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94 lines
4.0 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
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<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
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<link rel="stylesheet" type="text/css" href="../../../../boost.css">
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<title>Tests and Examples</title>
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</head>
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<body lang="en">
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<h1>Tests and Examples</h1>
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<p>In <code>libs/interval/test/</code> and
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<code>libs/interval/examples/</code> are some test and example programs.. The
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examples illustrate a few uses of intervals. For a general description and
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considerations on using this library, and some potential domains of
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application, please read this <a href="guide.htm">mini-guide</a>.</p>
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<h2>Tests</h2>
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<p>The test programs are as follows. Please note that they require the use of
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the Boost.test library and can be automatically tested by using
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<code>bjam</code> (except for interval_test.cpp).</p>
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<p><b>add.cpp</b> tests if the additive and substractive operators and the
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respective _std and _opp rounding functions are correctly implemented. It is
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done by using symbolic expressions as a base type.</p>
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<p><b>cmp.cpp</b> and <b>cmp_lex.cpp</b> test if the operators
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<code><</code> <code>></code> <code><=</code> <code>>=</code>
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<code>==</code> <code>!=</code> behave correctly for the default comparison
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and the lexicographic comparison. <b>cmp_exp.cpp</b> tests the explicit
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comparison functions <code>cer..</code> and <code>pos..</code> behave
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correctly. All these tests use some simple intervals ([1,2] and [3,4], [1,3]
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and [2,4], [1,2] and [2,3], etc).</p>
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<p><b>det.cpp</b> tests if the <code>_std</code> and <code>_opp</code>
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versions in protected and unprotected mode produce the same result when Gauss
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scheme is used on an unstable matrix (in order to exercise rounding). The
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tests are done for <code>interval<float></code> and
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<code>interval<double></code>.</p>
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<p><b>fmod.cpp</b> defines a minimalistic version of
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<code>interval<int></code> and uses it in order to test
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<code>fmod</code> on some specific interval values.</p>
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<p><b>mul.cpp</b> exercices the multiplication, the finite division, the
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square and the square root with some integer intervals leading to exact
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results.</p>
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<p><b>pi.cpp</b> tests if the interval value of π (for
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<code>int</code>, <code>float</code> and <code>double</code> base types)
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contains the number π (defined with 21 decimal digits) and if it is a
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subset of [π±1ulp] (in order to ensure some precision).</p>
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<p><b>pow.cpp</b> tests if the <code>pow</code> function behaves correctly on
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some simple test cases.</p>
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<p><strong>test_float.cpp</strong> exercises the arithmetic operations of the
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library for floating point base types.</p>
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<p><b>interval_test.cpp</b> tests if the interval library respects the
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inclusion property of interval arithmetic by computing some functions and
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operations for both <code>double</code> and
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<code>interval<double></code>.</p>
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<h2>Examples</h2>
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<p><b>findroot_demo.cpp</b> finds zeros of some functions by using dichotomy
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and even produces gnuplot datas for one of them. The processor has to
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correctly handle elementary functions for this example to properly work.</p>
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<p><b>horner.cpp</b> is a really basic example of unprotecting the interval
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operations for a whole function (which computes the value of a polynomial by
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using Horner scheme).</p>
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<p><b>newton-raphson.cpp</b> is a (bad) implementation of a specialized
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version of Newton-Raphson algorithm for finding the zeros of a function
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knowing its derivative. It exercises unprotecting, full division, some set
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operations and empty intervals.</p>
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<p><b>interval_speed.cpp</b> is not really an example but more like a
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benchmark for testing performance of the library. It needs to be compiled
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with <code>-DUSE_BOOST</code>. The compilation option
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<code>-DUSE_BOOST_UNPROTECTED</code> allows the program to use unprotected
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local rounding, leading to better performance.</p>
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<hr>
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<p>Revised: 2002-12-15<br>
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Copyright (c) Guillaume Melquiond, Sylvain Pion, Hervé Brönnimann, 2002.<br>
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Polytechnic University.</p>
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</body>
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</html>
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