/usr/share/doc/axiom-doc/hypertex/nummachinefloats.xhtml

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  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Machine Floats</div>
  <hr/>
Axiom provides two kinds of floating point numbers. The domain 
<a href="db.xhtml?Float">Float</a> 
(abbreviation <a href="db.xhtml?Float">FLOAT</a>) 
implements a model of arbitrary precisions floating point numbers. The
domain
<a href="db.xhtml?DoubleFloat">DoubleFloat</a> 
(abbreviation <a href="db.xhtml?DoubleFloat">DFLOAT</a>) 
is intended to make available hardware floating point arithmetic in Axiom.
The actual model of floating point 
<a href="db.xhtml?DoubleFloat">DoubleFloat</a> that Axiom
provides is system dependent. For example, on the IBM System 370, Axiom
uses IBM double precision which has fourteen hexadecimal digits of 
precision or roughly sixteen decimal digits. Arbitrary precision floats
allow the user to specify the precision at which arithmetic operations 
are computed. Although this is an attractive facility, it comes at a cost.
Arbitrary precision floating point arithmetic typically takes twenty to
two hundred times more time than hardware floating point.

By default, floating point numbers that you enter into Axiom are of type
<a href="db.xhtml?Float">Float</a>.
<ul>
 <li>
  <input type="submit" id="p1" class="subbut" 
    onclick="makeRequest('p1');"
    value="2.71828" />
  <div id="ansp1"><div></div></div>
 </li>
</ul>
You must therefore tell Axiom that you want to use 
<a href="db.xhtml?DoubleFloat">DoubleFloat</a> values and operations. The
following are some conservative guidelines for getting Axiom to use 
<a href="db.xhtml?DoubleFloat">DoubleFloat</a>.

To get a value of type <a href="db.xhtml?DoubleFloat">DoubleFloat</a>., 
use a target with
    "@", ...
<ul>
 <li>
  <input type="submit" id="p2" class="subbut" 
    onclick="makeRequest('p2');"
    value="2.71828@DoubleFloat" />
  <div id="ansp2"><div></div></div>
 </li>
</ul>
a conversion,...
<ul>
 <li>
  <input type="submit" id="p3" class="subbut" 
    onclick="makeRequest('p3');"
    value="2.71828::DoubleFloat" />
  <div id="ansp3"><div></div></div>
 </li>
</ul>
or an assignment to a declared variable. It is more efficient if you
use a target rather than an explicit or implicit conversion.
<ul>
 <li>
  <input type="submit" id="p4" class="subbut" 
    onclick="makeRequest('p4');"
    value="eApprox:DoubleFloat:=2.71828" />
  <div id="ansp4"><div></div></div>
 </li>
</ul>
You also need to declare functions that work with 
<a href="db.xhtml?DoubleFloat">DoubleFloat</a>.
<ul>
 <li>
  <input type="submit" id="p5" class="noresult" 
    onclick="makeRequest('p5');"
    value="avg:List DoubleFloat -> DoubleFloat" />
  <div id="ansp5"><div></div></div>
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 <li>
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    onclick="makeRequest('p6');"
    value="avg l==(empty? l => 0::DoubleFloat; reduce(_+,l)/#l)"/>
  <div id="ansp6"><div></div></div>
 </li>
 <li>
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    value="avg []" />
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    value="avg [3.4,9.7,-6.8]" />
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Use package calling for operations from 
<a href="db.xhtml?DoubleFloat">DoubleFloat</a>
unless the arguments themselves are already of type
<a href="db.xhtml?DoubleFloat">DoubleFloat</a>.
<ul>
 <li>
  <input type="submit" id="p9" class="subbut" 
    onclick="makeRequest('p9');"
    value="cos(3.1415926)$DoubleFloat" />
  <div id="ansp9"><div></div></div>
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 <li>
  <input type="submit" id="p10" class="subbut" 
    onclick="makeRequest('p10');"
    value="cos(3.1415926)::DoubleFloat" />
  <div id="ansp10"><div></div></div>
 </li>
</ul>
By far, the most common usage of 
<a href="db.xhtml?DoubleFloat">DoubleFloat</a>
is for functions to be graphied. For more information about Axiom's
numerical and graphical facilities, see
<a href="axbook/book-contents.xhtml#chapter7">Graphics</a>
in section 7, 
<a href="axbook/book-contents.xhtml#chapter8">Numeric Functions</a>
in section 8.1, and
<a href="numfloat.xhtml">Float</a>

The usual arithmetic and elementary functions are available for
<a href="db.xhtml?DoubleFloat">DoubleFloat</a>. Use 
<ul>
 <li>
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    onclick="showcall('p11');"
   value=")show DoubleFloat"/>
  <div id="ansp11"><div></div></div>
 </li>
</ul>
to get a list of operations.
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axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / nummachinefloats.xhtml
