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</pre><pre class='rust '>
<span class='doccomment'>//! Traits giving structural informations on linear algebra objects or the space they live in.</span>
<span class='kw'>use</span> <span class='ident'>std</span>::{<span class='ident'>f32</span>, <span class='ident'>f64</span>, <span class='ident'>i8</span>, <span class='ident'>i16</span>, <span class='ident'>i32</span>, <span class='ident'>i64</span>, <span class='ident'>u8</span>, <span class='ident'>u16</span>, <span class='ident'>u32</span>, <span class='ident'>u64</span>, <span class='ident'>isize</span>, <span class='ident'>usize</span>};
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>slice</span>::{<span class='ident'>Iter</span>, <span class='ident'>IterMut</span>};
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>ops</span>::{<span class='ident'>Add</span>, <span class='ident'>Sub</span>, <span class='ident'>Mul</span>, <span class='ident'>Div</span>, <span class='ident'>Rem</span>,
<span class='ident'>AddAssign</span>, <span class='ident'>SubAssign</span>, <span class='ident'>MulAssign</span>, <span class='ident'>DivAssign</span>, <span class='ident'>RemAssign</span>,
<span class='ident'>Index</span>, <span class='ident'>IndexMut</span>, <span class='ident'>Neg</span>};
<span class='kw'>use</span> <span class='ident'>num</span>::{<span class='ident'>Float</span>, <span class='ident'>Zero</span>, <span class='ident'>One</span>};
<span class='kw'>use</span> <span class='ident'>traits</span>::<span class='ident'>operations</span>::{<span class='ident'>Axpy</span>, <span class='ident'>Transpose</span>, <span class='ident'>Inverse</span>, <span class='ident'>Absolute</span>};
<span class='kw'>use</span> <span class='ident'>traits</span>::<span class='ident'>geometry</span>::{<span class='ident'>Dot</span>, <span class='ident'>Norm</span>, <span class='ident'>Origin</span>};
<span class='doccomment'>/// Basic integral numeric trait.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>BaseNum</span>: <span class='ident'>Copy</span> <span class='op'>+</span> <span class='ident'>Zero</span> <span class='op'>+</span> <span class='ident'>One</span> <span class='op'>+</span>
<span class='ident'>Add</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Sub</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Mul</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Div</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Rem</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>AddAssign</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>SubAssign</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>MulAssign</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>DivAssign</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>RemAssign</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>PartialEq</span> <span class='op'>+</span> <span class='ident'>Absolute</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Axpy</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span> {
}
<span class='doccomment'>/// Basic floating-point number numeric trait.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>BaseFloat</span>: <span class='ident'>Float</span> <span class='op'>+</span> <span class='ident'>Cast</span><span class='op'><</span><span class='ident'>f64</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>BaseNum</span> <span class='op'>+</span> <span class='ident'>Neg</span> {
<span class='doccomment'>/// Archimedes' constant.</span>
<span class='kw'>fn</span> <span class='ident'>pi</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// 2.0 * pi.</span>
<span class='kw'>fn</span> <span class='ident'>two_pi</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// pi / 2.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_2</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// pi / 3.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_3</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// pi / 4.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_4</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// pi / 6.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_6</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// pi / 8.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_8</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// 1.0 / pi.</span>
<span class='kw'>fn</span> <span class='ident'>frac_1_pi</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// 2.0 / pi.</span>
<span class='kw'>fn</span> <span class='ident'>frac_2_pi</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// 2.0 / sqrt(pi).</span>
<span class='kw'>fn</span> <span class='ident'>frac_2_sqrt_pi</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// Euler's number.</span>
<span class='kw'>fn</span> <span class='ident'>e</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// log2(e).</span>
<span class='kw'>fn</span> <span class='ident'>log2_e</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// log10(e).</span>
<span class='kw'>fn</span> <span class='ident'>log10_e</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// ln(2.0).</span>
<span class='kw'>fn</span> <span class='ident'>ln_2</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// ln(10.0).</span>
<span class='kw'>fn</span> <span class='ident'>ln_10</span>() <span class='op'>-></span> <span class='self'>Self</span>;
}
<span class='doccomment'>/// Traits of objects which can be created from an object of type `T`.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Cast</span><span class='op'><</span><span class='ident'>T</span><span class='op'>></span> {
<span class='doccomment'>/// Converts an element of type `T` to an element of type `Self`.</span>
<span class='kw'>fn</span> <span class='ident'>from</span>(<span class='ident'>t</span>: <span class='ident'>T</span>) <span class='op'>-></span> <span class='self'>Self</span>;
}
<span class='doccomment'>/// Trait of matrices.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// A matrix has rows and columns and are able to multiply them.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Matrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>R</span>, <span class='ident'>C</span>: <span class='ident'>Mul</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>R</span><span class='op'>>></span>: <span class='ident'>Sized</span> <span class='op'>+</span>
<span class='ident'>Row</span><span class='op'><</span><span class='ident'>R</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Column</span><span class='op'><</span><span class='ident'>C</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>R</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>C</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Index</span><span class='op'><</span>(<span class='ident'>usize</span>, <span class='ident'>usize</span>), <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span>
{ }
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>M</span>, <span class='ident'>R</span>, <span class='ident'>C</span><span class='op'>></span> <span class='ident'>Matrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>R</span>, <span class='ident'>C</span><span class='op'>></span> <span class='kw'>for</span> <span class='ident'>M</span>
<span class='kw'>where</span> <span class='ident'>M</span>: <span class='ident'>Row</span><span class='op'><</span><span class='ident'>R</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Column</span><span class='op'><</span><span class='ident'>C</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>R</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>C</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Index</span><span class='op'><</span>(<span class='ident'>usize</span>, <span class='ident'>usize</span>), <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span>,
<span class='ident'>C</span>: <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>M</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>R</span><span class='op'>></span>,
{ }
<span class='doccomment'>/// Trait implemented by square matrices.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>SquareMatrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>V</span>: <span class='ident'>Mul</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>V</span><span class='op'>>></span>: <span class='ident'>Matrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>V</span>, <span class='ident'>V</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Mul</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Eye</span> <span class='op'>+</span> <span class='ident'>Transpose</span> <span class='op'>+</span> <span class='ident'>Diagonal</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Inverse</span> <span class='op'>+</span> <span class='ident'>Dimension</span> <span class='op'>+</span> <span class='ident'>One</span> {
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>V</span>, <span class='ident'>M</span><span class='op'>></span> <span class='ident'>SquareMatrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>V</span><span class='op'>></span> <span class='kw'>for</span> <span class='ident'>M</span>
<span class='kw'>where</span> <span class='ident'>M</span>: <span class='ident'>Matrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>V</span>, <span class='ident'>V</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>M</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>M</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Eye</span> <span class='op'>+</span> <span class='ident'>Transpose</span> <span class='op'>+</span> <span class='ident'>Diagonal</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Inverse</span> <span class='op'>+</span> <span class='ident'>Dimension</span> <span class='op'>+</span> <span class='ident'>One</span>,
<span class='ident'>V</span>: <span class='ident'>Mul</span><span class='op'><</span><span class='ident'>M</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>V</span><span class='op'>></span> {
}
<span class='doccomment'>/// Trait for constructing the identity matrix</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Eye</span> {
<span class='doccomment'>/// Return the identity matrix of specified dimension</span>
<span class='kw'>fn</span> <span class='ident'>new_identity</span>(<span class='ident'>dimension</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='self'>Self</span>;
}
<span class='doccomment'>/// Trait for constructiong an object repeating a value.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Repeat</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Returns a value with filled by `val`.</span>
<span class='kw'>fn</span> <span class='ident'>repeat</span>(<span class='ident'>val</span>: <span class='ident'>N</span>) <span class='op'>-></span> <span class='self'>Self</span>;
}
<span class='doccomment'>/// Types that have maximum and minimum value.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Bounded</span> {
<span class='doccomment'>/// The minimum value.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>min_value</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// The maximum value.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>max_value</span>() <span class='op'>-></span> <span class='self'>Self</span>;
}
<span class='comment'>// FIXME: return an iterator instead</span>
<span class='doccomment'>/// Traits of objects which can form a basis (typically vectors).</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Basis</span>: <span class='ident'>Sized</span> {
<span class='doccomment'>/// Iterates through the canonical basis of the space in which this object lives.</span>
<span class='kw'>fn</span> <span class='ident'>canonical_basis</span><span class='op'><</span><span class='ident'>F</span>: <span class='ident'>FnMut</span>(<span class='self'>Self</span>) <span class='op'>-></span> <span class='ident'>bool</span><span class='op'>></span>(<span class='ident'>F</span>);
<span class='doccomment'>/// Iterates through a basis of the subspace orthogonal to `self`.</span>
<span class='kw'>fn</span> <span class='ident'>orthonormal_subspace_basis</span><span class='op'><</span><span class='ident'>F</span>: <span class='ident'>FnMut</span>(<span class='self'>Self</span>) <span class='op'>-></span> <span class='ident'>bool</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='self'>Self</span>, <span class='ident'>F</span>);
<span class='doccomment'>/// Gets the ith element of the canonical basis.</span>
<span class='kw'>fn</span> <span class='ident'>canonical_basis_element</span>(<span class='ident'>i</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='prelude-ty'>Option</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span>;
}
<span class='doccomment'>/// Trait to access rows of a matrix or a vector.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Row</span><span class='op'><</span><span class='ident'>R</span><span class='op'>></span> {
<span class='doccomment'>/// The number of column of `self`.</span>
<span class='kw'>fn</span> <span class='ident'>nrows</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>usize</span>;
<span class='doccomment'>/// Reads the `i`-th row of `self`.</span>
<span class='kw'>fn</span> <span class='ident'>row</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>i</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='ident'>R</span>;
<span class='doccomment'>/// Writes the `i`-th row of `self`.</span>
<span class='kw'>fn</span> <span class='ident'>set_row</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>i</span>: <span class='ident'>usize</span>, <span class='ident'>R</span>);
<span class='comment'>// FIXME: add iterators on rows: this could be a very good way to generalize _and_ optimize</span>
<span class='comment'>// a lot of operations.</span>
}
<span class='doccomment'>/// Trait to access columns of a matrix or vector.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Column</span><span class='op'><</span><span class='ident'>C</span><span class='op'>></span> {
<span class='doccomment'>/// The number of column of this matrix or vector.</span>
<span class='kw'>fn</span> <span class='ident'>ncols</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>usize</span>;
<span class='doccomment'>/// Reads the `i`-th column of `self`.</span>
<span class='kw'>fn</span> <span class='ident'>column</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>i</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='ident'>C</span>;
<span class='doccomment'>/// Writes the `i`-th column of `self`.</span>
<span class='kw'>fn</span> <span class='ident'>set_column</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>i</span>: <span class='ident'>usize</span>, <span class='ident'>C</span>);
<span class='comment'>// FIXME: add iterators on columns: this could be a very good way to generalize _and_ optimize</span>
<span class='comment'>// a lot of operations.</span>
}
<span class='doccomment'>/// Trait to access part of a column of a matrix</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>ColumnSlice</span><span class='op'><</span><span class='ident'>C</span><span class='op'>></span> {
<span class='doccomment'>/// Returns a view to a slice of a column of a matrix.</span>
<span class='kw'>fn</span> <span class='ident'>column_slice</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>column_id</span>: <span class='ident'>usize</span>, <span class='ident'>row_start</span>: <span class='ident'>usize</span>, <span class='ident'>row_end</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='ident'>C</span>;
}
<span class='doccomment'>/// Trait to access part of a row of a matrix</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>RowSlice</span><span class='op'><</span><span class='ident'>R</span><span class='op'>></span> {
<span class='doccomment'>/// Returns a view to a slice of a row of a matrix.</span>
<span class='kw'>fn</span> <span class='ident'>row_slice</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>row_id</span>: <span class='ident'>usize</span>, <span class='ident'>column_start</span>: <span class='ident'>usize</span>, <span class='ident'>column_end</span>: <span class='ident'>usize</span>) <span class='op'>-></span> <span class='ident'>R</span>;
}
<span class='doccomment'>/// Trait of objects having a spacial dimension known at compile time.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Dimension</span>: <span class='ident'>Sized</span> {
<span class='doccomment'>/// The dimension of the object.</span>
<span class='kw'>fn</span> <span class='ident'>dimension</span>(<span class='ident'>_unused</span>: <span class='prelude-ty'>Option</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>usize</span>;
}
<span class='doccomment'>/// Trait to get the diagonal of square matrices.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Diagonal</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> {
<span class='doccomment'>/// Creates a new matrix with the given diagonal.</span>
<span class='kw'>fn</span> <span class='ident'>from_diagonal</span>(<span class='ident'>diagonal</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// The diagonal of this matrix.</span>
<span class='kw'>fn</span> <span class='ident'>diagonal</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>V</span>;
}
<span class='doccomment'>/// Trait to set the diagonal of square matrices.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>DiagMut</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span>: <span class='ident'>Diagonal</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> {
<span class='doccomment'>/// Sets the diagonal of this matrix.</span>
<span class='kw'>fn</span> <span class='ident'>set_diagonal</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>diagonal</span>: <span class='kw-2'>&</span><span class='ident'>V</span>);
}
<span class='doccomment'>/// The shape of an indexable object.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Shape</span><span class='op'><</span><span class='ident'>I</span><span class='op'>></span>: <span class='ident'>Index</span><span class='op'><</span><span class='ident'>I</span><span class='op'>></span> {
<span class='doccomment'>/// Returns the shape of an indexable object.</span>
<span class='kw'>fn</span> <span class='ident'>shape</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>I</span>;
}
<span class='doccomment'>/// This is a workaround of current Rust limitations.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// It exists because the `I` trait cannot be used to express write access.</span>
<span class='doccomment'>/// Thus, this is the same as the `I` trait but without the syntactic sugar and with a method</span>
<span class='doccomment'>/// to write to a specific index.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Indexable</span><span class='op'><</span><span class='ident'>I</span>, <span class='ident'>N</span><span class='op'>></span>: <span class='ident'>Shape</span><span class='op'><</span><span class='ident'>I</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>IndexMut</span><span class='op'><</span><span class='ident'>I</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Swaps the `i`-th element of `self` with its `j`-th element.</span>
<span class='kw'>fn</span> <span class='ident'>swap</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>i</span>: <span class='ident'>I</span>, <span class='ident'>j</span>: <span class='ident'>I</span>);
<span class='doccomment'>/// Reads the `i`-th element of `self`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// `i` is not checked.</span>
<span class='kw'>unsafe</span> <span class='kw'>fn</span> <span class='ident'>unsafe_at</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>i</span>: <span class='ident'>I</span>) <span class='op'>-></span> <span class='ident'>N</span>;
<span class='doccomment'>/// Writes to the `i`-th element of `self`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// `i` is not checked.</span>
<span class='kw'>unsafe</span> <span class='kw'>fn</span> <span class='ident'>unsafe_set</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>i</span>: <span class='ident'>I</span>, <span class='ident'>N</span>);
}
<span class='doccomment'>/// This is a workaround of current Rust limitations.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Traits of objects which can be iterated through like a vector.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Iterable</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Gets a vector-like read-only iterator.</span>
<span class='kw'>fn</span> <span class='ident'>iter</span><span class='op'><</span><span class='lifetime'>'l</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='lifetime'>'l</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>Iter</span><span class='op'><</span><span class='lifetime'>'l</span>, <span class='ident'>N</span><span class='op'>></span>;
}
<span class='doccomment'>/// This is a workaround of current Rust limitations.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Traits of mutable objects which can be iterated through like a vector.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>IterableMut</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Gets a vector-like read-write iterator.</span>
<span class='kw'>fn</span> <span class='ident'>iter_mut</span><span class='op'><</span><span class='lifetime'>'l</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='lifetime'>'l</span> <span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>IterMut</span><span class='op'><</span><span class='lifetime'>'l</span>, <span class='ident'>N</span><span class='op'>></span>;
}
<span class='comment'>/*
* Vector related traits.
*/</span>
<span class='doccomment'>/// Trait grouping most common operations on vectors.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>NumVector</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>: <span class='ident'>Add</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Sub</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='comment'>// Mul<Self, Output = Self> + Div<Self, Output = Self> +</span>
<span class='comment'>// Add<N, Output = Self> + Sub<N, Output = Self> + </span>
<span class='ident'>Mul</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Div</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>AddAssign</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>SubAssign</span><span class='op'><</span><span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='comment'>// MulAssign<Self> + DivAssign<Self> + </span>
<span class='comment'>// AddAssign<N> + SubAssign<N> + </span>
<span class='ident'>MulAssign</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>DivAssign</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Dimension</span> <span class='op'>+</span> <span class='ident'>Index</span><span class='op'><</span><span class='ident'>usize</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Zero</span> <span class='op'>+</span> <span class='ident'>PartialEq</span> <span class='op'>+</span> <span class='ident'>Dot</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Axpy</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
}
<span class='doccomment'>/// Trait of vector with components implementing the `BaseFloat` trait.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>FloatVector</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span>: <span class='ident'>NumVector</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Basis</span> {
}
<span class='comment'>/*
* Point related traits.
*/</span>
<span class='doccomment'>/// Trait that relates a point of an affine space to a vector of the associated vector space.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>PointAsVector</span> {
<span class='doccomment'>/// The vector type of the vector space associated to this point's affine space.</span>
<span class='kw'>type</span> <span class='ident'>Vector</span>;
<span class='doccomment'>/// Converts this point to its associated vector.</span>
<span class='kw'>fn</span> <span class='ident'>to_vector</span>(<span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span>::<span class='ident'>Vector</span>;
<span class='doccomment'>/// Converts a reference to this point to a reference to its associated vector.</span>
<span class='kw'>fn</span> <span class='ident'>as_vector</span><span class='op'><</span><span class='lifetime'>'a</span><span class='op'>></span>(<span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='kw-2'>&</span><span class='lifetime'>'a</span> <span class='self'>Self</span>::<span class='ident'>Vector</span>;
<span class='comment'>// NOTE: this is used in some places to overcome some limitations untill the trait reform is</span>
<span class='comment'>// done on rustc.</span>
<span class='doccomment'>/// Sets the coordinates of this point to match those of a given vector.</span>
<span class='kw'>fn</span> <span class='ident'>set_coords</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>coords</span>: <span class='self'>Self</span>::<span class='ident'>Vector</span>);
}
<span class='doccomment'>/// Trait grouping most common operations on points.</span>
<span class='comment'>// XXX: the vector space element `V` should be an associated type. Though this would prevent V from</span>
<span class='comment'>// having bounds (they are not supported yet). So, for now, we will just use a type parameter.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>NumPoint</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>:
<span class='ident'>Copy</span> <span class='op'>+</span>
<span class='ident'>PointAsVector</span> <span class='op'>+</span>
<span class='ident'>Dimension</span> <span class='op'>+</span>
<span class='ident'>Origin</span> <span class='op'>+</span>
<span class='ident'>PartialEq</span> <span class='op'>+</span>
<span class='ident'>Axpy</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Sub</span><span class='op'><</span><span class='self'>Self</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='op'><</span><span class='self'>Self</span> <span class='kw'>as</span> <span class='ident'>PointAsVector</span><span class='op'>></span>::<span class='ident'>Vector</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Mul</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Div</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Add</span><span class='op'><<</span><span class='self'>Self</span> <span class='kw'>as</span> <span class='ident'>PointAsVector</span><span class='op'>></span>::<span class='ident'>Vector</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='self'>Self</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>MulAssign</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>DivAssign</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>AddAssign</span><span class='op'><<</span><span class='self'>Self</span> <span class='kw'>as</span> <span class='ident'>PointAsVector</span><span class='op'>></span>::<span class='ident'>Vector</span><span class='op'>></span> <span class='op'>+</span>
<span class='ident'>Index</span><span class='op'><</span><span class='ident'>usize</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>N</span><span class='op'>></span> { <span class='comment'>// FIXME: + Sub<V, Self></span>
}
<span class='doccomment'>/// Trait of points with components implementing the `BaseFloat` trait.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>FloatPoint</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span>: <span class='ident'>NumPoint</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Sized</span>
<span class='kw'>where</span> <span class='op'><</span><span class='self'>Self</span> <span class='kw'>as</span> <span class='ident'>PointAsVector</span><span class='op'>></span>::<span class='ident'>Vector</span>: <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Computes the square distance between two points.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>distance_squared</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='self'>Self</span>) <span class='op'>-></span> <span class='ident'>N</span> {
(<span class='op'>*</span><span class='self'>self</span> <span class='op'>-</span> <span class='op'>*</span><span class='ident'>other</span>).<span class='ident'>norm_squared</span>()
}
<span class='doccomment'>/// Computes the distance between two points.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>distance</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='self'>Self</span>) <span class='op'>-></span> <span class='ident'>N</span> {
(<span class='op'>*</span><span class='self'>self</span> <span class='op'>-</span> <span class='op'>*</span><span class='ident'>other</span>).<span class='ident'>norm</span>()
}
}
<span class='comment'>/*
*
*
* Some implementations for builtin types.
*
*
*/</span>
<span class='comment'>// Bounded</span>
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>impl_bounded</span>(
(<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>: <span class='ident'>ty</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>min</span>: <span class='ident'>expr</span>, <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>max</span>: <span class='ident'>expr</span>) <span class='op'>=></span> {
<span class='kw'>impl</span> <span class='ident'>Bounded</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>min_value</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>min</span>
}
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>max_value</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>max</span>
}
}
}
);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>f32</span>, <span class='ident'>f32</span>::<span class='ident'>MIN</span>, <span class='ident'>f32</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>f64</span>, <span class='ident'>f64</span>::<span class='ident'>MIN</span>, <span class='ident'>f64</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>i8</span>, <span class='ident'>i8</span>::<span class='ident'>MIN</span>, <span class='ident'>i8</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>i16</span>, <span class='ident'>i16</span>::<span class='ident'>MIN</span>, <span class='ident'>i16</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>i32</span>, <span class='ident'>i32</span>::<span class='ident'>MIN</span>, <span class='ident'>i32</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>i64</span>, <span class='ident'>i64</span>::<span class='ident'>MIN</span>, <span class='ident'>i64</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>isize</span>, <span class='ident'>isize</span>::<span class='ident'>MIN</span>, <span class='ident'>isize</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>u8</span>, <span class='ident'>u8</span>::<span class='ident'>MIN</span>, <span class='ident'>u8</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>u16</span>, <span class='ident'>u16</span>::<span class='ident'>MIN</span>, <span class='ident'>u16</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>u32</span>, <span class='ident'>u32</span>::<span class='ident'>MIN</span>, <span class='ident'>u32</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>u64</span>, <span class='ident'>u64</span>::<span class='ident'>MIN</span>, <span class='ident'>u64</span>::<span class='ident'>MAX</span>);
<span class='macro'>impl_bounded</span><span class='macro'>!</span>(<span class='ident'>usize</span>, <span class='ident'>usize</span>::<span class='ident'>MIN</span>, <span class='ident'>usize</span>::<span class='ident'>MAX</span>);
<span class='comment'>// BaseFloat</span>
<span class='macro'>macro_rules</span><span class='macro'>!</span> <span class='ident'>impl_base_float</span>(
(<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>: <span class='ident'>ident</span>) <span class='op'>=></span> {
<span class='kw'>impl</span> <span class='ident'>BaseFloat</span> <span class='kw'>for</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='doccomment'>/// Archimedes' constant.</span>
<span class='kw'>fn</span> <span class='ident'>pi</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span>
}
<span class='doccomment'>/// 2.0 * pi.</span>
<span class='kw'>fn</span> <span class='ident'>two_pi</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='number'>2.0</span> <span class='op'>*</span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>PI</span>
}
<span class='doccomment'>/// pi / 2.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_2</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>FRAC_PI_2</span>
}
<span class='doccomment'>/// pi / 3.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_3</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>FRAC_PI_3</span>
}
<span class='doccomment'>/// pi / 4.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_4</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>FRAC_PI_4</span>
}
<span class='doccomment'>/// pi / 6.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_6</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>FRAC_PI_6</span>
}
<span class='doccomment'>/// pi / 8.0.</span>
<span class='kw'>fn</span> <span class='ident'>frac_pi_8</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>FRAC_PI_8</span>
}
<span class='doccomment'>/// 1.0 / pi.</span>
<span class='kw'>fn</span> <span class='ident'>frac_1_pi</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>FRAC_1_PI</span>
}
<span class='doccomment'>/// 2.0 / pi.</span>
<span class='kw'>fn</span> <span class='ident'>frac_2_pi</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>FRAC_2_PI</span>
}
<span class='doccomment'>/// 2.0 / sqrt(pi).</span>
<span class='kw'>fn</span> <span class='ident'>frac_2_sqrt_pi</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>FRAC_2_SQRT_PI</span>
}
<span class='doccomment'>/// Euler's number.</span>
<span class='kw'>fn</span> <span class='ident'>e</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>E</span>
}
<span class='doccomment'>/// log2(e).</span>
<span class='kw'>fn</span> <span class='ident'>log2_e</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>LOG2_E</span>
}
<span class='doccomment'>/// log10(e).</span>
<span class='kw'>fn</span> <span class='ident'>log10_e</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>LOG10_E</span>
}
<span class='doccomment'>/// ln(2.0).</span>
<span class='kw'>fn</span> <span class='ident'>ln_2</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>LN_2</span>
}
<span class='doccomment'>/// ln(10.0).</span>
<span class='kw'>fn</span> <span class='ident'>ln_10</span>() <span class='op'>-></span> <span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span> {
<span class='macro-nonterminal'>$</span><span class='macro-nonterminal'>n</span>::<span class='ident'>consts</span>::<span class='ident'>LN_10</span>
}
}
}
);
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>i8</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>i16</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>i32</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>i64</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>isize</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>u8</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>u16</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>u32</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>u64</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>usize</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>f32</span> { }
<span class='kw'>impl</span> <span class='ident'>BaseNum</span> <span class='kw'>for</span> <span class='ident'>f64</span> { }
<span class='macro'>impl_base_float</span><span class='macro'>!</span>(<span class='ident'>f32</span>);
<span class='macro'>impl_base_float</span><span class='macro'>!</span>(<span class='ident'>f64</span>);
</pre>
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