Prefix expression evaluators
=============================

.. currentmodule:: pyo

.. highlight:: none

Prefix audio expression evaluator. 

This family implements a tiny functional programming language that 
can be used to write synthesis or signal processing algorithms.

Objects in this category
------------------------------

- :py:class:`Expr` :     Prefix audio expression evaluator.

**API documentation**
---------------------

This API is in alpha stage and subject to future changes!

Builtin functions
-----------------

**Arithmetic operators**

- (+ x y) : returns the sum of two values.
- (- x y) : substracts the second value to the first and returns the result.
- (* x y) : returns the multiplication of two values.
- (/ x y) : returns the quotient of x/y.
- (^ x y) : returns x to the power y.
- (% x y) : returns the floating-point remainder of x/y.
- (neg x) : returns the negative of x.

**Moving phase operators**

- (++ x y) : increments its internal state by x and wrap around 0.0 and y.
- (-- x y) : decrements its internal state by x and wrap around 0.0 and y.
- (~ x y) : generates a periodic ramp from 0 to 1 with frequency x and phase y.

**Conditional operators**

- (< x y) : returns 1 if x is less than y, otherwise returns 0.
- (<= x y) : returns 1 if x is less than or equal to y, otherwise returns 0.
- (> x y) : returns 1 if x is greater than y, otherwise returns 0.
- (>= x y) : returns 1 if x is greater than or equal to y, otherwise returns 0.
- (== x y) : returns 1 if x is equal to y, otherwise returns 0.
- (!= x y) : returns 1 if x is not equal to y, otherwise returns 0.
- (if (cond) (then) (else)) : returns then for any non-zero value of cond, otherwise returns else.
- (and x y) : returns 1 if both x and y are not 0, otherwise returns 0.
- (or x y) : returns 1 if one of x or y are not 0, otherwise returns 0.

**Trigonometric functions**

- (sin x) : returns the sine of an angle of x radians.
- (cos x) : returns the cosine of an angle of x radians.
- (tan x) : returns the tangent of x radians.
- (tanh x) : returns the hyperbolic tangent of x radians.
- (atan x) : returns the principal value of the arc tangent of x, expressed in radians.
- (atan2 x y) : returns the principal value of the arc tangent of y/x, expressed in radians.

**Power and logarithmic functions**

- (sqrt x) : returns the square root of x.
- (log x) : returns the natural logarithm of x.
- (log2 x) : returns the binary (base-2) logarithm of x.
- (log10 x) : returns the common (base-10) logarithm of x.
- (pow x y) : returns x to the power y.

**Clipping functions**

- (abs x) : returns the absolute value of x.
- (floor x) : rounds x downward, returning the largest integral value that is not greater than x.
- (ceil x) : rounds x upward, returning the smallest integral value that is not less than x.
- (exp  x) : returns the constant e to the power x.
- (round x) : returns the integral value that is nearest to x.
- (min x y) : returns the smaller of its arguments: either x or y.
- (max x y) : returns the larger of its arguments: either x or y.
- (wrap x) : wraps x between 0 and 1.

**Random fuctions**

- (randf x y) : returns a pseudo-random floating-point number in the range between x and y.
- (randi x y) : returns a pseudo-random integral number in the range between x and y.

**Complex numbers**

- (complex x y) : returns a complex number where x is the real part and y the imaginary part.
- (real x) : returns the real part of the complex number x.
- (imag x) : returns the imaginary part of the complex number x.

**Filter functions**

- (delay x) : one sample delay.
- (sah x y) : samples and holds x value whenever y is smaller than its previous state.
- (rpole x y) : real one-pole recursive filter. returns x + last_out * y.
- (rzero x y) : real one-zero non-recursive filter. returns x - last_x * y.
- (cpole x y) : complex one-pole recursive filter. x is the complex signal to filter, y is a complex coefficient, it returns a complex signal.
- (czero x y) : complex one-zero non-recursive filter. x is the complex signal to filter, y is a complex coefficient, it returns a complex signal.

**Multi-output function**

- (out x y) : If using multiple outputs, creates an audio stream where x is the output channel and y the signal to write to the channel.

**Constants**

- (const x) : returns x.
- pi : returns an approximated value of pi.
- twopi : returns a constant with value pi*2.
- e : returns an approximated value of e.
- sr : returns the current sampling rate.

Comments
--------

A comment starts with two slashs ( // ) and ends at the end of the line::
    
    // This is a comment!

Input and Output signals
------------------------

User has access to the last buffer size of input and output samples. 

To use samples from past inputs, use $x0[n] notation, where 0 is the first
audio stream ($x1[0] would retrieve the second audio stream) and n is the
position from the current time. $x0[0] is the current input sample, $x0[-1]
is the previous one and $x0[-buffersize] is the last available input sample.

The first audio stream can also simply be named $x[0] ($x[0] is the same as
$x0[0]).

To use samples from past output, use $y0[n] notation, where 0 is the first
output audio stream ($y1[0] would retrieve the second output audio stream)
and n is the position from the current time. $y0[-1] is the previous output
and $y0[-buffersize] is the last available output sample of the stream.

The first output audio stream can also simply be named $y[-1] ($y[-1] is the
same as $y0[-1]).

If the object generates only one channel output (the default), the last
expression in the script is the output signal. Otherwise, output signals must
be created with the out function.

Here an example of a first-order IIR lowpass filter expression::

    // A first-order IIR lowpass filter
    + $x[0] (* (- $y[-1] $x[0]) 0.99)

A simple ring-modulation expression::

    // ring-modulation between the first two input signals
    * $x[0] $x1[0]

Two output channels::

    // First channel
    (out 0 (sin (* (twopi) (~ 400))))
    // Second channel
    (out 1 (sin (* (twopi) (~ 500))))

Defining custom functions
-------------------------

The `define` keyword starts the definition of a custom function::

    (define funcname (body))

funcname is the name used to call the function in the expression and body 
is the sequence of functions to execute. Arguments of the function are 
extracted directly from the body. They must be named $1, $2, $3, ..., $9.

Example of a sine wave function::

    (define osc (
        sin (* (twopi) (~ $1))
        )
    )
    // play a sine wave
    * (osc 440) 0.3


State variables
---------------

User can create state variable with the keyword `let`. This is useful
to set an intermediate state to be used in multiple places in the 
processing chain. The syntax is::

    (let #var (body))

The variable name must begin with a `#`::

    (let #sr 44100)
    (let #freq 1000)
    (let #coeff (
        ^ (e) (/ (* (* -2 (pi)) #freq) #sr)
        )
    )
    + $x[0] (* (- $y[-1] $x[0]) #coeff)

The variable is private to a function if created inside a custom function::

    (let #freq 250) // global #freq variable
    (define osc (
        (let #freq (* $1 $2)) // local #freq variable
        sin (* (twopi) (~ #freq))
        )
    )
    * (+ (osc 1 #freq) (osc 2 #freq)) 0.2

State variables can be used to do 1 sample feedback if used before created. 
Undefined variables are initialized to 0::

    (define oscloop (
            (let #xsin 
                (sin (+ (* (~ $1) (twopi)) (* #xsin $2))) // #xsin used before...
            ) // ... "let" statement finished!
            #xsin // oscloop function outputs #xsin variable
        )
    )
    * (oscloop 200 0.7) 0.3

A state variable can also contain a complex number::

    (let #v (complex 0.2 0.7)) // #v = (0.2 0.7)

User variables
--------------

User variables are created with the keyword `var`::

    (var #var (init)) 

The variable name must begin with a `#`.

They are computed only at initialization, but can be changed from the python
script with method calls (varname is a string and value is a float)::

    obj.setVar(varname, value) 

The following example shows how to control the cutoff fequency of a lowpass
filter with a user variable::

    expression = '''
    (var #freq 1000)
    (let #coeff (
        ^ e (/ (* (neg twopi) #freq) 44100)
        )
    )
    + $x[0] (* (- $y[-1] $x[0]) #coeff)
    '''
    ex = Expr(Noise(0.5), expression).out()
    freq = Sine(0.25).range(250, 10000)

    def update():
        ex.setVar("#freq", freq.get())

    pat = Pattern(update, 0.02).play()

Library importation
-------------------

Custom functions can be defined in an external file and imported with the 
`load` function::
    
    (load path/to/the/file)

The content of the file will be inserted where the load function is called
and all functions defined inside the file will then be accessible. The path
can be absolute or relative to the current working directory.

Complex numbers
---------------

A complex number is created with the `complex` function::

    (complex x y)

We can retrieve one part of a complex number with `real` and `imag` functions::

    // get the real part (x) of a number
    (real (complex x y))

If a complex number is used somewhere not waiting for a complex, real value
will be used.

If a real number is used somewhere waiting for a complex, the imaginary part
is set to 0.0.

Examples
--------

Here is some expression examples.

A first-order IIR lowpass filter::
    
    (var #sr 44100)
    (var #cutoff 1000)
    (let #coeff (exp (/ (* (* -2 (pi)) #cutoff) #sr)))
    + $x[0] (* (- $y[-1] $x[0]) #coeff)

A LFO'ed hyperbolic tangent distortion::
    
    // $1 = lfo frequency, $2 = lfo depth
    (define lfo (
            (+ (* (sin (* (twopi) (~ $1))) (- $2 1)) $2)
        )
    )
    tanh (* $x[0] (lfo .25 10))

A triangle waveform generator (use Sig(0) as input argument to bypass input)::
    
    (var #freq 440)
    // $1 = oscillator frequency
    (define triangle (
            (let #ph (~ $1))
            (- (* (min #ph (- 1 #ph)) 4) 1)
        )
    )
    triangle #freq

.. highlight:: python

**Objects**
-----------

*Expr*
----------

.. autoclass:: Expr
   :members:

   .. autoclasstoc::
