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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_multiprecision.ref.number"></a><a class="link" href="number.html" title="number">number</a> |
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| <h5> |
| <a name="boost_multiprecision.ref.number.h0"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.synopsis"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.synopsis">Synopsis</a> |
| </h5> |
| <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">multiprecision</span><span class="special">{</span> |
| |
| <span class="keyword">enum</span> <span class="identifier">expression_template_option</span> <span class="special">{</span> <span class="identifier">et_on</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">et_off</span> <span class="special">=</span> <span class="number">0</span> <span class="special">};</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">expression_template_default</span> |
| <span class="special">{</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">expression_template_option</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">et_on</span><span class="special">;</span> <span class="special">};</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span> <span class="special">=</span> <span class="identifier">expression_template_default</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>::</span><span class="identifier">value</span><span class="special">></span> |
| <span class="keyword">class</span> <span class="identifier">number</span> |
| <span class="special">{</span> |
| <span class="identifier">number</span><span class="special">();</span> |
| <span class="identifier">number</span><span class="special">(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">=(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="identifier">assign</span><span class="special">(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> |
| |
| <span class="comment">// Member operators</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">-=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">*=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">/=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">++();</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">--();</span> |
| <span class="identifier">number</span> <span class="keyword">operator</span><span class="special">++(</span><span class="keyword">int</span><span class="special">);</span> |
| <span class="identifier">number</span> <span class="keyword">operator</span><span class="special">--(</span><span class="keyword">int</span><span class="special">);</span> |
| |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">%=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">&=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">|=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">^=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special"><<=(</span><span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">>>=(</span><span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> |
| |
| <span class="comment">// Use in Boolean context:</span> |
| <span class="keyword">operator</span> <span class="emphasis"><em>convertible-to-bool-type</em></span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="comment">// swap:</span> |
| <span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">number</span><span class="special">&</span> <span class="identifier">other</span><span class="special">);</span> |
| <span class="comment">// Sign:</span> |
| <span class="keyword">bool</span> <span class="identifier">is_zero</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">int</span> <span class="identifier">sign</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="comment">// string conversion:</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">str</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="comment">// Generic conversion mechanism</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="identifier">T</span> <span class="identifier">convert_to</span><span class="special">()</span><span class="keyword">const</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">explicit</span> <span class="keyword">operator</span> <span class="identifier">T</span> <span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="comment">// precision control:</span> |
| <span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="identifier">default_precision</span><span class="special">();</span> |
| <span class="keyword">static</span> <span class="keyword">void</span> <span class="identifier">default_precision</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">digits10</span><span class="special">);</span> |
| <span class="keyword">unsigned</span> <span class="identifier">precision</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">void</span> <span class="identifier">precision</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">digits10</span><span class="special">);</span> |
| <span class="comment">// Comparison:</span> |
| <span class="keyword">int</span> <span class="identifier">compare</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>&</span> <span class="identifier">o</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">V</span><span class="special">></span> |
| <span class="keyword">typename</span> <span class="identifier">enable_if</span><span class="special"><</span><span class="identifier">is_convertible</span><span class="special"><</span><span class="identifier">V</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">int</span><span class="special">>::</span><span class="identifier">type</span> |
| <span class="identifier">compare</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">V</span><span class="special">&</span> <span class="identifier">o</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="comment">// Access to the underlying implementation:</span> |
| <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">backend</span><span class="special">();</span> |
| <span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">backend</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="special">};</span> |
| |
| <span class="comment">// Non member operators:</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">*(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">/(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="comment">// Integer only operations:</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">%(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">&(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">|(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">^(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special"><<(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">>>(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> |
| <span class="comment">// Comparison operators:</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">==(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">!=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special"><</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">></span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special"><=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">>=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| |
| <span class="comment">// Swap:</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> |
| |
| <span class="comment">// iostream support:</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>unmentionable-expression-template-type</em></span><span class="special">&</span> <span class="identifier">r</span><span class="special">);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">istream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special">>></span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">istream</span><span class="special">&</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> |
| |
| <span class="comment">// Arithmetic with a higher precision result:</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> |
| <span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</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">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> |
| <span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</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">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> |
| <span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> |
| |
| <span class="comment">// Non-member function standard library support:</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">abs</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fabs</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sqrt</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">floor</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ceil</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">trunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">itrunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ltrunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lltrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">round</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">iround</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lround</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">exp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">log</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">log10</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">cos</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sin</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">tan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">acos</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">asin</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">atan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">cosh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sinh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">tanh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ldexp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">frexp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">*);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">pow</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fmod</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">atan2</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">scalbn</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">logb</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>integer-type</em></span> <span class="identifier">ilogb</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| |
| <span class="comment">// Traits support:</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">struct</span> <span class="identifier">component_type</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">struct</span> <span class="identifier">number_category</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">struct</span> <span class="identifier">is_number</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">struct</span> <span class="identifier">is_number_expression</span><span class="special">;</span> |
| |
| <span class="comment">// Integer specific functions:</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">gcd</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lcm</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">pow</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">unsigned</span><span class="special">);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">powm</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">m</span><span class="special">);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">EXpressionTemplates</span><span class="special">></span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">EXpressionTemplates</span><span class="special">>&);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="keyword">void</span> <span class="identifier">divide_qr</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">y</span><span class="special">,</span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> |
| <span class="identifier">Integer</span> <span class="identifier">integer_modulus</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Integer</span> <span class="identifier">val</span><span class="special">);</span> |
| <span class="keyword">unsigned</span> <span class="identifier">lsb</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> |
| <span class="keyword">unsigned</span> <span class="identifier">msb</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="keyword">bool</span> <span class="identifier">bit_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_set</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_unset</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_flip</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Engine</span><span class="special">></span> |
| <span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">Engine</span><span class="special">&</span> <span class="identifier">gen</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">);</span> |
| |
| <span class="comment">// Rational number support:</span> |
| <span class="keyword">typename</span> <span class="identifier">component_type</span><span class="special"><</span><span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">numerator</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="keyword">typename</span> <span class="identifier">component_type</span><span class="special"><</span><span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">denominator</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces</span> |
| |
| <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="comment">// Boost.Math interoperability functions:</span> |
| <span class="keyword">int</span> <span class="identifier">fpclassify</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">isfinite</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">isnan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">isinf</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">isnormal</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces</span> |
| |
| <span class="comment">// numeric_limits support:</span> |
| <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">{</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="keyword">struct</span> <span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="special">></span> |
| <span class="special">{</span> |
| <span class="comment">/* Usual members here */</span> |
| <span class="special">};</span> |
| |
| <span class="special">}</span> |
| </pre> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h1"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.description"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.description">Description</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">enum</span> <span class="identifier">expression_template_option</span> <span class="special">{</span> <span class="identifier">et_on</span> <span class="special">=</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">et_off</span> <span class="special">=</span> <span class="number">0</span> <span class="special">};</span> |
| </pre> |
| <p> |
| This enumerated type is used to specify whether expression templates are |
| turned on (et_on) or turned off (et_off). |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">></span> <span class="keyword">struct</span> <span class="identifier">expression_template_default</span> |
| <span class="special">{</span> <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">expression_template_option</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">et_on</span><span class="special">;</span> <span class="special">};</span> |
| </pre> |
| <p> |
| This traits class specifies the default expression template option to be |
| used with a particular Backend type. It defaults to <code class="computeroutput"><span class="identifier">et_on</span></code>. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span> <span class="special">=</span> <span class="identifier">expression_template_default</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">>::</span><span class="identifier">value</span><span class="special">></span> |
| <span class="keyword">class</span> <span class="identifier">number</span><span class="special">;</span> |
| </pre> |
| <p> |
| Class <code class="computeroutput"><span class="identifier">number</span></code> has two template |
| arguments: |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl class="variablelist"> |
| <dt><span class="term">Backend</span></dt> |
| <dd><p> |
| The actual arithmetic back-end that does all the work. |
| </p></dd> |
| <dt><span class="term">ExpressionTemplates</span></dt> |
| <dd><p> |
| A Boolean value: when <code class="computeroutput"><span class="identifier">et_on</span></code>, |
| then expression templates are enabled, otherwise when set to <code class="computeroutput"><span class="identifier">et_off</span></code> they are disabled. The default |
| for this parameter is computed via the traits class <code class="computeroutput"><span class="identifier">expression_template_default</span></code> |
| whose member <code class="computeroutput"><span class="identifier">value</span></code> |
| defaults to <code class="computeroutput"><span class="identifier">et_on</span></code> unless |
| the traits class is specialized for a particular backend. |
| </p></dd> |
| </dl> |
| </div> |
| <pre class="programlisting"><span class="identifier">number</span><span class="special">();</span> |
| <span class="identifier">number</span><span class="special">(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">=(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="identifier">assign</span><span class="special">(</span><span class="identifier">see</span><span class="special">-</span><span class="identifier">below</span><span class="special">);</span> |
| </pre> |
| <p> |
| Type <code class="computeroutput"><span class="identifier">number</span></code> is default constructible, |
| and both copy constructible and assignable from: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Itself. |
| </li> |
| <li class="listitem"> |
| An expression template which is the result of one of the arithmetic operators. |
| </li> |
| <li class="listitem"> |
| Any builtin arithmetic type, as long as the result would not be lossy |
| (for example float to integer conversion). |
| </li> |
| <li class="listitem"> |
| Any type that the Backend is implicitly constructible or assignable from. |
| </li> |
| <li class="listitem"> |
| An rvalue reference to another <code class="computeroutput"><span class="identifier">number</span></code>. |
| Move-semantics are used for construction if the backend also supports |
| rvalue reference construction. In the case of assignment, move semantics |
| are always supported when the argument is an rvalue reference irrespective |
| of the backend. |
| </li> |
| <li class="listitem"> |
| Any type in the same family, as long as no loss of precision is involved. |
| For example from <code class="computeroutput"><span class="identifier">int128_t</span></code> |
| to <code class="computeroutput"><span class="identifier">int256_t</span></code>, or <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code> to <code class="computeroutput"><span class="identifier">cpp_dec_float_100</span></code>. |
| </li> |
| </ul></div> |
| <p> |
| Type <code class="computeroutput"><span class="identifier">number</span></code> is explicitly |
| constructible from: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Any type mentioned above. |
| </li> |
| <li class="listitem"> |
| A <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code> or any type which is convertible |
| to <code class="computeroutput"><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span></code>. |
| </li> |
| <li class="listitem"> |
| Any arithmetic type (including those that would result in lossy conversions). |
| </li> |
| <li class="listitem"> |
| Any type in the same family, including those that result in loss of precision. |
| </li> |
| <li class="listitem"> |
| Any type that the Backend is explicitly constructible from. |
| </li> |
| <li class="listitem"> |
| Any pair of types for which a generic interconversion exists: that is |
| from integer to integer, integer to rational, integer to float, rational |
| to rational, rational to float, or float to float. |
| </li> |
| </ul></div> |
| <p> |
| The assign member function is available for any type for which an explicit |
| converting constructor exists. It is intended to be used where a temporary |
| generated from an explicit assignment would be expensive, for example: |
| </p> |
| <pre class="programlisting"><span class="identifier">mpfr_float_50</span> <span class="identifier">f50</span><span class="special">;</span> |
| <span class="identifier">mpfr_float_100</span> <span class="identifier">f100</span><span class="special">;</span> |
| |
| <span class="identifier">f50</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">mpfr_float_50</span><span class="special">>(</span><span class="identifier">f100</span><span class="special">);</span> <span class="comment">// explicit cast create a temporary</span> |
| <span class="identifier">f50</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">f100</span><span class="special">);</span> <span class="comment">// explicit call to assign create no temporary</span> |
| </pre> |
| <p> |
| In addition, if the type has multiple components (for example rational or |
| complex number types), then there is a two argument constructor: |
| </p> |
| <pre class="programlisting"><span class="identifier">number</span><span class="special">(</span><span class="identifier">arg1</span><span class="special">,</span> <span class="identifier">arg2</span><span class="special">);</span> |
| </pre> |
| <p> |
| Where the two args must either be arithmetic types, or types that are convertible |
| to the two components of <code class="computeroutput"><span class="keyword">this</span></code>. |
| </p> |
| <pre class="programlisting"><span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">-=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">*=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">/=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">++();</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">--();</span> |
| <span class="identifier">number</span> <span class="keyword">operator</span><span class="special">++(</span><span class="keyword">int</span><span class="special">);</span> |
| <span class="identifier">number</span> <span class="keyword">operator</span><span class="special">--(</span><span class="keyword">int</span><span class="special">);</span> |
| <span class="comment">// Integer only operations:</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">%=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">&=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">|=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">^=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special"><<=(</span><span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> |
| <span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">>>=(</span><span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> |
| </pre> |
| <p> |
| These operators all take their usual arithmetic meanings. |
| </p> |
| <p> |
| The arguments to these operators is either: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| Another <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> |
| <span class="identifier">ExpressionTemplates</span><span class="special">></span></code>. |
| </li> |
| <li class="listitem"> |
| An expression template derived from <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">></span></code>. |
| </li> |
| <li class="listitem"> |
| Any type implicitly convertible to <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span></code>, including some other instance of |
| class <code class="computeroutput"><span class="identifier">number</span></code>. |
| </li> |
| </ul></div> |
| <p> |
| For the left and right shift operations, the argument must be a builtin integer |
| type with a positive value (negative values result in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> |
| being thrown). |
| </p> |
| <pre class="programlisting"><span class="keyword">operator</span> <span class="emphasis"><em>convertible-to-bool-type</em></span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| </pre> |
| <p> |
| Returns an <span class="emphasis"><em>unmentionable-type</em></span> that is usable in Boolean |
| contexts (this allows <code class="computeroutput"><span class="identifier">number</span></code> |
| to be used in any Boolean context - if statements, conditional statements, |
| or as an argument to a logical operator - without type <code class="computeroutput"><span class="identifier">number</span></code> |
| being convertible to type <code class="computeroutput"><span class="keyword">bool</span></code>. |
| </p> |
| <p> |
| This operator also enables the use of <code class="computeroutput"><span class="identifier">number</span></code> |
| with any of the following operators: <code class="computeroutput"><span class="special">!</span></code>, |
| <code class="computeroutput"><span class="special">||</span></code>, <code class="computeroutput"><span class="special">&&</span></code> |
| and <code class="computeroutput"><span class="special">?:</span></code>. |
| </p> |
| <pre class="programlisting"><span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">number</span><span class="special">&</span> <span class="identifier">other</span><span class="special">);</span> |
| </pre> |
| <p> |
| Swaps <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> |
| with <code class="computeroutput"><span class="identifier">other</span></code>. |
| </p> |
| <pre class="programlisting"><span class="keyword">bool</span> <span class="identifier">is_zero</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| </pre> |
| <p> |
| Returns <code class="computeroutput"><span class="keyword">true</span></code> is <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> is zero, |
| otherwise <code class="computeroutput"><span class="keyword">false</span></code>. |
| </p> |
| <pre class="programlisting"><span class="keyword">int</span> <span class="identifier">sign</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| </pre> |
| <p> |
| Returns a value less than zero if <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> is negative, a value greater than zero |
| if <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> |
| is positive, and zero if <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> |
| is zero. |
| </p> |
| <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">str</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">precision</span><span class="special">,</span> <span class="keyword">bool</span> <span class="identifier">scientific</span> <span class="special">=</span> <span class="keyword">true</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| </pre> |
| <p> |
| Returns the number formatted as a string, with at least <span class="emphasis"><em>precision</em></span> |
| digits, and in scientific format if <span class="emphasis"><em>scientific</em></span> is true. |
| </p> |
| <pre class="programlisting"><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="identifier">T</span> <span class="identifier">convert_to</span><span class="special">()</span><span class="keyword">const</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">explicit</span> <span class="keyword">operator</span> <span class="identifier">T</span> <span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| </pre> |
| <p> |
| Provides a generic conversion mechanism to convert <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> to type <code class="computeroutput"><span class="identifier">T</span></code>. |
| Type <code class="computeroutput"><span class="identifier">T</span></code> may be any arithmetic |
| type. Optionally other types may also be supported by specific <code class="computeroutput"><span class="identifier">Backend</span></code> types. |
| </p> |
| <pre class="programlisting"><span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="identifier">default_precision</span><span class="special">();</span> |
| <span class="keyword">static</span> <span class="keyword">void</span> <span class="identifier">default_precision</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">digits10</span><span class="special">);</span> |
| <span class="keyword">unsigned</span> <span class="identifier">precision</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">void</span> <span class="identifier">precision</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">digits10</span><span class="special">);</span> |
| </pre> |
| <p> |
| These functions are only available if the Backend template parameter supports |
| runtime changes to precision. They get and set the default precision and |
| the precision of <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code> |
| respectively. |
| </p> |
| <pre class="programlisting"><span class="keyword">int</span> <span class="identifier">compare</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">o</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">V</span><span class="special">></span> |
| <span class="keyword">typename</span> <span class="identifier">enable_if</span><span class="special"><</span><span class="identifier">is_convertible</span><span class="special"><</span><span class="identifier">V</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">int</span><span class="special">>::</span><span class="identifier">type</span> |
| <span class="identifier">compare</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">V</span><span class="special">&</span> <span class="identifier">other</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span> |
| </pre> |
| <p> |
| Returns: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| A value less that 0 for <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span> <span class="special"><</span> <span class="identifier">other</span></code> |
| </li> |
| <li class="listitem"> |
| A value greater that 0 for <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span> <span class="special">></span> <span class="identifier">other</span></code> |
| </li> |
| <li class="listitem"> |
| <p class="simpara"> |
| Zero for <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span> |
| <span class="special">==</span> <span class="identifier">other</span></code> |
| </p> |
| <pre class="programlisting"><span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">backend</span><span class="special">();</span> |
| <span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">backend</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span> |
| </pre> |
| </li> |
| </ul></div> |
| <p> |
| Returns the underlying back-end instance used by <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h2"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.non_member_operators"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.non_member_operators">Non-member |
| operators</a> |
| </h5> |
| <pre class="programlisting"><span class="comment">// Non member operators:</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">*(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">/(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="comment">// Integer only operations:</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">%(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">&(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">|(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">^(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special"><<(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="keyword">operator</span><span class="special">>>(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>integer-type</em></span><span class="special">&);</span> |
| <span class="comment">// Comparison operators:</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">==(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">!=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special"><</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">></span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special"><=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| <span class="keyword">bool</span> <span class="keyword">operator</span><span class="special">>=(</span><span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>see-below</em></span><span class="special">&);</span> |
| </pre> |
| <p> |
| These operators all take their usual arithmetic meanings. |
| </p> |
| <p> |
| The arguments to these functions must contain at least one of the following: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| A <code class="computeroutput"><span class="identifier">number</span></code>. |
| </li> |
| <li class="listitem"> |
| An expression template type derived from <code class="computeroutput"><span class="identifier">number</span></code>. |
| </li> |
| <li class="listitem"> |
| Any type for which <code class="computeroutput"><span class="identifier">number</span></code> |
| has an implicit constructor - for example a builtin arithmetic type. |
| </li> |
| </ul></div> |
| <p> |
| The return type of these operators is either: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> |
| <li class="listitem"> |
| An <span class="emphasis"><em>unmentionable-type</em></span> expression template type when |
| <code class="computeroutput"><span class="identifier">ExpressionTemplates</span></code> is |
| <code class="computeroutput"><span class="keyword">true</span></code>. |
| </li> |
| <li class="listitem"> |
| Type <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> |
| <span class="identifier">et_off</span><span class="special">></span></code> |
| when <code class="computeroutput"><span class="identifier">ExpressionTemplates</span></code> |
| is <code class="computeroutput"><span class="keyword">false</span></code>. |
| </li> |
| <li class="listitem"> |
| Type <code class="computeroutput"><span class="keyword">bool</span></code> if the operator |
| is a comparison operator. |
| </li> |
| </ul></div> |
| <p> |
| Finally note that the second argument to the left and right shift operations |
| must be a builtin integer type, and that the argument must be positive (negative |
| arguments result in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> |
| being thrown). |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h3"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.swap"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.swap">swap</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="keyword">void</span> <span class="identifier">swap</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> |
| </pre> |
| <p> |
| Swaps <code class="computeroutput"><span class="identifier">a</span></code> and <code class="computeroutput"><span class="identifier">b</span></code>. |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h4"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.iostream_support"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.iostream_support">Iostream |
| Support</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Unspecified</span><span class="special">...></span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special"><<</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">unmentionable</span><span class="special">-</span><span class="identifier">expression</span><span class="special">-</span><span class="keyword">template</span><span class="special">&</span> <span class="identifier">r</span><span class="special">);</span> |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="keyword">inline</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">istream</span><span class="special">&</span> <span class="keyword">operator</span> <span class="special">>></span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">istream</span><span class="special">&</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">)</span> |
| </pre> |
| <p> |
| These operators provided formatted input-output operations on <code class="computeroutput"><span class="identifier">number</span></code> types, and expression templates |
| derived from them. |
| </p> |
| <p> |
| It's down to the back-end type to actually implement string conversion. However, |
| the back-ends provided with this library support all of the iostream formatting |
| flags, field width and precision settings. |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h5"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.arithmetic_with_a_higher_precisi"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.arithmetic_with_a_higher_precisi">Arithmetic |
| with a higher precision result</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> |
| <span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</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">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> |
| <span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</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">ResultType</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Source1</span> <span class="keyword">class</span> <span class="identifier">Source2</span><span class="special">></span> |
| <span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">multiply</span><span class="special">(</span><span class="identifier">ResultType</span><span class="special">&</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source1</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">Source2</span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> |
| </pre> |
| <p> |
| These functions apply the named operator to the arguments <span class="emphasis"><em>a</em></span> |
| and <span class="emphasis"><em>b</em></span> and store the result in <span class="emphasis"><em>result</em></span>, |
| returning <span class="emphasis"><em>result</em></span>. In all cases they behave "as |
| if" arguments <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> were |
| first promoted to type <code class="computeroutput"><span class="identifier">ResultType</span></code> |
| before applying the operator, though particular backends may well avoid that |
| step by way of an optimization. |
| </p> |
| <p> |
| The type <code class="computeroutput"><span class="identifier">ResultType</span></code> must |
| be an instance of class <code class="computeroutput"><span class="identifier">number</span></code>, |
| and the types <code class="computeroutput"><span class="identifier">Source1</span></code> and |
| <code class="computeroutput"><span class="identifier">Source2</span></code> may be either instances |
| of class <code class="computeroutput"><span class="identifier">number</span></code> or native |
| integer types. The latter is an optimization that allows arithmetic to be |
| performed on native integer types producing an extended precision result. |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h6"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.non_member_standard_library_func"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.non_member_standard_library_func">Non-member |
| standard library function support</a> |
| </h5> |
| <pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">abs</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fabs</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sqrt</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">floor</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ceil</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">trunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">itrunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ltrunc</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lltrunc</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">round</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">iround</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lround</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">llround</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">exp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">log</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">log10</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">cos</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sin</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">tan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">acos</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">asin</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">atan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">cosh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sinh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">tanh</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">ldexp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">frexp</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">*);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">pow</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fmod</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">atan2</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">scalbn</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="emphasis"><em>integer-type</em></span><span class="special">);</span> |
| <span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">logb</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="emphasis"><em>integer-type</em></span> <span class="identifier">ilogb</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| </pre> |
| <p> |
| These functions all behave exactly as their standard library C++11 counterparts |
| do: their argument is either an instance of <code class="computeroutput"><span class="identifier">number</span></code> |
| or an expression template derived from it; If the argument is of type <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">et_off</span><span class="special">></span></code> |
| then that is also the return type, otherwise the return type is an expression |
| template. |
| </p> |
| <p> |
| The integer type arguments to <code class="computeroutput"><span class="identifier">ldexp</span></code>, |
| <code class="computeroutput"><span class="identifier">frexp</span></code>, <code class="computeroutput"><span class="identifier">scalbn</span></code> |
| and <code class="computeroutput"><span class="identifier">ilogb</span></code> may be either type |
| <code class="computeroutput"><span class="keyword">int</span></code>, or the actual type of the |
| exponent of the number type. |
| </p> |
| <p> |
| These functions are normally implemented by the Backend type. However, default |
| versions are provided for Backend types that don't have native support for |
| these functions. Please note however, that this default support requires |
| the precision of the type to be a compile time constant - this means for |
| example that the <a href="http://gmplib.org" target="_top">GMP</a> MPF Backend will |
| not work with these functions when that type is used at variable precision. |
| </p> |
| <p> |
| Also note that with the exception of <code class="computeroutput"><span class="identifier">abs</span></code> |
| that these functions can only be used with floating-point Backend types (if |
| any other types such as fixed precision or complex types are added to the |
| library later, then these functions may be extended to support those number |
| types). |
| </p> |
| <p> |
| The precision of these functions is generally determined by the backend implementation. |
| For example the precision of these functions when used with <a class="link" href="../tut/floats/mpfr_float.html" title="mpfr_float">mpfr_float</a> |
| is determined entirely by <a href="http://www.mpfr.org" target="_top">MPFR</a>. |
| When these functions use our own implementations, the accuracy of the transcendental |
| functions is generally a few epsilon. Note however, that the trigonometrical |
| functions incur the usual accuracy loss when reducing arguments by large |
| multiples of π. Also note that both <a class="link" href="../tut/floats/gmp_float.html" title="gmp_float">gmp_float</a> |
| and <a class="link" href="../tut/floats/cpp_dec_float.html" title="cpp_dec_float">cpp_dec_float</a> |
| have a number of guard digits beyond their stated precision, so the error |
| rates listed for these are in some sense artificially low. |
| </p> |
| <p> |
| The following table shows the error rates we observe for these functions |
| with various backend types, functions not listed here are exact (tested on |
| Win32 with VC++10, MPFR-3.0.0, MPIR-2.1.1): |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| Function |
| </p> |
| </th> |
| <th> |
| <p> |
| mpfr_float_50 |
| </p> |
| </th> |
| <th> |
| <p> |
| mpf_float_50 |
| </p> |
| </th> |
| <th> |
| <p> |
| cpp_dec_float_50 |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| sqrt |
| </p> |
| </td> |
| <td> |
| <p> |
| 1eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| exp |
| </p> |
| </td> |
| <td> |
| <p> |
| 1eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| log |
| </p> |
| </td> |
| <td> |
| <p> |
| 1eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| log10 |
| </p> |
| </td> |
| <td> |
| <p> |
| 1eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| cos |
| </p> |
| </td> |
| <td> |
| <p> |
| 700eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| sin |
| </p> |
| </td> |
| <td> |
| <p> |
| 1eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| tan |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| acos |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| asin |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| atan |
| </p> |
| </td> |
| <td> |
| <p> |
| 1eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| cosh |
| </p> |
| </td> |
| <td> |
| <p> |
| 1045eps<a href="#ftn.boost_multiprecision.ref.number.f0" class="footnote"><sup class="footnote"><a name="boost_multiprecision.ref.number.f0"></a>[1]</sup></a> |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| sinh |
| </p> |
| </td> |
| <td> |
| <p> |
| 2eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| tanh |
| </p> |
| </td> |
| <td> |
| <p> |
| 1eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| pow |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 4eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 3eps |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| atan2 |
| </p> |
| </td> |
| <td> |
| <p> |
| 1eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| <td> |
| <p> |
| 0eps |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| <tbody class="footnotes"><tr><td colspan="4"><div id="ftn.boost_multiprecision.ref.number.f0" class="footnote"><p><a href="#boost_multiprecision.ref.number.f0" class="para"><sup class="para">[1] </sup></a> |
| It's likely that the inherent error in the input values to our |
| test cases are to blame here. |
| </p></div></td></tr></tbody> |
| </table></div> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h7"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.traits_class_support"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.traits_class_support">Traits Class |
| Support</a> |
| </h5> |
| <pre class="programlisting"><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">struct</span> <span class="identifier">component_type</span><span class="special">;</span> |
| </pre> |
| <p> |
| If this is a type with multiple components (for example rational or complex |
| types), then this trait has a single member <code class="computeroutput"><span class="identifier">type</span></code> |
| that is the type of those components. |
| </p> |
| <pre class="programlisting"><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">struct</span> <span class="identifier">number_category</span><span class="special">;</span> |
| </pre> |
| <p> |
| A traits class that inherits from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span></code> |
| where <code class="computeroutput"><span class="identifier">N</span></code> is one of the enumerated |
| values <code class="computeroutput"><span class="identifier">number_kind_integer</span></code>, |
| <code class="computeroutput"><span class="identifier">number_kind_floating_point</span></code>, |
| <code class="computeroutput"><span class="identifier">number_kind_rational</span></code>, <code class="computeroutput"><span class="identifier">number_kind_fixed_point</span></code>, or <code class="computeroutput"><span class="identifier">number_kind_unknown</span></code>. This traits class |
| is specialized for any type that has <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> |
| support as well as for classes in this library: which means it can be used |
| for generic code that must work with built in arithmetic types as well as |
| multiprecision ones. |
| </p> |
| <pre class="programlisting"><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">struct</span> <span class="identifier">is_number</span><span class="special">;</span> |
| </pre> |
| <p> |
| A traits class that inherits from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span></code> |
| if T is an instance of <code class="computeroutput"><span class="identifier">number</span><span class="special"><></span></code>, otherwise from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code>. |
| </p> |
| <pre class="programlisting"><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">struct</span> <span class="identifier">is_number_expression</span><span class="special">;</span> |
| </pre> |
| <p> |
| A traits class that inherits from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span></code> |
| if T is an expression template type derived from <code class="computeroutput"><span class="identifier">number</span><span class="special"><></span></code>, otherwise from <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code>. |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h8"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.integer_functions"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.integer_functions">Integer |
| functions</a> |
| </h5> |
| <p> |
| In addition to functioning with types from this library, these functions |
| are also overloaded for built in integer types if you include <code class="computeroutput"><span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code>. |
| Further, when used with fixed precision types (whether built in integers |
| or multiprecision ones), the functions will promote to a wider type internally |
| when the algorithm requires it. Versions overloaded for built in integer |
| types return that integer type rather than an expression template. |
| </p> |
| <pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">gcd</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the largest integer <code class="computeroutput"><span class="identifier">x</span></code> |
| that divides both <code class="computeroutput"><span class="identifier">a</span></code> and |
| <code class="computeroutput"><span class="identifier">b</span></code>. |
| </p> |
| <pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">lcm</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the smallest integer <code class="computeroutput"><span class="identifier">x</span></code> |
| that is divisible by both <code class="computeroutput"><span class="identifier">a</span></code> |
| and <code class="computeroutput"><span class="identifier">b</span></code>. |
| </p> |
| <pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">pow</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">p</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns <span class="emphasis"><em>b<sup>p</sup></em></span> as an expression template. Note that this |
| function should be used with extreme care as the result can grow so large |
| as to take "effectively forever" to compute, or else simply run |
| the host machine out of memory. This is the one function in this category |
| that is not overloaded for built in integer types, further, it's probably |
| not a good idea to use it with fixed precision <code class="computeroutput"><span class="identifier">cpp_int</span></code>'s |
| either. |
| </p> |
| <pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">powm</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">p</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">m</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns <span class="emphasis"><em>b<sup>p</sup> mod m</em></span> as an expression template. Fixed precision |
| types are promoted internally to ensure accuracy. |
| </p> |
| <pre class="programlisting"><span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">a</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the largest integer <code class="computeroutput"><span class="identifier">x</span></code> |
| such that <code class="computeroutput"><span class="identifier">x</span> <span class="special">*</span> |
| <span class="identifier">x</span> <span class="special"><</span> |
| <span class="identifier">a</span></code>. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">EXpressionTemplates</span><span class="special">></span> <span class="identifier">sqrt</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">EXpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the largest integer <code class="computeroutput"><span class="identifier">x</span></code> |
| such that <code class="computeroutput"><span class="identifier">x</span> <span class="special">*</span> |
| <span class="identifier">x</span> <span class="special"><</span> |
| <span class="identifier">a</span></code>, and sets the remainder <code class="computeroutput"><span class="identifier">r</span></code> such that <code class="computeroutput"><span class="identifier">r</span> |
| <span class="special">=</span> <span class="identifier">a</span> <span class="special">-</span> <span class="identifier">x</span> <span class="special">*</span> |
| <span class="identifier">x</span></code>. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="keyword">void</span> <span class="identifier">divide_qr</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">y</span><span class="special">,</span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">q</span><span class="special">,</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">r</span><span class="special">);</span> |
| </pre> |
| <p> |
| Divides x by y and returns both the quotient and remainder. After the call |
| <code class="computeroutput"><span class="identifier">q</span> <span class="special">=</span> |
| <span class="identifier">x</span> <span class="special">/</span> <span class="identifier">y</span></code> and <code class="computeroutput"><span class="identifier">r</span> |
| <span class="special">=</span> <span class="identifier">x</span> <span class="special">%</span> <span class="identifier">y</span></code>. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Integer</span><span class="special">></span> |
| <span class="identifier">Integer</span> <span class="identifier">integer_modulus</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Integer</span> <span class="identifier">val</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the absolute value of <code class="computeroutput"><span class="identifier">x</span> |
| <span class="special">%</span> <span class="identifier">val</span></code>. |
| </p> |
| <pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">lsb</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the (zero-based) index of the least significant bit that is set to |
| 1. |
| </p> |
| <p> |
| Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">range_error</span></code> if the argument is <= 0. |
| </p> |
| <pre class="programlisting"><span class="keyword">unsigned</span> <span class="identifier">msb</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">x</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns the (zero-based) index of the most significant bit. |
| </p> |
| <p> |
| Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">range_error</span></code> if the argument is <= 0. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="keyword">bool</span> <span class="identifier">bit_test</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> |
| </pre> |
| <p> |
| Returns <code class="computeroutput"><span class="keyword">true</span></code> if the bit at |
| <span class="emphasis"><em>index</em></span> in <span class="emphasis"><em>val</em></span> is set. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_set</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> |
| </pre> |
| <p> |
| Sets the bit at <span class="emphasis"><em>index</em></span> in <span class="emphasis"><em>val</em></span>, and |
| returns <span class="emphasis"><em>val</em></span>. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_unset</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> |
| </pre> |
| <p> |
| Unsets the bit at <span class="emphasis"><em>index</em></span> in <span class="emphasis"><em>val</em></span>, |
| and returns <span class="emphasis"><em>val</em></span>. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">bit_flip</span><span class="special">(</span><span class="identifier">number</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">index</span><span class="special">);</span> |
| </pre> |
| <p> |
| Flips the bit at <span class="emphasis"><em>index</em></span> in <span class="emphasis"><em>val</em></span>, |
| and returns <span class="emphasis"><em>val</em></span>. |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Engine</span><span class="special">></span> |
| <span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">,</span> <span class="identifier">Engine</span><span class="special">&</span> <span class="identifier">gen</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">miller_rabin_test</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">trials</span><span class="special">);</span> |
| </pre> |
| <p> |
| Tests to see if the number <span class="emphasis"><em>n</em></span> is probably prime - the |
| test excludes the vast majority of composite numbers by excluding small prime |
| factors and performing a single Fermat test. Then performs <span class="emphasis"><em>trials</em></span> |
| Miller-Rabin tests. Returns <code class="computeroutput"><span class="keyword">false</span></code> |
| if <span class="emphasis"><em>n</em></span> is definitely composite, or <code class="computeroutput"><span class="keyword">true</span></code> |
| if <span class="emphasis"><em>n</em></span> is probably prime with the probability of it being |
| composite less than 0.25^trials. Fixed precision types are promoted internally |
| to ensure accuracy. |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h9"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.rational_number_functions"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.rational_number_functions">Rational |
| Number Functions</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">typename</span> <span class="identifier">component_type</span><span class="special"><</span><span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">numerator</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| <span class="keyword">typename</span> <span class="identifier">component_type</span><span class="special"><</span><span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">denominator</span><span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span> |
| </pre> |
| <p> |
| These functions return the numerator and denominator of a rational number |
| respectively. |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h10"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.boost_math_interoperability_supp"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.boost_math_interoperability_supp">Boost.Math |
| Interoperability Support</a> |
| </h5> |
| <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">int</span> <span class="identifier">fpclassify</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">isfinite</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">isnan</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">isinf</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| <span class="keyword">bool</span> <span class="identifier">isnormal</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&,</span> <span class="keyword">int</span><span class="special">);</span> |
| |
| <span class="special">}}</span> <span class="comment">// namespaces</span> |
| </pre> |
| <p> |
| These floating-point classification functions behave exactly as their Boost.Math |
| equivalents. |
| </p> |
| <p> |
| Other Boost.Math functions and templates may also be specialized or overloaded |
| to ensure interoperability. |
| </p> |
| <h5> |
| <a name="boost_multiprecision.ref.number.h11"></a> |
| <span class="phrase"><a name="boost_multiprecision.ref.number.std_numeric_limits_support"></a></span><a class="link" href="number.html#boost_multiprecision.ref.number.std_numeric_limits_support">std::numeric_limits |
| support</a> |
| </h5> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">{</span> |
| |
| <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> |
| <span class="keyword">struct</span> <span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special"><</span><span class="identifier">Backend</span><span class="special">,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="special">></span> |
| <span class="special">{</span> |
| <span class="comment">/* Usual members here */</span> |
| <span class="special">};</span> |
| |
| <span class="special">}</span> |
| </pre> |
| <p> |
| Class template <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code> is specialized for all instantiations |
| of <code class="computeroutput"><span class="identifier">number</span></code> whose precision |
| is known at compile time, plus those types whose precision is unlimited (though |
| it is much less useful in those cases). It is not specialized for types whose |
| precision can vary at compile time (such as <code class="computeroutput"><span class="identifier">mpf_float</span></code>). |
| </p> |
| </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 © 2002-2013 John Maddock and Christopher Kormanyos<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> |
| <hr> |
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