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<div class="ChapSects"><a href="chap2.html#X7E12358984CA3111">2 <span class="Heading">Float package</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2.html#X7B4092CA7ABB93B0">2.1 <span class="Heading">A sample run</span></a>
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<h3>2 <span class="Heading">Float package</span></h3>

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<h4>2.1 <span class="Heading">A sample run</span></h4>

<p>The extended floating-point capabilities of <strong class="pkg">GAP</strong> are installed by loading the package via <code class="code">LoadPackage("float");</code> and selecting new floating-point handlers via <code class="code">SetFloats(MPFR)</code>, <code class="code">SetFloats(MPFI)</code>, <code class="code">SetFloats(MPC)</code> or<code class="code">SetFloats(CXSC)</code>, depending on whether high-precision real, interval or complex arithmetic are desired, or whether a fast package containing all four real/complex element/interval arithmetic is desired:</p>


<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">LoadPackage("float");</span>
Loading FLOAT 0.7.0 ...
true
<span class="GAPprompt">gap></span> <span class="GAPinput">SetFloats(MPFR); # floating-point</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">x := 4*Atan(1.0);</span>
.314159e1
<span class="GAPprompt">gap></span> <span class="GAPinput">Sin(x);</span>
.169569e-30
<span class="GAPprompt">gap></span> <span class="GAPinput">SetFloats(MPFR,1000); # 1000 bits</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">x := 4*Atan(1.0);</span>
.314159e1
<span class="GAPprompt">gap></span> <span class="GAPinput">Sin(x);</span>
.125154e-300
<span class="GAPprompt">gap></span> <span class="GAPinput">String(x,300);</span>
".3141592653589793238462643383279502884197169399375105820974944592307816406286\
208998628034825342117067982148086513282306647093844609550582231725359408128481\
117450284102701938521105559644622948954930381964428810975665933446128475648233\
78678316527120190914564856692346034861045432664821339360726024914127e1"
gap>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetFloats(MPFI); # intervals</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">x := 4*Atan(1.0);</span>
.314159e1(99)
<span class="GAPprompt">gap></span> <span class="GAPinput">AbsoluteDiameter(x); Sup(x); Inf(x);</span>
.100441e-29
.314159e1
.314159e1
<span class="GAPprompt">gap></span> <span class="GAPinput">Sin(x);</span>
-.140815e-29(97)
<span class="GAPprompt">gap></span> <span class="GAPinput">0.0 in last;</span>
true
<span class="GAPprompt">gap></span> <span class="GAPinput">1.0; # exact representation</span>
.1e1(∞)
<span class="GAPprompt">gap></span> <span class="GAPinput">IncreaseInterval(last,0.001); # now only 8 significant bits</span>
.1e1(8)
<span class="GAPprompt">gap></span> <span class="GAPinput">IncreaseInterval(last,-0.002); # now becomes empty</span>
∅
<span class="GAPprompt">gap></span> <span class="GAPinput">r2 := Sqrt(2.0);</span>
.141421e1(99)
<span class="GAPprompt">gap></span> <span class="GAPinput">MinimalPolynomial(Rationals,r2);</span>
-2*x_1^2+1
<span class="GAPprompt">gap></span> <span class="GAPinput">Cyc(r2);</span>
E(8)-E(8)^3
gap>
<span class="GAPprompt">gap></span> <span class="GAPinput">SetFloats(MPC); # complex numbers</span>
<span class="GAPprompt">gap></span> <span class="GAPinput">z := 5.0-1.0i;</span>
.5e1-.1e1i
<span class="GAPprompt">gap></span> <span class="GAPinput">(1+1.0i)*last^4*(239+1.0i);</span>
.228488e6
<span class="GAPprompt">gap></span> <span class="GAPinput">Exp(6.2835i);</span>
.1e1+.314693e-3i
</pre></div>


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