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Robert Ramey 12f5843f90 Fixed problems in testing addition operations 
More carefully defined the concepts.  That is the concept of the library is now clear:

Trap at either compile or runtime integer operations which yield a result which differs from the normal arithmetic result.

Pending on this check in:
a) only addition is fixed up so far
b) uses BOOST_TYPEOF... rather than decltype(... - final decision sill pending.
c) comments out some compile time checks which should be re-instated.
d) fixed tests so that they actually work!
2014-04-05 12:22:25 -07:00

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