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<td><h2>Safe Numerics</h2></td>
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<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="safe_numerics.safe"></a>safe&lt;T, PP, EP&gt;</h3></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="safe.html#idm130203562112">Description</a></span></dt>
<dt><span class="section"><a href="safe.html#idm130203560112">Model of</a></span></dt>
<dt><span class="section"><a href="safe.html#idm130203556080">Notation</a></span></dt>
<dt><span class="section"><a href="safe.html#idm130203548784">Associated Types</a></span></dt>
<dt><span class="section"><a href="safe.html#idm130203541744">Template Parameters</a></span></dt>
<dt><span class="section"><a href="safe.html#idm130203523280">Valid Expressions</a></span></dt>
<dt><span class="section"><a href="safe.html#idm130203517392">Examples of use</a></span></dt>
<dt><span class="section"><a href="safe.html#idm130203247744">Header</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203562112"></a>Description</h4></div></div></div>
<p>A <code class="computeroutput">safe&lt;T, PP , EP&gt;</code> can be used anywhere a type T
can be used. Any expression which uses this type is guaranteed to return
an arithmetically correct value or to trap in some way.</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203560112"></a>Model of</h4></div></div></div>
<p><a class="link" href="numeric.html" title="Numeric&lt;T&gt;">Integer</a></p>
<p><a class="link" href="safe_numeric_concept.html" title="SafeNumeric&lt;T&gt;">SafeNumeric</a></p>
<p>This type inherits all the notation, associated types and template
parameters and valid expressions of <a class="link" href="safe_numeric_concept.html" title="SafeNumeric&lt;T&gt;">SafeNumeric</a> types. The
following specify additional features of this type.</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203556080"></a>Notation</h4></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col align="left">
<col align="left">
</colgroup>
<thead><tr>
<th align="left">Symbol</th>
<th align="left">Description</th>
</tr></thead>
<tbody><tr>
<td align="left"><code class="computeroutput">T</code></td>
<td align="left">Underlying type from which a safe type is being
derived</td>
</tr></tbody>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203548784"></a>Associated Types</h4></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col align="left">
<col align="left">
</colgroup>
<tbody>
<tr>
<td align="left"><code class="computeroutput">PP</code></td>
<td align="left">A type which specifies the result type of an expression
using safe types.</td>
</tr>
<tr>
<td align="left"><code class="computeroutput">EP</code></td>
<td align="left">A type containing members which are called when a correct
result cannot be returned</td>
</tr>
</tbody>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203541744"></a>Template Parameters</h4></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col align="left">
<col align="left">
</colgroup>
<thead><tr>
<th align="left">Parameter</th>
<th align="left">Type Requirements</th>
<th align="left">Description</th>
</tr></thead>
<tbody>
<tr>
<td><code class="computeroutput">T</code></td>
<td align="left"><a href="http://en.cppreference.com/w/cpp/types/is_integral" target="_top">Integer&lt;T&gt;</a></td>
<td align="left"><p>The underlying type. Currently only integer types are
supported</p></td>
</tr>
<tr>
<td><code class="computeroutput">PP</code></td>
<td align="left"><a class="link" href="numeric.html" title="Numeric&lt;T&gt;">PromotionPolicy&lt;PP&gt;</a></td>
<td align="left"><p>Optional promotion policy. Default value is <a class="link" href="promotion_policies/native.html" title="native"><code class="computeroutput">boost::numeric::native</code></a></p></td>
</tr>
<tr>
<td><code class="computeroutput">EP</code></td>
<td align="left"><a class="link" href="numeric.html" title="Numeric&lt;T&gt;">Exception
Policy&lt;EP&gt;</a></td>
<td align="left"><p>Optional exception policy. Default value is <a class="link" href="exception_policies.html#safe_numerics.exception_policies.default_exception_policy"><code class="computeroutput">boost::numeric::default_exception_policy</code></a></p></td>
</tr>
</tbody>
</table></div>
<p>See examples below.</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203523280"></a>Valid Expressions</h4></div></div></div>
<p>Implements all expressions and only those expressions defined by the
<a class="link" href="safe_numeric_concept.html" title="SafeNumeric&lt;T&gt;">SafeNumeric</a>&lt;T&gt;
type requirements. Note that all these expressions are
<code class="computeroutput">constexpr</code>. Thus, 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.</p>
<p>When a binary operand is applied to two instances of safe&lt;T, PP,
EP&gt;on of the following must be true:</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem"><p>The promotion policies of the two operands must be the same or
one of them must be void</p></li>
<li class="listitem"><p>The exception policies of the two operands must be the same or
one of them must be void</p></li>
</ul></div>
<p>If either of the above is not true, a compile error will
result.</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203517392"></a>Examples of use</h4></div></div></div>
<p>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.</p>
<p>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 constituent types of the operation. Here we refer to these rules as
"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.</p>
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="safe_numerics.drop_in_replacement"></a>As a Drop-in replacement for standard integer types.</h5></div></div></div>
<p>The following program will throw an exception and emit an error
message at runtime if any of several events result in an incorrect
arithmetic result. Behavior of this program could vary according to the
machine architecture in question.</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">exception</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">safe_integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">void</span> <span class="identifier">f</span><span class="special">(</span><span class="special">)</span><span class="special">{</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">;</span>
<span class="identifier">safe</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">j</span><span class="special">;</span>
<span class="keyword">try</span> <span class="special">{</span>
<span class="identifier">safe</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">i</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span> <span class="special">&gt;&gt;</span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// could overflow !</span>
<span class="identifier">j</span> <span class="special">=</span> <span class="identifier">i</span> <span class="special">*</span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// could overflow</span>
<span class="special">}</span>
<span class="keyword">catch</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">exception</span> <span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span><span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">(</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="special">}</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">j</span><span class="special">;</span>
<span class="special">}</span></pre>
<p>The term "drop-in replacement" reveals the aspiration of
this library. In most cases, this aspiration is realized. In the
following example, the normal implicit conversions function the same for
safe integers as they do for built-in integers. </p>
<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">safe_numerics</span><span class="special">/</span><span class="identifier">safe_integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">safe_numerics</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">f</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">)</span><span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">i</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">using</span> <span class="identifier">safe_t</span> <span class="special">=</span> <span class="identifier">safe</span><span class="special">&lt;</span><span class="keyword">long</span><span class="special">&gt;</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="special">)</span><span class="special">{</span>
<span class="keyword">const</span> <span class="keyword">long</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">97</span><span class="special">;</span>
<span class="identifier">f</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span><span class="special">;</span> <span class="comment">// OK - implicit conversion to int</span>
<span class="keyword">const</span> <span class="identifier">safe_t</span> <span class="identifier">y</span> <span class="special">=</span> <span class="number">97</span><span class="special">;</span>
<span class="identifier">f</span><span class="special">(</span><span class="identifier">y</span><span class="special">)</span><span class="special">;</span> <span class="comment">// Also OK - checked implicit conversion to int</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span></pre>
<p>When
the <code class="computeroutput">safe&lt;long&gt;</code> is implicitly converted to an
<code class="computeroutput">int</code> when calling <code class="computeroutput">f</code>, the value is checked to be
sure that it is within the legal range of an int and will invoke an
exception if it cannot. We can easily verify this by altering the
exception handling policy in the above example to
<code class="computeroutput">loose_trap_policy</code>. This will invoke a compile time error on
any conversion might invoke a runtime exception.</p>
<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">safe_numerics</span><span class="special">/</span><span class="identifier">safe_integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">safe_numerics</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">f</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">)</span><span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">i</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">using</span> <span class="identifier">safe_t</span> <span class="special">=</span> <span class="identifier">safe</span><span class="special">&lt;</span><span class="keyword">long</span><span class="special">,</span> <span class="identifier">native</span><span class="special">,</span> <span class="identifier">loose_trap_policy</span><span class="special">&gt;</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="special">)</span><span class="special">{</span>
<span class="keyword">const</span> <span class="keyword">long</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">97</span><span class="special">;</span>
<span class="identifier">f</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span><span class="special">;</span> <span class="comment">// OK - implicit conversion to int</span>
<span class="keyword">const</span> <span class="identifier">safe_t</span> <span class="identifier">y</span> <span class="special">=</span> <span class="number">97</span><span class="special">;</span>
<span class="identifier">f</span><span class="special">(</span><span class="identifier">y</span><span class="special">)</span><span class="special">;</span> <span class="comment">// Would be OK, but will invoke compile time error</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span></pre>
<p>But this raises it's own questions. We can see that in this
example, the program can never fail:</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem"><p>The value 97 is assigned to y</p></li>
<li class="listitem"><p>y is converted to an int</p></li>
<li class="listitem"><p>and used as an argument to f</p></li>
</ul></div>
<p>The conversion can never fail because the value of 97 can always
fit into an int. But the library code can't detect this and emits the
checking code even though it's not necessary.</p>
<p>This can be addressed by using a <a class="link" href="safe_literal.html" title="safe_signed_literal&lt;Value, PP , EP&gt; and safe_unsigned_literal&lt;Value, PP, EP&gt;"><code class="computeroutput">safe_literal</code></a>. A
safe literal can contain one and only one value. All the functions in
this library are marked <code class="computeroutput">constexpr</code>. So it can be determined
at compile time that conversion to an <code class="computeroutput">int</code> can never fail
and no runtime checking code need be emitted. Making this small change
will permit the above example to run with zero runtime overhead while
guaranteeing that no error can ever occur.</p>
<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">safe_numerics</span><span class="special">/</span><span class="identifier">safe_integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">safe_numerics</span><span class="special">/</span><span class="identifier">safe_integer_literal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">safe_numerics</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">f</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">)</span><span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">i</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="identifier">intmax_t</span> <span class="identifier">N</span><span class="special">&gt;</span>
<span class="keyword">using</span> <span class="identifier">safe_literal</span> <span class="special">=</span> <span class="identifier">safe_signed_literal</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span> <span class="identifier">native</span><span class="special">,</span> <span class="identifier">loose_trap_policy</span><span class="special">&gt;</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="special">)</span><span class="special">{</span>
<span class="keyword">const</span> <span class="keyword">long</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">97</span><span class="special">;</span>
<span class="identifier">f</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span><span class="special">;</span> <span class="comment">// OK - implicit conversion to int</span>
<span class="keyword">const</span> <span class="identifier">safe_literal</span><span class="special">&lt;</span><span class="number">97</span><span class="special">&gt;</span> <span class="identifier">y</span><span class="special">;</span>
<span class="identifier">f</span><span class="special">(</span><span class="identifier">y</span><span class="special">)</span><span class="special">;</span> <span class="comment">// OK - y is a type with min/max = 97;</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span></pre>
<p>With this trivial example, such efforts would hardly be deemed
necessary. But in a more complex case, perhaps including compile time
arithmetic expressions, it could be much more difficult to verify that
the constant is valid and/or no checking code is needed. And there is
also possibility that over the life time of the application, the compile
time constants might change, thus rendering any ad hoc analyse obsolete.
Using <a class="link" href="safe_literal.html" title="safe_signed_literal&lt;Value, PP , EP&gt; and safe_unsigned_literal&lt;Value, PP, EP&gt;"><code class="computeroutput">safe_literal</code></a>
will future-proof your code against well-meaning, but code-breaking
updates.</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="idm130203320752"></a>Adjust type promotion rules.</h5></div></div></div>
<p>Another way to avoid arithmetic errors like overflow is to promote
types to larger sizes before doing the arithmetic.</p>
<p>Stepping back, we can see that many of the cases of invalid
arithmetic wouldn't exist if the result 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
promotion policy <code class="computeroutput"><code class="computeroutput">automatic</code></code>. The policy stores
the result of an expression in the smallest size type that can
accommodate the largest value that an expression can yield. No checking
for exceptions is necessary. The following example illustrates
this.</p>
<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">safe_numerics</span><span class="special">/</span><span class="identifier">safe_integer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="keyword">int</span><span class="special">,</span> <span class="keyword">char</span><span class="special">[</span><span class="special">]</span><span class="special">)</span><span class="special">{</span>
<span class="keyword">using</span> <span class="identifier">safe_int</span> <span class="special">=</span> <span class="identifier">safe</span><span class="special">&lt;</span>
<span class="keyword">int</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">automatic</span><span class="special">,</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">default_exception_policy</span>
<span class="special">&gt;</span><span class="special">;</span>
<span class="identifier">safe_int</span> <span class="identifier">i</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span> <span class="special">&gt;&gt;</span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// might throw exception</span>
<span class="keyword">auto</span> <span class="identifier">j</span> <span class="special">=</span> <span class="identifier">i</span> <span class="special">*</span> <span class="identifier">i</span><span class="special">;</span> <span class="comment">// won't ever trap - result type can hold the maximum value of i * i</span>
<span class="identifier">static_assert</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">is_safe</span><span class="special">&lt;</span><span class="keyword">decltype</span><span class="special">(</span><span class="identifier">j</span><span class="special">)</span><span class="special">&gt;</span><span class="special">::</span><span class="identifier">value</span><span class="special">)</span><span class="special">;</span> <span class="comment">// result is another safe type</span>
<span class="identifier">static_assert</span><span class="special">(</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">decltype</span><span class="special">(</span><span class="identifier">i</span> <span class="special">*</span> <span class="identifier">i</span><span class="special">)</span><span class="special">&gt;</span><span class="special">::</span><span class="identifier">max</span><span class="special">(</span><span class="special">)</span> <span class="special">&gt;=</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">safe_int</span><span class="special">&gt;</span><span class="special">::</span><span class="identifier">max</span><span class="special">(</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">safe_int</span><span class="special">&gt;</span><span class="special">::</span><span class="identifier">max</span><span class="special">(</span><span class="special">)</span>
<span class="special">)</span><span class="special">;</span> <span class="comment">// always true</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span></pre>
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<div class="titlepage"><div><div><h4 class="title">
<a name="idm130203247744"></a>Header</h4></div></div></div>
<p><code class="filename"><a href="../../include/safe_integer.hpp" target="_top">#include
&lt;boost/numeric/safe_numerics/safe_integer.hpp&gt;</a></code></p>
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<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
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