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<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>
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