bump version to 12.2.2-pve1

[ceph.git] / ceph / src / boost / libs / qvm / doc / source / boost-qvm.reno

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												<string> mod=&quot;m&quot;:)&apos;&apos; obtained by &apos;&apos;(:link </string>
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												<string> mod=&quot;(&quot;:)&apos;&apos;, except that it uses the binary predicate &apos;&apos;pred&apos;&apos; to compare the individual quaternion elements.&#10;</string>
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												<string>!!!Vector-to-matrix (:link </string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;This is a list of all matrix operations implemented by Boost QVM -- click on functions for individual documentation. General notes:&#10;&#10;* All functions use (:link </string>
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												<string>:)&apos;&apos; template (for binary functions).&#10;* The type of scalar arguments is deduced independently from the type of the matrix argument, so they are not required to match. Scalar arguments must convert implicitly to the matrix scalar type.</string>
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												<string>----&#10;&#10;&apos;&apos;&apos;Tutorial navigation:&apos;&apos;&apos; (:link </string>
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												<string>:)&#10;</string>
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												<string>!!!Matrix-to-matrix (:link </string>
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												<string>!!!Interoperability&#10;&#10;An important design goal of Boost QVM is that it works seamlessly with 3rd-party quaternion, vector and matrix types and libraries. Even when such libraries overload the same C++ operators as Boost QVM, it is safe to bring the entire &apos;&apos;boost::(:link </string>
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												<string>:)&apos;&apos; namespace in scope lets you mix vector and matrix types that come from different APIs into a common, type-safe framework. In this case however, it should be considered what types should be returned by binary operations that return an object by value. For example, if you multiply a 3x3 matrix &apos;&apos;m1&apos;&apos; of type &apos;&apos;user_matrix1&apos;&apos; by a 3x3 matrix &apos;&apos;m2&apos;&apos; of type &apos;&apos;user_matrix2&apos;&apos;, what type should that operation return?&#10;&#10;The answer is that by default, Boost QVM returns some kind of compatible matrix type, so it is always safe to write:&#10;&#10;[@auto &amp; m = m1 (:link </string>
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												<string>:)&lt;user_matrix2,user_matrix1,3,3&gt;&#10;            { typedef user_matrix1 type; };&#10;        }&#10;    }@]&#10;&#10;Finally, any time you need to create a matrix of a particular C++ type from any other compatible matrix type, you can use the &apos;&apos;(:link </string>
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												<string>:)&lt;A,B&gt;::type&gt;::value&apos;&apos; must be &apos;&apos;true&apos;&apos;&#10;*&apos;&apos;(:link </string>
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												<string>:)&lt;A,B&gt;::type&apos;&apos; must be copyable&#10;*&apos;&apos;(:link </string>
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												<string>:)&lt;(:link </string>
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												<string>:)&lt;A,B&gt;::type&gt;::(:link </string>
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												<string> mod=&quot;m&quot;:)==Rows&apos;&apos;&#10;*&apos;&apos;(:link </string>
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												<string>:)&lt;(:link </string>
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												<string> mod=&quot;m&quot;:)==Cols&apos;&apos;&#10;&#10;This template is used by Boost QVM whenever it needs to deduce a matrix type of certain dimensions from the types of two user-supplied function parameters. The returned type must have accessible copy constructor (the &apos;&apos;A&apos;&apos; and &apos;&apos;B&apos;&apos; types themselves could be non-copyable, and either one of them may be a non-matrix type.)&#10;&#10;The main template definition returns an unspecified matrix type of the requested dimensions with &apos;&apos;(:link </string>
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												<string> mod=&quot;m&quot;:)&apos;&apos; obtained by &apos;&apos;(:link </string>
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												<string>:)&lt;A,B&gt;::type&apos;&apos;, except if &apos;&apos;A&apos;&apos; and &apos;&apos;B&apos;&apos; are the same matrix type &apos;&apos;M&apos;&apos; of dimensions &apos;&apos;Rows&apos;&apos; x &apos;&apos;Cols&apos;&apos;, in which case &apos;&apos;M&apos;&apos; is returned, which is only suitable for copyable types. Boost QVM also defines (partial) specializations for the non-copyable matrix types it produces. Users can define other (partial) specializations for their own types.&#10;&#10;A typical use of the &apos;&apos;(:link </string>
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												<string>:)&apos;&apos; template is for specifying the preferred matrix type to be returned by the generic function template overloads in Boost QVM depending on the type of their arguments.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Effects:&#10;&#10;As if:&#10;&#10;[@(:link </string>
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												<string> mod=&quot;(&quot;:)(&#10;    a,&#10;    (:link </string>
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												<string> mod=&quot;(&quot;:)(axis,angle));@]&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;This is the member type that user-defined (partial) specializations of the &apos;&apos;(:link </string>
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												<string>:)&apos;&apos; template define the scalar type of a matrix type. Valid scalar types are value types that satisfy the (:link </string>
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												<string>:).&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Effects:&#10;&#10;As if:&#10;&#10;[@a (:link </string>
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												<string>|*=:) (:link </string>
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												<string> mod=&quot;(&quot;:)(angle);@]&#10;</string>
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												<string>(:auto !!! mod=&quot;/&quot;:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Requirements:&#10;&#10;&apos;&apos;R&apos;&apos; must be copyable.&#10;&#10;!!!!Effects:&#10;&#10;The first overload is equivalent to: &apos;&apos;R r; (:link </string>
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												<string> mod=&quot;(&quot;:)(r,a); return r;&apos;&apos;&#10;&#10;The second overload assumes that &apos;&apos;m&apos;&apos; is an orthonormal rotation matrix and converts it to a quaternion that performs the same rotation.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;!!!!Assumption:&#10;&#10;&apos;&apos;(:link </string>
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												<string>:)&lt;V&gt;::value&apos;&apos; is &apos;&apos;true&apos;&apos;.&#10;&#10;!!!!Requirements:&#10;&#10;*&apos;&apos;(:link </string>
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												<string>:)&lt;V&gt;::type&gt;::value&apos;&apos; must be &apos;&apos;true&apos;&apos;&#10;*&apos;&apos;(:link </string>
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												<string>:)&lt;V&gt;::type&apos;&apos; must be copyable&#10;*&apos;&apos;(:link </string>
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												<string> mod=&quot;m&quot;:)==Dim&apos;&apos;&#10;&#10;This template is used by Boost QVM whenever it needs to deduce a copyable vector type of certain dimension from a single user-supplied function parameter of vector type. The returned type must have accessible copy constructor. Note that &apos;&apos;V&apos;&apos; may be non-copyable.&#10;&#10;The main template definition returns an unspecified copyable vector type of size &apos;&apos;Dim&apos;&apos;, except if &apos;&apos;(:link </string>
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												<string> mod=&quot;m&quot;:)==Dim&apos;&apos;, in which case it returns &apos;&apos;V&apos;&apos;, which is suitable only if &apos;&apos;V&apos;&apos; is a copyable type. Boost QVM also defines (partial) specializations for the non-copyable vector types it produces. Users can define other (partial) specializations for their own types.&#10;&#10;A typical use of the &apos;&apos;(:link </string>
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												<string>:)&apos;&apos; template is for specifying the preferred vector type to be returned by the generic function template overloads in Boost QVM depending on the type of their arguments.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;!!!Capturing view proxies with &apos;&apos;auto&apos;&apos;&#10;&#10;By design (:link </string>
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												<string> mod=&quot;p&quot;:) must not return temporary objects. They return reference to an argument they take by (const) reference, cast to reference of unspecified type that is not copyable. Because of this, the return value of a (:link </string>
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												<string>:) can not be captured by &apos;&apos;auto&apos;&apos;:&#10;&#10;[@auto tr=(:link </string>
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												<string>:)(m); //Error: the return type of (:link </string>
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												<string>:) can not be copied.@]&#10;&#10;The correct use of &apos;&apos;auto&apos;&apos; with (:link </string>
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												<string>:)(m);@]&#10;&#10;!!!!Note:&#10;&#10;many (:link </string>
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												<string>:) operate on the original object. This is another reason why they can not be captured by &apos;&apos;auto&apos;&apos; by value.&#10;&#10;!!!Binding QVM overloads from an unrelated namespace&#10;&#10;The operator overloads in namespace &apos;&apos;boost::qvm&apos;&apos; are designed to work with user-defined types. Typically it is sufficient to make these operators available in the namespace where the operator is used, by &apos;&apos;using namespace boost::qvm&apos;&apos;. A problem arises if the scope that uses the operator is not controlled by the user. For example:&#10;&#10;[@namespace ns1&#10;{&#10;    struct float2 { float x, y; };&#10;}&#10;&#10;namespace ns2&#10;{&#10;    using namespace boost::qvm;&#10;&#10;    void f()&#10;    {&#10;        ns1::float2 a, b;&#10;        a==b; //OK&#10;        ns1::float2 arr1[2], arr2[2];&#10;        std::equal(arr1,arr1+2,arr2); //Error: (:link </string>
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												<string> mod=&quot;(&quot;:) is inaccessible from namespace std&#10;    }&#10;}@]&#10;&#10;In the &apos;&apos;std::equal&apos;&apos; expression above, even though &apos;&apos;boost::qvm::(:link </string>
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												<string> mod=&quot;(&quot;:)&apos;&apos; is made visible in namespace &apos;&apos;ns2&apos;&apos; by &apos;&apos;using namespace boost::qvm&apos;&apos;, the call originates from namespace &apos;&apos;std&apos;&apos;. In this case the compiler can&apos;t bind &apos;&apos;boost::qvm::(:link </string>
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												<string> mod=&quot;(&quot;:)&apos;&apos; because only namespace &apos;&apos;ns1&apos;&apos; is visible through ADL, and it does not contain a suitable declaration. The solution is to declare &apos;&apos;operator==&apos;&apos; in namespace &apos;&apos;ns1&apos;&apos;, which can be done like this:&#10;&#10;[@namespace ns1 { using boost::qvm::(:link </string>
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												<string>:)&apos;&apos; in namespace &apos;&apos;boost::qvm&apos;&apos;. This allows the user to specialize these templates for user-defined (:link </string>
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												<string>:) types.&#10;&#10;Boost QVM itself defines specializations of the math function templates only for &apos;&apos;float&apos;&apos; and &apos;&apos;double&apos;&apos;, but it does not provide generic definitions. This is done to protect the user from unintentionally writing code that binds standard math functions that take &apos;&apos;double&apos;&apos; when passing arguments of lesser types, which would be suboptimal.&#10;&#10;Because of this, a call to e.g. &apos;&apos;(:link </string>
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												<string>|A&lt;I&gt;:))&apos;&apos; used to access vector elements as well as &apos;&apos;(m,(:link </string>
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												<string>(:auto !!!:)&#10;&#10;This header defines all available function overloads that operate on quaternion objects.&#10;&#10;!!!Synopsis:&#10;&#10;(:include synopsis:)&#10;</string>
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												<string>(:auto !!! mod=&quot;/&quot;:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Returns:&#10;&#10;A mutable reference to the &apos;&apos;i&apos;&apos;-th element of &apos;&apos;a&apos;&apos;.&#10;&#10;!!!!Preconditions:&#10;&#10;&apos;&apos;i &gt;= 0 &amp;&amp; i &lt; (:link </string>
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												<string>:)&lt;A&gt;::(:link </string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Effects:&#10;&#10;Subtracts the elements of &apos;&apos;b&apos;&apos; from the corresponding elements of &apos;&apos;a&apos;&apos;.&#10;&#10;!!!!Returns:&#10;&#10;&apos;&apos;a&apos;&apos;.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Effects:&#10;&#10;As if:&#10;&#10;[@a (:link </string>
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												<string>|*=:) (:link </string>
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												<string> mod=&quot;(&quot;:)&lt;(:link </string>
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												<string> mod=&quot;m&quot;:)&gt;(axis,angle);@]&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Returns:&#10;&#10;A matrix of the same size as &apos;&apos;a&apos;&apos; and &apos;&apos;b&apos;&apos;, with elements the elements of &apos;&apos;b&apos;&apos; added to the corresponding elements of &apos;&apos;a&apos;&apos;.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;</string>
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												<string> mod=&quot;m&quot;:)&apos;&apos; evaluates to the scalar type of the vector type &apos;&apos;T&apos;&apos; (if &apos;&apos;(:link </string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Returns:&#10;&#10;The (:link http://en.wikipedia.org/wiki/Dot_product|dot product:) of the vectors &apos;&apos;a&apos;&apos; and &apos;&apos;b&apos;&apos;.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;Swizzling allows zero-overhead direct access to a (possibly rearranged) subset of the elements of 2D, 3D and 4D vectors. For example, if &apos;&apos;v&apos;&apos; is a 4D vector, the expression &apos;&apos;(v,YX)&apos;&apos; is a 2D (:link </string>
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												<string>(:auto !!!:)&#10;&#10;While Boost QVM defines generic functions that operate on matrix and vector types of arbitrary static dimensions, it also provides a code generator that can be used to create compatible header files that define much simpler specializations of these functions for specific dimensions. This is useful during debugging since the generated code is much easier to read than the template metaprogramming-heavy generic implementations. It is also potentially friendlier to the optimizer.&#10;&#10;The code generator is a command-line utility program. Its source code can be found in the &apos;&apos;libs/qvm/gen&apos;&apos; directory. It was used to generate the following headers:&#10;&#10;* 2D, 3D and 4D matrix operations:&#10;** &apos;&apos;boost/qvm/gen/mat_operations2.hpp&apos;&apos; (matrices of size 2x2, 2x1 and 1x2, included by &apos;&apos;(:link </string>
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												<string>:)&apos;&apos; macro.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;This function is expected to be static member of user-defined specializations of the &apos;&apos;(:link </string>
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												<string>:) of &apos;&apos;a&apos;&apos;; that is, it simply accesses the elements of &apos;&apos;a&apos;&apos;.&#10;&#10;This allows calling Boost QVM operations when &apos;&apos;a&apos;&apos; is of built-in type, for example a plain old C array.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;This header defines all available operations between quaternions and vectors.&#10;&#10;!!!Synopsis:&#10;&#10;(:include synopsis:)&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Returns:&#10;&#10;A 4x4 projection matrix of unspecified type of the following form:&#10;&#10;[@xs             0              0                 0&#10;0              ys             0                 0&#10;0              0         zf/(zf-zn)   -zn*zf/(zf-zn)&#10;0              0              1                 0@]&#10;&#10;where ys=cot(fov_y/2) and xs=ys/aspect.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;&apos;&apos;&apos;Q:&apos;&apos;&apos; What is the motivation behind Boost QVM? Why not just use uBLAS/Eigen/CML/GLM/etc?&#10;&#10;-&gt;&apos;&apos;&apos;A:&apos;&apos;&apos; The primary domain of Boost QVM is realtime graphics and simulation applications, so it is not a complete linear algebra library. While (naturally) there is some overlap with such libraries, QVM puts the emphasis on 2, 3 and 4 dimensional zero-overhead operations (hence domain-specific features like </string>
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												<string>).&#10;&#10;&apos;&apos;&apos;Q:&apos;&apos;&apos; How does the &apos;&apos;qvm::(:link </string>
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												<string>:)&apos;&apos; (or &apos;&apos;qvm::(:link </string>
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												<string>:)&apos;&apos;, or &apos;&apos;qvm::(:link </string>
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												<string>:)&apos;&apos;) template compare to vector types from other libraries?&#10;&#10;-&gt;&apos;&apos;&apos;A:&apos;&apos;&apos; The &apos;&apos;qvm::(:link </string>
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												<string>:)&apos;&apos; template is not in any way central to the vector operations defined by QVM. The operations are designed to work with any user-defined vector type or with 3rd-party vector types (e.g. &apos;&apos;(:link https://msdn.microsoft.com/en-us/library/windows/desktop/bb172627%28v=vs.85%29.aspx|D3DVECTOR:)&apos;&apos;), while the &apos;&apos;qvm::(:link </string>
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												<string>:)&apos;&apos; template is simply a default return type for expressions that use arguments of different types that would be incompatible outside of QVM. For example, if the &apos;&apos;(:link </string>
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												<string>:)&apos;&apos; hasn&apos;t been specialized, calling &apos;&apos;(:link </string>
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												<string>:)&apos;&apos; with a user-defined type &apos;&apos;vec3&apos;&apos; and a user-defined type &apos;&apos;float3&apos;&apos; returns a &apos;&apos;qvm::(:link </string>
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												<string>:)&apos;&apos;.&#10;&#10;&apos;&apos;&apos;Q:&apos;&apos;&apos; Why doesn&apos;t QVM use [] or () to access vector and matrix elements?&#10;&#10;-&gt;&apos;&apos;&apos;A:&apos;&apos;&apos; Because it&apos;s designed to work with user-defined types, and the C++ standard requires these operators to be members. Of course if a user-defined type defines &apos;&apos;operator[]&apos;&apos; or &apos;&apos;operator()&apos;&apos; they are available for use with other QVM functions, but QVM defines its own mechanism for </string>
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												<string>, as well as </string>
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												<string> support.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;This is the member type that user-defined (partial) specializations of the &apos;&apos;(:link </string>
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												<string>:)&apos;&apos; template define the scalar type of a quaternion type. Valid scalar types are value types that satisfy the (:link </string>
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												<string>:).&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Assumptions:&#10;&#10;&apos;&apos;A&apos;&apos; and &apos;&apos;B&apos;&apos; satisfy the (:link </string>
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												<string>:).&#10;&#10;!!!!Returns:&#10;&#10;If &apos;&apos;A&apos;&apos; and &apos;&apos;B&apos;&apos; are the same type, &apos;&apos;impl&lt;A,B&gt;::type&apos;&apos; returns that type. Otherwise, &apos;&apos;impl&lt;A,B&gt;::type&apos;&apos; is well defined for the following types only: &apos;&apos;signed/unsigned char&apos;&apos;, &apos;&apos;signed/unsigned short&apos;&apos;, &apos;&apos;signed/unsigned int&apos;&apos;, &apos;&apos;signed/unsigned long&apos;&apos;, &apos;&apos;float&apos;&apos; and &apos;&apos;double&apos;&apos;. The deduction logic is as follows:&#10;&#10;*if either of &apos;&apos;A&apos;&apos; and &apos;&apos;B&apos;&apos; is &apos;&apos;double&apos;&apos;, the result is &apos;&apos;double&apos;&apos;;&#10;*else, if one of &apos;&apos;A&apos;&apos; and &apos;&apos;B&apos;&apos; is an integer type and the other is &apos;&apos;float&apos;&apos;, the result is &apos;&apos;float&apos;&apos;;&#10;*else, if &apos;&apos;A&apos;&apos; or &apos;&apos;B&apos;&apos; is a signed integer and the other type is unsigned integer, the signed type is changed to unsigned, and then the lesser of the two integers is promoted to the other.</string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;This type template defines a compile-time boolean constant value which can be used to determine whether a type &apos;&apos;T&apos;&apos; is a valid scalar type. It must be specialized together with the &apos;&apos;</string>
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												<string>&apos;&apos; template in order to introduce a user scalar type to Boost QVM. Such types must satisfy the </string>
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												<string>(:auto !!!:)&#10;&#10;(:include synopsis:)&#10;&#10;!!!!Returns:&#10;&#10;A quaternion of the negated elements of &apos;&apos;a&apos;&apos;.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;This header defines function and operator overloads that implement all the same operations defined in the &apos;&apos;(:link </string>
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												<string>:)&apos;&apos; header, but specifically and only for 4D vectors and matrices. You can include it instead of &apos;&apos;(:link </string>
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												<string>:)&apos;&apos; if you know you don&apos;t use vector objects of any other size.&#10;</string>
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												<string>(:auto !!!:)&#10;&#10;SFINAE stands for Substitution Failure Is Not An Error. This refers to a situation in C++ where an invalid substitution of template parameters (including when those parameters are deduced implicitly as a result of an unqualified call) is not in itself an error.&#10;&#10;In absence of concepts support, SFINAE can be used to disable function template overloads that would otherwise present a signature that is too generic. More formally, this is supported by the (:link http://www.boost.org/doc/libs/release/libs/utility/enable_if.html|Boost enable_if library:).&#10;&#10;For example, Boost QVM defines &apos;&apos;operator*&apos;&apos; overload which works with any user-defined matrix and vector types. The naive approach would be to declare this overload as follows:&#10;&#10;[@template &lt;class Matrix,class Vector&gt;&#10;Vector operator*( Matrix const &amp; m, Vector const &amp; v );@]&#10;&#10;Even if the function definition might contain code that would compile only for &apos;&apos;Matrix&apos;&apos; and &apos;&apos;Vector&apos;&apos; types, because the function declaration itself is valid, it will participate in overload rezolutions when multiplying objects of any two types whatsoever. This typically renders overload resolutions ambiguous and the compiler (correctly) issues an error.&#10;&#10;Using &apos;&apos;(:link </string>
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												<string>:)&apos;&apos;, Boost QVM declares such overloads in a way that they retain their generic signature but only participate (in overload resolutions) if the passed parameters make sense depending on the semantics of the operation being defined:&#10;&#10;[@template &lt;class A,class B&gt;&#10;typename (:link </string>
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												<string>(:auto !!!:)&#10;&#10;This header introduces in the &apos;&apos;boost::qvm&apos;&apos; namespace function template declarations corresponding to the functions defined in the standard C header file &apos;&apos;&lt;math.h&gt;&apos;&apos;, and defines &apos;&apos;float&apos;&apos; and &apos;&apos;double&apos;&apos; specializations which simply call the appropriate C function.&#10;&#10;!!!Synopsis:&#10;&#10;(:include synopsis:)&#10;</string>
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												<string> mod=&quot;(&quot;:)(angle);@]&#10;</string>
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												<string> (:link https://en.wikipedia.org/wiki/Quaternion|quaternion:) of unspecified type and scalar type &apos;&apos;Angle&apos;&apos;, which performs a rotation around the Y axis at &apos;&apos;angle&apos;&apos; radians.&#10;</string>
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										<shared_ptr>
											<id>-84</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-85</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-86</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-87</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-88</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-91</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-94</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-95</id>
										</shared_ptr>
									</weak_ptr>
									<string>macro</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-96</id>
										</shared_ptr>
									</weak_ptr>
									<string>view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-97</id>
										</shared_ptr>
									</weak_ptr>
									<string>constant</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-99</id>
										</shared_ptr>
									</weak_ptr>
									<string>noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-100</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-101</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-102</id>
										</shared_ptr>
									</weak_ptr>
									<string>category noalso noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-103</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-104</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-105</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-106</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-107</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-108</id>
										</shared_ptr>
									</weak_ptr>
									<string>noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-110</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-111</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-112</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-113</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-114</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-115</id>
										</shared_ptr>
									</weak_ptr>
									<string>category noalso noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-116</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-117</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-118</id>
										</shared_ptr>
									</weak_ptr>
									<string>view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-119</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-120</id>
										</shared_ptr>
									</weak_ptr>
									<string>noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-121</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-122</id>
										</shared_ptr>
									</weak_ptr>
									<string>view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-123</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-124</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-125</id>
										</shared_ptr>
									</weak_ptr>
									<string>constant</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-127</id>
										</shared_ptr>
									</weak_ptr>
									<string>function throws</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-128</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-129</id>
										</shared_ptr>
									</weak_ptr>
									<string>noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-130</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-131</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-133</id>
										</shared_ptr>
									</weak_ptr>
									<string>exception</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-134</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-135</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-136</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-137</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-138</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-139</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-140</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-141</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-142</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-143</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-146</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-147</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-148</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-149</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-151</id>
										</shared_ptr>
									</weak_ptr>
									<string>namespace</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-152</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-153</id>
										</shared_ptr>
									</weak_ptr>
									<string>function throws</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-154</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-155</id>
										</shared_ptr>
									</weak_ptr>
									<string>macro</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-156</id>
										</shared_ptr>
									</weak_ptr>
									<string></string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-157</id>
										</shared_ptr>
									</weak_ptr>
									<string>function throws</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-160</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-161</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-162</id>
										</shared_ptr>
									</weak_ptr>
									<string>macro</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-163</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-165</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-166</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-169</id>
										</shared_ptr>
									</weak_ptr>
									<string>noalso noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-170</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-171</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-172</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-173</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-176</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-177</id>
										</shared_ptr>
									</weak_ptr>
									<string>category noalso noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-180</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-182</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-183</id>
										</shared_ptr>
									</weak_ptr>
									<string>type</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-184</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-186</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-187</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-190</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-191</id>
										</shared_ptr>
									</weak_ptr>
									<string>category noalso noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-192</id>
										</shared_ptr>
									</weak_ptr>
									<string>noindex</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-193</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-194</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-195</id>
										</shared_ptr>
									</weak_ptr>
									<string>function</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-196</id>
										</shared_ptr>
									</weak_ptr>
									<string>function view</string>
								</pair>
								<pair>
									<weak_ptr>
										<expired>0</expired>
										<shared_ptr>
											<id>-197</id>
										</shared_ptr>
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