148 lines
6.7 KiB
HTML
148 lines
6.7 KiB
HTML
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<!DOCTYPE html>
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<html>
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<!-- Created by GNU Texinfo 7.1, https://www.gnu.org/software/texinfo/ -->
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<!-- This manual documents Guile version 3.0.10.
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Copyright (C) 1996-1997, 2000-2005, 2009-2023 Free Software Foundation,
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Inc.
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Copyright (C) 2021 Maxime Devos
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Copyright (C) 2024 Tomas Volf
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Permission is granted to copy, distribute and/or modify this document
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under the terms of the GNU Free Documentation License, Version 1.3 or
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any later version published by the Free Software Foundation; with no
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Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A
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copy of the license is included in the section entitled "GNU Free
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Documentation License." -->
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<title>Numerical Tower (Guile Reference Manual)</title>
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<meta name="description" content="Numerical Tower (Guile Reference Manual)">
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<meta name="keywords" content="Numerical Tower (Guile Reference Manual)">
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<meta name="viewport" content="width=device-width,initial-scale=1">
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<link href="index.html" rel="start" title="Top">
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<link href="Concept-Index.html" rel="index" title="Concept Index">
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<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents">
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<link href="Numbers.html" rel="up" title="Numbers">
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<link href="Integers.html" rel="next" title="Integers">
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<style type="text/css">
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<!--
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a.copiable-link {visibility: hidden; text-decoration: none; line-height: 0em}
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</style>
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<link rel="stylesheet" type="text/css" href="https://www.gnu.org/software/gnulib/manual.css">
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</head>
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<body lang="en">
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<div class="subsubsection-level-extent" id="Numerical-Tower">
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<div class="nav-panel">
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<p>
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Next: <a href="Integers.html" accesskey="n" rel="next">Integers</a>, Up: <a href="Numbers.html" accesskey="u" rel="up">Numerical data types</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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<hr>
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<h4 class="subsubsection" id="Scheme_0027s-Numerical-_0060_0060Tower_0027_0027"><span>6.6.2.1 Scheme’s Numerical “Tower”<a class="copiable-link" href="#Scheme_0027s-Numerical-_0060_0060Tower_0027_0027"> ¶</a></span></h4>
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<a class="index-entry-id" id="index-number_003f-2"></a>
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<p>Scheme’s numerical “tower” consists of the following categories of
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numbers:
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</p>
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<dl class="table">
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<dt><em class="dfn">integers</em></dt>
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<dd><p>Whole numbers, positive or negative; e.g. –5, 0, 18.
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</p>
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</dd>
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<dt><em class="dfn">rationals</em></dt>
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<dd><p>The set of numbers that can be expressed as <em class="math"><var class="var">p</var>/<var class="var">q</var></em>
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where <var class="var">p</var> and <var class="var">q</var> are integers; e.g. <em class="math">9/16</em> works, but
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pi (an irrational number) doesn’t. These include integers
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(<em class="math"><var class="var">n</var>/1</em>).
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</p>
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</dd>
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<dt><em class="dfn">real numbers</em></dt>
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<dd><p>The set of numbers that describes all possible positions along a
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one-dimensional line. This includes rationals as well as irrational
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numbers.
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</p>
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</dd>
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<dt><em class="dfn">complex numbers</em></dt>
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<dd><p>The set of numbers that describes all possible positions in a two
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dimensional space. This includes real as well as imaginary numbers
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(<em class="math"><var class="var">a</var>+<var class="var">b</var>i</em>, where <var class="var">a</var> is the <em class="dfn">real part</em>,
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<var class="var">b</var> is the <em class="dfn">imaginary part</em>, and <em class="math">i</em> is the square root of
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−1.)
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</p></dd>
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</dl>
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<p>It is called a tower because each category “sits on” the one that
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follows it, in the sense that every integer is also a rational, every
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rational is also real, and every real number is also a complex number
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(but with zero imaginary part).
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</p>
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<p>In addition to the classification into integers, rationals, reals and
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complex numbers, Scheme also distinguishes between whether a number is
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represented exactly or not. For example, the result of
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<em class="math">2*sin(pi/4)</em> is exactly <em class="math">2^(1/2)</em>, but Guile
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can represent neither <em class="math">pi/4</em> nor <em class="math">2^(1/2)</em> exactly.
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Instead, it stores an inexact approximation, using the C type
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<code class="code">double</code>.
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</p>
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<p>Guile can represent exact rationals of any magnitude, inexact
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rationals that fit into a C <code class="code">double</code>, and inexact complex numbers
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with <code class="code">double</code> real and imaginary parts.
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</p>
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<p>The <code class="code">number?</code> predicate may be applied to any Scheme value to
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discover whether the value is any of the supported numerical types.
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</p>
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<dl class="first-deffn">
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<dt class="deffn" id="index-number_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">number?</strong> <var class="def-var-arguments">obj</var><a class="copiable-link" href="#index-number_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-scm_005fnumber_005fp"><span class="category-def">C Function: </span><span><strong class="def-name">scm_number_p</strong> <var class="def-var-arguments">(obj)</var><a class="copiable-link" href="#index-scm_005fnumber_005fp"> ¶</a></span></dt>
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<dd><p>Return <code class="code">#t</code> if <var class="var">obj</var> is any kind of number, else <code class="code">#f</code>.
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</p></dd></dl>
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<p>For example:
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</p>
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<div class="example lisp">
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<pre class="lisp-preformatted">(number? 3)
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⇒ #t
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(number? "hello there!")
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⇒ #f
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(define pi 3.141592654)
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(number? pi)
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⇒ #t
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</pre></div>
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<dl class="first-deftypefn">
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<dt class="deftypefn" id="index-scm_005fis_005fnumber"><span class="category-def">C Function: </span><span><code class="def-type">int</code> <strong class="def-name">scm_is_number</strong> <code class="def-code-arguments">(SCM obj)</code><a class="copiable-link" href="#index-scm_005fis_005fnumber"> ¶</a></span></dt>
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<dd><p>This is equivalent to <code class="code">scm_is_true (scm_number_p (obj))</code>.
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</p></dd></dl>
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<p>The next few subsections document each of Guile’s numerical data types
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in detail.
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</p>
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</div>
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<hr>
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<div class="nav-panel">
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<p>
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Next: <a href="Integers.html">Integers</a>, Up: <a href="Numbers.html">Numerical data types</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Concept-Index.html" title="Index" rel="index">Index</a>]</p>
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</div>
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</body>
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</html>
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