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<li class="nav-item" data-level="3"><a href="#masr" class="nav-link">(ma.)SR</a>
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<li class="nav-item" data-level="3"><a href="#mat" class="nav-link">(ma.)T</a>
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<li class="nav-item" data-level="3"><a href="#mabs" class="nav-link">(ma.)BS</a>
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<li class="nav-item" data-level="3"><a href="#mae" class="nav-link">(ma.)E</a>
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<li class="nav-item" data-level="3"><a href="#maepsilon" class="nav-link">(ma.)EPSILON</a>
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<li class="nav-item" data-level="3"><a href="#mamin" class="nav-link">(ma.)MIN</a>
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<li class="nav-item" data-level="3"><a href="#mamax" class="nav-link">(ma.)MAX</a>
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</ul>
</li>
<li class="nav-item" data-level="3"><a href="#madiffn" class="nav-link">(ma.)diffn</a>
<ul class="nav flex-column">
</ul>
</li>
<li class="nav-item" data-level="3"><a href="#masignum" class="nav-link">(ma.)signum</a>
<ul class="nav flex-column">
</ul>
</li>
<li class="nav-item" data-level="3"><a href="#manextpow2" class="nav-link">(ma.)nextpow2</a>
<ul class="nav flex-column">
</ul>
</li>
<li class="nav-item" data-level="3"><a href="#mazc" class="nav-link">(ma.)zc</a>
<ul class="nav flex-column">
</ul>
</li>
<li class="nav-item" data-level="3"><a href="#maunwrap" class="nav-link">(ma.)unwrap</a>
<ul class="nav flex-column">
</ul>
</li>
<li class="nav-item" data-level="3"><a href="#maprimes" class="nav-link">(ma.)primes</a>
<ul class="nav flex-column">
</ul>
</li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div></div>
<div class="col-md-9 main-container" role="main">
<h1 id="mathslib">maths.lib</h1>
<p>Mathematic library for Faust. Its official prefix is <code>ma</code>.</p>
<h4 id="references">References</h4>
<ul>
<li><a href="https://github.com/grame-cncm/faustlibraries/blob/master/maths.lib">https://github.com/grame-cncm/faustlibraries/blob/master/maths.lib</a></li>
</ul>
<h2 id="functions-reference">Functions Reference</h2>
<hr />
<h3 id="masr"><code>(ma.)SR</code></h3>
<p>Current sampling rate given at init time. Constant during program execution.</p>
<h4 id="usage">Usage</h4>
<pre><code>SR : _
</code></pre>
<hr />
<h3 id="mat"><code>(ma.)T</code></h3>
<p>Current sample duration in seconds computed from the sampling rate given at init time. Constant during program execution.</p>
<h4 id="usage_1">Usage</h4>
<pre><code>T : _
</code></pre>
<hr />
<h3 id="mabs"><code>(ma.)BS</code></h3>
<p>Current block-size. Can change during the execution at each block.</p>
<h4 id="usage_2">Usage</h4>
<pre><code>BS : _
</code></pre>
<hr />
<h3 id="mapi"><code>(ma.)PI</code></h3>
<p>Constant PI in double precision.</p>
<h4 id="usage_3">Usage</h4>
<pre><code>PI : _
</code></pre>
<hr />
<h3 id="madeg2rad"><code>(ma.)deg2rad</code></h3>
<p>Convert degrees to radians.</p>
<h4 id="usage_4">Usage</h4>
<pre><code>45. : deg2rad
</code></pre>
<hr />
<h3 id="marad2deg"><code>(ma.)rad2deg</code></h3>
<p>Convert radians to degrees.</p>
<h4 id="usage_5">Usage</h4>
<pre><code>ma.PI : rad2deg
</code></pre>
<hr />
<h3 id="mae"><code>(ma.)E</code></h3>
<p>Constant e in double precision.</p>
<h4 id="usage_6">Usage</h4>
<pre><code>E : _
</code></pre>
<hr />
<h3 id="maepsilon"><code>(ma.)EPSILON</code></h3>
<p>Constant EPSILON available in simple/double/quad precision,
as defined in the <a href="https://en.wikipedia.org/wiki/IEEE_754">floating-point standard</a>
and <a href="https://en.wikipedia.org/wiki/Machine_epsilon">machine epsilon</a>,
that is smallest positive number such that <code>1.0 + EPSILON != 1.0</code>.</p>
<h4 id="usage_7">Usage</h4>
<pre><code>EPSILON : _
</code></pre>
<hr />
<h3 id="mamin"><code>(ma.)MIN</code></h3>
<p>Constant MIN available in simple/double/quad precision (minimal positive value).</p>
<h4 id="usage_8">Usage</h4>
<pre><code>MIN : _
</code></pre>
<hr />
<h3 id="mamax"><code>(ma.)MAX</code></h3>
<p>Constant MAX available in simple/double/quad precision (maximal positive value).</p>
<h4 id="usage_9">Usage</h4>
<pre><code>MAX : _
</code></pre>
<hr />
<h3 id="maftz"><code>(ma.)FTZ</code></h3>
<p>Flush to zero: force samples under the "maximum subnormal number"
to be zero. Usually not needed in C++ because the architecture
file take care of this, but can be useful in JavaScript for instance.</p>
<h4 id="usage_10">Usage</h4>
<pre><code>_ : FTZ : _
</code></pre>
<h4 id="reference">Reference</h4>
<ul>
<li><a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_math.html">http://docs.oracle.com/cd/E19957-01/806-3568/ncg_math.html</a></li>
</ul>
<hr />
<h3 id="macopysign"><code>(ma.)copysign</code></h3>
<p>Changes the sign of x (first input) to that of y (second input).</p>
<h4 id="usage_11">Usage</h4>
<pre><code>_,_ : copysign : _
</code></pre>
<hr />
<h3 id="maneg"><code>(ma.)neg</code></h3>
<p>Invert the sign (-x) of a signal.</p>
<h4 id="usage_12">Usage</h4>
<pre><code>_ : neg : _
</code></pre>
<hr />
<h3 id="manot"><code>(ma.)not</code></h3>
<p>Bitwise <code>not</code> implemented with <a href="https://faustdoc.grame.fr/manual/syntax/#xor-primitive">xor</a> as <code>not(x) = x xor -1;</code>.
So working regardless of the size of the integer, assuming negative numbers in two's complement.</p>
<h4 id="usage_13">Usage</h4>
<pre><code>_ : not : _
</code></pre>
<hr />
<h3 id="masubxy"><code>(ma.)sub(x,y)</code></h3>
<p>Subtract <code>x</code> and <code>y</code>.</p>
<h4 id="usage_14">Usage</h4>
<pre><code>_,_ : sub : _
</code></pre>
<hr />
<h3 id="mainv"><code>(ma.)inv</code></h3>
<p>Compute the inverse (1/x) of the input signal.</p>
<h4 id="usage_15">Usage</h4>
<pre><code>_ : inv : _
</code></pre>
<hr />
<h3 id="macbrt"><code>(ma.)cbrt</code></h3>
<p>Computes the cube root of of the input signal.</p>
<h4 id="usage_16">Usage</h4>
<pre><code>_ : cbrt : _
</code></pre>
<hr />
<h3 id="mahypot"><code>(ma.)hypot</code></h3>
<p>Computes the euclidian distance of the two input signals
sqrt(x<em>x+y</em>y) without undue overflow or underflow.</p>
<h4 id="usage_17">Usage</h4>
<pre><code>_,_ : hypot : _
</code></pre>
<hr />
<h3 id="maldexp"><code>(ma.)ldexp</code></h3>
<p>Takes two input signals: x and n, and multiplies x by 2 to the power n.</p>
<h4 id="usage_18">Usage</h4>
<pre><code>_,_ : ldexp : _
</code></pre>
<hr />
<h3 id="mascalb"><code>(ma.)scalb</code></h3>
<p>Takes two input signals: x and n, and multiplies x by 2 to the power n.</p>
<h4 id="usage_19">Usage</h4>
<pre><code>_,_ : scalb : _
</code></pre>
<hr />
<h3 id="malog1p"><code>(ma.)log1p</code></h3>
<p>Computes log(1 + x) without undue loss of accuracy when x is nearly zero.</p>
<h4 id="usage_20">Usage</h4>
<pre><code>_ : log1p : _
</code></pre>
<hr />
<h3 id="malogb"><code>(ma.)logb</code></h3>
<p>Return exponent of the input signal as a floating-point number.</p>
<h4 id="usage_21">Usage</h4>
<pre><code>_ : logb : _
</code></pre>
<hr />
<h3 id="mailogb"><code>(ma.)ilogb</code></h3>
<p>Return exponent of the input signal as an integer number.</p>
<h4 id="usage_22">Usage</h4>
<pre><code>_ : ilogb : _
</code></pre>
<hr />
<h3 id="malog2"><code>(ma.)log2</code></h3>
<p>Returns the base 2 logarithm of x.</p>
<h4 id="usage_23">Usage</h4>
<pre><code>_ : log2 : _
</code></pre>
<hr />
<h3 id="maexpm1"><code>(ma.)expm1</code></h3>
<p>Return exponent of the input signal minus 1 with better precision.</p>
<h4 id="usage_24">Usage</h4>
<pre><code>_ : expm1 : _
</code></pre>
<hr />
<h3 id="maacosh"><code>(ma.)acosh</code></h3>
<p>Computes the principle value of the inverse hyperbolic cosine
of the input signal.</p>
<h4 id="usage_25">Usage</h4>
<pre><code>_ : acosh : _
</code></pre>
<hr />
<h3 id="maasinh"><code>(ma.)asinh</code></h3>
<p>Computes the inverse hyperbolic sine of the input signal.</p>
<h4 id="usage_26">Usage</h4>
<pre><code>_ : asinh : _
</code></pre>
<hr />
<h3 id="maatanh"><code>(ma.)atanh</code></h3>
<p>Computes the inverse hyperbolic tangent of the input signal.</p>
<h4 id="usage_27">Usage</h4>
<pre><code>_ : atanh : _
</code></pre>
<hr />
<h3 id="masinh"><code>(ma.)sinh</code></h3>
<p>Computes the hyperbolic sine of the input signal.</p>
<h4 id="usage_28">Usage</h4>
<pre><code>_ : sinh : _
</code></pre>
<hr />
<h3 id="macosh"><code>(ma.)cosh</code></h3>
<p>Computes the hyperbolic cosine of the input signal.</p>
<h4 id="usage_29">Usage</h4>
<pre><code>_ : cosh : _
</code></pre>
<hr />
<h3 id="matanh"><code>(ma.)tanh</code></h3>
<p>Computes the hyperbolic tangent of the input signal.</p>
<h4 id="usage_30">Usage</h4>
<pre><code>_ : tanh : _
</code></pre>
<hr />
<h3 id="maerf"><code>(ma.)erf</code></h3>
<p>Computes the error function of the input signal.</p>
<h4 id="usage_31">Usage</h4>
<pre><code>_ : erf : _
</code></pre>
<hr />
<h3 id="maerfc"><code>(ma.)erfc</code></h3>
<p>Computes the complementary error function of the input signal.</p>
<h4 id="usage_32">Usage</h4>
<pre><code>_ : erfc : _
</code></pre>
<hr />
<h3 id="magamma"><code>(ma.)gamma</code></h3>
<p>Computes the gamma function of the input signal.</p>
<h4 id="usage_33">Usage</h4>
<pre><code>_ : gamma : _
</code></pre>
<hr />
<h3 id="malgamma"><code>(ma.)lgamma</code></h3>
<p>Calculates the natural logorithm of the absolute value of
the gamma function of the input signal.</p>
<h4 id="usage_34">Usage</h4>
<pre><code>_ : lgamma : _
</code></pre>
<hr />
<h3 id="maj0"><code>(ma.)J0</code></h3>
<p>Computes the Bessel function of the first kind of order 0
of the input signal.</p>
<h4 id="usage_35">Usage</h4>
<pre><code>_ : J0 : _
</code></pre>
<hr />
<h3 id="maj1"><code>(ma.)J1</code></h3>
<p>Computes the Bessel function of the first kind of order 1
of the input signal.</p>
<h4 id="usage_36">Usage</h4>
<pre><code>_ : J1 : _
</code></pre>
<hr />
<h3 id="majn"><code>(ma.)Jn</code></h3>
<p>Computes the Bessel function of the first kind of order n
(first input signal) of the second input signal.</p>
<h4 id="usage_37">Usage</h4>
<pre><code>_,_ : Jn : _
</code></pre>
<hr />
<h3 id="may0"><code>(ma.)Y0</code></h3>
<p>Computes the linearly independent Bessel function of the second kind
of order 0 of the input signal.</p>
<h4 id="usage_38">Usage</h4>
<pre><code>_ : Y0 : _
</code></pre>
<hr />
<h3 id="may1"><code>(ma.)Y1</code></h3>
<p>Computes the linearly independent Bessel function of the second kind
of order 1 of the input signal.</p>
<h4 id="usage_39">Usage</h4>
<pre><code>_ : Y0 : _
</code></pre>
<hr />
<h3 id="mayn"><code>(ma.)Yn</code></h3>
<p>Computes the linearly independent Bessel function of the second kind
of order n (first input signal) of the second input signal.</p>
<h4 id="usage_40">Usage</h4>
<pre><code>_,_ : Yn : _
</code></pre>
<hr />
<h3 id="mafabs-mafmax-mafmin"><code>(ma.)fabs</code>, <code>(ma.)fmax</code>, <code>(ma.)fmin</code></h3>
<p>Just for compatibility...</p>
<pre><code>fabs = abs
fmax = max
fmin = min
</code></pre>
<hr />
<h3 id="manp2"><code>(ma.)np2</code></h3>
<p>Gives the next power of 2 of x.</p>
<h4 id="usage_41">Usage</h4>
<pre><code>np2(n) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>n</code>: an integer</li>
</ul>
<hr />
<h3 id="mafrac"><code>(ma.)frac</code></h3>
<p>Gives the fractional part of n.</p>
<h4 id="usage_42">Usage</h4>
<pre><code>frac(n) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>n</code>: a decimal number</li>
</ul>
<hr />
<h3 id="mamodulo"><code>(ma.)modulo</code></h3>
<p>Modulus operation using the <code>(x%y+y)%y</code> formula to ensures the result is always non-negative, even if <code>x</code> is negative.</p>
<h4 id="usage_43">Usage</h4>
<pre><code>modulo(x,y) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>x</code>: the numerator</li>
<li><code>y</code>: the denominator</li>
</ul>
<hr />
<h3 id="maisnan"><code>(ma.)isnan</code></h3>
<p>Return non-zero if x is a NaN.</p>
<h4 id="usage_44">Usage</h4>
<pre><code>isnan(x)
_ : isnan : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>x</code>: signal to analyse</li>
</ul>
<hr />
<h3 id="maisinf"><code>(ma.)isinf</code></h3>
<p>Return non-zero if x is a positive or negative infinity.</p>
<h4 id="usage_45">Usage</h4>
<pre><code>isinf(x)
_ : isinf : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>x</code>: signal to analyse</li>
</ul>
<hr />
<h3 id="machebychev"><code>(ma.)chebychev</code></h3>
<p>Chebychev transformation of order N.</p>
<h4 id="usage_46">Usage</h4>
<pre><code>_ : chebychev(N) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>N</code>: the order of the polynomial, a constant numerical expression</li>
</ul>
<h4 id="semantics">Semantics</h4>
<pre><code>T[0](x) = 1,
T[1](x) = x,
T[n](x) = 2x*T[n-1](x) - T[n-2](x)
</code></pre>
<h4 id="reference_1">Reference</h4>
<ul>
<li><a href="http://en.wikipedia.org/wiki/Chebyshev_polynomial">http://en.wikipedia.org/wiki/Chebyshev_polynomial</a></li>
</ul>
<hr />
<h3 id="machebychevpoly"><code>(ma.)chebychevpoly</code></h3>
<p>Linear combination of the first Chebyshev polynomials.</p>
<h4 id="usage_47">Usage</h4>
<pre><code>_ : chebychevpoly((c0,c1,...,cn)) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>cn</code>: the different Chebychevs polynomials such that:
chebychevpoly((c0,c1,...,cn)) = Sum of chebychev(i)*ci</li>
</ul>
<h4 id="reference_2">Reference</h4>
<ul>
<li><a href="http://www.csounds.com/manual/html/chebyshevpoly.html">http://www.csounds.com/manual/html/chebyshevpoly.html</a></li>
</ul>
<hr />
<h3 id="madiffn"><code>(ma.)diffn</code></h3>
<p>Negated first-order difference.</p>
<h4 id="usage_48">Usage</h4>
<pre><code>_ : diffn : _
</code></pre>
<hr />
<h3 id="masignum"><code>(ma.)signum</code></h3>
<p>The signum function signum(x) is defined as
-1 for x<0, 0 for x==0, and 1 for x>0.</p>
<h4 id="usage_49">Usage</h4>
<pre><code>_ : signum : _
</code></pre>
<hr />
<h3 id="manextpow2"><code>(ma.)nextpow2</code></h3>
<p>The nextpow2(x) returns the lowest integer m such that
2^m >= x.</p>
<h4 id="usage_50">Usage</h4>
<pre><code>2^nextpow2(n) : _
</code></pre>
<p>Useful for allocating delay lines, e.g., </p>
<pre><code>delay(2^nextpow2(maxDelayNeeded), currentDelay);
</code></pre>
<hr />
<h3 id="mazc"><code>(ma.)zc</code></h3>
<p>Indicator function for zero-crossing: it returns 1 if a zero-crossing
occurs, 0 otherwise.</p>
<h4 id="usage_51">Usage</h4>
<pre><code>_ : zc : _
</code></pre>
<hr />
<h3 id="maunwrap"><code>(ma.)unwrap</code></h3>
<p>Unwrap the input signal so that successive output values never differ
by more than <code>pi</code>, switching to a 2*pi-complementary value when needed.</p>
<h4 id="usage_52">Usage</h4>
<pre><code>_ : unwrap(pi) : _
</code></pre>
<p>Where:</p>
<ul>
<li><code>pi</code>: maximum discontinuity between the output values (typically <code>ma.PI</code>)</li>
</ul>
<h4 id="example-test-program">Example test program</h4>
<pre><code>process = 0 - os.oscrc(1000) // the true phase is either -PI or +PI
: an.resonator(1,1000) : !,_ // oscillates between -PI and +PI
: ma.unwrap(ma.PI); // oscillates near +PI
</code></pre>
<hr />
<h3 id="maprimes"><code>(ma.)primes</code></h3>
<p>Return the n-th prime using a waveform primitive. Note that primes(0) is 2,
primes(1) is 3, and so on. The waveform is length 2048, so the largest
precomputed prime is primes(2047) which is 17863.</p>
<h4 id="usage_53">Usage</h4>
<pre><code>_ : primes : _
</code></pre></div>
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