measures/

define_measure_types.rs

#[macro_export]
macro_rules! if_all_true {
    ( { } $( $fragment:item )* ) => { $( $fragment )* };
    ( { false $($rest:tt)* } $( $fragment:item )* ) => { };
    ( { true $($rest:tt)* } $( $fragment:item )* ) => { measures::if_all_true! { { $($rest)* } $( $fragment )* } };
}

#[macro_export]
macro_rules! define_scalar_property {
    ( $scalar_property:tt ) => {};
}

#[macro_export]
macro_rules! define_vector_property {
    // ( $vector_property:tt ) => {};
    ( $property_name:ident [ $( $unit:tt )* ]) => {};
}

#[macro_export]
macro_rules! define_measure_types_aux {
    // Empty case
    {
        ,

        with_points: $with_points:tt,
        with_directions: $with_directions:tt,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        with_transformations: $with_transformations:tt,
        exact: $exact:tt,
        with_approx: $with_approx:tt,
        with_correlation: $with_correlation:tt;

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    } => {
        use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
        use measures::{
            dimensionless::{Dimensionless, One},
            angle::{Angle, Radian},
            traits::{
                AngleMeasurementUnit, ArithmeticOps, LossyFrom, MeasurementUnit, Sqrt, VectorProperty, Trigonometry,
            },
        };
        use core::fmt;
        use core::marker::PhantomData;

        measures::inner_define_measure! { $with_approx }
        measures::if_all_true! { { $with_approx }
            measures::inner_define_approx_measure! { $exact }
        }
        measures::if_all_true! { { $with_points }
            measures::inner_define_measure_point! { $with_approx }
        }
        measures::if_all_true! { { $with_approx $with_points }
            measures::inner_define_approx_measure_point ! { $exact }
        }
        measures::if_all_true! { { $exact $with_directions }
            measures::inner_define_unsigned_direction! { $with_points }
        }
        measures::if_all_true! { { $exact $with_directions }
            measures::inner_define_signed_direction! { $with_points }
        }
        measures::if_all_true! { { $with_2d }
            measures::inner_define_measure_2d! { $with_points $with_directions $with_approx }
        }
        measures::if_all_true! { { $with_2d $with_points $exact }
            measures::inner_define_measure_point_2d! { $with_approx }
        }
        measures::if_all_true! { { $with_3d }
            measures::inner_define_measure_3d! { $with_approx }
        }
        measures::if_all_true! { { $with_points $with_3d }
            measures::inner_define_measure_point_3d! { $with_approx }
        }
        measures::if_all_true! { { $with_2d $with_transformations }
            measures::inner_define_linear_map_2d! {}
        }
        measures::if_all_true! { { $with_3d $with_transformations }
            measures::inner_define_linear_map_3d! {}
        }
        measures::if_all_true! { { $with_2d $with_transformations $with_points }
            measures::inner_define_affine_map_2d! {}
        }
        measures::if_all_true! { { $with_3d $with_transformations $with_points }
            measures::inner_define_affine_map_3d! {}
        }

        measures::if_all_true! { { $with_approx $with_2d }
            measures::inner_define_approx_measure_2d! { $exact }
        }
        measures::if_all_true! { { $with_approx $with_points $with_2d }
            measures::inner_define_approx_measure_point_2d! { $exact }
        }
        measures::if_all_true! { { $with_approx $with_3d }
            measures::inner_define_approx_measure_3d! { $exact }
        }
        measures::if_all_true! { { $with_approx $with_points $with_3d }
            measures::inner_define_approx_measure_point_3d! { $exact }
        }

        // `scalar_properties` section
        $(
            $(
                measures::measurement_scalar_property! { $scalar_prop }
                $(
                    measures::measurement_unit! {
                        name: $scalar_unit,
                        property: $scalar_prop,
                        $(
                            $scalar_key: $scalar_val,
                        )*
                        with_2d: $with_2d,
                        with_3d: $with_3d,
                        vector: false,
                    }
                )*
            )*
        )?

        // `vector_properties` section
        $(
            $(
                measures::measurement_vector_property! { $vector_prop }
                $(
                    measures::measurement_unit! {
                        name: $vector_unit,
                        property: $vector_prop,
                        $(
                            $vector_key: $vector_val,
                        )*
                        with_2d: $with_2d,
                        with_3d: $with_3d,
                        vector: true,
                    }
                )*
            )*
        )?

        // `angle_measurement_units` section
        $(
            $(
                measures::angle_measurement_unit! {
                    name: $angle_unit,
                    $(
                        $angle_key: $angle_val,
                    )*
                }
            )*
        )?

        // `relationships` section
        $(
            $(
                measures::define_units_relationship! {
                    $exact $with_approx $with_correlation,
                    $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                }
            )*
        )?
    };

    // First option is "with_points"
    {
        with_points $( $flag:ident )*,

        with_points: false,
        with_directions: $with_directions:tt,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        with_transformations: $with_transformations:tt,
        exact: $exact:tt,
        with_approx: $with_approx:tt,
        with_correlation: $with_correlation:tt;

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    } => {
        measures::define_measure_types_aux!{
            $( $flag ) *,

            with_points: true,
            with_directions: $with_directions,
            with_2d: $with_2d,
            with_3d: $with_3d,
            with_transformations: $with_transformations,
            exact: $exact,
            with_approx: $with_approx,
            with_correlation: $with_correlation;

            $(
                scalar_properties [
                    $(
                        $scalar_prop [
                            $(
                                $scalar_unit {
                                    $($scalar_key : $scalar_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                vector_properties [
                    $(
                        $vector_prop [
                            $(
                                $vector_unit {
                                    $($vector_key : $vector_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                angle_measurement_units [
                    $(
                        $angle_unit {
                            $($angle_key : $angle_val),*
                        }
                    )*
                ]
            )?

            $(
                relationships [
                    $(
                        $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                    )*
                ]
            )?
        }
    };

    // First option is "with_directions"
    {
        with_directions $( $flag:ident )*,

        with_points: $with_points:tt,
        with_directions: false,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        with_transformations: $with_transformations:tt,
        exact: $exact:tt,
        with_approx: $with_approx:tt,
        with_correlation: $with_correlation:tt;

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    } => {
        measures::define_measure_types_aux!{
            $( $flag ) *,

            with_points: $with_points,
            with_directions: true,
            with_2d: $with_2d,
            with_3d: $with_3d,
            with_transformations: $with_transformations,
            exact: $exact,
            with_approx: $with_approx,
            with_correlation: $with_correlation;

            $(
                scalar_properties [
                    $(
                        $scalar_prop [
                            $(
                                $scalar_unit {
                                    $($scalar_key : $scalar_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                vector_properties [
                    $(
                        $vector_prop [
                            $(
                                $vector_unit {
                                    $($vector_key : $vector_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                angle_measurement_units [
                    $(
                        $angle_unit {
                            $($angle_key : $angle_val),*
                        }
                    )*
                ]
            )?

            $(
                relationships [
                    $(
                        $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                    )*
                ]
            )?
        }
    };

    // First option is "with_2d"
    {
        with_2d $( $flag:ident )*,

        with_points: $with_points:tt,
        with_directions: $with_directions:tt,
        with_2d: false,
        with_3d: $with_3d:tt,
        with_transformations: $with_transformations:tt,
        exact: $exact:tt,
        with_approx: $with_approx:tt,
        with_correlation: $with_correlation:tt;

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    } => {
        measures::define_measure_types_aux!{
            $( $flag ) *,

            with_points: $with_points,
            with_directions: $with_directions,
            with_2d: true,
            with_3d: $with_3d,
            with_transformations: $with_transformations,
            exact: $exact,
            with_approx: $with_approx,
            with_correlation: $with_correlation;

            $(
                scalar_properties [
                    $(
                        $scalar_prop [
                            $(
                                $scalar_unit {
                                    $($scalar_key : $scalar_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                vector_properties [
                    $(
                        $vector_prop [
                            $(
                                $vector_unit {
                                    $($vector_key : $vector_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                angle_measurement_units [
                    $(
                        $angle_unit {
                            $($angle_key : $angle_val),*
                        }
                    )*
                ]
            )?

            $(
                relationships [
                    $(
                        $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                    )*
                ]
            )?
        }
    };

    // First option is "with_3d"
    {
        with_3d $( $flag:ident )*,

        with_points: $with_points:tt,
        with_directions: $with_directions:tt,
        with_2d: $with_2d:tt,
        with_3d: false,
        with_transformations: $with_transformations:tt,
        exact: $exact:tt,
        with_approx: $with_approx:tt,
        with_correlation: $with_correlation:tt;

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    } => {
        measures::define_measure_types_aux!{
            $( $flag ) *,

            with_points: $with_points,
            with_directions: $with_directions,
            with_2d: $with_2d,
            with_3d: true,
            with_transformations: $with_transformations,
            exact: $exact,
            with_approx: $with_approx,
            with_correlation: $with_correlation;

            $(
                scalar_properties [
                    $(
                        $scalar_prop [
                            $(
                                $scalar_unit {
                                    $($scalar_key : $scalar_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                vector_properties [
                    $(
                        $vector_prop [
                            $(
                                $vector_unit {
                                    $($vector_key : $vector_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                angle_measurement_units [
                    $(
                        $angle_unit {
                            $($angle_key : $angle_val),*
                        }
                    )*
                ]
            )?

            $(
                relationships [
                    $(
                        $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                    )*
                ]
            )?
        }
    };

    // First option is "with_transformations"
    {
        with_transformations $( $flag:ident )*,

        with_points: $with_points:tt,
        with_directions: $with_directions:tt,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        with_transformations: false,
        exact: $exact:tt,
        with_approx: $with_approx:tt,
        with_correlation: $with_correlation:tt;

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    } => {
        measures::define_measure_types_aux!{
            $( $flag ) *,

            with_points: $with_points,
            with_directions: $with_directions,
            with_2d: $with_2d,
            with_3d: $with_3d,
            with_transformations: true,
            exact: $exact,
            with_approx: $with_approx,
            with_correlation: $with_correlation;

            $(
                scalar_properties [
                    $(
                        $scalar_prop [
                            $(
                                $scalar_unit {
                                    $($scalar_key : $scalar_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                vector_properties [
                    $(
                        $vector_prop [
                            $(
                                $vector_unit {
                                    $($vector_key : $vector_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                angle_measurement_units [
                    $(
                        $angle_unit {
                            $($angle_key : $angle_val),*
                        }
                    )*
                ]
            )?

            $(
                relationships [
                    $(
                        $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                    )*
                ]
            )?
        }
    };

    // First option is "exact"
    {
        exact $( $flag:ident )*,

        with_points: $with_points:tt,
        with_directions: $with_directions:tt,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        with_transformations: $with_transformations:tt,
        exact: false,
        with_approx: $with_approx:tt,
        with_correlation: $with_correlation:tt;

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    } => {
        measures::define_measure_types_aux!{
            $( $flag ) *,

            with_points: $with_points,
            with_directions: $with_directions,
            with_2d: $with_2d,
            with_3d: $with_3d,
            with_transformations: $with_transformations,
            exact: true,
            with_approx: $with_approx,
            with_correlation: $with_correlation;

            $(
                scalar_properties [
                    $(
                        $scalar_prop [
                            $(
                                $scalar_unit {
                                    $($scalar_key : $scalar_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                vector_properties [
                    $(
                        $vector_prop [
                            $(
                                $vector_unit {
                                    $($vector_key : $vector_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                angle_measurement_units [
                    $(
                        $angle_unit {
                            $($angle_key : $angle_val),*
                        }
                    )*
                ]
            )?

            $(
                relationships [
                    $(
                        $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                    )*
                ]
            )?
        }
    };

    // First option is "with_approx"
    {
        with_approx $( $flag:ident )*,

        with_points: $with_points:tt,
        with_directions: $with_directions:tt,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        with_transformations: $with_transformations:tt,
        exact: $exact:tt,
        with_approx: false,
        with_correlation: $with_correlation:tt;

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    } => {
        measures::define_measure_types_aux!{
            $( $flag ) *,

            with_points: $with_points,
            with_directions: $with_directions,
            with_2d: $with_2d,
            with_3d: $with_3d,
            with_transformations: $with_transformations,
            exact: $exact,
            with_approx: true,
            with_correlation: $with_correlation;

            $(
                scalar_properties [
                    $(
                        $scalar_prop [
                            $(
                                $scalar_unit {
                                    $($scalar_key : $scalar_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                vector_properties [
                    $(
                        $vector_prop [
                            $(
                                $vector_unit {
                                    $($vector_key : $vector_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                angle_measurement_units [
                    $(
                        $angle_unit {
                            $($angle_key : $angle_val),*
                        }
                    )*
                ]
            )?

            $(
                relationships [
                    $(
                        $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                    )*
                ]
            )?
        }
    };

    // First option is "with_correlation"
    {
        with_correlation $( $flag:ident )*,

        with_points: $with_points:tt,
        with_directions: $with_directions:tt,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        with_transformations: $with_transformations:tt,
        exact: $exact:tt,
        with_approx: $with_approx:tt,
        with_correlation: false;

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    } => {
        measures::define_measure_types_aux!{
            $( $flag ) *,
            with_points: $with_points,
            with_directions: $with_directions,
            with_2d: $with_2d,
            with_3d: $with_3d,
            with_transformations: $with_transformations,
            exact: $exact,
            with_approx: $with_approx,
            with_correlation: true;

            $(
                scalar_properties [
                    $(
                        $scalar_prop [
                            $(
                                $scalar_unit {
                                    $($scalar_key : $scalar_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                vector_properties [
                    $(
                        $vector_prop [
                            $(
                                $vector_unit {
                                    $($vector_key : $vector_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                angle_measurement_units [
                    $(
                        $angle_unit {
                            $($angle_key : $angle_val),*
                        }
                    )*
                ]
            )?

            $(
                relationships [
                    $(
                        $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                    )*
                ]
            )?
        }
    };
}

#[macro_export]
macro_rules! define_measure_types {
    (
        $( $flag:ident )* ,

        $(
            scalar_properties [
                $(
                    $scalar_prop:ident [
                        $(
                            $scalar_unit:ident {
                                $($scalar_key:ident : $scalar_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            vector_properties [
                $(
                    $vector_prop:ident [
                        $(
                            $vector_unit:ident {
                                $($vector_key:ident : $vector_val:expr),* $(,)?
                            }
                        )*
                    ]
                )*
            ]
        )?

        $(
            angle_measurement_units [
                $(
                    $angle_unit:ident {
                        $($angle_key:ident : $angle_val:expr),* $(,)?
                    }
                )*
            ]
        )?

        $(
            relationships [
                $(
                    $unit1:ident $dim1:tt == $unit2:ident $dim2:tt $op:tt $unit3:ident $dim3:tt $(,)?
                )*
            ]
        )?
    ) => {
        measures::define_measure_types_aux! {
            $( $flag )* ,

            with_points: false,
            with_directions: false,
            with_2d: false,
            with_3d: false,
            with_transformations: false,
            exact: false,
            with_approx: false,
            with_correlation: false;

            $(
                scalar_properties [
                    $(
                        $scalar_prop [
                            $(
                                $scalar_unit {
                                    $($scalar_key : $scalar_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                vector_properties [
                    $(
                        $vector_prop [
                            $(
                                $vector_unit {
                                    $($vector_key : $vector_val),*
                                }
                            )*
                        ]
                    )*
                ]
            )?

            $(
                angle_measurement_units [
                    $(
                        $angle_unit {
                            $($angle_key : $angle_val),*
                        }
                    )*
                ]
            )?

            $(
                relationships [
                    $(
                        $unit1 $dim1 == $unit2 $dim2 $op $unit3 $dim3
                    )*
                ]
            )?
        }
    };
}

#[macro_export]
macro_rules! measurement_scalar_property {
    ($name:ident) => {
        /// A scalar measure property.
        pub struct $name;
        impl $crate::traits::MeasurementProperty for $name {}
        impl $crate::traits::ScalarProperty for $name {}
    };
}

#[macro_export]
macro_rules! measurement_vector_property {
    ($name:ident) => {
        /// A vector measure property.
        pub struct $name;
        impl $crate::traits::MeasurementProperty for $name {}
        impl $crate::traits::VectorProperty for $name {}
    };
}

#[macro_export]
macro_rules! angle_measurement_unit {
    {
        name: $name:ident,
        suffix: $suffix:expr,
        cycle_fraction: $cycle_fraction:expr,
    } => {
        $crate::angle_measurement_unit! {
            name: $name,
            suffix: $suffix,
            offset: 0.,
            cycle_fraction: $cycle_fraction,
        }
    };
    {
        name: $name:ident,
        suffix: $suffix:expr,
        offset: $offset:expr,
        cycle_fraction: $cycle_fraction:expr,
    } => {
        /// An `Angle` unit of measurement.
        pub struct $name;
        impl measures::traits::MeasurementUnit for $name {
            type Property = $crate::angle::Angle;
            const RATIO: f64 = core::f64::consts::TAU / ($cycle_fraction);
            const OFFSET: f64 = $offset;
            const SUFFIX: &'static str = $suffix;
        }

        impl measures::traits::AngleMeasurementUnit for $name {
            const CYCLE_FRACTION: f64 = $cycle_fraction;
        }

        impl<Number> core::ops::Mul<Measure<$name, Number>> for Measure<measures::dimensionless::One, Number>
        where
            Number: measures::traits::ArithmeticOps,
        {
            type Output = Measure<$name, Number>;

            /// Measure<One> * AngleMeasure -> AngleMeasure
            fn mul(self, other: Measure<$name, Number>) -> Measure<$name, Number> {
                Measure::<$name, Number>::new(self.value * other.value)
            }
        }

        impl<Number> core::ops::Div<Measure<measures::dimensionless::One, Number>> for Measure<$name, Number>
        where
            Number: measures::traits::ArithmeticOps,
        {
            type Output = Self;

            /// AngleMeasure / Measure<One> -> AngleMeasure
            fn div(self, other: Measure<measures::dimensionless::One, Number>) -> Self::Output {
                Self::new(self.value / other.value)
            }
        }
    };
}

#[macro_export]
macro_rules! measurement_unit_aux {
    {
        name: $name:ident,
        property: $property:ident,
        suffix: $suffix:expr,
        ratio: $ratio:expr,
        offset: $offset:expr,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        vector: $vector:tt,
    } => {
        /// A unit of measurement.
        pub struct $name;
        impl measures::traits::MeasurementUnit for $name {
            type Property = $property;
            const RATIO: f64 = $ratio;
            const OFFSET: f64 = $offset;
            const SUFFIX: &'static str = $suffix;
        }

        impl<Number> core::ops::Mul<Measure<$name, Number>> for Measure<measures::dimensionless::One, Number>
        where
            Number: measures::traits::ArithmeticOps,
        {
            type Output = Measure<$name, Number>;

            /// Measure<One> * Measure -> Measure
            fn mul(self, other: Measure<$name, Number>) -> Measure<$name, Number> {
                Measure::<$name, Number>::new(self.value * other.value)
            }
        }

        impl<Number> core::ops::Div<Measure<measures::dimensionless::One, Number>> for Measure<$name, Number>
        where
            Number: measures::traits::ArithmeticOps,
        {
            type Output = Self;

            /// Measure / Measure<One> -> Measure
            fn div(self, other: Measure<measures::dimensionless::One, Number>) -> Self::Output {
                Self::new(self.value / other.value)
            }
        }

        measures::if_all_true! { { $with_2d $vector }
            impl<Number> core::ops::Mul<Measure<$name, Number>> for Measure2d<measures::dimensionless::One, Number>
            where
                Number: measures::traits::ArithmeticOps,
            {
                type Output = Measure2d<$name, Number>;

                /// Measure2d<One> * Measure -> Measure2d
                fn mul(self, other: Measure<$name, Number>) -> Self::Output {
                    Measure2d::<$name, Number>::new([
                        self.values[0] * other.value,
                        self.values[1] * other.value,
                    ])
                }
            }

            impl<Number> core::ops::Mul<Measure2d<One, Number>> for Measure<$name, Number>
            where
                Number: measures::traits::ArithmeticOps,
            {
                type Output = Measure2d<$name, Number>;

                /// Measure * Measure2d<One> -> Measure2d
                fn mul(self, other: Measure2d<One, Number>) -> Self::Output {
                    Measure2d::<$name, Number>::new([
                        self.value * other.values[0],
                        self.value * other.values[1],
                    ])
                }
            }

            impl<Number> core::ops::Div<Measure<measures::dimensionless::One, Number>> for Measure2d<$name, Number>
            where
                Number: measures::traits::ArithmeticOps,
            {
                type Output = Self;

                /// Measure2d / Measure<One> -> Measure2d
                fn div(self, other: Measure<measures::dimensionless::One, Number>) -> Self::Output {
                    Self::new([
                        self.values[0] / other.value,
                        self.values[1] / other.value,
                    ])
                }
            }
        }

        measures::if_all_true! { { $with_3d $vector }
            impl<Number> core::ops::Mul<Measure<$name, Number>> for Measure3d<measures::dimensionless::One, Number>
            where
                Number: measures::traits::ArithmeticOps,
            {
                type Output = Measure3d<$name, Number>;

                /// Measure3d<One> * Measure -> Measure3d
                fn mul(self, other: Measure<$name, Number>) -> Self::Output {
                    Measure3d::<$name, Number>::new([
                        self.values[0] * other.value,
                        self.values[1] * other.value,
                        self.values[2] * other.value,
                    ])
                }
            }

            impl<Number> core::ops::Mul<Measure3d<One, Number>> for Measure<$name, Number>
            where
                Number: measures::traits::ArithmeticOps,
            {
                type Output = Measure3d<$name, Number>;

                /// Measure * Measure3d<One> -> Measure3d
                fn mul(self, other: Measure3d<One, Number>) -> Self::Output {
                    Measure3d::<$name, Number>::new([
                        self.value * other.values[0],
                        self.value * other.values[1],
                        self.value * other.values[2],
                    ])
                }
            }

            impl<Number> core::ops::Div<Measure<measures::dimensionless::One, Number>> for Measure3d<$name, Number>
            where
                Number: measures::traits::ArithmeticOps,
            {
                type Output = Self;

                /// Measure3d / Measure<One> -> Measure2d
                fn div(self, other: Measure<measures::dimensionless::One, Number>) -> Self::Output {
                    Self::new([
                        self.values[0] / other.value,
                        self.values[1] / other.value,
                        self.values[2] / other.value,
                    ])
                }
            }
        }
    };
}

#[macro_export]
macro_rules! measurement_unit {
    {
        name: $name:ident,
        property: $property:ident,
        suffix: $suffix:expr,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        vector: $vector:tt,
    } => {
        $crate::measurement_unit! {
            name: $name,
            property: $property,
            suffix: $suffix,
            ratio: 1.,
            with_2d: $with_2d,
            with_3d: $with_3d,
            vector: $vector,
        }
    };
    {
        name: $name:ident,
        property: $property:ident,
        suffix: $suffix:expr,
        ratio: $ratio:expr,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        vector: true,
    } => {
        $crate::measurement_unit_aux! {
            name: $name,
            property: $property,
            suffix: $suffix,
            ratio: $ratio,
            offset: 0.,
            with_2d: $with_2d,
            with_3d: $with_3d,
            vector: true,
        }
    };
    {
        name: $name:ident,
        property: $property:ident,
        suffix: $suffix:expr,
        ratio: $ratio:expr,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        vector: false,
    } => {
        $crate::measurement_unit_aux! {
            name: $name,
            property: $property,
            suffix: $suffix,
            ratio: $ratio,
            offset: 0.,
            with_2d: $with_2d,
            with_3d: $with_3d,
            vector: false,
        }
    };
    {
        name: $name:ident,
        property: $property:ident,
        suffix: $suffix:expr,
        ratio: $ratio:expr,
        offset: $offset:expr,
        with_2d: $with_2d:tt,
        with_3d: $with_3d:tt,
        vector: false,
    } => {
        $crate::measurement_unit_aux! {
            name: $name,
            property: $property,
            suffix: $suffix,
            ratio: $ratio,
            offset: $offset,
            with_2d: $with_2d,
            with_3d: $with_3d,
            vector: false,
        }
    };
}