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<!doctype html><html lang='en'><head><title>Operators | SuperCollider 3.12.2 Help</title>
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<div id='toctitle'>Operators:</div>
<span class='toc_search'>Filter: <input id='toc_search'></span><ul class='toc'><li class='toc1'><a href='#Unary%20Operators'>Unary Operators</a></li>
<ul class='toc'><li class='toc2'><a href='#Arithmetics'>Arithmetics</a></li>
<ul class='toc'><li class='toc3'><a href='#.neg'>neg</a> </li>
<li class='toc3'><a href='#.reciprocal'>reciprocal</a> </li>
<li class='toc3'><a href='#.abs'>abs</a> </li>
<li class='toc3'><a href='#.floor'>floor</a> </li>
<li class='toc3'><a href='#.ceil'>ceil</a> </li>
<li class='toc3'><a href='#.frac'>frac</a> </li>
<li class='toc3'><a href='#.sign'>sign</a> </li>
<li class='toc3'><a href='#.squared'>squared</a> </li>
<li class='toc3'><a href='#.cubed'>cubed</a> </li>
<li class='toc3'><a href='#.sqrt'>sqrt</a> </li>
<li class='toc3'><a href='#.exp'>exp</a> </li>
</ul><li class='toc2'><a href='#Musical%20acoustics'>Musical acoustics</a></li>
<ul class='toc'><li class='toc3'><a href='#.midicps'>midicps</a> </li>
<li class='toc3'><a href='#.cpsmidi'>cpsmidi</a> </li>
<li class='toc3'><a href='#.midiratio'>midiratio</a> </li>
<li class='toc3'><a href='#.ratiomidi'>ratiomidi</a> </li>
<li class='toc3'><a href='#.dbamp'>dbamp</a> </li>
<li class='toc3'><a href='#.ampdb'>ampdb</a> </li>
<li class='toc3'><a href='#.octcps'>octcps</a> </li>
<li class='toc3'><a href='#.cpsoct'>cpsoct</a> </li>
</ul><li class='toc2'><a href='#Random%20operators'>Random operators</a></li>
<ul class='toc'><li class='toc3'><a href='#.rand'>rand</a> </li>
<li class='toc3'><a href='#.rand2'>rand2</a> </li>
<li class='toc3'><a href='#.linrand'>linrand</a> </li>
<li class='toc3'><a href='#.bilinrand'>bilinrand</a> </li>
<li class='toc3'><a href='#.sum3rand'>sum3rand</a> </li>
<li class='toc3'><a href='#.coin'>coin</a> </li>
</ul><li class='toc2'><a href='#Other'>Other</a></li>
<ul class='toc'><li class='toc3'><a href='#.log'>log</a> </li>
<li class='toc3'><a href='#.log2'>log2</a> </li>
<li class='toc3'><a href='#.log10'>log10</a> </li>
<li class='toc3'><a href='#.sin'>sin</a> </li>
<li class='toc3'><a href='#.cos'>cos</a> </li>
<li class='toc3'><a href='#.tan'>tan</a> </li>
<li class='toc3'><a href='#.asin'>asin</a> </li>
<li class='toc3'><a href='#.acos'>acos</a> </li>
<li class='toc3'><a href='#.atan'>atan</a> </li>
<li class='toc3'><a href='#.sinh'>sinh</a> </li>
<li class='toc3'><a href='#.cosh'>cosh</a> </li>
<li class='toc3'><a href='#.tanh'>tanh</a> </li>
<li class='toc3'><a href='#.distort'>distort</a> </li>
<li class='toc3'><a href='#.softclip'>softclip</a> </li>
<li class='toc3'><a href='#.isPositive'>isPositive</a> </li>
<li class='toc3'><a href='#.isNegative'>isNegative</a> </li>
<li class='toc3'><a href='#.isStrictlyPositive'>isStrictlyPositive</a> </li>
</ul></ul><li class='toc1'><a href='#Binary%20Operators'>Binary Operators</a></li>
<ul class='toc'><li class='toc2'><a href='#Arithmetics'>Arithmetics</a></li>
<ul class='toc'><li class='toc3'><a href='#.+'>+</a> </li>
<li class='toc3'><a href='#.-'>-</a> </li>
<li class='toc3'><a href='#.*'>*</a> </li>
<li class='toc3'><a href='#./'>/</a> </li>
<li class='toc3'><a href='#.%'>%</a> </li>
<li class='toc3'><a href='#.**'>**</a> </li>
<li class='toc3'><a href='#.pow'>pow</a> </li>
<li class='toc3'><a href='#.lcm'>lcm</a> </li>
<li class='toc3'><a href='#.gcd'>gcd</a> </li>
</ul><li class='toc2'><a href='#Comparisons'>Comparisons</a></li>
<ul class='toc'><li class='toc3'><a href='#.<'>&lt;</a> </li>
<li class='toc3'><a href='#.<='>&lt;=</a> </li>
<li class='toc3'><a href='#.>'>&gt;</a> </li>
<li class='toc3'><a href='#.>='>&gt;=</a> </li>
<li class='toc3'><a href='#.=='>==</a> </li>
<li class='toc3'><a href='#.!='>!=</a> </li>
<li class='toc3'><a href='#.|==|'>|==|</a> </li>
</ul><li class='toc2'><a href='#Other'>Other</a></li>
<ul class='toc'><li class='toc3'><a href='#.<!'>&lt;!</a> </li>
<li class='toc3'><a href='#.min'>min</a> </li>
<li class='toc3'><a href='#.max'>max</a> </li>
<li class='toc3'><a href='#.round'>round</a> </li>
<li class='toc3'><a href='#.trunc'>trunc</a> </li>
<li class='toc3'><a href='#.hypot'>hypot</a> </li>
<li class='toc3'><a href='#.hypotApx'>hypotApx</a> </li>
<li class='toc3'><a href='#.atan2'>atan2</a> </li>
<li class='toc3'><a href='#.ring1'>ring1</a> </li>
<li class='toc3'><a href='#.ring2'>ring2</a> </li>
<li class='toc3'><a href='#.ring3'>ring3</a> </li>
<li class='toc3'><a href='#.ring4'>ring4</a> </li>
<li class='toc3'><a href='#.sumsqr'>sumsqr</a> </li>
<li class='toc3'><a href='#.difsqr'>difsqr</a> </li>
<li class='toc3'><a href='#.sqrsum'>sqrsum</a> </li>
<li class='toc3'><a href='#.sqrdif'>sqrdif</a> </li>
<li class='toc3'><a href='#.absdif'>absdif</a> </li>
<li class='toc3'><a href='#.moddif'>moddif</a> </li>
<li class='toc3'><a href='#.thresh'>thresh</a> </li>
<li class='toc3'><a href='#.amclip'>amclip</a> </li>
<li class='toc3'><a href='#.scaleneg'>scaleneg</a> </li>
<li class='toc3'><a href='#.clip2'>clip2</a> </li>
<li class='toc3'><a href='#.wrap2'>wrap2</a> </li>
<li class='toc3'><a href='#.fold2'>fold2</a> </li>
<li class='toc3'><a href='#.excess'>excess</a> </li>
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<span id='folder'>Overviews</span>
| <span id='categories'><a href='./../Browse.html#Language'>Language</a> | <a href='./../Browse.html#Common methods'>Common methods</a></span>
</div><h1>Operators</h1>
<div id='summary'>common unary and binary operators</div>
</div>
<div class='subheader'>
<div id='related'>See also: <a href="./../Reference/Adverbs.html">Adverbs for Binary Operators</a></div>
</div>
<p>SuperCollider supports operator overloading. Operators can thus be applied to a variety of different objects; Numbers, Ugens, Collections, and so on. When operators are applied to ugens they result in <a href="./../Classes/BinaryOpUGen.html">BinaryOpUGen</a>s or <a href="./../Classes/UnaryOpUGen.html">UnaryOpUGen</a>s, through the methods of <a href="./../Classes/AbstractFunction.html">AbstractFunction</a>.
<p>This is a list of some of the common unary and binary operators that are implemented by several classes. See the specific classes for details and other operators.
<p>You can see which classes implements a specific operator by clicking on the method name.<h2><a class='anchor' name='Unary%20Operators'>Unary Operators</a></h2>
<p>Unary operators may be written in two ways:<textarea class='editor'>a.operator
operator(a)</textarea>
<h3><a class='anchor' name='Arithmetics'>Arithmetics</a></h3>
<h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='neg' href='./../Overviews/Methods.html#neg'>neg</a></h3>
<div class='method'>
<p>Inversion.<h4>Discussion:</h4>
<textarea class='editor'>{
var a;
a = FSinOsc.ar(300);
[ a, a.neg ]
}.plot</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='reciprocal' href='./../Overviews/Methods.html#reciprocal'>reciprocal</a></h3>
<div class='method'>
<p>Reciprocal (1/x).</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='abs' href='./../Overviews/Methods.html#abs'>abs</a></h3>
<div class='method'>
<p>Absolute value.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='floor' href='./../Overviews/Methods.html#floor'>floor</a></h3>
<div class='method'>
<p>Next lower integer.<h4>Discussion:</h4>
<textarea class='editor'>{
var a;
a = Line.ar(-1, 1, 0.01);
[ a, a.floor ]
}.plot</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='ceil' href='./../Overviews/Methods.html#ceil'>ceil</a></h3>
<div class='method'>
<p>Next higher integer.<h4>Discussion:</h4>
<textarea class='editor'>{
var a;
a = Line.ar(-1, 1, 0.01);
[ a, a.ceil ]
}.plot</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='frac' href='./../Overviews/Methods.html#frac'>frac</a></h3>
<div class='method'>
<p>Fractional part.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='sign' href='./../Overviews/Methods.html#sign'>sign</a></h3>
<div class='method'>
<p>Sign function.<h4>Returns:</h4>
<div class='returnvalue'>
<p>-1 when a &lt; 0, +1 when a &gt; 0, 0 when a is 0</div></div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='squared' href='./../Overviews/Methods.html#squared'>squared</a></h3>
<div class='method'>
<p>Squared value.<h4>Returns:</h4>
<div class='returnvalue'>
<p><code>a*a</code></div></div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='cubed' href='./../Overviews/Methods.html#cubed'>cubed</a></h3>
<div class='method'>
<p>Cubed value.<h4>Returns:</h4>
<div class='returnvalue'>
<p><code>a*a*a</code></div></div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='sqrt' href='./../Overviews/Methods.html#sqrt'>sqrt</a></h3>
<div class='method'>
<p>Square root.<h4>Discussion:</h4>
<p>The definition of square root is extended for signals so that sqrt(a) when a&lt;0 returns -sqrt(-a).</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='exp' href='./../Overviews/Methods.html#exp'>exp</a></h3>
<div class='method'>
<p>Exponential.</div><h3><a class='anchor' name='Musical%20acoustics'>Musical acoustics</a></h3>
<h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='midicps' href='./../Overviews/Methods.html#midicps'>midicps</a></h3>
<div class='method'>
<p>Convert MIDI note number to cycles per second.<h4>Discussion:</h4>
<textarea class='editor'>{
Saw.ar(Line.kr(24,108,10).midicps, 0.2)
}.play</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='cpsmidi' href='./../Overviews/Methods.html#cpsmidi'>cpsmidi</a></h3>
<div class='method'>
<p>Convert cycles per second to MIDI note.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='midiratio' href='./../Overviews/Methods.html#midiratio'>midiratio</a></h3>
<div class='method'>
<p>Convert an interval in MIDI notes into a frequency ratio.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='ratiomidi' href='./../Overviews/Methods.html#ratiomidi'>ratiomidi</a></h3>
<div class='method'>
<p>Convert a frequency ratio to an interval in MIDI notes.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='dbamp' href='./../Overviews/Methods.html#dbamp'>dbamp</a></h3>
<div class='method'>
<p>Convert decibels to linear amplitude.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='ampdb' href='./../Overviews/Methods.html#ampdb'>ampdb</a></h3>
<div class='method'>
<p>Convert linear amplitude to decibels.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='octcps' href='./../Overviews/Methods.html#octcps'>octcps</a></h3>
<div class='method'>
<p>Convert decimal octaves to cycles per second.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='cpsoct' href='./../Overviews/Methods.html#cpsoct'>cpsoct</a></h3>
<div class='method'>
<p>Convert cycles per second to decimal octaves.</div><h3><a class='anchor' name='Random%20operators'>Random operators</a></h3>
<p>See also <a href="./../Guides/Randomness.html">Randomness</a><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='rand' href='./../Overviews/Methods.html#rand'>rand</a></h3>
<div class='method'>
<p>Returns an evenly distributed random value between this and zero.<textarea class='editor'>10.rand;
{ SinOsc.ar(110).rand }.plot;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='rand2' href='./../Overviews/Methods.html#rand2'>rand2</a></h3>
<div class='method'>
<p>Returns an evenly distributed random value between [+this ... - this].<textarea class='editor'>10.rand2;
{ SinOsc.ar(110).rand2 }.plot;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='linrand' href='./../Overviews/Methods.html#linrand'>linrand</a></h3>
<div class='method'>
<p>Returns a linearly distributed random value between this and zero.<textarea class='editor'>10.linrand;
{ SinOsc.ar(110).linrand }.plot;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='bilinrand' href='./../Overviews/Methods.html#bilinrand'>bilinrand</a></h3>
<div class='method'>
<p>Returns a linearly distributed random value between [+this ... - this].<textarea class='editor'>10.bilinrand;
{ SinOsc.ar(110).bilinrand }.plot;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='sum3rand' href='./../Overviews/Methods.html#sum3rand'>sum3rand</a></h3>
<div class='method'>
<p>Returns a value from a gaussian-like random distribution between this and zero. This was suggested by Larry Polansky as a loose approximation of gaussian. Follows the formula:<textarea class='editor'>{ 1.0.rand }.dup(3).sum - 1.5 * (2/3)</textarea>
<textarea class='editor'>10.sum3rand;
{ SinOsc.ar(110).sum3rand }.plot;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='coin' href='./../Overviews/Methods.html#coin'>coin</a></h3>
<div class='method'>
<p>Returns one or zero with the probability given by the argument.<textarea class='editor'>0.4.coin;
{ SinOsc.ar(110).coin }.plot;</textarea>
</div><h3><a class='anchor' name='Other'>Other</a></h3>
<h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='log' href='./../Overviews/Methods.html#log'>log</a></h3>
<div class='method'>
<p>Natural logarithm.<h4>Discussion:</h4>
<textarea class='editor'>{
var a, e;
e = exp(1);
a = Line.ar(e, 1/e, 0.01);
a.log
}.plot</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='log2' href='./../Overviews/Methods.html#log2'>log2</a></h3>
<div class='method'>
<p>Base 2 logarithm.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='log10' href='./../Overviews/Methods.html#log10'>log10</a></h3>
<div class='method'>
<p>Base 10 logarithm.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='sin' href='./../Overviews/Methods.html#sin'>sin</a></h3>
<div class='method'>
<p>Sine.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='cos' href='./../Overviews/Methods.html#cos'>cos</a></h3>
<div class='method'>
<p>Cosine.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='tan' href='./../Overviews/Methods.html#tan'>tan</a></h3>
<div class='method'>
<p>Tangent.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='asin' href='./../Overviews/Methods.html#asin'>asin</a></h3>
<div class='method'>
<p>Arcsine.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='acos' href='./../Overviews/Methods.html#acos'>acos</a></h3>
<div class='method'>
<p>Arccosine.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='atan' href='./../Overviews/Methods.html#atan'>atan</a></h3>
<div class='method'>
<p>Arctangent.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='sinh' href='./../Overviews/Methods.html#sinh'>sinh</a></h3>
<div class='method'>
<p>Hyperbolic sine.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='cosh' href='./../Overviews/Methods.html#cosh'>cosh</a></h3>
<div class='method'>
<p>Hyperbolic cosine.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='tanh' href='./../Overviews/Methods.html#tanh'>tanh</a></h3>
<div class='method'>
<p>Hyperbolic tangent.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='distort' href='./../Overviews/Methods.html#distort'>distort</a></h3>
<div class='method'>
<p>Nonlinear distortion.<h4>Discussion:</h4>
<p>The formula used is :<textarea class='editor'>x / (1 + abs(x))</textarea>
<p>Here is an example :<textarea class='editor'>(
{
var a;
a = Line.ar(-4, 4, 0.01);
a.distort
}.plot
)
{ FSinOsc.ar(500, 0.0, XLine.kr(0.1, 10, 10)).distort * 0.25 }.scope;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='softclip' href='./../Overviews/Methods.html#softclip'>softclip</a></h3>
<div class='method'>
<p>Nonlinear distortion.<h4>Discussion:</h4>
<p>Distortion with a perfectly linear region from -0.5 to +0.5<textarea class='editor'>(
{
var a;
a = Line.ar(-2, 2, 0.01);
a.softclip
}.plot
)
{ FSinOsc.ar(500,0.0, XLine.kr(0.1, 10, 10)).softclip * 0.25 }.scope(2);</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='isPositive' href='./../Overviews/Methods.html#isPositive'>isPositive</a></h3>
<div class='method'>
<p>Test if signal is &gt;= 0.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='isNegative' href='./../Overviews/Methods.html#isNegative'>isNegative</a></h3>
<div class='method'>
<p>Test if signal is &lt; 0.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='isStrictlyPositive' href='./../Overviews/Methods.html#isStrictlyPositive'>isStrictlyPositive</a></h3>
<div class='method'>
<p>Test if signal is &gt; 0.</div><h2><a class='anchor' name='Binary%20Operators'>Binary Operators</a></h2>
<p>Three different syntaxes can be used for binary operators consisting of letters:<textarea class='editor'>operator(a, b)
a operator: b
a.operator(b)</textarea>
<p>Operators consisting of symbols are written like this:<textarea class='editor'>a + b</textarea>
<h3><a class='anchor' name='Arithmetics'>Arithmetics</a></h3>
<h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='+' href='./../Overviews/Methods.html#+'>+</a></h3>
<div class='method'>
<p>Addition.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='-' href='./../Overviews/Methods.html#-'>-</a></h3>
<div class='method'>
<p>Subtraction.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='*' href='./../Overviews/Methods.html#*'>*</a></h3>
<div class='method'>
<p>Multiplication.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='/' href='./../Overviews/Methods.html#/'>/</a></h3>
<div class='method'>
<p>Division.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='%' href='./../Overviews/Methods.html#%'>%</a></h3>
<div class='method'>
<p>Floating point modulo.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='**' href='./../Overviews/Methods.html#**'>**</a></h3>
<div class='method'>
<p>Exponentiation. Same as pow.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='pow' href='./../Overviews/Methods.html#pow'>pow</a></h3>
<div class='method'>
<p>Exponentiation.<div class='note'><span class='notelabel'>NOTE:</span> When used with UGens which produce a negative signal this function extends the usual definition of exponentiation and returns <code>neg(neg(a) ** b)</code>. This allows exponentiation of negative signal values by noninteger exponents.</div></div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='lcm' href='./../Overviews/Methods.html#lcm'>lcm</a></h3>
<div class='method'>
<p>Least common multiple. This definition extends the usual definition and returns a negative number if <strong>any of the operands</strong> is negative. This makes it consistent with the lattice-theoretical interpretation and its idempotency, commutative, associative, absorption laws.
<p>Following the example of the programming language J (see: <a href="./../Guides/J-concepts-in-SC.html">J concepts in SC</a>), lcm is analogous to logical <strong>and</strong> (see also: <a href="http://www.jsoftware.com/papers/eem/gcd.htm">http://www.jsoftware.com/papers/eem/gcd.htm</a>).<textarea class='editor'>lcm(4, 6);
lcm(1, 1); // and
lcm(1624, 26);
lcm(1624, -26);
lcm(-1624, -26);
lcm(513, gcd(513, 44)) // absorption law -&gt; 513.</textarea>
<p><textarea class='editor'>(
{
var mx = MouseX.kr(-20, 20);
var my = MouseY.kr(-20, 20);
SinOsc.ar(SinOsc.kr(0.3) * 20 lcm: [mx, my] * 30 + 500) * 0.1
}.play;
)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='gcd' href='./../Overviews/Methods.html#gcd'>gcd</a></h3>
<div class='method'>
<p>Greatest common divisor. This definition extends the usual definition and returns a negative number if <strong>both operands</strong> are negative. This makes it consistent with the lattice-theoretical interpretation and its idempotency, commutative, associative, absorption laws.
<p>"greater" means "divisible by" in this interpretation, so <code>gcd(-1, -1)</code> returns a negative number. This is necessary to make the whole system consistent (fundamental law of arithmetics, idempotency and absorption laws would fail). See examples below.
<p>Following the example of the programming language J (see: <a href="./../Guides/J-concepts-in-SC.html">J concepts in SC</a>), gcd is analogous to logical <strong>or</strong> (see also: <a href="http://www.jsoftware.com/papers/eem/gcd.htm">http://www.jsoftware.com/papers/eem/gcd.htm</a>).<textarea class='editor'>gcd(4, 6);
gcd(0, 1); // or
gcd(1024, 256);
gcd(1024, -256);
gcd(-1024, -256); // "greater" means "divisible by" in this case, so this returns a negative number.
gcd(-1024, lcm(-1024, 256)) // absorption law -&gt; -1024.
gcd(66, 54) * lcm(66, 54) == (66 * 54); // true</textarea>
<textarea class='editor'>(
{
var mx = MouseX.kr(-200, 200);
var my = MouseY.kr(-200, 200);
SinOsc.ar(SinOsc.kr(0.3) * 20 gcd: [mx, my] * 30 + 500) * 0.1
}.play;
)</textarea>
<p>Here is an overview of how negative numbers are treated:<textarea class='editor'>lcm(4, 6) // -&gt; 12. "least multiple" interpreted as smallest in Z
lcm(4, -6) // -&gt; -12 "least multiple" interpreted as smallest in Z
lcm(-4, -6) // -&gt; -12 "least multiple" interpreted as smallest in Z
gcd(4, 6) // -&gt; 2 "greatest divisor" interpreted as highest in Z
gcd(4, -6) // -&gt; 2 "greatest divisor" is interpreted as highest in Z
gcd(-4, -6) // -&gt; -2 "greatest divisor" is interpreted as *inverse* in Z. This is the only necessary asymmetry.</textarea>
</div><h3><a class='anchor' name='Comparisons'>Comparisons</a></h3>
<h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='<' href='./../Overviews/Methods.html#&lt;'>&lt;</a></h3>
<div class='method'>
<p>Less than.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='<=' href='./../Overviews/Methods.html#&lt;='>&lt;=</a></h3>
<div class='method'>
<p>Less than or equal.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='>' href='./../Overviews/Methods.html#&gt;'>&gt;</a></h3>
<div class='method'>
<p>Greater than.<h4>Discussion:</h4>
<p>With UGens, this can be useful for triggering purposes, among other things:<textarea class='editor'>(
{ // trigger an envelope
var trig;
trig = SinOsc.ar(1) &gt; 0;
EnvGen.kr(Env.perc, trig, doneAction: Done.none)
* SinOsc.ar(440, 0, 0.1)
}.play
)
// trigger a synth
(
SynthDef("help-EnvGen", { arg out=0;
Out.ar(out,
EnvGen.kr(Env.perc,1.0,doneAction: Done.freeSelf)
* SinOsc.ar(440, 0, 0.1)
)
}).add;
// This synth has no output. It only checks amplitude of input and looks for a transition from &lt; 0.2
// to &gt; 0.2
{ SendTrig.kr(Amplitude.kr(SoundIn.ar(0)) &gt; 0.2) }.play;
// OSCFunc to trigger synth
OSCFunc({ "triggered".postln; Synth.new("help-EnvGen") },'/tr', s.addr);
)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='>=' href='./../Overviews/Methods.html#&gt;='>&gt;=</a></h3>
<div class='method'>
<p>Greater than or equal.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='==' href='./../Overviews/Methods.html#=='>==</a></h3>
<div class='method'>
<p>Equal.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='!=' href='./../Overviews/Methods.html#!='>!=</a></h3>
<div class='method'>
<p>Not equal.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='|==|' href='./../Overviews/Methods.html#|==|'>|==|</a></h3>
<div class='method'>
<p>"Lazy equality." See <a href="./../Classes/Object.html#-|==|">Object: -|==|</a>.</div><h3><a class='anchor' name='Other'>Other</a></h3>
<h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='<!' href='./../Overviews/Methods.html#&lt;!'>&lt;!</a></h3>
<div class='method'>
<p>Return first argument.<textarea class='editor'>// this is useful when two ugens need to be called, but only one of their outputs is needed
(
{
var a, b, c;
a = Dseq([1, 2, 3, 4], inf).dpoll("a");
b = Dseq([1955, 1952, 1823, 1452], inf).dpoll("b");
c = (a &lt;! b).dpoll("------&gt; a &lt;! b = "); // c only
Duty.kr(0.4, 0, c);
0.0
}.play
)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='min' href='./../Overviews/Methods.html#min'>min</a></h3>
<div class='method'>
<p>Minimum.<h4>Discussion:</h4>
<textarea class='editor'>{ // distorts and envelopes z
var z;
z = FSinOsc.ar(500);
z min: FSinOsc.ar(0.1);
}.play;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='max' href='./../Overviews/Methods.html#max'>max</a></h3>
<div class='method'>
<p>Maximum.<h4>Discussion:</h4>
<textarea class='editor'>{ // modulates and envelopes z
var z;
z = FSinOsc.ar(500);
z max: FSinOsc.ar(0.1);
}.play;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='round' href='./../Overviews/Methods.html#round'>round</a></h3>
<div class='method'>
<p>Quantization by rounding. Rounds a to the nearest multiple of b.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='trunc' href='./../Overviews/Methods.html#trunc'>trunc</a></h3>
<div class='method'>
<p>Quantization by truncation. Truncate a to a multiple of b.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='hypot' href='./../Overviews/Methods.html#hypot'>hypot</a></h3>
<div class='method'>
<p>Hypotenuse. Returns the square root of the sum of the squares of a and b. Or equivalently, the distance from the origin to the point (x, y).<h4>Discussion:</h4>
<p>In this example, hypot is used to calculate a doppler shift pitch and amplitude based on distance.<textarea class='editor'>(
{
var x, y, distance, velocity, pitchRatio, amplitude;
// object travels 200 meters in 6 secs (=120kph) passing 10 meters
// from the listener
x = 10;
y = LFSaw.kr(1/6, 0, 100);
distance = hypot(x, y);
velocity = Slope.kr(distance);
pitchRatio = (344 - velocity) / 344; // speed of sound is 344 meters/sec
amplitude = 10 / distance.squared;
FSinOsc.ar(1000 * pitchRatio, 0, amplitude)
}.play)</textarea>
<p>The next example uses the distance to modulate a delay line.<textarea class='editor'>(
{
var x, y, distance, velocity, pitchRatio, amplitude, motorSound;
// object travels 200 meters in 6 secs (=120kph) passing 10 meters
// from the listener
x = 10;
y = LFSaw.kr(1/6, 0, 100);
distance = hypot(x, y);
amplitude = 40 / distance.squared;
motorSound = RLPF.ar(FSinOsc.ar(200, 0, LFPulse.ar(31.3, 0, 0.4)), 400, 0.3);
DelayL.ar(motorSound, 110/344, distance/344, amplitude)
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='hypotApx' href='./../Overviews/Methods.html#hypotApx'>hypotApx</a></h3>
<div class='method'>
<p>Hypotenuse approximation. Returns an approximation of the square root of the sum of the squares of x and y.<h4>Discussion:</h4>
<p>The formula used is :<textarea class='editor'>abs(x) + abs(y) - ((sqrt(2) - 1) * min(abs(x), abs(y)))</textarea>
<p>hypotApx is used to implement Complex method magnitudeApx. This should not be used for simulating a doppler shift because it is discontinuous. Use hypot.
<p>See also <a href="#hypot">hypot</a>, <a href="#atan2">atan2</a>.</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='atan2' href='./../Overviews/Methods.html#atan2'>atan2</a></h3>
<div class='method'>
<p>Returns the arctangent of y/x.<h4>Discussion:</h4>
<p>OK, now we can add a pan to the <a href="#hypot">hypot</a> doppler examples by using atan2 to find the azimuth, or direction angle, of the sound source. Assume speakers at +/- 45 degrees and clip the direction to between those.<textarea class='editor'>(
{
var x, y, distance, velocity, pitchRatio, amplitude, azimuth, panValue;
// object travels 200 meters in 6 secs (=120kph) passing 10 meters
// from the listener
x = 10;
y = LFSaw.kr(1/6, 0, 100);
distance = hypot(x, y);
velocity = Slope.kr(distance);
pitchRatio = (344 - velocity) / 344; // speed of sound is 344 meters/sec
amplitude = 10 / distance.squared;
azimuth = atan2(y, x); // azimuth in radians
panValue = (azimuth / 0.5pi).clip2(1);
Pan2.ar(FSinOsc.ar(1000 * pitchRatio), panValue, amplitude)
}.play)
(
{
var x, y, distance, velocity, pitchRatio, amplitude, motorSound,
azimuth, panValue;
// object travels 200 meters in 6 secs (=120kph) passing 10 meters
// from the listener
x = 10;
y = LFSaw.kr(1/6, 0, 100);
distance = hypot(x, y);
amplitude = 40 / distance.squared;
motorSound = RLPF.ar(FSinOsc.ar(200, 0, LFPulse.ar(31.3, 0, 0.4)), 400, 0.3);
azimuth = atan2(y, x); // azimuth in radians
panValue = (azimuth / 0.5pi).clip2(1); // make a value for Pan2 from azimuth
Pan2.ar(DelayL.ar(motorSound, 110/344, distance/344), panValue, amplitude)
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='ring1' href='./../Overviews/Methods.html#ring1'>ring1</a></h3>
<div class='method'>
<p>Ring modulation plus first source.<h4>Discussion:</h4>
<p>Return the value of ((a*b) + a). This is more efficient than using separate unit generators for the multiply and add.
<p>See also <a href="#*">*</a>, <a href="#ring1">ring1</a>, <a href="#ring2">ring2</a>, <a href="#ring3">ring3</a>, <a href="#ring4">ring4</a>.<textarea class='editor'>{ (FSinOsc.ar(800) ring1: FSinOsc.ar(XLine.kr(200,500,5))) * 0.125 }.play;</textarea>
<p>same as :<textarea class='editor'>(
{
var a, b;
a = FSinOsc.ar(800);
b = FSinOsc.ar(XLine.kr(200,500,5));
((a * b) + a) * 0.125
}.play)</textarea>
<p>normal ring modulation:<textarea class='editor'>(
{
var a, b;
a = FSinOsc.ar(800);
b = FSinOsc.ar(XLine.kr(200,500,5));
(a * b) * 0.125
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='ring2' href='./../Overviews/Methods.html#ring2'>ring2</a></h3>
<div class='method'>
<p>Ring modulation plus both sources.<h4>Discussion:</h4>
<p>Return the value of ((a*b) + a + b). This is more efficient than using separate unit generators for the multiply and adds.<textarea class='editor'>{ (FSinOsc.ar(800) ring2: FSinOsc.ar(XLine.kr(200,500,5))) * 0.125 }.play;</textarea>
<p>same as :<textarea class='editor'>(
{
var a, b;
a = FSinOsc.ar(800);
b = FSinOsc.ar(XLine.kr(200,500,5));
((a * b) + a + b) * 0.125
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='ring3' href='./../Overviews/Methods.html#ring3'>ring3</a></h3>
<div class='method'>
<p>Ring modulation variant.<h4>Discussion:</h4>
<p>Return the value of (a*a *b). This is more efficient than using separate unit generators for each multiply.<textarea class='editor'>{ (FSinOsc.ar(800) ring3: FSinOsc.ar(XLine.kr(200,500,5))) * 0.125 }.play;</textarea>
<p>same as :<textarea class='editor'>(
{
var a, b;
a = FSinOsc.ar(800);
b = FSinOsc.ar(XLine.kr(200,500,5));
(a * a * b) * 0.125;
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='ring4' href='./../Overviews/Methods.html#ring4'>ring4</a></h3>
<div class='method'>
<p>Ring modulation variant.<h4>Discussion:</h4>
<p>Return the value of ((a*a *b) - (a*b*b)). This is more efficient than using separate unit generators for each operation.<textarea class='editor'>{ (FSinOsc.ar(800) ring4: FSinOsc.ar(XLine.kr(200,500,5))) * 0.125 }.play;</textarea>
<p>same as :<textarea class='editor'>(
{
var a, b;
a = FSinOsc.ar(800);
b = FSinOsc.ar(XLine.kr(200,500,5));
((a * a * b) - (a * b * b)) * 0.125
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='sumsqr' href='./../Overviews/Methods.html#sumsqr'>sumsqr</a></h3>
<div class='method'>
<p>Sum of squares.<h4>Discussion:</h4>
<p>Return the value of (a*a) + (b*b). This is more efficient than using separate unit generators for each operation.<textarea class='editor'>{ (FSinOsc.ar(800) sumsqr: FSinOsc.ar(XLine.kr(200,500,5))) * 0.125 }.play;</textarea>
<p>same as :<textarea class='editor'>(
{
var a, b;
a = FSinOsc.ar(800);
b = FSinOsc.ar(XLine.kr(200,500,5));
((a * a) + (b * b)) * 0.125
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='difsqr' href='./../Overviews/Methods.html#difsqr'>difsqr</a></h3>
<div class='method'>
<p>Difference of squares.<h4>Discussion:</h4>
<p>Return the value of (a*a) - (b*b). This is more efficient than using separate unit generators for each operation.<textarea class='editor'>{ (FSinOsc.ar(800) difsqr: FSinOsc.ar(XLine.kr(200,500,5))) * 0.125 }.play;</textarea>
<p>same as :<textarea class='editor'>(
{
var a, b;
a = FSinOsc.ar(800);
b = FSinOsc.ar(XLine.kr(200,500,5));
((a * a) - (b * b)) * 0.125
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='sqrsum' href='./../Overviews/Methods.html#sqrsum'>sqrsum</a></h3>
<div class='method'>
<p>Square of the sum.<h4>Discussion:</h4>
<p>Return the value of (a + b)**2. This is more efficient than using separate unit generators for each operation.<textarea class='editor'>{ (FSinOsc.ar(800) sqrsum: FSinOsc.ar(XLine.kr(200,500,5))) * 0.125 }.play;</textarea>
<p>same as :<textarea class='editor'>(
{
var a, b, c;
a = FSinOsc.ar(800);
b = FSinOsc.ar(XLine.kr(200,500,5));
c = a + b;
(c * c) * 0.125
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='sqrdif' href='./../Overviews/Methods.html#sqrdif'>sqrdif</a></h3>
<div class='method'>
<p>Square of the difference.<h4>Discussion:</h4>
<p>Return the value of (a - b)**2. This is more efficient than using separate unit generators for each operation.<textarea class='editor'>{ (FSinOsc.ar(800) sqrdif: FSinOsc.ar(XLine.kr(200,500,5))) * 0.125 }.play;</textarea>
<p>same as :<textarea class='editor'>(
{
var a, b, c;
a = FSinOsc.ar(800);
b = FSinOsc.ar(XLine.kr(200,500,5));
c = a - b;
(c * c) * 0.125
}.play)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='absdif' href='./../Overviews/Methods.html#absdif'>absdif</a></h3>
<div class='method'>
<p>Absolute value of the difference. <code>abs(a - b)</code><h4>Discussion:</h4>
<textarea class='editor'>(
{ // creates a rhythm
var mul = 0.2 absdif: FSinOsc.ar(2, 0, 0.5);
FSinOsc.ar(440, 0, mul);
}.play;
)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='moddif' href='./../Overviews/Methods.html#moddif'>moddif</a></h3>
<div class='method'>
<p>On a circle, there are two distances between two points. This operator returns the smaller value of the two.<h4>Discussion:</h4>
<textarea class='editor'>{ Line.ar(0, 4, 0.01).moddif(0) }.plot;
(
{
var mul = 0.2 moddif: FSinOsc.ar(2, 0, 0.5);
FSinOsc.ar(440, 0, mul);
}.play;
)</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='thresh' href='./../Overviews/Methods.html#thresh'>thresh</a></h3>
<div class='method'>
<p>Thresholding.<h4>Discussion:</h4>
<p>0 when a &lt; b, otherwise a.<textarea class='editor'>{ LFNoise0.ar(50, 0.5) thresh: 0.45 }.play // a low-rent gate</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='amclip' href='./../Overviews/Methods.html#amclip'>amclip</a></h3>
<div class='method'>
<p>Two quadrant multiply.<h4>Discussion:</h4>
<p>0 when b &lt;= 0, a*b when b &gt; 0<textarea class='editor'>{ WhiteNoise.ar.amclip(FSinOsc.kr(1,0.2)) }.play; // makes a sine envelope</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='scaleneg' href='./../Overviews/Methods.html#scaleneg'>scaleneg</a></h3>
<div class='method'>
<p>Scale negative part of input.<h4>Discussion:</h4>
<p>a*b when a &lt; 0, otherwise a.<textarea class='editor'>{ FSinOsc.ar(500).scaleneg(Line.ar(1,-1,4)) }.play;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='clip2' href='./../Overviews/Methods.html#clip2'>clip2</a></h3>
<div class='method'>
<p>Bilateral clipping.<h4>Discussion:</h4>
<p>clips input wave a to +/- b<textarea class='editor'>(
{
var a;
a = Line.ar(-2, 2, 0.01);
a.clip2
}.plot2
)
{ FSinOsc.ar(400).clip2(0.2) }.scope; // clipping distortion
{ FSinOsc.ar(1000).clip2(Line.kr(0,1,8)) }.scope;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='wrap2' href='./../Overviews/Methods.html#wrap2'>wrap2</a></h3>
<div class='method'>
<p>Bilateral wrapping.<h4>Discussion:</h4>
<p>wraps input wave to +/- b<textarea class='editor'>(
{
var a;
a = Line.ar(-2, 2, 0.01);
a.wrap2
}.plot
)
{ FSinOsc.ar(1000).wrap2(Line.kr(0,1.01,8)) }.scope;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='fold2' href='./../Overviews/Methods.html#fold2'>fold2</a></h3>
<div class='method'>
<p>Bilateral folding.<h4>Discussion:</h4>
<p>folds input wave a to +/- b<textarea class='editor'>(
{
var a;
a = Line.ar(-2, 2, 0.01);
a.fold2
}.plot
)
{ FSinOsc.ar(1000).fold2(Line.kr(0,1,8)) }.scope;</textarea>
</div><h3 class='method-code'><span class='method-prefix'></span><a class='method-name' name='excess' href='./../Overviews/Methods.html#excess'>excess</a></h3>
<div class='method'>
<p>Residual of clipping.<h4>Discussion:</h4>
<p>Returns the difference of the original signal and its clipped form: (a - clip2(a,b)).<textarea class='editor'>(
{
var a;
a = Line.ar(-2, 2, 0.01);
a.excess
}.plot
)
{ FSinOsc.ar(1000).excess(Line.kr(0,1,8)) }.play;</textarea>
<p></div><div class='doclink'>helpfile source: <a href='file:///Applications/SuperCollider.app/Contents/Resources/HelpSource/Overviews/Operators.schelp'>/Applications/SuperCollider.app/Contents/Resources/HelpSource/Overviews/Operators.schelp</a><br>link::Overviews/Operators::<br></div></div><script src='./../editor.js' type='text/javascript'></script>
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