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diff --git a/src/boost/libs/rational/CMakeLists.txt b/src/boost/libs/rational/CMakeLists.txt new file mode 100644 index 000000000..f4b66bd27 --- /dev/null +++ b/src/boost/libs/rational/CMakeLists.txt @@ -0,0 +1,33 @@ +# Copyright 2019 Mike Dev +# Distributed under the Boost Software License, Version 1.0. +# See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt +# +# NOTE: CMake support for Boost.Rational is currently experimental at best +# and the interface is likely to change in the future + +cmake_minimum_required( VERSION 3.5 ) +project( BoostRational LANGUAGES CXX) +option( BOOST_RATIONAL_INCLUDE_TESTS "Add boost rational tests" OFF ) + +add_library( boost_rational INTERFACE ) +add_library( Boost::rational ALIAS boost_rational ) + +target_include_directories( boost_rational INTERFACE include ) + +target_link_libraries( boost_rational + INTERFACE + Boost::assert + Boost::config + Boost::core + Boost::integer + Boost::static_assert + Boost::throw_exception + Boost::type_traits + Boost::utility +) + +if( BOOST_RATIONAL_INCLUDE_TESTS ) + enable_testing() + add_subdirectory( test ) +endif() + diff --git a/src/boost/libs/rational/Jamfile b/src/boost/libs/rational/Jamfile new file mode 100644 index 000000000..facdaeec8 --- /dev/null +++ b/src/boost/libs/rational/Jamfile @@ -0,0 +1,10 @@ +# Boost.Rational Library Jamfile +# +# Copyright (c) 2018 James E. King III +# +# Use, modification, and distribution are subject to the +# Boost Software License, Version 1.0. (See accompanying file +# LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +# please order by name to ease maintenance +build-project test ; diff --git a/src/boost/libs/rational/LICENSE b/src/boost/libs/rational/LICENSE new file mode 100644 index 000000000..36b7cd93c --- /dev/null +++ b/src/boost/libs/rational/LICENSE @@ -0,0 +1,23 @@ +Boost Software License - Version 1.0 - August 17th, 2003 + +Permission is hereby granted, free of charge, to any person or organization +obtaining a copy of the software and accompanying documentation covered by +this license (the "Software") to use, reproduce, display, distribute, +execute, and transmit the Software, and to prepare derivative works of the +Software, and to permit third-parties to whom the Software is furnished to +do so, all subject to the following: + +The copyright notices in the Software and this entire statement, including +the above license grant, this restriction and the following disclaimer, +must be included in all copies of the Software, in whole or in part, and +all derivative works of the Software, unless such copies or derivative +works are solely in the form of machine-executable object code generated by +a source language processor. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT +SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE +FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, +ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER +DEALINGS IN THE SOFTWARE. diff --git a/src/boost/libs/rational/README.md b/src/boost/libs/rational/README.md new file mode 100644 index 000000000..ed1608c2b --- /dev/null +++ b/src/boost/libs/rational/README.md @@ -0,0 +1,32 @@ +Rational, part of collection of the [Boost C++ Libraries](http://github.com/boostorg), provides an implementation of rational numbers. + +### License + +Distributed under the [Boost Software License, Version 1.0](http://www.boost.org/LICENSE_1_0.txt). + +### Properties + +* C++03 +* Header-Only + +### Build Status + +Branch | Travis | Appveyor | Coverity Scan | codecov.io | Deps | Docs | Tests | +:-------------: | ------ | -------- | ------------- | ---------- | ---- | ---- | ----- | +[`master`](https://github.com/boostorg/rational/tree/master) | [](https://travis-ci.org/boostorg/rational) | [](https://ci.appveyor.com/project/jeking3/rational-lqu73/branch/master) | [](https://scan.coverity.com/projects/boostorg-rational) | [](https://codecov.io/gh/boostorg/rational/branch/master)| [](https://pdimov.github.io/boostdep-report/master/rational.html) | [](http://www.boost.org/doc/libs/master/doc/html/rational.html) | [](http://www.boost.org/development/tests/master/developer/rational.html) +[`develop`](https://github.com/boostorg/rational/tree/develop) | [](https://travis-ci.org/boostorg/rational) | [](https://ci.appveyor.com/project/jeking3/rational-lqu73/branch/develop) | [](https://scan.coverity.com/projects/boostorg-rational) | [](https://codecov.io/gh/boostorg/rational/branch/develop) | [](https://pdimov.github.io/boostdep-report/develop/rational.html) | [](http://www.boost.org/doc/libs/develop/doc/html/rational.html) | [](http://www.boost.org/development/tests/develop/developer/rational.html) + +### Directories + +| Name | Purpose | +| ----------- | ------------------------------ | +| `include` | header | +| `test` | unit tests | + +### More information + +* [Ask questions](http://stackoverflow.com/questions/ask?tags=c%2B%2B,boost,boost-rational) +* [Report bugs](https://github.com/boostorg/rational/issues): Be sure to mention Boost version, platform and compiler you're using. A small compilable code sample to reproduce the problem is always good as well. +* Submit your patches as pull requests against **develop** branch. Note that by submitting patches you agree to license your modifications under the [Boost Software License, Version 1.0](http://www.boost.org/LICENSE_1_0.txt). +* Discussions about the library are held on the [Boost developers mailing list](http://www.boost.org/community/groups.html#main). Be sure to read the [discussion policy](http://www.boost.org/community/policy.html) before posting and add the `[rational]` tag at the beginning of the subject line. + diff --git a/src/boost/libs/rational/index.html b/src/boost/libs/rational/index.html new file mode 100644 index 000000000..3f3d676e8 --- /dev/null +++ b/src/boost/libs/rational/index.html @@ -0,0 +1,47 @@ +<html> + +<head> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<title>Boost Rational Number Library</title> +</head> + +<body bgcolor="#FFFFFF" text="#000000"> + +<table border="1" bgcolor="#007F7F" cellpadding="2"> + <tr> + <td bgcolor="#FFFFFF"><img src="../../boost.png" alt="boost.png (6897 bytes)" WIDTH="277" HEIGHT="86"></td> + <td><a href="../../index.htm"><font face="Arial" color="#FFFFFF"><big>Home </big></font></a></td> + <td><a href="../libraries.htm"><font face="Arial" color="#FFFFFF"><big>Libraries </big></font></a></td> + <td><a href="http://www.boost.org/people/people.htm"><font face="Arial" color="#FFFFFF"><big>People </big></font></a></td> + <td><a href="http://www.boost.org/more/faq.htm"><font face="Arial" color="#FFFFFF"><big>FAQ </big></font></a></td> + <td><a href="../../more/index.htm"><font face="Arial" color="#FFFFFF"><big>More </big></font></a></td> + </tr> +</table> + +<h1>Rational Number library</h1> + +<p>The header rational.hpp provides an implementation of rational numbers. +The implementation is template-based, in a similar manner to the standard +complex number class.</p> + +<p>This implementation is intended for general use. If you are a number +theorist, or otherwise have very stringent requirements, you would be advised +to use one of the more specialist packages available.</p> + +<ul> + <li><a href="rational.html">Documentation</a> (HTML).</li> + <li>Header <a href="../../boost/rational.hpp">rational.hpp</a>.</li> + <li>See the <a href="rational.html">documentation</a> for links to sample programs.</li> + <li>Submitted by <a href="http://www.boost.org/people/paul_moore.htm"> Paul Moore</a>.</li> +</ul> + +<p>Revised December 14, 1999</p> + +<p>© Copyright Paul Moore 1999. Permission to copy, use, modify, sell +and distribute this document is granted provided this copyright notice +appears in all copies. This document is provided "as is" without +express or implied warranty, and with no claim as to its suitability for +any purpose.</p> +<!-- boostinspect:nolicense (can't find Paul Moore to change license) --> +</body> +</html> diff --git a/src/boost/libs/rational/meta/libraries.json b/src/boost/libs/rational/meta/libraries.json new file mode 100644 index 000000000..471b24297 --- /dev/null +++ b/src/boost/libs/rational/meta/libraries.json @@ -0,0 +1,14 @@ +{ + "key": "rational", + "name": "Rational", + "authors": [ + "Paul Moore" + ], + "description": "A rational number class.", + "category": [ + "Math" + ], + "maintainers": [ + "Jonathan Turkanis <turkanis -at- coderage.com>" + ] +} diff --git a/src/boost/libs/rational/rational.html b/src/boost/libs/rational/rational.html new file mode 100644 index 000000000..ebacab7f4 --- /dev/null +++ b/src/boost/libs/rational/rational.html @@ -0,0 +1,768 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<title>Rational Number Library</title> +</head> +<body> +<h1><img src="../../boost.png" alt="boost.png (6897 bytes)" + align="middle" width="277" height="86"> +Rational Numbers</h1> + +<h2><a name="Contents">Contents</a></h2> + +<ol> + <li><a href="#Class%20rational%20synopsis">Class rational synopsis</a></li> + <li><a href="#Rationale">Rationale</a></li> + <li><a href="#Background">Background</a></li> + <li><a href="#Integer%20Type%20Requirements">Integer Type Requirements</a></li> + <li><a href="#Interface">Interface</a> + <ul> + <li><a href="#Utility%20functions">Utility functions</a></li> + <li><a href="#Constructors">Constructors</a></li> + <li><a href="#Arithmetic%20operations">Arithmetic operations</a></li> + <li><a href="#Input%20and%20Output">Input and Output</a></li> + <li><a href="#In-place%20assignment">In-place assignment</a></li> + <li><a href="#Conversions">Conversions</a></li> + <li><a href="#Numerator%20and%20Denominator">Numerator and Denominator</a></li> + </ul></li> + <li><a href="#Performance">Performance</a></li> + <li><a href="#Exceptions">Exceptions</a></li> + <li><a href="#Internal%20representation">Internal representation</a></li> + <li><a href="#Design%20notes">Design notes</a> + <ul> + <li><a href="#Minimal%20Implementation">Minimal Implementation</a></li> + <li><a href="#Limited-range%20integer%20types">Limited-range integer types</a></li> + <li><a href="#Conversion%20from%20floating%20point">Conversion from floating point</a></li> + <li><a href="#Absolute%20Value">Absolute Value</a></li> + </ul></li> + <li><a href="#References">References</a></li> + <li><a href="#History%20and%20Acknowledgements">History and Acknowledgements</a></li> +</ol> + +<h2><a name="Class rational synopsis">Class rational synopsis</a></h2> +<pre> +#include <boost/rational.hpp> + +namespace boost { + +class bad_rational; + +template<typename I> class rational { + typedef <em>implementation-defined</em> bool_type; + +public: + typedef I int_type; + + // Constructors + rational(); // Zero; constexpr since C++11 + rational(I n); // Equal to n/1; constexpr since C++11 + rational(I n, I d); // General case (n/d); constexpr since C++14 + template<typename J> + explicit rational(const rational<J> &r); // Cross-instantiation; constexpr since C++11 + + // Normal copy constructors and assignment operators + + // Assignment from I + rational& operator=(I n); // constexpr since C++14 + + // Assign in place + rational& assign(I n, I d); // constexpr since C++14 + + // Representation + I numerator() const; // constexpr since C++11 + I denominator() const; // constexpr since C++11 + + // In addition to the following operators, all of the "obvious" derived + // operators are available - see <a href="../utility/operators.htm">operators.hpp</a> + + // Arithmetic operators + rational& operator+= (const rational& r); // constexpr since C++14 + rational& operator-= (const rational& r); // constexpr since C++14 + rational& operator*= (const rational& r); // constexpr since C++14 + rational& operator/= (const rational& r); // constexpr since C++14 + + // Arithmetic with integers + rational& operator+= (I i); // constexpr since C++14 + rational& operator-= (I i); // constexpr since C++14 + rational& operator*= (I i); // constexpr since C++14 + rational& operator/= (I i); // constexpr since C++14 + + // Increment and decrement + const rational& operator++(); // constexpr since C++14 + const rational& operator--(); // constexpr since C++14 + + // Operator not + bool operator!() const; // constexpr since C++11 + + // Boolean conversion + operator bool_type() const; // constexpr since C++11 + + // Comparison operators + bool operator< (const rational& r) const; // constexpr since C++14 + bool operator== (const rational& r) const; // constexpr since C++11 + + // Comparison with integers + bool operator< (I i) const; // constexpr since C++14 + bool operator> (I i) const; // constexpr since C++14 + bool operator== (I i) const; // constexpr since C++11 +}; + +// Unary operators +template <typename I> rational<I> operator+ (const rational<I>& r); // constexpr since C++11 +template <typename I> rational<I> operator- (const rational<I>& r); // constexpr since C++14 + +// Reversed order operators for - and / between (types convertible to) I and rational +template <typename I, typename II> inline rational<I> operator- (II i, const rational<I>& r); // constexpr since C++14 +template <typename I, typename II> inline rational<I> operator/ (II i, const rational<I>& r); // constexpr since C++14 + +// Absolute value +template <typename I> rational<I> abs (const rational<I>& r); // constexpr since C++14 + +// Input and output +template <typename I> std::istream& operator>> (std::istream& is, rational<I>& r); +template <typename I> std::ostream& operator<< (std::ostream& os, const rational<I>& r); + +// Type conversion +template <typename T, typename I> T rational_cast (const rational<I>& r); // constexpr since C++11 +</pre> + +<h2><a name="Rationale">Rationale</a></h2> + +Numbers come in many different forms. The most basic forms are natural numbers +(non-negative "whole" numbers), integers and real numbers. These types are +approximated by the C++ built-in types <b>unsigned int</b>, <b>int</b>, and +<b>float</b> (and their various equivalents in different sizes). + +<p>The C++ Standard Library extends the range of numeric types available by +providing the <b>complex</b> type. + +<p>This library provides a further numeric type, the <b>rational</b> numbers. + +<p>The <b>rational</b> class is actually a implemented as a template, in a +similar manner to the standard <b>complex</b> class. + +<h2><a name="Background">Background</a></h2> + +The mathematical concept of a rational number is what is commonly thought of +as a fraction - that is, a number which can be represented as the ratio of two +integers. This concept is distinct from that of a real number, which can take +on many more values (for example, the square root of 2, which cannot be +represented as a fraction). + +<p> +Computers cannot represent mathematical concepts exactly - there are always +compromises to be made. Machine integers have a limited range of values (often +32 bits), and machine approximations to reals are limited in precision. The +compromises have differing motivations - machine integers allow exact +calculation, but with a limited range, whereas machine reals allow a much +greater range, but at the expense of exactness. + +<p> +The rational number class provides an alternative compromise. Calculations +with rationals are exact, but there are limitations on the available range. To +be precise, rational numbers are exact as long as the numerator and +denominator (which are always held in normalized form, with no common factors) +are within the range of the underlying integer type. When values go outside +these bounds, overflow occurs and the results are undefined. + +<p> +The rational number class is a template to allow the programmer to control the +overflow behaviour somewhat. If an unlimited precision integer type is +available, rational numbers based on it will never overflow (modulo resource +limits) and will provide exact calculations in all circumstances. + +<h2><a name="Integer Type Requirements">Integer Type Requirements</a></h2> + +<p> The rational type takes a single template type parameter I. This is the +<em>underlying integer type</em> for the rational type. Any of the built-in +integer types provided by the C++ implementation are supported as values for +I. User-defined types may also be used, but users should be aware that the +performance characteristics of the rational class are highly dependent upon +the performance characteristics of the underlying integer type (often in +complex ways - for specific notes, see the <a href="#Performance">Performance</a> +section below). Note: Should the boost library support an unlimited-precision +integer type in the future, this type will be fully supported as the underlying +integer type for the rational class. +</p> + +<p> +A user-defined integer type which is to be used as the underlying integer type +for the rational type must be a model of the following concepts. +</p> + +<ul> +<li>Assignable +<li>Default Constructible +<li>Equality Comparable +<li>LessThan Comparable +</ul> + +<p> +Furthermore, I must be an <em>integer-like</em> type, that is the following +expressions must be valid for any two values n and m of type I, with the +"expected" semantics. + +<ul> +<li><code>n + m</code> +<li><code>n - m</code> +<li><code>n * m</code> +<li><code>n / m</code> (must truncate; must be nonnegative if <var>n</var> and + <var>m</var> are positive) +<li><code>n % m</code> (must be nonnegative if <var>n</var> and <var>m</var> + are positive) +<li>Assignment versions of the above +<li><code>+n</code>, <code>-n</code> +<li><code>!n</code> (must be <code>true</code> iff <var>n</var> is zero) +</ul> + +<p> +There must be <em>zero</em> and <em>one</em> values available for I. It should +be possible to generate these as <tt>I(0)</tt> and <tt>I(1)</tt>, +respectively. <em>Note:</em> This does not imply that I needs to have an +implicit conversion from integer - an <tt>explicit</tt> constructor is +adequate. + +<p> +It is valid for I to be an unsigned type. In that case, the derived rational +class will also be unsigned. Underflow behaviour of subtraction, where results +would otherwise be negative, is unpredictable in this case. + +<ul> +<li> +The implementation of rational_cast<T>(rational<I>) relies on the +ability to static_cast from type I to type T, and on the expression x/y being +valid for any two values of type T. +<li> +The input and output operators rely on the existence of corresponding input +and output operators for type I. +</ul> + +<p> +The <code>std::numeric_limits<I></code> specialization must exist (and be +visible before <code>boost::rational<I></code> needs to be specified). +The value of its <code>is_specialized</code> static data member must be +<var>true</var> and the value of its <code>is_signed</code> static data member +must be accurate. + +<h2><a name="Interface">Interface</a></h2> + +<h3><a name="Utility functions">Utility functions</a></h3> + +<p>Two utility function templates may be provided, that should work with <a +href="#Integer%20Type%20Requirements">any type that can be used</a> with the +<code>boost::rational<></code> class template.</p> + +<table summary="Common-factor utility functions"> +<tr> +<td width=5%></td> +<td><tt>gcd(n, m)</tt></td> +<td width=5%></td> +<td>The greatest common divisor of n and m</td> +</tr> +<tr> +<td width=5%></td> +<td><tt>lcm(n, m)</tt></td> +<td width=5%></td> +<td>The least common multiple of n and m</td> +</tr> +</table> + +<p>These function templates now forward calls to their equivalents in the <a +href="../integer/">Boost.Integer library</a>. Their presence can be controlled at +compile time with the <code>BOOST_CONTROL_RATIONAL_HAS_GCD</code> preprocessor +constant. + +<h3><a name="Constructors">Constructors</a></h3> +<p>Rationals can be constructed from zero, one, or two integer arguments; +representing default construction as zero, conversion from an integer posing as +the numerator with an implicit denominator of one, or a numerator and +denominator pair in that order, respectively. An integer argument should be of +the rational's integer type, or implicitly convertible to that type. (For the +two-argument constructor, any needed conversions are evaluated independently, +of course.) The components are stored in normalized form. + +<p>Rationals can also be constructed from another rational. When the source and +destination underlying integer types match, the automatically-defined copy- or +move-constructor is used. Otherwise, a converting constructor template is used. +The constructor does member-wise initialization of the numerator and denominator. +Component-level conversions that are marked <code>explicit</code> are fine. When +the conversion ends up value-preserving, it is already normalized; but a check +for normalization is performed in case value-preservation is violated. + +<p>These imply that the following statements are valid: + +<pre> + I n, d; + rational<I> zero; + rational<I> r1(n); + rational<I> r2(n, d); + rational<J> r3(r2); // assuming J(n) and J(d) are well-formed +</pre> + +<p>In C++11, the no-argument constructor, single-argument constructor, and +cross-version constructor template are marked as <code>constexpr</code>, making +them viable in constant-expressions when the initializers (if any) are also constant +expressions (and the necessary operations from the underlying integer type(s) +are <code>constexpr</code>-enabled). Since C++14, all constructors are +<code>constexpr</code>-enabled. + +<p>The single-argument constructor is <em>not</em> declared as explicit, so +there is an implicit conversion from the underlying integer type to the +rational type. The two-argument constructor can be considered an implicit +conversion with C++11's uniform initialization syntax, since it is also not +declared explicit. The cross-version constructor template is declared explicit, +so the direction of conversion between two rational instantiations must be +specified. + +<h3><a name="Arithmetic operations">Arithmetic operations</a></h3> +All of the standard numeric operators are defined for the <b>rational</b> +class. These include: +<br> + +<pre> + + += + - -= + * *= + / /= + ++ -- (both prefix and postfix) + == != + < > + <= >= + + Unary: + - ! +</pre> + +<p>Since C++14, all of these operations are <code>constexpr</code>-enabled. +In C++11, only <code>operator==</code>, <code>operator!=</code>, +unary <code>operator+</code>, and <code>operator!</code> are. + +<h3><a name="Input and Output">Input and Output</a></h3> +Input and output operators <tt><<</tt> and <tt>>></tt> +are provided. The external representation of a rational is +two integers, separated by a slash (<tt>/</tt>). On input, the format must be +exactly an integer, followed with no intervening whitespace by a slash, +followed (again with no intervening whitespace) by a second integer. The +external representation of an integer is defined by the underlying integer +type. + +<h3><a name="In-place assignment">In-place assignment</a></h3> +For any <tt>rational<I> r</tt>, <tt>r.assign(n, m)</tt> provides an +alternate to <tt>r = rational<I>(n, m);</tt>, without a user-specified +construction of a temporary. While this is probably unnecessary for rationals +based on machine integer types, it could offer a saving for rationals based on +unlimited-precision integers, for example. + +<p>The function will throw if the given components cannot be formed into a valid +rational number. Otherwise, it could throw only if the component-level move +assignment (in C++11; copy-assignment for earlier C++ versions) can throw. The +strong guarantee is kept if throwing happens in the first part, but there is a +risk of neither the strong nor basic guarantees happening if an exception is +thrown during the component assignments. + +<h3><a name="Conversions">Conversions</a></h3> +<p>There is a conversion operator to an unspecified Boolean type (most likely a +member pointer). This operator converts a rational to <code>false</code> if it +represents zero, and <code>true</code> otherwise. This conversion allows a +rational for use as the first argument of operator <code>?:</code>; as either +argument of operators <code>&&</code> or <code>||</code> without +forfeiting short-circuit evaluation; as a condition for a <code>do</code>, +<code>if</code>, <code>while</code>, or <code>for</code> statement; and as a +conditional declaration for <code>if</code>, <code>while</code>, or +<code>for</code> statements. The nature of the type used, and that any names +for that nature are kept private, should prevent any inappropriate non-Boolean +use like numeric or pointer operations or as a <code>switch</code> condition. + +<p>There are <em>no other</em> implicit conversions from a rational +type. Besides the explicit cross-version constructor template, there is an +explicit type-conversion function, <tt>rational_cast<T>(r)</tt>. This can +be used as follows: + +<pre> + rational<int> r(22,7); + double nearly_pi = boost::rational_cast<double>(r); +</pre> + +<p>The <tt>rational_cast<T></tt> function's behaviour is undefined if the +source rational's numerator or denominator cannot be safely cast to the +appropriate floating point type, or if the division of the numerator and +denominator (in the target floating point type) does not evaluate correctly. +Also, since this function has a custom name, it cannot be called in generic code +for trading between two instantiations of the same class template, unlike the +cross-version constructor. + +<p>In essence, all required conversions should be value-preserving, and all +operations should behave "sensibly". If these constraints cannot be met, a +separate user-defined conversion will be more appropriate. + +<p>Boolean conversion and <tt>rational_cast</tt> are <code>constexpr</code>-enabled. + +<p><em>Implementation note:</em> + +<p>The implementation of the rational_cast function was + +<pre> + template <typename Float, typename Int> + Float rational_cast(const rational<Int>& src) + { + return static_cast<Float>(src.numerator()) / src.denominator(); + } +</pre> + +Programs should not be written to depend upon this implementation, however, +especially since this implementation is now obsolete. (It required a mixed-mode +division between types <var>Float</var> and <var>Int</var>, contrary to the <a +href="#Integer%20Type%20Requirements">Integer Type Requirements</a>.) + +<h3><a name="Numerator and Denominator">Numerator and Denominator</a></h3> +Finally, access to the internal representation of rationals is provided by +the two member functions <tt>numerator()</tt> and <tt>denominator()</tt>. +These functions are <code>constexpr</code>-enabled. + +<p>These functions allow user code to implement any additional required +functionality. In particular, it should be noted that there may be cases where +the above rational_cast operation is inappropriate - particularly in cases +where the rational type is based on an unlimited-precision integer type. In +this case, a specially-written user-defined conversion to floating point will +be more appropriate. + +<h2><a name="Performance">Performance</a></h2> +The rational class has been designed with the implicit assumption that the +underlying integer type will act "like" the built in integer types. The +behavioural aspects of this assumption have been explicitly described above, +in the <a href="#Integer%20Type%20Requirements">Integer Type Requirements</a> +section. However, in addition to behavioural assumptions, there are implicit +performance assumptions. + +<p> No attempt will be made to provide detailed performance guarantees for the +operations available on the rational class. While it is possible for such +guarantees to be provided (in a similar manner to the performance +specifications of many of the standard library classes) it is by no means +clear that such guarantees will be of significant value to users of the +rational class. Instead, this section will provide a general discussion of the +performance characteristics of the rational class. + +<p>There now follows a list of the fundamental operations defined in the +<a href="../../boost/rational.hpp"> <boost/rational.hpp></a> header +and an informal description of their performance characteristics. Note that +these descriptions are based on the current implementation, and as such should +be considered subject to change. + +<ul> +<li>Construction of a rational is essentially just two constructions of the +underlying integer type, plus a normalization. + +<li>Increment and decrement operations are essentially as cheap as addition and +subtraction on the underlying integer type. + +<li>(In)equality comparison is essentially as cheap as two equality operations +on the underlying integer type. + +<li>I/O operations are not cheap, but their performance is essentially +dominated by the I/O time itself. + +<li>An (implicit) GCD routine call is essentially a repeated modulus operation. +Its other significant operations are construction, assignment, and comparison +against zero of IntType values. These latter operations are assumed to be +trivial in comparison with the modulus operation. + +<li>The (implicit) LCM operation is essentially a GCD plus a multiplication, +division, and comparison. + +<li>The addition and subtraction operations are complex. They will require +approximately two gcd operations, 3 divisions, 3 multiplications and an +addition on the underlying integer type. + +<li>The multiplication and division operations require two gcd operations, two +multiplications, and four divisions. + +<li>The compare-with-integer operation does a single integer division & +modulus pair, at most one extra integer addition and decrement, and at most +three integer comparisons. + +<li>The compare-with-rational operation does two double-sized GCD operations, +two extra additions and decrements, and three comparisons in the worst case. +(The GCD operations are double-sized because they are done in piecemeal and the +interim quotients are retained and compared, whereas a direct GCD function only +retains and compares the remainders.) + +<li>The final fundamental operation is normalizing a rational. This operation +is performed whenever a rational is constructed (and assigned in place). All +other operations are careful to maintain rationals in a normalized state. +Normalization costs the equivalent of one gcd and two divisions. +</ul> + +<p>Note that it is implicitly assumed that operations on IntType have the +"usual" performance characteristics - specifically, that the expensive +operations are multiplication, division, and modulo, with addition and +subtraction being significantly cheaper. It is assumed that construction (from +integer literals 0 and 1, and copy construction) and assignment are relatively +cheap, although some effort is taken to reduce unnecessary construction and +copying. It is also assumed that comparison (particularly against zero) is +cheap. + +<p>Integer types which do not conform to these assumptions will not be +particularly effective as the underlying integer type for the rational class. +Specifically, it is likely that performance will be severely sub-optimal. + +<h2><a name="Exceptions">Exceptions</a></h2> +Rationals can never have a denominator of zero. (This library does not support +representations for infinity or NaN). Should a rational result ever generate a +denominator of zero, or otherwise fail during normalization, the exception +<tt>boost::bad_rational</tt> (a subclass of <tt>std::domain_error</tt>) is +thrown. This should only occur if the user attempts to explicitly construct a +rational with a denominator of zero, to divide a rational by a zero value, or +generate a negative denominator too large to be normalized. The exception can +be thrown during a cross-instantiation conversion, when at least one of the +components ends up not being value-preserved and the new combination is not +considered normalized. + +<p>In addition, if operations on the underlying integer type can generate +exceptions, these will be propagated out of the operations on the rational +class. No particular assumptions should be made - it is only safe to assume +that any exceptions which can be thrown by the integer class could be thrown +by any rational operation. In particular, the rational constructor may throw +exceptions from the underlying integer type as a result of the normalization +step. The only exception to this rule is that the rational destructor will +only throw exceptions which can be thrown by the destructor of the underlying +integer type (usually none). + +<p>If the component-level assignment operator(s) can throw, then a rational +object's invariants may be violated if an exception happens during the second +component's assignment. (The <code>assign</code> member function counts here +too.) This violates both the strong and basic guarantees. + +<h2><a name="Internal representation">Internal representation</a></h2> +<em>Note:</em> This information is for information only. Programs should not +be written in such a way as to rely on these implementation details. + +<p>Internally, rational numbers are stored as a pair (numerator, denominator) +of integers (whose type is specified as the template parameter for the +rational type). Rationals are always stored in fully normalized form (ie, +gcd(numerator,denominator) = 1, and the denominator is always positive). + +<h2><a name="Design notes">Design notes</a></h2> +<h3><a name="Minimal Implementation">Minimal Implementation</a></h3> +The rational number class is designed to keep to the basics. The minimal +operations required of a numeric class are provided, along with access to the +underlying representation in the form of the numerator() and denominator() +member functions. With these building-blocks, it is possible to implement any +additional functionality required. + +<p>Areas where this minimality consideration has been relaxed are in providing +input/output operators, and rational_cast. The former is generally +uncontroversial. However, there are a number of cases where rational_cast is +not the best possible method for converting a rational to a floating point +value (notably where user-defined types are involved). In those cases, a +user-defined conversion can and should be implemented. There is no need +for such an operation to be named rational_cast, and so the rational_cast +function does <em>not</em> provide the necessary infrastructure to allow for +specialisation/overloading. + +<h3><a name="Limited-range integer types">Limited-range integer types</a></h3> +The rational number class is designed for use in conjunction with an +unlimited precision integer class. With such a class, rationals are always +exact, and no problems arise with precision loss, overflow or underflow. + +<p>Unfortunately, the C++ standard does not offer such a class <s>(and neither +does boost, at the present time)</s>. It is therefore likely that the rational +number class will in many cases be used with limited-precision integer types, +such as the built-in <tt>int</tt> type. + +<p>When used with a limited precision integer type, the rational class suffers +from many of the precision issues which cause difficulty with floating point +types. While it is likely that precision issues will not affect simple uses of +the rational class, users should be aware that such issues exist. + +<p>As a simple illustration of the issues associated with limited precision +integers, consider a case where the C++ <tt>int</tt> type is a 32-bit signed +representation. In this case, the smallest possible positive +rational<int> is <tt>1/0x7FFFFFFF</tt>. In other words, the +"granularity" of the rational<int> representation around zero is +approximately 4.66e-10. At the other end of the representable range, the +largest representable rational<int> is <tt>0x7FFFFFFF/1</tt>, and the +next lower representable rational<int> is <tt>0x7FFFFFFE/1</tt>. Thus, +at this end of the representable range, the granularity ia 1. This type of +magnitude-dependent granularity is typical of floating point representations. +However, it does not "feel" natural when using a rational number class. + +<p>Limited-precision integer types may raise issues with the range sizes of +their allowable negative values and positive values. If the negative range is +larger, then the extremely-negative numbers will not have an additive inverse in +the positive range, making them unusable as denominator values since they cannot +be normalized to positive values (unless the user is lucky enough that the input +components are not relatively prime pre-normalization). + +<p>It is up to the user of a rational type based on a limited-precision integer +type to be aware of, and code in anticipation of, such issues. + +<h3><a name="Conversion from floating point">Conversion from floating point</a></h3> +The library does not offer a conversion function from floating point to +rational. A number of requests were received for such a conversion, but +extensive discussions on the boost list reached the conclusion that there was +no "best solution" to the problem. As there is no reason why a user of the +library cannot write their own conversion function which suits their +particular requirements, the decision was taken not to pick any one algorithm +as "standard". + +<p>The key issue with any conversion function from a floating point value is +how to handle the loss of precision which is involved in floating point +operations. To provide a concrete example, consider the following code: + +<pre> + // These two values could in practice be obtained from user input, + // or from some form of measuring instrument. + double x = 1.0; + double y = 3.0; + + double z = x/y; + + rational<I> r = rational_from_double(z); +</pre> + +<p>The fundamental question is, precisely what rational should r be? A naive +answer is that r should be equal to 1/3. However, this ignores a multitude of +issues. + +<p>In the first instance, z is not exactly 1/3. Because of the limitations of +floating point representation, 1/3 is not exactly representable in any of the +common representations for the double type. Should r therefore not contain an +(exact) representation of the actual value represented by z? But will the user +be happy with a value of 33333333333333331/100000000000000000 for r? + +<p>Before even considering the above issue, we have to consider the accuracy +of the original values, x and y. If they came from an analog measuring +instrument, for example, they are not infinitely accurate in any case. In such +a case, a rational representation like the above promises far more accuracy +than there is any justification for. + +<p>All of this implies that we should be looking for some form of "nearest +simple fraction". Algorithms to determine this sort of value do exist. +However, not all applications want to work like this. In other cases, the +whole point of converting to rational is to obtain an exact representation, in +order to prevent accuracy loss during a series of calculations. In this case, +a completely precise representation is required, regardless of how "unnatural" +the fractions look. + +<p>With these conflicting requirements, there is clearly no single solution +which will satisfy all users. Furthermore, the algorithms involved are +relatively complex and specialised, and are best implemented with a good +understanding of the application requirements. All of these factors make such +a function unsuitable for a general-purpose library such as this. + +<h3><a name="Absolute Value">Absolute Value</a></h3> +In the first instance, it seems logical to implement +abs(rational<IntType>) in terms of abs(IntType). +However, there are a number of issues which arise with doing so. + +<p>The first issue is that, in order to locate the appropriate implementation +of abs(IntType) in the case where IntType is a user-defined type in a user +namespace, Koenig lookup is required. Not all compilers support Koenig lookup +for functions at the current time. For such compilers, clumsy workarounds, +which require cooperation from the user of the rational class, are required to +make things work. + +<p>The second, and potentially more serious, issue is that for non-standard +built-in integer types (for example, 64-bit integer types such as +<em>long long</em> or <em>__int64</em>), there is no guarantee that the vendor +has supplied a built in abs() function operating on such types. This is a +quality-of-implementation issue, but in practical terms, vendor support for +types such as <em>long long</em> is still very patchy. + +<p>As a consequence of these issues, it does not seem worth implementing +abs(rational<IntType>) in terms of abs(IntType). Instead, a simple +implementation with an inline implementation of abs() is used: + +<pre> + template <typename IntType> + inline rational<IntType> abs(const rational<IntType>& r) + { + if (r.numerator() >= IntType(0)) + return r; + + return rational<IntType>(-r.numerator(), r.denominator()); + } +</pre> + +<p>The same arguments imply that where the absolute value of an IntType is +required elsewhere, the calculation is performed inline. + +<h2><a name="References">References</a></h2> +<ul> +<li>The rational number header itself: <a href="../../boost/rational.hpp">rational.hpp</a> +<li>Some example code: <a href="test/rational_example.cpp">rational_example.cpp</a> +<li>The regression test: <a href="test/rational_test.cpp">rational_test.cpp</a> +</ul> + +<h2><a name="History and Acknowledgements">History and Acknowledgements</a></h2> + + <p> + In December, 1999, I implemented the initial version of the rational number + class, and submitted it to the <A HREF="http://www.boost.org/">boost.org</A> + mailing list. Some discussion of the implementation took place on the mailing + list. In particular, Andrew D. Jewell pointed out the importance of ensuring + that the risk of overflow was minimised, and provided overflow-free + implementations of most of the basic operations. The name rational_cast was + suggested by Kevlin Henney. Ed Brey provided invaluable comments - not least + in pointing out some fairly stupid typing errors in the original code!</p> + + <p>David Abrahams contributed helpful feedback on the documentation.</p> + + <p> + A long discussion of the merits of providing a conversion from floating + point to rational took place on the boost list in November 2000. Key + contributors included Reggie Seagraves, Lutz Kettner and Daniel Frey (although + most of the boost list seemed to get involved at one point or another!). Even + though the end result was a decision <em>not</em> to implement anything, the + discussion was very valuable in understanding the issues. + </p> + + <p> + Stephen Silver contributed useful experience on using the rational class + with a user-defined integer type. + </p> + + <p> + Nickolay Mladenov provided the current implementation of operator+= and + operator-=. + </p> + <p> + Discussion of the issues surrounding Koenig lookup and std::swap took place + on the boost list in January 2001. + </p> + <p> + Daryle Walker provided a Boolean conversion operator, so that a rational can + be used in the same Boolean contexts as the built-in numeric types, in December + 2005. He added the cross-instantiation constructor template in August 2013. + </p> + <p> + July 2014: Updated numerator/denominator accessors to return values by constant + reference: this gives a performance improvement when using with multiprecision (class) types. + </p> + <p> + July 2014: Updated to use BOOST_THROW_EXCEPTION uniformly throughout. + </p> + <p> + July 2014: Added support for C++11 constexpr constructors, plus tests to match. + </p> + <p> + Nov 2014: Added support for gcd and lcm of rational numbers. + </p> + <p> + Dec 2016: Reworked constructors and operators to prohibit narrowing implicit + conversions, in particular accidental conversion from floating point types. + </p> + <p> + Oct/Nov 2018: Add more constexpr. + </p> + +<p>Revised July 14, 2017</p> + +<p>© Copyright Paul Moore 1999-2001; © Daryle Walker 2005, 2013. +Permission to copy, use, modify, sell and distribute this document is granted +provided this copyright notice appears in all copies. This document is provided +"as is" without express or implied warranty, and with no claim as to +its suitability for any purpose.</p> +<!-- boostinspect:nolicense (can't find Paul Moore to change license) --> +</body> +</html> diff --git a/src/boost/libs/rational/test/CMakeLists.txt b/src/boost/libs/rational/test/CMakeLists.txt new file mode 100644 index 000000000..d6bd0299a --- /dev/null +++ b/src/boost/libs/rational/test/CMakeLists.txt @@ -0,0 +1,25 @@ +# Copyright 2019 Mike Dev +# Distributed under the Boost Software License, Version 1.0. +# See accompanying file LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt +# +# NOTE: CMake support for Boost.Rational is currently experimental at best +# and the interface is likely to change in the future + +# NOTE: Boost::test not yet available, so we can't run the regular test +# add_executable( test_boost_rational_test rational_test.cpp ) +# target_link_libraries( test_boost_rational_test +# PUBLIC +# Boost::rational +# Boost::mpl +# Boost::test +# ) +# add_test( NAME test_boost_rational_test COMMAND test_boost_rational_test ) + +add_executable( test_boost_rational_constexpr_test constexpr_test.cpp ) +target_link_libraries( test_boost_rational_constexpr_test + PUBLIC + Boost::rational +) + +add_test( NAME test_boost_rational_constexpr_test COMMAND test_boost_rational_constexpr_test ) + diff --git a/src/boost/libs/rational/test/Jamfile.v2 b/src/boost/libs/rational/test/Jamfile.v2 new file mode 100644 index 000000000..aec0b53ac --- /dev/null +++ b/src/boost/libs/rational/test/Jamfile.v2 @@ -0,0 +1,25 @@ +#~ Copyright Rene Rivera 2008 +#~ Distributed under the Boost Software License, Version 1.0. +#~ (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +import testing ; +import ../../config/checks/config : requires ; + +test-suite rational + : [ run rational_example.cpp ] + [ run rational_test.cpp + /boost/test//boost_unit_test_framework/<link>static ] + [ run constexpr_test.cpp : : : [ requires cxx11_constexpr ] ] + [ compile-fail expected_fail_01.cpp ] + [ compile-fail expected_fail_02.cpp ] + [ compile-fail expected_fail_03.cpp ] + [ compile-fail expected_fail_04.cpp ] + [ compile-fail expected_fail_05.cpp ] + [ compile-fail expected_fail_06.cpp ] + [ compile-fail expected_fail_07.cpp ] + [ compile-fail expected_fail_08.cpp ] + [ compile-fail expected_fail_09.cpp ] + [ compile-fail expected_fail_10.cpp ] + [ compile-fail expected_fail_11.cpp ] + [ compile expected_compile_12.cpp ] + ; diff --git a/src/boost/libs/rational/test/constexpr_test.cpp b/src/boost/libs/rational/test/constexpr_test.cpp new file mode 100644 index 000000000..22be172d6 --- /dev/null +++ b/src/boost/libs/rational/test/constexpr_test.cpp @@ -0,0 +1,29 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + + +int main() +{ +#ifndef BOOST_NO_CXX11_CONSTEXPR + constexpr boost::rational<int> i1; + constexpr boost::rational<int> i2(3); + constexpr boost::rational<long long> i3(i2); + constexpr boost::rational<short> i4(i2); + constexpr boost::rational<long long> i5(23u); // converting constructor + // constexpr boost::rational<short> i6(23u); // Not supported, needs an explicit typecast in constructor. + + static_assert(i1.numerator() == 0, "constexpr test"); + static_assert(i1.denominator() == 1, "constexpr test"); + static_assert(i2.numerator() == 3, "constexpr test"); + static_assert(i2.denominator() == 1, "constexpr test"); + static_assert(i3.numerator() == 3, "constexpr test"); + static_assert(i3.denominator() == 1, "constexpr test"); + static_assert(!i1, "constexpr test"); + static_assert(i2, "constexpr test"); +#endif + return 0; +} diff --git a/src/boost/libs/rational/test/expected_compile_12.cpp b/src/boost/libs/rational/test/expected_compile_12.cpp new file mode 100644 index 000000000..0cc9f61da --- /dev/null +++ b/src/boost/libs/rational/test/expected_compile_12.cpp @@ -0,0 +1,24 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2019. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +// For more information read https://github.com/boostorg/rational/issues/26 + +#include <boost/rational.hpp> + +void test(const char* text) +{ + (void)text; +} + +void test(const boost::rational<int>& rational) +{ + (void)rational; +} + +int main() +{ + test("Some text"); + return 0; +} diff --git a/src/boost/libs/rational/test/expected_fail_01.cpp b/src/boost/libs/rational/test/expected_fail_01.cpp new file mode 100644 index 000000000..5c15433ad --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_01.cpp @@ -0,0 +1,11 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(3.14); +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_02.cpp b/src/boost/libs/rational/test/expected_fail_02.cpp new file mode 100644 index 000000000..032070004 --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_02.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + rat = 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_03.cpp b/src/boost/libs/rational/test/expected_fail_03.cpp new file mode 100644 index 000000000..4b5645c2a --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_03.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + return rat == 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_04.cpp b/src/boost/libs/rational/test/expected_fail_04.cpp new file mode 100644 index 000000000..62c764ae9 --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_04.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + rat += 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_05.cpp b/src/boost/libs/rational/test/expected_fail_05.cpp new file mode 100644 index 000000000..14c5ec4e6 --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_05.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + rat -= 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_06.cpp b/src/boost/libs/rational/test/expected_fail_06.cpp new file mode 100644 index 000000000..924e19307 --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_06.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + rat *= 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_07.cpp b/src/boost/libs/rational/test/expected_fail_07.cpp new file mode 100644 index 000000000..9c087afb9 --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_07.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + rat /= 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_08.cpp b/src/boost/libs/rational/test/expected_fail_08.cpp new file mode 100644 index 000000000..7efeb3b3e --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_08.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + rat = rat + 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_09.cpp b/src/boost/libs/rational/test/expected_fail_09.cpp new file mode 100644 index 000000000..c0cdb88da --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_09.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + rat = rat - 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_10.cpp b/src/boost/libs/rational/test/expected_fail_10.cpp new file mode 100644 index 000000000..126988fce --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_10.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + rat = rat / 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/expected_fail_11.cpp b/src/boost/libs/rational/test/expected_fail_11.cpp new file mode 100644 index 000000000..32d4232f7 --- /dev/null +++ b/src/boost/libs/rational/test/expected_fail_11.cpp @@ -0,0 +1,12 @@ +/////////////////////////////////////////////////////////////////////////////// +// Copyright 2015 John Maddock. Distributed under the Boost +// Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#include <boost/rational.hpp> + +int main() +{ + boost::rational<int> rat(2); + rat = rat * 0.5; +}
\ No newline at end of file diff --git a/src/boost/libs/rational/test/rational_example.cpp b/src/boost/libs/rational/test/rational_example.cpp new file mode 100644 index 000000000..16c3fe63c --- /dev/null +++ b/src/boost/libs/rational/test/rational_example.cpp @@ -0,0 +1,108 @@ +// rational number example program ----------------------------------------// + +// (C) Copyright Paul Moore 1999. Permission to copy, use, modify, sell +// and distribute this software is granted provided this copyright notice +// appears in all copies. This software is provided "as is" without express or +// implied warranty, and with no claim as to its suitability for any purpose. + +// boostinspect:nolicense (don't complain about the lack of a Boost license) +// (Paul Moore hasn't been in contact for years, so there's no way to change the +// license.) + +// Revision History +// 14 Dec 99 Initial version + +#include <iostream> +#include <cassert> +#include <cstdlib> +#include <boost/config.hpp> +#ifndef BOOST_NO_LIMITS +#include <limits> +#else +#include <limits.h> +#endif +#include <exception> +#include <boost/rational.hpp> + +using std::cout; +using std::endl; +using boost::rational; + +#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP +// This is a nasty hack, required because MSVC does not implement "Koenig +// Lookup". Basically, if I call abs(r), the C++ standard says that the +// compiler should look for a definition of abs in the namespace which +// contains r's class (in this case boost) - among other places. + +// Koenig Lookup is a relatively recent feature, and other compilers may not +// implement it yet. If so, try including this line. + +using boost::abs; +#endif + +int main () +{ + rational<int> half(1,2); + rational<int> one(1); + rational<int> two(2); + + // Some basic checks + assert(half.numerator() == 1); + assert(half.denominator() == 2); + assert(boost::rational_cast<double>(half) == 0.5); + + // Arithmetic + assert(half + half == one); + assert(one - half == half); + assert(two * half == one); + assert(one / half == two); + + // With conversions to integer + assert(half+half == 1); + assert(2 * half == one); + assert(2 * half == 1); + assert(one / half == 2); + assert(1 / half == 2); + + // Sign handling + rational<int> minus_half(-1,2); + assert(-half == minus_half); + assert(abs(minus_half) == half); + + // Do we avoid overflow? +#ifndef BOOST_NO_LIMITS + int maxint = (std::numeric_limits<int>::max)(); +#else + int maxint = INT_MAX; +#endif + rational<int> big(maxint, 2); + assert(2 * big == maxint); + + // Print some of the above results + cout << half << "+" << half << "=" << one << endl; + cout << one << "-" << half << "=" << half << endl; + cout << two << "*" << half << "=" << one << endl; + cout << one << "/" << half << "=" << two << endl; + cout << "abs(" << minus_half << ")=" << half << endl; + cout << "2 * " << big << "=" << maxint + << " (rational: " << rational<int>(maxint) << ")" << endl; + + // Some extras + rational<int> pi(22,7); + cout << "pi = " << boost::rational_cast<double>(pi) << " (nearly)" << endl; + + // Exception handling + try { + rational<int> r; // Forgot to initialise - set to 0 + r = 1/r; // Boom! + } + catch (const boost::bad_rational &e) { + cout << "Bad rational, as expected: " << e.what() << endl; + } + catch (...) { + cout << "Wrong exception raised!" << endl; + } + + return 0; +} + diff --git a/src/boost/libs/rational/test/rational_test.cpp b/src/boost/libs/rational/test/rational_test.cpp new file mode 100644 index 000000000..ccd58ea59 --- /dev/null +++ b/src/boost/libs/rational/test/rational_test.cpp @@ -0,0 +1,1608 @@ +/* + * A test program for boost/rational.hpp. + * Change the typedef at the beginning of run_tests() to try out different + * integer types. (These tests are designed only for signed integer + * types. They should work for short, int and long.) + * + * (C) Copyright Stephen Silver, 2001. Permission to copy, use, modify, sell + * and distribute this software is granted provided this copyright notice + * appears in all copies. This software is provided "as is" without express or + * implied warranty, and with no claim as to its suitability for any purpose. + * + * Incorporated into the boost rational number library, and modified and + * extended, by Paul Moore, with permission. + */ + +// boostinspect:nolicense (don't complain about the lack of a Boost license) +// (Stephen Silver hasn't been contacted yet for permission to change the +// license. If Paul Moore's permission is also needed, then that's a problem +// since he hasn't been in contact for years.) + +// Revision History +// 30 Aug 13 Add bug-test of assignments holding the basic and/or strong +// guarantees (Daryle Walker) +// 27 Aug 13 Add test for cross-version constructor template (Daryle Walker) +// 23 Aug 13 Add bug-test of narrowing conversions during order comparison; +// spell logical-negation in it as "!" because MSVC won't accept +// "not" (Daryle Walker) +// 05 Nov 06 Add testing of zero-valued denominators & divisors; casting with +// types that are not implicitly convertible (Daryle Walker) +// 04 Nov 06 Resolve GCD issue with depreciation (Daryle Walker) +// 02 Nov 06 Add testing for operator<(int_type) w/ unsigneds (Daryle Walker) +// 31 Oct 06 Add testing for operator<(rational) overflow (Daryle Walker) +// 18 Oct 06 Various fixes for old compilers (JoaquÃn M López Muñoz) +// 27 Dec 05 Add testing for Boolean conversion operator (Daryle Walker) +// 24 Dec 05 Change code to use Boost.Test (Daryle Walker) +// 04 Mar 01 Patches for Intel C++ and GCC (David Abrahams) + +#define BOOST_TEST_MAIN "Boost::Rational unit tests" + +#include <boost/config.hpp> +#include <boost/limits.hpp> +#include <boost/mpl/list.hpp> +#include <boost/operators.hpp> +#include <boost/preprocessor/stringize.hpp> +#include <boost/integer/common_factor_rt.hpp> +#include <boost/cstdint.hpp> + +#include <boost/rational.hpp> + +#include <boost/test/unit_test.hpp> + +#include <climits> +#include <iomanip> +#include <ios> +#include <iostream> +#include <istream> +#include <ostream> +#include <sstream> +#include <stdexcept> +#include <string> + +#ifdef _MSC_VER +#pragma warning(disable:4146) +#endif + + +// We can override this on the compile, as -DINT_TYPE=short or whatever. +// The default test is against rational<long>. +#ifndef INT_TYPE +#define INT_TYPE long +#endif + +namespace { + +class MyOverflowingUnsigned; + +// This is a trivial user-defined wrapper around the built in int type. +// It can be used as a test type for rational<> +class MyInt : boost::operators<MyInt> +{ + friend class MyOverflowingUnsigned; + int val; +public: + MyInt(int n = 0) : val(n) {} + friend MyInt operator+ (const MyInt&); + friend MyInt operator- (const MyInt&); + MyInt& operator+= (const MyInt& rhs) { val += rhs.val; return *this; } + MyInt& operator-= (const MyInt& rhs) { val -= rhs.val; return *this; } + MyInt& operator*= (const MyInt& rhs) { val *= rhs.val; return *this; } + MyInt& operator/= (const MyInt& rhs) { val /= rhs.val; return *this; } + MyInt& operator%= (const MyInt& rhs) { val %= rhs.val; return *this; } + MyInt& operator|= (const MyInt& rhs) { val |= rhs.val; return *this; } + MyInt& operator&= (const MyInt& rhs) { val &= rhs.val; return *this; } + MyInt& operator^= (const MyInt& rhs) { val ^= rhs.val; return *this; } + const MyInt& operator++() { ++val; return *this; } + const MyInt& operator--() { --val; return *this; } + bool operator< (const MyInt& rhs) const { return val < rhs.val; } + bool operator== (const MyInt& rhs) const { return val == rhs.val; } + bool operator! () const { return !val; } + friend std::istream& operator>>(std::istream&, MyInt&); + friend std::ostream& operator<<(std::ostream&, const MyInt&); +}; + +inline MyInt operator+(const MyInt& rhs) { return rhs; } +inline MyInt operator-(const MyInt& rhs) { return MyInt(-rhs.val); } +inline std::istream& operator>>(std::istream& is, MyInt& i) { is >> i.val; return is; } +inline std::ostream& operator<<(std::ostream& os, const MyInt& i) { os << i.val; return os; } +inline MyInt abs(MyInt rhs) { if (rhs < MyInt()) rhs = -rhs; return rhs; } + +// This is an "unsigned" wrapper, that throws on overflow. It can be used to +// test rational<> when an operation goes out of bounds. +class MyOverflowingUnsigned + : private boost::unit_steppable<MyOverflowingUnsigned> + , private boost::ordered_euclidian_ring_operators1<MyOverflowingUnsigned> +{ + // Helper type-aliases + typedef MyOverflowingUnsigned self_type; + typedef unsigned self_type::* bool_type; + + // Member data + unsigned v_; + +public: + // Exception base class + class exception_base { protected: virtual ~exception_base() throw() {} }; + + // Divide-by-zero exception class + class divide_by_0_error + : public virtual exception_base + , public std::domain_error + { + public: + explicit divide_by_0_error( std::string const &w ) + : std::domain_error( w ) {} + + virtual ~divide_by_0_error() throw() {} + }; + + // Overflow exception class + class overflowing_error + : public virtual exception_base + , public std::overflow_error + { + public: + explicit overflowing_error( std::string const &w ) + : std::overflow_error( w ) {} + + virtual ~overflowing_error() throw() {} + }; + + // Lifetime management (use automatic dtr & copy-ctr) + MyOverflowingUnsigned( unsigned v = 0 ) : v_( v ) {} + explicit MyOverflowingUnsigned( MyInt const &m ) : v_( m.val ) {} + + // Operators (use automatic copy-assignment); arithmetic & comparison only + self_type & operator ++() + { + if ( this->v_ == UINT_MAX ) throw overflowing_error( "increment" ); + else ++this->v_; + return *this; + } + self_type & operator --() + { + if ( !this->v_ ) throw overflowing_error( "decrement" ); + else --this->v_; + return *this; + } + + operator bool_type() const { return this->v_ ? &self_type::v_ : 0; } + + bool operator !() const { return !this->v_; } + self_type operator +() const { return self_type( +this->v_ ); } + self_type operator -() const { return self_type( -this->v_ ); } + + bool operator <(self_type const &r) const { return this->v_ < r.v_; } + bool operator ==(self_type const &r) const { return this->v_ == r.v_; } + + self_type & operator *=( self_type const &r ) + { + if ( r.v_ && this->v_ > UINT_MAX / r.v_ ) + { + throw overflowing_error( "oversized factors" ); + } + this->v_ *= r.v_; + return *this; + } + self_type & operator /=( self_type const &r ) + { + if ( !r.v_ ) throw divide_by_0_error( "division" ); + this->v_ /= r.v_; + return *this; + } + self_type & operator %=( self_type const &r ) + { + if ( !r.v_ ) throw divide_by_0_error( "modulus" ); + this->v_ %= r.v_; + return *this; + } + self_type & operator +=( self_type const &r ) + { + if ( this->v_ > UINT_MAX - r.v_ ) + { + throw overflowing_error( "oversized addends" ); + } + this->v_ += r.v_; + return *this; + } + self_type & operator -=( self_type const &r ) + { + if ( this->v_ < r.v_ ) + { + throw overflowing_error( "oversized subtrahend" ); + } + this->v_ -= r.v_; + return *this; + } + + // Input & output + template < typename Ch, class Tr > + friend std::basic_istream<Ch, Tr> & + operator >>( std::basic_istream<Ch, Tr> &i, self_type &x ) + { return i >> x.v_; } + + template < typename Ch, class Tr > + friend std::basic_ostream<Ch, Tr> & + operator <<( std::basic_ostream<Ch, Tr> &o, self_type const &x ) + { return o << x.v_; } + +}; // MyOverflowingUnsigned + +inline MyOverflowingUnsigned abs( MyOverflowingUnsigned const &x ) { return x; } + +} // namespace + + +// Specialize numeric_limits for the custom types +namespace std +{ + +template < > +class numeric_limits< MyInt > +{ + typedef numeric_limits<int> limits_type; + +public: + static const bool is_specialized = limits_type::is_specialized; + + static MyInt min BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return + limits_type::min BOOST_PREVENT_MACRO_SUBSTITUTION (); } + static MyInt max BOOST_PREVENT_MACRO_SUBSTITUTION () throw() { return + limits_type::max BOOST_PREVENT_MACRO_SUBSTITUTION (); } + static MyInt lowest() throw() { return min BOOST_PREVENT_MACRO_SUBSTITUTION + (); } // C++11 + + static const int digits = limits_type::digits; + static const int digits10 = limits_type::digits10; + static const int max_digits10 = 0; // C++11 + static const bool is_signed = limits_type::is_signed; + static const bool is_integer = limits_type::is_integer; + static const bool is_exact = limits_type::is_exact; + static const int radix = limits_type::radix; + static MyInt epsilon() throw() { return limits_type::epsilon(); } + static MyInt round_error() throw() { return limits_type::round_error(); } + + static const int min_exponent = limits_type::min_exponent; + static const int min_exponent10 = limits_type::min_exponent10; + static const int max_exponent = limits_type::max_exponent; + static const int max_exponent10 = limits_type::max_exponent10; + + static const bool has_infinity = limits_type::has_infinity; + static const bool has_quiet_NaN = limits_type::has_quiet_NaN; + static const bool has_signaling_NaN = limits_type::has_signaling_NaN; + static const float_denorm_style has_denorm = limits_type::has_denorm; + static const bool has_denorm_loss = limits_type::has_denorm_loss; + + static MyInt infinity() throw() { return limits_type::infinity(); } + static MyInt quiet_NaN() throw() { return limits_type::quiet_NaN(); } + static MyInt signaling_NaN() throw() {return limits_type::signaling_NaN();} + static MyInt denorm_min() throw() { return limits_type::denorm_min(); } + + static const bool is_iec559 = limits_type::is_iec559; + static const bool is_bounded = limits_type::is_bounded; + static const bool is_modulo = limits_type::is_modulo; + + static const bool traps = limits_type::traps; + static const bool tinyness_before = limits_type::tinyness_before; + static const float_round_style round_style = limits_type::round_style; + +}; // std::numeric_limits<MyInt> + +template < > +class numeric_limits< MyOverflowingUnsigned > +{ + typedef numeric_limits<unsigned> limits_type; + +public: + static const bool is_specialized = limits_type::is_specialized; + + static MyOverflowingUnsigned min BOOST_PREVENT_MACRO_SUBSTITUTION () throw() + { return limits_type::min BOOST_PREVENT_MACRO_SUBSTITUTION (); } + static MyOverflowingUnsigned max BOOST_PREVENT_MACRO_SUBSTITUTION () throw() + { return limits_type::max BOOST_PREVENT_MACRO_SUBSTITUTION (); } + static MyOverflowingUnsigned lowest() throw() + { return min BOOST_PREVENT_MACRO_SUBSTITUTION (); } // C++11 + + static const int digits = limits_type::digits; + static const int digits10 = limits_type::digits10; + static const int max_digits10 = 0; // C++11 + static const bool is_signed = limits_type::is_signed; + static const bool is_integer = limits_type::is_integer; + static const bool is_exact = limits_type::is_exact; + static const int radix = limits_type::radix; + static MyOverflowingUnsigned epsilon() throw() + { return limits_type::epsilon(); } + static MyOverflowingUnsigned round_error() throw() + {return limits_type::round_error();} + + static const int min_exponent = limits_type::min_exponent; + static const int min_exponent10 = limits_type::min_exponent10; + static const int max_exponent = limits_type::max_exponent; + static const int max_exponent10 = limits_type::max_exponent10; + + static const bool has_infinity = limits_type::has_infinity; + static const bool has_quiet_NaN = limits_type::has_quiet_NaN; + static const bool has_signaling_NaN = limits_type::has_signaling_NaN; + static const float_denorm_style has_denorm = limits_type::has_denorm; + static const bool has_denorm_loss = limits_type::has_denorm_loss; + + static MyOverflowingUnsigned infinity() throw() + { return limits_type::infinity(); } + static MyOverflowingUnsigned quiet_NaN() throw() + { return limits_type::quiet_NaN(); } + static MyOverflowingUnsigned signaling_NaN() throw() + { return limits_type::signaling_NaN(); } + static MyOverflowingUnsigned denorm_min() throw() + { return limits_type::denorm_min(); } + + static const bool is_iec559 = limits_type::is_iec559; + static const bool is_bounded = limits_type::is_bounded; + static const bool is_modulo = limits_type::is_modulo; + + static const bool traps = limits_type::traps; + static const bool tinyness_before = limits_type::tinyness_before; + static const float_round_style round_style = limits_type::round_style; + +}; // std::numeric_limits<MyOverflowingUnsigned> + +} // namespace std + + +namespace { + +// This fixture replaces the check of rational's packing at the start of main. +class rational_size_check +{ + typedef INT_TYPE int_type; + typedef ::boost::rational<int_type> rational_type; + +public: + rational_size_check() + { + using ::std::cout; + + char const * const int_name = BOOST_PP_STRINGIZE( INT_TYPE ); + + cout << "Running tests for boost::rational<" << int_name << ">\n\n"; + + cout << "Implementation issue: the minimal size for a rational\n" + << "is twice the size of the underlying integer type.\n\n"; + + cout << "Checking to see if space is being wasted.\n" + << "\tsizeof(" << int_name << ") == " << sizeof( int_type ) + << "\n"; + cout << "\tsizeof(boost::rational<" << int_name << ">) == " + << sizeof( rational_type ) << "\n\n"; + + cout << "Implementation has " + << ( + (sizeof( rational_type ) > 2u * sizeof( int_type )) + ? "included padding bytes" + : "minimal size" + ) + << "\n\n"; + } +}; + +// This fixture groups all the common settings. +class my_configuration +{ +public: + template < typename T > + class hook + { + public: + typedef ::boost::rational<T> rational_type; + + private: + struct parts { rational_type parts_[ 9 ]; }; + + static parts generate_rationals() + { + rational_type r1, r2( 0 ), r3( 1 ), r4( -3 ), r5( 7, 2 ), + r6( 5, 15 ), r7( 14, -21 ), r8( -4, 6 ), + r9( -14, -70 ); + parts result; + result.parts_[0] = r1; + result.parts_[1] = r2; + result.parts_[2] = r3; + result.parts_[3] = r4; + result.parts_[4] = r5; + result.parts_[5] = r6; + result.parts_[6] = r7; + result.parts_[7] = r8; + result.parts_[8] = r9; + + return result; + } + + parts p_; // Order Dependency + + public: + rational_type ( &r_ )[ 9 ]; // Order Dependency + + hook() : p_( generate_rationals() ), r_( p_.parts_ ) {} + }; +}; + +// Instead of controlling the integer type needed with a #define, use a list of +// all available types. Since the headers #included don't change because of the +// integer #define, only the built-in types and MyInt are available. (Any other +// arbitrary integer type introduced by the #define would get compiler errors +// because its header can't be #included.) +typedef ::boost::mpl::list<short, int, long> builtin_signed_test_types; +typedef ::boost::mpl::list<short, int, long, MyInt> all_signed_test_types; + +// Without these explicit instantiations, MSVC++ 6.5/7.0 does not find +// some friend operators in certain contexts. +::boost::rational<short> dummy1; +::boost::rational<int> dummy2; +::boost::rational<long> dummy3; +::boost::rational<MyInt> dummy4; +::boost::rational<MyOverflowingUnsigned> dummy5; +::boost::rational<unsigned> dummy6; + +// Should there be regular tests with unsigned integer types? + +} // namespace + + +// Check if rational is the smallest size possible +BOOST_GLOBAL_FIXTURE( rational_size_check ); + + +#if BOOST_CONTROL_RATIONAL_HAS_GCD +// The factoring function template suite +BOOST_AUTO_TEST_SUITE( factoring_suite ) + +// GCD tests +BOOST_AUTO_TEST_CASE_TEMPLATE( gcd_test, T, all_signed_test_types ) +{ + BOOST_CHECK_EQUAL( boost::gcd<T>( 1, -1), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( -1, 1), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( 1, 1), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( -1, -1), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( 0, 0), static_cast<T>( 0) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( 7, 0), static_cast<T>( 7) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( 0, 9), static_cast<T>( 9) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( -7, 0), static_cast<T>( 7) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( 0, -9), static_cast<T>( 9) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( 42, 30), static_cast<T>( 6) ); + BOOST_CHECK_EQUAL( boost::gcd<T>( 6, -9), static_cast<T>( 3) ); + BOOST_CHECK_EQUAL( boost::gcd<T>(-10, -10), static_cast<T>(10) ); + BOOST_CHECK_EQUAL( boost::gcd<T>(-25, -10), static_cast<T>( 5) ); +} + +// LCM tests +BOOST_AUTO_TEST_CASE_TEMPLATE( lcm_test, T, all_signed_test_types ) +{ + BOOST_CHECK_EQUAL( boost::lcm<T>( 1, -1), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( -1, 1), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( 1, 1), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( -1, -1), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( 0, 0), static_cast<T>( 0) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( 6, 0), static_cast<T>( 0) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( 0, 7), static_cast<T>( 0) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( -5, 0), static_cast<T>( 0) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( 0, -4), static_cast<T>( 0) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( 18, 30), static_cast<T>(90) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( -6, 9), static_cast<T>(18) ); + BOOST_CHECK_EQUAL( boost::lcm<T>(-10, -10), static_cast<T>(10) ); + BOOST_CHECK_EQUAL( boost::lcm<T>( 25, -10), static_cast<T>(50) ); +} + +BOOST_AUTO_TEST_SUITE_END() +#endif // BOOST_CONTROL_RATIONAL_HAS_GCD + + +// The basic test suite +BOOST_FIXTURE_TEST_SUITE( basic_rational_suite, my_configuration ) + +// Initialization tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_initialization_test, T, + all_signed_test_types ) +{ + my_configuration::hook<T> h; + boost::rational<T> &r1 = h.r_[ 0 ], &r2 = h.r_[ 1 ], &r3 = h.r_[ 2 ], + &r4 = h.r_[ 3 ], &r5 = h.r_[ 4 ], &r6 = h.r_[ 5 ], + &r7 = h.r_[ 6 ], &r8 = h.r_[ 7 ], &r9 = h.r_[ 8 ]; + + BOOST_CHECK_EQUAL( r1.numerator(), static_cast<T>( 0) ); + BOOST_CHECK_EQUAL( r2.numerator(), static_cast<T>( 0) ); + BOOST_CHECK_EQUAL( r3.numerator(), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( r4.numerator(), static_cast<T>(-3) ); + BOOST_CHECK_EQUAL( r5.numerator(), static_cast<T>( 7) ); + BOOST_CHECK_EQUAL( r6.numerator(), static_cast<T>( 1) ); + BOOST_CHECK_EQUAL( r7.numerator(), static_cast<T>(-2) ); + BOOST_CHECK_EQUAL( r8.numerator(), static_cast<T>(-2) ); + BOOST_CHECK_EQUAL( r9.numerator(), static_cast<T>( 1) ); + + BOOST_CHECK_EQUAL( r1.denominator(), static_cast<T>(1) ); + BOOST_CHECK_EQUAL( r2.denominator(), static_cast<T>(1) ); + BOOST_CHECK_EQUAL( r3.denominator(), static_cast<T>(1) ); + BOOST_CHECK_EQUAL( r4.denominator(), static_cast<T>(1) ); + BOOST_CHECK_EQUAL( r5.denominator(), static_cast<T>(2) ); + BOOST_CHECK_EQUAL( r6.denominator(), static_cast<T>(3) ); + BOOST_CHECK_EQUAL( r7.denominator(), static_cast<T>(3) ); + BOOST_CHECK_EQUAL( r8.denominator(), static_cast<T>(3) ); + BOOST_CHECK_EQUAL( r9.denominator(), static_cast<T>(5) ); + + BOOST_CHECK_THROW( boost::rational<T>( 3, 0), boost::bad_rational ); + BOOST_CHECK_THROW( boost::rational<T>(-2, 0), boost::bad_rational ); + BOOST_CHECK_THROW( boost::rational<T>( 0, 0), boost::bad_rational ); +} + +// Assignment (non-operator) tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_assign_test, T, all_signed_test_types ) +{ + my_configuration::hook<T> h; + boost::rational<T> & r = h.r_[ 0 ]; + + r.assign( 6, 8 ); + BOOST_CHECK_EQUAL( r.numerator(), static_cast<T>(3) ); + BOOST_CHECK_EQUAL( r.denominator(), static_cast<T>(4) ); + + r.assign( 0, -7 ); + BOOST_CHECK_EQUAL( r.numerator(), static_cast<T>(0) ); + BOOST_CHECK_EQUAL( r.denominator(), static_cast<T>(1) ); + + BOOST_CHECK_THROW( r.assign( 4, 0), boost::bad_rational ); + BOOST_CHECK_THROW( r.assign( 0, 0), boost::bad_rational ); + BOOST_CHECK_THROW( r.assign(-7, 0), boost::bad_rational ); +} + +// Comparison tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_comparison_test, T, + all_signed_test_types ) +{ + my_configuration::hook<T> h; + const boost::rational<T> &r1 = h.r_[ 0 ], &r2 = h.r_[ 1 ], &r3 = h.r_[ 2 ], + &r4 = h.r_[ 3 ], &r5 = h.r_[ 4 ], &r6 = h.r_[ 5 ], + &r7 = h.r_[ 6 ], &r8 = h.r_[ 7 ], &r9 = h.r_[ 8 ]; + + BOOST_CHECK( r1 == r2 ); + BOOST_CHECK( r2 != r3 ); + BOOST_CHECK( r4 < r3 ); + BOOST_CHECK( r4 <= r5 ); + BOOST_CHECK( r1 <= r2 ); + BOOST_CHECK( r5 > r6 ); + BOOST_CHECK( r5 >= r6 ); + BOOST_CHECK( r7 >= r8 ); + + BOOST_CHECK( !(r3 == r2) ); + BOOST_CHECK( !(r1 != r2) ); + BOOST_CHECK( !(r1 < r2) ); + BOOST_CHECK( !(r5 < r6) ); + BOOST_CHECK( !(r9 <= r2) ); + BOOST_CHECK( !(r8 > r7) ); + BOOST_CHECK( !(r8 > r2) ); + BOOST_CHECK( !(r4 >= r6) ); + + BOOST_CHECK( r1 == static_cast<T>( 0) ); + BOOST_CHECK( r2 != static_cast<T>(-1) ); + BOOST_CHECK( r3 < static_cast<T>( 2) ); + BOOST_CHECK( r4 <= static_cast<T>(-3) ); + BOOST_CHECK( r5 > static_cast<T>( 3) ); + BOOST_CHECK( r6 >= static_cast<T>( 0) ); + + BOOST_CHECK( static_cast<T>( 0) == r2 ); + BOOST_CHECK( static_cast<T>( 0) != r7 ); + BOOST_CHECK( static_cast<T>(-1) < r8 ); + BOOST_CHECK( static_cast<T>(-2) <= r9 ); + BOOST_CHECK( static_cast<T>( 1) > r1 ); + BOOST_CHECK( static_cast<T>( 1) >= r3 ); + + // Extra tests with values close in continued-fraction notation + boost::rational<T> const x1( static_cast<T>(9), static_cast<T>(4) ); + boost::rational<T> const x2( static_cast<T>(61), static_cast<T>(27) ); + boost::rational<T> const x3( static_cast<T>(52), static_cast<T>(23) ); + boost::rational<T> const x4( static_cast<T>(70), static_cast<T>(31) ); + + BOOST_CHECK( x1 < x2 ); + BOOST_CHECK( !(x1 < x1) ); + BOOST_CHECK( !(x2 < x2) ); + BOOST_CHECK( !(x2 < x1) ); + BOOST_CHECK( x2 < x3 ); + BOOST_CHECK( x4 < x2 ); + BOOST_CHECK( !(x3 < x4) ); + BOOST_CHECK( r7 < x1 ); // not actually close; wanted -ve v. +ve instead + BOOST_CHECK( !(x2 < r7) ); +} + +// Increment & decrement tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_1step_test, T, all_signed_test_types ) +{ + my_configuration::hook<T> h; + boost::rational<T> &r1 = h.r_[ 0 ], &r2 = h.r_[ 1 ], &r3 = h.r_[ 2 ], + &r7 = h.r_[ 6 ], &r8 = h.r_[ 7 ]; + + BOOST_CHECK( r1++ == r2 ); + BOOST_CHECK( r1 != r2 ); + BOOST_CHECK( r1 == r3 ); + BOOST_CHECK( --r1 == r2 ); + BOOST_CHECK( r8-- == r7 ); + BOOST_CHECK( r8 != r7 ); + BOOST_CHECK( ++r8 == r7 ); +} + +// Absolute value tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_abs_test, T, all_signed_test_types ) +{ + typedef my_configuration::hook<T> hook_type; + typedef typename hook_type::rational_type rational_type; + + hook_type h; + rational_type &r2 = h.r_[ 1 ], &r5 = h.r_[ 4 ], &r8 = h.r_[ 7 ]; + +#ifdef BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP + // This is a nasty hack, required because some compilers do not implement + // "Koenig Lookup." Basically, if I call abs(r), the C++ standard says that + // the compiler should look for a definition of abs in the namespace which + // contains r's class (in this case boost)--among other places. + + using boost::abs; +#endif + + BOOST_CHECK_EQUAL( abs(r2), r2 ); + BOOST_CHECK_EQUAL( abs(r5), r5 ); + BOOST_CHECK_EQUAL( abs(r8), rational_type(2, 3) ); +} + +// Unary operator tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_unary_test, T, all_signed_test_types ) +{ + my_configuration::hook<T> h; + boost::rational<T> &r2 = h.r_[ 1 ], &r3 = h.r_[ 2 ], + &r4 = h.r_[ 3 ], &r5 = h.r_[ 4 ]; + + BOOST_CHECK_EQUAL( +r5, r5 ); + + BOOST_CHECK( -r3 != r3 ); + BOOST_CHECK_EQUAL( -(-r3), r3 ); + BOOST_CHECK_EQUAL( -r4, static_cast<T>(3) ); + + BOOST_CHECK( !r2 ); + BOOST_CHECK( !!r3 ); + + BOOST_CHECK( ! static_cast<bool>(r2) ); + BOOST_CHECK( r3 ); +} + +BOOST_AUTO_TEST_SUITE_END() + + +// The rational arithmetic operations suite +BOOST_AUTO_TEST_SUITE( rational_arithmetic_suite ) + +// Addition & subtraction tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_additive_test, T, + all_signed_test_types ) +{ + typedef boost::rational<T> rational_type; + + BOOST_CHECK_EQUAL( rational_type( 1, 2) + rational_type(1, 2), + static_cast<T>(1) ); + BOOST_CHECK_EQUAL( rational_type(11, 3) + rational_type(1, 2), + rational_type( 25, 6) ); + BOOST_CHECK_EQUAL( rational_type(-8, 3) + rational_type(1, 5), + rational_type(-37, 15) ); + BOOST_CHECK_EQUAL( rational_type(-7, 6) + rational_type(1, 7), + rational_type( 1, 7) - rational_type(7, 6) ); + BOOST_CHECK_EQUAL( rational_type(13, 5) - rational_type(1, 2), + rational_type( 21, 10) ); + BOOST_CHECK_EQUAL( rational_type(22, 3) + static_cast<T>(1), + rational_type( 25, 3) ); + BOOST_CHECK_EQUAL( rational_type(12, 7) - static_cast<T>(2), + rational_type( -2, 7) ); + BOOST_CHECK_EQUAL( static_cast<T>(3) + rational_type(4, 5), + rational_type( 19, 5) ); + BOOST_CHECK_EQUAL( static_cast<T>(4) - rational_type(9, 2), + rational_type( -1, 2) ); + + rational_type r( 11 ); + + r -= rational_type( 20, 3 ); + BOOST_CHECK_EQUAL( r, rational_type(13, 3) ); + + r += rational_type( 1, 2 ); + BOOST_CHECK_EQUAL( r, rational_type(29, 6) ); + + r -= static_cast<T>( 5 ); + BOOST_CHECK_EQUAL( r, rational_type( 1, -6) ); + + r += rational_type( 1, 5 ); + BOOST_CHECK_EQUAL( r, rational_type( 1, 30) ); + + r += static_cast<T>( 2 ); + BOOST_CHECK_EQUAL( r, rational_type(61, 30) ); +} + +// Assignment tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_assignment_test, T, + all_signed_test_types ) +{ + typedef boost::rational<T> rational_type; + + rational_type r; + + r = rational_type( 1, 10 ); + BOOST_CHECK_EQUAL( r, rational_type( 1, 10) ); + + r = static_cast<T>( -9 ); + BOOST_CHECK_EQUAL( r, rational_type(-9, 1) ); +} + +// Multiplication tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_multiplication_test, T, + all_signed_test_types ) +{ + typedef boost::rational<T> rational_type; + + BOOST_CHECK_EQUAL( rational_type(1, 3) * rational_type(-3, 4), + rational_type(-1, 4) ); + BOOST_CHECK_EQUAL( rational_type(2, 5) * static_cast<T>(7), + rational_type(14, 5) ); + BOOST_CHECK_EQUAL( static_cast<T>(-2) * rational_type(1, 6), + rational_type(-1, 3) ); + + rational_type r = rational_type( 3, 7 ); + + r *= static_cast<T>( 14 ); + BOOST_CHECK_EQUAL( r, static_cast<T>(6) ); + + r *= rational_type( 3, 8 ); + BOOST_CHECK_EQUAL( r, rational_type(9, 4) ); +} + +// Division tests +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_division_test, T, + all_signed_test_types ) +{ + typedef boost::rational<T> rational_type; + + BOOST_CHECK_EQUAL( rational_type(-1, 20) / rational_type(4, 5), + rational_type(-1, 16) ); + BOOST_CHECK_EQUAL( rational_type( 5, 6) / static_cast<T>(7), + rational_type( 5, 42) ); + BOOST_CHECK_EQUAL( static_cast<T>(8) / rational_type(2, 7), + static_cast<T>(28) ); + + BOOST_CHECK_THROW( rational_type(23, 17) / rational_type(), + boost::bad_rational ); + BOOST_CHECK_THROW( rational_type( 4, 15) / static_cast<T>(0), + boost::bad_rational ); + + rational_type r = rational_type( 4, 3 ); + + r /= rational_type( 5, 4 ); + BOOST_CHECK_EQUAL( r, rational_type(16, 15) ); + + r /= static_cast<T>( 4 ); + BOOST_CHECK_EQUAL( r, rational_type( 4, 15) ); + + BOOST_CHECK_THROW( r /= rational_type(), boost::bad_rational ); + BOOST_CHECK_THROW( r /= static_cast<T>(0), boost::bad_rational ); + + BOOST_CHECK_EQUAL( rational_type(-1) / rational_type(-3), + rational_type(1, 3) ); +} + +// Tests for operations on self +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_self_operations_test, T, + all_signed_test_types ) +{ + typedef boost::rational<T> rational_type; + + rational_type r = rational_type( 4, 3 ); + + r += r; + BOOST_CHECK_EQUAL( r, rational_type( 8, 3) ); + + r *= r; + BOOST_CHECK_EQUAL( r, rational_type(64, 9) ); + + r /= r; + BOOST_CHECK_EQUAL( r, rational_type( 1, 1) ); + + r -= r; + BOOST_CHECK_EQUAL( r, rational_type( 0, 1) ); + + BOOST_CHECK_THROW( r /= r, boost::bad_rational ); +} + +BOOST_AUTO_TEST_CASE_TEMPLATE( gcd_and_lcm_on_rationals, T, all_signed_test_types ) +{ + typedef boost::rational<T> rational; + BOOST_CHECK_EQUAL(boost::integer::gcd(rational(1, 4), rational(1, 3)), + rational(1, 12)); + BOOST_CHECK_EQUAL(boost::integer::lcm(rational(1, 4), rational(1, 3)), + rational(1)); +} + +// Assignment tests +BOOST_AUTO_TEST_CASE_TEMPLATE(rational_mixed_test, T, + /*all_signed_test_types*/ builtin_signed_test_types) +{ + { + typedef boost::rational<boost::intmax_t> rational_type; + T val1 = 20; + boost::intmax_t val2 = 30; + + rational_type r(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + + r.assign(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + } + { + typedef boost::rational<boost::uintmax_t> rational_type2; + + T val1 = 20; + boost::uintmax_t val3 = 30; + + rational_type2 r2(val1, val3); + BOOST_CHECK_EQUAL(r2, rational_type2(20, 30)); + + r2.assign(val1, val3); + BOOST_CHECK_EQUAL(r2, rational_type2(20, 30)); + } + { + typedef boost::rational<short> rational_type; + T val1 = 20; + short val2 = 30; + + rational_type r(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + + r.assign(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + } + { + typedef boost::rational<unsigned short> rational_type; + T val1 = 20; + unsigned short val2 = 30; + + rational_type r(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + + r.assign(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + } + { + typedef boost::rational<long> rational_type; + T val1 = 20; + long val2 = 30; + + rational_type r(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + + r.assign(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + } + { + typedef boost::rational<unsigned long> rational_type; + T val1 = 20; + unsigned long val2 = 30; + + rational_type r(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + + r.assign(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, 30)); + } + { + typedef boost::rational<boost::intmax_t> rational_type; + T val1 = 20; + boost::intmax_t val2 = -30; + + rational_type r(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, -30)); + + r.assign(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(20, -30)); + } + { + typedef boost::rational<short> rational_type; + T val1 = -20; + short val2 = -30; + + rational_type r(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(-20, -30)); + + r.assign(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(-20, -30)); + } + { + typedef boost::rational<long> rational_type; + T val1 = -20; + long val2 = 30; + + rational_type r(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(-20, 30)); + + r.assign(val1, val2); + BOOST_CHECK_EQUAL(r, rational_type(-20, 30)); + } +} + +BOOST_AUTO_TEST_CASE(conversions) +{ + typedef boost::rational<boost::int32_t> signed_rat; + + boost::int32_t signed_max = (std::numeric_limits<boost::int32_t>::max)(); + boost::int32_t signed_min = (std::numeric_limits<boost::int32_t>::min)(); + boost::int32_t signed_min_num = signed_min + 1; + + BOOST_CHECK_EQUAL(signed_rat(signed_max).numerator(), signed_max); + BOOST_CHECK_EQUAL(signed_rat(signed_min).numerator(), signed_min); + BOOST_CHECK_EQUAL(signed_rat(signed_max, 1).numerator(), signed_max); + BOOST_CHECK_EQUAL(signed_rat(signed_min, 1).numerator(), signed_min); + BOOST_CHECK_EQUAL(signed_rat(1, signed_max).denominator(), signed_max); + BOOST_CHECK_EQUAL(signed_rat(1, signed_min_num).denominator(), -signed_min_num); + // This throws because we can't negate signed_min: + BOOST_CHECK_THROW(signed_rat(1, signed_min).denominator(), std::domain_error); + + signed_rat sr; + BOOST_CHECK_EQUAL(sr.assign(signed_max, 1).numerator(), signed_max); + BOOST_CHECK_EQUAL(sr.assign(1, signed_max).denominator(), signed_max); + BOOST_CHECK_EQUAL(sr.assign(signed_min, 1).numerator(), signed_min); + BOOST_CHECK_EQUAL(sr.assign(1, signed_min_num).denominator(), -signed_min_num); + BOOST_CHECK_THROW(sr.assign(1, signed_min), std::domain_error); + + BOOST_CHECK_EQUAL((sr = signed_max).numerator(), signed_max); + BOOST_CHECK_EQUAL((sr = signed_min).numerator(), signed_min); + + boost::int64_t big_signed_max = (std::numeric_limits<boost::int32_t>::max)(); + boost::int64_t big_signed_min = (std::numeric_limits<boost::int32_t>::min)(); + boost::int64_t big_signed_min_num = signed_min + 1; + + BOOST_CHECK_EQUAL(signed_rat(big_signed_max).numerator(), big_signed_max); + BOOST_CHECK_EQUAL(signed_rat(big_signed_min).numerator(), big_signed_min); + BOOST_CHECK_EQUAL(signed_rat(big_signed_max, 1).numerator(), big_signed_max); + BOOST_CHECK_EQUAL(signed_rat(big_signed_min, 1).numerator(), big_signed_min); + BOOST_CHECK_EQUAL(signed_rat(1, big_signed_max).denominator(), big_signed_max); + BOOST_CHECK_EQUAL(signed_rat(1, big_signed_min_num).denominator(), -big_signed_min_num); + // This throws because we can't negate big_signed_min: + BOOST_CHECK_THROW(signed_rat(1, big_signed_min).denominator(), std::domain_error); + + BOOST_CHECK_EQUAL(sr.assign(big_signed_max, 1).numerator(), big_signed_max); + BOOST_CHECK_EQUAL(sr.assign(1, big_signed_max).denominator(), big_signed_max); + BOOST_CHECK_EQUAL(sr.assign(big_signed_min, 1).numerator(), big_signed_min); + BOOST_CHECK_EQUAL(sr.assign(1, big_signed_min_num).denominator(), -big_signed_min_num); + BOOST_CHECK_THROW(sr.assign(1, big_signed_min), std::domain_error); + + BOOST_CHECK_EQUAL((sr = big_signed_max).numerator(), big_signed_max); + BOOST_CHECK_EQUAL((sr = big_signed_min).numerator(), big_signed_min); + + ++big_signed_max; + --big_signed_min; + BOOST_CHECK_THROW(signed_rat(big_signed_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(signed_rat(big_signed_min).numerator(), std::domain_error); + BOOST_CHECK_THROW(signed_rat(big_signed_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(signed_rat(big_signed_min, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(signed_rat(1, big_signed_max).denominator(), std::domain_error); + + BOOST_CHECK_THROW(sr.assign(big_signed_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(sr.assign(1, big_signed_max).denominator(), std::domain_error); + BOOST_CHECK_THROW(sr.assign(big_signed_min, 1).numerator(), std::domain_error); + + BOOST_CHECK_THROW((sr = big_signed_max).numerator(), std::domain_error); + BOOST_CHECK_THROW((sr = big_signed_min).numerator(), std::domain_error); + + boost::int16_t small_signed_max = (std::numeric_limits<boost::int16_t>::max)(); + boost::int16_t small_signed_min = (std::numeric_limits<boost::int16_t>::min)(); + + BOOST_CHECK_EQUAL(signed_rat(small_signed_max).numerator(), small_signed_max); + BOOST_CHECK_EQUAL(signed_rat(small_signed_min).numerator(), small_signed_min); + BOOST_CHECK_EQUAL(signed_rat(small_signed_max, 1).numerator(), small_signed_max); + BOOST_CHECK_EQUAL(signed_rat(small_signed_min, 1).numerator(), small_signed_min); + BOOST_CHECK_EQUAL(signed_rat(1, small_signed_max).denominator(), small_signed_max); + BOOST_CHECK_EQUAL(signed_rat(1, small_signed_min).denominator(), -static_cast<boost::int32_t>(small_signed_min)); + + BOOST_CHECK_EQUAL(sr.assign(small_signed_max, 1).numerator(), small_signed_max); + BOOST_CHECK_EQUAL(sr.assign(1, small_signed_max).denominator(), small_signed_max); + BOOST_CHECK_EQUAL(sr.assign(small_signed_min, 1).numerator(), small_signed_min); + BOOST_CHECK_EQUAL(sr.assign(1, small_signed_min).denominator(), -static_cast<boost::int32_t>(small_signed_min)); + + BOOST_CHECK_EQUAL((sr = small_signed_max).numerator(), small_signed_max); + BOOST_CHECK_EQUAL((sr = small_signed_min).numerator(), small_signed_min); + + boost::uint32_t unsigned_max = signed_max; + BOOST_CHECK_EQUAL(signed_rat(unsigned_max).numerator(), signed_max); + BOOST_CHECK_EQUAL(signed_rat(unsigned_max, 1).numerator(), signed_max); + BOOST_CHECK_EQUAL(signed_rat(1, unsigned_max).denominator(), signed_max); + + BOOST_CHECK_EQUAL(sr.assign(unsigned_max, 1).numerator(), signed_max); + BOOST_CHECK_EQUAL(sr.assign(1, unsigned_max).denominator(), signed_max); + BOOST_CHECK_EQUAL((sr = unsigned_max).numerator(), signed_max); + ++unsigned_max; + BOOST_CHECK_THROW(signed_rat(unsigned_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(signed_rat(unsigned_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(signed_rat(1, unsigned_max).denominator(), std::domain_error); + + BOOST_CHECK_THROW(sr.assign(unsigned_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(sr.assign(1, unsigned_max).denominator(), std::domain_error); + BOOST_CHECK_THROW((sr = unsigned_max).numerator(), std::domain_error); + + boost::uint64_t big_unsigned_max = signed_max; + BOOST_CHECK_EQUAL(signed_rat(big_unsigned_max).numerator(), signed_max); + BOOST_CHECK_EQUAL(signed_rat(big_unsigned_max, 1).numerator(), signed_max); + BOOST_CHECK_EQUAL(signed_rat(1, big_unsigned_max).denominator(), signed_max); + + BOOST_CHECK_EQUAL(sr.assign(big_unsigned_max, 1).numerator(), signed_max); + BOOST_CHECK_EQUAL(sr.assign(1, big_unsigned_max).denominator(), signed_max); + BOOST_CHECK_EQUAL((sr = big_unsigned_max).numerator(), signed_max); + ++big_unsigned_max; + BOOST_CHECK_THROW(signed_rat(big_unsigned_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(signed_rat(big_unsigned_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(signed_rat(1, big_unsigned_max).denominator(), std::domain_error); + + BOOST_CHECK_THROW(sr.assign(big_unsigned_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(sr.assign(1, big_unsigned_max).denominator(), std::domain_error); + BOOST_CHECK_THROW((sr = big_unsigned_max).numerator(), std::domain_error); + + boost::uint16_t small_unsigned_max = signed_max; + BOOST_CHECK_EQUAL(signed_rat(small_unsigned_max).numerator(), small_unsigned_max); + BOOST_CHECK_EQUAL(signed_rat(small_unsigned_max, 1).numerator(), small_unsigned_max); + BOOST_CHECK_EQUAL(signed_rat(1, small_unsigned_max).denominator(), small_unsigned_max); + + BOOST_CHECK_EQUAL(sr.assign(small_unsigned_max, 1).numerator(), small_unsigned_max); + BOOST_CHECK_EQUAL(sr.assign(1, small_unsigned_max).denominator(), small_unsigned_max); + BOOST_CHECK_EQUAL((sr = small_unsigned_max).numerator(), small_unsigned_max); + + // Over again with unsigned rational type: + typedef boost::rational<boost::uint32_t> unsigned_rat; + + unsigned_max = (std::numeric_limits<boost::uint32_t>::max)(); + + BOOST_CHECK_EQUAL(unsigned_rat(unsigned_max).numerator(), unsigned_max); + BOOST_CHECK_EQUAL(unsigned_rat(unsigned_max, 1).numerator(), unsigned_max); + BOOST_CHECK_EQUAL(unsigned_rat(1, unsigned_max).denominator(), unsigned_max); + + unsigned_rat ur; + BOOST_CHECK_EQUAL((ur = unsigned_max).numerator(), unsigned_max); + BOOST_CHECK_EQUAL(ur.assign(unsigned_max, 1).numerator(), unsigned_max); + BOOST_CHECK_EQUAL(ur.assign(1, unsigned_max).denominator(), unsigned_max); + + big_unsigned_max = unsigned_max; + BOOST_CHECK_EQUAL(unsigned_rat(big_unsigned_max).numerator(), big_unsigned_max); + BOOST_CHECK_EQUAL(unsigned_rat(big_unsigned_max, 1).numerator(), big_unsigned_max); + BOOST_CHECK_EQUAL(unsigned_rat(1, big_unsigned_max).denominator(), big_unsigned_max); + BOOST_CHECK_EQUAL((ur = big_unsigned_max).numerator(), big_unsigned_max); + BOOST_CHECK_EQUAL(ur.assign(big_unsigned_max, 1).numerator(), big_unsigned_max); + BOOST_CHECK_EQUAL(ur.assign(1, big_unsigned_max).denominator(), big_unsigned_max); + ++big_unsigned_max; + BOOST_CHECK_THROW(unsigned_rat(big_unsigned_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(big_unsigned_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(1, big_unsigned_max).denominator(), std::domain_error); + BOOST_CHECK_THROW((ur = big_unsigned_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(big_unsigned_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(1, big_unsigned_max).denominator(), std::domain_error); + + BOOST_CHECK_EQUAL(unsigned_rat(small_unsigned_max).numerator(), small_unsigned_max); + BOOST_CHECK_EQUAL(unsigned_rat(small_unsigned_max, 1).numerator(), small_unsigned_max); + BOOST_CHECK_EQUAL(unsigned_rat(1, small_unsigned_max).denominator(), small_unsigned_max); + BOOST_CHECK_EQUAL((ur = small_unsigned_max).numerator(), small_unsigned_max); + BOOST_CHECK_EQUAL(ur.assign(small_unsigned_max, 1).numerator(), small_unsigned_max); + BOOST_CHECK_EQUAL(ur.assign(1, small_unsigned_max).denominator(), small_unsigned_max); + + BOOST_CHECK_EQUAL(unsigned_rat(signed_max).numerator(), signed_max); + BOOST_CHECK_EQUAL(unsigned_rat(signed_max, 1).numerator(), signed_max); + BOOST_CHECK_EQUAL(unsigned_rat(1, signed_max).denominator(), signed_max); + BOOST_CHECK_EQUAL((ur = signed_max).numerator(), signed_max); + BOOST_CHECK_EQUAL(ur.assign(signed_max, 1).numerator(), signed_max); + BOOST_CHECK_EQUAL(ur.assign(1, signed_max).denominator(), signed_max); + BOOST_CHECK_THROW(unsigned_rat(signed_min).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(signed_min, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(1, signed_min).denominator(), std::domain_error); + BOOST_CHECK_THROW((ur = signed_min).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(signed_min, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(1, signed_min).denominator(), std::domain_error); + + big_signed_max = unsigned_max; + BOOST_CHECK_EQUAL(unsigned_rat(big_signed_max).numerator(), unsigned_max); + BOOST_CHECK_EQUAL(unsigned_rat(big_signed_max, 1).numerator(), unsigned_max); + BOOST_CHECK_EQUAL(unsigned_rat(1, big_signed_max).denominator(), unsigned_max); + BOOST_CHECK_EQUAL((ur = big_signed_max).numerator(), unsigned_max); + BOOST_CHECK_EQUAL(ur.assign(big_signed_max, 1).numerator(), unsigned_max); + BOOST_CHECK_EQUAL(ur.assign(1, big_signed_max).denominator(), unsigned_max); + ++big_signed_max; + BOOST_CHECK_THROW(unsigned_rat(big_signed_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(big_signed_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(1, big_signed_max).denominator(), std::domain_error); + BOOST_CHECK_THROW((ur = big_signed_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(big_signed_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(1, big_signed_max).denominator(), std::domain_error); + big_signed_max = -1; + BOOST_CHECK_THROW(unsigned_rat(big_signed_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(big_signed_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(1, big_signed_max).denominator(), std::domain_error); + BOOST_CHECK_THROW((ur = big_signed_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(big_signed_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(1, big_signed_max).denominator(), std::domain_error); + + BOOST_CHECK_EQUAL(unsigned_rat(small_signed_max).numerator(), small_signed_max); + BOOST_CHECK_EQUAL(unsigned_rat(small_signed_max, 1).numerator(), small_signed_max); + BOOST_CHECK_EQUAL(unsigned_rat(1, small_signed_max).denominator(), small_signed_max); + BOOST_CHECK_EQUAL((ur = small_signed_max).numerator(), small_signed_max); + BOOST_CHECK_EQUAL(ur.assign(small_signed_max, 1).numerator(), small_signed_max); + BOOST_CHECK_EQUAL(ur.assign(1, small_signed_max).denominator(), small_signed_max); + small_signed_max = -1; + BOOST_CHECK_THROW(unsigned_rat(small_signed_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(small_signed_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(unsigned_rat(1, small_signed_max).denominator(), std::domain_error); + BOOST_CHECK_THROW((ur = small_signed_max).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(small_signed_max, 1).numerator(), std::domain_error); + BOOST_CHECK_THROW(ur.assign(1, small_signed_max).denominator(), std::domain_error); +} + +BOOST_AUTO_TEST_SUITE_END() + + +// The non-basic rational operations suite +BOOST_AUTO_TEST_SUITE( rational_extras_suite ) + +#ifndef BOOST_NO_IOSTREAM +// Output test +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_output_test, T, all_signed_test_types ) +{ + using namespace std; + typedef boost::rational<T> rational_type; + + // Basic test + ostringstream oss; + + oss << rational_type( 44, 14 ); + BOOST_CHECK_EQUAL( oss.str(), "22/7" ); + + // Width + oss.clear(); oss.str( "" ); + oss << setw( 5 ) << setfill('*') << rational_type( 1, 2 ) << 'r'; + BOOST_CHECK_EQUAL( oss.str(), "**1/2r" ); // not "****1/2r" + + // Positive-sign + oss.clear(); oss.str( "" ); + oss << showpos << rational_type( 2, 3 ) << noshowpos; + BOOST_CHECK_EQUAL( oss.str(), "+2/3" ); // not "+2/+3" + + // Internal padding + oss.clear(); oss.str( "" ); + oss << setw( 8 ) << internal << rational_type( 36, -15 ) << right << 'r'; + BOOST_CHECK_EQUAL( oss.str(), "-***12/5r" ); // not "-*****12/5r" + + // Showbase prefix + oss.clear(); oss.str( "" ); + oss << showbase << hex << rational_type( 34, 987 ) << noshowbase << dec; + BOOST_CHECK_EQUAL( oss.str(), "0x22/3db" ); // not "0x22/0x3db" +} + +// Input test, failing +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_input_failing_test, T, + all_signed_test_types ) +{ + std::istringstream iss( "" ); + boost::rational<T> r; + + iss >> r; + BOOST_CHECK( !iss ); + BOOST_CHECK( !iss.bad() ); + + iss.clear(); + iss.str( "42" ); + iss >> r; + BOOST_CHECK( !iss ); + + iss.clear(); + iss.str( "57A" ); + iss >> r; + BOOST_CHECK( !iss ); + + iss.clear(); + iss.str( "20-20" ); + iss >> r; + BOOST_CHECK( !iss ); + + iss.clear(); + iss.str( "1/" ); + iss >> r; + BOOST_CHECK( !iss ); + + iss.clear(); + iss.str( "1/ 2" ); + iss >> r; + BOOST_CHECK( !iss ); + + iss.clear(); + iss.str( "1 /2" ); + iss >> r; + BOOST_CHECK( !iss ); + + // Illegal value check(s) + typedef std::numeric_limits<T> limits_type; + + iss.clear(); + iss.str( "3/0" ); + iss >> r; + BOOST_CHECK( !iss ); + + if ( limits_type::is_signed && limits_type::is_bounded && + limits_type::min BOOST_PREVENT_MACRO_SUBSTITUTION () + + limits_type::max BOOST_PREVENT_MACRO_SUBSTITUTION () < T(0) ) + { + std::ostringstream oss; + + oss << 1 << '/' << limits_type::min BOOST_PREVENT_MACRO_SUBSTITUTION (); + iss.clear(); + iss.str( oss.str() ); + iss.exceptions( std::ios::failbit ); + BOOST_CHECK( iss.good() ); + BOOST_CHECK_THROW( iss >> r, boost::bad_rational ); + BOOST_CHECK( iss.fail() && !iss.bad() ); + iss.exceptions( std::ios::goodbit ); + } +} + +// Input test, passing +BOOST_AUTO_TEST_CASE_TEMPLATE( rational_input_passing_test, T, + all_signed_test_types ) +{ + typedef boost::rational<T> rational_type; + + std::istringstream iss( "1/2 12" ); + rational_type r; + int n = 0; + + BOOST_CHECK( iss >> r >> n ); + BOOST_CHECK_EQUAL( r, rational_type(1, 2) ); + BOOST_CHECK_EQUAL( n, 12 ); + + iss.clear(); + iss.str( "34/67" ); + BOOST_CHECK( iss >> r ); + BOOST_CHECK_EQUAL( r, rational_type(34, 67) ); + + iss.clear(); + iss.str( "-3/-6" ); + BOOST_CHECK( iss >> r ); + BOOST_CHECK_EQUAL( r, rational_type(1, 2) ); +} +#endif // BOOST_NO_IOSTREAM + +// Conversion test +BOOST_AUTO_TEST_CASE( rational_cast_test ) +{ + // Note that these are not generic. The problem is that rational_cast<T> + // requires a conversion from IntType to T. However, for a user-defined + // IntType, it is not possible to define such a conversion except as an + // "operator T()". This causes problems with overloading resolution. + boost::rational<int> const half( 1, 2 ); + + BOOST_CHECK_CLOSE( boost::rational_cast<double>(half), 0.5, 0.01 ); + BOOST_CHECK_EQUAL( boost::rational_cast<int>(half), 0 ); + BOOST_CHECK_EQUAL( boost::rational_cast<MyInt>(half), MyInt() ); + BOOST_CHECK_EQUAL( boost::rational_cast<boost::rational<MyInt> >(half), + boost::rational<MyInt>(1, 2) ); + + // Conversions via explicit-marked constructors + // (Note that the "explicit" mark prevents conversion to + // boost::rational<MyOverflowingUnsigned>.) + boost::rational<MyInt> const threehalves( 3, 2 ); + + BOOST_CHECK_EQUAL( boost::rational_cast<MyOverflowingUnsigned>(threehalves), + MyOverflowingUnsigned(1u) ); + // + // Converting constructor should throw if a bad rational number results: + // + BOOST_CHECK_THROW(boost::rational<short>(boost::rational<long>(1, 1 << sizeof(short) * CHAR_BIT)), boost::bad_rational); + // + // New tests from checked narrowing conversions: + // + BOOST_CHECK_THROW(boost::rational<unsigned>(-1), boost::bad_rational); + BOOST_CHECK_THROW(boost::rational<unsigned>(-1, 1), boost::bad_rational); + BOOST_CHECK_THROW(boost::rational<unsigned>(1, -1), boost::bad_rational); + unsigned ui_max = (std::numeric_limits<unsigned>::max)(); + BOOST_CHECK_THROW(boost::rational<int>(static_cast<unsigned>(ui_max)), boost::bad_rational); + BOOST_CHECK_THROW(boost::rational<int>(ui_max, 1u), boost::bad_rational); + BOOST_CHECK_THROW(boost::rational<int>(1u, ui_max), boost::bad_rational); + // + // Check assignments that should succeed from both wider and narrower types: + // + boost::rational<boost::int32_t> rat; +#ifndef BOOST_NO_INT64_T + boost::int64_t ll, ll1(1); + boost::uint64_t ull, ull1(1); + boost::int32_t imax = (std::numeric_limits<boost::int32_t>::max)(); + boost::int32_t imin = (std::numeric_limits<boost::int32_t>::min)(); + ll = imax; + rat.assign(ll, ll1); + BOOST_CHECK_EQUAL(rat.numerator(), imax); + BOOST_CHECK_EQUAL(rat.denominator(), 1); + ++ll; + BOOST_CHECK_THROW(rat.assign(ll, ll1), boost::bad_rational); + ll = imin; + rat.assign(ll, ll1); + BOOST_CHECK_EQUAL(rat.numerator(), imin); + BOOST_CHECK_EQUAL(rat.denominator(), 1); + --ll; + BOOST_CHECK_THROW(rat.assign(ll, ll1), boost::bad_rational); + ull = imax; + rat.assign(ull, ull1); + BOOST_CHECK_EQUAL(rat.numerator(), imax); + BOOST_CHECK_EQUAL(rat.denominator(), 1); + ++ull; + BOOST_CHECK_THROW(rat.assign(ull, ull1), boost::bad_rational); + ull = 0; + rat.assign(ull, ull1); + BOOST_CHECK_EQUAL(rat.numerator(), 0); + BOOST_CHECK_EQUAL(rat.denominator(), 1); +#endif + boost::int16_t smax = (std::numeric_limits<boost::int16_t>::max)(); + boost::int16_t smin = (std::numeric_limits<boost::int16_t>::min)(); + boost::int16_t s1 = 1; + rat.assign(smax, s1); + BOOST_CHECK_EQUAL(rat.numerator(), smax); + BOOST_CHECK_EQUAL(rat.denominator(), 1); + rat.assign(smin, s1); + BOOST_CHECK_EQUAL(rat.numerator(), smin); + BOOST_CHECK_EQUAL(rat.denominator(), 1); + boost::uint16_t usmax = (std::numeric_limits<boost::uint16_t>::max)(); + boost::uint16_t usmin = (std::numeric_limits<boost::uint16_t>::min)(); + boost::uint16_t us1 = 1; + rat.assign(usmax, us1); + BOOST_CHECK_EQUAL(rat.numerator(), usmax); + BOOST_CHECK_EQUAL(rat.denominator(), 1); + rat.assign(usmin, us1); + BOOST_CHECK_EQUAL(rat.numerator(), usmin); + BOOST_CHECK_EQUAL(rat.denominator(), 1); + // + // Over again with unsigned rational: + // + boost::rational<boost::uint32_t> urat; + unsigned uimax = (std::numeric_limits<boost::uint32_t>::max)(); + unsigned uimin = (std::numeric_limits<boost::uint32_t>::min)(); +#ifndef BOOST_NO_INT64_T + ll = uimax; + urat.assign(ll, ll1); + BOOST_CHECK_EQUAL(urat.numerator(), uimax); + BOOST_CHECK_EQUAL(urat.denominator(), 1); + ++ll; + BOOST_CHECK_THROW(urat.assign(ll, ll1), boost::bad_rational); + ll = uimin; + urat.assign(ll, ll1); + BOOST_CHECK_EQUAL(urat.numerator(), uimin); + BOOST_CHECK_EQUAL(urat.denominator(), 1); + --ll; + BOOST_CHECK_THROW(urat.assign(ll, ll1), boost::bad_rational); + ull = uimax; + urat.assign(ull, ull1); + BOOST_CHECK_EQUAL(urat.numerator(), uimax); + BOOST_CHECK_EQUAL(urat.denominator(), 1); + ++ull; + BOOST_CHECK_THROW(urat.assign(ull, ull1), boost::bad_rational); + ull = 0; + urat.assign(ull, ull1); + BOOST_CHECK_EQUAL(urat.numerator(), 0); + BOOST_CHECK_EQUAL(urat.denominator(), 1); +#endif + smin = 0; + s1 = 1; + urat.assign(smax, s1); + BOOST_CHECK_EQUAL(urat.numerator(), smax); + BOOST_CHECK_EQUAL(urat.denominator(), 1); + urat.assign(smin, s1); + BOOST_CHECK_EQUAL(urat.numerator(), smin); + BOOST_CHECK_EQUAL(urat.denominator(), 1); + urat.assign(usmax, us1); + BOOST_CHECK_EQUAL(urat.numerator(), usmax); + BOOST_CHECK_EQUAL(urat.denominator(), 1); + urat.assign(usmin, us1); + BOOST_CHECK_EQUAL(urat.numerator(), usmin); + BOOST_CHECK_EQUAL(urat.denominator(), 1); + // + // Conversions that must not be allowed: + // + BOOST_STATIC_ASSERT(!boost::is_convertible<float, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(!boost::is_convertible<double, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(!boost::is_convertible<long double, boost::rational<int> >::value); + // And ones that should: + BOOST_STATIC_ASSERT(boost::is_convertible<char, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(boost::is_convertible<signed char, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(boost::is_convertible<unsigned char, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(boost::is_convertible<short, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(boost::is_convertible<unsigned short, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(boost::is_convertible<int, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(boost::is_convertible<unsigned int, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(boost::is_convertible<long, boost::rational<int> >::value); + BOOST_STATIC_ASSERT(boost::is_convertible<unsigned long, boost::rational<int> >::value); +} + +#ifndef BOOST_NO_MEMBER_TEMPLATES +// Cross-conversion constructor test +BOOST_AUTO_TEST_CASE( rational_cross_constructor_test ) +{ + // This template will be repeated a lot. + using boost::rational; + + // Create a bunch of explicit conversions. + rational<int> const half_i( 2, 4 ); + rational<unsigned> const half_u( half_i ); + rational<MyInt> const half_mi( half_i ); + rational<MyOverflowingUnsigned> const half_mu1(half_u), half_mu2(half_mi); + + BOOST_CHECK_EQUAL( half_u.numerator(), 1u ); + BOOST_CHECK_EQUAL( half_u.denominator(), 2u ); + BOOST_CHECK_EQUAL( half_mi.numerator(), MyInt(1) ); + BOOST_CHECK_EQUAL( half_mi.denominator(), MyInt(2) ); + BOOST_CHECK_EQUAL( half_mu1.numerator(), MyOverflowingUnsigned(1u) ); + BOOST_CHECK_EQUAL( half_mu1.denominator(), MyOverflowingUnsigned(2u) ); + BOOST_CHECK_EQUAL( half_mu2.numerator(), MyOverflowingUnsigned(1u) ); + BOOST_CHECK_EQUAL( half_mu2.denominator(), MyOverflowingUnsigned(2u) ); + +#if 0 + // This will fail since it needs an implicit conversion. + // (Try it if your compiler supports C++11 lambdas.) + BOOST_CHECK( [](rational<unsigned> x){return !!x;}(half_i) ); +#endif + + // Translation from a built-in unsigned type to a signed one is + // implementation-defined, so hopefully we won't get a trap value. + // (We're counting on static_cast<int>(UINT_MAX) being negative.) + rational<unsigned> const too_small( 1u, UINT_MAX ); + rational<int> receiver; + + BOOST_CHECK_THROW( receiver=rational<int>(too_small), boost::bad_rational ); +} +#endif // BOOST_NO_MEMBER_TEMPLATES + +// Dice tests (a non-main test) +BOOST_AUTO_TEST_CASE_TEMPLATE( dice_roll_test, T, all_signed_test_types ) +{ + typedef boost::rational<T> rational_type; + + // Determine the mean number of times a fair six-sided die + // must be thrown until each side has appeared at least once. + rational_type r = T( 0 ); + + for ( int i = 1 ; i <= 6 ; ++i ) + { + r += rational_type( 1, i ); + } + r *= static_cast<T>( 6 ); + + BOOST_CHECK_EQUAL( r, rational_type(147, 10) ); +} + +BOOST_AUTO_TEST_SUITE_END() + + +// The bugs, patches, and requests checking suite +BOOST_AUTO_TEST_SUITE( bug_patch_request_suite ) + +// "rational operator< can overflow" +BOOST_AUTO_TEST_CASE( bug_798357_test ) +{ + // Choose values such that rational-number comparisons will overflow if + // the multiplication method (n1/d1 ? n2/d2 == n1*d2 ? n2*d1) is used. + // (And make sure that the large components are relatively prime, so they + // won't partially cancel to make smaller, more reasonable, values.) + unsigned const n1 = UINT_MAX - 2u, d1 = UINT_MAX - 1u; + unsigned const n2 = d1, d2 = UINT_MAX; + boost::rational<MyOverflowingUnsigned> const r1( n1, d1 ), r2( n2, d2 ); + + BOOST_REQUIRE_EQUAL( boost::integer::gcd(n1, d1), 1u ); + BOOST_REQUIRE_EQUAL( boost::integer::gcd(n2, d2), 1u ); + BOOST_REQUIRE( n1 > UINT_MAX / d2 ); + BOOST_REQUIRE( n2 > UINT_MAX / d1 ); + BOOST_CHECK( r1 < r2 ); + BOOST_CHECK( !(r1 < r1) ); + BOOST_CHECK( !(r2 < r1) ); +} + +// "rational::operator< fails for unsigned value types" +BOOST_AUTO_TEST_CASE( patch_1434821_test ) +{ + // If a zero-rational v. positive-integer comparison involves negation, then + // it may fail with unsigned types, which wrap around (for built-ins) or + // throw/be-undefined (for user-defined types). + boost::rational<unsigned> const r( 0u ); + + BOOST_CHECK( r < 1u ); +} + +// "rational.hpp::gcd returns a negative value sometimes" +BOOST_AUTO_TEST_CASE( patch_1438626_test ) +{ + // The issue only manifests with 2's-complement integers that use their + // entire range of bits. [This means that ln(-INT_MIN)/ln(2) is an integer + // and INT_MAX + INT_MIN == -1.] The common computer platforms match this. +#if (INT_MAX + INT_MIN == -1) && ((INT_MAX ^ INT_MIN) == -1) + // If a GCD routine takes the absolute value of an argument only before + // processing, it won't realize that -INT_MIN -> INT_MIN (i.e. no change + // from negation) and will propagate a negative sign to its result. + BOOST_REQUIRE_EQUAL( boost::integer::gcd(INT_MIN, 6), 2 ); + + // That is bad if the rational number type does not check for that + // possibility during normalization. + boost::rational<int> const r1( INT_MIN / 2 + 3, 6 ), + r2( INT_MIN / 2 - 3, 6 ), r3 = r1 + r2; + + // If the error happens, the signs of the components will be switched. + // (The numerators' sum is INT_MIN, and its GCD with 6 would be negated.) + BOOST_CHECK_EQUAL( r3.numerator(), INT_MIN / 2 ); + BOOST_CHECK_EQUAL( r3.denominator(), 3 ); +#endif +} + +// The bug/patch numbers for the above 3 tests are from our SourceForge repo +// before we moved to our own SVN & Trac server. At the time this note is +// written, it seems that SourceForge has reset their tracking numbers at least +// once, so I don't know how to recover those old tickets. The ticket numbers +// for the following tests are from our SVN/Trac repo. + +//"narrowing conversion error with -std=c++0x in operator< with int_type != int" +BOOST_AUTO_TEST_CASE( ticket_5855_test ) +{ + // The internals of operator< currently store a structure of two int_type + // (where int_type is the component type of a boost::rational template + // class) and two computed types. These computed types, results of + // arithmetic operations among int_type values, are either int_type + // themselves or a larger type that can implicitly convert to int_type. + // Those conversions aren't usually a problem. But when an arithmetic + // operation involving two values of a built-in scalar type smaller than int + // are involved, the result is an int. But the resulting int-to-shorter + // conversion is considered narrowing, resulting in a warning or error on + // some compilers. Notably, C++11 compilers are supposed to consider it an + // error. + // + // The solution is to force an explicit conversion, although it's otherwise + // not needed. (The compiler can rescind the narrowing warning if the + // results of the larger type still fit in the smaller one, and that proof + // can be generated at constexpr time.) + typedef short shorter_than_int_type; + typedef boost::rational<shorter_than_int_type> rational_type; + + bool const dummy = rational_type() < rational_type(); + + BOOST_REQUIRE( !dummy ); +} + +// "rational::assign" doesn't even have the basic guarantee +BOOST_AUTO_TEST_CASE( ticket_9067_test ) +{ + using boost::rational; + using boost::integer::gcd; + + rational<int> a( 6, -8 ); + + // Normalize to maintain invariants + BOOST_CHECK_EQUAL( a.numerator(), -3 ); + BOOST_CHECK_EQUAL( a.denominator(), 4 ); + BOOST_CHECK( a.denominator() > 0 ); + BOOST_CHECK_EQUAL( gcd(a.numerator(), a.denominator()), 1 ); + + // Do we maintain the basic guarantee after a failed component-assign? + BOOST_CHECK_THROW( a.assign(1, 0), boost::bad_rational ); + BOOST_CHECK_NE( a.denominator(), 0 ); + BOOST_CHECK( a.denominator() > 0 ); + BOOST_CHECK_EQUAL( gcd(a.numerator(), a.denominator()), 1 ); + + // Do we get the strong guarantee? + BOOST_CHECK_EQUAL( a.numerator(), -3 ); + BOOST_CHECK_EQUAL( a.denominator(), 4 ); + +#if INT_MIN + INT_MAX < 0 + // Try an example without a zero-denominator + a = rational<int>( -9, 12 ); + BOOST_CHECK_EQUAL( a.numerator(), -3 ); + BOOST_CHECK_EQUAL( a.denominator(), 4 ); + BOOST_CHECK( a.denominator() > 0 ); + BOOST_CHECK_EQUAL( gcd(a.numerator(), a.denominator()), 1 ); + BOOST_CHECK_THROW( a.assign(-(INT_MIN + 1), INT_MIN), boost::bad_rational ); + BOOST_CHECK( a.denominator() > 0 ); + BOOST_CHECK_EQUAL( gcd(a.numerator(), a.denominator()), 1 ); + BOOST_CHECK_EQUAL( a.numerator(), -3 ); + BOOST_CHECK_EQUAL( a.denominator(), 4 ); +#endif +} + +BOOST_AUTO_TEST_SUITE_END() |