156 lines
7.3 KiB
HTML
156 lines
7.3 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>Faster Integers (Guile Reference Manual)</title>
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<meta name="description" content="Faster Integers (Guile Reference Manual)">
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<meta name="keywords" content="Faster Integers (Guile Reference Manual)">
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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="Data-Representation.html" rel="up" title="Data Representation">
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<link href="Cheaper-Pairs.html" rel="next" title="Cheaper Pairs">
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<link href="A-Simple-Representation.html" rel="prev" title="A Simple Representation">
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</head>
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<body lang="en">
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<div class="subsection-level-extent" id="Faster-Integers">
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<div class="nav-panel">
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<p>
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Next: <a href="Cheaper-Pairs.html" accesskey="n" rel="next">Cheaper Pairs</a>, Previous: <a href="A-Simple-Representation.html" accesskey="p" rel="prev">A Simple Representation</a>, Up: <a href="Data-Representation.html" accesskey="u" rel="up">Data Representation</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="subsection" id="Faster-Integers-1"><span>9.2.2 Faster Integers<a class="copiable-link" href="#Faster-Integers-1"> ¶</a></span></h4>
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<p>Unfortunately, the above representation has a serious disadvantage. In
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order to return an integer, an expression must allocate a <code class="code">struct
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value</code>, initialize it to represent that integer, and return a pointer to
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it. Furthermore, fetching an integer’s value requires a memory
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reference, which is much slower than a register reference on most
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processors. Since integers are extremely common, this representation is
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too costly, in both time and space. Integers should be very cheap to
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create and manipulate.
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</p>
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<p>One possible solution comes from the observation that, on many
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architectures, heap-allocated data (i.e., what you get when you call
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<code class="code">malloc</code>) must be aligned on an eight-byte boundary. (Whether or
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not the machine actually requires it, we can write our own allocator for
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<code class="code">struct value</code> objects that assures this is true.) In this case,
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the lower three bits of the structure’s address are known to be zero.
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</p>
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<p>This gives us the room we need to provide an improved representation
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for integers. We make the following rules:
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</p><ul class="itemize mark-bullet">
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<li>If the lower three bits of an <code class="code">SCM</code> value are zero, then the SCM
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value is a pointer to a <code class="code">struct value</code>, and everything proceeds as
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before.
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</li><li>Otherwise, the <code class="code">SCM</code> value represents an integer, whose value
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appears in its upper bits.
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</li></ul>
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<p>Here is C code implementing this convention:
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</p><div class="example">
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<pre class="example-preformatted">enum type { pair, string, vector, ... };
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typedef struct value *SCM;
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struct value {
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enum type type;
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union {
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struct { SCM car, cdr; } pair;
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struct { int length; char *elts; } string;
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struct { int length; SCM *elts; } vector;
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...
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} value;
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};
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#define POINTER_P(x) (((int) (x) & 7) == 0)
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#define INTEGER_P(x) (! POINTER_P (x))
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#define GET_INTEGER(x) ((int) (x) >> 3)
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#define MAKE_INTEGER(x) ((SCM) (((x) << 3) | 1))
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</pre></div>
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<p>Notice that <code class="code">integer</code> no longer appears as an element of <code class="code">enum
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type</code>, and the union has lost its <code class="code">integer</code> member. Instead, we
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use the <code class="code">POINTER_P</code> and <code class="code">INTEGER_P</code> macros to make a coarse
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classification of values into integers and non-integers, and do further
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type testing as before.
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</p>
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<p>Here’s how we would answer the questions posed above (again, assume
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<var class="var">x</var> is an <code class="code">SCM</code> value):
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</p><ul class="itemize mark-bullet">
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<li>To test if <var class="var">x</var> is an integer, we can write <code class="code">INTEGER_P (<var class="var">x</var>)</code>.
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</li><li>To find its value, we can write <code class="code">GET_INTEGER (<var class="var">x</var>)</code>.
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</li><li>To test if <var class="var">x</var> is a vector, we can write:
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<div class="example">
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<pre class="example-preformatted"> <code class="code">POINTER_P (<var class="var">x</var>) && <var class="var">x</var>->type == vector</code>
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</pre></div>
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<p>Given the new representation, we must make sure <var class="var">x</var> is truly a
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pointer before we dereference it to determine its complete type.
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</p></li><li>If we know <var class="var">x</var> is a vector, we can write
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<code class="code"><var class="var">x</var>->value.vector.elts[0]</code> to refer to its first element, as
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before.
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</li><li>If we know <var class="var">x</var> is a pair, we can write
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<code class="code"><var class="var">x</var>->value.pair.car</code> to extract its car, just as before.
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</li></ul>
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<p>This representation allows us to operate more efficiently on integers
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than the first. For example, if <var class="var">x</var> and <var class="var">y</var> are known to be
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integers, we can compute their sum as follows:
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</p><div class="example">
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<pre class="example-preformatted">MAKE_INTEGER (GET_INTEGER (<var class="var">x</var>) + GET_INTEGER (<var class="var">y</var>))
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</pre></div>
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<p>Now, integer math requires no allocation or memory references. Most real
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Scheme systems actually implement addition and other operations using an
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even more efficient algorithm, but this essay isn’t about
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bit-twiddling. (Hint: how do you decide when to overflow to a bignum?
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How would you do it in assembly?)
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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="Cheaper-Pairs.html">Cheaper Pairs</a>, Previous: <a href="A-Simple-Representation.html">A Simple Representation</a>, Up: <a href="Data-Representation.html">Data Representation</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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