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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><title>5 Arbitrary-Precision Floating-Point Numbers (Bigfloats)</title><link rel="stylesheet" type="text/css" href="../scribble.css" title="default"/><link rel="stylesheet" type="text/css" href="../racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-style.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../manual-racket.css" title="default"/><link rel="stylesheet" type="text/css" href="../doc-site.css" title="default"/><script type="text/javascript" src="../scribble-common.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../manual-racket.js"></script><script type="text/javascript" src="../doc-site.js"></script><script type="text/javascript" src="../local-redirect/local-redirect.js"></script><script type="text/javascript" src="../local-redirect/local-user-redirect.js"></script><!--[if IE 6]><style type="text/css">.SIEHidden { overflow: hidden; }</style><![endif]--></head><body id="doc-racket-lang-org"><div class="tocset"><div class="tocview"><div class="tocviewlist tocviewlisttopspace"><div class="tocviewtitle"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_0");">▼</a></td><td></td><td><a href="index.html" class="tocviewlink" data-pltdoc="x">Math Library</a></td></tr></table></div><div class="tocviewsublisttop" style="display: block;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1 </td><td><a href="base.html" class="tocviewlink" data-pltdoc="x">Constants and Elementary Functions</a></td></tr><tr><td align="right">2 </td><td><a href="flonum.html" class="tocviewlink" data-pltdoc="x">Flonums</a></td></tr><tr><td align="right">3 </td><td><a href="special.html" class="tocviewlink" data-pltdoc="x">Special Functions</a></td></tr><tr><td align="right">4 </td><td><a href="number-theory.html" class="tocviewlink" data-pltdoc="x">Number Theory</a></td></tr><tr><td align="right">5 </td><td><a href="" class="tocviewselflink" data-pltdoc="x">Arbitrary-<wbr></wbr>Precision Floating-<wbr></wbr>Point Numbers (<a name="(tech._bigfloat)"></a><span style="font-style: italic">Bigfloats</span>)</a></td></tr><tr><td align="right">6 </td><td><a href="array.html" class="tocviewlink" data-pltdoc="x">Arrays</a></td></tr><tr><td align="right">7 </td><td><a href="matrices.html" class="tocviewlink" data-pltdoc="x">Matrices and Linear Algebra</a></td></tr><tr><td align="right">8 </td><td><a href="stats.html" class="tocviewlink" data-pltdoc="x">Statistics Functions</a></td></tr><tr><td align="right">9 </td><td><a href="dist.html" class="tocviewlink" data-pltdoc="x">Probability Distributions</a></td></tr><tr><td align="right">10 </td><td><a href="utils.html" class="tocviewlink" data-pltdoc="x">Stuff That Doesn’t Belong Anywhere Else</a></td></tr></table></div></div><div class="tocviewlist"><table cellspacing="0" cellpadding="0"><tr><td style="width: 1em;"><a href="javascript:void(0);" title="Expand/Collapse" class="tocviewtoggle" onclick="TocviewToggle(this,"tocview_1");">►</a></td><td>5 </td><td><a href="" class="tocviewselflink" data-pltdoc="x">Arbitrary-<wbr></wbr>Precision Floating-<wbr></wbr>Point Numbers (<a name="(tech._bigfloat)"></a><span style="font-style: italic">Bigfloats</span>)</a></td></tr></table><div class="tocviewsublistbottom" style="display: none;" id="tocview_1"><table cellspacing="0" cellpadding="0"><tr><td align="right">5.1 </td><td><a href="#%28part._quick%29" class="tocviewlink" data-pltdoc="x">Quick Start</a></td></tr><tr><td align="right">5.2 </td><td><a href="#%28part._.Fictionally_.Asked_.Questions%29" class="tocviewlink" data-pltdoc="x">Fictionally Asked Questions</a></td></tr><tr><td align="right">5.3 </td><td><a href="#%28part._.Type_and_.Constructors%29" class="tocviewlink" data-pltdoc="x">Type and Constructors</a></td></tr><tr><td align="right">5.4 </td><td><a href="#%28part._.Accessors_and_.Conversion_.Functions%29" class="tocviewlink" data-pltdoc="x">Accessors and Conversion Functions</a></td></tr><tr><td align="right">5.5 </td><td><a href="#%28part._.Parameters%29" class="tocviewlink" data-pltdoc="x">Parameters</a></td></tr><tr><td align="right">5.6 </td><td><a href="#%28part._constants%29" class="tocviewlink" data-pltdoc="x">Constants</a></td></tr><tr><td align="right">5.7 </td><td><a href="#%28part._predicates%29" class="tocviewlink" data-pltdoc="x">Predicates</a></td></tr><tr><td align="right">5.8 </td><td><a href="#%28part._rounding%29" class="tocviewlink" data-pltdoc="x">Rounding</a></td></tr><tr><td align="right">5.9 </td><td><a href="#%28part._ops%29" class="tocviewlink" data-pltdoc="x">Mathematical Operations</a></td></tr><tr><td align="right">5.10 </td><td><a href="#%28part._misc%29" class="tocviewlink" data-pltdoc="x">Low-<wbr></wbr>level Functions</a></td></tr></table></div></div></div><div class="tocsub"><div class="tocsubtitle">On this page:</div><table class="tocsublist" cellspacing="0"><tr><td><span class="tocsublinknumber">5.1<tt> </tt></span><a href="#%28part._quick%29" class="tocsubseclink" data-pltdoc="x">Quick Start</a></td></tr><tr><td><span class="tocsublinknumber">5.2<tt> </tt></span><a href="#%28part._.Fictionally_.Asked_.Questions%29" class="tocsubseclink" data-pltdoc="x">Fictionally Asked Questions</a></td></tr><tr><td><span class="tocsublinknumber">5.3<tt> </tt></span><a href="#%28part._.Type_and_.Constructors%29" class="tocsubseclink" data-pltdoc="x">Type and Constructors</a></td></tr><tr><td><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktStxLink">Bigfloat</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfrandom%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfrandom</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcopy%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfcopy</span></span></a></td></tr><tr><td><span class="tocsublinknumber">5.4<tt> </tt></span><a href="#%28part._.Accessors_and_.Conversion_.Functions%29" class="tocsubseclink" data-pltdoc="x">Accessors and Conversion Functions</a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-precision%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>precision</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-signbit%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>signbit</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-significand%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>significand</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-exponent%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>exponent</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3esig%2Bexp%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>>sig+<span class="mywbr"> </span>exp</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3einteger%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>>integer</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3erational%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>>rational</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3ereal%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>>real</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3eflonum%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>>flonum</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3estring%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>>string</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._string-~3ebigfloat%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">string-<wbr></wbr>>bigfloat</span></span></a></td></tr><tr><td><span class="tocsublinknumber">5.5<tt> </tt></span><a href="#%28part._.Parameters%29" class="tocsubseclink" data-pltdoc="x">Parameters</a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf-<wbr></wbr>precision</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-rounding-mode%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf-<wbr></wbr>rounding-<wbr></wbr>mode</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-min-precision%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf-<wbr></wbr>min-<wbr></wbr>precision</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-max-precision%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf-<wbr></wbr>max-<wbr></wbr>precision</span></span></a></td></tr><tr><td><span class="tocsublinknumber">5.6<tt> </tt></span><a href="#%28part._constants%29" class="tocsubseclink" data-pltdoc="x">Constants</a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._pi..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">pi.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._phi..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">phi.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._gamma..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">gamma.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._catalan..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">catalan.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._log2..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">log2.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-inf..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>i</span>nf.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-max..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>m</span>ax.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-min..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>m</span>in.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-0..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>0</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._0..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">0.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Bmin..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">+<span class="mywbr"> </span>min.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Bmax..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">+<span class="mywbr"> </span>max.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Binf..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">+<span class="mywbr"> </span>inf.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Bnan..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">+<span class="mywbr"> </span>nan.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._epsilon..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">epsilon.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-10..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>1</span>0.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-9..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>9</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-8..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>8</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-7..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>7</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-6..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>6</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-5..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>5</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-4..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>4</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-3..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>3</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-2..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>2</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-1..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink"><span class="nobreak">-<wbr></wbr>1</span>.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._1..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">1.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._2..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">2.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._3..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">3.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._4..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">4.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._5..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">5.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._6..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">6.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._7..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">7.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._8..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">8.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._9..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">9.bf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._10..bf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">10.bf</span></span></a></td></tr><tr><td><span class="tocsublinknumber">5.7<tt> </tt></span><a href="#%28part._predicates%29" class="tocsubseclink" data-pltdoc="x">Predicates</a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfzero~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfzero?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfpositive~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfpositive?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfnegative~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfnegative?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfinteger~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfinteger?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfeven~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfeven?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfodd~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfodd?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfrational~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfrational?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfinfinite~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfinfinite?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfnan~3f%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfnan?</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3d%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf=</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3e%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf></span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3c%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf<</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3e~3d%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf>=</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3c~3d%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf<=</span></span></a></td></tr><tr><td><span class="tocsublinknumber">5.8<tt> </tt></span><a href="#%28part._rounding%29" class="tocsubseclink" data-pltdoc="x">Rounding</a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bftruncate%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bftruncate</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bffloor%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bffloor</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfceiling%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfceiling</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfround%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfround</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bffrac%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bffrac</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfrint%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfrint</span></span></a></td></tr><tr><td><span class="tocsublinknumber">5.9<tt> </tt></span><a href="#%28part._ops%29" class="tocsubseclink" data-pltdoc="x">Mathematical Operations</a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfmax%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfmax</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfmin%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfmin</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2B%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf+</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2A%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf*</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf-</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2F%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf/</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsqr%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfsqr</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfabs%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfabs</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsgn%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfsgn</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsqrt%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfsqrt</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf1%2Fsqrt%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bf1/<span class="mywbr"> </span>sqrt</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcbrt%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfcbrt</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfroot%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfroot</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfhypot%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfhypot</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bflog</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog2%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bflog2</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog10%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bflog10</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfexp</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp2%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfexp2</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp10%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfexp10</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog1p%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bflog1p</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexpm1%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfexpm1</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexpt%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfexpt</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsin%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfsin</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcos%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfcos</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bftan%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bftan</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfasin%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfasin</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfacos%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfacos</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfatan%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfatan</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfatan2%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfatan2</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsinh%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfsinh</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcosh%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfcosh</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bftanh%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bftanh</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfasinh%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfasinh</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfacosh%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfacosh</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfatanh%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfatanh</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsec%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfsec</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcsc%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfcsc</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcot%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfcot</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsech%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfsech</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcsch%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfcsch</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcoth%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfcoth</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsin%2Bcos%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfsin+<span class="mywbr"> </span>cos</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsinh%2Bcosh%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfsinh+<span class="mywbr"> </span>cosh</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bffactorial%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bffactorial</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfgamma%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfgamma</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog-gamma%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bflog-<wbr></wbr>gamma</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog-gamma%2Fsign%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bflog-<wbr></wbr>gamma/<span class="mywbr"> </span>sign</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfpsi0%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfpsi0</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfeint%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfeint</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfli2%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfli2</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfzeta%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfzeta</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bferf%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bferf</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bferfc%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bferfc</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesj0%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfbesj0</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesj1%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfbesj1</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesj%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfbesj</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesy0%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfbesy0</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesy1%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfbesy1</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesy%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfbesy</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfagm%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfagm</span></span></a></td></tr><tr><td><span class="tocsublinknumber">5.10<tt> </tt></span><a href="#%28part._misc%29" class="tocsubseclink" data-pltdoc="x">Low-<wbr></wbr>level Functions</a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3eordinal%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloat-<wbr></wbr>>ordinal</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._ordinal-~3ebigfloat%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">ordinal-<wbr></wbr>>bigfloat</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloats-between%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bigfloats-<wbr></wbr>between</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfstep%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfstep</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfnext%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfnext</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfprev%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfprev</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfshift%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfshift</span></span></a></td></tr><tr><td><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcanonicalize%29%29" class="tocsubnonseclink" data-pltdoc="x"><span class="RktSym"><span class="RktValLink">bfcanonicalize</span></span></a></td></tr></table></div></div><div class="maincolumn"><div class="main"><div class="versionbox"><span class="version">6.7</span></div><div class="navsettop"><span class="navleft"><form class="searchform"><input class="searchbox" style="color: #888;" type="text" value="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "6.7", "../");" onfocus="this.style.color="black"; this.style.textAlign="left"; if (this.value == "...search manuals...") this.value="";" onblur="if (this.value.match(/^ *$/)) { this.style.color="#888"; this.style.textAlign="center"; this.value="...search manuals..."; }"/></form> <a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("6.7");">top</a></span><span class="navright"> <a href="number-theory.html" title="backward to "4 Number Theory"" data-pltdoc="x">← prev</a> <a href="index.html" title="up to "Math Library"" data-pltdoc="x">up</a> <a href="array.html" title="forward to "6 Arrays"" data-pltdoc="x">next →</a></span> </div><h3 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""bigfloat"">5<tt> </tt><a name="(part._bigfloat)"></a><a name="(mod-path._math/bigfloat)"></a>Arbitrary-Precision Floating-Point Numbers (<a name="(tech._bigfloat)"></a><span style="font-style: italic">Bigfloats</span>)</h3><div class="SAuthorListBox"><span class="SAuthorList"><p class="author">Neil Toronto <<a href="mailto:ntoronto@racket-lang.org">ntoronto@racket-lang.org</a>></p></span></div><p><table cellspacing="0" cellpadding="0" class="defmodule"><tr><td align="left"><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._require%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">require</a></span><span class="stt"> </span><a href="" class="RktModLink" data-pltdoc="x"><span class="RktSym">math/bigfloat</span></a><span class="RktPn">)</span></td><td align="right"><span class="RpackageSpec"><span class="Smaller"> package:</span> <span class="stt">math-lib</span></span></td></tr></table></p><p><div class="SIntrapara">This library provides a Typed Racket interface to <a href="http://www.mpfr.org/">MPFR</a>,
a C library that provides
</div><div class="SIntrapara"><ul><li><p>A C type of arbitrary-precision floating-point numbers.</p></li><li><p>Elementary and special functions that are efficient and proved correct.</p></li><li><p>Well-defined semantics that correspond with the latest IEEE 754 standard.</p></li></ul></div><div class="SIntrapara">The arbitrary-precision floating-point numbers MPFR provides and operates on are represented by the
Typed Racket type <span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span> and identified by the predicate <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat~3f%29%29" class="RktValLink" data-pltdoc="x">bigfloat?</a></span>.</div></p><p>With a few noted exceptions, bigfloat functions regard their arguments as if they were exact,
regardless of their precision.
Conceptually, they compute exact results using infinitely many bits, and return results with
<span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span> bits by rounding them using <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-rounding-mode%29%29" class="RktValLink" data-pltdoc="x">bf-rounding-mode</a></span><span class="RktPn">)</span>.
In practice, they use finite algorithms that have been painstakingly proved to be
equivalent to that conceptual, infinite process.</p><p>MPFR is free and license-compatible with commercial software. It is distributed with Racket
for Windows and Mac OS X, is installed on most Linux systems, and is
<a href="http://www.mpfr.org/ports.html">easy to install</a> on major Unix-like platforms.</p><table cellspacing="0" cellpadding="0"><tr><td><p><span class="hspace"> </span><a href="#%28part._quick%29" class="toclink" data-pltdoc="x">5.1<span class="hspace"> </span>Quick Start</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="#%28part._.Fictionally_.Asked_.Questions%29" class="toclink" data-pltdoc="x">5.2<span class="hspace"> </span>Fictionally Asked Questions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="#%28part._.Type_and_.Constructors%29" class="toclink" data-pltdoc="x">5.3<span class="hspace"> </span>Type and Constructors</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="#%28part._.Accessors_and_.Conversion_.Functions%29" class="toclink" data-pltdoc="x">5.4<span class="hspace"> </span>Accessors and Conversion Functions</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="#%28part._.Parameters%29" class="toclink" data-pltdoc="x">5.5<span class="hspace"> </span>Parameters</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="#%28part._constants%29" class="toclink" data-pltdoc="x">5.6<span class="hspace"> </span>Constants</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="#%28part._predicates%29" class="toclink" data-pltdoc="x">5.7<span class="hspace"> </span>Predicates</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="#%28part._rounding%29" class="toclink" data-pltdoc="x">5.8<span class="hspace"> </span>Rounding</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="#%28part._ops%29" class="toclink" data-pltdoc="x">5.9<span class="hspace"> </span>Mathematical Operations</a></p></td></tr><tr><td><p><span class="hspace"> </span><a href="#%28part._misc%29" class="toclink" data-pltdoc="x">5.10<span class="hspace"> </span>Low-level Functions</a></p></td></tr></table><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""quick"">5.1<tt> </tt><a name="(part._quick)"></a>Quick Start</h4><ol><li><p>Set the bigfloat function result precision using <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="stt"> </span><span class="RktSym"><some-number-of-bits></span><span class="RktPn">)</span>.</p></li><li><p>Use <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span> to convert real values and well-formed strings to bigfloats.</p></li><li><p>Operate on bigfloats using <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span>-prefixed functions like <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2B%29%29" class="RktValLink" data-pltdoc="x">bf+</a></span> and <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsin%29%29" class="RktValLink" data-pltdoc="x">bfsin</a></span>.</p></li><li><p>Convert bigfloats to real values using <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3ereal%29%29" class="RktValLink" data-pltdoc="x">bigfloat->real</a></span>, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3eflonum%29%29" class="RktValLink" data-pltdoc="x">bigfloat->flonum</a></span>,
and <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3einteger%29%29" class="RktValLink" data-pltdoc="x">bigfloat->integer</a></span>. Format them for display using <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3estring%29%29" class="RktValLink" data-pltdoc="x">bigfloat->string</a></span>.</p></li></ol><p>For examples, continue through the FAQ.</p><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""Fictionally_Asked_Questions"">5.2<tt> </tt><a name="(part._.Fictionally_.Asked_.Questions)"></a>Fictionally Asked Questions</h4><p><span style="font-weight: bold">Why use <a href="" class="RktModLink" data-pltdoc="x"><span class="RktSym">math/bigfloat</span></a></span>?</p><p>There are a few reasons.</p><p><span style="font-style: italic">Reason:</span> Flonums have either too much or too little precision for your application.</p><p><div class="SIntrapara">Examples:</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=flonums.html%23%2528def._%2528%2528lib._racket%252Fflonum..rkt%2529._flsqrt%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">flsqrt</a></span><span class="hspace"> </span><span class="RktVal">3.0</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">1.7320508075688772</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528lib._racket%252Fmath..rkt%2529._pi%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">pi</a></span></td></tr><tr><td><p><span class="RktRes">3.141592653589793</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">16</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsqrt%29%29" class="RktValLink" data-pltdoc="x">bfsqrt</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">3</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf #e1.73206)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">179</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._pi..bf%29%29" class="RktValLink" data-pltdoc="x">pi.bf</a></span></td></tr><tr><td><p><span class="RktRes">(bf #e3.141592653589793238462643383279502884197169399375105819)</span></p></td></tr></table></blockquote></div></p><p>A flonum has a 53-bit significand (we’ll say it has 53 bits of
<span style="font-style: italic">precision</span>) and an 11-bit <span style="font-style: italic">exponent</span>. A bigfloat
has an arbitrary precision of at least 2 bits and a 31-bit exponent.</p><p><span style="font-style: italic">Reason:</span> To compute ridiculously large or small numbers with confidence.</p><p><div class="SIntrapara">Examples:</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">128</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="RktValLink" data-pltdoc="x">bfexp</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="RktValLink" data-pltdoc="x">bfexp</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="RktValLink" data-pltdoc="x">bfexp</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">3</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf "2.050986436051648895105860942072054674579e229520860")</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog%29%29" class="RktValLink" data-pltdoc="x">bflog</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog%29%29" class="RktValLink" data-pltdoc="x">bflog</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog%29%29" class="RktValLink" data-pltdoc="x">bflog</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="RktValLink" data-pltdoc="x">bfexp</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="RktValLink" data-pltdoc="x">bfexp</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="RktValLink" data-pltdoc="x">bfexp</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">3</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf 3)</span></p></td></tr></table></blockquote></div></p><p><span style="font-style: italic">Reason:</span> To verify your floating-point hardware.</p><p><a href="http://en.wikipedia.org/wiki/IEEE_754-2008">IEEE 754-2008</a> stipulates
that conforming implementations must correctly round the results of all operations.
Roughly speaking, results can’t be more than half a bit off, where the bit in
question is the least significant in the significand.</p><p><div class="SIntrapara">Of course, implementations don’t always adhere to standards. For example, on my old
laptop, evaluating <span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._exp%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">exp</a></span><span class="stt"> </span><span class="RktVal">400</span><span class="RktPn">)</span> results in <span class="RktVal">5.221469689764346e+173</span>.
Note the last four decimal digits in the significand: <span class="RktVal">4346</span>. But they should be <span class="RktVal">4144</span>:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">53</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3eflonum%29%29" class="RktValLink" data-pltdoc="x">bigfloat->flonum</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="RktValLink" data-pltdoc="x">bfexp</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">400</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">5.221469689764144e+173</span></p></td></tr></table></blockquote></div><div class="SIntrapara">My new laptop computes <span class="RktVal">5.221469689764144e+173</span> as it should.</div></p><p><span style="font-style: italic">Reason:</span> To control rounding of the least significant bit.</p><p>IEEE 754 provides for different rounding modes for the smallest bit of
a flonum result, such as round to even and round toward zero. We might use
this to implement interval arithmetic correctly, by rounding lower bounds
downward and upper bounds upward. But there isn’t a portable way to set the
rounding mode!</p><p>MPFR allows the rounding mode to be different for any operation, and
<a href="" class="RktModLink" data-pltdoc="x"><span class="RktSym">math/bigfloat</span></a> exposes this capability using the parameter
<span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-rounding-mode%29%29" class="RktValLink" data-pltdoc="x">bf-rounding-mode</a></span>.</p><p><span style="font-weight: bold">When shouldn’t I use <a href="" class="RktModLink" data-pltdoc="x"><span class="RktSym">math/bigfloat</span></a>?</span></p><p>When you need raw speed. Bigfloat functions can be hundreds to thousands of times slower
than flonum functions.</p><p>That’s not to say that they’re <span style="font-style: italic">inefficient</span>. For example, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog%29%29" class="RktValLink" data-pltdoc="x">bflog</a></span>
implements the algorithm with the best known asymptotic complexity. It just doesn’t
run directly on hardware, and it can’t take fixed-precision-only shortcuts.</p><p><span style="font-weight: bold">Why are there junk digits on the end of <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="stt"> </span><span class="RktVal">1.1</span><span class="RktPn">)</span>?</span></p><p>That’s approximately the value of the flonum <span class="RktVal">1.1</span>. Use <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">#e1.1</span><span class="RktPn">)</span><span class="RktMeta"></span> or
<span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="RktMeta"></span><span class="hspace"> </span><span class="RktMeta"></span><span class="RktVal">"1.1"</span><span class="RktPn">)</span><span class="RktMeta"></span> to make the junk go away. In general, you should prefer to convert
exact rationals and strings to bigfloats.</p><p><span style="font-weight: bold">Why is the last digit of <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._pi..bf%29%29" class="RktValLink" data-pltdoc="x">pi.bf</a></span> not rounded correctly?</span></p><p>All the <span style="font-style: italic">bits</span> but the last is exact, and the last bit is correctly rounded.
This doesn’t guarantee that the last digit will be.</p><p>A decimal digit represents at most log(10)/log(2) ≈ 3.3 bits. This is an irrational
number, so the decimal/bit boundary never lines up except at the decimal point.
Thus, the last decimal digit of any bigfloat must represent fewer than 3.3 bits,
so it’s wrong more often than not. But it’s the last <span style="font-style: italic">bit</span> that counts.</p><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""Type_and_Constructors"">5.3<tt> </tt><a name="(part._.Type_and_.Constructors)"></a>Type and Constructors</h4><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>syntax</p></div></div><p class="RForeground"><a name="(form._((lib._math/bigfloat..rkt)._.Bigfloat))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxDef RktStxLink" data-pltdoc="x">Bigfloat</a></span></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat?</a></span></span><span class="hspace"> </span><span class="RktVar">v</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">v</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Any%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Any</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">An opaque type that represents an arbitrary-precision floating-point number, or a <a href="#%28tech._bigfloat%29" class="techoutside" data-pltdoc="x"><span class="techinside">bigfloat</span></a>,
and the opaque type’s predicate.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.U%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">U</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.String%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">String</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Real%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Real</a></span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf</a></span></span><span class="hspace"> </span><span class="RktVar">sig</span><span class="hspace"> </span><span class="RktVar">exp</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">sig</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">exp</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr></table></blockquote></div><div class="SIntrapara">The one-argument variant converts a string or real <span class="RktVar">x</span> to a bigfloat.</div></p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">128</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">4</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf 4)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">1/7</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf #e0.1428571428571428571428571428571428571426)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">41/10</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf #e4.099999999999999999999999999999999999995)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">"not a number"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktErr">bf: expected a well-formed decimal number; given "not a number"</span></p></td></tr><tr><td><p></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">"15e200000000"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf "1.499999999999999999999999999999999999998e200000001")</span></p></td></tr></table></blockquote><p>In the last example, the result of <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="stt"> </span><span class="RktVal">"15e200000000"</span><span class="RktPn">)</span> is displayed as a
string conversion because the exact rational number would be very large.</p><p><div class="SIntrapara"><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p>* It can be a good idea if you’re testing a flonum implementation of a function
against a bigfloat implementation.</p></blockquote></blockquote></blockquote></div><div class="SIntrapara">Converting from flonum literals is usually a bad idea* because flonums have only
53 bits precision. Prefer to pass exact rationals and strings to <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span>.</div></p><p><div class="SIntrapara">The two-argument variant converts a signed significand <span class="RktVar">sig</span> and a power of
2 <span class="RktVar">exp</span> to a bigfloat. Generally, <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="stt"> </span><span class="RktVar">sig</span><span class="stt"> </span><span class="RktVar">exp</span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252A%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">*</a></span><span class="stt"> </span><span class="RktVar">sig</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._expt%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">expt</a></span><span class="stt"> </span><span class="RktVal">2</span><span class="stt"> </span><span class="RktVar">exp</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span>,
but the two-argument variant is much faster, especially for large <span class="RktVar">exp</span>.
</div><div class="SIntrapara"><p><div class="SIntrapara">Examples:</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">200</span><span class="hspace"> </span><span class="RktVal">56</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf 14411518807585587200)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252A%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">*</a></span><span class="hspace"> </span><span class="RktVal">200</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._expt%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktVal">56</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf 14411518807585587200)</span></p></td></tr></table></blockquote></div></p></div></p><p><div class="SIntrapara">The <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfrandom%29%29" class="RktValLink" data-pltdoc="x">bfrandom</a></span> function generates random bigfloats between 0 and 1 using
the two-argument variant in this way:
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._require%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">require</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=require.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._only-in%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">only-in</a></span><span class="hspace"> </span><span class="RktSym">math/base</span><span class="hspace"> </span><span class="RktSym"><a href="base.html#%28def._%28%28lib._math%2Fbase..rkt%29._random-bits%29%29" class="RktValLink" data-pltdoc="x">random-bits</a></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">64</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="base.html#%28def._%28%28lib._math%2Fbase..rkt%29._random-bits%29%29" class="RktValLink" data-pltdoc="x">random-bits</a></span><span class="hspace"> </span><span class="RktVal">64</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-6</span>4</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf #e0.416872969910248753552)</span></p></td></tr></table></blockquote></div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfrandom))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfrandom%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfrandom</a></span></span><span class="RktPn"></span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></blockquote></div><div class="SIntrapara">Returns a uniformly distributed random bigfloat in the interval [0,1].</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfcopy))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcopy%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfcopy</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span>-bit bigfloat closest to <span class="RktVar">x</span>,
under the current <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-rounding-mode%29%29" class="RktValLink" data-pltdoc="x">bf-rounding-mode</a></span>.</div></p><p><div class="SIntrapara">A common pattern to compute bigfloats in higher precision is
</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">64</span><span class="RktPn">)</span></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcopy%29%29" class="RktValLink" data-pltdoc="x">bfcopy</a></span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=parameters.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fmore-scheme..rkt%2529._parameterize%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">parameterize</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktPn">[</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252B%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">+</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">10</span><span class="RktPn">)</span><span class="RktPn">]</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2F%29%29" class="RktValLink" data-pltdoc="x">bf/</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2B%29%29" class="RktValLink" data-pltdoc="x">bf+</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._1..bf%29%29" class="RktValLink" data-pltdoc="x">1.bf</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsqrt%29%29" class="RktValLink" data-pltdoc="x">bfsqrt</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._5..bf%29%29" class="RktValLink" data-pltdoc="x">5.bf</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._2..bf%29%29" class="RktValLink" data-pltdoc="x">2.bf</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p><span class="RktRes">(bf #e1.61803398874989484821)</span></p></td></tr></table></blockquote></div><div class="SIntrapara">This example computes the golden ratio (<span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._phi..bf%29%29" class="RktValLink" data-pltdoc="x">phi.bf</a></span>) with 10 bits more than requested,
to make up for triple rounding error.</div></p><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""Accessors_and_Conversion_Functions"">5.4<tt> </tt><a name="(part._.Accessors_and_.Conversion_.Functions)"></a>Accessors and Conversion Functions</h4><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-precision))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-precision%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat-precision</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Exact-.Positive-.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Exact-Positive-Integer</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the number of bits in the significand of <span class="RktVar">x</span>. This is almost always
the value of <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span> when <span class="RktVar">x</span> was created.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-signbit))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-signbit%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat-signbit</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.U%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">U</a></span><span class="hspace"> </span><span class="RktVal">0</span><span class="hspace"> </span><span class="RktVal">1</span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the sign bit of the significand of <span class="RktVar">x</span>.
</div><div class="SIntrapara"><p><div class="SIntrapara">Examples:</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-signbit%29%29" class="RktValLink" data-pltdoc="x">bigfloat-signbit</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-1..bf%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-1</span>.bf</a></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">1</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-signbit%29%29" class="RktValLink" data-pltdoc="x">bigfloat-signbit</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._0..bf%29%29" class="RktValLink" data-pltdoc="x">0.bf</a></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">0</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-signbit%29%29" class="RktValLink" data-pltdoc="x">bigfloat-signbit</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-0..bf%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-0</span>.bf</a></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">1</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-signbit%29%29" class="RktValLink" data-pltdoc="x">bigfloat-signbit</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-inf..bf%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-i</span>nf.bf</a></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">1</span></p></td></tr></table></blockquote></div></p></div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-significand))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-significand%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat-significand</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-exponent))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-exponent%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat-exponent</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Return the <span style="font-style: italic">signed</span> significand or exponent of <span class="RktVar">x</span>.</div></p><p>To access the significand and exponent at the same time, use <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3esig%2Bexp%29%29" class="RktValLink" data-pltdoc="x">bigfloat->sig+exp</a></span>.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-~3esig+exp))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3esig%2Bexp%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat->sig+exp</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.Values%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Values</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the <span style="font-style: italic">signed</span> significand and exponent of <span class="RktVar">x</span>.</div></p><p>If <span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=values.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._values%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">values</a></span><span class="stt"> </span><span class="RktSym">sig</span><span class="stt"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._exp%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">exp</a></span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3esig%2Bexp%29%29" class="RktValLink" data-pltdoc="x">bigfloat->sig+exp</a></span><span class="stt"> </span><span class="RktVar">x</span><span class="RktPn">)</span>, its value as an exact rational
is <span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252A%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">*</a></span><span class="stt"> </span><span class="RktSym">sig</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._expt%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">expt</a></span><span class="stt"> </span><span class="RktVal">2</span><span class="stt"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._exp%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">exp</a></span><span class="RktPn">)</span><span class="RktPn">)</span>. In fact, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3erational%29%29" class="RktValLink" data-pltdoc="x">bigfloat->rational</a></span> converts
bigfloats to rationals in exactly this way, after ensuring that <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfrational~3f%29%29" class="RktValLink" data-pltdoc="x">bfrational?</a></span><span class="stt"> </span><span class="RktVar">x</span><span class="RktPn">)</span>
is <span class="RktVal">#t</span>.</p><p>This function and the two-argument variant of <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span> are mutual inverses.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-~3einteger))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3einteger%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat->integer</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-~3erational))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3erational%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat->rational</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Exact-.Rational%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Exact-Rational</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-~3ereal))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3ereal%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat->real</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.U%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">U</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Exact-.Rational%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Exact-Rational</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Flonum%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Flonum</a></span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-~3eflonum))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3eflonum%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat->flonum</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Flonum%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Flonum</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Convert bigfloats to integer, exact rational, real and flonum values respectively.</div></p><p><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3einteger%29%29" class="RktValLink" data-pltdoc="x">bigfloat->integer</a></span>, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3erational%29%29" class="RktValLink" data-pltdoc="x">bigfloat->rational</a></span> and <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3ereal%29%29" class="RktValLink" data-pltdoc="x">bigfloat->real</a></span> return values
that can be converted exactly back to <span class="RktVar">x</span> using <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span>. For the first two, this is done
by raising an error if <span class="RktVar">x</span> is not respectively integer or rational. On the other hand,
<span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3ereal%29%29" class="RktValLink" data-pltdoc="x">bigfloat->real</a></span> returns <span class="RktVal">+inf.0</span>, <span class="RktVal"><span class="nobreak">-i</span>nf.0</span> or <span class="RktVal">+nan.0</span> when <span class="RktVar">x</span>
is not a rational bigfloat.</p><p><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3eflonum%29%29" class="RktValLink" data-pltdoc="x">bigfloat->flonum</a></span> rounds <span class="RktVar">x</span> to 53 bits precision to fit the value into a flonum,
using the current value of <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-rounding-mode%29%29" class="RktValLink" data-pltdoc="x">bf-rounding-mode</a></span>.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">64</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3einteger%29%29" class="RktValLink" data-pltdoc="x">bigfloat->integer</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">21/10</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><table cellspacing="0" cellpadding="0"><tr><td><p><span class="RktErr">bigfloat->integer: contract violation</span></p></td></tr><tr><td><p><span class="RktErr"></span><span class="hspace"> </span><span class="RktErr">expected: bfinteger?</span></p></td></tr><tr><td><p><span class="RktErr"></span><span class="hspace"> </span><span class="RktErr">given: (bf #e2.09999999999999999991)</span></p></td></tr></table></td></tr><tr><td><p></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3einteger%29%29" class="RktValLink" data-pltdoc="x">bigfloat->integer</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfround%29%29" class="RktValLink" data-pltdoc="x">bfround</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">21/10</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">2</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">1/7</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3eflonum%29%29" class="RktValLink" data-pltdoc="x">bigfloat->flonum</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">0.14285714285714285</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3erational%29%29" class="RktValLink" data-pltdoc="x">bigfloat->rational</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">10540996613548315209/73786976294838206464</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528lib._racket%252Fprivate%252Fmisc..rkt%2529._rationalize%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">rationalize</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3erational%29%29" class="RktValLink" data-pltdoc="x">bigfloat->rational</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._expt%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">expt</a></span><span class="hspace"> </span><span class="RktVal">2</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._-%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><span class="nobreak">-</span></a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">1/7</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3d%29%29" class="RktValLink" data-pltdoc="x">bf=</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3erational%29%29" class="RktValLink" data-pltdoc="x">bigfloat->rational</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr></table></blockquote><p><span style="font-weight: bold">Be careful with exact conversions.</span> Bigfloats with large exponents may not fit in memory as
integers or exact rationals. Worse, they might fit, but have all your RAM and swap space for lunch.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-~3estring))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3estring%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat->string</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.String%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">String</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._string-~3ebigfloat))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._string-~3ebigfloat%29%29" class="RktValDef RktValLink" data-pltdoc="x">string->bigfloat</a></span></span><span class="hspace"> </span><span class="RktVar">s</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.U%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">U</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span><span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.False%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">False</a></span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">s</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.String%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">String</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Convert a bigfloat <span class="RktVar">x</span> to a string <span class="RktVar">s</span> and back.</div></p><p>The string returned by <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3estring%29%29" class="RktValLink" data-pltdoc="x">bigfloat->string</a></span> includes enough digits that
<span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._string-~3ebigfloat%29%29" class="RktValLink" data-pltdoc="x">string->bigfloat</a></span> can reconstruct the bigfloat precisely. In other words,
<span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._string-~3ebigfloat%29%29" class="RktValLink" data-pltdoc="x">string->bigfloat</a></span> is a left inverse of <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3estring%29%29" class="RktValLink" data-pltdoc="x">bigfloat->string</a></span>.</p><p>If <span class="RktVar">s</span> isn’t a well-formed decimal number with an optional exponent part,
<span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._string-~3ebigfloat%29%29" class="RktValLink" data-pltdoc="x">string->bigfloat</a></span> returns <span class="RktVal">#f</span>. (In contrast, <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="stt"> </span><span class="RktVar">s</span><span class="RktPn">)</span> raises an error.)</p><p><div class="SIntrapara">Examples:</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">64</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3estring%29%29" class="RktValLink" data-pltdoc="x">bigfloat->string</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">4</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">"4"</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3estring%29%29" class="RktValLink" data-pltdoc="x">bigfloat->string</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">1/10000</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">"1.00000000000000000001e-4"</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._string-~3ebigfloat%29%29" class="RktValLink" data-pltdoc="x">string->bigfloat</a></span><span class="hspace"> </span><span class="RktVal">"0.14285714285714285714"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf #e0.142857142857142857141)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._string-~3ebigfloat%29%29" class="RktValLink" data-pltdoc="x">string->bigfloat</a></span><span class="hspace"> </span><span class="RktVal">"square root of two"</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._string-~3ebigfloat%29%29" class="RktValLink" data-pltdoc="x">string->bigfloat</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3estring%29%29" class="RktValLink" data-pltdoc="x">bigfloat->string</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._pi..bf%29%29" class="RktValLink" data-pltdoc="x">pi.bf</a></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf #e3.14159265358979323851)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._pi..bf%29%29" class="RktValLink" data-pltdoc="x">pi.bf</a></span></td></tr><tr><td><p><span class="RktRes">(bf #e3.14159265358979323851)</span></p></td></tr></table></blockquote></div></p><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""Parameters"">5.5<tt> </tt><a name="(part._.Parameters)"></a>Parameters</h4><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>parameter</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf-precision))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf-precision</a></span></span><span class="RktPn"></span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></p></blockquote></td></tr><tr><td><span class="RktPn">(</span><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf-precision</a></span></span><span class="hspace"> </span><span class="RktVar">bits</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=void.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._void%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">void?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">bits</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr></table></blockquote></div><div class="SIntrapara">A parameter that determines the precision of bigfloats returned from most bigfloat functions.
Exceptions are noted in the documentation for functions that do not use <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span>.</div></p><p>For nonzero, rational bigfloats, the number of bits <span class="RktVar">bits</span> includes the leading one bit.
For example, to simulate 64-bit floating point, use <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="stt"> </span><span class="RktVal">53</span><span class="RktPn">)</span> even though
flonums have a 52-bit significand, because the one bit is implicit in a flonum.</p><p>This parameter has a guard that ensures <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span> is between
<span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-min-precision%29%29" class="RktValLink" data-pltdoc="x">bf-min-precision</a></span> and <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-max-precision%29%29" class="RktValLink" data-pltdoc="x">bf-max-precision</a></span>.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>parameter</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf-rounding-mode))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-rounding-mode%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf-rounding-mode</a></span></span><span class="RktPn"></span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.U%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">U</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">nearest</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">zero</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">up</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">down</span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="RktPn">(</span><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-rounding-mode%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf-rounding-mode</a></span></span><span class="hspace"> </span><span class="RktVar">mode</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=void.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._void%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">void?</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">mode</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.U%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">U</a></span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">nearest</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">zero</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">up</span><span class="hspace"> </span><span class="RktVal">'</span><span class="RktVal">down</span><span class="RktPn">)</span></td></tr></table></blockquote></div><div class="SIntrapara">A parameter that determines the mode used to round the results of most bigfloat functions.
Conceptually, rounding is applied to infinite-precision results to fit them into
<span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span> bits.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._bf-min-precision))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-min-precision%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf-min-precision</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Exact-.Positive-.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Exact-Positive-Integer</a></span></p></blockquote></td></tr></table></blockquote></div><div class="SIntrapara">Equal to <span class="RktVal">2</span>, because single-bit bigfloats can’t be correctly rounded.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._bf-max-precision))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-max-precision%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf-max-precision</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Exact-.Positive-.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Exact-Positive-Integer</a></span></p></blockquote></td></tr></table></blockquote></div><div class="SIntrapara">The largest value of <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span>. This is platform-dependent, and probably much
larger than you’ll ever need.</div></p><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""constants"">5.6<tt> </tt><a name="(part._constants)"></a>Constants</h4><p>Most bigfloat “constants” are actually identifier macros that expand to the application
of a zero-argument function. This allows, for example, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._pi..bf%29%29" class="RktValLink" data-pltdoc="x">pi.bf</a></span> to depend on the
current value of <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span>, and allows all of them to be constructed lazily.
Most constants are memoized, possibly at multiple precisions.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._pi..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._pi..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">pi.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._phi..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._phi..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">phi.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._gamma..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._gamma..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">gamma.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._catalan..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._catalan..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">catalan.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._log2..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._log2..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">log2.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Approximations of π, φ, γ, G and log(2).
</div><div class="SIntrapara"><p><div class="SIntrapara">Examples:</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">10</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._pi..bf%29%29" class="RktValLink" data-pltdoc="x">pi.bf</a></span></td></tr><tr><td><p><span class="RktRes">(bf #e3.1406)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">179</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._pi..bf%29%29" class="RktValLink" data-pltdoc="x">pi.bf</a></span></td></tr><tr><td><p><span class="RktRes">(bf #e3.141592653589793238462643383279502884197169399375105819)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._phi..bf%29%29" class="RktValLink" data-pltdoc="x">phi.bf</a></span></td></tr><tr><td><p><span class="RktRes">bf #e1.618033988749894848204586834365638117720309179805762863)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._gamma..bf%29%29" class="RktValLink" data-pltdoc="x">gamma.bf</a></span></td></tr><tr><td><p><span class="RktRes">(bf #e0.5772156649015328606065120900824024310421593359399235988)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._catalan..bf%29%29" class="RktValLink" data-pltdoc="x">catalan.bf</a></span></td></tr><tr><td><p><span class="RktRes">(bf #e0.9159655941772190150546035149323841107741493742816721343)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._log2..bf%29%29" class="RktValLink" data-pltdoc="x">log2.bf</a></span></td></tr><tr><td><p><span class="RktRes">(bf #e0.6931471805599453094172321214581765680755001343602552545)</span></p></td></tr></table></blockquote></div></p></div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-inf..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-inf..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-i</span>nf.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-max..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-max..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-m</span>ax.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-min..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-min..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-m</span>in.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-0..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-0..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-0</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._0..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._0..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">0.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._+min..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Bmin..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">+min.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._+max..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Bmax..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">+max.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._+inf..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Binf..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">+inf.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._+nan..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Bnan..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">+nan.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._epsilon..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._epsilon..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">epsilon.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Bigfloat constants corresponding to
<span class="RktVal"><span class="nobreak">-i</span>nf.0</span>, <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._-max..0%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-m</span>ax.0</a></span> <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._-min..0%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-m</span>in.0</a></span>, <span class="RktVal"><span class="nobreak">-0</span>.0</span>,
<span class="RktVal">0.0</span>, <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._%2Bmin..0%29%29" class="RktValLink" data-pltdoc="x">+min.0</a></span>, <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._%2Bmax..0%29%29" class="RktValLink" data-pltdoc="x">+max.0</a></span>, <span class="RktVal">+inf.0</span>,
<span class="RktVal">+nan.0</span> and <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._epsilon..0%29%29" class="RktValLink" data-pltdoc="x">epsilon.0</a></span>.</div></p><p>The constants <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-inf..bf%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-i</span>nf.bf</a></span>, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-0..bf%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-0</span>.bf</a></span>, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._0..bf%29%29" class="RktValLink" data-pltdoc="x">0.bf</a></span>, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Binf..bf%29%29" class="RktValLink" data-pltdoc="x">+inf.bf</a></span>,
and <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Bnan..bf%29%29" class="RktValLink" data-pltdoc="x">+nan.bf</a></span> have fixed precision.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-10..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-10..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-1</span>0.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-9..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-9..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-9</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-8..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-8..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-8</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-7..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-7..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-7</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-6..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-6..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-6</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-5..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-5..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-5</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-4..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-4..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-4</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-3..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-3..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-3</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-2..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-2..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-2</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._-1..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-1..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x"><span class="nobreak">-1</span>.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._1..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._1..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">1.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._2..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._2..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">2.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._3..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._3..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">3.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._4..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._4..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">4.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._5..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._5..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">5.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._6..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._6..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">6.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._7..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._7..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">7.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._8..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._8..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">8.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._9..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._9..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">9.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>value</p></div></div><p class="RForeground"><a name="(def._((lib._math/bigfloat..rkt)._10..bf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._10..bf%29%29" class="RktValDef RktValLink" data-pltdoc="x">10.bf</a></span></span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">More fixed-precision bigfloat constants.</div></p><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""predicates"">5.7<tt> </tt><a name="(part._predicates)"></a>Predicates</h4><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfzero~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfzero~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfzero?</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfpositive~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfpositive~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfpositive?</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfnegative~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfnegative~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfnegative?</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfinteger~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfinteger~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfinteger?</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfeven~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfeven~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfeven?</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfodd~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfodd~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfodd?</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfrational~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfrational~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfrational?</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfinfinite~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfinfinite~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfinfinite?</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfnan~3f))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfnan~3f%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfnan?</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Unary predicates corresponding to <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._zero%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">zero?</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._positive%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">positive?</a></span>,
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._negative%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">negative?</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._integer%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">integer?</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._even%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">even?</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._odd%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">odd?</a></span>,
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._rational%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">rational?</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528lib._racket%252Fmath..rkt%2529._infinite%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">infinite?</a></span> and <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528lib._racket%252Fmath..rkt%2529._nan%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">nan?</a></span>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf~3d))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3d%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf=</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf~3e))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3e%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf></a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf~3c))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3c%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf<</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf~3e~3d))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3e~3d%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf>=</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf~3c~3d))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf~3c~3d%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf<=</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Boolean%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Boolean</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Standard comparison functions. As is usual, infinities are either greater or less
than any other bigfloat, and every comparison returns <span class="RktVal">#f</span> when either argument
is <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Bnan..bf%29%29" class="RktValLink" data-pltdoc="x">+nan.bf</a></span>.</div></p><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""rounding"">5.8<tt> </tt><a name="(part._rounding)"></a>Rounding</h4><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bftruncate))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bftruncate%29%29" class="RktValDef RktValLink" data-pltdoc="x">bftruncate</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bffloor))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bffloor%29%29" class="RktValDef RktValLink" data-pltdoc="x">bffloor</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfceiling))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfceiling%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfceiling</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfround))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfround%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfround</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Like <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._truncate%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">truncate</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._floor%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">floor</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._ceiling%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">ceiling</a></span> and <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._round%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">round</a></span>, but
for bigfloats.</div></p><p><div class="SIntrapara">Rounding is to the nearest integer, with ties broken by rounding to even.
</div><div class="SIntrapara"><p><div class="SIntrapara">Examples:</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfround%29%29" class="RktValLink" data-pltdoc="x">bfround</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">1.5</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf 2)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfround%29%29" class="RktValLink" data-pltdoc="x">bfround</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">2.5</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf 2)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfround%29%29" class="RktValLink" data-pltdoc="x">bfround</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-1</span>.5</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf -2)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfround%29%29" class="RktValLink" data-pltdoc="x">bfround</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-2</span>.5</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf -2)</span></p></td></tr></table></blockquote></div></p></div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bffrac))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bffrac%29%29" class="RktValDef RktValLink" data-pltdoc="x">bffrac</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the fractional part of <span class="RktVar">x</span>, with the same sign as <span class="RktVar">x</span>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfrint))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfrint%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfrint</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Rounds <span class="RktVar">x</span> to the nearest integer bigfloat, in the direction specified by
<span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-rounding-mode%29%29" class="RktValLink" data-pltdoc="x">bf-rounding-mode</a></span><span class="RktPn">)</span>.</div></p><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""ops"">5.9<tt> </tt><a name="(part._ops)"></a>Mathematical Operations</h4><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfmax))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfmax%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfmax</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfmin))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfmin%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfmin</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Return the maximum and minimum of their arguments, respectively.</div></p><p>When given no arguments, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfmin%29%29" class="RktValLink" data-pltdoc="x">bfmin</a></span> returns <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Binf..bf%29%29" class="RktValLink" data-pltdoc="x">+inf.bf</a></span>, and
<span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfmax%29%29" class="RktValLink" data-pltdoc="x">bfmax</a></span> returns <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-inf..bf%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-i</span>nf.bf</a></span>.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf+))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2B%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf+</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf*))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2A%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf*</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf-))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf-</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf/))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2F%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf/</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span><span class="RktMeta">...</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfsqr))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsqr%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfsqr</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfabs))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfabs%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfabs</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfsgn))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsgn%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfsgn</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Standard arithmetic functions, corresponding to <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252B%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">+</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252A%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">*</a></span>,
<span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._-%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x"><span class="nobreak">-</span></a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252F%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">/</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528lib._racket%252Fmath..rkt%2529._sqr%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">sqr</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._abs%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">abs</a></span> and <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528lib._racket%252Fmath..rkt%2529._sgn%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">sgn</a></span>.</div></p><p>When <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2B%29%29" class="RktValLink" data-pltdoc="x">bf+</a></span> and <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-%29%29" class="RktValLink" data-pltdoc="x">bf-</a></span> are given more than two arguments, they compute
the answers in a way that incurs rounding error only once.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfsqrt))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsqrt%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfsqrt</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bf1/sqrt))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf1%2Fsqrt%29%29" class="RktValDef RktValLink" data-pltdoc="x">bf1/sqrt</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfcbrt))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcbrt%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfcbrt</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Return the square root, <span style="font-style: italic">reciprocal</span> square root, and cube root of <span class="RktVar">x</span>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfroot))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfroot%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfroot</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">n</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">n</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the <span class="RktVar">n</span>th root of <span class="RktVar">x</span>. <span class="RktVar">n</span> must be a nonnegative fixnum.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfhypot))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfhypot%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfhypot</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Computes <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsqrt%29%29" class="RktValLink" data-pltdoc="x">bfsqrt</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2B%29%29" class="RktValLink" data-pltdoc="x">bf+</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsqr%29%29" class="RktValLink" data-pltdoc="x">bfsqr</a></span><span class="stt"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsqr%29%29" class="RktValLink" data-pltdoc="x">bfsqr</a></span><span class="stt"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span> without uncessary overflow,
incurring rounding error only once. See <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._flhypot%29%29" class="RktValLink" data-pltdoc="x">flhypot</a></span> for an example using flonums.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bflog))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog%29%29" class="RktValDef RktValLink" data-pltdoc="x">bflog</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bflog2))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog2%29%29" class="RktValDef RktValLink" data-pltdoc="x">bflog2</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bflog10))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog10%29%29" class="RktValDef RktValLink" data-pltdoc="x">bflog10</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Return the log of <span class="RktVar">x</span> in base <span style="font-style: italic">e</span>, 2 and 10.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfexp))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfexp</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfexp2))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp2%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfexp2</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfexp10))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp10%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfexp10</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Return the exponential of <span class="RktVar">x</span> in base <span style="font-style: italic">e</span>, 2 and 10.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bflog1p))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog1p%29%29" class="RktValDef RktValLink" data-pltdoc="x">bflog1p</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfexpm1))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexpm1%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfexpm1</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Like <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog%29%29" class="RktValLink" data-pltdoc="x">bflog</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2B%29%29" class="RktValLink" data-pltdoc="x">bf+</a></span><span class="stt"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._1..bf%29%29" class="RktValLink" data-pltdoc="x">1.bf</a></span><span class="stt"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="RktPn">)</span> and <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-%29%29" class="RktValLink" data-pltdoc="x">bf-</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexp%29%29" class="RktValLink" data-pltdoc="x">bfexp</a></span><span class="stt"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="stt"> </span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._1..bf%29%29" class="RktValLink" data-pltdoc="x">1.bf</a></span><span class="RktPn">)</span>, but correct
when <span class="RktVar">x</span> is near zero. See <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._fllog1p%29%29" class="RktValLink" data-pltdoc="x">fllog1p</a></span> for motivation and examples.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfexpt))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexpt%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfexpt</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Computes <span class="RktVar">x</span><span style="vertical-align: super; font-size: 80%"><span class="RktVar">y</span></span>. See <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=flonums.html%23%2528def._%2528%2528lib._racket%252Fflonum..rkt%2529._flexpt%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">flexpt</a></span> and <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._expt%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">expt</a></span>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfsin))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsin%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfsin</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfcos))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcos%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfcos</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bftan))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bftan%29%29" class="RktValDef RktValLink" data-pltdoc="x">bftan</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfasin))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfasin%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfasin</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfacos))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfacos%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfacos</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfatan))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfatan%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfatan</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfatan2))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfatan2%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfatan2</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Standard trigonometric functions and their inverses.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfsinh))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsinh%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfsinh</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfcosh))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcosh%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfcosh</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bftanh))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bftanh%29%29" class="RktValDef RktValLink" data-pltdoc="x">bftanh</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfasinh))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfasinh%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfasinh</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfacosh))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfacosh%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfacosh</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfatanh))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfatanh%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfatanh</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Standard hyperbolic functions and their inverses.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfsec))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsec%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfsec</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfcsc))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcsc%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfcsc</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfcot))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcot%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfcot</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Standard <span style="font-style: italic">reciprocal</span> trigonometric functions. MPFR does not implement their inverses.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfsech))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsech%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfsech</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfcsch))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcsch%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfcsch</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfcoth))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcoth%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfcoth</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Standard <span style="font-style: italic">reciprocal</span> hyperbolic functions. MPFR does not implement their inverses.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfsin+cos))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsin%2Bcos%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfsin+cos</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.Values%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Values</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Simultaneously computes the sine and cosine of <span class="RktVar">x</span>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfsinh+cosh))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfsinh%2Bcosh%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfsinh+cosh</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.Values%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Values</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Simultaneously computes the hyperbolic sine and cosine of <span class="RktVar">x</span>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bffactorial))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bffactorial%29%29" class="RktValDef RktValLink" data-pltdoc="x">bffactorial</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the factorial of <span class="RktVar">x</span>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfgamma))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfgamma%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfgamma</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Computes the <a href="http://en.wikipedia.org/wiki/Gamma_function">gamma function</a>,
a generalization of the factorial function.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bflog-gamma))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog-gamma%29%29" class="RktValDef RktValLink" data-pltdoc="x">bflog-gamma</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bflog-gamma/sign))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog-gamma%2Fsign%29%29" class="RktValDef RktValLink" data-pltdoc="x">bflog-gamma/sign</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.Values%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Values</a></span><span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types-extra..rkt%2529._.U%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">U</a></span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-1</span></span><span class="hspace"> </span><span class="RktVal">1</span><span class="RktPn">)</span><span class="RktPn">)</span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Computes the <a href="http://mathworld.wolfram.com/LogGammaFunction.html">log-gamma function</a>,
or the log of the absolute value of the gamma function. <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog-gamma%2Fsign%29%29" class="RktValLink" data-pltdoc="x">bflog-gamma/sign</a></span> additionally
returns the sign of <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfgamma%29%29" class="RktValLink" data-pltdoc="x">bfgamma</a></span><span class="stt"> </span><span class="RktVar">x</span><span class="RktPn">)</span>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfpsi0))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfpsi0%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfpsi0</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Computes the <a href="http://en.wikipedia.org/wiki/Digamma_function">digamma function</a>,
the logarithmic derivative of the gamma function.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfeint))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfeint%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfeint</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the <a href="http://en.wikipedia.org/wiki/Exponential_integral">exponential integral</a>
of <span class="RktVar">x</span>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfli2))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfli2%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfli2</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the dilogarithm of <span class="RktVar">x</span>, or the
<a href="http://en.wikipedia.org/wiki/Polylogarithm">polylogarithm</a> of order 2.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfzeta))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfzeta%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfzeta</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Computes the <a href="http://en.wikipedia.org/wiki/Riemann_zeta_function">Riemann zeta function</a>.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bferf))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bferf%29%29" class="RktValDef RktValLink" data-pltdoc="x">bferf</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bferfc))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bferfc%29%29" class="RktValDef RktValLink" data-pltdoc="x">bferfc</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Compute the <a href="http://en.wikipedia.org/wiki/Error_function">error function and
complementary error function</a>, respectively.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfbesj0))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesj0%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfbesj0</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfbesj1))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesj1%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfbesj1</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfbesj))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesj%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfbesj</a></span></span><span class="hspace"> </span><span class="RktVar">n</span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">n</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfbesy0))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesy0%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfbesy0</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfbesy1))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesy1%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfbesy1</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfbesy))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfbesy%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfbesy</a></span></span><span class="hspace"> </span><span class="RktVar">n</span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">n</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">These compute <a href="http://en.wikipedia.org/wiki/Bessel_function">Bessel functions</a>.</div></p><p>A “<span class="RktSym">j</span>” in the name indicates that a function computes a Bessel function of the
first kind. A “<span class="RktSym">y</span>” indicates the second kind.</p><p>The “<span class="RktSym">j</span>” or “<span class="RktSym">y</span>” is followed by the <span style="font-style: italic">order</span>: zero, one, or
<span class="RktVar">n</span> (user-specified).</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfagm))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfagm%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfagm</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym">bigfloat</span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Returns the
<a href="http://en.wikipedia.org/wiki/Arithmetic-geometric_mean">arithmetic-geometric mean</a>
of <span class="RktVar">x</span> and <span class="RktVar">y</span>. Typically, this isn’t directly useful, but it’s used in some
asymptotically fast algorithms such as the one that computes <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bflog%29%29" class="RktValLink" data-pltdoc="x">bflog</a></span>.</div></p><h4 x-source-module="(lib "math/scribblings/math.scrbl")" x-source-pkg="math-doc" x-part-tag=""misc"">5.10<tt> </tt><a name="(part._misc)"></a>Low-level Functions</h4><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloat-~3eordinal))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-~3eordinal%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloat->ordinal</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._ordinal-~3ebigfloat))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._ordinal-~3ebigfloat%29%29" class="RktValDef RktValLink" data-pltdoc="x">ordinal->bigfloat</a></span></span><span class="hspace"> </span><span class="RktVar">n</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">n</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bigfloats-between))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloats-between%29%29" class="RktValDef RktValLink" data-pltdoc="x">bigfloats-between</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">y</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">y</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfstep))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfstep%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfstep</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">n</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">n</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfnext))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfnext%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfnext</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr><tr><td><table cellspacing="0" cellpadding="0" class="together"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfprev))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfprev%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfprev</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></td></tr></table></blockquote></div><div class="SIntrapara">Like <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._flonum-~3eordinal%29%29" class="RktValLink" data-pltdoc="x">flonum->ordinal</a></span>, <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._ordinal-~3eflonum%29%29" class="RktValLink" data-pltdoc="x">ordinal->flonum</a></span>, <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._flonums-between%29%29" class="RktValLink" data-pltdoc="x">flonums-between</a></span>,
<span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._flstep%29%29" class="RktValLink" data-pltdoc="x">flstep</a></span>, <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._flnext%29%29" class="RktValLink" data-pltdoc="x">flnext</a></span> and <span class="RktSym"><a href="flonum.html#%28def._%28%28lib._math%2Fflonum..rkt%29._flprev%29%29" class="RktValLink" data-pltdoc="x">flprev</a></span>, but for bigfloats.</div></p><p>The major difference is that these operate using <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span> bits.
Additionally, unlike other bigfloat functions, all of these convert their bigfloat arguments
to <span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="RktPn">)</span> bits.</p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfshift))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfshift%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfshift</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktVar">n</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">n</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=ts-reference&rel=type-ref.html%23%2528form._%2528%2528lib._typed-racket%252Fbase-env%252Fbase-types..rkt%2529._.Integer%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">Integer</a></span></td></tr></table></blockquote></div><div class="SIntrapara">Like <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._arithmetic-shift%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">arithmetic-shift</a></span>, but for bigfloats. More precisely, this returns
<span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%2A%29%29" class="RktValLink" data-pltdoc="x">bf*</a></span><span class="stt"> </span><span class="RktVar">x</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfexpt%29%29" class="RktValLink" data-pltdoc="x">bfexpt</a></span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="stt"> </span><span class="RktVal">2</span><span class="RktPn">)</span><span class="stt"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="stt"> </span><span class="RktVar">n</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span>, but is much faster.</div></p><p><div class="SIntrapara"><blockquote class="SVInsetFlow"><table cellspacing="0" cellpadding="0" class="boxed RBoxed"><tr><td><blockquote class="SubFlow"><div class="RBackgroundLabel SIEHidden"><div class="RBackgroundLabelInner"><p>procedure</p></div></div><p class="RForeground"><span class="RktPn">(</span><a name="(def._((lib._math/bigfloat..rkt)._bfcanonicalize))"></a><span title="Provided from: math/bigfloat | Package: math-lib"><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcanonicalize%29%29" class="RktValDef RktValLink" data-pltdoc="x">bfcanonicalize</a></span></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="hspace"> </span>→<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></p></blockquote></td></tr><tr><td><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span>:<span class="hspace"> </span><span class="RktSym"><a href="#%28form._%28%28lib._math%2Fbigfloat..rkt%29._.Bigfloat%29%29" class="RktStxLink" data-pltdoc="x">Bigfloat</a></span></td></tr></table></blockquote></div><div class="SIntrapara"><span class="refelem"><span class="refcolumn"><span class="refcontent">Bigfloats are canonicalized before hashing, to ensure that equality
implies an equal hash.</span></span></span>
If <span class="RktVar">x</span> is nonzero and rational, returns a new bigfloat with no more bits of
precision than are necessary to encode <span class="RktVar">x</span> exactly, by removing all low-order
zeros from the significand and adjusting the exponent.</div></p><p>For zero or non-rational <span class="RktVar">x</span>, returns <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-inf..bf%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-i</span>nf.bf</a></span>, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._-0..bf%29%29" class="RktValLink" data-pltdoc="x"><span class="nobreak">-0</span>.bf</a></span>,
<span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._0..bf%29%29" class="RktValLink" data-pltdoc="x">0.bf</a></span>, <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Binf..bf%29%29" class="RktValLink" data-pltdoc="x">+inf.bf</a></span>, or <span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._%2Bnan..bf%29%29" class="RktValLink" data-pltdoc="x">+nan.bf</a></span>, depending on the value of <span class="RktVar">x</span>.</p><p>Two nonzero, rational bigfloats are <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._equal%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">equal?</a></span> if and only if their canonicalized
significands and exponents are equal. Two zero or non-rational bigfloats are <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._equal%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">equal?</a></span>
if and only if their canonicalizations are <span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=booleans.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._eq%7E3f%2529%2529&version=6.7" class="RktValLink Sq" data-pltdoc="x">eq?</a></span>.</p><p>Canonicalizing bigfloats won’t change answers computed from them.</p><p><div class="SIntrapara">Examples:</div><div class="SIntrapara"><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf-precision%29%29" class="RktValLink" data-pltdoc="x">bf-precision</a></span><span class="hspace"> </span><span class="RktVal">64</span><span class="RktPn">)</span></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/docs/6.7/html/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=6.7" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bf%29%29" class="RktValLink" data-pltdoc="x">bf</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-2</span></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p></p></td></tr><tr><td><span class="stt">> </span><span class="RktVar">x</span></td></tr><tr><td><p><span class="RktRes">(bf #e0.25)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcanonicalize%29%29" class="RktValLink" data-pltdoc="x">bfcanonicalize</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">(bf #e0.25)</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-precision%29%29" class="RktValLink" data-pltdoc="x">bigfloat-precision</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">64</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bigfloat-precision%29%29" class="RktValLink" data-pltdoc="x">bigfloat-precision</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="#%28def._%28%28lib._math%2Fbigfloat..rkt%29._bfcanonicalize%29%29" class="RktValLink" data-pltdoc="x">bfcanonicalize</a></span><span class="hspace"> </span><span class="RktVar">x</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">2</span></p></td></tr></table></blockquote></div></p><div class="navsetbottom"><span class="navleft"><form class="searchform"><input class="searchbox" style="color: #888;" type="text" value="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "6.7", "../");" onfocus="this.style.color="black"; this.style.textAlign="left"; if (this.value == "...search manuals...") this.value="";" onblur="if (this.value.match(/^ *$/)) { this.style.color="#888"; this.style.textAlign="center"; this.value="...search manuals..."; }"/></form> <a href="../index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("6.7");">top</a></span><span class="navright"> <a href="number-theory.html" title="backward to "4 Number Theory"" data-pltdoc="x">← prev</a> <a href="index.html" title="up to "Math Library"" data-pltdoc="x">up</a> <a href="array.html" title="forward to "6 Arrays"" data-pltdoc="x">next →</a></span> </div></div></div><div id="contextindicator"> </div></body></html>
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