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271 lines
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<div class="subsubsection-level-extent" id="rnrs-arithmetic-fixnums">
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Next: <a href="rnrs-arithmetic-flonums.html" accesskey="n" rel="next">rnrs arithmetic flonums</a>, Previous: <a href="rnrs-programs.html" accesskey="p" rel="prev">rnrs programs</a>, Up: <a href="R6RS-Standard-Libraries.html" accesskey="u" rel="up">R6RS Standard Libraries</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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<h4 class="subsubsection" id="rnrs-arithmetic-fixnums-1"><span>7.6.2.21 rnrs arithmetic fixnums<a class="copiable-link" href="#rnrs-arithmetic-fixnums-1"> ¶</a></span></h4>
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<p>The <code class="code">(rnrs arithmetic fixnums (6))</code> library provides procedures for
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performing arithmetic operations on an implementation-dependent range of
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exact integer values, which R6RS refers to as <em class="dfn">fixnums</em>. In Guile,
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the size of a fixnum is determined by the size of the <code class="code">SCM</code> type; a
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single SCM struct is guaranteed to be able to hold an entire fixnum,
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making fixnum computations particularly
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efficient—(see <a class="pxref" href="The-SCM-Type.html">The SCM Type</a>). On 32-bit systems, the most
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negative and most positive fixnum values are, respectively, -536870912
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and 536870911.
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</p>
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<p>Unless otherwise specified, all of the procedures below take fixnums as
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arguments, and will raise an <code class="code">&assertion</code> condition if passed a
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non-fixnum argument or an <code class="code">&implementation-restriction</code> condition
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if their result is not itself a fixnum.
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</p>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fixnum_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fixnum?</strong> <var class="def-var-arguments">obj</var><a class="copiable-link" href="#index-fixnum_003f"> ¶</a></span></dt>
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<dd><p>Returns <code class="code">#t</code> if <var class="var">obj</var> is a fixnum, <code class="code">#f</code> otherwise.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fixnum_002dwidth"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fixnum-width</strong><a class="copiable-link" href="#index-fixnum_002dwidth"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-least_002dfixnum"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">least-fixnum</strong><a class="copiable-link" href="#index-least_002dfixnum"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-greatest_002dfixnum"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">greatest-fixnum</strong><a class="copiable-link" href="#index-greatest_002dfixnum"> ¶</a></span></dt>
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<dd><p>These procedures return, respectively, the maximum number of bits
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necessary to represent a fixnum value in Guile, the minimum fixnum
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value, and the maximum fixnum value.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fx_003d_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx=?</strong> <var class="def-var-arguments">fx1 fx2 fx3 ...</var><a class="copiable-link" href="#index-fx_003d_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fx_003e_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx>?</strong> <var class="def-var-arguments">fx1 fx2 fx3 ...</var><a class="copiable-link" href="#index-fx_003e_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fx_003c_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx<?</strong> <var class="def-var-arguments">fx1 fx2 fx3 ...</var><a class="copiable-link" href="#index-fx_003c_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fx_003e_003d_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx>=?</strong> <var class="def-var-arguments">fx1 fx2 fx3 ...</var><a class="copiable-link" href="#index-fx_003e_003d_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fx_003c_003d_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx<=?</strong> <var class="def-var-arguments">fx1 fx2 fx3 ...</var><a class="copiable-link" href="#index-fx_003c_003d_003f"> ¶</a></span></dt>
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<dd><p>These procedures return <code class="code">#t</code> if their fixnum arguments are
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(respectively): equal, monotonically increasing, monotonically
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decreasing, monotonically nondecreasing, or monotonically nonincreasing;
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<code class="code">#f</code> otherwise.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxzero_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxzero?</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fxzero_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxpositive_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxpositive?</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fxpositive_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxnegative_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxnegative?</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fxnegative_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxodd_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxodd?</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fxodd_003f"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxeven_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxeven?</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fxeven_003f"> ¶</a></span></dt>
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<dd><p>These numerical predicates return <code class="code">#t</code> if <var class="var">fx</var> is,
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respectively, zero, greater than zero, less than zero, odd, or even;
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<code class="code">#f</code> otherwise.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxmax"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxmax</strong> <var class="def-var-arguments">fx1 fx2 ...</var><a class="copiable-link" href="#index-fxmax"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxmin"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxmin</strong> <var class="def-var-arguments">fx1 fx2 ...</var><a class="copiable-link" href="#index-fxmin"> ¶</a></span></dt>
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<dd><p>These procedures return the maximum or minimum of their arguments.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fx_002b"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx+</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fx_002b"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fx_002a"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx*</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fx_002a"> ¶</a></span></dt>
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<dd><p>These procedures return the sum or product of their arguments.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fx_002d"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx-</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fx_002d"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fx_002d-1"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx-</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fx_002d-1"> ¶</a></span></dt>
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<dd><p>Returns the difference of <var class="var">fx1</var> and <var class="var">fx2</var>, or the negation of
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<var class="var">fx</var>, if called with a single argument.
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</p>
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<p>An <code class="code">&assertion</code> condition is raised if the result is not itself a
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fixnum.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxdiv_002dand_002dmod"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxdiv-and-mod</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxdiv_002dand_002dmod"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxdiv"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxdiv</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxdiv"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxmod"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxmod</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxmod"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxdiv0_002dand_002dmod0"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxdiv0-and-mod0</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxdiv0_002dand_002dmod0"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxdiv0"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxdiv0</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxdiv0"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxmod0"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxmod0</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxmod0"> ¶</a></span></dt>
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<dd><p>These procedures implement number-theoretic division on fixnums;
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See <a data-manual="rnrs base" href="../rnrs%20base_html/index.html">(rnrs base)</a>, for a description of their semantics.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fx_002b_002fcarry"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx+/carry</strong> <var class="def-var-arguments">fx1 fx2 fx3</var><a class="copiable-link" href="#index-fx_002b_002fcarry"> ¶</a></span></dt>
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<dd><p>Returns the two fixnum results of the following computation:
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</p><div class="example lisp">
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<pre class="lisp-preformatted">(let* ((s (+ fx1 fx2 fx3))
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(s0 (mod0 s (expt 2 (fixnum-width))))
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(s1 (div0 s (expt 2 (fixnum-width)))))
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(values s0 s1))
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</pre></div>
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</dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fx_002d_002fcarry"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx-/carry</strong> <var class="def-var-arguments">fx1 fx2 fx3</var><a class="copiable-link" href="#index-fx_002d_002fcarry"> ¶</a></span></dt>
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<dd><p>Returns the two fixnum results of the following computation:
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</p><div class="example lisp">
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<pre class="lisp-preformatted">(let* ((d (- fx1 fx2 fx3))
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(d0 (mod0 d (expt 2 (fixnum-width))))
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(d1 (div0 d (expt 2 (fixnum-width)))))
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(values d0 d1))
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</pre></div>
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</dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fx_002a_002fcarry"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fx*/carry</strong> <var class="def-var-arguments">fx1 fx2 fx3</var><a class="copiable-link" href="#index-fx_002a_002fcarry"> ¶</a></span></dt>
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<dd><div class="example lisp">
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<pre class="lisp-preformatted">Returns the two fixnum results of the following computation:
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(let* ((s (+ (* fx1 fx2) fx3))
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(s0 (mod0 s (expt 2 (fixnum-width))))
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(s1 (div0 s (expt 2 (fixnum-width)))))
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(values s0 s1))
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</pre></div>
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</dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxnot"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxnot</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fxnot"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxand"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxand</strong> <var class="def-var-arguments">fx1 ...</var><a class="copiable-link" href="#index-fxand"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxior"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxior</strong> <var class="def-var-arguments">fx1 ...</var><a class="copiable-link" href="#index-fxior"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxxor"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxxor</strong> <var class="def-var-arguments">fx1 ...</var><a class="copiable-link" href="#index-fxxor"> ¶</a></span></dt>
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<dd><p>These procedures are identical to the <code class="code">lognot</code>, <code class="code">logand</code>,
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<code class="code">logior</code>, and <code class="code">logxor</code> procedures provided by Guile’s core
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library. See <a class="xref" href="Bitwise-Operations.html">Bitwise Operations</a>, for documentation.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxif"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxif</strong> <var class="def-var-arguments">fx1 fx2 fx3</var><a class="copiable-link" href="#index-fxif"> ¶</a></span></dt>
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<dd><p>Returns the bitwise “if” of its fixnum arguments. The bit at position
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<code class="code">i</code> in the return value will be the <code class="code">i</code>th bit from <var class="var">fx2</var>
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if the <code class="code">i</code>th bit of <var class="var">fx1</var> is 1, the <code class="code">i</code>th bit from
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<var class="var">fx3</var>.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxbit_002dcount"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxbit-count</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fxbit_002dcount"> ¶</a></span></dt>
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<dd><p>Returns the number of 1 bits in the two’s complement representation of
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<var class="var">fx</var>.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxlength"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxlength</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fxlength"> ¶</a></span></dt>
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<dd><p>Returns the number of bits necessary to represent <var class="var">fx</var>.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxfirst_002dbit_002dset"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxfirst-bit-set</strong> <var class="def-var-arguments">fx</var><a class="copiable-link" href="#index-fxfirst_002dbit_002dset"> ¶</a></span></dt>
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<dd><p>Returns the index of the least significant 1 bit in the two’s complement
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representation of <var class="var">fx</var>.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxbit_002dset_003f"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxbit-set?</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxbit_002dset_003f"> ¶</a></span></dt>
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<dd><p>Returns <code class="code">#t</code> if the <var class="var">fx2</var>th bit in the two’s complement
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representation of <var class="var">fx1</var> is 1, <code class="code">#f</code> otherwise.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxcopy_002dbit"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxcopy-bit</strong> <var class="def-var-arguments">fx1 fx2 fx3</var><a class="copiable-link" href="#index-fxcopy_002dbit"> ¶</a></span></dt>
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<dd><p>Returns the result of setting the <var class="var">fx2</var>th bit of <var class="var">fx1</var> to the
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<var class="var">fx2</var>th bit of <var class="var">fx3</var>.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxbit_002dfield"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxbit-field</strong> <var class="def-var-arguments">fx1 fx2 fx3</var><a class="copiable-link" href="#index-fxbit_002dfield"> ¶</a></span></dt>
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<dd><p>Returns the integer representation of the contiguous sequence of bits in
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<var class="var">fx1</var> that starts at position <var class="var">fx2</var> (inclusive) and ends at
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position <var class="var">fx3</var> (exclusive).
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxcopy_002dbit_002dfield"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxcopy-bit-field</strong> <var class="def-var-arguments">fx1 fx2 fx3 fx4</var><a class="copiable-link" href="#index-fxcopy_002dbit_002dfield"> ¶</a></span></dt>
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<dd><p>Returns the result of replacing the bit field in <var class="var">fx1</var> with start
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and end positions <var class="var">fx2</var> and <var class="var">fx3</var> with the corresponding bit
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field from <var class="var">fx4</var>.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxarithmetic_002dshift"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxarithmetic-shift</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxarithmetic_002dshift"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxarithmetic_002dshift_002dleft"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxarithmetic-shift-left</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxarithmetic_002dshift_002dleft"> ¶</a></span></dt>
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<dt class="deffnx def-cmd-deffn" id="index-fxarithmetic_002dshift_002dright"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxarithmetic-shift-right</strong> <var class="def-var-arguments">fx1 fx2</var><a class="copiable-link" href="#index-fxarithmetic_002dshift_002dright"> ¶</a></span></dt>
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<dd><p>Returns the result of shifting the bits of <var class="var">fx1</var> right or left by
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the <var class="var">fx2</var> positions. <code class="code">fxarithmetic-shift</code> is identical
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to <code class="code">fxarithmetic-shift-left</code>.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxrotate_002dbit_002dfield"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxrotate-bit-field</strong> <var class="def-var-arguments">fx1 fx2 fx3 fx4</var><a class="copiable-link" href="#index-fxrotate_002dbit_002dfield"> ¶</a></span></dt>
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<dd><p>Returns the result of cyclically permuting the bit field in <var class="var">fx1</var>
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with start and end positions <var class="var">fx2</var> and <var class="var">fx3</var> by <var class="var">fx4</var> bits
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in the direction of more significant bits.
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</p></dd></dl>
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<dl class="first-deffn">
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<dt class="deffn" id="index-fxreverse_002dbit_002dfield"><span class="category-def">Scheme Procedure: </span><span><strong class="def-name">fxreverse-bit-field</strong> <var class="def-var-arguments">fx1 fx2 fx3</var><a class="copiable-link" href="#index-fxreverse_002dbit_002dfield"> ¶</a></span></dt>
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<dd><p>Returns the result of reversing the order of the bits of <var class="var">fx1</var>
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between position <var class="var">fx2</var> (inclusive) and position <var class="var">fx3</var>
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(exclusive).
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</p></dd></dl>
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</div>
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