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Classes.html
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@ -205,7 +205,7 @@ secure PRNG.</p>
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@ -339,7 +339,7 @@ cryptographically secure PRNG.</p>
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@ -280,7 +280,7 @@ using cryptographically secure random bytes.</p>
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Extensions.html
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@ -274,7 +274,7 @@
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Extensions/BinaryInteger.html
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@ -161,8 +161,8 @@
</ul>
<p><a href="#/Factoring%20(Fixed-Width)">Factoring (Fixed-Width)</a></p>
<ul>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_s010ArithmeticK0O8overflowtx_xtFZ">gcdReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_s010ArithmeticK0O8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_Sb8overflowtx_xtFZ">gcdReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE07lcmFullF0x4high_AF3lowtx_xtFZ">lcmFullWidth(_:_:)</a></li>
</ul>
<p><a href="#/Initializers">Initializers</a></p>
@ -327,7 +327,7 @@ a runtime error may occur.</p>
<ul>
<li>
<div>
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_s010ArithmeticK0O8overflowtx_xtFZ"></a>
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_Sb8overflowtx_xtFZ"></a>
<a name="//apple_ref/swift/Method/gcdReportingOverflow(_:_:)" class="dashAnchor"></a>
<h4>
<code>gcdReportingOverflow(_:_:)</code>
@ -343,14 +343,14 @@ whether overflow occurred during the operation.</p>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">gcdReportingOverflow</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">ArithmeticOverflow</span><span class="p">)</span></code></pre>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">Bool</span><span class="p">)</span></code></pre>
</div>
</div>
</li>
<li>
<div>
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_s010ArithmeticK0O8overflowtx_xtFZ"></a>
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ"></a>
<a name="//apple_ref/swift/Method/lcmReportingOverflow(_:_:)" class="dashAnchor"></a>
<h4>
<code>lcmReportingOverflow(_:_:)</code>
@ -366,7 +366,7 @@ whether overflow occurred during the operation.</p>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcmReportingOverflow</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">ArithmeticOverflow</span><span class="p">)</span></code></pre>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">Bool</span><span class="p">)</span></code></pre>
</div>
</div>
@ -459,7 +459,7 @@ a runtime error may occur.</p>
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2
Extensions/Double.html
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@ -794,7 +794,7 @@
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2
Extensions/Float.html
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@ -794,7 +794,7 @@
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2
Extensions/FloatingPoint.html
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@ -304,7 +304,7 @@ the value with more trailing zeros in its significand bit pattern.</p>
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8
Extensions/UnsignedInteger.html
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@ -153,7 +153,7 @@
</ul>
<p><a href="#/Factoring%20(Fixed-Width)">Factoring (Fixed-Width)</a></p>
<ul>
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_s010ArithmeticI0O8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE07lcmFullF0x4high_9Magnitudes0C0PQz3lowtx_xtFZ">lcmFullWidth(_:_:)</a></li>
</ul>
</div>
@ -251,7 +251,7 @@
<ul>
<li>
<div>
<a name="/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_s010ArithmeticI0O8overflowtx_xtFZ"></a>
<a name="/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ"></a>
<a name="//apple_ref/swift/Method/lcmReportingOverflow(_:_:)" class="dashAnchor"></a>
<h4>
<code>lcmReportingOverflow(_:_:)</code>
@ -267,7 +267,7 @@ whether overflow occurred during the operation.</p>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcmReportingOverflow</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">ArithmeticOverflow</span><span class="p">)</span></code></pre>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">Bool</span><span class="p">)</span></code></pre>
</div>
</div>
@ -302,7 +302,7 @@ computed using full-width arithmetic.</p>
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2
Functions.html
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@ -314,7 +314,7 @@ of <code>x</code>.</p>
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12
Protocols.html
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@ -224,10 +224,11 @@ minimum and maximum values for the uniform distribution.</p>
</h4>
</div>
<div class="abstract">
<p>A floating-point type that provides a selection of special functions.</p>
<p>A floating-point type that supports elementary functions and a selection of
special functions.</p>
<p>The <code>Real</code> protocol provides a suitable basis for writing functions that
work on any floating-point type that provides the required functions.</p>
work on any floating-point type that supports the required functions.</p>
<a href="Protocols/Real.html">See more…</a>
</div>
@ -253,11 +254,10 @@ work on any floating-point type that provides the required functions.</p>
</h4>
</div>
<div class="abstract">
<p>A signed numeric type that provides square root, cube root, and elementary
transcendental functions.</p>
<p>A signed numeric type that supports elementary functions.</p>
<p>The <code>Math</code> protocol provides a suitable basis for writing functions that
work on any real or complex floating-point type which provides the required
work on any real or complex floating-point type that supports the required
functions.</p>
<a href="Protocols/Math.html">See more…</a>
@ -278,7 +278,7 @@ functions.</p>
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7
Protocols/Math.html
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@ -134,11 +134,10 @@
</div>
</div>
<p>A signed numeric type that provides square root, cube root, and elementary
transcendental functions.</p>
<p>A signed numeric type that supports elementary functions.</p>
<p>The <code>Math</code> protocol provides a suitable basis for writing functions that
work on any real or complex floating-point type which provides the required
work on any real or complex floating-point type that supports the required
functions.</p>
</div>
@ -1590,7 +1589,7 @@ rounded to a representable value.</p>
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2
Protocols/PRNG.html
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@ -807,7 +807,7 @@ distribution.</p>
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7
Protocols/Real.html
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@ -134,10 +134,11 @@
</div>
</div>
<p>A floating-point type that provides a selection of special functions.</p>
<p>A floating-point type that supports elementary functions and a selection of
special functions.</p>
<p>The <code>Real</code> protocol provides a suitable basis for writing functions that
work on any floating-point type that provides the required functions.</p>
work on any floating-point type that supports the required functions.</p>
</div>
</div>
@ -517,7 +518,7 @@ determine the quadrant of the computed angle.</p>
</article>
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8
Structs.html
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@ -239,8 +239,8 @@ division (<code>/</code>) operator. For example:</p>
<span class="nf">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="c1">// Prints "3/3"</span>
</code></pre>
<p>All arithmetic operations with values in canonical form (i.e. reduced to
lowest terms) return results in canonical form. However, operations with
<p>All arithmetic operations on values in canonical form (i.e. reduced to
lowest terms) return results in canonical form. However, operations on
values not in canonical form may or may not return results that are
themselves in canonical form. The property <code>canonicalized</code> is the canonical
form of any value.</p>
@ -262,7 +262,7 @@ of the same sign compare equal to each other.</p>
any other value, including another NaN. Use the property <code>isNaN</code> to test if
a value is NaN. <code>Rational&lt;T&gt;</code> arithmetic operations are intended to
propagate NaN in the same manner as analogous floating-point operations.</p>
<h3 id='fixed-width-binary-parts' class='heading'>Fixed-Width Binary Parts</h3>
<h3 id='numerical-limits' class='heading'>Numerical Limits</h3>
<p>When a value of type <code>Rational&lt;T&gt;</code> is in canonical form, the sign of the
numerator is the sign of the value; that is, in canonical form, the sign of
@ -296,7 +296,7 @@ occurs when the division (<code>/</code>) operator is used to create a value of
</article>
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2
Structs/Complex.html
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@ -1607,7 +1607,7 @@ preserved in the sign of zero; that is,
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8
Structs/Rational.html
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@ -159,8 +159,8 @@ division (<code>/</code>) operator. For example:</p>
<span class="nf">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="c1">// Prints "3/3"</span>
</code></pre>
<p>All arithmetic operations with values in canonical form (i.e. reduced to
lowest terms) return results in canonical form. However, operations with
<p>All arithmetic operations on values in canonical form (i.e. reduced to
lowest terms) return results in canonical form. However, operations on
values not in canonical form may or may not return results that are
themselves in canonical form. The property <code>canonicalized</code> is the canonical
form of any value.</p>
@ -182,7 +182,7 @@ of the same sign compare equal to each other.</p>
any other value, including another NaN. Use the property <code>isNaN</code> to test if
a value is NaN. <code>Rational&lt;T&gt;</code> arithmetic operations are intended to
propagate NaN in the same manner as analogous floating-point operations.</p>
<h3 id='fixed-width-binary-parts' class='heading'>Fixed-Width Binary Parts</h3>
<h3 id='numerical-limits' class='heading'>Numerical Limits</h3>
<p>When a value of type <code>Rational&lt;T&gt;</code> is in canonical form, the sign of the
numerator is the sign of the value; that is, in canonical form, the sign of
@ -1381,7 +1381,7 @@ the available rounding rules.</p>
</article>
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@ -202,7 +202,7 @@
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@ -205,7 +205,7 @@ secure PRNG.</p>
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2
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@ -339,7 +339,7 @@ cryptographically secure PRNG.</p>
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2
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@ -280,7 +280,7 @@ using cryptographically secure random bytes.</p>
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@ -274,7 +274,7 @@
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@ -161,8 +161,8 @@
</ul>
<p><a href="#/Factoring%20(Fixed-Width)">Factoring (Fixed-Width)</a></p>
<ul>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_s010ArithmeticK0O8overflowtx_xtFZ">gcdReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_s010ArithmeticK0O8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_Sb8overflowtx_xtFZ">gcdReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE07lcmFullF0x4high_AF3lowtx_xtFZ">lcmFullWidth(_:_:)</a></li>
</ul>
<p><a href="#/Initializers">Initializers</a></p>
@ -327,7 +327,7 @@ a runtime error may occur.</p>
<ul>
<li>
<div>
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_s010ArithmeticK0O8overflowtx_xtFZ"></a>
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20gcdReportingOverflowx12partialValue_Sb8overflowtx_xtFZ"></a>
<a name="//apple_ref/swift/Method/gcdReportingOverflow(_:_:)" class="dashAnchor"></a>
<h4>
<code>gcdReportingOverflow(_:_:)</code>
@ -343,14 +343,14 @@ whether overflow occurred during the operation.</p>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">gcdReportingOverflow</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">ArithmeticOverflow</span><span class="p">)</span></code></pre>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">Bool</span><span class="p">)</span></code></pre>
</div>
</div>
</li>
<li>
<div>
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_s010ArithmeticK0O8overflowtx_xtFZ"></a>
<a name="/s:s13BinaryIntegerP12NumericAnnexs010FixedWidthB0RzsAD9MagnitudeRpzs08UnsignedB0AFRQAE_AEs0C0PQZAFRSlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ"></a>
<a name="//apple_ref/swift/Method/lcmReportingOverflow(_:_:)" class="dashAnchor"></a>
<h4>
<code>lcmReportingOverflow(_:_:)</code>
@ -366,7 +366,7 @@ whether overflow occurred during the operation.</p>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcmReportingOverflow</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">ArithmeticOverflow</span><span class="p">)</span></code></pre>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">Bool</span><span class="p">)</span></code></pre>
</div>
</div>
@ -459,7 +459,7 @@ a runtime error may occur.</p>
</article>
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@ -794,7 +794,7 @@
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@ -794,7 +794,7 @@
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2
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@ -304,7 +304,7 @@ the value with more trailing zeros in its significand bit pattern.</p>
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8
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@ -153,7 +153,7 @@
</ul>
<p><a href="#/Factoring%20(Fixed-Width)">Factoring (Fixed-Width)</a></p>
<ul>
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_s010ArithmeticI0O8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ">lcmReportingOverflow(_:_:)</a></li>
<li><a href="#/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE07lcmFullF0x4high_9Magnitudes0C0PQz3lowtx_xtFZ">lcmFullWidth(_:_:)</a></li>
</ul>
</div>
@ -251,7 +251,7 @@
<ul>
<li>
<div>
<a name="/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_s010ArithmeticI0O8overflowtx_xtFZ"></a>
<a name="/s:s15UnsignedIntegerP12NumericAnnexs010FixedWidthB0RzsAARzlE20lcmReportingOverflowx12partialValue_Sb8overflowtx_xtFZ"></a>
<a name="//apple_ref/swift/Method/lcmReportingOverflow(_:_:)" class="dashAnchor"></a>
<h4>
<code>lcmReportingOverflow(_:_:)</code>
@ -267,7 +267,7 @@ whether overflow occurred during the operation.</p>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight"><code><span class="kd">public</span> <span class="kd">static</span> <span class="kd">func</span> <span class="nf">lcmReportingOverflow</span><span class="p">(</span><span class="n">_</span> <span class="nv">a</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="n">_</span> <span class="nv">b</span><span class="p">:</span> <span class="k">Self</span><span class="p">)</span>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">ArithmeticOverflow</span><span class="p">)</span></code></pre>
<span class="o">-&gt;</span> <span class="p">(</span><span class="nv">partialValue</span><span class="p">:</span> <span class="k">Self</span><span class="p">,</span> <span class="nv">overflow</span><span class="p">:</span> <span class="kt">Bool</span><span class="p">)</span></code></pre>
</div>
</div>
@ -302,7 +302,7 @@ computed using full-width arithmetic.</p>
</article>
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@ -314,7 +314,7 @@ of <code>x</code>.</p>
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@ -224,10 +224,11 @@ minimum and maximum values for the uniform distribution.</p>
</h4>
</div>
<div class="abstract">
<p>A floating-point type that provides a selection of special functions.</p>
<p>A floating-point type that supports elementary functions and a selection of
special functions.</p>
<p>The <code>Real</code> protocol provides a suitable basis for writing functions that
work on any floating-point type that provides the required functions.</p>
work on any floating-point type that supports the required functions.</p>
<a href="Protocols/Real.html">See more…</a>
</div>
@ -253,11 +254,10 @@ work on any floating-point type that provides the required functions.</p>
</h4>
</div>
<div class="abstract">
<p>A signed numeric type that provides square root, cube root, and elementary
transcendental functions.</p>
<p>A signed numeric type that supports elementary functions.</p>
<p>The <code>Math</code> protocol provides a suitable basis for writing functions that
work on any real or complex floating-point type which provides the required
work on any real or complex floating-point type that supports the required
functions.</p>
<a href="Protocols/Math.html">See more…</a>
@ -278,7 +278,7 @@ functions.</p>
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7
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@ -134,11 +134,10 @@
</div>
</div>
<p>A signed numeric type that provides square root, cube root, and elementary
transcendental functions.</p>
<p>A signed numeric type that supports elementary functions.</p>
<p>The <code>Math</code> protocol provides a suitable basis for writing functions that
work on any real or complex floating-point type which provides the required
work on any real or complex floating-point type that supports the required
functions.</p>
</div>
@ -1590,7 +1589,7 @@ rounded to a representable value.</p>
</article>
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@ -807,7 +807,7 @@ distribution.</p>
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@ -134,10 +134,11 @@
</div>
</div>
<p>A floating-point type that provides a selection of special functions.</p>
<p>A floating-point type that supports elementary functions and a selection of
special functions.</p>
<p>The <code>Real</code> protocol provides a suitable basis for writing functions that
work on any floating-point type that provides the required functions.</p>
work on any floating-point type that supports the required functions.</p>
</div>
</div>
@ -517,7 +518,7 @@ determine the quadrant of the computed angle.</p>
</article>
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8
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@ -239,8 +239,8 @@ division (<code>/</code>) operator. For example:</p>
<span class="nf">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="c1">// Prints "3/3"</span>
</code></pre>
<p>All arithmetic operations with values in canonical form (i.e. reduced to
lowest terms) return results in canonical form. However, operations with
<p>All arithmetic operations on values in canonical form (i.e. reduced to
lowest terms) return results in canonical form. However, operations on
values not in canonical form may or may not return results that are
themselves in canonical form. The property <code>canonicalized</code> is the canonical
form of any value.</p>
@ -262,7 +262,7 @@ of the same sign compare equal to each other.</p>
any other value, including another NaN. Use the property <code>isNaN</code> to test if
a value is NaN. <code>Rational&lt;T&gt;</code> arithmetic operations are intended to
propagate NaN in the same manner as analogous floating-point operations.</p>
<h3 id='fixed-width-binary-parts' class='heading'>Fixed-Width Binary Parts</h3>
<h3 id='numerical-limits' class='heading'>Numerical Limits</h3>
<p>When a value of type <code>Rational&lt;T&gt;</code> is in canonical form, the sign of the
numerator is the sign of the value; that is, in canonical form, the sign of
@ -296,7 +296,7 @@ occurs when the division (<code>/</code>) operator is used to create a value of
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@ -1607,7 +1607,7 @@ preserved in the sign of zero; that is,
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@ -159,8 +159,8 @@ division (<code>/</code>) operator. For example:</p>
<span class="nf">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="c1">// Prints "3/3"</span>
</code></pre>
<p>All arithmetic operations with values in canonical form (i.e. reduced to
lowest terms) return results in canonical form. However, operations with
<p>All arithmetic operations on values in canonical form (i.e. reduced to
lowest terms) return results in canonical form. However, operations on
values not in canonical form may or may not return results that are
themselves in canonical form. The property <code>canonicalized</code> is the canonical
form of any value.</p>
@ -182,7 +182,7 @@ of the same sign compare equal to each other.</p>
any other value, including another NaN. Use the property <code>isNaN</code> to test if
a value is NaN. <code>Rational&lt;T&gt;</code> arithmetic operations are intended to
propagate NaN in the same manner as analogous floating-point operations.</p>
<h3 id='fixed-width-binary-parts' class='heading'>Fixed-Width Binary Parts</h3>
<h3 id='numerical-limits' class='heading'>Numerical Limits</h3>
<p>When a value of type <code>Rational&lt;T&gt;</code> is in canonical form, the sign of the
numerator is the sign of the value; that is, in canonical form, the sign of
@ -1381,7 +1381,7 @@ the available rounding rules.</p>
</article>
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<p>&copy; 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-07-16)</p>
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@ -202,7 +202,7 @@
</article>
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@ -157,10 +157,12 @@ production-ready at this time.</p>
</blockquote>
<h2 id='requirements' class='heading'>Requirements</h2>
<p>NumericAnnex now requires a recent development snapshot of Swift 4.0 that
includes the revised numeric protocols. It requires either <code>Darwin.C</code> or <code>Glibc</code>
for transcendental functions provided by the C standard library and either
<code>Security</code> or <code>Glibc</code> for cryptographically secure random bytes.</p>
<p>NumericAnnex now requires Xcode 9 beta 5 or a recent development snapshot of
Swift 4.0 that includes the revised numeric protocols.</p>
<p>It requires either <code>Darwin.C</code> (macOS) or <code>Glibc</code> (Linux) for transcendental
functions provided by the C standard library and either <code>Security</code> (macOS) or
<code>Glibc</code> (Linux) for cryptographically secure random bytes.</p>
<h2 id='installation' class='heading'>Installation</h2>
<p>After NumericAnnex has been cloned or downloaded locally, build the library with
@ -237,7 +239,7 @@ under the MIT and UIUC/NCSA licenses.</p>
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<p>&copy; 2017 <a class="link" href="https://diploid.ca" target="_blank" rel="external">Xiaodi Wu</a>. All rights reserved. (Last updated: 2017-07-16)</p>
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@ -157,10 +157,12 @@ production-ready at this time.</p>
</blockquote>
<h2 id='requirements' class='heading'>Requirements</h2>
<p>NumericAnnex now requires a recent development snapshot of Swift 4.0 that
includes the revised numeric protocols. It requires either <code>Darwin.C</code> or <code>Glibc</code>
for transcendental functions provided by the C standard library and either
<code>Security</code> or <code>Glibc</code> for cryptographically secure random bytes.</p>
<p>NumericAnnex now requires Xcode 9 beta 5 or a recent development snapshot of
Swift 4.0 that includes the revised numeric protocols.</p>
<p>It requires either <code>Darwin.C</code> (macOS) or <code>Glibc</code> (Linux) for transcendental
functions provided by the C standard library and either <code>Security</code> (macOS) or
<code>Glibc</code> (Linux) for cryptographically secure random bytes.</p>
<h2 id='installation' class='heading'>Installation</h2>
<p>After NumericAnnex has been cloned or downloaded locally, build the library with
@ -237,7 +239,7 @@ under the MIT and UIUC/NCSA licenses.</p>
</article>
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