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improved TOC and chunking. This is complicated by the fact we that we desire different depths. put copies of boost logo in subdirectories
272 lines
7.2 KiB
XML
272 lines
7.2 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.safe_numeric_concept">
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<title>SafeNumeric<T></title>
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<?dbhtml stop-chunking?>
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<section>
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<title>Description</title>
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<para>This holds an arithmetic value which can be used as a replacement
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for built-in C++ arithmetic values. These types differ from their built-in
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counter parts in that the are guaranteed not to produce invalid arithmetic
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results.</para>
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</section>
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<section>
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<title>Refinement of</title>
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<para><link linkend="safe_numerics.numeric">Numeric</link></para>
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</section>
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<section>
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<title>Notation</title>
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<informaltable>
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<tgroup cols="2">
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<colspec align="left" colwidth="2*"/>
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<colspec align="left" colwidth="10*"/>
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<thead>
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<row>
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<entry align="left">Symbol</entry>
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<entry align="left">Description</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>Types fulfilling <link
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linkend="safe_numerics.numeric">Numeric</link> type
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requirements</entry>
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</row>
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<row>
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<entry>t, u</entry>
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<entry>objects of types T, U</entry>
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</row>
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<row>
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<entry>S, S1, S2</entry>
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<entry>A type fulfilling SafeNumeric type requirements</entry>
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</row>
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<row>
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<entry>s, s1, s2</entry>
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<entry>objects of types S</entry>
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</row>
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<row>
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<entry>op</entry>
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<entry>C++ infix operator</entry>
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</row>
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<row>
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<entry>prefix_op</entry>
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<entry>C++ prefix operator</entry>
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</row>
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<row>
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<entry>postfix_op</entry>
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<entry>C++ postfix operator</entry>
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</row>
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<row>
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<entry>assign_op</entry>
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<entry>C++ assignment operator</entry>
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</row>
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</tbody>
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</tgroup>
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</informaltable>
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</section>
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<section>
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<title>Valid Expressions</title>
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<para><informaltable>
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<tgroup cols="3">
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<colspec align="left" colwidth="2*"/>
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<colspec align="left" colwidth="2*"/>
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<colspec align="left" colwidth="8*"/>
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<thead>
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<row>
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<entry align="left">Expression</entry>
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<entry align="left">Result Type</entry>
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<entry>Description</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>s op t</code></entry>
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<entry>unspecified S</entry>
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<entry><para>invoke safe C++ operator op and return another
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SafeNumeric type.</para></entry>
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</row>
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<row>
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<entry><code>t op s</code></entry>
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<entry>unspecified S</entry>
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<entry><para>invoke safe C++ operator op and return another
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SafeNumeric type.</para></entry>
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</row>
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<row>
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<entry><code>s1 op s2</code></entry>
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<entry>unspecified S</entry>
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<entry><para>invoke safe C++ operator op and return another
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SafeNumeric type.</para></entry>
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</row>
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<row>
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<entry><code>prefix_op S</code></entry>
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<entry>unspecified S</entry>
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<entry><para>invoke safe C++ operator op and return another
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SafeNumeric type.</para></entry>
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</row>
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<row>
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<entry><code>S postfix_op</code></entry>
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<entry>unspecified S</entry>
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<entry><para>invoke safe C++ operator op and return another
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SafeNumeric type.</para></entry>
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</row>
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<row>
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<entry><code>s assign_op t</code></entry>
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<entry>S1</entry>
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<entry><para>convert t to type S1 and assign it to s1. If the
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value t cannot be represented as an instance of type S1, it is
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an error.</para></entry>
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</row>
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<row>
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<entry><code>S(t)</code></entry>
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<entry>unspecified S</entry>
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<entry><para>construct a instance of S from a value of type T. f
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the value t cannot be represented as an instance of type S1, it
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is an error.</para></entry>
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</row>
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<row>
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<entry><code>S</code></entry>
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<entry>S</entry>
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<entry><para>construct a uninitialized instance of
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S.</para></entry>
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</row>
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<row>
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<entry><code>is_safe<S></code></entry>
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<entry><code>std::true_type</code> or
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<code>std::false_type</code></entry>
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<entry><para>type trait to query whether any type T fulfills the
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requirements for a SafeNumeric type.</para></entry>
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</row>
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<row>
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<entry><code>static_cast<T>(s)</code></entry>
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<entry>T</entry>
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<entry><para>convert the value of s to type T. If the value of s
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cannot be correctly represented as a type T, it is an
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error.</para></entry>
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</row>
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</tbody>
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</tgroup>
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</informaltable></para>
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<itemizedlist>
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<listitem>
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<para>Result of any binary operation where one or both of the operands
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is a SafeNumeric type is also a SafeNumeric type.</para>
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</listitem>
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<listitem>
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<para>All the expressions in the above table are
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<code>constexpr</code> expressions</para>
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</listitem>
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<listitem>
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<para>Binary expressions which are not assignments require that
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promotion and exception policies be identical.</para>
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</listitem>
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</itemizedlist>
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</section>
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<section>
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<title>Complexity Guarantees</title>
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<para>There are no explicit complexity guarantees here. However, it would
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be very surprising if any implementation were to be more complex that
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O(0);</para>
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</section>
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<section>
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<title>Invariants</title>
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<para>The fundamental requirement of a SafeNumeric type is that implements
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all C++ operations permitted on it's base type in a way the prevents the
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return of an incorrect arithmetic result. Various implementations of this
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concept may handle circumstances which produce such results differently (
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throw exception, compile time trap, etc..) no implementation should return
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an arithmetically incorrect result.</para>
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</section>
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<section>
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<title>Header</title>
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<para><ulink
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url="../../include/concept/exception_policy.hpp"><code>#include
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<safe_numerics/include/concepts/safe_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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<para>safe<T></para>
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<para>safe_signed_range<-11, 11></para>
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<para>safe_unsigned_range<0, 11></para>
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<para>safe_literal<4></para>
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</section>
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</section>
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