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https://github.com/boostorg/safe_numerics.git
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461 lines
10 KiB
XML
461 lines
10 KiB
XML
<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE section PUBLIC "-//Boost//DTD BoostBook XML V1.1//EN"
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"http://www.boost.org/tools/boostbook/dtd/boostbook.dtd">
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<section id="safe_numerics.numeric">
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<title>Numeric<T></title>
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<section>
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<title>Description</title>
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<para>A type is Numeric if it has the properties of a number.</para>
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<para>More specifically, a type T is Numeric if there exists
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specialization of <code>std::numeric_limits<T></code>. See the
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documentation for standard library class numeric_limits. The standard
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library includes such specializations for all the primitive numeric types.
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Note that this concept is distinct from the C++ standard library type
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traits <code>is_integral</code> and <code>is_arithmetic</code>. These
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latter fullfill the requirement of the concept Numeric. But there are
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types T which fullfill this concept for which
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<code>is_arithmetic<T>::value == false</code>. For example see
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<code>safe_signed_integer<int></code>.</para>
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</section>
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<section>
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<title>Notation</title>
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<table colsep="0" frame="all" rowsep="0">
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<title>Notation</title>
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<tgroup cols="2" colsep="1" rowsep="1">
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<colspec align="left"/>
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<colspec align="left" colwidth="3*"/>
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<tbody>
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<row>
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<entry><code>T, U, V</code></entry>
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<entry>A type that is a model of the Numeric</entry>
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</row>
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<row>
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<entry><code>t, u, v</code></entry>
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<entry>An object of type modeling Numeric</entry>
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</row>
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</tbody>
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</tgroup>
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</table>
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</section>
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<section>
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<title>Associated Types</title>
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<table>
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<title>Associated Types</title>
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<tgroup cols="2">
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<colspec align="left"/>
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<colspec align="left" colwidth="3*"/>
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<tbody>
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<row>
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<entry><code>std::numeric_limits<T></code></entry>
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<entry>The numeric_limits class template provides a C++ program
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with information about various properties of the implementation’s
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representation of the arithmetic types. See C++ standard
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18.3.2.2.</entry>
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</row>
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</tbody>
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</tgroup>
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</table>
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</section>
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<section>
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<title>Valid Expressions</title>
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<para>In addition to the expressions defined in <ulink
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url="http://www.sgi.com/tech/stl/Assignable.html">Assignable</ulink> the
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following expressions must be valid.</para>
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<para>Any operations which result in integers which cannot be represented
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as some Numeric type will throw an exception.<table>
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<title>General</title>
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<tgroup cols="2">
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<colspec align="left"/>
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<colspec align="left"/>
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<thead>
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<row>
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<entry align="left">Expression</entry>
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<entry>Return Value</entry>
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</row>
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</thead>
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<tbody>
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<row>
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<entry><code>std::numeric_limits<T>.is_bounded
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</code></entry>
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<entry>true</entry>
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</row>
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<row>
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<entry><code>std::numeric_limits<T>.is_integer</code></entry>
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<entry>true</entry>
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</row>
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<row>
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<entry><code>std::numeric_limits<T>.is_specialized
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</code></entry>
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<entry>true</entry>
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</row>
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</tbody>
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</tgroup>
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</table></para>
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<table>
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<title>Unary Operators</title>
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<tgroup cols="3">
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<colspec align="left"/>
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<colspec align="left"/>
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<colspec align="left" colwidth="3*"/>
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<thead>
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<row>
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<entry align="left">Expression</entry>
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<entry>Return Type</entry>
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<entry>Semantics</entry>
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</row>
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</thead>
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<tbody>
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<row>
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<entry><code>-t</code></entry>
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<entry>T</entry>
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<entry>Invert sign</entry>
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</row>
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<row>
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<entry><code>+t</code></entry>
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<entry>T</entry>
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<entry>unary plus - a no op</entry>
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</row>
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<row>
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<entry><code>t--</code></entry>
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<entry>T</entry>
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<entry>post decrement</entry>
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</row>
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<row>
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<entry><code>t++</code></entry>
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<entry>T</entry>
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<entry>post increment</entry>
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</row>
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<row>
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<entry><code>--t</code></entry>
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<entry>T</entry>
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<entry>predecrement</entry>
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</row>
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<row>
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<entry><code>++t</code></entry>
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<entry>T</entry>
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<entry>preincrement</entry>
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</row>
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<row>
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<entry><code>~</code></entry>
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<entry>T</entry>
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<entry>complement</entry>
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</row>
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</tbody>
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</tgroup>
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</table>
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<table>
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<title>Binary Operators</title>
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<tgroup cols="3">
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<colspec align="left"/>
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<colspec align="left"/>
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<colspec align="left" colwidth="3*"/>
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<thead>
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<row>
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<entry align="left">Expression</entry>
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<entry>Return Type</entry>
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<entry>Semantics</entry>
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</row>
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</thead>
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<tbody>
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<row>
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<entry><code>t - u</code></entry>
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<entry>V</entry>
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<entry>Invert sign</entry>
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</row>
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<row>
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<entry><code>t + u</code></entry>
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<entry>V</entry>
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<entry>unary plus - a no op</entry>
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</row>
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<row>
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<entry><code>t * u</code></entry>
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<entry>V</entry>
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<entry>multiply t by u</entry>
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</row>
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<row>
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<entry><code>t / u</code></entry>
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<entry>T</entry>
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<entry>divide t by u</entry>
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</row>
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<row>
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<entry><code>t % u</code></entry>
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<entry>T</entry>
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<entry>t modulus u</entry>
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</row>
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<row>
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<entry><code>t << u</code></entry>
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<entry>T</entry>
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<entry>shift t left u bits</entry>
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</row>
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<row>
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<entry><code>t >> u</code></entry>
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<entry>T</entry>
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<entry>shift t right by ubits</entry>
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</row>
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<row>
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<entry><code>t < u</code></entry>
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<entry>bool</entry>
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<entry>true if t less than u, false otherwise</entry>
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</row>
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<row>
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<entry><code>t <= u</code></entry>
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<entry>bool</entry>
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<entry>true if t less than or equal to u, false otherwise</entry>
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</row>
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<row>
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<entry><code>t > u</code></entry>
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<entry>bool</entry>
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<entry>true if t greater than u, false otherwise</entry>
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</row>
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<row>
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<entry><code>t >= u</code></entry>
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<entry>bool</entry>
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<entry>true if t greathan or equal to u, false otherwise</entry>
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</row>
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<row>
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<entry><code>t == u</code></entry>
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<entry>bool</entry>
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<entry>true if t equal to u, false otherwise</entry>
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</row>
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<row>
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<entry><code>t != u</code></entry>
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<entry>bool</entry>
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<entry>true if t not equal to u, false otherwise</entry>
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</row>
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<row>
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<entry><code>t & u</code></entry>
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<entry>V</entry>
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<entry>and of t and u padded out max # bits in t, u</entry>
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</row>
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<row>
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<entry><code>t | u</code></entry>
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<entry>V</entry>
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<entry>or of t and u padded out max # bits in t, u</entry>
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</row>
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<row>
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<entry><code>t ^ u</code></entry>
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<entry>V</entry>
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<entry>exclusive or of t and u padded out max # bits in t,
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u</entry>
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</row>
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<row>
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<entry><code>t = u</code></entry>
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<entry><code>T</code></entry>
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<entry>assign value of u to t</entry>
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</row>
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<row>
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<entry><code>t += u</code></entry>
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<entry><code>T</code></entry>
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<entry>add u to t and assign to t</entry>
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</row>
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<row>
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<entry><code>t -= u</code></entry>
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<entry><code>T</code></entry>
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<entry>subtract u from t and assign to t</entry>
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</row>
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<row>
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<entry><code>t *= u</code></entry>
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<entry><code>T</code></entry>
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<entry>multiply t by u and assign to t</entry>
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</row>
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<row>
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<entry><code>t /= u</code></entry>
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<entry><code>T</code></entry>
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<entry>divide t by u and assign to t</entry>
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</row>
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<row>
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<entry><code>t &= u</code></entry>
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<entry><code>T</code></entry>
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<entry>and t with u and assign to t</entry>
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</row>
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<row>
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<entry><code>t <<= u</code></entry>
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<entry>T</entry>
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<entry>left shift the value of t by u bits</entry>
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</row>
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<row>
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<entry><code>t >>= u</code></entry>
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<entry>T</entry>
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<entry>right shift the value of t by u bits</entry>
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</row>
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<row>
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<entry><code>t &= u</code></entry>
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<entry>T</entry>
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<entry>and the value of t with u and assign to t</entry>
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</row>
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<row>
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<entry><code>t |= u</code></entry>
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<entry>T</entry>
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<entry>or the value of t with u and assign to t</entry>
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</row>
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<row>
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<entry><code>t ^= u</code></entry>
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<entry>T</entry>
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<entry>exclusive or the value of t with u and assign to t</entry>
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</row>
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</tbody>
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</tgroup>
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</table>
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</section>
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<section>
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<title>Header</title>
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<para><ulink url="../../include/concept/numeric.hpp"><code>#include
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<safe_numerics/include/concepts/numeric.hpp> </code></ulink></para>
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</section>
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<section>
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<title>Models</title>
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|
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<para><code>int, safe_signed_integer<int>,
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safe_signed_range<int>, etc.</code></para>
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</section>
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</section>
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