# basics.lib

A library of basic elements. Its official prefix is ba.

## Conversion Tools

### (ba.)samp2sec

Converts a number of samples to a duration in seconds at the current sampling rate (see ma.SR). samp2sec is a standard Faust function.

#### Usage

samp2sec(n) : _

Where:

• n: number of samples

### (ba.)sec2samp

Converts a duration in seconds to a number of samples at the current sampling rate (see ma.SR). samp2sec is a standard Faust function.

#### Usage

sec2samp(d) : _

Where:

• d: duration in seconds

### (ba.)db2linear

dB-to-linear value converter. It can be used to convert an amplitude in dB to a linear gain ]0-N]. db2linear is a standard Faust function.

#### Usage

db2linear(l) : _

Where:

• l: amplitude in dB

### (ba.)linear2db

linea-to-dB value converter. It can be used to convert a linear gain ]0-N] to an amplitude in dB. linear2db is a standard Faust function.

#### Usage

linear2db(g) : _

Where:

• g: a linear gain

### (ba.)lin2LogGain

Converts a linear gain (0-1) to a log gain (0-1).

#### Usage

lin2LogGain(n) : _

Where:

• n: the linear gain

### (ba.)log2LinGain

Converts a log gain (0-1) to a linear gain (0-1).

#### Usage

log2LinGain(n) : _

Where:

• n: the log gain

### (ba.)tau2pole

Returns a real pole giving exponential decay. Note that t60 (time to decay 60 dB) is ~6.91 time constants. tau2pole is a standard Faust function.

#### Usage

_ : smooth(tau2pole(tau)) : _

Where:

• tau: time-constant in seconds

### (ba.)pole2tau

Returns the time-constant, in seconds, corresponding to the given real, positive pole in (0-1). pole2tau is a standard Faust function.

#### Usage

pole2tau(pole) : _

Where:

• pole: the pole

### (ba.)midikey2hz

Converts a MIDI key number to a frequency in Hz (MIDI key 69 = A440). midikey2hz is a standard Faust function.

#### Usage

midikey2hz(mk) : _

Where:

• mk: the MIDI key number

### (ba.)hz2midikey

Converts a frequency in Hz to a MIDI key number (MIDI key 69 = A440). hz2midikey is a standard Faust function.

#### Usage

hz2midikey(freq) : _

Where:

• freq: frequency in Hz

### (ba.)semi2ratio

Converts semitones in a frequency multiplicative ratio. semi2ratio is a standard Faust function.

#### Usage

semi2ratio(semi) : _

Where:

• semi: number of semitone

### (ba.)ratio2semi

Converts a frequency multiplicative ratio in semitones. ratio2semi is a standard Faust function.

#### Usage

ratio2semi(ratio) : _

Where:

• ratio: frequency multiplicative ratio

### (ba.)cent2ratio

Converts cents in a frequency multiplicative ratio.

#### Usage

cent2ratio(cent) : _

Where:

• cent: number of cents

### (ba.)ratio2cent

Converts a frequency multiplicative ratio in cents.

#### Usage

ratio2cent(ratio) : _

Where:

• ratio: frequency multiplicative ratio

### (ba.)pianokey2hz

Converts a piano key number to a frequency in Hz (piano key 49 = A440).

#### Usage

pianokey2hz(pk) : _

Where:

• pk: the piano key number

### (ba.)hz2pianokey

Converts a frequency in Hz to a piano key number (piano key 49 = A440).

#### Usage

hz2pianokey(freq) : _

Where:

• freq: frequency in Hz

## Counters and Time/Tempo Tools

### (ba.)counter

Starts counting 0, 1, 2, 3..., and raise the current integer value at each upfront of the trigger.

#### Usage

counter(trig) : _

Where:

• trig: the trigger signal, each upfront will move the counter to the next integer

### (ba.)countdown

Starts counting down from n included to 0. While trig is 1 the output is n. The countdown starts with the transition of trig from 1 to 0. At the end of the countdown the output value will remain at 0 until the next trig. countdown is a standard Faust function.

#### Usage

countdown(n,trig) : _

Where:

• n: the starting point of the countdown
• trig: the trigger signal (1: start at n; 0: decrease until 0)

### (ba.)countup

Starts counting up from 0 to n included. While trig is 1 the output is 0. The countup starts with the transition of trig from 1 to 0. At the end of the countup the output value will remain at n until the next trig. countup is a standard Faust function.

#### Usage

countup(n,trig) : _

Where:

• n: the maximum count value
• trig: the trigger signal (1: start at 0; 0: increase until n)

### (ba.)sweep

Counts from 0 to period-1 repeatedly, generating a sawtooth waveform, like os.lf_rawsaw, starting at 1 when run transitions from 0 to 1. Outputs zero while run is 0.

#### Usage

sweep(period,run) : _

### (ba.)time

A simple timer that counts every samples from the beginning of the process. time is a standard Faust function.

time : _

### (ba.)ramp

A linear ramp with a slope of '(+/-)1/n' samples to reach the next target value.

#### Usage

_ : ramp(n) : _

Where:

• n: number of samples to increment/decrement the value by one

### (ba.)line

A ramp interpolator that generates a linear transition to reach a target value:

• the interpolation process restarts each time a new and distinct input value is received
• it utilizes 'n' samples to achieve the transition to the target value
• after reaching the target value, the output value is maintained.

#### Usage

_ : line(n) : _

Where:

• n: number of samples to reach the new target received at its input

### (ba.)tempo

Converts a tempo in BPM into a number of samples.

#### Usage

tempo(t) : _

Where:

• t: tempo in BPM

### (ba.)period

Basic sawtooth wave of period p.

#### Usage

period(p) : _

Where:

• p: period as a number of samples

### (ba.)spulse

Produces a single pulse of n samples when trig goes from 0 to 1.

#### Usage

spulse(n,trig) : _

Where:

• n: pulse length as a number of samples
• trig: the trigger signal (1: start the pulse)

### (ba.)pulse

Pulses (like 10000) generated at period p.

#### Usage

pulse(p) : _

Where:

• p: period as a number of samples

### (ba.)pulsen

Pulses (like 11110000) of length n generated at period p.

#### Usage

pulsen(n,p) : _

Where:

• n: pulse length as a number of samples
• p: period as a number of samples

### (ba.)cycle

Split nonzero input values into n cycles.

#### Usage

_ : cycle(n) : si.bus(n)

Where:

• n: the number of cycles/output signals

### (ba.)beat

Pulses at tempo t. beat is a standard Faust function.

#### Usage

beat(t) : _

Where:

• t: tempo in BPM

### (ba.)pulse_countup

Starts counting up pulses. While trig is 1 the output is counting up, while trig is 0 the counter is reset to 0.

#### Usage

_ : pulse_countup(trig) : _

Where:

• trig: the trigger signal (1: start at next pulse; 0: reset to 0)

### (ba.)pulse_countdown

Starts counting down pulses. While trig is 1 the output is counting down, while trig is 0 the counter is reset to 0.

#### Usage

_ : pulse_countdown(trig) : _

Where:

• trig: the trigger signal (1: start at next pulse; 0: reset to 0)

### (ba.)pulse_countup_loop

Starts counting up pulses from 0 to n included. While trig is 1 the output is counting up, while trig is 0 the counter is reset to 0. At the end of the countup (n) the output value will be reset to 0.

#### Usage

_ : pulse_countup_loop(n,trig) : _

Where:

• n: the highest number of the countup (included) before reset to 0
• trig: the trigger signal (1: start at next pulse; 0: reset to 0)

### (ba.)pulse_countdown_loop

Starts counting down pulses from 0 to n included. While trig is 1 the output is counting down, while trig is 0 the counter is reset to 0. At the end of the countdown (n) the output value will be reset to 0.

#### Usage

_ : pulse_countdown_loop(n,trig) : _

Where:

• n: the highest number of the countup (included) before reset to 0
• trig: the trigger signal (1: start at next pulse; 0: reset to 0)

### (ba.)resetCtr

Function that lets through the mth impulse out of each consecutive group of n impulses.

#### Usage

_ : resetCtr(n,m) : _

Where:

• n: the total number of impulses being split
• m: index of impulse to allow to be output

## Array Processing/Pattern Matching

### (ba.)count

Count the number of elements of list l. count is a standard Faust function.

#### Usage

count(l)
count((10,20,30,40)) -> 4

Where:

• l: list of elements

### (ba.)take

Take an element from a list. take is a standard Faust function.

#### Usage

take(P,l)
take(3,(10,20,30,40)) -> 30

Where:

• P: position (int, known at compile time, P > 0)
• l: list of elements

### (ba.)subseq

Extract a part of a list.

#### Usage

subseq(l, P, N)
subseq((10,20,30,40,50,60), 1, 3) -> (20,30,40)
subseq((10,20,30,40,50,60), 4, 1) -> 50

Where:

• l: list
• P: start point (int, known at compile time, 0: begin of list)
• N: number of elements (int, known at compile time)

#### Note:

Faust doesn't have proper lists. Lists are simulated with parallel compositions and there is no empty list.

## Function tabulation

The purpose of function tabulation is to speed up the computation of heavy functions over an interval, so that the computation at runtime can be faster than directly using the function. Two techniques are implemented:

• tabulate computes the function in a table and read the points using interpolation. tabulateNd is the N dimensions version of tabulate

• tabulate_chebychev uses Chebyshev polynomial approximation

#### Comparison program example

process = line(50000, r0, r1) <: FX-tb,FX-ch : par(i, 2, maxerr)
with {
C = 0;
FX = sin;
NX = 50;
CD = 3;
r0 = 0;
r1 = ma.PI;
tb(x) = ba.tabulate(C, FX, NX*(CD+1), r0, r1, x).cub;
ch(x) = ba.tabulate_chebychev(C, FX, NX, CD, r0, r1, x);
maxerr = abs : max ~ _;
line(n, x0, x1) = x0 + (ba.time%n)/n * (x1-x0);
};

### (ba.)tabulate

Tabulate a 1D function over the range [r0, r1] for access via nearest-value, linear, cubic interpolation. In other words, the uniformly tabulated function can be evaluated using interpolation of order 0 (none), 1 (linear), or 3 (cubic).

#### Usage

tabulate(C, FX, S, r0, r1, x).(val|lin|cub) : _
• C: whether to dynamically force the x value to the range [r0, r1]: 1 forces the check, 0 deactivates it (constant numerical expression)
• FX: unary function Y=F(X) with one output (scalar function of one variable)
• S: size of the table in samples (constant numerical expression)
• r0: minimum value of argument x
• r1: maximum value of argument x
tabulate(C, FX, S, r0, r1, x).val uses the value in the table closest to x
tabulate(C, FX, S, r0, r1, x).lin evaluates at x using linear interpolation between the closest stored values
tabulate(C, FX, S, r0, r1, x).cub evaluates at x using cubic interpolation between the closest stored values

#### Example test program

midikey2hz(mk) = ba.tabulate(1, ba.midikey2hz, 512, 0, 127, mk).lin;
process = midikey2hz(ba.time), ba.midikey2hz(ba.time);

### (ba.)tabulate_chebychev

Tabulate a 1D function over the range [r0, r1] for access via Chebyshev polynomial approximation. In contrast to (ba.)tabulate, which interpolates only between tabulated samples, (ba.)tabulate_chebychev stores coefficients of Chebyshev polynomials that are evaluated to provide better approximations in many cases. Two new arguments controlling this are NX, the number of segments into which [r0, r1] is divided, and CD, the maximum Chebyshev polynomial degree to use for each segment. A rdtable of size NX*(CD+1) is internally used.

Note that processing r1 the last point in the interval is not safe. So either be sure the input stays in [r0, r1[ or use C = 1.

#### Usage

_ : tabulate_chebychev(C, FX, NX, CD, r0, r1) : _
• C: whether to dynamically force the value to the range [r0, r1]: 1 forces the check, 0 deactivates it (constant numerical expression)
• FX: unary function Y=F(X) with one output (scalar function of one variable)
• NX: number of segments for uniformly partitioning [r0, r1] (constant numerical expression)
• CD: maximum polynomial degree for each Chebyshev polynomial (constant numerical expression)
• r0: minimum value of argument x
• r1: maximum value of argument x

#### Example test program

midikey2hz_chebychev(mk) = ba.tabulate_chebychev(1, ba.midikey2hz, 100, 4, 0, 127, mk);
process = midikey2hz_chebychev(ba.time), ba.midikey2hz(ba.time);

### (ba.)tabulateNd

Tabulate an nD function for access via nearest-value or linear or cubic interpolation. In other words, the tabulated function can be evaluated using interpolation of order 0 (none), 1 (linear), or 3 (cubic).

The table size and parameter range of each dimension can and must be separately specified. You can use it anywhere you have an expensive function with multiple parameters with known ranges. You could use it to build a wavetable synth, for example.

The number of dimensions is deduced from the number of parameters you give, see below.

Note that processing the last point in each interval is not safe. So either be sure the inputs stay in their respective ranges, or use C = 1. Similarly for the first point when doing cubic interpolation.

#### Usage

tabulateNd(C, function, (parameters) ).(val|lin|cub) : _
• C: whether to dynamically force the parameter values for each dimension to the ranges specified in parameters: 1 forces the check, 0 deactivates it (constant numerical expression)
• function: the function we want to tabulate. Can have any number of inputs, but needs to have just one output.
• (parameters): sizes, ranges and read values. Note: these need to be in brackets, to make them one entity.

If N is the number of dimensions, we need:

• N times S: number of values to store for this dimension (constant numerical expression)
• N times r0: minimum value of this dimension
• N times r1: maximum value of this dimension
• N times x: read value of this dimension

By providing these parameters, you indirectly specify the number of dimensions; it's the number of parameters divided by 4.

The user facing functions are:

tabulateNd(C, function, S, parameters).val
• Uses the value in the table closest to x.
tabulateNd(C, function, S, parameters).lin
• Evaluates at x using linear interpolation between the closest stored values.
tabulateNd(C, function, S, parameters).cub
• Evaluates at x using cubic interpolation between the closest stored values.

#### Example test program

powSin(x,y) = sin(pow(x,y)); // The function we want to tabulate
powSinTable(x,y) = ba.tabulateNd(1, powSin, (sizeX,sizeY, rx0,ry0, rx1,ry1, x,y) ).lin;
sizeX = 512; // table size of the first parameter
sizeY = 512; // table size of the second parameter
rx0 = 2; // start of the range of the first parameter
ry0 = 2; // start of the range of the second parameter
rx1 = 10; // end of the range of the first parameter
ry1 = 10; // end of the range of the second parameter
x = hslider("x", rx0, rx0, rx1, 0.001):si.smoo;
y = hslider("y", ry0, ry0, ry1, 0.001):si.smoo;
process = powSinTable(x,y), powSin(x,y);

#### Working principle

The .val function just outputs the closest stored value. The .lin and .cub functions interpolate in N dimensions.

##### Multi dimensional interpolation

To understand what it means to interpolate in N dimensions, here's a quick reminder on the general principle of 2D linear interpolation:

• We have a grid of values, and we want to find the value at a point (x, y) within this grid.
• We first find the four closest points (A, B, C, D) in the grid surrounding the point (x, y).

Then, we perform linear interpolation in the x-direction between points A and B, and between points C and D. This gives us two new points E and F. Finally, we perform linear interpolation in the y-direction between points E and F to get our value.

To implement this in Faust, we need N sequential groups of interpolators, where N is the number of dimensions.
Each group feeds into the next, with the last "group" being a single interpolator, and the group before it containing one interpolator for each input of the group it's feeding.

Some examples:

• Our 2D linear example has two interpolators feeding into one.
• A 3D linear interpolator has four interpolators feeding into two, feeding into one.
• A 2D cubic interpolater has four interpolators feeding into one.
• A 3D cubic interpolator has sixteen interpolators feeding into four, feeding into one.

To understand which values we need to look up, let's consider the 2D linear example again. The four values going into the first group represent the four closest points (A, B, C, D) mentioned above.

1) The first interpolator gets:

• The closest value that is stored (A)
• The next value in the x dimension, keeping y fixed (B)

2) The second interpolator gets:

• One step over in the y dimension, keeping x fixed (C)
• One step over in both the x dimension and the y dimension (D)

The outputs of these two interpolators are points E and F. In other words: the interpolated x values and, respectively, the following y values:

• The closest stored value of the y dimension
• One step forward in the y dimension

The last interpolator takes these two values and interpolates them in the y dimension.

To generalize for N dimensions and linear interpolation:

• The first group has 2^(n-1) parallel interpolators interpolating in the first dimension.
• The second group has 2^(n-2) parallel interpolators interpolating in the second dimension.
• The process continues until the n-th group, which has a single interpolator interpolating in the n-th dimension.

The same principle applies to the cubic interpolation in nD. The only difference is that there would be 4^(n-1) parallel interpolators in the first group, compared to 2^(n-1) for linear interpolation.

This is what the mixers function does.

Besides the values, each interpolator also needs to know the weight of each value in it's output.
Let's call this d, like in ba.interpolate. It is the same for each group of interpolators, since it correlates to a dimension.
It's value is calculated the similarly to ba.interpolate:

• First we prepare a "float table read-index" for that dimension (id in ba.tabulate)
• If the table only had that dimension and it could read a float index, what would it be.
• Then we int the float index to get the value we have stored that is closest to, but lower than the input value; the actual index for that dimension. Our d is the difference between the float index and the actual index.

The ids function calculates the id for each dimension and inside the mixer function they get turned into ds.

##### Storage method

The elephant in the room is: how do we get these indexes? For that we need to know how the values are stored. We use one big table to store everything.

To understand the concept, let's look at the 2D example again, and then we'll extend it to 3d and the general nD case.

Let's say we have a 2D table with dimensions A and B where: A has 3 values between 0 and 5 and B has 4 values between 0 and 1. The 1D array representation of this 2D table will have a size of 3 * 4 = 12.

The values are stored in the following way:

• First 3 values: A is 0, then 3, then 5 while B is at 0.
• Next 3 values: A changes from 0 to 5 while B is at 1/3.
• Next 3 values: A changes from 0 to 5 while B is at 2/3.
• Last 3 values: A changes from 0 to 5 while B is at 1.

For the 3D example, let's extend the 2D example with an additional dimension C having 2 values between 0 and 2. The total size will be 3 * 4 * 2 = 24.

The values are stored like so:

• First 3 values: A changes from 0 to 5, B is at 0, and C is at 0.
• Next 3 values: A changes from 0 to 5, B is at 1/3, and C is at 0.
• Next 3 values: A changes from 0 to 5, B is at 2/3, and C is at 0.
• Next 3 values: A changes from 0 to 5, B is at 1, and C is at 0.

The last 12 values are the same as the first 12, but with C at 2.

For the general n-dimensional case, we iterate through all dimensions, changing the values of the innermost dimension first, then moving towards the outer dimensions.

To get the float read index (id) corresponding to a particular dimension, we scale the function input value to be between 0 and 1, and multiply it by the size of that dimension minus one.

To understand how we get the readIndexfor .val, let's work trough how we'd do it in our 2D linear example.
For simplicity's sake, the ranges of the inputs to our function are both 0 to 1.
Say we wanted to read the value closest to x=0.5 and y=0, so the id of x is 1 (the second value) and the id of y is 0 (first value). In this case, the read index is just the id of x, rounded to the nearest integer, just like in ba.tabulate.

If we want to read the value belonging to x=0.5 and y=2/3, things get more complicated. The id for y is now 2, the third value. For each step in the y direction, we need to increase the index by 3, the number of values that are stored for x. So the influence of the y is: the size of x times the rounded id of y. The final read index is the rounded id of x plus the influence of y.

For the general nD case, we need to do the same operation N times, each feeding into the next. This operation is the riN function. We take four parameters: the size of the dimension before it prevSize, the index of the previous dimension prevIX, the current size sizeX and the current id idX. riN has 2 outputs, the size, for feeding into the next dimension's prevSize, and the read index feeding into the next dimension's prevIX.
The size is the sizeX times prevSize. The read index is the rounded idX times prevSize added to the prevIX. Our final readIndex is the read index output of the last dimension.

To get the read values for the interpolators need a pattern of offsets in each dimension, since we are looking for the read indexes surrounding the point of interest. These offsets are best explained by looking at the code of tabulate2d, the hardcoded 2D version:

tabulate2d(C,function, sizeX,sizeY, rx0,ry0, rx1,ry1, x,y) =
environment {
size = sizeX*sizeY;
// Maximum X index to access
midX = sizeX-1;
// Maximum Y index to access
midY = sizeY-1;
// Maximum total index to access
mid = size-1;
// Create the table
wf = function(wfX,wfY);
// Prepare the 'float' table read index for X
idX = (x-rx0)/(rx1-rx0)*midX;
// Prepare the 'float' table read index for Y
idY = ((y-ry0)/(ry1-ry0))*midY;
// table creation X:
wfX =
rx0+float(ba.time%sizeX)*(rx1-rx0)
/float(midX);
// table creation Y:
wfY =
ry0+
((float(ba.time-(ba.time%sizeX))
/float(sizeX))
*(ry1-ry0))
/float(midY);

// Limit the table read index in [0, mid] if C = 1
rid(x,mid, 0) = x;
rid(x,mid, 1) = max(0, min(x, mid));

// Tabulate a binary 'FX' function on a range [rx0, rx1] [ry0, ry1]
val(x,y) =
rid(
rid(int(idX+0.5),midX, C)
+yOffset
, mid, C);
yOffset = sizeX*rid(int(idY),midY,C);

// Tabulate a binary 'FX' function over the range [rx0, rx1] [ry0, ry1] with linear interpolation
lin =
it.interpolate_linear(
dy
, it.interpolate_linear(dx,v0,v1)
, it.interpolate_linear(dx,v2,v3))
with {
i0 = rid(int(idX), midX, C)+yOffset;
i1 = i0+1;
i2 = i0+sizeX;
i3 = i1+sizeX;
dx  = idX-int(idX);
dy  = idY-int(idY);
v0 = rdtable(size, wf, rid(i0, mid, C));
v1 = rdtable(size, wf, rid(i1, mid, C));
v2 = rdtable(size, wf, rid(i2, mid, C));
v3 = rdtable(size, wf, rid(i3, mid, C));
};

// Tabulate a binary 'FX' function over the range [rx0, rx1] [ry0, ry1] with cubic interpolation
cub =
it.interpolate_cubic(
dy
, it.interpolate_cubic(dx,v0,v1,v2,v3)
, it.interpolate_cubic(dx,v4,v5,v6,v7)
, it.interpolate_cubic(dx,v8,v9,v10,v11)
, it.interpolate_cubic(dx,v12,v13,v14,v15)
)
with {
i0  = i4-sizeX;
i1  = i5-sizeX;
i2  = i6-sizeX;
i3  = i7-sizeX;

i4  = i5-1;
i5  = rid(int(idX), midX, C)+yOffset;
i6  = i5+1;
i7  = i6+1;

i8  = i4+sizeX;
i9  = i5+sizeX;
i10 = i6+sizeX;
i11 = i7+sizeX;

i12 = i4+(2*sizeX);
i13 = i5+(2*sizeX);
i14 = i6+(2*sizeX);
i15 = i7+(2*sizeX);

dx  = idX-int(idX);
dy  = idY-int(idY);
v0  = rdtable(size, wf, rid(i0 , mid, C));
v1  = rdtable(size, wf, rid(i1 , mid, C));
v2  = rdtable(size, wf, rid(i2 , mid, C));
v3  = rdtable(size, wf, rid(i3 , mid, C));
v4  = rdtable(size, wf, rid(i4 , mid, C));
v5  = rdtable(size, wf, rid(i5 , mid, C));
v6  = rdtable(size, wf, rid(i6 , mid, C));
v7  = rdtable(size, wf, rid(i7 , mid, C));
v8  = rdtable(size, wf, rid(i8 , mid, C));
v9  = rdtable(size, wf, rid(i9 , mid, C));
v10 = rdtable(size, wf, rid(i10, mid, C));
v11 = rdtable(size, wf, rid(i11, mid, C));
v12 = rdtable(size, wf, rid(i12, mid, C));
v13 = rdtable(size, wf, rid(i13, mid, C));
v14 = rdtable(size, wf, rid(i14, mid, C));
v15 = rdtable(size, wf, rid(i15, mid, C));
};
};

In the interest of brevity, we'll stop explaining here. If you have any more questions, feel free to open an issue on faustlibraries and tag @magnetophon.

## Selectors (Conditions)

### (ba.)if

if-then-else implemented with a select2. WARNING: since select2 is strict (always evaluating both branches), the resulting if does not have the usual "lazy" semantic of the C if form, and thus cannot be used to protect against forbidden computations like division-by-zero for instance.

#### Usage

• if(cond, then, else) : _

Where:

• cond: condition
• then: signal selected while cond is true
• else: signal selected while cond is false

### (ba.)ifNc

if-then-elseif-then-...elsif-then-else implemented on top of ba.if.

#### Usage

ifNc((cond1,then1, cond2,then2, ... condN,thenN, else)) : _
or
ifNc(Nc, cond1,then1, cond2,then2, ... condN,thenN, else) : _
or
cond1,then1, cond2,then2, ... condN,thenN, else : ifNc(Nc) : _

Where:

• Nc : number of branches/conditions (constant numerical expression)
• condX: condition
• thenX: signal selected if condX is the 1st true condition
• else: signal selected if all the cond1-condN conditions are false

#### Example test program

process(x,y) = ifNc((x<y,-1, x>y,+1, 0));
or
process(x,y) = ifNc(2, x<y,-1, x>y,+1, 0);
or
process(x,y) = x<y,-1, x>y,+1, 0 : ifNc(2);

outputs -1 if x<y, +1 if x>y, 0 otherwise.

### (ba.)ifNcNo

ifNcNo(Nc,No) is similar to ifNc(Nc) above but then/else branches have No outputs.

#### Usage

ifNcNo(Nc,No, cond1,then1, cond2,then2, ... condN,thenN, else) : sig.bus(No)

Where:

• Nc : number of branches/conditions (constant numerical expression)
• No : number of outputs (constant numerical expression)
• condX: condition
• thenX: list of No signals selected if condX is the 1st true condition
• else: list of No signals selected if all the cond1-condN conditions are false

#### Example test program

process(x) = ifNcNo(2,3, x<0, -1,-1,-1, x>0, 1,1,1, 0,0,0);

outputs -1,-1,-1 if x<0, 1,1,1 if x>0, 0,0,0 otherwise.

### (ba.)selector

Selects the ith input among n at compile time.

#### Usage

selector(I,N)
_,_,_,_ : selector(2,4) : _ // selects the 3rd input among 4

Where:

• I: input to select (int, numbered from 0, known at compile time)
• N: number of inputs (int, known at compile time, N > I)

There is also cselector for selecting among complex input signals of the form (real,imag).

### (ba.)select2stereo

Select between 2 stereo signals.

#### Usage

_,_,_,_ : select2stereo(bpc) : _,_

Where:

• bpc: the selector switch (0/1)

### (ba.)selectn

Selects the ith input among N at run time.

#### Usage

selectn(N,i)
_,_,_,_ : selectn(4,2) : _ // selects the 3rd input among 4

Where:

• N: number of inputs (int, known at compile time, N > 0)
• i: input to select (int, numbered from 0)

#### Example test program

N = 64;
process = par(n, N, (par(i,N,i) : selectn(N,n)));

### (ba.)selectbus

Select a bus among NUM_BUSES buses, where each bus has BUS_SIZE outputs. The order of the signal inputs should be the signals of the first bus, the signals of the second bus, and so on.

#### Usage

process = si.bus(BUS_SIZE*NUM_BUSES) : selectbus(BUS_SIZE, NUM_BUSES, id) : si.bus(BUS_SIZE);

Where:

• BUS_SIZE: number of outputs from each bus (int, known at compile time).
• NUM_BUSES: number of buses (int, known at compile time).
• id: index of the bus to select (int, 0<=id<NUM_BUSES)

### (ba.)selectxbus

Like ba.selectbus, but with a cross-fade when selecting the bus using the same technique than ba.selectmulti.

#### Usage

process = si.bus(BUS_SIZE*NUM_BUSES) : selectbus(BUS_SIZE, NUM_BUSES, FADE, id) : si.bus(BUS_SIZE);

Where:

• BUS_SIZE: number of outputs from each bus (int, known at compile time).
• NUM_BUSES: number of buses (int, known at compile time).
• id: index of the bus to select (int, 0<=id<NUM_BUSES)

### (ba.)selectmulti

Selects the ith circuit among N at run time (all should have the same number of inputs and outputs) with a crossfade.

#### Usage

selectmulti(n,lgen,id)

Where:

• lgen: list of circuits
• id: circuit to select (int, numbered from 0)

#### Example test program

process = selectmulti(ma.SR/10, ((3,9),(2,8),(5,7)), nentry("choice", 0, 0, 2, 1));
process = selectmulti(ma.SR/10, ((_*3,_*9),(_*2,_*8),(_*5,_*7)), nentry("choice", 0, 0, 2, 1));

### (ba.)selectoutn

Route input to the output among N at run time.

#### Usage

_ : selectoutn(N, i) : si.bus(N)

Where:

• N: number of outputs (int, known at compile time, N > 0)
• i: output number to route to (int, numbered from 0) (i.e. slider)

#### Example test program

process = 1 : selectoutn(3, sel) : par(i, 3, vbargraph("v.bargraph %i", 0, 1));
sel = hslider("volume", 0, 0, 2, 1) : int;

## Other

### (ba.)latch

Latch input on positive-going transition of trig: "records" the input when trig switches from 0 to 1, outputs a frozen values everytime else.

#### Usage

_ : latch(trig) : _

Where:

• trig: hold trigger (0 for hold, 1 for bypass)

### (ba.)sAndH

Sample And Hold: "records" the input when trig is 1, outputs a frozen value when trig is 0. sAndH is a standard Faust function.

#### Usage

_ : sAndH(trig) : _

Where:

• trig: hold trigger (0 for hold, 1 for bypass)

### (ba.)downSample

Down sample a signal. WARNING: this function doesn't change the rate of a signal, it just holds samples... downSample is a standard Faust function.

#### Usage

_ : downSample(freq) : _

Where:

• freq: new rate in Hz

### (ba.)downSampleCV

A version of ba.downSample where the frequency parameter has been replaced by an amount parameter that is in the range zero to one. WARNING: this function doesn't change the rate of a signal, it just holds samples...

#### Usage

_ : downSampleCV(amount) : _

Where:

• amount: The amount of down-sampling to perform [0..1]

### (ba.)peakhold

Outputs current max value above zero.

#### Usage

_ : peakhold(mode) : _

Where:

mode means:

0 - Pass through. A single sample 0 trigger will work as a reset.

1 - Track and hold max value.

### (ba.)peakholder

While peak-holder functions are scarcely discussed in the literature (please do send me an email if you know otherwise), common sense tells that the expected behaviour should be as follows: the absolute value of the input signal is compared with the output of the peak-holder; if the input is greater or equal to the output, a new peak is detected and sent to the output; otherwise, a timer starts and the current peak is held for N samples; once the timer is out and no new peaks have been detected, the absolute value of the current input becomes the new peak.

#### Usage

_ : peakholder(holdTime) : _

Where:

• holdTime: hold time in samples

### (ba.)kr2ar

Force a control rate signal to be used as an audio rate signal.

#### Usage

hslider("freq", 200, 200, 2000, 0.1) : kr2ar;

### (ba.)impulsify

Turns a signal into an impulse with the value of the current sample (0.3,0.2,0.1 becomes 0.3,0.0,0.0). This function is typically used with a button to turn its output into an impulse. impulsify is a standard Faust function.

#### Usage

button("gate") : impulsify;

### (ba.)automat

Record and replay in a loop the successives values of the input signal.

#### Usage

hslider(...) : automat(t, size, init) : _

Where:

• t: tempo in BPM
• size: number of items in the loop
• init: init value in the loop

### (ba.)bpf

bpf is an environment (a group of related definitions) that can be used to create break-point functions. It contains three functions:

• start(x,y) to start a break-point function
• end(x,y) to end a break-point function
• point(x,y) to add intermediate points to a break-point function, using linear interpolation

A minimal break-point function must contain at least a start and an end point:

f = bpf.start(x0,y0) : bpf.end(x1,y1);

A more involved break-point function can contains any number of intermediate points:

f = bpf.start(x0,y0) : bpf.point(x1,y1) : bpf.point(x2,y2) : bpf.end(x3,y3);

In any case the x_{i} must be in increasing order (for all i, x_{i} < x_{i+1}). For example the following definition:

f = bpf.start(x0,y0) : ... : bpf.point(xi,yi) : ... : bpf.end(xn,yn);

implements a break-point function f such that:

• f(x) = y_{0} when x < x_{0}
• f(x) = y_{n} when x > x_{n}
• f(x) = y_{i} + (y_{i+1}-y_{i})*(x-x_{i})/(x_{i+1}-x_{i}) when x_{i} <= x and x < x_{i+1}

In addition to bpf.point, there are also step and curve functions:

• step(x,y) to add a flat section
• step_end(x,y) to end with a flat section
• curve(B,x,y) to add a curved section
• curve_end(B,x,y) to end with a curved section

These functions can be combined with the other bpf functions.

Here's an example using bpf.step:

f(x) = x : bpf.start(0,0) : bpf.step(.2,.3) : bpf.step(.4,.6) : bpf.step_end(1,1);

For x < 0.0, the output is 0.0. For 0.0 <= x < 0.2, the output is 0.0. For 0.2 <= x < 0.4, the output is 0.3. For 0.4 <= x < 1.0, the output is 0.6. For 1.0 <= x, the output is 1.0

For the curve functions, B (compile-time constant) is a "bias" value strictly greater than zero and less than or equal to 1. When B is 0.5, the output curve is exactly linear and equivalent to bpf.point. When B is less than 0.5, the output is biased towards the y value of the previous breakpoint. When B is greater than 0.5, the output is biased towards the y value of the curve breakpoint. Here's an example:

f = bpf.start(0,0) : bpf.curve(.15,.5,.5) : bpf.curve_end(.85,1,1);

In the following example, the output is biased towards zero (the latter y value) instead of being a linear ramp from 1 to 0.

f = bpf.start(0,1) : bpf.curve_end(.9,1,0);

bpf is a standard Faust function.

### (ba.)listInterp

Linearly interpolates between the elements of a list.

#### Usage

index = 1.69; // range is 0-4
process = listInterp((800,400,350,450,325),index);

Where:

• index: the index (float) to interpolate between the different values. The range of index depends on the size of the list.

### (ba.)bypass1

Takes a mono input signal, route it to e and bypass it if bpc = 1. When bypassed, e is feed with zeros so that its state is cleanup up. bypass1 is a standard Faust function.

#### Usage

_ : bypass1(bpc,e) : _

Where:

• bpc: bypass switch (0/1)
• e: a mono effect

### (ba.)bypass2

Takes a stereo input signal, route it to e and bypass it if bpc = 1. When bypassed, e is feed with zeros so that its state is cleanup up. bypass2 is a standard Faust function.

#### Usage

_,_ : bypass2(bpc,e) : _,_

Where:

• bpc: bypass switch (0/1)
• e: a stereo effect

### (ba.)bypass1to2

Bypass switch for effect e having mono input signal and stereo output. Effect e is bypassed if bpc = 1.When bypassed, e is feed with zeros so that its state is cleanup up. bypass1to2 is a standard Faust function.

#### Usage

_ : bypass1to2(bpc,e) : _,_

Where:

• bpc: bypass switch (0/1)
• e: a mono-to-stereo effect

Bypass an arbitrary (N x N) circuit with 'n' samples crossfade. Inputs and outputs signals are faded out when 'e' is bypassed, so that 'e' state is cleanup up. Once bypassed the effect is replaced by par(i,N,_). Bypassed circuits can be chained.

#### Usage

or
• n: number of samples for the crossfade
• b: bypass switch (0/1)
• e: N x N circuit

#### Example test program

process = bypass_fade(ma.SR/10, checkbox("bypass echo"), echo);
process = bypass_fade(ma.SR/10, checkbox("bypass reverb"), freeverb);

### (ba.)toggle

Triggered by the change of 0 to 1, it toggles the output value between 0 and 1.

_ : toggle : _

#### Example test program

button("toggle") : toggle : vbargraph("output", 0, 1)
(an.amp_follower(0.1) > 0.01) : toggle : vbargraph("output", 0, 1) // takes audio input

### (ba.)on_and_off

The first channel set the output to 1, the second channel to 0.

#### Usage

_,_ : on_and_off : _

#### Example test program

button("on"), button("off") : on_and_off : vbargraph("output", 0, 1)

### (ba.)bitcrusher

Produce distortion by reduction of the signal resolution.

#### Usage

_ : bitcrusher(nbits) : _

Where:

• nbits: the number of bits of the wanted resolution

## Sliding Reduce

Provides various operations on the last n samples using a high order slidingReduce(op,n,maxN,disabledVal,x) fold-like function:

• slidingSum(n): the sliding sum of the last n input samples, CPU-light
• slidingSump(n,maxN): the sliding sum of the last n input samples, numerically stable "forever"
• slidingMax(n,maxN): the sliding max of the last n input samples
• slidingMin(n,maxN): the sliding min of the last n input samples
• slidingMean(n): the sliding mean of the last n input samples, CPU-light
• slidingMeanp(n,maxN): the sliding mean of the last n input samples, numerically stable "forever"
• slidingRMS(n): the sliding RMS of the last n input samples, CPU-light
• slidingRMSp(n,maxN): the sliding RMS of the last n input samples, numerically stable "forever"

#### Working Principle

If we want the maximum of the last 8 values, we can do that as:

simpleMax(x) =
(
(
max(x@0,x@1),
max(x@2,x@3)
) :max
),
(
(
max(x@4,x@5),
max(x@6,x@7)
) :max
)
:max;

max(x@2,x@3) is the same as max(x@0,x@1)@2 but the latter re-uses a value we already computed,so is more efficient. Using the same trick for values 4 trough 7, we can write:

efficientMax(x)=
(
(
max(x@0,x@1),
max(x@0,x@1)@2
) :max
),
(
(
max(x@0,x@1),
max(x@0,x@1)@2
) :max@4
)
:max;

We can rewrite it recursively, so it becomes possible to get the maximum at have any number of values, as long as it's a power of 2.

recursiveMax =
case {
(1,x) => x;
(N,x) => max(recursiveMax(N/2,x), recursiveMax(N/2,x)@(N/2));
};

What if we want to look at a number of values that's not a power of 2? For each value, we will have to decide whether to use it or not. If n is bigger than the index of the value, we use it, otherwise we replace it with (0-(ma.MAX)):

variableMax(n,x) =
max(
max(
(
(x@0 : useVal(0)),
(x@1 : useVal(1))
):max,
(
(x@2 : useVal(2)),
(x@3 : useVal(3))
):max
),
max(
(
(x@4 : useVal(4)),
(x@5 : useVal(5))
):max,
(
(x@6 : useVal(6)),
(x@7 : useVal(7))
):max
)
)
with {
useVal(i) = select2((n>=i) , (0-(ma.MAX)),_);
};

Now it becomes impossible to re-use any values. To fix that let's first look at how we'd implement it using recursiveMax, but with a fixed n that is not a power of 2. For example, this is how you'd do it with n=3:

binaryMaxThree(x) =
(
recursiveMax(1,x)@0, // the first x
recursiveMax(2,x)@1  // the second and third x
):max;

n=6

binaryMaxSix(x) =
(
recursiveMax(2,x)@0, // first two
recursiveMax(4,x)@2  // third trough sixth
):max;

Note that recursiveMax(2,x) is used at a different delay then in binaryMaxThree, since it represents 1 and 2, not 2 and 3. Each block is delayed the combined size of the previous blocks.

n=7

binaryMaxSeven(x) =
(
(
recursiveMax(1,x)@0, // first x
recursiveMax(2,x)@1  // second and third
):max,
(
recursiveMax(4,x)@3  // fourth trough seventh
)
):max;

To make a variable version, we need to know which powers of two are used, and at which delay time.

Then it becomes a matter of:

• lining up all the different block sizes in parallel: sequentialOperatorParOut()
• delaying each the appropriate amount: sumOfPrevBlockSizes()
• turning it on or off: useVal()
• getting the maximum of all of them: parallelOp()

In Faust, we can only do that for a fixed maximum number of values: maxN, known at compile time.

### (ba.)slidingReduce

Fold-like high order function. Apply a commutative binary operation op to the last n consecutive samples of a signal x. For example : slidingReduce(max,128,128,0-(ma.MAX)) will compute the maximum of the last 128 samples. The output is updated each sample, unlike reduce, where the output is constant for the duration of a block.

#### Usage

_ : slidingReduce(op,n,maxN,disabledVal) : _

Where:

• n: the number of values to process
• maxN: the maximum number of values to process (int, known at compile time, maxN > 0)
• op: the operator. Needs to be a commutative one.
• disabledVal: the value to use when we want to ignore a value.

In other words, op(x,disabledVal) should equal to x. For example, +(x,0) equals x and min(x,ma.MAX) equals x. So if we want to calculate the sum, we need to give 0 as disabledVal, and if we want the minimum, we need to give ma.MAX as disabledVal.

### (ba.)slidingSum

The sliding sum of the last n input samples.

It will eventually run into numerical trouble when there is a persistent dc component. If that matters in your application, use the more CPU-intensive ba.slidingSump.

#### Usage

_ : slidingSum(n) : _

Where:

• n: the number of values to process

### (ba.)slidingSump

The sliding sum of the last n input samples.

It uses a lot more CPU than ba.slidingSum, but is numerically stable "forever" in return.

#### Usage

_ : slidingSump(n,maxN) : _

Where:

• n: the number of values to process
• maxN: the maximum number of values to process (int, known at compile time, maxN > 0)

### (ba.)slidingMax

The sliding maximum of the last n input samples.

#### Usage

_ : slidingMax(n,maxN) : _

Where:

• n: the number of values to process
• maxN: the maximum number of values to process (int, known at compile time, maxN > 0)

### (ba.)slidingMin

The sliding minimum of the last n input samples.

#### Usage

_ : slidingMin(n,maxN) : _

Where:

• n: the number of values to process
• maxN: the maximum number of values to process (int, known at compile time, maxN > 0)

### (ba.)slidingMean

The sliding mean of the last n input samples.

It will eventually run into numerical trouble when there is a persistent dc component. If that matters in your application, use the more CPU-intensive ba.slidingMeanp.

#### Usage

_ : slidingMean(n) : _

Where:

• n: the number of values to process

### (ba.)slidingMeanp

The sliding mean of the last n input samples.

It uses a lot more CPU than ba.slidingMean, but is numerically stable "forever" in return.

#### Usage

_ : slidingMeanp(n,maxN) : _

Where:

• n: the number of values to process
• maxN: the maximum number of values to process (int, known at compile time, maxN > 0)

### (ba.)slidingRMS

The root mean square of the last n input samples.

It will eventually run into numerical trouble when there is a persistent dc component. If that matters in your application, use the more CPU-intensive ba.slidingRMSp.

#### Usage

_ : slidingRMS(n) : _

Where:

• n: the number of values to process

### (ba.)slidingRMSp

The root mean square of the last n input samples.

It uses a lot more CPU than ba.slidingRMS, but is numerically stable "forever" in return.

#### Usage

_ : slidingRMSp(n,maxN) : _

Where:

• n: the number of values to process
• maxN: the maximum number of values to process (int, known at compile time, maxN > 0)

## Parallel Operators

Provides various operations on N parallel inputs using a high order parallelOp(op,N,x) function:

• parallelMax(N): the max of n parallel inputs
• parallelMin(N): the min of n parallel inputs
• parallelMean(N): the mean of n parallel inputs
• parallelRMS(N): the RMS of n parallel inputs

### (ba.)parallelOp

Apply a commutative binary operation op to N parallel inputs.

#### usage

si.bus(N) : parallelOp(op,N) : _

where:

• N: the number of parallel inputs known at compile time
• op: the operator which needs to be commutative

### (ba.)parallelMax

The maximum of N parallel inputs.

#### Usage

si.bus(N) : parallelMax(N) : _

Where:

• N: the number of parallel inputs known at compile time

### (ba.)parallelMin

The minimum of N parallel inputs.

#### Usage

si.bus(N) : parallelMin(N) : _

Where:

• N: the number of parallel inputs known at compile time

### (ba.)parallelMean

The mean of N parallel inputs.

#### Usage

si.bus(N) : parallelMean(N) : _

Where:

• N: the number of parallel inputs known at compile time

### (ba.)parallelRMS

The RMS of N parallel inputs.

#### Usage

si.bus(N) : parallelRMS(N) : _

Where:

• N: the number of parallel inputs known at compile time