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  </script></head><body><hr/><div><a class="rout" href="../../pdf/X02/x02amf.pdf">X02AMF (PDF version)</a></div><div><a class="chap" href="x02conts.xml">X02 Chapter Contents</a></div><div><a class="chapint" href="x02intro.xml">X02 Chapter Introduction</a></div>
<div><a class="htmltoc" href="../FRONTMATTER/manconts.xml">NAG Library Manual</a></div><hr/><h1 class="libdoc">NAG Library Routine Document<br/><br/>X02AMF</h1><div class="paramtext"><div class="header"><b>Note:</b>&#160; before using this routine, please read the Users' Note for your implementation to check the interpretation of <span class="bitalic">bold italicised</span> terms and other implementation-dependent details.</div></div> 
<div class="htmltoc">
<h2 class="htmltoc"><span class="htmltochead" onclick="showLevel('htmltoc');"><span class="htmltocplus" id="htmltocplus">+</span><span class="htmltocminus" id="htmltocminus">&#8722;</span></span>&#160;Contents</h2>
<div class="htmltocitem" id="htmltoc">
<div class="htmltoc">
<span class="htmltocplus">&#160;&#160;&#160;</span>
<a class="htmltoc" href="#purpose">1&#160;&#160;<b>Purpose</b></a>
</div><div class="htmltoc">
<span class="htmltocplus">&#160;&#160;&#160;</span>
<a class="htmltoc" href="#specification">2&#160;&#160;<b>Specification</b></a>
</div><div class="htmltoc">
<span class="htmltocplus">&#160;&#160;&#160;</span>
<a class="htmltoc" href="#description">3&#160;&#160;<b>Description</b></a>
</div><div class="htmltoc">
<span class="htmltocplus">&#160;&#160;&#160;</span>
<a class="htmltoc" href="#references">4&#160;&#160;<b>References</b></a>
</div><div class="htmltoc">
<span class="htmltocplus">&#160;&#160;&#160;</span>
<a class="htmltoc" href="#parameters">5&#160;&#160;<b>Parameters</b></a>
</div><div class="htmltoc">
<span class="htmltocplus">&#160;&#160;&#160;</span>
<a class="htmltoc" href="#errors">6&#160;&#160;<b>Error Indicators and Warnings</b></a>
</div><div class="htmltoc">
<span class="htmltocplus">&#160;&#160;&#160;</span>
<a class="htmltoc" href="#accuracy">7&#160;&#160;<b>Accuracy</b></a>
</div><div class="htmltoc">
<span class="htmltocplus">&#160;&#160;&#160;</span>
<a class="htmltoc" href="#fcomments">8&#160;&#160;<b>Further Comments</b></a>
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<span class="htmltocplus">&#160;&#160;&#160;</span>
<a class="htmltoc" href="#example">9&#160;&#160;<b>Example</b></a>
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</div><h2 class="standard"><a class="sec" name="purpose" id="purpose"/>1&#160;&#160;Purpose</h2>
<div class="paramtext">X02AMF returns the <b>safe range</b> of floating-point arithmetic.  </div><h2 class="standard"><a class="sec" name="specification" id="specification"/>2&#160;&#160;Specification</h2>
<table class="fspec"><tr><td class="tdfspec1"><b><i>double&#160;precision</i></b>&#160;FUNCTION&#160;X02AMF&#160;(</td><td class="tdfspec2">)</td></tr></table><h2 class="standard"><a class="sec" name="description" id="description"/>3&#160;&#160;Description</h2>
<div class="paramtext">X02AMF is defined to be the smallest positive model number <m:math><m:mi>z</m:mi></m:math>&#160;such that for any <m:math><m:mi>x</m:mi></m:math>&#160;in the range [<m:math><m:mi>z</m:mi><m:mo>,</m:mo><m:mn>1</m:mn><m:mo>/</m:mo><m:mi>z</m:mi></m:math>] the following can be computed without undue loss of accuracy, overflow, underflow or other error:
<ul class="listind"><li class="listind"><m:math><m:mrow><m:mo>-</m:mo><m:mi>x</m:mi></m:mrow></m:math></li><li class="listind"><m:math><m:mn>1</m:mn><m:mo>/</m:mo><m:mi>x</m:mi></m:math></li><li class="listind"><m:math><m:mrow><m:mo>-</m:mo><m:mn>1</m:mn></m:mrow><m:mo>/</m:mo><m:mi>x</m:mi></m:math></li><li class="listind"><m:math><m:msqrt><m:mi>x</m:mi></m:msqrt></m:math></li><li class="listind"><m:math><m:mrow><m:mi>log</m:mi><m:mfenced separators=""><m:mi>x</m:mi></m:mfenced></m:mrow></m:math></li><li class="listind"><m:math><m:mrow><m:mi>exp</m:mi><m:mfenced separators=""><m:mrow><m:mi>log</m:mi><m:mfenced separators=""><m:mi>x</m:mi></m:mfenced></m:mrow></m:mfenced></m:mrow></m:math></li><li class="listind">
  <m:math>
   <m:msup>
    <m:mi>y</m:mi>
    <m:mfenced separators="">
     <m:mrow><m:mi>log</m:mi><m:mfenced separators=""><m:mi>x</m:mi></m:mfenced></m:mrow>
     <m:mo>/</m:mo>
     <m:mrow><m:mi>log</m:mi><m:mfenced separators=""><m:mi>y</m:mi></m:mfenced></m:mrow>
    </m:mfenced>
   </m:msup>
  </m:math>&#160;for any <m:math><m:mi>y</m:mi></m:math>&#160;</li></ul>
</div><h2 class="standard"><a class="sec" name="references" id="references"/>4&#160;&#160;References</h2>
<div class="paramtext">None.</div><h2 class="standard"><a class="sec" name="parameters" id="parameters"/>5&#160;&#160;Parameters</h2>
<div class="paramtext">None.</div><h2 class="standard"><a class="sec" name="errors" id="errors"/>6&#160;&#160;Error Indicators and Warnings</h2>
<div class="paramtext">None.</div><h2 class="standard"><a class="sec" name="accuracy" id="accuracy"/>7&#160;&#160;Accuracy</h2>
<div class="paramtext">None.</div><h2 class="standard"><a class="sec" name="fcomments" id="fcomments"/>8&#160;&#160;Further Comments</h2>
<div class="paramtext">None.</div><h2 class="standard"><a class="sec" name="example" id="example"/>9&#160;&#160;Example</h2>
<div class="paramtext">See <a class="sec" href="../X02/x02ajf.xml#example">Section 9</a> in X02AJF.</div>
<hr/><div><a class="rout" href="../../pdf/X02/x02amf.pdf">X02AMF (PDF version)</a></div><div><a class="chap" href="x02conts.xml">X02 Chapter Contents</a></div><div><a class="chapint" href="x02intro.xml">X02 Chapter Introduction</a></div>
<div><a class="htmltoc" href="../FRONTMATTER/manconts.xml">NAG Library Manual</a></div>
<div><hr/><a class="genint" href="../FRONTMATTER/copyright.xml">&#169; The Numerical Algorithms Group Ltd, Oxford, UK. 2009</a></div></body></html>
