safe_numerics/doc/boostbook/safe.xml

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<section id="safe_numerics.safe">
  <title>safe&lt;T, PP, EP&gt;</title>

  <section>
    <title>Description</title>

    <para>A <code>safe&lt;T, PP, EP&gt;</code> can be used anywhere a type T
    can be used. Any expression which uses this type is guarenteed to return
    an arithmetically correct value or trap in some way.</para>
  </section>

  <section>
    <title>Notation</title>

    <informaltable>
      <tgroup cols="2">
        <colspec align="left" colwidth="1*"/>

        <colspec align="left" colwidth="10*"/>

        <thead>
          <row>
            <entry align="left">Symbol</entry>

            <entry align="left">Description</entry>
          </row>
        </thead>

        <tbody>
          <row>
            <entry><code>T</code></entry>

            <entry>Underlying type from which a safe type is being
            derived</entry>
          </row>
        </tbody>
      </tgroup>
    </informaltable>
  </section>

  <section>
    <title>Associated Types</title>

    <informaltable>
      <tgroup cols="2">
        <colspec align="left" colwidth="1*"/>

        <colspec align="left" colwidth="10*"/>

        <tbody>
          <row>
            <entry><code>PP</code></entry>

            <entry>A type which specifes the result type of an expression
            using safe types. </entry>
          </row>

          <row>
            <entry><code>EP</code></entry>

            <entry>A type containing members which are called when a correct
            result cannot be returned</entry>
          </row>
        </tbody>
      </tgroup>
    </informaltable>
  </section>

  <section>
    <title>Template Parameters</title>

    <informaltable>
      <tgroup cols="3">
        <colspec colwidth="1*"/>

        <colspec align="left" colwidth="3*"/>

        <colspec align="left" colwidth="7*"/>

        <thead>
          <row>
            <entry align="left">Parameter</entry>

            <entry align="left">Type Requirements</entry>

            <entry>Description</entry>
          </row>
        </thead>

        <tbody>
          <row>
            <entry><code>T</code></entry>

            <entry><ulink
            url="http://en.cppreference.com/w/cpp/types/is_integral">Integer&lt;T&gt;</ulink></entry>

            <entry><para>The underlying type. Currently only integer types
            supported</para></entry>
          </row>

          <row>
            <entry><code>PP</code></entry>

            <entry><link linkend="safe_numerics.numeric"><link
            linkend="safe_numerics.promotion_policy">PromotionPolicy&lt;PP&gt;</link></link></entry>

            <entry><para>Default value is <link
            linkend="safe_numerics.promotion_policy.models.native">boost::numeric::native</link></para></entry>
          </row>

          <row>
            <entry><code>EP</code></entry>

            <entry><link linkend="safe_numerics.numeric"><link
            linkend="safe_numerics.exception_policy">Exception
            Policy&lt;EP&gt;</link></link></entry>

            <entry><para>Default value is <link
            linkend="safe_numerics.exception_policy.models.thow_exception">boost::throw_exception</link></para></entry>
          </row>
        </tbody>
      </tgroup>
    </informaltable>

    <para>See examples below.</para>
  </section>

  <section>
    <title>Model of</title>

    <para><link linkend="safe_numerics.numeric">Integer</link></para>

    <para><link
    linkend="safe_numerics.safe_numeric_concept">SafeNumeric</link></para>
  </section>

  <section>
    <title>Valid Expressions</title>

    <para>Implements all expressions and only those expressions defined by the
    <link linkend="safe_numerics.safe_numeric_concept">SafeNumeric</link> type
    requirements. This, the result type of such an expression will be another
    safe type. The actual type of the result of such an expression will depend
    upon the specific promotion policy template parameter.</para>
  </section>

  <section>
    <title>Header</title>

    <para><filename><ulink url="../../include/safe_integer.hpp">#include
    &lt;boost/safe_numerics/safe_integer.hpp&gt;</ulink></filename></para>
  </section>

  <section>
    <title>Examples of use</title>

    <para>The most common usage would be safe&lt;T&gt; which uses the default
    promotion and exception policies. This type is meant to be a "drop-in"
    replacement of the intrinsic integer types. That is, expressions involving
    these types will be evaluated into result types which reflect the standard
    rules for evaluation of C++ expressions. Should it occur that such
    evaluation cannot return a correct result, an exception will be
    thrown.</para>

    <para>There are two aspects of the operation of this type which can be
    customized with a policy. The first is the result type of an arithmetic
    operation. C++ defines the rules which define this result type in terms of
    the constintuent types of the operation. Here we refer to these rules a
    "type promotion" rules. These rules will sometimes result in a type which
    cannot hold the actual arithmetic result of the operation. This is the
    main motivation for making this library in the first place. One way to
    deal with this problem is to substitute our own type promotion rules for
    the C++ ones.</para>

    <section>
      <title>Drop-in replacement for standard integer type.</title>

      <para>The following program will throw an exception and emit a error
      message at runtime if any of several events result in an incorrect
      arithmetic type. Behavior of this program could vary according to the
      machine architecture in question.</para>

      <para><programlisting>#include &lt;iostream&gt;
#include &lt;stdexcept&gt; // std::runtime_error
#include &lt;boost/numeric/safe.hpp&gt;

void f(){
    safe&lt;int&gt; j;
    try {
        safe&lt;int&gt; i;
        std::cin &gt;&gt; i;  // could overflow !
        j = i * i;      // could overflow
    }
    catch(std::runtime_error &amp; re){
       std::cout &lt;&lt; re.what() &lt;&lt; std::endl;
    }
    std::cout &lt;&lt; j;
}</programlisting></para>
    </section>

    <section>
      <title>Guarantee correct behavior at compile time.</title>

      <para>In some instance catching an error at run time is not sufficient.
      We want to be sure that the program can never fail. To achieve this, use
      the trap_exception exception policy rather than the default throw
      exception policy.</para>

      <para>The following program will emit a compile error at any statement
      which might possibly result in incorrect behavior. </para>

      <para>This is because there is no way to guarantee that the expression i
      * i will return an arithmetically correct result. Since we know that the
      program cannot compile if there is any possibility of arithmetic error,
      we can dispense with the exception handling used above.</para>

      <para><programlisting>#include &lt;boost/numeric/safe.hpp&gt;
#include &lt;iostream&gt;
void f(){
    using safe_int = safe&lt;int, boost::numeric::native, boost::numeric::trap_exception&gt;t; 
    safe_int i;
    std::cin &gt;&gt; i;  // could throw exception here !!!
    safe_int j;
    j = i * i; // could throw exception here !!!
}</programlisting></para>
    </section>

    <section>
      <title>Adjust type promotion rules.</title>

      <para>Another way to avoid arithmetic errors like overflow is to promote
      types to larger sizes before doing the arithmetic. This can be justified
      by the observ</para>

      <para>Stepping back, we can see that many of the cases of invalid
      arithmetic are wouldn't exist if results types were larger. So we can
      avoid these problems by replacing the C++ type promotion rules for
      expressions with our own rules. This can be done by specifying a
      non-default type promotion policy automatic. The policy stores the
      result of an expression in the smallest size that can accomodate the
      largest value that an expression can yield. All the work is done at
      compile time - checking for exceptions necessary (input is of course an
      exception). The following example illustrates this.</para>

      <para><programlisting>#include &lt;boost/numeric/safe.hpp&gt;
#include &lt;iostream&gt;
void f(){
    using safe_int = safe&lt;int, boost::numeric::automatic, boost::numeric::throw_exception&gt;; 
    safe_int i;
    std::cin &gt;&gt; i; // might throw exception
    auto j = i * i; // won't ever trap - result type can hold the maximum value of i * i
    static_assert(boost::numeric::is_safe&lt;decltype(j)&gt;::value); // result is another safe type
    static_assert(
        std::numeric_limits&lt;decltype(i * i)&gt;::max() &gt;=
        std::numeric_limits&lt;safe_int&gt;::max() * std::numeric_limits&lt;safe_int&gt;::max()
    ); // always true
}</programlisting></para>
    </section>
  </section>
</section>