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<html><head>
<title>Rounding and Truncation</title>
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<a href="../../start.htm">Nyquist / XLISP 2.0</a> -
<a href="../../manual/contents.htm">Contents</a> |
<a href="../../tutorials/tutorials.htm">Tutorials</a> |
<a href="../examples.htm">Examples</a> |
<a href="../../reference/reference-index.htm">Reference</a>
<hr>
<h1>Rounding and Truncation</h1>
<hr>
<p>The <a href="round.htm">cl:round</a>,
<a href="truncate.htm">cl:truncate</a>,
<a href="ceiling.htm">cl:ceiling</a> and
<a href="floor.htm">cl:floor</a> functions divide a number by a divisor,
returning a quotient and a remainder:</p>
<p><div class="box">
<p><table cellpadding="0" cellspacing="0"><tbody>
<tr valign="top">
<td align="right"><nobr>(<a href="round.htm">cl:round</a> </nobr></td>
<td><nobr><i>number</i> [<i>divisor</i>])</nobr></td>
<td><nobr> ⇒ </nobr></td>
<td><nobr><i>quotient</i>, <i>remainder</i></nobr></td>
</tr>
<tr valign="top">
<td align="right"><nobr>(<a href="truncate.htm">cl:truncate</a> </nobr></td>
<td><nobr><i>number</i> [<i>divisor</i>])</nobr></td>
<td><nobr> ⇒ </nobr></td>
<td><nobr><i>quotient</i>, <i>remainder</i></nobr></td>
</tr>
<tr valign="top">
<td align="right"><nobr>(<a href="ceiling.htm">cl:ceiling</a> </nobr></td>
<td><nobr><i>number</i> [<i>divisor</i>])</nobr></td>
<td><nobr> ⇒ </nobr></td>
<td><nobr><i>quotient</i>, <i>remainder</i></nobr></td>
</tr>
<tr valign="top">
<td align="right"><nobr>(<a href="floor.htm">cl:floor</a> </nobr></td>
<td><nobr><i>number</i> [<i>divisor</i>])</nobr></td>
<td><nobr> ⇒ </nobr></td>
<td><nobr><i>quotient</i>, <i>remainder</i></nobr></td>
</tr>
</tbody></table></p>
<p><nobr>
<i>quotient</i> * <i>divisor</i> + <i>remainder</i> = <i>number</i></nobr></p>
</div></p>
<p>The 'quotient' always represents a mathematical integer. <nobr>The
'remainder'</nobr> is an integer if both 'number' and 'divisor' arguments
are integers, and a <nobr>floating-point</nobr> number if either the
'number' or the 'divisor' or both are <nobr>floating-point</nobr>
numbers.</p>
<p>With Nyquist/XLISP, the 'quotient' is always directly returned by the
function, while a list:</p>
<pre class="example">
(<font color="#0000CC">quotient remainder</font>)
</pre>
<p>is stored in the Nyquist/XLISP
<a href="../../reference/global-rslt.htm">*rslt*</a> variable and the
<a href="global-multiple-values.htm">cl:*multiple-values*</a> is set to
<a href="../../reference/t.htm"> T </a> to signal that
<a href="multiple-values.htm">Multiple Values</a> are returned.</p>
Examples:
<pre class="example">
(cl:round 3.5) => 4 <font color="#008844">; *rslt* = ( 4 -0.5)</font>
(cl:truncate 3.5) => 3 <font color="#008844">; *rslt* = ( 3 0.5)</font>
(cl:ceiling 3.5) => 4 <font color="#008844">; *rslt* = ( 4 -0.5)</font>
(cl:floor 3.5) => 3 <font color="#008844">; *rslt* = ( 3 0.5)</font>
(cl:round -3.5) => -4 <font color="#008844">; *rslt* = (-4 0.5)</font>
(cl:truncate -3.5) => -3 <font color="#008844">; *rslt* = (-3 -0.5)</font>
(cl:ceiling -3.5) => -3 <font color="#008844">; *rslt* = (-3 -0.5)</font>
(cl:floor -3.5) => -4 <font color="#008844">; *rslt* = (-4 0.5)</font>
</pre>
<p>Force an integer division:</p>
<pre class="example">
(cl:truncate 3.0 2.0) => 1 <font color="#008844">; Common Lisp</font>
(/ (truncate 3.0) (truncate 2.0)) => 1 <font color="#008844">; Nyquist/XLISP</font>
(/ 3 2) => 1 <font color="#008844">; integer division</font>
</pre>
<p><div class="box">
<p><b>Implementation Notes</b></p>
<pre class="example">
(defun <font color="#0000CC">name</font> (number &optional (divisor (if (<font color="#AA0000">integerp</font> number) 1 1.0)))
... )
</pre>
<p>The <a href="../../reference/integerp.htm">integerp</a> test in the
parameter list signals an error if the 'number' argument is not a number,
also the <nobr><a href="../../reference/division.htm"> / </a>
[division]</nobr> function signals errors if the 'divisor' argument is zero
or not a number, so we do not explicitely need to test the arguments.</p>
<p>The <nobr><a href="ceiling.htm">cl:ceiling</a></nobr> and
<nobr><a href="floor.htm">cl:floor</a></nobr> functions test if 'number' is
an integer multiple of 'divisor' by comparing the results of an integer
division and a <nobr>floating-point</nobr> division:</p>
<pre class="example">
(let ((<font color="#AA0000">i-quotient</font> (/ (truncate number) (truncate divisor)))
(<font color="#AA0000">f-quotient</font> (/ (float number) divisor)))
(if (= <font color="#AA0000">i-quotient f-quotient</font>)
...
</pre>
<p>I'm not sure if this really catches all cases <nobr>[e.g.
regarding</nobr> floating point precision], but have found no problems so
far.</p>
</div></p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
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