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diff --git a/doc/groff.html.node/Numeric-Expressions.html b/doc/groff.html.node/Numeric-Expressions.html new file mode 100644 index 0000000..7da6bd3 --- /dev/null +++ b/doc/groff.html.node/Numeric-Expressions.html @@ -0,0 +1,395 @@ +<!DOCTYPE html> +<html> +<!-- Created by GNU Texinfo 7.0.3, https://www.gnu.org/software/texinfo/ --> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> +<!-- This manual documents GNU troff version 1.23.0. + +Copyright © 1994-2023 Free Software Foundation, Inc. + +Permission is granted to copy, distribute and/or modify this document +under the terms of the GNU Free Documentation License, Version 1.3 or +any later version published by the Free Software Foundation; with no +Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A +copy of the license is included in the section entitled "GNU Free +Documentation License". --> +<title>Numeric Expressions (The GNU Troff Manual)</title> + +<meta name="description" content="Numeric Expressions (The GNU Troff Manual)"> +<meta name="keywords" content="Numeric Expressions (The GNU Troff Manual)"> +<meta name="resource-type" content="document"> +<meta name="distribution" content="global"> +<meta name="Generator" content="makeinfo"> +<meta name="viewport" content="width=device-width,initial-scale=1"> + +<link href="index.html" rel="start" title="Top"> +<link href="Request-Index.html" rel="index" title="Request Index"> +<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents"> +<link href="GNU-troff-Reference.html" rel="up" title="GNU troff Reference"> +<link href="Identifiers.html" rel="next" title="Identifiers"> +<link href="Measurements.html" rel="prev" title="Measurements"> +<style type="text/css"> +<!-- +a.copiable-link {visibility: hidden; text-decoration: none; line-height: 0em} +div.example {margin-left: 3.2em} +span.r {font-family: initial; font-weight: normal; font-style: normal} +span:hover a.copiable-link {visibility: visible} +strong.def-name {font-family: monospace; font-weight: bold; font-size: larger} +--> +</style> + + +</head> + +<body lang="en"> +<div class="section-level-extent" id="Numeric-Expressions"> +<div class="nav-panel"> +<p> +Next: <a href="Identifiers.html" accesskey="n" rel="next">Identifiers</a>, Previous: <a href="Measurements.html" accesskey="p" rel="prev">Measurements</a>, Up: <a href="GNU-troff-Reference.html" accesskey="u" rel="up">GNU <code class="code">troff</code> Reference</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Request-Index.html" title="Index" rel="index">Index</a>]</p> +</div> +<hr> +<h3 class="section" id="Numeric-Expressions-1">5.4 Numeric Expressions</h3> +<a class="index-entry-id" id="index-numeric-expressions"></a> +<a class="index-entry-id" id="index-expressions_002c-numeric"></a> + +<p>A <em class="dfn">numeric expression</em> evaluates to an integer: it can be as +simple as a literal ‘<samp class="samp">0</samp>’ or it can be a complex sequence of register +and string interpolations interleaved with measurements and operators. +</p> +<p>GNU <code class="code">troff</code> provides a set of mathematical and logical operators +familiar to programmers—as well as some unusual ones—but supports +only integer arithmetic.<a class="footnote" id="DOCF35" href="groff.html_fot.html#FOOT35"><sup>35</sup></a> The internal data type +used for computing results is usually a 32-bit signed integer, which +suffices to represent magnitudes within a range of ±2 +billion.<a class="footnote" id="DOCF36" href="groff.html_fot.html#FOOT36"><sup>36</sup></a> +</p> +<a class="index-entry-id" id="index-arithmetic-operators"></a> +<a class="index-entry-id" id="index-operators_002c-arithmetic"></a> +<a class="index-entry-id" id="index-truncating-division"></a> +<a class="index-entry-id" id="index-addition"></a> +<a class="index-entry-id" id="index-subtraction"></a> +<a class="index-entry-id" id="index-multiplication"></a> +<a class="index-entry-id" id="index-division_002c-truncating"></a> +<a class="index-entry-id" id="index-modulus"></a> +<a class="index-entry-id" id="index-_002b"></a> +<a class="index-entry-id" id="index-_002d"></a> +<a class="index-entry-id" id="index-_002a"></a> +<a class="index-entry-id" id="index-_002f"></a> +<a class="index-entry-id" id="index-_0025"></a> +<p>Arithmetic infix operators perform a function on the numeric expressions +to their left and right; they are <code class="code">+</code> (addition), <code class="code">-</code> +(subtraction), <code class="code">*</code> (multiplication), <code class="code">/</code> (truncating +division), and <code class="code">%</code> (modulus). <em class="dfn">Truncating division</em> rounds to +the integer nearer to zero, no matter how large the fractional portion. +Overflow and division (or modulus) by zero are errors and abort +evaluation of a numeric expression. +<a class="index-entry-id" id="index-unary-arithmetic-operators"></a> +<a class="index-entry-id" id="index-operators_002c-unary-arithmetic"></a> +<a class="index-entry-id" id="index-negation"></a> +<a class="index-entry-id" id="index-assertion-_0028arithmetic-operator_0029"></a> +<a class="index-entry-id" id="index-_002d-1"></a> +<a class="index-entry-id" id="index-_002b-1"></a> +<a class="index-entry-id" id="index-if-request_002c-and-the-_0021-operator"></a> +<a class="index-entry-id" id="index-while-request_002c-and-the-_0021-operator"></a> +</p> +<p>Arithmetic unary operators operate on the numeric expression to their +right; they are <code class="code">-</code> (negation) and <code class="code">+</code> (assertion—for +completeness; it does nothing). The unary minus must often be used +with parentheses to avoid confusion with the decrementation operator, +discussed below. +</p> +<p>Observe the rounding behavior and effect of negative operands on the +modulus and truncating division operators. +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">.nr T 199/100 +.nr U 5/2 +.nr V (-5)/2 +.nr W 5/-2 +.nr X 5%2 +.nr Y (-5)%2 +.nr Z 5%-2 +T=\n[T] U=\n[U] V=\n[V] W=\n[W] X=\n[X] Y=\n[Y] Z=\n[Z] + ⇒ T=1 U=2 V=-2 W=-2 X=1 Y=-1 Z=1 +</pre></div></div> + +<p>The sign of the modulus of operands of mixed signs is determined by the +sign of the first. Division and modulus operators satisfy the following +property: given a dividend <var class="var">a</var> and a divisor <var class="var">b</var>, a +quotient <var class="var">q</var> formed by ‘<samp class="samp">(a / b)</samp>’ and a +remainder <var class="var">r</var> by ‘<samp class="samp">(a % b)</samp>’, then <em class="math">qb + r = a</em>. +</p> +<a class="index-entry-id" id="index-scaling-operator"></a> +<a class="index-entry-id" id="index-operator_002c-scaling"></a> +<a class="index-entry-id" id="index-_003b"></a> +<p>GNU <code class="code">troff</code>’s scaling operator, used with parentheses as +<code class="code">(<var class="var">c</var>;<var class="var">e</var>)</code>, evaluates a numeric expression <var class="var">e</var> +using <var class="var">c</var> as the default scaling unit. If <var class="var">c</var> is omitted, +scaling units are ignored in the evaluation of <var class="var">e</var>. This +operator can save typing by avoiding the attachment of scaling units to +every operand out of caution. Your macros can select a sensible default +unit in case the user neglects to supply one. +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">.\" Indent by amount given in first argument; assume ens. +.de Indent +. in (n;\\$1) +.. +</pre></div></div> + +<p>Without the scaling operator, the foregoing macro would, if called with +a unitless argument, cause indentation by the <code class="code">in</code> request’s +default scaling unit (ems). The result would be twice as much +indentation as expected. +</p> +<a class="index-entry-id" id="index-extremum-operators-_0028_003e_003f_002c-_003c_003f_0029"></a> +<a class="index-entry-id" id="index-operators_002c-extremum-_0028_003e_003f_002c-_003c_003f_0029"></a> +<a class="index-entry-id" id="index-maximum-operator"></a> +<a class="index-entry-id" id="index-minimum-operator"></a> +<a class="index-entry-id" id="index-_003e_003f"></a> +<a class="index-entry-id" id="index-_003c_003f"></a> +<p>GNU <code class="code">troff</code> also provides a pair of operators to compute the +extrema of two operands: <code class="code">>?</code> (maximum) and <code class="code"><?</code> (minimum). +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">.nr slots 5 +.nr candidates 3 +.nr salaries (\n[slots] <? \n[candidates]) +Looks like we'll end up paying \n[salaries] salaries. + ⇒ Looks like we'll end up paying 3 salaries. +</pre></div></div> + +<a class="index-entry-id" id="index-comparison-operators"></a> +<a class="index-entry-id" id="index-operators_002c-comparison"></a> +<a class="index-entry-id" id="index-greater-than-_0028or-equal-to_0029-operator"></a> +<a class="index-entry-id" id="index-less-than-_0028or-equal-to_0029-operator"></a> +<a class="index-entry-id" id="index-equality-operator"></a> +<a class="index-entry-id" id="index-_003c"></a> +<a class="index-entry-id" id="index-_003e"></a> +<a class="index-entry-id" id="index-_003e_003d"></a> +<a class="index-entry-id" id="index-_003c_003d"></a> +<a class="index-entry-id" id="index-_003d"></a> +<a class="index-entry-id" id="index-_003d_003d"></a> +<p>Comparison operators comprise <code class="code"><</code> (less than), <code class="code">></code> (greater +than), <code class="code"><=</code> (less than or equal), <code class="code">>=</code> (greater than or +equal), and <code class="code">=</code> (equal). <code class="code">==</code> is a synonym for <code class="code">=</code>. +When evaluated, a comparison is replaced with ‘<samp class="samp">0</samp>’ if it is false +and ‘<samp class="samp">1</samp>’ if true. In the <code class="code">roff</code> language, positive values are +true, others false. +</p> +<a class="index-entry-id" id="index-logical-operators"></a> +<a class="index-entry-id" id="index-operators_002c-logical"></a> +<a class="index-entry-id" id="index-logical-_0060_0060and_0027_0027-operator"></a> +<a class="index-entry-id" id="index-logical-conjunction-operator"></a> +<a class="index-entry-id" id="index-logical-_0060_0060or_0027_0027-operator"></a> +<a class="index-entry-id" id="index-logical-disjunction-operator"></a> +<a class="index-entry-id" id="index-_0026"></a> +<a class="index-entry-id" id="index-_003a"></a> +<p>We can operate on truth values with the logical operators <code class="code">&</code> +(logical conjunction or “and”) and <code class="code">:</code> (logical disjunction or +“or”). They evaluate as comparison operators do. +</p> +<a class="index-entry-id" id="index-_0021"></a> +<a class="index-entry-id" id="index-complementation_002c-logical"></a> +<a class="index-entry-id" id="index-logical-complementation-operator"></a> +<a class="index-entry-id" id="index-logical-not_002c-limitation-in-expression"></a> +<a class="index-entry-id" id="index-expression_002c-limitation-of-logical-not-in"></a> +<p>A logical complementation (“not”) operator, <code class="code">!</code>, works only +within <code class="code">if</code>, <code class="code">ie</code>, and <code class="code">while</code> requests. +Furthermore, <code class="code">!</code> is recognized only at the beginning of a numeric +expression not contained by another numeric expression. In other words, +it must be the “outermost” operator. Including it elsewhere in the +expression produces a warning in the ‘<samp class="samp">number</samp>’ category +(see <a class="pxref" href="Warnings.html">Warnings</a>), and its expression evaluates false. This +unfortunate limitation maintains compatibility with <abbr class="acronym">AT&T</abbr> +<code class="code">troff</code>. Test a numeric expression for falsity by +comparing it to a false value.<a class="footnote" id="DOCF37" href="groff.html_fot.html#FOOT37"><sup>37</sup></a> +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">.nr X 1 +.nr Y 0 +.\" This does not work as expected. +.if (\n[X])&(!\n[Y]) .nop A: X is true, Y is false +. +.\" Use this construct instead. +.if (\n[X])&(\n[Y]<=0) .nop B: X is true, Y is false + error→ warning: expected numeric expression, got '!' + ⇒ B: X is true, Y is false +</pre></div></div> + +<a class="index-entry-id" id="index-parentheses"></a> +<a class="index-entry-id" id="index-order-of-evaluation-in-expressions"></a> +<a class="index-entry-id" id="index-expression_002c-order-of-evaluation"></a> +<a class="index-entry-id" id="index-_0028"></a> +<a class="index-entry-id" id="index-_0029"></a> +<p>The <code class="code">roff</code> language has no operator precedence: expressions are +evaluated strictly from left to right, in contrast to schoolhouse +arithmetic. Use parentheses <code class="code">(</code> <code class="code">)</code> to impose a desired +precedence upon subexpressions. +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">.nr X 3+5*4 +.nr Y (3+5)*4 +.nr Z 3+(5*4) +X=\n[X] Y=\n[Y] Z=\n[Z] + ⇒ X=32 Y=32 Z=23 +</pre></div></div> + +<a class="index-entry-id" id="index-_002b_002c-and-page-motion"></a> +<a class="index-entry-id" id="index-_002d_002c-and-page-motion"></a> +<a class="index-entry-id" id="index-motion-operators"></a> +<a class="index-entry-id" id="index-operators_002c-motion"></a> +<a class="index-entry-id" id="index-_002b-_0028unary_0029"></a> +<a class="index-entry-id" id="index-_002d-_0028unary_0029"></a> +<p>For many requests and escape sequences that cause motion on the page, +the unary operators <code class="code">+</code> and <code class="code">-</code> work differently when leading +a numeric expression. They then indicate a motion relative to the +drawing position: positive is down in vertical contexts, right in +horizontal ones. +</p> +<a class="index-entry-id" id="index-bp-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-in-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-ll-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-lt-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-nm-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-nr-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-pl-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-pn-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-po-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-ps-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-pvs-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-rt-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-ti-request_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-_005cH_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-_005cR_002c-using-_002b-and-_002d-with"></a> +<a class="index-entry-id" id="index-_005cs_002c-using-_002b-and-_002d-with"></a> +<p><code class="code">+</code> and <code class="code">-</code> are also treated differently by the following +requests and escape sequences: <code class="code">bp</code>, <code class="code">in</code>, <code class="code">ll</code>, +<code class="code">lt</code>, <code class="code">nm</code>, <code class="code">nr</code>, <code class="code">pl</code>, <code class="code">pn</code>, <code class="code">po</code>, +<code class="code">ps</code>, <code class="code">pvs</code>, <code class="code">rt</code>, <code class="code">ti</code>, <code class="code">\H</code>, <code class="code">\R</code>, and +<code class="code">\s</code>. Here, leading plus and minus signs serve as incrementation +and decrementation operators, respectively. To negate an expression, +subtract it from zero or include the unary minus in parentheses with its +argument. See <a class="xref" href="Setting-Registers.html">Setting Registers</a>, for examples. +</p> +<a class="index-entry-id" id="index-_007c"></a> +<a class="index-entry-id" id="index-_007c_002c-and-page-motion"></a> +<a class="index-entry-id" id="index-absolute-_0028sic_0029-position-operator-_0028_007c_0029"></a> +<a class="index-entry-id" id="index-position_002c-absolute-_0028sic_0029-operator-_0028_007c_0029"></a> +<a class="index-entry-id" id="index-boundary_002drelative-motion-operator-_0028_007c_0029"></a> +<p>A leading <code class="code">|</code> operator indicates a motion relative not to the +drawing position but to a boundary. For horizontal motions, the +measurement specifies a distance relative to a drawing position +corresponding to the beginning of the <em class="emph">input</em> line. By default, +tab stops reckon movements in this way. Most escape sequences do not; +<code class="code">|</code> tells them to do so. +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">Mind the \h'1.2i'gap. +.br +Mind the \h'|1.2i'gap. +.br +Mind the +\h'|1.2i'gap. + ⇒ Mind the gap. + ⇒ Mind the gap. + ⇒ Mind the gap. +</pre></div></div> + +<p>One use of this feature is to define macros whose scope is limited to +the output they format. +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">.\" underline word $1 with trailing punctuation $2 +.de Underline +. nop \\$1\l'|0\[ul]'\\$2 +.. +Typographical emphasis is best used +.Underline sparingly . +</pre></div></div> + +<p>In the above example, ‘<samp class="samp">|0</samp>’ specifies a negative motion from the +current position (at the end of the argument just emitted, <code class="code">\$1</code>) +to the beginning of the input line. Thus, the <code class="code">\l</code> escape sequence +in this case draws a line from right to left. A macro call occurs at +the beginning of an input line;<a class="footnote" id="DOCF38" href="groff.html_fot.html#FOOT38"><sup>38</sup></a> if the <code class="code">|</code> +operator were omitted, then the underline would be drawn at zero +distance from the current position, producing device-dependent, and +likely undesirable, results. On the ‘<samp class="samp">ps</samp>’ output device, it +underlines the period. +</p> +<p>For vertical motions, the <code class="code">|</code> operator specifies a distance from +the first text baseline on the page or in the current +diversion,<a class="footnote" id="DOCF39" href="groff.html_fot.html#FOOT39"><sup>39</sup></a> using the current vertical +spacing. +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">A +.br +B \Z'C'\v'|0'D + ⇒ A D + ⇒ B C +</pre></div></div> + +<p>In the foregoing example, we’ve used the <code class="code">\Z</code> escape sequence +(see <a class="pxref" href="Page-Motions.html">Page Motions</a>) to restore the drawing position after formatting +‘<samp class="samp">C</samp>’, then moved vertically to the first text baseline on the page. +</p> +<dl class="first-deffn"> +<dt class="deffn" id="index-_005cB_0027anything_0027"><span class="category-def">Escape sequence: </span><span><strong class="def-name"><code class="t">\B<code class="code">'</code></code><span class="r"><i class="slanted">anything</i></span><code class="t"><code class="code">'</code></code></strong><a class="copiable-link" href='#index-_005cB_0027anything_0027'> ¶</a></span></dt> +<dd><a class="index-entry-id" id="index-_005cB"></a> +<a class="index-entry-id" id="index-numeric-expression_002c-valid"></a> +<a class="index-entry-id" id="index-valid-numeric-expression"></a> +<p>Interpolate 1 if <var class="var">anything</var> is a valid numeric expression, +and 0 otherwise. The delimiter need not be a neutral apostrophe; +see <a class="ref" href="Delimiters.html">Delimiters</a>. +</p></dd></dl> + +<p>You might use <code class="code">\B</code> along with the <code class="code">if</code> request to filter out +invalid macro or string arguments. See <a class="xref" href="Conditionals-and-Loops.html">Conditionals and Loops</a>. +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">.\" Indent by amount given in first argument; assume ens. +.de Indent +. if \B'\\$1' .in (n;\\$1) +.. +</pre></div></div> + +<p>A register interpolated as an operand in a numeric expression must have +an Arabic format; luckily, this is the default. See <a class="xref" href="Assigning-Register-Formats.html">Assigning Register Formats</a>. +</p> +<a class="index-entry-id" id="index-space-characters_002c-in-expressions"></a> +<a class="index-entry-id" id="index-expressions_002c-and-space-characters"></a> +<p>Because spaces separate arguments to requests, spaces are not allowed in +numeric expressions unless the (sub)expression containing them is +surrounded by parentheses. See <a class="xref" href="Invoking-Requests.html">Invoking Requests</a>, and +<a class="ref" href="Conditionals-and-Loops.html">Conditionals and Loops</a>. +</p> +<div class="example"> +<div class="group"><pre class="example-preformatted">.nf +.nr a 1+2 + 2+1 +\na + error→ expected numeric expression, got a space + ⇒ 3 +.nr a 1+(2 + 2)+1 +\na + ⇒ 6 +</pre></div></div> + +<p>The <code class="code">nr</code> request (see <a class="pxref" href="Setting-Registers.html">Setting Registers</a>) expects its second and +optional third arguments to be numeric expressions; a bare <code class="code">+</code> does +not qualify, so our first attempt got a warning. +</p> + + +</div> +<hr> +<div class="nav-panel"> +<p> +Next: <a href="Identifiers.html">Identifiers</a>, Previous: <a href="Measurements.html">Measurements</a>, Up: <a href="GNU-troff-Reference.html">GNU <code class="code">troff</code> Reference</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Request-Index.html" title="Index" rel="index">Index</a>]</p> +</div> + + + +</body> +</html> |