# 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. 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. samp2sec is a standard Faust function.

#### Usage

sec2samp(d) : _


Where:

• d: duration in seconds

### (ba.)db2linear

Converts a loudness in dB to a linear gain (0-1). db2linear is a standard Faust function.

#### Usage

db2linear(l) : _


Where:

• l: loudness in dB

### (ba.)linear2db

Converts a linear gain (0-1) to a loudness 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) : _


### (ba.)log2LinGain

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

#### Usage

log2LinGain(n) : _


### (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(f) : _


Where:

• f: 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.)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(f) : _


Where:

• f: frequency in Hz

## Counters and Time/Tempo Tools

### (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.

#### Usage

time : _


### (ba.)ramp

An linear ramp of 'n' samples to reach the next value

#### Usage

_ : ramp(n) : _


Where:

• n: number of samples to reach the next value

### (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.)pulse

Pulses (10000) generated at period p.

#### Usage

pulse(p) : _


Where:

• p: period as a number of samples

### (ba.)pulsen

Pulses (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) <:


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.)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

### (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)

## 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 (0: begin of list)
• n: number of elements

#### Note:

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

## 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.)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.)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:

• n: crossfade in samples
• 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));


## Other

### (ba.)latch

Latch input on positive-going transition of "clock" ("sample-and-hold").

#### Usage

_ : latch(clocksig) : _


Where:

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

### (ba.)sAndH

Sample And Hold. sAndH is a standard Faust function.

#### Usage

_ : sAndH(t) : _


Where:

• t: 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.)peakhold

Outputs current max value above zero.

#### Usage

_ : peakhold(mode) : _;


Where:

mode means: 1 - Track and hold max value.

### (ba.)peakholder

Tracks abs peak and holds peak for 'n' samples.

#### Usage

_ : peakholder(n) : _;


Where:

• n: number of samples

### (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 to the values the input signal in a loop.

#### Usage

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


### (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

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}

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

### (ba.)bypass_fade

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

_ : bypass_fade(n,b,e) : _
or

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

#### Examples

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.

#### Usage

_ : toggle : _


#### Examples

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

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


### (ba.)selectoutn

Route input to the output among N at run time.

#### Usage

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

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


## 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.INFINITY)):

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.INFINITY)),_);
};


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: the first par() statement
• delaying each the appropriate amount: sumOfPrevBlockSizes()
• turning it on or off: useVal()
• getting the maximum of all of them: combine()

In Faust, we can only do that for a fixed maximum number of values: maxN

variableBinaryMaxN(N,maxN,x) =
par(i,maxNrBits,recursiveMax(pow2(i),x)@sumOfPrevBlockSizes(N,maxN,i) : useVal(i)) : combine(maxNrBits) with {
// The sum of all the sizes of the previous blocks
sumOfPrevBlockSizes(N,maxN,0) = 0;
sumOfPrevBlockSizes(N,maxN,i) = (subseq((allBlockSizes(N,maxN)),0,i):>_);
allBlockSizes(N,maxN) = par(i, maxNrBits, pow2(i) * isUsed(i) );
maxNrBits = int2nrOfBits(maxN);
// get the maximum of all blocks
combine(2) = max;
combine(N) = max(combine(N-1),_);
// Decide wether or not to use a certain value, based on N
useVal(i) = select2(isUsed(i), (0-(ma.INFINITY)),_);
isUsed(i) = take(i+1, (int2bin(N,maxN)));
};


### (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,-(ma.INFINITY)) 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, needs to be a power of 2
• 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.INFINITY) 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.INFINITY 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 then (ba.)slidingSum(n,maxn), 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, needs to be a power of 2

### (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, needs to be a power of 2

### (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, needs to be a power of 2

### (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.)slidinRMSp.

#### Usage

_ : slidingMean(N,maxN) : _


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 then (ba.)slidingMean(n,maxn), 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, needs to be a power of 2

### (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.)slidinRMSp.

#### 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 then (ba.)slidingRMS(n,maxn), 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, needs to be a power of 2

## Parallel Operator

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