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<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"/><meta name="viewport" content="width=device-width, initial-scale=0.8"/><title>3.2 Numbers</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="icons.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">The Racket Guide</a></td></tr></table></div><div class="tocviewsublisttop" style="display: none;" id="tocview_0"><table cellspacing="0" cellpadding="0"><tr><td align="right">1 </td><td><a href="intro.html" class="tocviewlink" data-pltdoc="x">Welcome to Racket</a></td></tr><tr><td align="right">2 </td><td><a href="to-scheme.html" class="tocviewlink" data-pltdoc="x">Racket Essentials</a></td></tr><tr><td align="right">3 </td><td><a href="datatypes.html" class="tocviewselflink" data-pltdoc="x">Built-<wbr></wbr>In Datatypes</a></td></tr><tr><td align="right">4 </td><td><a href="scheme-forms.html" class="tocviewlink" data-pltdoc="x">Expressions and Definitions</a></td></tr><tr><td align="right">5 </td><td><a href="define-struct.html" class="tocviewlink" data-pltdoc="x">Programmer-<wbr></wbr>Defined Datatypes</a></td></tr><tr><td align="right">6 </td><td><a href="modules.html" class="tocviewlink" data-pltdoc="x">Modules</a></td></tr><tr><td align="right">7 </td><td><a href="contracts.html" class="tocviewlink" data-pltdoc="x">Contracts</a></td></tr><tr><td align="right">8 </td><td><a href="i_o.html" class="tocviewlink" data-pltdoc="x">Input and Output</a></td></tr><tr><td align="right">9 </td><td><a href="regexp.html" class="tocviewlink" data-pltdoc="x">Regular Expressions</a></td></tr><tr><td align="right">10 </td><td><a href="control.html" class="tocviewlink" data-pltdoc="x">Exceptions and Control</a></td></tr><tr><td align="right">11 </td><td><a href="for.html" class="tocviewlink" data-pltdoc="x">Iterations and Comprehensions</a></td></tr><tr><td align="right">12 </td><td><a href="match.html" class="tocviewlink" data-pltdoc="x">Pattern Matching</a></td></tr><tr><td align="right">13 </td><td><a href="classes.html" class="tocviewlink" data-pltdoc="x">Classes and Objects</a></td></tr><tr><td align="right">14 </td><td><a href="units.html" class="tocviewlink" data-pltdoc="x">Units</a></td></tr><tr><td align="right">15 </td><td><a href="reflection.html" class="tocviewlink" data-pltdoc="x">Reflection and Dynamic Evaluation</a></td></tr><tr><td align="right">16 </td><td><a href="macros.html" class="tocviewlink" data-pltdoc="x">Macros</a></td></tr><tr><td align="right">17 </td><td><a href="languages.html" class="tocviewlink" data-pltdoc="x">Creating Languages</a></td></tr><tr><td align="rig
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<span class="RktVal">99999999999999999</span>, or <span class="RktVal"><span class="nobreak">-1</span>7</span>;</p></li><li><p>a rational that is exactly the ratio of two arbitrarily
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small or large integers, such as <span class="RktVal">1/2</span>,
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<span class="RktVal">99999999999999999/2</span>, or <span class="RktVal"><span class="nobreak">-3</span>/4</span>; or</p></li><li><p>a complex number with exact real and imaginary parts
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(where the imaginary part is not zero), such as <span class="RktVal">1+2i</span> or
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<span class="RktVal">1/2+3/4i</span>.</p></li></ul></li><li><p>An <span style="font-style: italic">inexact</span> number is either</p><ul><li><p>an IEEE floating-point representation of a number, such
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as <span class="RktVal">2.0</span> or <span class="RktVal">3.14e+87</span>, where the IEEE
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infinities and not-a-number are written
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<span class="RktVal">+inf.0</span>, <span class="RktVal"><span class="nobreak">-i</span>nf.0</span>, and <span class="RktVal">+nan.0</span>
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(or <span class="RktVal">-nan.0</span>); or</p></li><li><p>a complex number with real and imaginary parts that are
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IEEE floating-point representations, such as
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<span class="RktVal">2.0+3.0i</span> or <span class="RktVal"><span class="nobreak">-i</span>nf.0+nan.0i</span>; as a
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special case, an inexact complex number can have an
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exact zero real part with an inexact imaginary part.</p></li></ul></li></ul><p>Inexact numbers print with a decimal point or exponent specifier, and
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exact numbers print as integers and fractions. The same conventions
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apply for reading number constants, but <span class="RktInBG"><span class="hspace"></span><span class="RktIn">#e</span><span class="hspace"></span></span> or
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">#i</span><span class="hspace"></span></span> can prefix a number to force its parsing as an exact
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or inexact number. The prefixes <span class="RktInBG"><span class="hspace"></span><span class="RktIn">#b</span><span class="hspace"></span></span>, <span class="RktInBG"><span class="hspace"></span><span class="RktIn">#o</span><span class="hspace"></span></span>, and
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<span class="RktInBG"><span class="hspace"></span><span class="RktIn">#x</span><span class="hspace"></span></span> specify binary, octal, and hexadecimal
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interpretation of digits.</p><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p><span class="imageleft"><img src="magnify.png" alt="+" width="24" height="24"/></span><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=reader.html%23%2528part._parse-number%2529&version=8.6" class="Sq" data-pltdoc="x">Reading Numbers</a> in <a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=index.html&version=8.6" class="Sq" data-pltdoc="x">The Racket Reference</a> documents the fine points of the syntax of numbers.</p></blockquote></blockquote></blockquote><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="RktVal">0.5</span></td></tr><tr><td><p><span class="RktRes">0.5</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktVal">#e0.5</span></td></tr><tr><td><p><span class="RktRes">1/2</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktVal">#x03BB</span></td></tr><tr><td><p><span class="RktRes">955</span></p></td></tr></table></blockquote></div></p><p>Computations that involve an inexact number produce inexact results,
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so that inexactness acts as a kind of taint on numbers. Beware,
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however, that Racket offers no “inexact booleans,” so computations
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that branch on the comparison of inexact numbers can nevertheless
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produce exact results. The procedures <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._exact-%7E3einexact%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">exact->inexact</a></span> and
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<span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._inexact-%7E3eexact%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">inexact->exact</a></span> convert between the two
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types of numbers.</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/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252F%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">/</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">2</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">1/2</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252F%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">/</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">2.0</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">0.5</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._if%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">if</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktVal">3.0</span><span class="hspace"> </span><span class="RktVal">2.999</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">2</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/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._inexact-%7E3eexact%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">inexact->exact</a></span><span class="hspace"> </span><span class="RktVal">0.1</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">3602879701896397/36028797018963968</span></p></td></tr></table></blockquote></div></p><p>Inexact results are also produced by procedures such as <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._sqrt%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">sqrt</a></span>,
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<span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._log%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">log</a></span>, and <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._sin%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">sin</a></span> when an exact result would require
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representing real numbers that are not rational. Racket can represent
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only rational numbers and complex numbers with rational parts.</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/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._sin%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">sin</a></span><span class="hspace"> </span><span class="RktVal">0</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">rational...</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="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._sin%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">sin</a></span><span class="hspace"> </span><span class="RktVal">1/2</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktCmt">;</span><span class="RktCmt"> </span><span class="RktCmt">not rational...</span></td></tr><tr><td><p><span class="RktRes">0.479425538604203</span></p></td></tr></table></blockquote></div></p><p>In terms of performance, computations with small integers are
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typically the fastest, where “small” means that the number fits into
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one bit less than the machine’s word-sized representation for signed
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numbers. Computation with very large exact integers or with
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non-integer exact numbers can be much more expensive than computation
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with inexact numbers.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0"><tr><td><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=define.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fbase..rkt%2529._define%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">define</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">sigma</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=if.html%23%2528form._%2528%2528quote._%7E23%7E25kernel%2529._if%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">if</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace"> </span><span class="RktVal">0</span></td></tr><tr><td><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252B%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">+</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktSym">a</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">sigma</span><span class="hspace"> </span><span class="RktSym">f</span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%252B%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">+</a></span><span class="hspace"> </span><span class="RktSym">a</span><span class="hspace"> </span><span class="RktVal">1</span><span class="RktPn">)</span><span class="hspace"> </span><span class="RktSym">b</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></td></tr><tr><td><p> </p></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="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=time.html%23%2528form._%2528%2528lib._racket%252Fprivate%252Fmore-scheme..rkt%2529._time%2529%2529&version=8.6" class="RktStxLink Sq" data-pltdoc="x">time</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._round%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">round</a></span><span class="hspace"> </span><span class="RktPn">(</span><span class="RktSym">si
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<a name="(tech._real)"></a><span style="font-style: italic">real</span> (always rational), and <a name="(tech._complex)"></a><span style="font-style: italic">complex</span> are defined in
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the usual way, and are recognized by the procedures <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._integer%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">integer?</a></span>,
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<span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._rational%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">rational?</a></span>, <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._real%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">real?</a></span>, and <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._complex%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">complex?</a></span>, in addition
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to the generic <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._number%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">number?</a></span>. A few mathematical procedures accept
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only real numbers, but most implement standard extensions to complex
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numbers.</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/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._integer%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktVal">5</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._complex%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">complex?</a></span><span class="hspace"> </span><span class="RktVal">5</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._integer%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktVal">5.0</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._integer%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">integer?</a></span><span class="hspace"> </span><span class="RktVal">1+2i</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="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._complex%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">complex?</a></span><span class="hspace"> </span><span class="RktVal">1+2i</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._complex%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">complex?</a></span><span class="hspace"> </span><span class="RktVal">1.0+2.0i</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._abs%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">abs</a></span><span class="hspace"> </span><span class="RktVal"><span class="nobreak">-5</span></span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">5</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._abs%2529%2529&
|
||
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|
it is given both inexact and exact numbers to compare, it essentially
|
||
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|
converts the inexact numbers to exact before comparing. The
|
||
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|
<span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=Equality.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._eqv%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">eqv?</a></span> (and therefore <span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=Equality.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._equal%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">equal?</a></span>) procedure, in contrast,
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compares numbers considering both exactness and numerical equality.</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/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1.0</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=Equality.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._eqv%7E3f%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">eqv?</a></span><span class="hspace"> </span><span class="RktVal">1</span><span class="hspace"> </span><span class="RktVal">1.0</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#f</span></p></td></tr></table></blockquote></div></p><p>Beware of comparisons involving inexact numbers, which by their nature
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||
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|
can have surprising behavior. Even apparently simple inexact numbers
|
||
|
|
may not mean what you think they mean; for example, while a base-2
|
||
|
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IEEE floating-point number can represent <span class="RktVal">1/2</span> exactly, it
|
||
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can only approximate <span class="RktVal">1/10</span>:</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/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktVal">1/2</span><span class="hspace"> </span><span class="RktVal">0.5</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">#t</span></p></td></tr><tr><td><span class="stt">> </span><span class="RktPn">(</span><span class="RktSym"><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=generic-numbers.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._%7E3d%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">=</a></span><span class="hspace"> </span><span class="RktVal">1/10</span><span class="hspace"> </span><span class="RktVal">0.1</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="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=number-types.html%23%2528def._%2528%2528quote._%7E23%7E25kernel%2529._inexact-%7E3eexact%2529%2529&version=8.6" class="RktValLink Sq" data-pltdoc="x">inexact->exact</a></span><span class="hspace"> </span><span class="RktVal">0.1</span><span class="RktPn">)</span></td></tr><tr><td><p><span class="RktRes">3602879701896397/36028797018963968</span></p></td></tr></table></blockquote></div></p><blockquote class="refpara"><blockquote class="refcolumn"><blockquote class="refcontent"><p><span class="imageleft"><img src="magnify.png" alt="+" width="24" height="24"/></span><a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=numbers.html&version=8.6" class="Sq" data-pltdoc="x">Numbers</a> in <a href="https://download.racket-lang.org/releases/8.6/doc/local-redirect/index.html?doc=reference&rel=index.html&version=8.6" class="Sq" data-pltdoc="x">The Racket Reference</a> provides more on numbers and number procedures.</p></blockquote></blockquote></blockquote><div class="navsetbottom"><span class="navleft"><form class="searchform"><input class="searchbox" id="searchbox" type="text" tabindex="1" placeholder="...search manuals..." title="Enter a search string to search the manuals" onkeypress="return DoSearchKey(event, this, "8.6", "../");"/></form> <a href="https://docs.racket-lang.org/index.html" title="up to the documentation top" data-pltdoc="x" onclick="return GotoPLTRoot("8.6");">top</a><span class="tocsettoggle"> <a href="javascript:void(0);" title="show/hide table of contents" onclick="TocsetToggle();">contents</a></span></span><span class="navright"> <a href="booleans.html" title="backward to "3.1 Booleans"" data-pltdoc="x">← prev</a> <a href="datatypes.html" title="up to "3 Built-In Datatypes"" data-pltdoc="x">up</a> <a href="characters.html" title="forward to "3.3 Characters"" data-pltdoc="x">next →</a></span> </div></div></div><div id="contextindicator"> </div></body></html>
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