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#[cfg(feature = "decimal")] use decimal::d128; use num::Zero; use num_complex::Complex; /// Nested sets and conversions between them (using an injective mapping). Useful to work with /// substructures. In generic code, it is preferable to use `SupersetOf` as trait bound whenever /// possible instead of `SubsetOf` (because SupersetOf is automatically implemented whenever /// `SubsetOf` is). /// /// The notion of "nested sets" is very broad and applies to what the types are _supposed to /// represent_, independently from their actual implementation details and limitations. For /// example: /// * f32 and f64 are both supposed to represent reals and are thus considered equal (even if in /// practice f64 has more elements). /// * u32 and i8 are respectively supposed to represent natural and relative numbers. Thus, u32 is /// a subset of i8. /// * A quaternion and a 3x3 orthogonal matrix with unit determinant are both sets of rotations. /// They can thus be considered equal. /// /// In other words, implementation details due to machine limitations are ignored (otherwise we /// could not even, e.g., convert a u64 to an i64). If considering those limitations are /// important, other crates allowing you to query the limitations of given types should be used. pub trait SubsetOf<T>: Sized { /// The inclusion map: converts `self` to the equivalent element of its superset. fn to_superset(&self) -> T; /// The inverse inclusion map: attempts to construct `self` from the equivalent element of its /// superset. /// /// Must return `None` if `element` has no equivalent in `Self`. fn from_superset(element: &T) -> Option<Self> { if Self::is_in_subset(element) { Some(unsafe { Self::from_superset_unchecked(element) }) } else { None } } /// Use with care! Same as `self.to_superset` but without any property checks. Always succeeds. unsafe fn from_superset_unchecked(element: &T) -> Self; /// Checks if `element` is actually part of the subset `Self` (and can be converted to it). fn is_in_subset(element: &T) -> bool; } /// Nested sets and conversions between them. Useful to work with substructures. It is preferable /// to implement the `SupersetOf` trait instead of `SubsetOf` whenever possible (because /// `SupersetOf` is automatically implemented whenever `SubsetOf` is. /// /// The notion of "nested sets" is very broad and applies to what the types are _supposed to /// represent_, independently from their actual implementation details and limitations. For /// example: /// * f32 and f64 are both supposed to represent reals and are thus considered equal (even if in /// practice f64 has more elements). /// * u32 and i8 are respectively supposed to represent natural and relative numbers. Thus, i8 is /// a superset of u32. /// * A quaternion and a 3x3 orthogonal matrix with unit determinant are both sets of rotations. /// They can thus be considered equal. /// /// In other words, implementation details due to machine limitations are ignored (otherwise we /// could not even, e.g., convert a u64 to an i64). If considering those limitations are /// important, other crates allowing you to query the limitations of given types should be used. pub trait SupersetOf<T>: Sized { /// The inverse inclusion map: attempts to construct `self` from the equivalent element of its /// superset. /// /// Must return `None` if `element` has no equivalent in `Self`. fn to_subset(&self) -> Option<T> { if self.is_in_subset() { Some(unsafe { self.to_subset_unchecked() }) } else { None } } /// Checks if `self` is actually part of its subset `T` (and can be converted to it). fn is_in_subset(&self) -> bool; /// Use with care! Same as `self.to_subset` but without any property checks. Always succeeds. unsafe fn to_subset_unchecked(&self) -> T; /// The inclusion map: converts `self` to the equivalent element of its superset. fn from_subset(element: &T) -> Self; } impl<SS: SubsetOf<SP>, SP> SupersetOf<SS> for SP { #[inline] fn to_subset(&self) -> Option<SS> { SS::from_superset(self) } #[inline] fn is_in_subset(&self) -> bool { SS::is_in_subset(self) } #[inline] unsafe fn to_subset_unchecked(&self) -> SS { SS::from_superset_unchecked(self) } #[inline] fn from_subset(element: &SS) -> Self { element.to_superset() } } macro_rules! impl_subset( ($($subset: ty as $( $superset: ty),+ );* $(;)*) => { $($( impl SubsetOf<$superset> for $subset { #[inline] fn to_superset(&self) -> $superset { *self as $superset } #[inline] unsafe fn from_superset_unchecked(element: &$superset) -> $subset { *element as $subset } #[inline] fn is_in_subset(_: &$superset) -> bool { true } } )+)* } ); impl_subset!( u8 as u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize, f32, f64; u16 as u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize, f32, f64; u32 as u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize, f32, f64; u64 as u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize, f32, f64; u128 as u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize, f32, f64; usize as u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize, f32, f64; i8 as i8, i16, i32, i64, i128, isize, f32, f64; i16 as i8, i16, i32, i64, i128, isize, f32, f64; i32 as i8, i16, i32, i64, i128, isize, f32, f64; i64 as i8, i16, i32, i64, i128, isize, f32, f64; i128 as i8, i16, i32, i64, i128, isize, f32, f64; isize as i8, i16, i32, i64, i128, isize, f32, f64; f32 as f32, f64; f64 as f32, f64; ); //#[cfg(feature = "decimal")] //impl_subset!( // u8 as d128; // u16 as d128; // u32 as d128; // u64 as d128; // usize as d128; // // i8 as d128; // i16 as d128; // i32 as d128; // i64 as d128; // isize as d128; // // f32 as d128; // f64 as d128; // d128 as d128; //); impl<N1, N2: SupersetOf<N1>> SubsetOf<Complex<N2>> for Complex<N1> { #[inline] fn to_superset(&self) -> Complex<N2> { Complex { re: N2::from_subset(&self.re), im: N2::from_subset(&self.im), } } #[inline] unsafe fn from_superset_unchecked(element: &Complex<N2>) -> Complex<N1> { Complex { re: element.re.to_subset_unchecked(), im: element.im.to_subset_unchecked(), } } #[inline] fn is_in_subset(c: &Complex<N2>) -> bool { c.re.is_in_subset() && c.im.is_in_subset() } } macro_rules! impl_scalar_subset_of_complex( ($($t: ident),*) => {$( impl<N2: Zero + SupersetOf<$t>> SubsetOf<Complex<N2>> for $t { #[inline] fn to_superset(&self) -> Complex<N2> { Complex { re: N2::from_subset(self), im: N2::zero() } } #[inline] unsafe fn from_superset_unchecked(element: &Complex<N2>) -> $t { element.re.to_subset_unchecked() } #[inline] fn is_in_subset(c: &Complex<N2>) -> bool { c.re.is_in_subset() && c.im.is_zero() } } )*} ); impl_scalar_subset_of_complex!(u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize, f32, f64); #[cfg(feature = "decimal")] impl_scalar_subset_of_complex!(d128);