp_units-pow-05[pow](link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept;
----

[.small]#link:#mp_units-pow-05[_» more&period;&period;&period;_]#

== Return Value

* The result of computation
* Dimension The result of computation
* QuantitySpec The result of computation
* Unit The result of computation
* Quantity The result of computation

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Num*
| Exponent numerator
| *Den*
| Exponent denominator
|===

== Parameters

[cols=2]
|===
| Name
| Description
| *r*
| Reference being the base of the operation
| *d*
| Dimension being the base of the operation
| *q*
| Quantity specification being the base of the operation
| *u*
| Unit being the base of the operation
|===

Computes the value of a reference raised to the `Num&sol;Den` power

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    intmax&lowbar;t Num,
    intmax&lowbar;t Den = 1&gt;
requires (Den !&equals; 0)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
pow(link:#mp_units-reference[reference]);
----

== Return Value

The result of computation

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Num*
| Exponent numerator
| *Den*
| Exponent denominator
|===

== Parameters

[cols=2]
|===
| Name
| Description
| *r*
| Reference being the base of the operation
|===

Computes the value of a dimension raised to the `Num&sol;Den` power

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    intmax&lowbar;t Num,
    intmax&lowbar;t Den = 1,
    link:#mp_units-Unit[Unit] D&gt;
requires (Den !&equals; 0)
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
pow(D d);
----

== Return Value

* Dimension The result of computation
* QuantitySpec The result of computation
* Unit The result of computation

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Num*
| Exponent numerator
| *Den*
| Exponent denominator
|===

== Parameters

[cols=2]
|===
| Name
| Description
| *d*
| Dimension being the base of the operation
| *q*
| Quantity specification being the base of the operation
| *u*
| Unit being the base of the operation
|===

Computes the value of a quantity raised to the `Num&sol;Den` power

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    intmax&lowbar;t Num,
    intmax&lowbar;t Den = 1,
    auto R,
    typename Rep&gt;
requires (Den !&equals; 0) &amp;&amp; requires(Rep v) &lcub;
    representation&lowbar;values&lt;Rep&gt;&colon;&colon;one()&semi;
    requires requires &lcub; pow(v, 1&period;0)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;pow(v, 1&period;0)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;pow&lt;Num, Den&gt;(R), Rep&gt;]
pow(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept;
----

== Description

Both the quantity value and its quantity specification are the base of the operation&period;

== Return Value

Quantity The result of computation

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Num*
| Exponent numerator
| *Den*
| Exponent denominator
|===

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| Quantity being the base of the operation
|===

`quantity&lowbar;cast` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;cast&period;h&gt;`

Explicit cast of a quantity type


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] auto ToQS,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (castable(Q&colon;&colon;quantity&lowbar;spec, ToQS)) &amp;&amp; (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(Q&colon;&colon;unit), ToQS))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-quantity_cast-0b[quantity&lowbar;cast](FwdQ&& q);
----

[.small]#link:#mp_units-quantity_cast-0b[_» more&period;&period;&period;_]#

Explicit cast of a quantity point type


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] auto ToQS,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (castable(QP&colon;&colon;quantity&lowbar;spec, ToQS)) &amp;&amp; (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(QP&colon;&colon;unit), ToQS))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
link:#mp_units-quantity_cast-05[quantity&lowbar;cast](FwdQP&& qp);
----

[.small]#link:#mp_units-quantity_cast-05[_» more&period;&period;&period;_]#

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToQS*
| a quantity specification to use for a target quantity
|===

Explicit cast of a quantity type

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] auto ToQS,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (castable(Q&colon;&colon;quantity&lowbar;spec, ToQS)) &amp;&amp; (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(Q&colon;&colon;unit), ToQS))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
quantity&lowbar;cast(FwdQ&& q);
----

== Description

This cast converts only a quantity type&period; It might be used to force some quantity type conversions that are not implicitly allowed but are allowed explicitly&period;

For example&colon;

[,cpp]
----
{.cpp}
 auto length = isq::length(42 * m);
 auto distance = quantity_cast<isq::distance>(length);
----
[NOTE]
This cast does not affect the underlying value of a number stored in a quantity&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToQS*
| a quantity specification to use for a target quantity
|===

Explicit cast of a quantity point type

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantitySpec[QuantitySpec] auto ToQS,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (castable(QP&colon;&colon;quantity&lowbar;spec, ToQS)) &amp;&amp; (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(QP&colon;&colon;unit), ToQS))
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
quantity&lowbar;cast(FwdQP&& qp);
----

== Description

This cast converts only a quantity point type&period; It might be used to force some quantity point type conversions that are not implicitly allowed but are allowed explicitly&period;

For example&colon;

[,cpp]
----
{.cpp}
 auto length = isq::length(quantity_point{42 * m});
 auto altitude = quantity_cast<isq::altitude>(length);
----
[NOTE]
This cast does not affect the underlying value of a number stored in a quantity point&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToQS*
| a quantity specification to use for a target quantity point
|===

Computes the IEEE remainder of the floating point division operation x &sol; y&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R1,
    typename Rep1,
    auto R2,
    typename Rep2&gt;
requires requires(Rep1 v1, Rep2 v2) &lcub;
    get&lowbar;common&lowbar;reference(R1, R2)&semi;
    requires requires &lcub; remainder(v1, v2)&semi; &rcub; &verbar;&verbar; requires &lcub; std&colon;&colon;remainder(v1, v2)&semi; &rcub;&semi;
  &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityOf[QuantityOf&lt;get&lowbar;quantity&lowbar;spec(R1)&gt;] auto
remainder(
    link:#mp_units-quantity-01[quantity&lt;R1, Rep1&gt;] const& x,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& y) noexcept;
----

== Parameters

[cols=2]
|===
| Name
| Description
| *x*
| A quantity
| *y*
| A quantity
|===

Computes the nearest quantity with integer representation and unit type `To` to `q`

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto To,
    auto R,
    typename Rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;detail&colon;&colon;clone&lowbar;reference&lowbar;with&lt;To&gt;(R), Rep&gt;]
round(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept
requires requires &lcub;
    mp&lowbar;units&colon;&colon;floor&lt;To&gt;(q)&semi;
    representation&lowbar;values&lt;Rep&gt;&colon;&colon;one()&semi;
  &rcub; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;std&colon;&colon;int64&lowbar;t, Rep&gt;;
----

== Description

Returns the value `res` representable in `To` unit that is the closest to `q`&period; If there are two such values, returns the even value (that is, the value `res` such that `res % 2 &equals;&equals; 0`)&period;

== Return Value

Quantity The quantity rounded to the nearest unit `To`, rounding to even in halfway cases&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *q*
| Quantity being the base of the operation
|===

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| A quantity
|===

`sqrt` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

Computes the square root of a dimension


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
link:#mp_units-sqrt-09[sqrt](auto d);
----

[.small]#link:#mp_units-sqrt-09[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
link:#mp_units-sqrt-0f[sqrt](link:#mp_units-reference[reference]);
----

[.small]#link:#mp_units-sqrt-0f[_» more&period;&period;&period;_]#

Computes the square root of a quantity


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; sqrt(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;sqrt(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;sqrt(R), Rep&gt;]
link:#mp_units-sqrt-0b[sqrt](link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept;
----

[.small]#link:#mp_units-sqrt-0b[_» more&period;&period;&period;_]#

== Return Value

* Dimension The result of computation
* QuantitySpec The result of computation
* Unit The result of computation
* Quantity The result of computation

== Parameters

[cols=2]
|===
| Name
| Description
| *d*
| Dimension being the base of the operation
| *q*
| Quantity specification being the base of the operation
| *u*
| Unit being the base of the operation
|===

Computes the square root of a dimension

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
sqrt(auto d);
----

== Return Value

* Dimension The result of computation
* QuantitySpec The result of computation
* Unit The result of computation

== Parameters

[cols=2]
|===
| Name
| Description
| *d*
| Dimension being the base of the operation
| *q*
| Quantity specification being the base of the operation
| *u*
| Unit being the base of the operation
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
&sol;&ast; implementation-defined &ast;&sol;
sqrt(link:#mp_units-reference[reference]);
----

Computes the square root of a quantity

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;math&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto R,
    typename Rep&gt;
requires requires(Rep v) &lcub; sqrt(v)&semi; &rcub; &verbar;&verbar; requires(Rep v) &lcub; std&colon;&colon;sqrt(v)&semi; &rcub;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;sqrt(R), Rep&gt;]
sqrt(link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q) noexcept;
----

== Description

Both the quantity value and its quantity specification are the base of the operation&period;

== Return Value

Quantity The result of computation

== Parameters

[cols=2]
|===
| Name
| Description
| *q*
| Quantity being the base of the operation
|===

Computes the square power of a unit

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
link:#mp_units-Unit[Unit] auto
square(auto u);
----

== Return Value

Unit The result of computation

== Parameters

[cols=2]
|===
| Name
| Description
| *u*
| Unit being the base of the operation
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    class CharT,
    std::size&lowbar;t N&gt;
constexpr
void
swap(
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N&gt;]& x,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N&gt;]& y) noexcept;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-unit_symbol_formatting[unit&lowbar;symbol&lowbar;formatting] fmt = unit&lowbar;symbol&lowbar;formatting&lcub;&rcub;,
    typename CharT = char,
    link:#mp_units-Unit[Unit] U&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
std::basic&lowbar;string&lowbar;view&lt;CharT&gt;
unit&lowbar;symbol(U);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT = char,
    std::output&lowbar;iterator&lt;CharT&gt; Out,
    link:#mp_units-Unit[Unit] U&gt;
constexpr
Out
unit&lowbar;symbol&lowbar;to(
    Out out,
    U u,
    link:#mp_units-unit_symbol_formatting[unit&lowbar;symbol&lowbar;formatting] const& fmt = unit&lowbar;symbol&lowbar;formatting&lcub;&rcub;);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector]
unit&lowbar;vector(link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector] const& vec)
requires treat&lowbar;as&lowbar;floating&lowbar;point&lt;T&gt;;
----

`value&lowbar;cast` overloads

== Synopses

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

Explicit cast of a quantity&apos;s representation


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Quantity[Quantity] ToQ,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (ToQ&colon;&colon;quantity&lowbar;spec &equals;&equals; Q&colon;&colon;quantity&lowbar;spec) &amp;&amp;
          (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(ToQ&colon;&colon;unit), Q&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          std&colon;&colon;constructible&lowbar;from&lt;typename ToQ&colon;&colon;rep, typename Q&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;Q&colon;&colon;unit, ToQ&colon;&colon;unit, typename ToQ&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-value_cast-0a[value&lowbar;cast](FwdQ&& q);
----

[.small]#link:#mp_units-value_cast-0a[_» more&period;&period;&period;_]#

Explicit cast of a quantity&apos;s representation type


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename ToRep,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires RepresentationOf&lt;ToRep, Q&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename Q&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;Q&colon;&colon;reference, ToRep&gt;]
link:#mp_units-value_cast-028[value&lowbar;cast](FwdQ&& q);
----

[.small]#link:#mp_units-value_cast-028[_» more&period;&period;&period;_]#

Explicit cast of a quantity&apos;s unit


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto ToU,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), Q&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;Q&colon;&colon;unit, ToU, typename Q&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-value_cast-04[value&lowbar;cast](FwdQ&& q);
----

[.small]#link:#mp_units-value_cast-04[_» more&period;&period;&period;_]#

Explicit cast of a quantity point&apos;s representation


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Quantity[Quantity] ToQ,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (ToQ&colon;&colon;quantity&lowbar;spec &equals;&equals; QP&colon;&colon;quantity&lowbar;spec) &amp;&amp;
          (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(ToQ&colon;&colon;unit), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          std&colon;&colon;constructible&lowbar;from&lt;typename ToQ&colon;&colon;rep, typename QP&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToQ&colon;&colon;unit, typename ToQ&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
link:#mp_units-value_cast-035[value&lowbar;cast](FwdQP&& qp);
----

[.small]#link:#mp_units-value_cast-035[_» more&period;&period;&period;_]#

Explicit cast of a quantity point&apos;s representation, including potentially the point origin


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantityPoint[QuantityPoint] ToQP,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (ToQP&colon;&colon;quantity&lowbar;spec &equals;&equals; QP&colon;&colon;quantity&lowbar;spec) &amp;&amp;
          (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(ToQP&colon;&colon;unit), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          (detail&colon;&colon;same&lowbar;absolute&lowbar;point&lowbar;origins(ToQP&colon;&colon;point&lowbar;origin, QP&colon;&colon;point&lowbar;origin)) &amp;&amp;
          std&colon;&colon;constructible&lowbar;from&lt;typename ToQP&colon;&colon;rep, typename QP&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToQP&colon;&colon;unit, typename ToQP&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
link:#mp_units-value_cast-0c[value&lowbar;cast](FwdQP&& qp);
----

[.small]#link:#mp_units-value_cast-0c[_» more&period;&period;&period;_]#

Explicit cast of a quantity point&apos;s representation type


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename ToRep,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires RepresentationOf&lt;ToRep, QP&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename QP&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;QP&colon;&colon;reference, QP&colon;&colon;point&lowbar;origin, ToRep&gt;]
link:#mp_units-value_cast-021[value&lowbar;cast](FwdQP&& qp);
----

[.small]#link:#mp_units-value_cast-021[_» more&period;&period;&period;_]#

Explicit cast of a quantity point&apos;s unit


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto ToU,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToU, typename QP&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
link:#mp_units-value_cast-027[value&lowbar;cast](FwdQP&& qp);
----

[.small]#link:#mp_units-value_cast-027[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename ToRep,
    link:#mp_units-Unit[Unit] auto ToU,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), Q&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          RepresentationOf&lt;ToRep, Q&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename Q&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;Q&colon;&colon;unit, ToU, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-value_cast-01[value&lowbar;cast](FwdQ&& q);
----

[.small]#link:#mp_units-value_cast-01[_» more&period;&period;&period;_]#

Explicit cast of a quantity&apos;s unit and representation type


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto ToU,
    typename ToRep,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), Q&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          RepresentationOf&lt;ToRep, Q&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename Q&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;Q&colon;&colon;unit, ToU, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
link:#mp_units-value_cast-02e[value&lowbar;cast](FwdQ&& q);
----

[.small]#link:#mp_units-value_cast-02e[_» more&period;&period;&period;_]#


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename ToRep,
    link:#mp_units-Unit[Unit] auto ToU,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          RepresentationOf&lt;ToRep, QP&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename QP&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToU, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
link:#mp_units-value_cast-05[value&lowbar;cast](FwdQP&& qp);
----

[.small]#link:#mp_units-value_cast-05[_» more&period;&period;&period;_]#

Explicit cast of a quantity point&apos;s unit and representation type


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto ToU,
    typename ToRep,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          RepresentationOf&lt;ToRep, QP&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename QP&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToU, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
link:#mp_units-value_cast-0d[value&lowbar;cast](FwdQP&& qp);
----

[.small]#link:#mp_units-value_cast-0d[_» more&period;&period;&period;_]#

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToQ*
| a target quantity type to which to cast the representation
| *ToRep*
| a representation type to use for a target quantity
| *ToU*
| a unit to use for a target quantity
| *ToQP*
| a target quantity point type to which to cast the representation of the point
|===

Explicit cast of a quantity&apos;s representation

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Quantity[Quantity] ToQ,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (ToQ&colon;&colon;quantity&lowbar;spec &equals;&equals; Q&colon;&colon;quantity&lowbar;spec) &amp;&amp;
          (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(ToQ&colon;&colon;unit), Q&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          std&colon;&colon;constructible&lowbar;from&lt;typename ToQ&colon;&colon;rep, typename Q&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;Q&colon;&colon;unit, ToQ&colon;&colon;unit, typename ToQ&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
value&lowbar;cast(FwdQ&& q);
----

== Description

Implicit conversions between quantities of different types are allowed only for &quot;safe&quot; (e&period;g&period; non&hyphen;truncating) conversion&period; In truncating cases an explicit cast have to be used&period;

using ToQ &equals; quantity&lt;us, int&gt;&semi; auto q &equals; value&lowbar;cast&lt;ToQ&gt;(1&period;23 ms)&semi;

Note that value&lowbar;cast only changes the &quot;representation aspects&quot; (unit and representation type), but not the &quot;meaning&quot; (quantity type)&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToQ*
| a target quantity type to which to cast the representation
|===

Explicit cast of a quantity&apos;s representation type

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename ToRep,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires RepresentationOf&lt;ToRep, Q&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename Q&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity-01[quantity&lt;Q&colon;&colon;reference, ToRep&gt;]
value&lowbar;cast(FwdQ&& q);
----

== Description

Implicit conversions between quantities of different types are allowed only for &quot;safe&quot; (e&period;g&period; non&hyphen;truncating) conversion&period; In truncating cases an explicit cast have to be used&period;

auto q &equals; value&lowbar;cast&lt;int&gt;(1&period;23 ms)&semi;

== Return Value

A quantity

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToRep*
| a representation type to use for a target quantity
|===

Explicit cast of a quantity&apos;s unit

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto ToU,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), Q&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;Q&colon;&colon;unit, ToU, typename Q&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
value&lowbar;cast(FwdQ&& q);
----

== Description

Implicit conversions between quantities of different types are allowed only for &quot;safe&quot; (e&period;g&period; non&hyphen;truncating) conversion&period; In truncating cases an explicit cast have to be used&period;

auto d &equals; value&lowbar;cast&lt;si&colon;&colon;second&gt;(1234 ms)&semi;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToU*
| a unit to use for a target quantity
|===

Explicit cast of a quantity point&apos;s representation

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Quantity[Quantity] ToQ,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (ToQ&colon;&colon;quantity&lowbar;spec &equals;&equals; QP&colon;&colon;quantity&lowbar;spec) &amp;&amp;
          (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(ToQ&colon;&colon;unit), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          std&colon;&colon;constructible&lowbar;from&lt;typename ToQ&colon;&colon;rep, typename QP&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToQ&colon;&colon;unit, typename ToQ&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
value&lowbar;cast(FwdQP&& qp);
----

== Description

Implicit conversions between quantities of different types are allowed only for &quot;safe&quot; (e&period;g&period; non&hyphen;truncating) conversion&period; In truncating cases an explicit cast have to be used&period;

inline constexpr struct A &colon; absolute&lowbar;point&lowbar;origin&lt;A, isq&colon;&colon;distance&gt; A&semi;

using ToQ &equals; quantity&lt;mm, int&gt;&semi; auto qp &equals; value&lowbar;cast&lt;ToQ&gt;(quantity&lowbar;point&lcub;1&period;23 m&rcub;)&semi;

Note that value&lowbar;cast only changes the &quot;representation aspects&quot; (unit and representation type), but not the &quot;meaning&quot; (quantity type or the actual point that is being described)&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToQ*
| a target quantity type to which to cast the representation of the point
|===

Explicit cast of a quantity point&apos;s representation, including potentially the point origin

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-QuantityPoint[QuantityPoint] ToQP,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (ToQP&colon;&colon;quantity&lowbar;spec &equals;&equals; QP&colon;&colon;quantity&lowbar;spec) &amp;&amp;
          (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(ToQP&colon;&colon;unit), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          (detail&colon;&colon;same&lowbar;absolute&lowbar;point&lowbar;origins(ToQP&colon;&colon;point&lowbar;origin, QP&colon;&colon;point&lowbar;origin)) &amp;&amp;
          std&colon;&colon;constructible&lowbar;from&lt;typename ToQP&colon;&colon;rep, typename QP&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToQP&colon;&colon;unit, typename ToQP&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
value&lowbar;cast(FwdQP&& qp);
----

== Description

Implicit conversions between quantities of different types are allowed only for &quot;safe&quot; (e&period;g&period; non&hyphen;truncating) conversion&period; In truncating cases an explicit cast have to be used&period;

inline constexpr struct A &colon; absolute&lowbar;point&lowbar;origin&lt;A, isq&colon;&colon;distance&gt; A&semi; inline constexpr struct B &colon; relative&lowbar;point&lowbar;origin&lt;A &plus; 1&ast;m&gt; B&semi;

using ToQP &equals; quantity&lowbar;point&lt;mm, B, int&gt;&semi; auto qp &equals; value&lowbar;cast&lt;ToQP&gt;(quantity&lowbar;point&lcub;1&period;23 m&rcub;)&semi;

Note that value&lowbar;cast only changes the &quot;representation aspects&quot; (unit, representation type and point origin), but not the &quot;meaning&quot; (quantity type or the actual point that is being described)&period;

Note also that changing the point origin bears risks regarding truncation and overflow similar to other casts that change representation (which is why we require a `value&lowbar;cast` and disallow implicit conversions)&period; This cast is guaranteed not to cause overflow of any intermediate representation type provided that the input quantity point is within the range of `ToQP`&period; Calling `value&lowbar;cast&lt;ToQP&gt;(qp)` on a `qp` outside of the range of `ToQP` is potentially undefined behaviour&period; The implementation further attempts not to cause more than rounding error than approximately the sum of the resolution of `qp` as represented in `FromQP`, plust the resolution of `qp` as represented in `ToQP`&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToQP*
| a target quantity point type to which to cast the representation of the point
|===

Explicit cast of a quantity point&apos;s representation type

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename ToRep,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires RepresentationOf&lt;ToRep, QP&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename QP&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;QP&colon;&colon;reference, QP&colon;&colon;point&lowbar;origin, ToRep&gt;]
value&lowbar;cast(FwdQP&& qp);
----

== Description

Implicit conversions between quantity points of different types are allowed only for &quot;safe&quot; (e&period;g&period; non&hyphen;truncating) conversion&period; In truncating cases an explicit cast have to be used&period;

auto qp &equals; value&lowbar;cast&lt;int&gt;(quantity&lowbar;point&lcub;1&period;23 ms&rcub;)&semi;

== Return Value

A quantity point

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToRep*
| a representation type to use for a target quantity point
|===

Explicit cast of a quantity point&apos;s unit

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto ToU,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToU, typename QP&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
value&lowbar;cast(FwdQP&& qp);
----

== Description

Implicit conversions between quantity points of different types are allowed only for &quot;safe&quot; (e&period;g&period; non&hyphen;truncating) conversion&period; In truncating cases an explicit cast have to be used&period;

auto qp &equals; value&lowbar;cast&lt;si&colon;&colon;second&gt;(quantity&lowbar;point&lcub;1234 ms&rcub;)&semi;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToU*
| a unit to use for a target quantity point
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename ToRep,
    link:#mp_units-Unit[Unit] auto ToU,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), Q&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          RepresentationOf&lt;ToRep, Q&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename Q&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;Q&colon;&colon;unit, ToU, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
value&lowbar;cast(FwdQ&& q);
----

Explicit cast of a quantity&apos;s unit and representation type

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto ToU,
    typename ToRep,
    typename FwdQ,
    link:#mp_units-Quantity[Quantity] Q = std::remove&lowbar;cvref&lowbar;t&lt;FwdQ&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), Q&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          RepresentationOf&lt;ToRep, Q&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename Q&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;Q&colon;&colon;unit, ToU, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-Quantity[Quantity] auto
value&lowbar;cast(FwdQ&& q);
----

== Description

Implicit conversions between quantities of different types are allowed only for &quot;safe&quot; (e&period;g&period; non&hyphen;truncating) conversion&period; In truncating cases an explicit cast have to be used&period;

auto q &equals; value&lowbar;cast&lt;us, int&gt;(1&period;23 ms)&semi;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToU*
| a unit to use for the target quantity
| *ToRep*
| a representation type to use for the target quantity
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename ToRep,
    link:#mp_units-Unit[Unit] auto ToU,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          RepresentationOf&lt;ToRep, QP&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename QP&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToU, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
value&lowbar;cast(FwdQP&& qp);
----

Explicit cast of a quantity point&apos;s unit and representation type

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;value&lowbar;cast&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Unit[Unit] auto ToU,
    typename ToRep,
    typename FwdQP,
    link:#mp_units-QuantityPoint[QuantityPoint] QP = std::remove&lowbar;cvref&lowbar;t&lt;FwdQP&gt;&gt;
requires (MP&lowbar;UNITS&lowbar;WEAK&lowbar;UNIT&lowbar;OF(MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(ToU)), QP&colon;&colon;quantity&lowbar;spec)) &amp;&amp;
          RepresentationOf&lt;ToRep, QP&colon;&colon;quantity&lowbar;spec&gt; &amp;&amp; std&colon;&colon;constructible&lowbar;from&lt;ToRep, typename QP&colon;&colon;rep&gt; &amp;&amp;
          detail&colon;&colon;SaneScaling&lt;QP&colon;&colon;unit, ToU, ToRep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
link:#mp_units-QuantityPoint[QuantityPoint] auto
value&lowbar;cast(FwdQP&& qp);
----

== Description

Implicit conversions between quantities of different types are allowed only for &quot;safe&quot; (e&period;g&period; non&hyphen;truncating) conversion&period; In truncating cases an explicit cast have to be used&period;

auto qp &equals; value&lowbar;cast&lt;us, int&gt;(quantity&lowbar;point&lcub;1&period;23 ms&rcub;)&semi;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *ToU*
| a unit to use for the target quantity
| *ToRep*
| a representation type to use for the target quantity
|===

Stream insertion operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

Stream insertion operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
std::basic&lowbar;ostream&lt;CharT&gt;&
link:#mp_units-operator_lshift-0e6[operator&lt;&lt;](
    std::basic&lowbar;ostream&lt;CharT&gt;& os,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& str);
----

[.small]#link:#mp_units-operator_lshift-0e6[_» more&period;&period;&period;_]#

Stream insertion operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT,
    typename Traits,
    link:#mp_units-Unit[Unit] D&gt;
std::basic&lowbar;ostream&lt;CharT, Traits&gt;&
link:#mp_units-operator_lshift-04[operator&lt;&lt;](
    std::basic&lowbar;ostream&lt;CharT, Traits&gt;& os,
    D d);
----

[.small]#link:#mp_units-operator_lshift-04[_» more&period;&period;&period;_]#

Stream insertion operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT,
    typename Traits,
    auto R,
    typename Rep&gt;
std::basic&lowbar;ostream&lt;CharT, Traits&gt;&
link:#mp_units-operator_lshift-0e0[operator&lt;&lt;](
    std::basic&lowbar;ostream&lt;CharT, Traits&gt;& os,
    link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q)
requires requires &lcub; os &lt;&lt; q&period;numerical&lowbar;value&lowbar;ref&lowbar;in(q&period;unit)&semi; &rcub;;
----

[.small]#link:#mp_units-operator_lshift-0e0[_» more&period;&period;&period;_]#

Stream insertion operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
std::ostream&
link:#mp_units-operator_lshift-0b[operator&lt;&lt;](
    std::ostream& os,
    link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector] const& vec);
----

[.small]#link:#mp_units-operator_lshift-0b[_» more&period;&period;&period;_]#

Stream insertion operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
std::basic&lowbar;ostream&lt;CharT&gt;&
operator&lt;&lt;(
    std::basic&lowbar;ostream&lt;CharT&gt;& os,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& str);
----

== Return Value

Reference to the current output stream

== Parameters

[cols=2]
|===
| Name
| Description
| *os*
| An output stream
| *str*
| The object to output
|===

Stream insertion operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT,
    typename Traits,
    link:#mp_units-Unit[Unit] D&gt;
std::basic&lowbar;ostream&lt;CharT, Traits&gt;&
operator&lt;&lt;(
    std::basic&lowbar;ostream&lt;CharT, Traits&gt;& os,
    D d);
----

== Return Value

Reference to the current output stream

== Parameters

[cols=2]
|===
| Name
| Description
| *os*
| An output stream
| *d*
| The object to output
|===

Stream insertion operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT,
    typename Traits,
    auto R,
    typename Rep&gt;
std::basic&lowbar;ostream&lt;CharT, Traits&gt;&
operator&lt;&lt;(
    std::basic&lowbar;ostream&lt;CharT, Traits&gt;& os,
    link:#mp_units-quantity-01[quantity&lt;R, Rep&gt;] const& q)
requires requires &lcub; os &lt;&lt; q&period;numerical&lowbar;value&lowbar;ref&lowbar;in(q&period;unit)&semi; &rcub;;
----

== Return Value

Reference to the current output stream

== Parameters

[cols=2]
|===
| Name
| Description
| *os*
| An output stream
| *q*
| The object to output
|===

Stream insertion operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
constexpr
std::ostream&
operator&lt;&lt;(
    std::ostream& os,
    link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector] const& vec);
----

== Return Value

Reference to the current output stream

== Parameters

[cols=2]
|===
| Name
| Description
| *os*
| An output stream
| *vec*
| The object to output
|===

Equality operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

Equality operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
link:#mp_units-operator_eq-03d[operator&equals;&equals;](
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    CharT const(& rhs)[]);
----

[.small]#link:#mp_units-operator_eq-03d[_» more&period;&period;&period;_]#

Equality operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-operator_eq-032[operator&equals;&equals;](
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_eq-032[_» more&period;&period;&period;_]#

Equality operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::size&lowbar;t N2,
    std::size&lowbar;t M2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-operator_eq-0a[operator&equals;&equals;](
    link:#mp_units-symbol_text-032[symbol&lowbar;text] const& lhs,
    link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N2, M2&gt;] const& rhs) noexcept;
----

[.small]#link:#mp_units-operator_eq-0a[_» more&period;&period;&period;_]#

Equality operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
link:#mp_units-operator_eq-02[operator&equals;&equals;](
    link:#mp_units-reference[reference] lhs,
    U2 u2);
----

[.small]#link:#mp_units-operator_eq-02[_» more&period;&period;&period;_]#

Equality operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q2,
    typename U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
link:#mp_units-operator_eq-07[operator&equals;&equals;](
    link:#mp_units-reference[reference] lhs,
    link:#mp_units-reference[reference&lt;Q2, U2&gt;] rhs);
----

[.small]#link:#mp_units-operator_eq-07[_» more&period;&period;&period;_]#

Equality operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp; std&colon;&colon;equality&lowbar;comparable&lowbar;with&lt;rep, Value&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-operator_eq-037[operator&equals;&equals;](
    Q const& lhs,
    Value const& rhs);
----

[.small]#link:#mp_units-operator_eq-037[_» more&period;&period;&period;_]#

Equality operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires requires &lcub; typename std&colon;&colon;common&lowbar;type&lowbar;t&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;&semi; &rcub; &amp;&amp;
             std&colon;&colon;equality&lowbar;comparable&lt;typename std&colon;&colon;common&lowbar;type&lowbar;t&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-operator_eq-01[operator&equals;&equals;](
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_eq-01[_» more&period;&period;&period;_]#

Equality operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP2&gt;
requires std&colon;&colon;equality&lowbar;comparable&lowbar;with&lt;quantity&lowbar;type, typename QP2&colon;&colon;quantity&lowbar;type&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
link:#mp_units-operator_eq-0ca[operator&equals;&equals;](
    QP const& lhs,
    QP2 const& rhs);
----

[.small]#link:#mp_units-operator_eq-0ca[_» more&period;&period;&period;_]#

Equality operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
operator&equals;&equals;(
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    CharT const(& rhs)[]);
----

== Return Value

`true` if the objects are equal, `false` otherwise

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Equality operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
operator&equals;&equals;(
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N2&gt;] const& rhs);
----

== Return Value

`true` if the objects are equal, `false` otherwise

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Equality operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::size&lowbar;t N2,
    std::size&lowbar;t M2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
operator&equals;&equals;(
    link:#mp_units-symbol_text-032[symbol&lowbar;text] const& lhs,
    link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N2, M2&gt;] const& rhs) noexcept;
----

== Return Value

`true` if the objects are equal, `false` otherwise

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Equality operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-AssociatedUnit[AssociatedUnit] U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
operator&equals;&equals;(
    link:#mp_units-reference[reference] lhs,
    U2 u2);
----

== Return Value

`true` if the objects are equal, `false` otherwise

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *u2*
| The right operand
|===

Equality operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q2,
    typename U2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
bool
operator&equals;&equals;(
    link:#mp_units-reference[reference] lhs,
    link:#mp_units-reference[reference&lt;Q2, U2&gt;] rhs);
----

== Return Value

`true` if the objects are equal, `false` otherwise

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Equality operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp; std&colon;&colon;equality&lowbar;comparable&lowbar;with&lt;rep, Value&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
operator&equals;&equals;(
    Q const& lhs,
    Value const& rhs);
----

== Return Value

`true` if the objects are equal, `false` otherwise

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Equality operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires requires &lcub; typename std&colon;&colon;common&lowbar;type&lowbar;t&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;&semi; &rcub; &amp;&amp;
             std&colon;&colon;equality&lowbar;comparable&lt;typename std&colon;&colon;common&lowbar;type&lowbar;t&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
operator&equals;&equals;(
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

== Return Value

`true` if the objects are equal, `false` otherwise

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Equality operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP2&gt;
requires std&colon;&colon;equality&lowbar;comparable&lowbar;with&lt;quantity&lowbar;type, typename QP2&colon;&colon;quantity&lowbar;type&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
bool
operator&equals;&equals;(
    QP const& lhs,
    QP2 const& rhs);
----

== Return Value

`true` if the objects are equal, `false` otherwise

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Three&hyphen;way comparison operators

== Synopses

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

Three&hyphen;way comparison operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
link:#mp_units-operator_3way-05[operator&lt;&equals;&gt;](
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    CharT const(& rhs)[]);
----

[.small]#link:#mp_units-operator_3way-05[_» more&period;&period;&period;_]#

Three&hyphen;way comparison operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
link:#mp_units-operator_3way-0d[operator&lt;&equals;&gt;](
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_3way-0d[_» more&period;&period;&period;_]#

Three&hyphen;way comparison operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::size&lowbar;t N2,
    std::size&lowbar;t M2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
link:#mp_units-operator_3way-0b[operator&lt;&equals;&gt;](
    link:#mp_units-symbol_text-032[symbol&lowbar;text] const& lhs,
    link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N2, M2&gt;] const& rhs) noexcept;
----

[.small]#link:#mp_units-operator_3way-0b[_» more&period;&period;&period;_]#

Three&hyphen;way comparison operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp; std&colon;&colon;three&lowbar;way&lowbar;comparable&lowbar;with&lt;rep, Value&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
link:#mp_units-operator_3way-0c3[operator&lt;&equals;&gt;](
    Q const& lhs,
    Value const& rhs);
----

[.small]#link:#mp_units-operator_3way-0c3[_» more&period;&period;&period;_]#

Three&hyphen;way comparison operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires requires &lcub; typename std&colon;&colon;common&lowbar;type&lowbar;t&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;&semi; &rcub; &amp;&amp;
             std&colon;&colon;three&lowbar;way&lowbar;comparable&lt;typename std&colon;&colon;common&lowbar;type&lowbar;t&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
link:#mp_units-operator_3way-01[operator&lt;&equals;&gt;](
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

[.small]#link:#mp_units-operator_3way-01[_» more&period;&period;&period;_]#

Three&hyphen;way comparison operator


[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP2&gt;
requires std&colon;&colon;three&lowbar;way&lowbar;comparable&lowbar;with&lt;quantity&lowbar;type, typename QP2&colon;&colon;quantity&lowbar;type&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
link:#mp_units-operator_3way-0c8[operator&lt;&equals;&gt;](
    QP const& lhs,
    QP2 const& rhs);
----

[.small]#link:#mp_units-operator_3way-0c8[_» more&period;&period;&period;_]#

Three&hyphen;way comparison operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
consteval
auto
operator&lt;&equals;&gt;(
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    CharT const(& rhs)[]);
----

== Return Value

The relative order of the objects

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Three&hyphen;way comparison operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
operator&lt;&equals;&gt;(
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string] const& lhs,
    link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N2&gt;] const& rhs);
----

== Return Value

The relative order of the objects

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Three&hyphen;way comparison operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::size&lowbar;t N2,
    std::size&lowbar;t M2&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
operator&lt;&equals;&gt;(
    link:#mp_units-symbol_text-032[symbol&lowbar;text] const& lhs,
    link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N2, M2&gt;] const& rhs) noexcept;
----

== Return Value

The relative order of the objects

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Three&hyphen;way comparison operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;quantity&lowbar;spec&gt;] Value&gt;
requires detail&colon;&colon;DimensionlessOne&lt;Q&colon;&colon;reference&gt; &amp;&amp; std&colon;&colon;three&lowbar;way&lowbar;comparable&lowbar;with&lt;rep, Value&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
operator&lt;&equals;&gt;(
    Q const& lhs,
    Value const& rhs);
----

== Return Value

The relative order of the objects

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Three&hyphen;way comparison operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&gt; Q,
    auto R2,
    typename Rep2&gt;
requires requires &lcub; typename std&colon;&colon;common&lowbar;type&lowbar;t&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;&semi; &rcub; &amp;&amp;
             std&colon;&colon;three&lowbar;way&lowbar;comparable&lt;typename std&colon;&colon;common&lowbar;type&lowbar;t&lt;quantity, quantity&lt;R2, Rep2&gt;&gt;&colon;&colon;rep&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
operator&lt;&equals;&gt;(
    Q const& lhs,
    link:#mp_units-quantity-01[quantity&lt;R2, Rep2&gt;] const& rhs);
----

== Return Value

The relative order of the objects

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

Three&hyphen;way comparison operator

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::derived&lowbar;from&lt;quantity&lowbar;point&gt; QP,
    link:#mp_units-QuantityPointOf[QuantityPointOf&lt;absolute&lowbar;point&lowbar;origin&gt;] QP2&gt;
requires std&colon;&colon;three&lowbar;way&lowbar;comparable&lowbar;with&lt;quantity&lowbar;type, typename QP2&colon;&colon;quantity&lowbar;type&gt;
&lsqb;&lsqb;nodiscard&rsqb;&rsqb;
constexpr
auto
operator&lt;&equals;&gt;(
    QP const& lhs,
    QP2 const& rhs);
----

== Return Value

The relative order of the objects

== Parameters

[cols=2]
|===
| Name
| Description
| *lhs*
| The left operand
| *rhs*
| The right operand
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;construction&lowbar;helpers&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
template&lt;link:#mp_units-Reference[Reference] auto R&gt;
constexpr link:#mp_units-point_[point&lowbar;&lt;decltype(R)&gt;] absolute = &lcub;&rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;construction&lowbar;helpers&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Reference[Reference] auto R&gt;
constexpr link:#mp_units-delta_[delta&lowbar;&lt;decltype(R)&gt;] delta = &lcub;&rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr link:#mp_units-dimension_one-063[dimension&lowbar;one] dimension&lowbar;one = dimension&lowbar;one;
----

Quantity of dimension one

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr link:#mp_units-dimensionless-0f[dimensionless] dimensionless = dimensionless;
----

== Description

Quantity of dimension one also commonly named as &quot;dimensionless&quot; is a quantity with a dimension for which all the exponents of the factors corresponding to the base dimensions are zero&period;

&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol; REAL SCALAR &sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;representation&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
constexpr bool disable&lowbar;real = false;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;representation&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&gt;
inline constexpr bool disable&lowbar;real&lt;bool&gt; = true;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;representation&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr &sol;&ast; implementation-defined &ast;&sol; imag = imag;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
template&lt;typename Rep&gt;
constexpr bool is&lowbar;complex = false;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    template&lt;typename&period;&period;&period;&gt; typename Type&gt;
constexpr bool is&lowbar;derived&lowbar;from&lowbar;specialization&lowbar;of = requires(T&ast; t) &lcub; detail&colon;&colon;to&lowbar;base&lowbar;specialization&lowbar;of&lt;Type&gt;(t)&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    template&lt;auto&period;&period;&period;&gt; typename Type&gt;
constexpr bool is&lowbar;derived&lowbar;from&lowbar;specialization&lowbar;of&lowbar;v = requires(T&ast; t) &lcub; detail&colon;&colon;to&lowbar;base&lowbar;specialization&lowbar;of&lowbar;v&lt;Type&gt;(t)&semi; &rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr link:#mp_units-is_kind-06[is&lowbar;kind] is&lowbar;kind = is&lowbar;kind;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    class T,
    class U&gt;
constexpr bool is&lowbar;same&lowbar;v = false;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;class T&gt;
constexpr bool is&lowbar;same&lowbar;v&lt;T, T&gt; = true;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
template&lt;typename Rep&gt;
constexpr bool is&lowbar;scalar = false;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    template&lt;typename&period;&period;&period;&gt; typename Type&gt;
constexpr bool is&lowbar;specialization&lowbar;of = false;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename&period;&period;&period; Params,
    template&lt;typename&period;&period;&period;&gt; typename Type&gt;
constexpr bool is&lowbar;specialization&lowbar;of&lt;Type&lt;Params&period;&period;&period;&gt;, Type&gt; = true;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    template&lt;auto&period;&period;&period;&gt; typename Type&gt;
constexpr bool is&lowbar;specialization&lowbar;of&lowbar;v = false;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;type&lowbar;traits&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    auto Params&period;&period;&period;,
    template&lt;auto&period;&period;&period;&gt; typename Type&gt;
constexpr bool is&lowbar;specialization&lowbar;of&lowbar;v&lt;Type&lt;Params&period;&period;&period;&gt;, Type&gt; = true;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
template&lt;typename Rep&gt;
constexpr bool is&lowbar;tensor = false;
----

Specifies if a specific conversion between two types preserves the value

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename From,
    typename To&gt;
constexpr bool is&lowbar;value&lowbar;preserving = treat&lowbar;as&lowbar;floating&lowbar;point&lt;To&gt; &verbar;&verbar; !treat&lowbar;as&lowbar;floating&lowbar;point&lt;From&gt;;
----

== Description

This type trait should be specialized for a custom representation types to specify weather the conversion from the source type to the destination type preserves the value or not&period; Value&hyphen;truncating conversions should be forced by the user with explicit casts&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *From*
| a source representation type
| *To*
| a destination representation type
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
template&lt;typename Rep&gt;
constexpr bool is&lowbar;vector = false;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantitySpec[QuantitySpec] auto Q&gt;
requires requires &lcub; typename kind&lowbar;of&lowbar;&lt;decltype(Q)&gt;&semi; &rcub;
constexpr link:#mp_units-kind_of_-00[kind&lowbar;of&lowbar;&lt;decltype(Q)&gt;] kind&lowbar;of;
----

&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;&sol;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
template&lt;intmax&lowbar;t N&gt;
constexpr std::optional&lt;intmax&lowbar;t&gt; known&lowbar;first&lowbar;factor = std&colon;&colon;nullopt;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;&sol;&ast; implementation-defined &ast;&sol; auto V&gt;
requires (detail&colon;&colon;get&lowbar;base&lowbar;value(V) &gt; 0)
constexpr link:#mp_units-UnitMagnitude[UnitMagnitude] auto mag = detail&colon;&colon;make&lowbar;magnitude&lt;V&gt;();
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
&lsqb;&lsqb;deprecated&rsqb;&rsqb;
inline constexpr link:#mp_units-UnitMagnitude[UnitMagnitude] auto mag&lowbar;pi = mag&lt;pi&gt;;
----

Create a Magnitude which is some rational number raised to a rational power&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    &sol;&ast; implementation-defined &ast;&sol; auto Base,
    int Num,
    int Den = 1&gt;
requires (detail&colon;&colon;get&lowbar;base&lowbar;value(Base) &gt; 0)
constexpr link:#mp_units-UnitMagnitude[UnitMagnitude] auto mag&lowbar;power = pow&lt;Num, Den&gt;(mag&lt;Base&gt;);
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    intmax&lowbar;t N,
    intmax&lowbar;t D&gt;
requires (N &gt; 0)
constexpr link:#mp_units-UnitMagnitude[UnitMagnitude] auto mag&lowbar;ratio = detail&colon;&colon;prime&lowbar;factorization&lowbar;v&lt;N&gt; &sol; detail&colon;&colon;prime&lowbar;factorization&lowbar;v&lt;D&gt;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;representation&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr &sol;&ast; implementation-defined &ast;&sol; magnitude = magnitude;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;representation&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr &sol;&ast; implementation-defined &ast;&sol; modulus = modulus;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr link:#mp_units-one-0f[one] one = one;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr link:#mp_units-parts_per_million-0f[parts&lowbar;per&lowbar;million] parts&lowbar;per&lowbar;million = parts&lowbar;per&lowbar;million;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr link:#mp_units-per_mille-01[per&lowbar;mille] per&lowbar;mille = per&lowbar;mille;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr link:#mp_units-percent-02[percent] percent = percent;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr link:#mp_units-pi-0c[pi] pi = pi;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;construction&lowbar;helpers&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Reference[Reference] auto R&gt;
constexpr link:#mp_units-point_[point&lowbar;&lt;decltype(R)&gt;] point = &lcub;&rcub;;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr auto ppm = parts&lowbar;per&lowbar;million;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;representation&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr &sol;&ast; implementation-defined &ast;&sol; real = real;
----

Puts a space &apos; &apos; sign before a unit symbol

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Unit[Unit] auto U&gt;
constexpr bool space&lowbar;before&lowbar;unit&lowbar;symbol = true;
----

== Description

Quantities of some units (e&period;g&period; degree, arcminute, arcsecond) should not be printed with the space between a number and a unit&period; For those a partial specialization with the value `false` should be provided&period;

Specifies if a value of a type should be treated as a floating&hyphen;point value

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;customization&lowbar;points&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename Rep&gt;
constexpr bool treat&lowbar;as&lowbar;floating&lowbar;point = std&colon;&colon;chrono&colon;&colon;treat&lowbar;as&lowbar;floating&lowbar;point&lowbar;v&lt;value&lowbar;type&lowbar;t&lt;Rep&gt;&gt;;
----

== Description

This type trait should be specialized for a custom representation type to specify that values of this type should be treated by the library as a floating&hyphen;point ones which will enable implicit conversions between quantities&period;

== Template Parameters

[cols=2]
|===
| Name
| Description
| *Rep*
| a representation type for which a type trait is defined
|===

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantitySpec[QuantitySpec] auto QS&gt;
constexpr link:#mp_units-zeroth_point_origin_[zeroth&lowbar;point&lowbar;origin&lowbar;&lt;QS&gt;] zeroth&lowbar;point&lowbar;origin;
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
inline constexpr auto π = pi;
----

A concept matching all units that can be used as quantity references

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename U&gt;
concept AssociatedUnit = Unit&lt;U&gt; &amp;&amp; detail&colon;&colon;has&lowbar;associated&lowbar;quantity(U&lcub;&rcub;);
----

A concept matching all dimensions in the library&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept Dimension = std&colon;&colon;derived&lowbar;from&lt;T, detail&colon;&colon;dimension&lowbar;interface&gt; &amp;&amp; detail&colon;&colon;SymbolicConstant&lt;T&gt;;
----

== Description

Satisfied by all dimension types in the library&period;

A concept checking if the argument is of the same dimension&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;dimension&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    auto D&gt;
concept DimensionOf = Dimension&lt;T&gt; &amp;&amp; Dimension&lt;MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(D))&gt; &amp;&amp; (T&lcub;&rcub; &equals;&equals; D);
----

== Description

Satisfied when both argument satisfy a `Dimension` concept and when they compare equal&period;

A concept matching all quantity point origins in the library

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept PointOrigin = std&colon;&colon;derived&lowbar;from&lt;T, detail&colon;&colon;point&lowbar;origin&lowbar;interface&gt; &amp;&amp; detail&colon;&colon;SymbolicConstant&lt;T&gt;;
----

== Description

Satisfied by either quantity points or by all types derived from `absolute&lowbar;point&lowbar;origin` class template&period;

A concept matching all quantity point origins for a specified quantity type in the library

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    auto QS&gt;
concept PointOriginFor = PointOrigin&lt;T&gt; &amp;&amp; QuantitySpecOf&lt;MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(QS)), T&colon;&colon;&lowbar;quantity&lowbar;spec&lowbar;&gt;;
----

== Description

Satisfied by all quantity point origins that are defined using a provided quantity specification&period;

A concept to be used to define prefixes for a unit

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept PrefixableUnit = Unit&lt;T&gt; &amp;&amp; is&lowbar;derived&lowbar;from&lowbar;specialization&lowbar;of&lowbar;v&lt;T, named&lowbar;unit&gt;;
----

A concept matching all quantities in the library

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept Quantity = detail&colon;&colon;is&lowbar;derived&lowbar;from&lowbar;specialization&lowbar;of&lowbar;quantity&lt;T&gt;;
----

== Description

Satisfied by all types being a either specialization or derived from `quantity`

A concept matching all external quantities like types

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept QuantityLike = !Quantity&lt;T&gt; &amp;&amp; detail&colon;&colon;QuantityLikeImpl&lt;T, quantity&lowbar;like&lowbar;traits&gt; &amp;&amp; requires &lcub;
  typename quantity&lt;quantity&lowbar;like&lowbar;traits&lt;T&gt;&colon;&colon;reference, typename quantity&lowbar;like&lowbar;traits&lt;T&gt;&colon;&colon;rep&gt;&semi;
&rcub;;
----

== Description

Satisfied by all external types (not&hyphen;defined in mp&hyphen;units) that via a `quantity&lowbar;like&lowbar;traits` provide all quantity&hyphen;specific information&period;

A concept matching all quantities of the provided quantity spec

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Q,
    auto QS&gt;
concept QuantityOf = Quantity&lt;Q&gt; &amp;&amp; QuantitySpec&lt;MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(QS))&gt; &amp;&amp;
                     ReferenceOf&lt;MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(Q&colon;&colon;reference), QS&gt;;
----

== Description

Satisfied by all quantities with the reference satisfying `ReferenceOf&lt;QS&gt;&period;`

A concept matching all quantity points in the library

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept QuantityPoint = detail&colon;&colon;is&lowbar;quantity&lowbar;point&lt;T&gt;;
----

== Description

Satisfied by all types being either a specialization or derived from `quantity&lowbar;point`

A concept matching all external quantity point like types

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept QuantityPointLike = !QuantityPoint&lt;T&gt; &amp;&amp; detail&colon;&colon;QuantityLikeImpl&lt;T, quantity&lowbar;point&lowbar;like&lowbar;traits&gt; &amp;&amp; requires &lcub;
  typename quantity&lowbar;point&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;T&gt;&colon;&colon;reference, quantity&lowbar;point&lowbar;like&lowbar;traits&lt;T&gt;&colon;&colon;point&lowbar;origin,
                          typename quantity&lowbar;point&lowbar;like&lowbar;traits&lt;T&gt;&colon;&colon;rep&gt;&semi;
&rcub;;
----

== Description

Satisfied by all external types (not&hyphen;defined in mp&hyphen;units) that via a `quantity&lowbar;point&lowbar;like&lowbar;traits` provide all quantity&lowbar;point&hyphen;specific information&period;

A concept matching all quantity points of the provided property

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename QP,
    auto V&gt;
concept QuantityPointOf = QuantityPoint&lt;QP&gt; &amp;&amp; (ReferenceOf&lt;MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(QP&colon;&colon;reference), V&gt; &verbar;&verbar;
                        detail&colon;&colon;SameAbsolutePointOriginAs&lt;MP&lowbar;UNITS&lowbar;NONCONST&lowbar;TYPE(QP&colon;&colon;absolute&lowbar;point&lowbar;origin), V&gt;);
----

== Description

Satisfied by all quantity points with a quantity&lowbar;spec being the instantiation derived from the provided quantity&lowbar;spec type, or quantity points having the origin with the same `absolute&lowbar;point&lowbar;origin`&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept QuantitySpec = std&colon;&colon;derived&lowbar;from&lt;T, detail&colon;&colon;quantity&lowbar;spec&lowbar;interface&lowbar;base&gt; &amp;&amp; detail&colon;&colon;SymbolicConstant&lt;T&gt;;
----

A concept matching all quantity specifications of a provided quantity spec value

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;spec&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    auto QS&gt;
concept QuantitySpecOf = QuantitySpec&lt;T&gt; &amp;&amp; QuantitySpec&lt;MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(QS))&gt; &amp;&amp; (mp&lowbar;units&colon;&colon;implicitly&lowbar;convertible(T&lcub;&rcub;, QS));
----

== Description

Satisfied by all quantity specifications that are implicitly convertible to the provided `QS` value&period;

A concept matching all references in the library&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept Reference = MP&lowbar;UNITS&lowbar;ASSOCIATED&lowbar;UNIT&lowbar;T(T) &verbar;&verbar; is&lowbar;specialization&lowbar;of&lt;T, reference&gt;;
----

== Description

Satisfied by all specializations of `reference&period;`

A concept matching all references of the provided quantity spec

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;reference&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    auto QS&gt;
concept ReferenceOf = Reference&lt;T&gt; &amp;&amp; QuantitySpec&lt;MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(QS))&gt; &amp;&amp;
                      QuantitySpecOf&lt;decltype(get&lowbar;quantity&lowbar;spec(T&lcub;&rcub;)), QS&gt;;
----

== Description

Satisfied by all references for which `QuantitySpecOf&lt;QS&gt;` is true&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;representation&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename T,
    auto V&gt;
concept RepresentationOf = ((QuantitySpec&lt;MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(V))&gt; &amp;&amp;
    ((detail&colon;&colon;QuantityKindSpec&lt;MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(V))&gt; &amp;&amp; detail&colon;&colon;SomeRepresentation&lt;T&gt;) &verbar;&verbar;
     detail&colon;&colon;IsOfCharacter&lt;T, V&period;character&gt;)) &verbar;&verbar;
   (std&colon;&colon;same&lowbar;as&lt;quantity&lowbar;character, decltype(V)&gt; &amp;&amp; detail&colon;&colon;IsOfCharacter&lt;T, V&gt;));
----

A concept matching all unit types in the library

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept Unit = std&colon;&colon;derived&lowbar;from&lt;T, detail&colon;&colon;unit&lowbar;interface&gt; &amp;&amp; detail&colon;&colon;SymbolicConstant&lt;T&gt;;
----

== Description

Satisfied by all unit types provided by the library&period;

Concept to detect whether T is a valid UnitMagnitude&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;magnitude&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;typename T&gt;
concept UnitMagnitude = is&lowbar;specialization&lowbar;of&lowbar;v&lt;T, detail&colon;&colon;unit&lowbar;magnitude&gt;;
----

A concept matching all units associated with the provided quantity spec

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;unit&lowbar;concepts&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename U,
    auto QS&gt;
concept UnitOf = MP&lowbar;UNITS&lowbar;ASSOCIATED&lowbar;UNIT&lt;U&gt; &amp;&amp; QuantitySpec&lt;MP&lowbar;UNITS&lowbar;REMOVE&lowbar;CONST(decltype(QS))&gt; &amp;&amp;
  (implicitly&lowbar;convertible(get&lowbar;quantity&lowbar;spec(U&lcub;&rcub;), QS) &verbar;&verbar;
   (unsatisfied&lt;&quot;Unit &apos;&lcub;&rcub;&apos; is associated with quantity of kind &apos;&lcub;&rcub;&apos; which is not convertible to the &apos;&lcub;&rcub;&apos; quantity&quot;&gt;(
     U&lcub;&rcub;, type&lowbar;name(get&lowbar;quantity&lowbar;spec(U&lcub;&rcub;)&period;&lowbar;quantity&lowbar;spec&lowbar;), type&lowbar;name(QS))));
----

== Description

Satisfied by all units for which an associated quantity spec is implicitly convertible to the provided `QS` value&period;

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT,
    std::size&lowbar;t N&gt;
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N &hyphen; 1&gt;](CharT const(& str)[]) -> link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N &hyphen; 1&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT,
    std::same&lowbar;as&lt;CharT&gt;&period;&period;&period; Rest&gt;
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, 1 &plus; sizeof&period;&period;&period;(Rest)&gt;](
    CharT,
    Rest&period;&period;&period;) -> link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, 1 &plus; sizeof&period;&period;&period;(Rest)&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;ext&sol;fixed&lowbar;string&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename CharT,
    std::size&lowbar;t N&gt;
link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N&gt;](
    std::from&lowbar;range&lowbar;t,
    std::array&lt;CharT, N&gt;) -> link:#mp_units-basic_fixed_string-08[basic&lowbar;fixed&lowbar;string&lt;CharT, N&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;cartesian&lowbar;vector&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    typename Arg,
    typename&period;&period;&period; Args&gt;
requires (sizeof&period;&period;&period;(Args) &lt;&equals; 2) &amp;&amp; requires &lcub; typename std&colon;&colon;common&lowbar;type&lowbar;t&lt;Arg, Args&period;&period;&period;&gt;&semi; &rcub;
link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;std::common&lowbar;type&lowbar;t&lt;Arg, Args&period;&period;&period;&gt;&gt;](
    Arg,
    Args&period;&period;&period;) -> link:#mp_units-cartesian_vector-08[cartesian&lowbar;vector&lt;std::common&lowbar;type&lowbar;t&lt;Arg, Args&period;&period;&period;&gt;&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityLike[QuantityLike] Q&gt;
link:#mp_units-quantity-01[quantity&lt;quantity&lowbar;like&lowbar;traits&lt;Q&gt;&colon;&colon;reference, quantity&lowbar;like&lowbar;traits&lt;Q&gt;::rep&gt;](Q) -> link:#mp_units-quantity-01[quantity&lt;quantity&lowbar;like&lowbar;traits&lt;Q&gt;&colon;&colon;reference, quantity&lowbar;like&lowbar;traits&lt;Q&gt;::rep&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Reference[Reference] R,
    link:#mp_units-RepresentationOf[RepresentationOf&lt;get&lowbar;quantity&lowbar;spec(R&lcub;&rcub;)&gt;] Value&gt;
link:#mp_units-quantity-01[quantity&lt;R&lcub;&rcub;, Value&gt;](
    Value v,
    R) -> link:#mp_units-quantity-01[quantity&lt;R&lcub;&rcub;, Value&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-Quantity[Quantity] Q&gt;
link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;Q&colon;&colon;reference, default&lowbar;point&lowbar;origin(Q&colon;&colon;reference), Q::rep&gt;](Q q) -> link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;Q&colon;&colon;reference, default&lowbar;point&lowbar;origin(Q&colon;&colon;reference), Q::rep&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;link:#mp_units-QuantityPointLike[QuantityPointLike] QP&gt;
link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference, quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;point&lowbar;origin, quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;::rep&gt;](QP) -> link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;reference, quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;&colon;&colon;point&lowbar;origin, quantity&lowbar;point&lowbar;like&lowbar;traits&lt;QP&gt;::rep&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;quantity&lowbar;point&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    link:#mp_units-Quantity[Quantity] Q,
    link:#mp_units-PointOriginFor[PointOriginFor&lt;Q&colon;&colon;quantity&lowbar;spec&gt;] PO&gt;
link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;Q&colon;&colon;reference, PO&lcub;&rcub;, Q::rep&gt;](
    Q q,
    PO) -> link:#mp_units-quantity_point-08[quantity&lowbar;point&lt;Q&colon;&colon;reference, PO&lcub;&rcub;, Q::rep&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;1, 1&gt;](char) -> link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;1, 1&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N&gt;
link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N, N&gt;](link:#mp_units-fixed_string[fixed&lowbar;string&lt;N&gt;] const&) -> link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N, N&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;std::size&lowbar;t N&gt;
link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N &hyphen; 1, N &hyphen; 1&gt;](char const(&)[]) -> link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N &hyphen; 1, N &hyphen; 1&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::size&lowbar;t N,
    std::size&lowbar;t M&gt;
link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N, M&gt;](
    link:#mp_units-fixed_u8string[fixed&lowbar;u8string&lt;N&gt;] const&,
    link:#mp_units-fixed_string[fixed&lowbar;string&lt;M&gt;] const&) -> link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N, M&gt;];
----

== Synopsis

Declared in `&lt;mp&hyphen;units&sol;framework&sol;symbol&lowbar;text&period;h&gt;`

[source,cpp,subs="verbatim,replacements,macros,-callouts"]
----
template&lt;
    std::size&lowbar;t N,
    std::size&lowbar;t M&gt;
link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N &hyphen; 1, M &hyphen; 1&gt;](
    char8&lowbar;t const(&)[],
    char const(&)[]) -> link:#mp_units-symbol_text-032[symbol&lowbar;text&lt;N &hyphen; 1, M &hyphen; 1&gt;];
----


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