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<html><head>
<title>Math</title>
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<body>
<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>Math</h1>
<hr>
<ol>
<li><nobr><a href="#number-types">Number Types</a></nobr></li>
<li><nobr><a href="#integer-limits">Integer Limits</a></nobr></li>
<li><nobr><a href="#rounding-and-truncation">Rounding and Truncation</a></nobr></li>
<ul>
<li><nobr><a href="#cl-round">cl:round</a> - round towards the next integer</nobr></li>
<li><nobr><a href="#cl-truncate">cl:truncate</a> - truncate towards zero</nobr></li>
<li><nobr><a href="#cl-ceiling">cl:ceiling</a> - truncate towards positive infinity</nobr></li>
<li><nobr><a href="#cl-floor">cl:floor</a> - truncate towards negative infinity</nobr></li>
</ul>
<li><nobr><li><nobr><a href="#remainder-and-modulus">Remainder and Modulus</a></nobr></li></nobr></li>
<ul>
<li><nobr><a href="#cl-rem">cl:rem</a></nobr></li>
<li><nobr><a href="#cl-mod">cl:mod</a></nobr></li>
</ul>
<li><nobr>Power and Roots</nobr></li>
<ul>
<li><nobr><a href="#cl-exp">cl:exp</a> - compute 'e' to the power of 'x'</nobr></li>
<li><nobr><a href="#cl-expt">cl:expt</a> - compute 'x' to the power of 'y'</nobr></li>
<li><nobr><a href="#cl-log">cl:log</a></nobr></li>
<li><nobr><a href="#cl-sqrt">cl:sqrt</a></nobr></li>
</ul>
</ol>
<hr>
<h2>Number Types</h2>
<hr>
<p>Nyquist/XLISP only knows two types of numers:</p>
<ul>
<li><nobr><b>fixnum</b> - integer numbers</nobr></li>
<li><nobr><b>flonum</b> - floating-point numbers</nobr></li>
</ul>
<p>In Nyquist/XLISP, there are no ratios or complex numbers. Even if the
math functions on this page are modelled after <nobr>Common Lisp</nobr>, no
attempt is made to emulate these numbers.</p>
<a name="integer-limits"></a>
<hr>
<h2>Integer Limits</h2>
<hr>
<pre class="example">
(setq <font color="#AA5500">*most-positive-fixnum*</font> 2147483647)
(setq <font color="#AA5500">*most-negative-fixnum*</font> -2147483648)
</pre>
<p><b>Note:</b> these are the limits for <nobr>32-bit</nobr> machines.</p>
<pre class="example">
(defun <font color="#0000CC">fixnum-bits</font> ()
(dolist (bits '(15 31 63) nil)
(let ((fixnum (round (expt 2.0 bits))))
(and (plusp (1- fixnum))
(minusp fixnum)
(return (1+ bits))))))
</pre>
<pre class="example">
(defun <font color="#0000CC">fixnum-limits</font> ()
(if (dolist (bits '(15 31 63) nil)
(let* ((negative (round (expt 2.0 bits)))
(positive (1- negative)))
(when (and (plusp positive)
(minusp negative))
(setq most-positive-fixnum positive
most-negative-fixnum negative)
(return t))))
most-positive-fixnum
(error <font color="#880000">"fixnum limit not found"</font>)))
</pre>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="print-float"></a>
<hr>
<h2>print-float</h2>
<hr>
<p>The '<nobr>print-float</nobr>' function prints
<nobr>floating-point</nobr> numbers ending in '.0' as
<nobr>floating-point</nobr> numbers and not as integers:</p>
<pre class="example">
(defun <font color="#0000CC">print-float</font> (item)
(if (not (floatp item))
item
(let ((string (format nil <font color="#880000">"~a"</font> item)))
(if (not (string-search <font color="#880000">"."</font> string))
(strcat string <font color="#880000">".0"</font>)
string))))
</pre>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="divide-float"></a>
<hr>
<h2>divide-float</h2>
<hr>
<p>An easy way to force a sequence of integers to be divided as floating
point numbers is to insert the number 1.0 after the first argument in the
list of arguments to the divider function or to explicitely convert the
first argument into a floating point number by using the XLISP <a
href="float.htm">float</a> function:</p>
<pre class="example">
(defun <font color="#0000CC">divide-float</font> (&rest args)
(if (null args)
(error <font color="#880000">"too few arguments"</font>)
(apply #'/ (cons (float (first args)) (rest args)))))
</pre>
<p>See <a href="apply.htm">apply</a>, <a href="cons.htm">cons</a>,
<a href="defun.htm">defun</a>, <a href="error.htm">error</a>,
<a href="first.htm">first</a>, <a href="float.htm">float</a>,
<a href="if.htm">if</a>, <a href="null.htm">null</a>,
<a href="rest.htm">rest</a>,
<a href="lambda-keyword-rest.htm">&rest</a>.</p>
<p>Examples:</p>
<pre class="example">
(divide-float 1) => 1.0
(divide-float 1 2) => 0.5
</pre>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="rounding-and-truncation"></a>
<hr>
<h2>Rounding and Truncation</h2>
<hr>
<p>The <a href="#cl-round">cl:round</a>,
<a href="#cl-truncate">cl:truncate</a>,
<a href="#cl-ceiling">cl:ceiling</a> and
<a href="#cl-floor">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="#cl-round">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="#cl-truncate">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="#cl-ceiling">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="#cl-floor">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="values.htm#cl-global-multiple-values">cl:*multiple-values*</a> is
set to <a href="../reference/t.htm"> T </a> to signal that
<a href="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>
Force integer division:
<pre class="example">
(cl:truncate 3.0 2.0) => 1
(/ (truncate 3.0) (truncate 2.0)) => 1
(/ 3 4) => 1
</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="#cl-ceiling">cl:ceiling</a></nobr> and <nobr><a
href="#cl-floor">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>
<a name="cl-round"></a>
<hr>
<h2>cl:round</h2>
<hr>
<p>The '<nobr>cl:round</nobr>' function truncates towards the next
integer:</p>
<p><div class="box">
<dl>
<dt>(cl:<b>round</b> <i>number </i> [<i>divisor</i>])</dt>
<dd><i>number</i> - an integer or <nobr>floating-point</nobr> number<br>
<i>divisor</i> - an integer or <nobr>floating-point</nobr> number, except zero<br>
<table cellpadding="0" cellspacing="0"><tbody>
<tr>
<td valign="top"><nobr>returns</nobr></td>
<td valign="top"><nobr> - </nobr></td>
<td width="100%">the result of runding the result of <i>number</i> divided by <i>divisor</i></td>
</tr>
<tr>
<td></td>
<td valign="top"><nobr> - </nobr></td>
<td width="100%">the remainder of the round operation</td>
</tr>
</tbody></table></dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:round</font> (number &optional (divisor
(if (integerp number) 1 1.0)
divisor-p))
(let* ((x (/ (float number) divisor))
(quotient (cond ((and (not divisor-p) (integerp number)) number)
((= number divisor) 1)
((plusp x) (truncate (+ x 0.5)))
((= (- x 0.5) (truncate (- x 0.5)))
(if (minusp x)
(1- (truncate x))
(truncate x)))
(t (truncate (- x 0.5))))))
(setq <font color="#AA5500">*rslt*</font> (list quotient (- number (* quotient divisor)))
<font color="#AA5500">cl:*multiple-values*</font> t)
quotient))
</pre>
<p>The '<nobr>cl:round</nobr>' function computes a quotient that has been rounded to the
nearest mathematical integer. <nobr>If the</nobr> mathematical quotient is
exactly halfway between two integers, [that is, it has the form
<nobr>'integer+1/2']</nobr>, then the quotient has been rounded to the even
[divisible <nobr>by two]</nobr> integer. <nobr>See
<a href="#rounding-and-truncation">Rounding and Truncation</a></nobr>
above for more details.</p>
<pre class="example">
(round 3.5) => 4
(round -3.5) => -3
(cl:round 3.5) => 4 <font color="#008844">; *rslt* = ( 4 -0.5)</font>
(cl:round -3.5) => -4 <font color="#008844">; *rslt* = (-4 0.5)</font>
</pre>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="cl-truncate"></a>
<hr>
<h2>cl:truncate</h2>
<hr>
<p>The '<nobr>cl:truncate</nobr>' function truncates towards zero:</p>
<p><div class="box">
<dl>
<dt>(cl:<b>truncate</b> <i>number </i> [<i>divisor</i>])</dt>
<dd><i>number</i> - an integer or <nobr>floating-point</nobr> number<br>
<i>divisor</i> - an integer or <nobr>floating-point</nobr> number, except zero<br>
<table cellpadding="0" cellspacing="0"><tbody>
<tr>
<td valign="top"><nobr>returns</nobr></td>
<td valign="top"><nobr> - </nobr></td>
<td width="100%">the result of truncating the result of <i>number</i> divided by <i>divisor</i></td>
</tr>
<tr>
<td></td>
<td valign="top"><nobr> - </nobr></td>
<td width="100%">the remainder of the truncate operation</td>
</tr>
</tbody></table></dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:truncate</font> (number &optional (divisor (if (integerp number) 1 1.0)))
(let ((quotient (truncate (/ (float number) divisor))))
(setq <font color="#AA5500">*rslt*</font> (list quotient (- number (* quotient divisor)))
<font color="#AA5500">cl:*multiple-values*</font> t)
quotient))
</pre>
<p>The '<nobr>cl:truncate</nobr>' function computes a quotient that has been
truncated towards zero. That is, the quotient represents the mathematical
integer of the same sign as the mathematical quotient, and that has the
greatest integral magnitude not greater than that of the mathematical
quotient. <nobr>See
<a href="#rounding-and-truncation">Rounding and Truncation</a></nobr>
above for more details.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="cl-ceiling"></a>
<hr>
<h2>cl:ceiling</h2>
<hr>
<p>The '<nobr>cl:ceiling</nobr>' function truncates towards positive
infinity:</p>
<p><div class="box">
<dl>
<dt>(cl:<b>ceiling</b> <i>number </i> [<i>divisor</i>])</dt>
<dd><i>number</i> - an integer or <nobr>floating-point</nobr> number<br>
<i>divisor</i> - an integer or <nobr>floating-point</nobr> number, except zero<br>
<table cellpadding="0" cellspacing="0"><tbody>
<tr>
<td valign="top"><nobr>returns</nobr></td>
<td valign="top"><nobr> - </nobr></td>
<td width="100%">the result of truncating the result of <i>number</i> divided by <i>divisor</i></td>
</tr>
<tr>
<td></td>
<td valign="top"><nobr> - </nobr></td>
<td width="100%">the remainder of the truncate operation</td>
</tr>
</tbody></table></dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:ceiling</font> (number &optional (divisor
(if (integerp number) 1 1.0)
divisor-p))
(let ((quotient
(cond ((and (not divisor-p) (integerp number)) number)
((= number divisor) 1)
(t (let ((i-quotient (/ (truncate number) (truncate divisor)))
(f-quotient (/ (float number) divisor)))
(if (or (= i-quotient f-quotient) <font color="#008844">; integer result</font>
(not (plusp f-quotient)))
(truncate f-quotient)
(1+ (truncate f-quotient))))))))
(setq <font color="#AA5500">*rslt*</font> (list quotient (- number (* quotient divisor)))
<font color="#AA5500">cl:*multiple-values*</font> t)
quotient))
</pre>
<p>The '<nobr>cl:ceiling</nobr>' function computes a quotient that has been
truncated toward positive infinity. That is, the quotient represents the
smallest mathematical integer that is not smaller than the mathematical
result. <nobr>See
<a href="#rounding-and-truncation">Rounding and Truncation</a></nobr>
above for more details.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="cl-floor"></a>
<hr>
<h2>cl:floor</h2>
<hr>
<p>The '<nobr>cl:floor</nobr>' function truncates towards negative infinity:</p>
<p><div class="box">
<dl>
<dt>(cl:<b>floor</b> <i>number </i> [<i>divisor</i>])</dt>
<dd><i>number</i> - an integer or <nobr>floating-point</nobr> number<br>
<i>divisor</i> - an integer or <nobr>floating-point</nobr> number, except zero<br>
<table cellpadding="0" cellspacing="0"><tbody>
<tr>
<td valign="top"><nobr>returns</nobr></td>
<td valign="top"><nobr> - </nobr></td>
<td width="100%">the result of truncating the result of <i>number</i> divided by <i>divisor</i></td>
</tr>
<tr>
<td></td>
<td valign="top"><nobr> - </nobr></td>
<td width="100%">the remainder of the truncate operation</td>
</tr>
</tbody></table></dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:floor</font> (number &optional (divisor
(if (integerp number) 1 1.0)
divisor-p))
(let ((quotient
(cond ((and (not divisor-p) (integerp number)) number)
((= number divisor) 1)
(t (let ((i-quotient (/ (truncate number) (truncate divisor)))
(f-quotient (/ (float number) divisor)))
(if (or (= i-quotient f-quotient) <font color="#008844">; integer result</font>
(not (minusp f-quotient)))
(truncate f-quotient)
(1- (truncate f-quotient))))))))
(setq <font color="#AA5500">*rslt*</font> (list quotient (- number (* quotient divisor)))
<font color="#AA5500">cl:*multiple-values*</font> t)
quotient))
</pre>
<p>The <nobr>'cl:floor</nobr>' function computes a quotient that has been
truncated toward negative infinity. That is, the quotient represents the
largest mathematical integer that is not larger than the mathematical
quotient. <nobr>See
<a href="#rounding-and-truncation">Rounding and Truncation</a></nobr>
above for more details.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="remainder-and-modulus"></a>
<hr>
<h2>Remainder and Modulus</h2>
<hr>
<p>The <a href="#cl-mod">cl:mod</a> and <a href="#cl-rem">cl:rem</a>
function are generalizations of the modulus and remainder functions.
<nobr>The <a href="#cl-mod">cl:mod</a></nobr> function performs the
<a href="#cl-floor">cl:floor</a> operation on its arguments and returns the
remainder of the <a href="#cl-floor">cl:floor</a> operation.
<nobr>The <a href="#cl-rem">cl:rem</a></nobr> function performs the
<a href="cl-truncate">cl:truncate</a> operation on its arguments and returns
the remainder of the <a href="cl-truncate">cl:truncate</a> operation.
<nobr>The <a href="#cl-mod">cl:mod</a></nobr> and
<a href="#cl-rem">cl:rem</a> functions are the modulus and remainder
functions when the 'number' and 'divisor' arguments both are integers.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="cl-rem"></a>
<hr>
<h2>cl:rem</h2>
<hr>
<p><div class="box">
<dl>
<dt>(cl:<b>rem</b> <i>number divisor</i>)</dt>
<dd><i>number</i> - an integer or floating-point number<br>
<i>divisor</i> - an integer or floating-point number<br>
returns - the remainder of a <a href="cl-truncate">cl:truncate</a> operation</dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:rem</font> (number divisor)
(if (= (abs number) (abs divisor))
(if (and (integerp number) (integerp divisor)) 0 0.0)
(let ((quotient (truncate (/ (float number) divisor))))
(- number (* quotient divisor)))))
</pre>
<p>The '<nobr>cl:rem</nobr>' function performs the
<a href="cl-truncate">cl:truncate</a> operation on its arguments and returns
the remainder of the <a href="cl-truncate">cl:truncate</a> operation.
<nobr>The result</nobr> is either zero or an integer or
<nobr>floating-point</nobr> number with the same sign as the 'number'
argument. <nobr>If both</nobr> arguments are integer numbers, the
'<nobr>cl:rem</nobr>' function is equal to the mathematical remainder
function.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="cl-mod"></a>
<hr>
<h2>cl:mod</h2>
<hr>
<p><div class="box">
<dl>
<dt>(cl:<b>mod</b> <i>number divisor</i>)</dt>
<dd><i>number</i> - an integer or floating-point number<br>
<i>divisor</i> - an integer or floating-point number<br>
returns - the remainder of a <a href="#cl-floor">cl:floor</a> operation</dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:mod</font> (number divisor)
(if (= (abs number) (abs divisor))
(if (and (integerp number) (integerp divisor)) 0 0.0)
(let* ((i-quotient (/ (truncate number) (truncate divisor)))
(f-quotient (/ (float number) divisor))
(quotient (if (or (= i-quotient f-quotient) <font color="#008844">; integer result</font>
(not (minusp f-quotient)))
(truncate f-quotient)
(1- (truncate f-quotient)))))
(- number (* quotient divisor)))))
</pre>
<p>The '<nobr>cl:mod</nobr>' function performs the
<a href="#cl-floor">cl:floor</a> operation on its arguments and returns the
remainder of the <a href="#cl-floor">cl:floor</a> operation. <nobr>The
result</nobr> is either zero or an integer or <nobr>floating-point</nobr>
number with the same sign as the 'divisor' argument. <nobr>If both</nobr>
arguments are integer numbers, the '<nobr>cl:rem</nobr>' function is equal
to the mathematical modulus function.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="cl-exp"></a>
<hr>
<h2>cl:exp</h2>
<hr>
<p>The '<nobr>cl:exp</nobr>' function does the same as the Nyquist/XLISP
<a href="../reference/exp.htm">exp</a> function, but it also accepts
integer numbers as argument:</p>
<p><div class="box">
<dl>
<dt>(cl:<b>exp</b> <i>power</i>)</dt>
<dd><i>power</i> - an integer or floating-point number<br>
returns - the result of <nobr>'e' [2.7128]</nobr> to the power of <i>power</i></dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:exp</font> (x)
(exp (float x)))
</pre>
<p>The '<nobr>cl:exp</nobr>' function computes <nobr>'e' [2.7128]</nobr>
raised to the specified 'power'. <nobr>The result</nobr> is always a
<nobr>floating-point</nobr> number.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="cl-expt"></a>
<hr>
<h2>cl:expt</h2>
<hr>
<p>The '<nobr>cl:expt</nobr>' function computes the result of 'x' to the
power <nobr>of 'y'</nobr>:</p>
<p><div class="box">
<dl>
<dt>(cl:<b>expt</b> <i>base power</i>)</dt>
<dd><i>base</i> - the base<br>
<i>power</i> - the exponent<br>
returns - the result of <i>base</i> to the power of <i>power</i></dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:expt</font> (x y)
(let ((power (expt (float x) y)))
(if (and (integerp x) (integerp y))
(round power)
power)))
</pre>
<p>See <a href="../reference/and.htm">and</a>,
<a href="../reference/defun.htm">defun</a>,
<a href="../reference/expt.htm">expt</a>,
<a href="../reference/float.htm">float</a>,
<nobr><a href="../reference/if.htm"> if </a></nobr>,
<a href="../reference/integerp.htm">integerp</a>,
<a href="../reference/let.htm">let</a>,
<a href="../reference/power.htm">power</a>,
<a href="../reference/round.htm">round</a>.</p>
<p>The '<nobr>cl:expt</nobr>' function accepts integer and floating point
numbers as arguments. <nobr>If both</nobr> arguments are integer numbers,
the result will be an integer number, <nobr>if one</nobr> or both arguments
are <nobr>floating-point</nobr> numbers, the result will be a
<nobr>floating-point</nobr> number. <nobr>In contrast</nobr> to the
Nyquist/XLISP <a href="../reference/expt.htm">expt</a> function, the
'<nobr>cl:expt</nobr>' function specifies exactly two arguments.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="cl-log"></a>
<hr>
<h2>cl:log</h2>
<hr>
<p>The '<nobr>cl:log</nobr>' function does the same as the Nyquist/XLISP
<a href="../reference/log.htm">log</a> function, but also accepts
integer numbers and has an optional 'base' argument:</p>
<p><div class="box">
<dl>
<dt>(cl:<b>log</b> <i>number</i> [<i>base</i>])</dt>
<dd><i>number</i> - an integer or floating-point number<br>
<i>base</i> - an integer or floating-point number<br>
returns - the the logarithm of <i>number</i> in base <i>base</i></dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:log</font> (number &optional base)
(if base
(if (zerop base)
0.0
(/ (log (float number)) (log (float base))))
(log (float number))))
</pre>
<p>The '<nobr>cl:log</nobr>' function returns the logarithm of 'number' in
base 'base'. <nobr>If 'base'</nobr> is not supplied its value <nobr>is
'e'</nobr>, the base of the natural logarithms. <nobr>If the</nobr> 'base'
argument is zero, then 'cl:log' returns zero. <nobr>The result</nobr> is
always a <nobr>floating-point</nobr> number.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<a name="cl-sqrt"></a>
<hr>
<h2>cl:sqrt</h2>
<hr>
<p>The '<nobr>cl:sqrt</nobr>' function does the same as the Nyquist/XLISP
<a href="../reference/sqrt.htm">sqrt</a> function, but it also accepts
integer numbers as argument:</p>
<p><div class="box">
<dl>
<dt>(cl:<b>sqrt</b> <i>number</i>)</dt>
<dd><i>number</i> - an integer or floating-point number<br>
returns - the square root of <i>number</i></dd>
</dl>
</div></p>
<pre class="example">
(defun <font color="#0000CC">cl:sqrt</font> (x)
(sqrt (float x)))
</pre>
<p><nobr>The result</nobr> is always a <nobr>floating-point</nobr>
number.</p>
<p><nobr> <a href="#top">Back to top</a></nobr></p>
<hr>
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