mirror of
https://github.com/boostorg/safe_numerics.git
synced 2026-02-22 03:32:24 +00:00
63dd89210e
improved TOC and chunking. This is complicated by the fact we that we desire different depths. put copies of boost logo in subdirectories
336 lines
8.8 KiB
XML
336 lines
8.8 KiB
XML
<?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.interval">
|
|
<title>interval<typename R></title>
|
|
|
|
<?dbhtml stop-chunking?>
|
|
|
|
<section>
|
|
<title>Description</title>
|
|
|
|
<para>A closed arithmetic interval represented by a pair of elements of
|
|
type R.</para>
|
|
</section>
|
|
|
|
<section>
|
|
<title>Template Parameters</title>
|
|
|
|
<para>R must model the type requirements <link
|
|
linkend="safe_numerics.numeric">Numeric</link></para>
|
|
</section>
|
|
|
|
<section>
|
|
<title>Notation</title>
|
|
|
|
<informaltable>
|
|
<tgroup cols="2">
|
|
<colspec align="left" colwidth="1*"/>
|
|
|
|
<colspec align="left" colwidth="4*"/>
|
|
|
|
<thead>
|
|
<row>
|
|
<entry align="left">Symbol</entry>
|
|
|
|
<entry align="left">Description</entry>
|
|
</row>
|
|
</thead>
|
|
|
|
<tbody>
|
|
<row>
|
|
<entry><code>I</code></entry>
|
|
|
|
<entry>An interval type</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>i, j</code></entry>
|
|
|
|
<entry>An interval</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>R, T</code></entry>
|
|
|
|
<entry>Numeric types which can be used to make an interval</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>l, u</code></entry>
|
|
|
|
<entry>lower and upper Numeric limits of an interval</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>checked_result<interval<R>></entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>os</code></entry>
|
|
|
|
<entry>std::basic_ostream<Char, CharT></entry>
|
|
</row>
|
|
</tbody>
|
|
</tgroup>
|
|
</informaltable>
|
|
</section>
|
|
|
|
<section>
|
|
<title>Associated Types</title>
|
|
|
|
<informaltable>
|
|
<tgroup cols="2">
|
|
<colspec align="left" colwidth="1*"/>
|
|
|
|
<colspec align="left" colwidth="4*"/>
|
|
|
|
<tbody>
|
|
<row>
|
|
<entry><link
|
|
linkend="safenumerics.checked_result"><code>checked_result</code></link></entry>
|
|
|
|
<entry>holds either the result of an operation or information as
|
|
to why it failed</entry>
|
|
</row>
|
|
</tbody>
|
|
</tgroup>
|
|
</informaltable>
|
|
</section>
|
|
|
|
<section>
|
|
<title>Valid Expressions</title>
|
|
|
|
<para>Note that all expressions are constexpr .</para>
|
|
|
|
<para><informaltable>
|
|
<tgroup cols="3">
|
|
<colspec align="left" colwidth="1*"/>
|
|
|
|
<colspec align="left" colwidth="1*"/>
|
|
|
|
<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>interval<R>(l, u)</code></entry>
|
|
|
|
<entry><code>interval<R></code></entry>
|
|
|
|
<entry>construct a new interval from a pair of limits</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>interval<R>(p)</code></entry>
|
|
|
|
<entry><code>interval<R></code></entry>
|
|
|
|
<entry>construct a new interval from a pair of limits</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>interval<R>(i)</code></entry>
|
|
|
|
<entry><code>interval<R></code></entry>
|
|
|
|
<entry>copy constructor</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>i.includes(j)</code></entry>
|
|
|
|
<entry><code>bool</code></entry>
|
|
|
|
<entry>return true if interval i includes interval j</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>i.includes(t)</code></entry>
|
|
|
|
<entry><code>bool</code></entry>
|
|
|
|
<entry>return true if interval i includes value t</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>add<R>(i, j)</code></entry>
|
|
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>add two intervals and return the result</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>subtract<R>(i, j)</code></entry>
|
|
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>subtract two intervals and return the result</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>multiply<R>(i, j)</code></entry>
|
|
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>multiply two intervals and return the result</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>divide_nz<R>(i, j)</code></entry>
|
|
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>divide one interval by another excluding the value zero
|
|
and return the result</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>divide<R>(i, j)</code></entry>
|
|
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>divide one interval by another and return the
|
|
result</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>modulus_nz<R>(i, j)</code></entry>
|
|
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>calculate modulus of one interval by another excluding
|
|
the value zero and return the result</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>modulus<R>(i, j)</code></entry>
|
|
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>calculate modulus of one interval by another and return
|
|
the result</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>left_shift<R>(i, j)</code></entry>
|
|
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>calculate the range that would result from shifting one
|
|
interval by another</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>right_shift<R>(i, j)</code></entry>
|
|
|
|
<entry><code>C</code></entry>
|
|
|
|
<entry>calculate the range that would result from shifting one
|
|
interval by another</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>t < u</code></entry>
|
|
|
|
<entry><code>boost::logic::tribool</code></entry>
|
|
|
|
<entry>true if every element in t is less than every element in
|
|
u</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>t > u</code></entry>
|
|
|
|
<entry><code>boost::logic::tribool</code></entry>
|
|
|
|
<entry>true if every element in t is greater than every element
|
|
in u</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>t <= u</code></entry>
|
|
|
|
<entry><code>boost::logic::tribool</code></entry>
|
|
|
|
<entry>true if every element in t is less than or equal to every
|
|
element in u</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>t >= u</code></entry>
|
|
|
|
<entry><code>boost::logic::tribool</code></entry>
|
|
|
|
<entry>true if every element in t is greater than or equal to
|
|
every element in u</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>t == u</code></entry>
|
|
|
|
<entry><code>bool</code></entry>
|
|
|
|
<entry>true if limits are equal</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>t != u</code></entry>
|
|
|
|
<entry><code>bool</code></entry>
|
|
|
|
<entry>true if limits are not equal</entry>
|
|
</row>
|
|
|
|
<row>
|
|
<entry><code>os << i</code></entry>
|
|
|
|
<entry><code>os &</code></entry>
|
|
|
|
<entry>print interval to output stream</entry>
|
|
</row>
|
|
</tbody>
|
|
</tgroup>
|
|
</informaltable></para>
|
|
</section>
|
|
|
|
<section>
|
|
<title>Header</title>
|
|
|
|
<para><code>#include "interval.hpp"</code></para>
|
|
</section>
|
|
|
|
<section>
|
|
<title>Example of use</title>
|
|
|
|
<programlisting>#include <iostream>
|
|
#include <cstdint>
|
|
#include <cassert>
|
|
#include <boost/numeric/interval.hpp>
|
|
|
|
int main(){
|
|
std::cout << "test1" << std::endl;
|
|
interval<std::int16_t> x = {-64, 63};
|
|
std::cout << "x = " << x << std::endl;
|
|
interval<std::int16_t> y(-128, 126);
|
|
std::cout << "y = " << y << std::endl;
|
|
assert(static_cast<interval<std::int16_t>>(add<std::int16_t>(x,x)) == y);
|
|
std::cout << "x + x =" << add<std::int16_t>(x, x) << std::endl;
|
|
std::cout << "x - x = " << subtract<std::int16_t>(x, x) << std::endl;
|
|
return 0;
|
|
}</programlisting>
|
|
</section>
|
|
</section>
|