tgwaveforms.h File Reference

Type-generic waveform functions. More...

#include "waveforms.h"

Go to the source code of this file.

Macros
#define	nec_wrap(phase)
	Maps an arbitrary phase into the domain [0, 1).
#define	nec_fill_wrap(len, phase, output)
	Maps a buffer of arbitrary phases into the domain [0, 1).
#define	nec_analog_sawtooth(phase)
	Analog-like sawtooth waveform.
#define	nec_fill_analog_sawtooth(len, phase, output)
	Fills a buffer with an analog-like sawtooth waveform.
#define	nec_analog_square(phase, duty)
	Analog-like square waveform.
#define	nec_fill_analog_square(len, phase, duty, output)
	Fills a buffer with an analog-like square waveform.
#define	nec_analog_triangle(phase)
	Analog-like triangle waveform.
#define	nec_fill_analog_triangle(len, phase, output)
	Fills a buffer with an analog-like triangle waveform.
#define	nec_parabol(phase)
	Fast sine approximation waveform.
#define	nec_fill_parabol(len, phase, output)
	Fills a buffer with a fast sine approximation waveform.
#define	nec_sin(phase)
	Accurate sine approximation waveform.
#define	nec_fill_sin(len, phase, output)
	Fills a buffer with an accurate sine approximation waveform.
#define	nec_circle(phase)
	Circle waveform function.
#define	nec_fill_circle(len, phase, output)
	Fills a buffer with a circle waveform.
#define	nec_sawtooth(phase)
	Basic sawtooth waveform.
#define	nec_fill_sawtooth(len, phase, output)
	Fills a buffer with a sawtooth waveform.
#define	nec_square(phase, duty)
	Basic square waveform.
#define	nec_fill_square(len, phase, duty, output)
	Fills a buffer with a square waveform.
#define	nec_triangle(phase)
	Basic triangle waveform.
#define	nec_fill_triangle(len, phase, output)
	Fills a buffer with a triangle waveform.

Detailed Description

Type-generic waveform functions.

Macro Definition Documentation

nec_analog_sawtooth

#define nec_analog_sawtooth

(

phase

)

Value:

    _Generic((phase),\
    long double : nec_analog_sawtoothl,\
    double      : nec_analog_sawtooth,\
    float       : nec_analog_sawtoothf\
)(phase)

Analog-like sawtooth waveform.

This sawtooth waveform changes with an exponential curve to emulate a discharging capacitor (or charging, when inverted).

To be more precise, it approximates the exponential curve \(\frac{2e}{e-1}\left(e^{-x}-1\right)+1\) using a rational function.

Parameters

phase

The input phase of the waveform, in domain [0, 1).

Returns

A sample of a sawtooth waveform, with range [-1, 1].

nec_analog_square

#define nec_analog_square	(		phase,
			duty )

Value:

    _Generic((phase),\
    long double : nec_analog_squarel,\
    double      : nec_analog_square,\
    float       : nec_analog_squaref\
)((phase), (duty))

Analog-like square waveform.

This square waveform decays with an exponential curve to emulate a discharging capacitor.

To be more precise, it approximates the exponential curve \(\frac{e}{2\left(e-1\right)}\left(e^{-x}-1\right)+1\) using a rational function.

Parameters

phase	The input phase of the waveform, in domain [0, 1).
duty	The duty cycle of the waveform, in domain [0, 1].

Returns

A sample of a square waveform, with range [-1, 1].

nec_analog_triangle

#define nec_analog_triangle

(

phase

)

Value:

    _Generic((phase),\
    long double : nec_analog_trianglel,\
    double      : nec_analog_triangle,\
    float       : nec_analog_trianglef\
)(phase)

Analog-like triangle waveform.

This triangle waveform changes with an exponential curve to emulate a charging and discharging capacitor.

To be more precise, it approximates the exponential curve \(\frac{2e}{e-1}\left(e^{-x}-1\right)+1\) using a rational function.

Parameters

phase

The input phase of the waveform, in domain [0, 1).

Returns

A sample of a triangle waveform, with range [-1, 1].

nec_circle

#define nec_circle

(

phase

)

Value:

    _Generic((phase),\
    long double : nec_circlel,\
    double      : nec_circle,\
    float       : nec_circlef\
)(phase)

Circle waveform function.

This waveform looks like an alternating semicircle.

Parameters

phase

The input phase of the waveform, in domain [0, 1).

Returns

A sample of circle waveform, with range [-1, 1].

nec_fill_analog_sawtooth

#define nec_fill_analog_sawtooth	(		len,
			phase,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_analog_sawtoothl,\
    double*      : nec_fill_analog_sawtooth,\
    float*       : nec_fill_analog_sawtoothf\
)((len), (phase), (output))

Fills a buffer with an analog-like sawtooth waveform.

See also

nec_analog_sawtooth()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of input phases in domain [0, 1).
[out]	output	A buffer to be filled with samples of a sawtooth waveform, with range [-1, 1].

nec_fill_analog_square

#define nec_fill_analog_square	(		len,
			phase,
			duty,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_analog_squarel,\
    double*      : nec_fill_analog_square,\
    float*       : nec_fill_analog_squaref\
)((len), (phase), (duty), (output))

Fills a buffer with an analog-like square waveform.

See also

nec_analog_square()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of input phases in domain [0, 1).
[in]	duty	A buffer full of duty cycles in domain [0, 1].
[out]	output	A buffer to be filled with samples of a square waveform, with range [-1, 1].

nec_fill_analog_triangle

#define nec_fill_analog_triangle	(		len,
			phase,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_analog_trianglel,\
    double*      : nec_fill_analog_triangle,\
    float*       : nec_fill_analog_trianglef\
)((len), (phase), (output))

Fills a buffer with an analog-like triangle waveform.

See also

nec_analog_triangle()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of input phases in domain [0, 1).
[out]	output	A buffer to be filled with samples of a triangle waveform, with range [-1, 1].

nec_fill_circle

#define nec_fill_circle	(		len,
			phase,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_circlel,\
    double*      : nec_fill_circle,\
    float*       : nec_fill_circlef\
)((len), (phase), (output))

Fills a buffer with a circle waveform.

See also

nec_circle()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of input phases in domain [0, 1).
[out]	output	A buffer to be filled with samples of a circle waveform, with range [-1, 1].

nec_fill_parabol

#define nec_fill_parabol	(		len,
			phase,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_paraboll,\
    double*      : nec_fill_parabol,\
    float*       : nec_fill_parabolf\
)((len), (phase), (output))

Fills a buffer with a fast sine approximation waveform.

See also

nec_parabol()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of input phases in domain [0, 1).
[out]	output	A buffer to be filled with samples of an approximated sine waveform, with range [-1, 1].

nec_fill_sawtooth

#define nec_fill_sawtooth	(		len,
			phase,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_sawtoothl,\
    double*      : nec_fill_sawtooth,\
    float*       : nec_fill_sawtoothf\
)((len), (phase), (output))

Fills a buffer with a sawtooth waveform.

See also

nec_sawtooth()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of input phases in domain [0, 1).
[out]	output	A buffer to be filled with samples of a sawtooth waveform, with range [-1, 1].

nec_fill_sin

#define nec_fill_sin	(		len,
			phase,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_sinl,\
    double*      : nec_fill_sin,\
    float*       : nec_fill_sinf\
)((len), (phase), (output))

Fills a buffer with an accurate sine approximation waveform.

See also

nec_sin()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of input phases in domain [0, 1).
[out]	output	A buffer to be filled with samples of a sine waveform, with range [-1, 1].

nec_fill_square

#define nec_fill_square	(		len,
			phase,
			duty,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_squarel,\
    double*      : nec_fill_square,\
    float*       : nec_fill_squaref\
)((len), (phase), (duty), (output))

Fills a buffer with a square waveform.

See also

nec_square()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of input phases in domain [0, 1).
[in]	duty	A buffer full of duty cycles in domain [0, 1].
[out]	output	A buffer to be filled with samples of a square waveform, with range [-1, 1].

nec_fill_triangle

#define nec_fill_triangle	(		len,
			phase,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_trianglel,\
    double*      : nec_fill_triangle,\
    float*       : nec_fill_trianglef\
)((len), (phase), (output))

Fills a buffer with a triangle waveform.

See also

nec_triangle()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of input phases in domain [0, 1).
[out]	output	A buffer to be filled with samples of a triangle waveform, with range [-1, 1].

nec_fill_wrap

#define nec_fill_wrap	(		len,
			phase,
			output )

Value:

    _Generic((output),\
    long double* : nec_fill_wrapl,\
    double*      : nec_fill_wrap,\
    float*       : nec_fill_wrapf\
)((len), (phase), (output))

Maps a buffer of arbitrary phases into the domain [0, 1).

See also

nec_wrap()

Parameters

[in]	len	The length of the input and output buffers, phase and output. Must be at least 1.
[in]	phase	A buffer full of arbitrary input phases.
[out]	output	A buffer to be filled with equivalent phases to the contents of phase, but within the domain [0, 1).

nec_parabol

#define nec_parabol

(

phase

)

Value:

    _Generic((phase),\
    long double : nec_paraboll,\
    double      : nec_parabol,\
    float       : nec_parabolf\
)(phase)

Fast sine approximation waveform.

This function generates a fast approximation of a sine waveform. It has a maximum absolute error of ±0.05601, which is quite large and produces audible harmonics, so it is intended for use in oscillators where these harmonics are desirable or LFOs where they aren't perceptible.

Parameters

phase

The input phase of the waveform, in domain [0, 1).

Returns

A sample of an approximated sine waveform, with range [-1, 1].

nec_sawtooth

#define nec_sawtooth

(

phase

)

Value:

    _Generic((phase),\
    long double : nec_sawtoothl,\
    double      : nec_sawtooth,\
    float       : nec_sawtoothf\
)(phase)

Basic sawtooth waveform.

Parameters

phase

The input phase of the waveform, in domain [0, 1).

Returns

A sample of a sawtooth waveform, with range [-1, 1].

nec_sin

#define nec_sin

(

phase

)

Value:

    _Generic((phase),\
    long double : nec_sinl,\
    double      : nec_sin,\
    float       : nec_sinf\
)(phase)

Accurate sine approximation waveform.

This function generates a sine approximation. It has a maximum absolute error of ±0.0010903. This error does produce harmonics, but they are very quiet.

A 2004 DevMaster.net forum thread by a user named "Nick" titled “Fast and accurate sine/cosine” first presents a fast but inaccurate sine/cosine approximation, then demonstrates an error correction method to drastically improve the accuracy. The fast-but-inaccurate version happens to be mathematically identical to nec_parabol() once the range of [0, τ) is remapped to [0, 1).

nec_sin() Uses the error correction method presented in Nick's forum post to greatly refine the accuracy of nec_parabol().

Parameters

phase

The input phase of the waveform, in domain [0, 1).

Returns

A sample of sine waveform, with range [-1, 1].

nec_square

#define nec_square	(		phase,
			duty )

Value:

    _Generic((phase),\
    long double : nec_squarel,\
    double      : nec_square,\
    float       : nec_squaref\
)((phase), (duty))

Basic square waveform.

Parameters

phase	The input phase of the waveform, in domain [0, 1).
duty	The duty cycle of the waveform, in domain [0, 1].

Returns

A sample of a square waveform, with range [-1, 1].

nec_triangle

#define nec_triangle

(

phase

)

Value:

    _Generic((phase),\
    long double : nec_trianglel,\
    double      : nec_triangle,\
    float       : nec_trianglef\
)(phase)

Basic triangle waveform.

Parameters

phase

The input phase of the waveform, in domain [0, 1).

Returns

A sample of a triangle waveform, with range [-1, 1].

nec_wrap

#define nec_wrap

(

phase

)

Value:

    _Generic((phase),\
    long double : nec_wrapl,\
    double      : nec_wrap,\
    float       : nec_wrapf\
)(phase)

Maps an arbitrary phase into the domain [0, 1).

All of nectarine's waveform functions require an input phase within the domain [0, 1) and misbehave outside that domain. This function can be used to produce an equivalent input phase within that domain.

This is desirable when storing an oscillator's phase also, since long-running oscillators can accumulate floating point precision error as the phase increases further and further away from zero. Wrapping an oscillator's stored phase periodically can help prevent this.

Parameters

phase

An arbitrary input phase.

Returns

An equivalent phase to phase, but within the domain [0, 1).