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  4. <title>Checked Arithmetic</title>
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  15. <td><h2>Safe Numerics</h2></td>
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  20. <div class="section">
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  21. <div class="titlepage"><div><div><h3 class="title">
    22. 

  22. <a name="safe_numerics.checked_arithmetic"></a>Checked Arithmetic</h3></div></div></div>
    23. 

  23. <div class="toc"><dl class="toc">
    24. 

  24. <dt><span class="section"><a href="checked_arithmetic.html#idm130202409440">Description</a></span></dt>
    25. 

  25. <dt><span class="section"><a href="checked_arithmetic.html#idm130202408112">Type requirements</a></span></dt>
    26. 

  26. <dt><span class="section"><a href="checked_arithmetic.html#idm130202406112">Complexity</a></span></dt>
    27. 

  27. <dt><span class="section"><a href="checked_arithmetic.html#idm130202404960">Example of use</a></span></dt>
    28. 

  28. <dt><span class="section"><a href="checked_arithmetic.html#idm130202387696">Notes</a></span></dt>
    29. 

  29. <dt><span class="section"><a href="checked_arithmetic.html#idm130202386128">Synopsis</a></span></dt>
    30. 

  30. <dt><span class="section"><a href="checked_arithmetic.html#idm130202157712">See Also</a></span></dt>
    31. 

  31. <dt><span class="section"><a href="checked_arithmetic.html#idm130202155984">Header</a></span></dt>
    32. 

  32. </dl></div>
    33. 

  33. <div class="section">
    34. 

  34. <div class="titlepage"><div><div><h4 class="title">
    35. 

  35. <a name="idm130202409440"></a>Description</h4></div></div></div>
    36. 

  36. <p>Perform binary operations on arithmetic types. Return either a valid
    37. 

  37.     result or an error code. Under no circumstances should an incorrect result
    38. 

  38.     be returned.</p>
    39. 

  39. </div>
    40. 

  40. <div class="section">
    41. 

  41. <div class="titlepage"><div><div><h4 class="title">
    42. 

  42. <a name="idm130202408112"></a>Type requirements</h4></div></div></div>
    43. 

  43. <p>All template parameters of the functions must model <a class="link" href="integer.html" title="Integer&lt;T&gt;">Numeric</a> type requirements.</p>
    44. 

  44. </div>
    45. 

  45. <div class="section">
    46. 

  46. <div class="titlepage"><div><div><h4 class="title">
    47. 

  47. <a name="idm130202406112"></a>Complexity</h4></div></div></div>
    48. 

  48. <p>Each function performs one and only one arithmetic operation.</p>
    49. 

  49. </div>
    50. 

  50. <div class="section">
    51. 

  51. <div class="titlepage"><div><div><h4 class="title">
    52. 

  52. <a name="idm130202404960"></a>Example of use</h4></div></div></div>
    53. 

  53. <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">safe_numerics</span><span class="special">/</span><span class="identifier">checked_default</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
    54. 

  54. 

  55. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">r</span> <span class="special">=</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">multiply</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;</span><span class="special">(</span><span class="number">24</span><span class="special">,</span> <span class="number">42</span><span class="special">)</span><span class="special">;</span>
    56. 

  56. </pre>
    57. 

  57. </div>
    58. 

  58. <div class="section">
    59. 

  59. <div class="titlepage"><div><div><h4 class="title">
    60. 

  60. <a name="idm130202387696"></a>Notes</h4></div></div></div>
    61. 

  61. <p>Some compilers have command line switches (e.g. -ftrapv) which
    62. 

  62.     enable special behavior such that erroneous integer operations are
    63. 

  63.     detected at run time. The library has been implemented in such a way that
    64. 

  64.     these facilities are not used. It's possible they might be helpful in
    65. 

  65.     particular environment. These could be be exploited by re-implementing
    66. 

  66.     some functions in this library.</p>
    67. 

  67. </div>
    68. 

  68. <div class="section">
    69. 

  69. <div class="titlepage"><div><div><h4 class="title">
    70. 

  70. <a name="idm130202386128"></a>Synopsis</h4></div></div></div>
    71. 

  71. <pre class="programlisting"><span class="comment">// safe casting on primitive types</span>
    72. 

  72. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
    73. 

  73. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">cast</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">)</span><span class="special">;</span>
    74. 

  74. 

  75. <span class="comment">// safe addition on primitive types</span>
    76. 

  76. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    77. 

  77. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    78. 

  78. 

  79. <span class="comment">// safe subtraction on primitive types</span>
    80. 

  80. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    81. 

  81. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">subtract</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    82. 

  82. 

  83. <span class="comment">// safe multiplication on primitive types</span>
    84. 

  84. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    85. 

  85. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">multiply</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    86. 

  86. 

  87. <span class="comment">// safe division on primitive types</span>
    88. 

  88. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    89. 

  89. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">divide</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    90. 

  90. 

  91. <span class="comment">// safe modulus on primitive types</span>
    92. 

  92. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    93. 

  93. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">modulus</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    94. 

  94. 

  95. <span class="comment">// safe less than predicate on primitive types</span>
    96. 

  96. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    97. 

  97. <span class="keyword">bool</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">less_than</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    98. 

  98. 

  99. <span class="comment">// safe greater_than_equal predicate on primitive types</span>
    100. 

  100. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    101. 

  101. <span class="keyword">bool</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">greater_than_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    102. 

  102. 

  103. <span class="comment">// safe greater_than predicate on primitive types</span>
    104. 

  104. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    105. 

  105. <span class="keyword">bool</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">greater_than</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    106. 

  106. 

  107. <span class="comment">// safe less_than_equal predicate on primitive types</span>
    108. 

  108. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    109. 

  109. <span class="keyword">bool</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">less_than_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    110. 

  110. 

  111. <span class="comment">// safe equal predicate on primitive types</span>
    112. 

  112. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    113. 

  113. <span class="keyword">bool</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    114. 

  114. 

  115. <span class="comment">// left shift</span>
    116. 

  116. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    117. 

  117. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">left_shift</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    118. 

  118. 

  119. <span class="comment">// right shift</span>
    120. 

  120. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    121. 

  121. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">right_shift</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    122. 

  122. 

  123. <span class="comment">// bitwise operations</span>
    124. 

  124. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    125. 

  125. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">bitwise_or</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    126. 

  126. 

  127. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    128. 

  128. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">bitwise_and</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    129. 

  129. 

  130. <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">R</span><span class="special">&gt;</span>
    131. 

  131. <span class="identifier">checked_result</span><span class="special">&lt;</span><span class="identifier">R</span><span class="special">&gt;</span> <span class="keyword">constexpr</span> <span class="identifier">checked</span><span class="special">::</span><span class="identifier">bitwise_xor</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">R</span> <span class="special">&amp;</span> <span class="identifier">u</span><span class="special">)</span><span class="special">;</span>
    132. 

  132. </pre>
    133. 

  133. </div>
    134. 

  134. <div class="section">
    135. 

  135. <div class="titlepage"><div><div><h4 class="title">
    136. 

  136. <a name="idm130202157712"></a>See Also</h4></div></div></div>
    137. 

  137. <p><a class="link" href="checked_result.html" title="checked_result&lt;R&gt;">checked_result&lt;R&gt;</a></p>
    138. 

  138. </div>
    139. 

  139. <div class="section">
    140. 

  140. <div class="titlepage"><div><div><h4 class="title">
    141. 

  141. <a name="idm130202155984"></a>Header</h4></div></div></div>
    142. 

  142. <p><a href="../../include/checked.hpp" target="_top"><code class="computeroutput">#include
    143. 

  143.     &lt;boost/numeric/safe_numerics/checked_default.hpp&gt;
    144. 

  144.     </code></a></p>
    145. 

  145. <p><a href="../../include/checked_integer.hpp" target="_top"><code class="computeroutput">#include
    146. 

  146.     &lt;boost/numeric/safe_numerics/checked_integer.hpp&gt;
    147. 

  147.     </code></a></p>
    148. 

  148. <p><a href="../../include/checked.hpp" target="_top"><code class="computeroutput"></code></a><a href="../../include/checked_float.hpp" target="_top"><code class="computeroutput">#include
    149. 

  149.     &lt;boost/numeric/safe_numerics/checked_float.hpp&gt;
    150. 

  150.     </code></a></p>
    151. 

  151. </div>
    152. 

  152. </div>
    153. 

  153. <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
    154. 

  154. <td align="left"></td>
    155. 

  155. <td align="right"><div class="copyright-footer">Copyright &#169; 2012-2018 Robert Ramey<p><a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">Subject to Boost
    156. 

  156.       Software License</a></p>
    157. 

  157. </div></td>
    158. 

  158. </tr></table>
    159. 

  159. <hr>
    160. 

  160. <div class="spirit-nav">
    161. 

  161. <a accesskey="p" href="checked_result.html"><img src="images/prev.png" alt="Prev"></a><a accesskey="u" href="library_implementation.html"><img src="images/up.png" alt="Up"></a><a accesskey="h" href="index.html"><img src="images/home.png" alt="Home"></a><a accesskey="n" href="interval.html"><img src="images/next.png" alt="Next"></a>
    162. 

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    163. 

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    164. 

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    165.