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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="boost_multiprecision.ref.number"></a><a class="link" href="number.html" title="number">number</a>
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<a name="boost_multiprecision.ref.number.h0"></a>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="keyword">class</span> <span class="identifier">number</span>
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<span class="special">{</span>
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<span class="keyword">public</span><span class="special">:</span>
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<span class="keyword">typedef</span> <span class="identifier">Backend</span> <span class="identifier">backend_type</span><span class="special">;</span>
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<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">component_type</span><span class="special"><</span><span class="identifier">self_type</span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">value_type</span><span class="special">;</span>
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<span class="identifier">number</span><span class="special">();</span>
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<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>
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<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>
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<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>
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<span class="comment">// Member operators</span>
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<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>
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<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>
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<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>
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<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>
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<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">++();</span>
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<span class="identifier">number</span><span class="special">&</span> <span class="keyword">operator</span><span class="special">--();</span>
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<span class="identifier">number</span> <span class="keyword">operator</span><span class="special">++(</span><span class="keyword">int</span><span class="special">);</span>
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<span class="identifier">number</span> <span class="keyword">operator</span><span class="special">--(</span><span class="keyword">int</span><span class="special">);</span>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="comment">// Use in Boolean context:</span>
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<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>
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<span class="comment">// swap:</span>
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<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>
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<span class="comment">// Sign:</span>
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<span class="keyword">bool</span> <span class="identifier">is_zero</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">int</span> <span class="identifier">sign</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
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<span class="comment">// string conversion:</span>
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<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>
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<span class="comment">// Generic conversion mechanism</span>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
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<span class="identifier">T</span> <span class="identifier">convert_to</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
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<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>
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<span class="comment">// precision control:</span>
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<span class="keyword">static</span> <span class="keyword">unsigned</span> <span class="identifier">default_precision</span><span class="special">();</span>
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<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>
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<span class="keyword">unsigned</span> <span class="identifier">precision</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
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<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>
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<span class="comment">// Comparison:</span>
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<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>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">V</span><span class="special">></span>
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<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>
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<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>
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<span class="comment">// real and imaginary parts:</span>
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<span class="identifier">value_type</span> <span class="identifier">real</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
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<span class="identifier">value_type</span> <span class="identifier">imag</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
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<span class="keyword">void</span> <span class="identifier">real</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">val</span><span class="special">);</span>
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<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span>
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<span class="keyword">void</span> <span class="identifier">imag</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">val</span><span class="special">);</span>
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<span class="comment">// Access to the underlying implementation:</span>
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<span class="identifier">Backend</span><span class="special">&</span> <span class="identifier">backend</span><span class="special">();</span>
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<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>
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<span class="special">};</span>
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<span class="comment">// Non member operators:</span>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="comment">// Integer only operations:</span>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="comment">// Comparison operators:</span>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="comment">// Swap:</span>
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<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>
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<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>
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<span class="comment">// iostream support:</span>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="comment">// Arithmetic with a higher precision result:</span>
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<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">// min and max overloads:</span>
|
|
<span class="emphasis"><em>number</em></span> <span class="identifier">min</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>number</em></span> <span class="identifier">max</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="comment">// C99 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">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>number</em></span> <span class="identifier">acosh</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>number</em></span> <span class="identifier">asinh</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">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>number</em></span> <span class="identifier">atanh</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>number</em></span> <span class="identifier">cbrt</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>number</em></span> <span class="identifier">copysign</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">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">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>number</em></span> <span class="identifier">erf</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>number</em></span> <span class="identifier">erfc</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>
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|
<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">exp2</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>
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|
<span class="emphasis"><em>number</em></span> <span class="identifier">expm1</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>
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|
<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">fdim</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>
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|
<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>
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|
<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fma</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="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&);</span>
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|
<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fmin</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>
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|
<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">fmax</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>
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|
<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>
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|
<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>
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|
<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">hypot</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>
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|
<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>
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<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>
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<span class="emphasis"><em>number</em></span> <span class="identifier">lgamma</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>
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<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">llrint</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>
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<span class="keyword">long</span> <span class="keyword">long</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>
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<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>
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<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">log2</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>
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<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>
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<span class="emphasis"><em>number</em></span> <span class="identifier">log1p</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>
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<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>
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<span class="keyword">long</span> <span class="identifier">lrint</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>
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<span class="keyword">long</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>
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<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">modf</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>
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<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">nearbyint</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>
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<span class="emphasis"><em>number</em></span> <span class="identifier">nextafter</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>
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<span class="emphasis"><em>number</em></span> <span class="identifier">nexttoward</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>
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<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>
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<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">remainder</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>
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<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">remquo</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="keyword">int</span><span class="special">*);</span>
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<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">rint</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>
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<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>
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<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>
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<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">scalbln</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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="emphasis"><em>number</em></span> <span class="identifier">tgamma</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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="keyword">int</span> <span class="identifier">signbit</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>
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<span class="keyword">bool</span> <span class="identifier">isgreater</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>
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<span class="keyword">bool</span> <span class="identifier">isgreaterequal</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>
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<span class="keyword">bool</span> <span class="identifier">isless</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>
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<span class="keyword">bool</span> <span class="identifier">islessequal</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>
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<span class="keyword">bool</span> <span class="identifier">islessgreater</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>
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<span class="keyword">bool</span> <span class="identifier">isunordered</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>
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<span class="comment">// Complex number functions:</span>
|
|
<span class="emphasis"><em>number<...>::value_type</em></span> <span class="identifier">real</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>number<...>::value_type</em></span> <span class="identifier">imag</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>number<...>::value_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>number<...>::value_type</em></span> <span class="identifier">arg</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>number<...>::value_type</em></span> <span class="identifier">norm</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>number</em></span> <span class="identifier">conj</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>number</em></span> <span class="identifier">proj</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>number</em></span> <span class="identifier">polar</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="comment">// Misc other common C library functions:</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">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>number</em></span> <span class="identifier">changesign</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>number</em></span> <span class="identifier">copysign</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="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>
|
|
<p>
|
|
Finally, when the type has a variable precision, then there are constructors:
|
|
</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">precision</span><span class="special">);</span>
|
|
<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> <span class="identifier">precision</span><span class="special">);</span>
|
|
</pre>
|
|
<p>
|
|
Where <code class="computeroutput"><span class="identifier">precision</span></code> is an unsigned
|
|
value, the 2 arg version is active for scalar types and/or copy-construction
|
|
with specific precision, and the 3-arg version for complex types.
|
|
</p>
|
|
<p>
|
|
Likewise <code class="computeroutput"><span class="identifier">assign</span></code> has a 2-arg
|
|
overloaded, with the second argument being the precision.
|
|
</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">value_type</span> <span class="identifier">real</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
|
<span class="identifier">value_type</span> <span class="identifier">imag</span><span class="special">()</span><span class="keyword">const</span><span class="special">;</span>
|
|
</pre>
|
|
</li>
|
|
</ul></div>
|
|
<p>
|
|
These return the real and imaginary parts respectively. If the number is
|
|
not a complex type, then the imaginary part is always zero.
|
|
</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">void</span> <span class="identifier">real</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">val</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">void</span> <span class="identifier">imag</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&</span> <span class="identifier">val</span><span class="special">);</span>
|
|
</pre>
|
|
<p>
|
|
These set the real and imaginary parts respectively of the number. If the
|
|
number is not a complex type, then setting the real part is equivalent to
|
|
assignment, and attempting to set the imaginary part will result in a compile
|
|
time error.
|
|
</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>
|
|
<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">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>number</em></span> <span class="identifier">acosh</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>number</em></span> <span class="identifier">asinh</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">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>number</em></span> <span class="identifier">atanh</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>number</em></span> <span class="identifier">cbrt</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>number</em></span> <span class="identifier">copysign</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">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">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>number</em></span> <span class="identifier">erf</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>number</em></span> <span class="identifier">erfc</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">exp2</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>number</em></span> <span class="identifier">expm1</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">fdim</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">fma</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="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">fmin</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">fmax</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">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">hypot</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>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="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>number</em></span> <span class="identifier">lgamma</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">long</span> <span class="keyword">long</span> <span class="identifier">llrint</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">long</span> <span class="keyword">long</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">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">log2</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>number</em></span> <span class="identifier">log1p</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">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="keyword">long</span> <span class="identifier">lrint</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">long</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">modf</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">nearbyint</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>number</em></span> <span class="identifier">nextafter</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>number</em></span> <span class="identifier">nexttoward</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">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">remainder</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">remquo</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="keyword">int</span><span class="special">*);</span>
|
|
<span class="emphasis"><em>unmentionable-expression-template-type</em></span> <span class="identifier">rint</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">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">scalbln</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">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">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">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">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">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>number</em></span> <span class="identifier">tgamma</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="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">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">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">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">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="identifier">signbit</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">bool</span> <span class="identifier">isgreater</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="keyword">bool</span> <span class="identifier">isgreaterequal</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="keyword">bool</span> <span class="identifier">isless</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="keyword">bool</span> <span class="identifier">islessequal</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="keyword">bool</span> <span class="identifier">islessgreater</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="keyword">bool</span> <span class="identifier">isunordered</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>
|
|
</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 unless otherwise stated.
|
|
</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>
|
|
Complex number types support the following functions:
|
|
</p>
|
|
<pre class="programlisting"><span class="comment">// Complex number functions:</span>
|
|
<span class="emphasis"><em>number<...>::value_type</em></span> <span class="identifier">real</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>number<...>::value_type</em></span> <span class="identifier">imag</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>number<...>::value_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>number<...>::value_type</em></span> <span class="identifier">arg</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>number<...>::value_type</em></span> <span class="identifier">norm</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>number</em></span> <span class="identifier">conj</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>number</em></span> <span class="identifier">proj</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>number</em></span> <span class="identifier">polar</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>
|
|
</pre>
|
|
<p>
|
|
In addition the functions <code class="computeroutput"><span class="identifier">real</span></code>,
|
|
<code class="computeroutput"><span class="identifier">imag</span></code>, <code class="computeroutput"><span class="identifier">arg</span></code>,
|
|
<code class="computeroutput"><span class="identifier">norm</span></code>, <code class="computeroutput"><span class="identifier">conj</span></code>
|
|
and <code class="computeroutput"><span class="identifier">proj</span></code> are overloaded for
|
|
scalar (ie non-complex) types in the same manner as <code class="computeroutput"><span class="special"><</span><span class="identifier">complex</span><span class="special">></span></code>
|
|
and treat the argument as a value whose imaginary part is zero.
|
|
</p>
|
|
<p>
|
|
There are also some functions implemented for compatibility with the Boost.Math
|
|
functions of the same name:
|
|
</p>
|
|
<pre class="programlisting"><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">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>number</em></span> <span class="identifier">changesign</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>number</em></span> <span class="identifier">copysign</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>
|
|
</pre>
|
|
<p>
|
|
All 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" name="boost_multiprecision.ref.number.f0"><sup class="footnote">[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 © 2002-2019 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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