build based on ab2edd8

dev/construction/index.html

@@ -45,4 +45,4 @@
 
 julia> sin(big"0.1") + cos(big"0.2") ∈ x
 true</code></pre></li></ul><ul><li><p><code>Interval(x)</code></p><p><code>Interval(x1, x2)</code></p><p><code>Interval</code> is the underlying interval constructor. Since v0.12 of the package, however, <em>for efficiency reasons this performs no tests on the validity of the interval, and allows invalid intervals to be created</em>. As a result, we recommend that <em>this should not be used in user code</em>; it should only be used in library functions which guarantee that the interval is already of the correct form.</p><p>For example, the following creates an invalid interval which will cause problems later:</p><pre><code class="nohighlight hljs">julia&gt; Interval(3, 2)  # do *not* do this
-[3, 2]</code></pre></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../intro/">« Interval Arithmetic</a><a class="docs-footer-nextpage" href="../usage/">Basic usage »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 10:51">Monday 28 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+[3, 2]</code></pre></li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../intro/">« Interval Arithmetic</a><a class="docs-footer-nextpage" href="../usage/">Basic usage »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 29 August 2023 04:51">Tuesday 29 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/decorations/index.html

@@ -42,4 +42,4 @@
 [0, 1.73206]_trv
 
 julia> sqrt(X6)
-[0, 1.73206]_com</code></pre><p>This shows that loose evaluation occurred in different parts of the expression in the two different cases.</p><p>In general, the <code>trv</code> decoration is thus used only to signal that &quot;something unexpected&quot; happened during the calculation. Often this is later used to split up the original interval into pieces and reevaluate the function on each piece to refine the information that is obtained about the function.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../usage/">« Basic usage</a><a class="docs-footer-nextpage" href="../multidim/">Multi-dimensional boxes »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 10:51">Monday 28 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+[0, 1.73206]_com</code></pre><p>This shows that loose evaluation occurred in different parts of the expression in the two different cases.</p><p>In general, the <code>trv</code> decoration is thus used only to signal that &quot;something unexpected&quot; happened during the calculation. Often this is later used to split up the original interval into pieces and reevaluate the function on each piece to refine the information that is obtained about the function.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../usage/">« Basic usage</a><a class="docs-footer-nextpage" href="../multidim/">Multi-dimensional boxes »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 29 August 2023 04:51">Tuesday 29 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/input_output/index.html

@@ -98,4 +98,4 @@
 
 julia> interval_to_string(Interval(35.55, 35.65), "9 : .  ? e")
 "3.560?6e1"  
-</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../api/">« API</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 10:51">Monday 28 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../api/">« API</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 29 August 2023 04:51">Tuesday 29 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/intro/index.html

@@ -11,4 +11,4 @@
 
 julia> f(X)
 [7, 14]</code></pre><p>Since <code>f(X)</code> does not contain 0, the true range of the function <span>$f$</span> over the set <span>$X$</span> is guaranteed not to contain 0, and hence we have</p><p><strong>Theorem:</strong> The function <span>$f$</span> has no root in the interval <span>$[3,4]$</span>.</p><p>This theorem has been obtained using <em>just floating-point calculations</em>!</p><p>Further, we can even extend this to semi-infinite intervals:</p><pre><code class="nohighlight hljs">julia&gt; f(3..∞)
-[7, ∞]</code></pre><p>Thus we have <em>excluded the entire domain [3, ∞) from possibly containing roots of <span>$f$</span>.</em></p><p>To move beyond just excluding regions and to actually guaranteeing existence and uniqueness for smooth functions, we use an interval version of the Newton method, which is described a bit <a href="https://juliaintervals.github.io/IntervalRootFinding.jl/latest/">here</a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Package</a><a class="docs-footer-nextpage" href="../construction/">Constructing intervals »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 10:51">Monday 28 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+[7, ∞]</code></pre><p>Thus we have <em>excluded the entire domain [3, ∞) from possibly containing roots of <span>$f$</span>.</em></p><p>To move beyond just excluding regions and to actually guaranteeing existence and uniqueness for smooth functions, we use an interval version of the Newton method, which is described a bit <a href="https://juliaintervals.github.io/IntervalRootFinding.jl/latest/">here</a>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Package</a><a class="docs-footer-nextpage" href="../construction/">Constructing intervals »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 29 August 2023 04:51">Tuesday 29 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/multidim/index.html

@@ -19,4 +19,4 @@
 ([3, 3], [-1, -1])
 
 julia> IntervalBox(f(X...))
-[3, 3] × [-1, -1]</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../decorations/">« Decorations</a><a class="docs-footer-nextpage" href="../rounding/">Rounding »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 10:51">Monday 28 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+[3, 3] × [-1, -1]</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../decorations/">« Decorations</a><a class="docs-footer-nextpage" href="../rounding/">Rounding »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 29 August 2023 04:51">Tuesday 29 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/rounding/index.html

@@ -17,4 +17,4 @@
 
 julia> showfull(f(a))
 Interval(0.39999999999999997, 0.4)</code></pre><p>The result correctly contains the true 0.4.</p><h2 id="More-detail:-the-internal-representation"><a class="docs-heading-anchor" href="#More-detail:-the-internal-representation">More detail: the internal representation</a><a id="More-detail:-the-internal-representation-1"></a><a class="docs-heading-anchor-permalink" href="#More-detail:-the-internal-representation" title="Permalink"></a></h2><p>Let&#39;s look at the internal representation of the <code>Float64</code> number 0.1:</p><pre><code class="language-julia-repl hljs">julia&gt; bitstring(0.1)
-&quot;0011111110111001100110011001100110011001100110011001100110011010&quot;</code></pre><p>The last 53 bits of these 64 bits correspond to the binary expansion of 0.1, which is</p><pre><code class="nohighlight hljs">0.000110011001100110011001100110011001100...</code></pre><p>We see that the expansion is periodic; in fact, the binary expansion of 0.1 has an infinite repetition of the sequence of digits <code>1100</code>. It is thus <em>impossible</em> to represent the decimal 0.1 in binary, with <em>any</em> precision.</p><p>The true value must be approximated by a floating-point number with fixed precision – this procedure is called <strong>rounding</strong>. For positive numbers, rounding down may be accomplished simply by truncating the expansion; rounding up is accomplished by incrementing the final binary digit and propagating any resulting changes.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../multidim/">« Multi-dimensional boxes</a><a class="docs-footer-nextpage" href="../api/">API »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Monday 28 August 2023 10:51">Monday 28 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+&quot;0011111110111001100110011001100110011001100110011001100110011010&quot;</code></pre><p>The last 53 bits of these 64 bits correspond to the binary expansion of 0.1, which is</p><pre><code class="nohighlight hljs">0.000110011001100110011001100110011001100...</code></pre><p>We see that the expansion is periodic; in fact, the binary expansion of 0.1 has an infinite repetition of the sequence of digits <code>1100</code>. It is thus <em>impossible</em> to represent the decimal 0.1 in binary, with <em>any</em> precision.</p><p>The true value must be approximated by a floating-point number with fixed precision – this procedure is called <strong>rounding</strong>. For positive numbers, rounding down may be accomplished simply by truncating the expansion; rounding up is accomplished by incrementing the final binary digit and propagating any resulting changes.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../multidim/">« Multi-dimensional boxes</a><a class="docs-footer-nextpage" href="../api/">API »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 29 August 2023 04:51">Tuesday 29 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>