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| <div class="section"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="math_toolkit.special_tut.special_tut_impl"></a><a class="link" href="special_tut_impl.html" title="Implementation">Implementation</a> |
| </h3></div></div></div> |
| <p> |
| In this section we'll provide a "recipe" for adding a new special |
| function to this library to make life easier for future authors wishing to |
| contribute. We'll assume the function returns a single floating point result, |
| and takes two floating point arguments. For the sake of exposistion we'll |
| give the function the name "my_special". |
| </p> |
| <p> |
| Normally the implementation of such a function is split into two layers - |
| a public user layer, and an internal implementation layer that does the actual |
| work. The implementation layer is declared inside a "detail" namespace |
| and has a simple signature: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">detail</span><span class="special">{</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">></span> |
| <span class="identifier">T</span> <span class="identifier">my_special_imp</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&</span> <span class="identifier">pol</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="comment">/* Implementation goes here */</span> |
| <span class="special">}</span> |
| |
| <span class="special">}}}</span> <span class="comment">// namespaces</span> |
| </pre> |
| <p> |
| We'll come back to what can go inside the implementation later, but first |
| lets look at the user layer. This consists of two overloads of the function, |
| with and without a <a class="link" href="../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a> argument: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">></span> |
| <span class="keyword">typename</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">U</span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">my_special</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">></span> |
| <span class="keyword">typename</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">U</span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">my_special</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&</span> <span class="identifier">pol</span><span class="special">);</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces</span> |
| </pre> |
| <p> |
| Note how each argument has a different template type - this allows for mixed |
| type arguments - the return type is computed from a traits class and is the |
| "common type" of all the arguments after any integer arguments |
| have been promoted to type <code class="computeroutput"><span class="keyword">double</span></code>. |
| </p> |
| <p> |
| The implementation of the non-policy overload is trivial: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">></span> |
| <span class="keyword">inline</span> <span class="keyword">typename</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">U</span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">my_special</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&</span> <span class="identifier">b</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="comment">// Simply forward with a default policy:</span> |
| <span class="keyword">return</span> <span class="identifier">my_special</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special"><>();</span> |
| <span class="special">}</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces</span> |
| </pre> |
| <p> |
| The implementation of the other overload is somewhat more complex, as there's |
| some meta-programming to do, but from a runtime perspective is still a one-line |
| forwarding function. Here it is with comments explaining what each line does: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">></span> |
| <span class="keyword">inline</span> <span class="keyword">typename</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">U</span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">my_special</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&</span> <span class="identifier">pol</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="comment">//</span> |
| <span class="comment">// We've found some standard library functions to misbehave if any FPU exception flags</span> |
| <span class="comment">// are set prior to their call, this code will clear those flags, then reset them</span> |
| <span class="comment">// on exit:</span> |
| <span class="comment">//</span> |
| <span class="identifier">BOOST_FPU_EXCEPTION_GUARD</span> |
| <span class="comment">//</span> |
| <span class="comment">// The type of the result - the common type of T and U after</span> |
| <span class="comment">// any integer types have been promoted to double:</span> |
| <span class="comment">//</span> |
| <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">promote_args</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">U</span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">result_type</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// The type used for the calculation. This may be a wider type than</span> |
| <span class="comment">// the result in order to ensure full precision:</span> |
| <span class="comment">//</span> |
| <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">policies</span><span class="special">::</span><span class="identifier">evaluation</span><span class="special"><</span><span class="identifier">result_type</span><span class="special">,</span> <span class="identifier">Policy</span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">value_type</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// The type of the policy to forward to the actual implementation.</span> |
| <span class="comment">// We disable promotion of float and double as that's [possibly]</span> |
| <span class="comment">// happened already in the line above. Also reset to the default</span> |
| <span class="comment">// any policies we don't use (reduces code bloat if we're called</span> |
| <span class="comment">// multiple times with differing policies we don't actually use).</span> |
| <span class="comment">// Also normalise the type, again to reduce code bloat in case we're</span> |
| <span class="comment">// called multiple times with functionally identical policies that happen</span> |
| <span class="comment">// to be different types.</span> |
| <span class="comment">//</span> |
| <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">policies</span><span class="special">::</span><span class="identifier">normalise</span><span class="special"><</span> |
| <span class="identifier">Policy</span><span class="special">,</span> |
| <span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_float</span><span class="special"><</span><span class="keyword">false</span><span class="special">>,</span> |
| <span class="identifier">policies</span><span class="special">::</span><span class="identifier">promote_double</span><span class="special"><</span><span class="keyword">false</span><span class="special">>,</span> |
| <span class="identifier">policies</span><span class="special">::</span><span class="identifier">discrete_quantile</span><span class="special"><>,</span> |
| <span class="identifier">policies</span><span class="special">::</span><span class="identifier">assert_undefined</span><span class="special"><></span> <span class="special">>::</span><span class="identifier">type</span> <span class="identifier">forwarding_policy</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// Whew. Now we can make the actual call to the implementation.</span> |
| <span class="comment">// Arguments are explicitly cast to the evaluation type, and the result</span> |
| <span class="comment">// passed through checked_narrowing_cast which handles things like overflow</span> |
| <span class="comment">// according to the policy passed:</span> |
| <span class="comment">//</span> |
| <span class="keyword">return</span> <span class="identifier">policies</span><span class="special">::</span><span class="identifier">checked_narrowing_cast</span><span class="special"><</span><span class="identifier">result_type</span><span class="special">,</span> <span class="identifier">forwarding_policy</span><span class="special">>(</span> |
| <span class="identifier">detail</span><span class="special">::</span><span class="identifier">my_special_imp</span><span class="special">(</span> |
| <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">value_type</span><span class="special">>(</span><span class="identifier">a</span><span class="special">),</span> |
| <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">value_type</span><span class="special">>(</span><span class="identifier">x</span><span class="special">),</span> |
| <span class="identifier">forwarding_policy</span><span class="special">()),</span> |
| <span class="string">"boost::math::my_special<%1%>(%1%, %1%)"</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces</span> |
| </pre> |
| <p> |
| We're now almost there, we just need to flesh out the details of the implementation |
| layer: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">detail</span><span class="special">{</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">></span> |
| <span class="identifier">T</span> <span class="identifier">my_special_imp</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span><span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Policy</span><span class="special">&</span> <span class="identifier">pol</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="comment">/* Implementation goes here */</span> |
| <span class="special">}</span> |
| |
| <span class="special">}}}</span> <span class="comment">// namespaces</span> |
| </pre> |
| <p> |
| The following guidelines indicate what (other than basic arithmetic) can |
| go in the implementation: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Error conditions (for example bad arguments) should be handled by calling |
| one of the <a class="link" href="../error_handling.html#math_toolkit.error_handling.finding_more_information">policy |
| based error handlers</a>. |
| </li> |
| <li class="listitem"> |
| Calls to standard library functions should be made unqualified (this |
| allows argument dependent lookup to find standard library functions for |
| user-defined floating point types such as those from Boost.Multiprecision). |
| In addition the macro <code class="computeroutput"><span class="identifier">BOOST_MATH_STD_USING</span></code> |
| should appear at the start of the function (note no semi-colon afterwards!) |
| so that all the math functions in <code class="computeroutput"><span class="keyword">namespace</span> |
| <span class="identifier">std</span></code> are visible in the current |
| scope. |
| </li> |
| <li class="listitem"> |
| Calls to other special functions should be made as fully qualified calls, |
| and include the policy parameter as the last argument, for example <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">pol</span><span class="special">)</span></code>. |
| </li> |
| <li class="listitem"> |
| Where possible, evaluation of series, continued fractions, polynomials, |
| or root finding should use one of the <a class="link" href="../../toolkit.html" title="Chapter 12. Internals (Series, Rationals and Continued Fractions, Root Finding, Function Minimization, Testing and Development Tools)">boiler |
| plate functions</a>. In any case, after any iterative method, you |
| should verify that the number of iterations did not exceed the maximum |
| specified in the <a class="link" href="../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a> type, and if it |
| did terminate as a result of exceeding the maximum, then the appropriate |
| error handler should be called (see existing code for examples). |
| </li> |
| <li class="listitem"> |
| Numeric constants such as π etc should be obtained via a call to the <a class="link" href="../constants.html" title="The Mathematical Constants">appropriate function</a>, for example: |
| <code class="computeroutput"><span class="identifier">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span></code>. |
| </li> |
| <li class="listitem"> |
| Where tables of coefficients are used (for example for rational approximations), |
| care should be taken to ensure these are initialized at program startup |
| to ensure thread safety when using user-defined number types. See for |
| example the use of <code class="computeroutput"><span class="identifier">erf_initializer</span></code> |
| in boost/math/special_functions/erf.hpp. |
| </li> |
| </ul></div> |
| <p> |
| Here are some other useful internal functions: |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| function |
| </p> |
| </th> |
| <th> |
| <p> |
| Meaning |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> |
| <span class="identifier">Policy</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Returns number of binary digits in T (possible overridden by the |
| policy). |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">policies</span><span class="special">::</span><span class="identifier">get_max_series_iterations</span><span class="special"><</span><span class="identifier">Policy</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Maximum number of iterations for series evaluation. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">policies</span><span class="special">::</span><span class="identifier">get_max_root_iterations</span><span class="special"><</span><span class="identifier">Policy</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Maximum number of iterations for root finding. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">polices</span><span class="special">::</span><span class="identifier">get_epsilon</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span> |
| <span class="identifier">Policy</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Epsilon for type T, possibly overridden by the Policy. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Returns the number of binary digits in T. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">tools</span><span class="special">::</span><span class="identifier">max_value</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Equivalent to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max</span><span class="special">()</span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">tools</span><span class="special">::</span><span class="identifier">min_value</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Equivalent to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min</span><span class="special">()</span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">tools</span><span class="special">::</span><span class="identifier">log_max_value</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Equivalent to the natural logarithm of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">max</span><span class="special">()</span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">tools</span><span class="special">::</span><span class="identifier">log_min_value</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Equivalent to the natural logarithm of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">min</span><span class="special">()</span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">tools</span><span class="special">::</span><span class="identifier">epsilon</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Equivalent to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">()</span></code>. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">tools</span><span class="special">::</span><span class="identifier">root_epsilon</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Equivalent to the square root of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">()</span></code>. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">tools</span><span class="special">::</span><span class="identifier">forth_root_epsilon</span><span class="special"><</span><span class="identifier">T</span><span class="special">>()</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Equivalent to the forth root of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">T</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">()</span></code>. |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, |
| Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert |
| Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, |
| Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
| </div></td> |
| </tr></table> |
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