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nalgebra/src/base/coordinates.rs

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Doc + slerp + conversions.
2017-02-13 01:17:09 +08:00
#![allow(missing_docs)]
//! Structures to which matrices and vector can be auto-dereferenced (through `Deref`) to access
//! components using their names. For example, if `v` is a 3D vector, one can write `v.z` instead
//! of `v[2]`.
Complete library rewrite. See comments on #207 for details.
2016-12-05 05:44:42 +08:00
use std::mem;
use std::ops::{Deref, DerefMut};
2018 edition.
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use crate::base::dimension::{U1, U2, U3, U4, U5, U6};
use crate::base::storage::{ContiguousStorage, ContiguousStorageMut};
use crate::base::{Matrix, Scalar};
Complete library rewrite. See comments on #207 for details.
2016-12-05 05:44:42 +08:00
/*
*
* Give coordinates to owned Vector{1 .. 6} and Matrix{1 .. 6}
*
*/
macro_rules! coords_impl(
($T: ident; $($comps: ident),*) => {
Doc + slerp + conversions.
2017-02-13 01:17:09 +08:00
/// Data structure used to provide access to matrix and vector coordinates with the dot
/// notation, e.g., `v.x` is the same as `v[0]` for a vector.
Complete library rewrite. See comments on #207 for details.
2016-12-05 05:44:42 +08:00
#[repr(C)]
Make serde optional behind the "serde-serialize" feature.
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#[derive(Eq, PartialEq, Clone, Hash, Debug, Copy)]
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
Move `Copy` constraint from the definition of `Scalar` to all its use-sites. This should semantically be a no-op, but enables refactorings to use non-Copy scalars on a case-by-case basis. Also, the only instance of a `One + Zero` trait bound was changed into a `Zero + One` bound to match the others. The following sed scripts were used in the refactoring (with each clause added to reduce the error count of `cargo check`): ```bash export RELEVANT_SOURCEFILES="$(find src -name '*.rs') $(find examples -name '*.rs')" for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar,/N: Scalar+Copy,/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Field/N: Scalar + Copy + Field/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Zero/N: Scalar + Copy + Zero/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Closed/N: Scalar + Copy + Closed/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Eq/N: Scalar + Copy + Eq/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialOrd/N: Scalar + Copy + PartialOrd/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + Zero/N: Scalar + Copy + Zero/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialEq/N: Scalar + Copy + PartialEq/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar>/N: Scalar+Copy>/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + $bound/N: Scalar + Copy + $bound/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $bound/N: Scalar + Copy + $bound/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar,/N\1: Scalar+Copy,/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $trait/N: Scalar + Copy + $trait/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + Superset/N\1: Scalar + Copy + Superset/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(hash::\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar {/N\1: Scalar + Copy {/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Bounded\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Lattice\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Meet\|Join\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(fmt::\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Ring\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Hash\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Send\|Sync\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/One + Zero/Zero + One/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \($marker\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar>/N\1: Scalar + Copy>/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/Scalar+Copy/Scalar + Copy/' $f; done ```
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pub struct $T<N: Scalar + Copy> {
Complete library rewrite. See comments on #207 for details.
2016-12-05 05:44:42 +08:00
$(pub $comps: N),*
}
}
);
macro_rules! deref_impl(
($R: ty, $C: ty; $Target: ident) => {
Move `Copy` constraint from the definition of `Scalar` to all its use-sites. This should semantically be a no-op, but enables refactorings to use non-Copy scalars on a case-by-case basis. Also, the only instance of a `One + Zero` trait bound was changed into a `Zero + One` bound to match the others. The following sed scripts were used in the refactoring (with each clause added to reduce the error count of `cargo check`): ```bash export RELEVANT_SOURCEFILES="$(find src -name '*.rs') $(find examples -name '*.rs')" for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar,/N: Scalar+Copy,/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Field/N: Scalar + Copy + Field/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Zero/N: Scalar + Copy + Zero/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Closed/N: Scalar + Copy + Closed/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Eq/N: Scalar + Copy + Eq/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialOrd/N: Scalar + Copy + PartialOrd/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + Zero/N: Scalar + Copy + Zero/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialEq/N: Scalar + Copy + PartialEq/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar>/N: Scalar+Copy>/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + $bound/N: Scalar + Copy + $bound/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $bound/N: Scalar + Copy + $bound/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar,/N\1: Scalar+Copy,/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $trait/N: Scalar + Copy + $trait/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + Superset/N\1: Scalar + Copy + Superset/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(hash::\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar {/N\1: Scalar + Copy {/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Bounded\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Lattice\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Meet\|Join\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(fmt::\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Ring\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Hash\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Send\|Sync\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/One + Zero/Zero + One/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \($marker\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar>/N\1: Scalar + Copy>/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/Scalar+Copy/Scalar + Copy/' $f; done ```
2019-11-20 04:57:37 +08:00
impl<N: Scalar + Copy, S> Deref for Matrix<N, $R, $C, S>
Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
where S: ContiguousStorage<N, $R, $C> {
Complete library rewrite. See comments on #207 for details.
2016-12-05 05:44:42 +08:00
type Target = $Target<N>;
#[inline]
fn deref(&self) -> &Self::Target {
Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
unsafe { mem::transmute(self.data.ptr()) }
Complete library rewrite. See comments on #207 for details.
2016-12-05 05:44:42 +08:00
}
}
Move `Copy` constraint from the definition of `Scalar` to all its use-sites. This should semantically be a no-op, but enables refactorings to use non-Copy scalars on a case-by-case basis. Also, the only instance of a `One + Zero` trait bound was changed into a `Zero + One` bound to match the others. The following sed scripts were used in the refactoring (with each clause added to reduce the error count of `cargo check`): ```bash export RELEVANT_SOURCEFILES="$(find src -name '*.rs') $(find examples -name '*.rs')" for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar,/N: Scalar+Copy,/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Field/N: Scalar + Copy + Field/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Zero/N: Scalar + Copy + Zero/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Closed/N: Scalar + Copy + Closed/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + Eq/N: Scalar + Copy + Eq/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialOrd/N: Scalar + Copy + PartialOrd/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + Zero/N: Scalar + Copy + Zero/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + PartialEq/N: Scalar + Copy + PartialEq/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar>/N: Scalar+Copy>/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: Scalar + $bound/N: Scalar + Copy + $bound/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $bound/N: Scalar + Copy + $bound/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar,/N\1: Scalar+Copy,/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N: *Scalar + $trait/N: Scalar + Copy + $trait/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + Superset/N\1: Scalar + Copy + Superset/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \([a-zA-Z]*Eq\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(hash::\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar {/N\1: Scalar + Copy {/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Bounded\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Lattice\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Meet\|Join\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(fmt::\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Ring\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Hash\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Send\|Sync\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/One + Zero/Zero + One/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \(Zero\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar + \($marker\)/N\1: Scalar + Copy + \2/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/N\([0-9]\?\): *Scalar>/N\1: Scalar + Copy>/' $f; done for f in $RELEVANT_SOURCEFILES; do sed -i 's/Scalar+Copy/Scalar + Copy/' $f; done ```
2019-11-20 04:57:37 +08:00
impl<N: Scalar + Copy, S> DerefMut for Matrix<N, $R, $C, S>
Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
where S: ContiguousStorageMut<N, $R, $C> {
Complete library rewrite. See comments on #207 for details.
2016-12-05 05:44:42 +08:00
#[inline]
fn deref_mut(&mut self) -> &mut Self::Target {
Add the most common matrix decompositions.
2017-08-03 01:37:44 +08:00
unsafe { mem::transmute(self.data.ptr_mut()) }
Complete library rewrite. See comments on #207 for details.
2016-12-05 05:44:42 +08:00
}
}
}
);
/*
*
* Vector coordinates.
*
*/
coords_impl!(X; x);
coords_impl!(XY; x, y);
coords_impl!(XYZ; x, y, z);
coords_impl!(XYZW; x, y, z, w);
coords_impl!(XYZWA; x, y, z, w, a);
coords_impl!(XYZWAB; x, y, z, w, a, b);
coords_impl!(IJKW; i, j, k, w);
/*
* Rectangular matrices with 2 rows.
*/
coords_impl!(M2x2; m11, m21,
m12, m22);
coords_impl!(M2x3; m11, m21,
m12, m22,
m13, m23);
coords_impl!(M2x4; m11, m21,
m12, m22,
m13, m23,
m14, m24);
coords_impl!(M2x5; m11, m21,
m12, m22,
m13, m23,
m14, m24,
m15, m25);
coords_impl!(M2x6; m11, m21,
m12, m22,
m13, m23,
m14, m24,
m15, m25,
m16, m26);
/*
* Rectangular matrices with 3 rows.
*/
coords_impl!(M3x2; m11, m21, m31,
m12, m22, m32);
coords_impl!(M3x3; m11, m21, m31,
m12, m22, m32,
m13, m23, m33);
coords_impl!(M3x4; m11, m21, m31,
m12, m22, m32,
m13, m23, m33,
m14, m24, m34);
coords_impl!(M3x5; m11, m21, m31,
m12, m22, m32,
m13, m23, m33,
m14, m24, m34,
m15, m25, m35);
coords_impl!(M3x6; m11, m21, m31,
m12, m22, m32,
m13, m23, m33,
m14, m24, m34,
m15, m25, m35,
m16, m26, m36);
/*
* Rectangular matrices with 4 rows.
*/
coords_impl!(M4x2; m11, m21, m31, m41,
m12, m22, m32, m42);
coords_impl!(M4x3; m11, m21, m31, m41,
m12, m22, m32, m42,
m13, m23, m33, m43);
coords_impl!(M4x4; m11, m21, m31, m41,
m12, m22, m32, m42,
m13, m23, m33, m43,
m14, m24, m34, m44);
coords_impl!(M4x5; m11, m21, m31, m41,
m12, m22, m32, m42,
m13, m23, m33, m43,
m14, m24, m34, m44,
m15, m25, m35, m45);
coords_impl!(M4x6; m11, m21, m31, m41,
m12, m22, m32, m42,
m13, m23, m33, m43,
m14, m24, m34, m44,
m15, m25, m35, m45,
m16, m26, m36, m46);
/*
* Rectangular matrices with 5 rows.
*/
coords_impl!(M5x2; m11, m21, m31, m41, m51,
m12, m22, m32, m42, m52);
coords_impl!(M5x3; m11, m21, m31, m41, m51,
m12, m22, m32, m42, m52,
m13, m23, m33, m43, m53);
coords_impl!(M5x4; m11, m21, m31, m41, m51,
m12, m22, m32, m42, m52,
m13, m23, m33, m43, m53,
m14, m24, m34, m44, m54);
coords_impl!(M5x5; m11, m21, m31, m41, m51,
m12, m22, m32, m42, m52,
m13, m23, m33, m43, m53,
m14, m24, m34, m44, m54,
m15, m25, m35, m45, m55);
coords_impl!(M5x6; m11, m21, m31, m41, m51,
m12, m22, m32, m42, m52,
m13, m23, m33, m43, m53,
m14, m24, m34, m44, m54,
m15, m25, m35, m45, m55,
m16, m26, m36, m46, m56);
/*
* Rectangular matrices with 6 rows.
*/
coords_impl!(M6x2; m11, m21, m31, m41, m51, m61,
m12, m22, m32, m42, m52, m62);
coords_impl!(M6x3; m11, m21, m31, m41, m51, m61,
m12, m22, m32, m42, m52, m62,
m13, m23, m33, m43, m53, m63);
coords_impl!(M6x4; m11, m21, m31, m41, m51, m61,
m12, m22, m32, m42, m52, m62,
m13, m23, m33, m43, m53, m63,
m14, m24, m34, m44, m54, m64);
coords_impl!(M6x5; m11, m21, m31, m41, m51, m61,
m12, m22, m32, m42, m52, m62,
m13, m23, m33, m43, m53, m63,
m14, m24, m34, m44, m54, m64,
m15, m25, m35, m45, m55, m65);
coords_impl!(M6x6; m11, m21, m31, m41, m51, m61,
m12, m22, m32, m42, m52, m62,
m13, m23, m33, m43, m53, m63,
m14, m24, m34, m44, m54, m64,
m15, m25, m35, m45, m55, m65,
m16, m26, m36, m46, m56, m66);
/*
*
* Attach coordinates to matrices.
*
*/
deref_impl!(U1, U1; X);
deref_impl!(U2, U1; XY);
deref_impl!(U3, U1; XYZ);
deref_impl!(U4, U1; XYZW);
deref_impl!(U5, U1; XYZWA);
deref_impl!(U6, U1; XYZWAB);
deref_impl!(U1, U2; XY);
deref_impl!(U1, U3; XYZ);
deref_impl!(U1, U4; XYZW);
deref_impl!(U1, U5; XYZWA);
deref_impl!(U1, U6; XYZWAB);
deref_impl!(U2, U2; M2x2);
deref_impl!(U2, U3; M2x3);
deref_impl!(U2, U4; M2x4);
deref_impl!(U2, U5; M2x5);
deref_impl!(U2, U6; M2x6);
deref_impl!(U3, U2; M3x2);
deref_impl!(U3, U3; M3x3);
deref_impl!(U3, U4; M3x4);
deref_impl!(U3, U5; M3x5);
deref_impl!(U3, U6; M3x6);
deref_impl!(U4, U2; M4x2);
deref_impl!(U4, U3; M4x3);
deref_impl!(U4, U4; M4x4);
deref_impl!(U4, U5; M4x5);
deref_impl!(U4, U6; M4x6);
deref_impl!(U5, U2; M5x2);
deref_impl!(U5, U3; M5x3);
deref_impl!(U5, U4; M5x4);
deref_impl!(U5, U5; M5x5);
deref_impl!(U5, U6; M5x6);
deref_impl!(U6, U2; M6x2);
deref_impl!(U6, U3; M6x3);
deref_impl!(U6, U4; M6x4);
deref_impl!(U6, U5; M6x5);
deref_impl!(U6, U6; M6x6);