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The Gaborator library is Copyright (C) 1992-2018 Andreas Gustafsson.
License to distribute and modify the code is hereby granted under the
terms of the GNU Affero General Public License, version 3 (henceforth,
the AGPLv3), but not under other versions of the AGPL. See the file
doc/agpl-3.0.txt for the full text of the AGPLv3.
If the terms of the AGPLv3 are not acceptable to you, commercial
licencing under a different license is possible. Please contact
info@gaborator.com for more information.

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See doc/index.html for HTML documentation.

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GNU AFFERO GENERAL PUBLIC LICENSE
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solutions will be better for different programs; see section 13 for the
specific requirements.
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU AGPL, see
<https://www.gnu.org/licenses/>.

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Copyright (C) 2017-2018 Andreas Gustafsson. This file is part of
the Gaborator library source distribution. See the file LICENSE at
the top level of the distribution for license information.
-->
<html>
<head>
<link rel="stylesheet" href="doc.css" />
<title>Gaborator Example 2: Frequency-Domain Filtering</title>
</head>
<body>
<h1>Example 2: Frequency-Domain Filtering</h1>
<h2>Introduction</h2>
<p>This example shows how to apply a filter to an audio file using
the Gaborator library, by turning the audio into spectrogram
coefficients, modifying the coefficients, and resynthesizing audio
from them.</p>
<p>The specific filter implemented here is a 3 dB/octave lowpass
filter. This is sometimes called a <i>pinking filter</i> because it
can be used to produce pink noise from white noise. In practice, the
3 dB/octave slope is only applied above some minimum frequency, for
example 20 Hz, because otherwise the gain of the filter would approach
infinity as the frequency approaches 0, and the impulse response would
have to be infinitely wide.
</p>
<p>Since the slope of this filter is not a multiple of 6 dB/octave, it
is difficult to implement as an analog filter, but by filtering
digitally in the frequency domain, arbitrary filter responses such as
this can easily be achieved.
</p>
<h2>Preamble</h2>
<pre>
#include &lt;memory.h&gt;
#include &lt;iostream&gt;
#include &lt;sndfile.h&gt;
#include &lt;gaborator/gaborator.h&gt;
int main(int argc, char **argv) {
if (argc < 3) {
std::cerr &lt;&lt; "usage: filter input.wav output.wav\n";
exit(1);
}
</pre>
<h2>Reading the Audio</h2>
<p>The code for reading the input audio file is identical to
that in <a href="render.html">Example 1</a>:</p>
<pre>
SF_INFO sfinfo;
memset(&amp;sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &amp;sfinfo);
if (! sf_in) {
std::cerr &lt;&lt; "could not open input audio file\n";
exit(1);
}
double fs = sfinfo.samplerate;
sf_count_t n_frames = sfinfo.frames;
sf_count_t n_samples = sfinfo.frames * sfinfo.channels;
std::vector&lt;float&gt; audio(n_samples);
sf_count_t n_read = sf_readf_float(sf_in, audio.data(), n_frames);
if (n_read != n_frames) {
std::cerr &lt;&lt; "read error\n";
exit(1);
}
sf_close(sf_in);
</pre>
<h2>Spectrum Analysis Parameters</h2>
<p>The spectrum analysis works much the same as in Example 1,
but uses slightly different parameters.
We use a larger number of frequency bands per octave (100)
to minimize ripple in the frequency response, and the
reference frequency argument is omitted as we don't care about the
exact alignment of the bands with respect to a musical scale.</p>
<pre>
gaborator::parameters params(100, 20.0 / fs);
gaborator::analyzer&lt;float&gt; analyzer(params);
</pre>
<h2>Precalculating Gains</h2>
<p>The filtering will be done by multiplying each spectrogram
coefficient with a frequency-dependent gain. To avoid having to
calculate the gain on the fly for each coefficient, which would
be slow, we will precalculate the gains into a vector <code>band_gains</code>
of one gain value per band, including one for the
special lowpass band that contains the frequencies from 0 to 20 Hz.</p>
<pre>
std::vector&lt;float&gt; band_gains(analyzer.bands_end());
</pre>
<p>First, we calculate the gains for the bandpass bands.
For a 3 dB/octave lowpass filter, the voltage gain needs to be
proportional to the square root of the inverse of the frequency.
To get the frequency of each band, we call the
<code>analyzer</code> method <code>band_ff()</code>, which
returns the center frequency of the band in units of the
sampling frequency. The gain is normalized to unity at 20 Hz.
</p>
<pre>
for (int band = analyzer.bandpass_bands_begin(); band &lt; analyzer.bandpass_bands_end(); band++) {
float f_hz = analyzer.band_ff(band) * fs;
band_gains[band] = 1.0 / sqrt(f_hz / 20.0);
}
</pre>
<p>The gain of the lowpass band is set to the the same value as the
lowest-frequency bandpass band, so that the overall filter gain
plateaus smoothly to a constant value below 20&nbsp;Hz.</p>
<pre>
band_gains[analyzer.band_lowpass()] = band_gains[analyzer.bandpass_bands_end() - 1];
</pre>
<h2>De-interleaving</h2>
<p>To handle stereo and other multi-channel audio files,
we will loop over the channels and filter each channel separately.
Since <i>libsndfile</i> produces interleaved samples, we first
de-interleave the current channel into a temporary vector called
<code>channel</code>:</p>
<pre>
for (sf_count_t ch = 0; ch &lt; sfinfo.channels; ch++) {
std::vector&lt;float&gt; channel(n_frames);
for (sf_count_t i = 0; i &lt; n_frames; i++)
channel[i] = audio[i * sfinfo.channels + ch];
</pre>
<h2>Spectrum Analysis</h2>
<p>Now we can spectrum analyze the current channel, producing
a set of coefficients:</p>
<pre>
gaborator::coefs&lt;float&gt; coefs(analyzer);
analyzer.analyze(channel.data(), 0, channel.size(), coefs);
</pre>
<h2>Filtering</h2>
<p>
The filtering is done using the function
<code>gaborator::apply()</code>, which applies a user-defined function to
each spectrogram coefficient. Here, that user-defined function is a
lambda expression that multiplies the coefficient by the appropriate
precalculated frequency-dependent gain, modifying the coefficient in
place. The unused <code>int64_t</code> argument is the time in units
of samples; this could be use to implement a time-varying filter if desired.</p>
<pre>
gaborator::apply(analyzer, coefs,
[&amp;](std::complex&lt;float&gt; &amp;coef, int band, int64_t) {
coef *= band_gains[band];
});
</pre>
<h2>Resynthesis</h2>
<p>We can now resynthesize audio from the filtered coefficients by
calling <code>synthesize()</code>. This is a mirror image of the call to
<code>analyze()</code>: now the coefficients are the input, and
the buffer of samples is the output. The <code>channel</code>
vector that originally contained the input samples for the channel
is now reused to hold the output samples.</p>
<pre>
analyzer.synthesize(coefs, 0, channel.size(), channel.data());
</pre>
<h2>Re-interleaving</h2>
<p>The <code>audio</code> vector that contained the
original interleaved audio is reused for the interleaved
filtered audio. This concludes the loop over the channels.
</p>
<pre>
for (sf_count_t i = 0; i &lt; n_frames; i++)
audio[i * sfinfo.channels + ch] = channel[i];
}
</pre>
<h2>Writing the Audio</h2>
<p>The filtered audio is written using <i>libsndfile</i>,
using code that closely mirrors that for reading.
Note that we use <code>SFC_SET_CLIPPING</code>
to make sure that any samples too loud for the file format
will saturate; by default, <i>libsndfile</i> makes them
wrap around, which sounds really bad.</p>
<pre>
SNDFILE *sf_out = sf_open(argv[2], SFM_WRITE, &amp;sfinfo);
if (! sf_out) {
std::cerr &lt;&lt; "could not output audio file\n";
exit(1);
}
sf_command(sf_out, SFC_SET_CLIPPING, NULL, SF_TRUE);
sf_count_t n_written = sf_writef_float(sf_out, audio.data(), n_frames);
if (n_written != n_frames) {
std::cerr &lt;&lt; "write error\n";
exit(1);
}
sf_close(sf_out);
</pre>
<h2>Postamble</h2>
<p>
We need a couple more lines of boilerplate to make the example a
complete program:
</p>
<pre>
return 0;
}
</pre>
<h2>Compiling</h2>
<p>Like <a href="render.html">Example 1</a>, this example
can be built using a one-line build command:
</p>
<pre class="build Darwin Linux NetBSD">
c++ -std=c++11 -I.. -O3 -ffast-math `pkg-config --cflags sndfile` filter.cc `pkg-config --libs sndfile` -o filter
</pre>
<p>Or using the vDSP FFT on macOS:</p>
<pre class="build Darwin">
c++ -std=c++11 -I.. -O3 -ffast-math -DGABORATOR_USE_VDSP `pkg-config --cflags sndfile` filter.cc `pkg-config --libs sndfile` -framework Accelerate -o filter
</pre>
<p>Or using PFFFT (see <a href="render.html">Example 1</a> for how to download and build PFFFT):</p>
<pre class="build Linux NetBSD">
c++ -std=c++11 -I.. -Ipffft -O3 -ffast-math -DGABORATOR_USE_PFFFT `pkg-config --cflags sndfile` render.cc pffft/pffft.o pffft/fftpack.o `pkg-config --libs sndfile` -o render
</pre>
<h2>Running</h2>
<p>To filter the file <code>guitar.wav</code> that was downloaded in
Example 1, simply run</p>
<pre class="run">
./filter guitar.wav guitar_filtered.wav
</pre>
<p>The resulting lowpass filtered audio in <code>guitar_filtered.wav</code> will
sound muffled compared to the original, but less so than it would with a
6&nbsp;dB/octave filter.</p>
<h2>Frequency response</h2>
<p>The following plot shows the actual measured frequency response of the
filter, with the expected 3 dB/octave slope above 20&nbsp;Hz and minimal
ripple:</p>
<img src="filter-response.png" alt="Frequency response plot">
</body>
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<!DOCTYPE html>
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Copyright (C) 2018 Andreas Gustafsson. This file is part of
the Gaborator library source distribution. See the file LICENSE at
the top level of the distribution for license information.
-->
<html>
<head>
<link rel="stylesheet" href="doc.css" />
<title>The Gaborator</title>
</head>
<body>
<h1>The Gaborator</h1>
<p>The Gaborator is a library that generates constant-Q spectrograms
for visualization and analysis of audio signals. It also supports an
accurate inverse transformation of the spectrogram coefficients back into
audio for spectral effects and editing.</p>
<p>The Gaborator implements the invertible constant-Q transform of
Velasco, Holighaus, D&ouml;rfler, and Grill, described in the papers
<i><a href="http://www.univie.ac.at/nonstatgab/pdf_files/dohogrve11_amsart.pdf">
Constructing an invertible constant-Q transform with nonstationary Gabor frames, 2011</a></i>
and <i><a href="http://www.univie.ac.at/nonstatgab/pdf_files/dogrhove12_amsart.pdf">
A Framework for invertible, real-time constant-Q transforms, 2012</a></i>.
</p>
<p>The Gaborator is written in C++11 and runs on POSIX systems such as
macOS, Linux, and NetBSD. It has been tested on Intel x86_64 and ARM
processors.</p>
<p>The Gaborator is open source under the GNU Affero General Public
License, version 3, and is also available for commercial licensing.
See the file <a href="LICENSE">LICENSE</a> for details.</p>
<h2>Release Notes</h2>
<p>This is the first public release of the Gaborator library. It
includes the core spectrum analysis, resynthesis, and spectrogram
rendering code, and some examples of how to use it.</p>
<p>Some features that have been implemented but are not yet ready for
release have been omitted, for example the support for parallel
analysis and synthesis using multiple CPU cores. Also, the current API
still lacks functions for convenient row- or column-wise access to
the coefficients at specific frequencies or times; the only way to
access the coefficients is the apply() method, which iterates over
the entire coefficient set in an indeterminate order.
</p>
<p>This initial release also still lacks reference documentation
formally defining the public library API. Until such documentation is
released, only the functions used in the example code should be
considered part of the API. All other functions are subject to change
or removal without notice.</p>
<h2>Example Code</h2>
<p>The following examples demonstrate the use of the library for a
couple of different applications. They are presented in a "literate
programming" style, with the code embedded in the explanatory
text rather than the other way around.
Concatenating the code fragments in each example yields a complete C++
program, which can also be found as a <code>.cc</code> file in
the <code>examples/</code> directory.</p>
<ul>
<li><a href="render.html">Example 1: Rendering a Spectrogram Image</a></li>
<li><a href="filter.html">Example 2: Frequency-Domain Filtering</a></li>
</ul>
<h2>Contact</h2>
<p>For more information, email the author at info@gaborator.com.</p>
</body>
</html>

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<!DOCTYPE html>
<!--
Copyright (C) 2017-2018 Andreas Gustafsson. This file is part of
the Gaborator library source distribution. See the file LICENSE at
the top level of the distribution for license information.
-->
<html>
<head>
<link rel="stylesheet" href="doc.css" />
<title>Gaborator Example 1: Rendering a Spectrogram Image</title>
</head>
<body>
<h1>Example 1: Rendering a Spectrogram Image</h1>
<h2>Introduction</h2>
<p>This example shows how to generate a greyscale constant-Q
spectrogram image from an audio file using the Gaborator library.
</p>
<h2>Preamble</h2>
<p>We start off with some boilerplate #includes.</p>
<pre>
#include &lt;memory.h&gt;
#include &lt;iostream&gt;
#include &lt;fstream&gt;
#include &lt;sndfile.h&gt;
</pre>
<p>The Gaborator is a header-only library &mdash; there are no C++ files
to compile, only header files to include.
The core spectrum analysis and resynthesis code is in
<code>gaborator/gaborator.h</code>, and the code for rendering
images from the spectrogram coefficients is in
<code>gaborator/render.h</code>.</p>
<pre>
#include &lt;gaborator/gaborator.h&gt;
#include &lt;gaborator/render.h&gt;
</pre>
<p>The program takes the names of the input audio file and output spectrogram
image file as command line arguments, so we check that they are present:</p>
<pre>
int main(int argc, char **argv) {
if (argc < 3) {
std::cerr &lt;&lt; "usage: render input.wav output.pgm\n";
exit(1);
}
</pre>
<h2>Reading the Audio</h2>
<p>The audio file is read using the <i>libsndfile</i> library
and stored in a <code>std::vector&lt;float&gt;</code>.
Note that although <i>libsndfile</i> is used in this example,
the Gaborator library itself does not depend or
use <i>libsndfile</i>.</p>
<pre>
SF_INFO sfinfo;
memset(&amp;sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &amp;sfinfo);
if (! sf_in) {
std::cerr &lt;&lt; "could not open input audio file\n";
exit(1);
}
double fs = sfinfo.samplerate;
sf_count_t n_frames = sfinfo.frames;
sf_count_t n_samples = sfinfo.frames * sfinfo.channels;
std::vector&lt;float&gt; audio(n_samples);
sf_count_t n_read = sf_readf_float(sf_in, audio.data(), n_frames);
if (n_read != n_frames) {
std::cerr &lt;&lt; "read error\n";
exit(1);
}
sf_close(sf_in);
</pre>
<p>In case the audio file is a stereo or multi-channel one,
mix down the channels to mono, into a new <code>std::vector&lt;float&gt;</code>:
<pre>
std::vector&lt;float&gt; mono(n_frames);
for (size_t i = 0; i &lt; (size_t)n_frames; i++) {
float v = 0;
for (size_t c = 0; c &lt; (size_t)sfinfo.channels; c++)
v += audio[i * sfinfo.channels + c];
mono[i] = v;
}
</pre>
<h2>The Spectrum Analysis Parameters</h2>
<p>Next, we need to choose some parameters for the spectrum analysis:
the frequency resolution, the frequency range, and optionally a
reference frequency.</p>
<p>The frequency resolution is specified as a number of frequency
bands per octave. A typical number for analyzing music signals is 48
bands per octave, or in other words, four bands per semitone
in the 12-note equal tempered scale.</p>
<p>The frequency range is specified by giving a minimum frequency;
this is the lowest frequency that will be included in the spectrogram
coefficients.
For audio signals, a typical minimum frequency is 20&nbsp;Hz,
the lower limit of human hearing. In the Gaborator library,
all frequencies are given in units of the sample rate rather
than in Hz, so we need to divide the 20&nbsp;Hz by the sample
rate of the input audio file: <code>20.0 / fs</code>.</p>
<p>Unlike the minimum frequency, the maximum frequency is not given
explicitly &mdash; instead, the analysis always produces coefficients
for frequencies all the way up to half the sample rate
(a.k.a. the Nyquist frequency). If you don't need the coefficients
for the highest frequencies, you can simply ignore them.</p>
<p>If desired, one of the frequency bands can be exactly aligned with
a <i>reference frequency</i>. When analyzing music signals, this is
typically 440 Hz, the standard tuning of the note <i>A<sub>4</sub></i>.
Like the minimum frequency, it is given in
units of the sample rate, so we pass <code>440.0 / fs</code>.</p>
<p>The parameters are held in an object of type
<code>gaborator::parameters</code>:
<pre>
gaborator::parameters params(48, 20.0 / fs, 440.0 / fs);
</pre>
<h2>The Spectrum Analyzer</h2>
<p>Next, we create an object of type <code>gaborator::analyzer</code>;
this is the workhorse that performs the actual spectrum analysis
(and/or resynthesis, but that's for a later example).
It is a template class, parametrized by the floating point type to
use for the calculations; this is typically <code>float</code>.
Constructing the <code>gaborator::analyzer</code> involves allocating and
precalculating all the filter coefficients and other auxiliary data needed
for the analysis and resynthesis, and this takes considerable time and memory,
so when analyzing multiple pieces of audio with the same
parameters, creating a single <code>gaborator::analyzer</code>
and reusing it is preferable to destroying and recreating it.</p>
<pre>
gaborator::analyzer&lt;float&gt; analyzer(params);
</pre>
<h2>The Spectrogram Coefficients</h2>
<p>The result of the spectrum analysis will be a set of <i>spectrogram
coefficients</i>. To store them, we will use a <code>gaborator::coefs</code>
object. Like the <code>analyzer</code>, this is a template class parametrized
by the data type. Because the layout of the coefficients is determined by
the spectrum analyzer, it must be passed as an argument to the constructor:</p>
<pre>
gaborator::coefs&lt;float&gt; coefs(analyzer);
</pre>
<h2>Running the Analysis</h2>
<p>Now we are ready to do the actual spectrum analysis,
by calling the <code>analyze</code> method of the spectrum
analyzer object.
The first argument to <code>analyze</code> is a <code>float</code> pointer
pointing to the first element in the array of samples to analyze.
The second and third arguments are of type
<code>int64_t</code> and indicate the time range covered by the
array, in units of samples. Since we are passing the whole file at
once, the beginning of the range is sample number zero, and the end is
sample number <code>mono.size()</code>. The fourth argument is a
reference to the set of coefficients that the results of the spectrum
analysis will be stored in.
</p>
<pre>
analyzer.analyze(mono.data(), 0, mono.size(), coefs);
</pre>
<h2>Rendering an Image</h2>
<p>Now there is a set of spectrogram coefficients in <code>coefs</code>.
To render them as an image, we will use the function
<code>gaborator::render_p2scale()</code>.
</p>
<p>Rendering involves two different coordinate
spaces: the time-frequency coordinates of the spectrogram
coefficients, and the x-y coordinates of the image.
The two spaces are related by an origin and a scale factor,
each with an x and y component.</p>
<p>The origin specifies the point in time-frequency space that
corresponds to the pixel coordinates (0, 0). Here, we will
use an origin where the x (time) component
is zero (the beginning of the signal), and the y (frequency) component
is the band number of the first (highest frequency) band:</p>
<pre>
int64_t x_origin = 0;
int64_t y_origin = analyzer.bandpass_bands_begin();
</pre>
<p><code>render_p2scale()</code> supports scaling the spectrogram in
both the time (horizontal) and frequency (vertical) dimension, but only
by power-of-two scale factors. These scale factors are specified
relative to a reference scale of one vertical pixel per frequency band
and one horizontal pixel per signal sample.
<p>Although a horizontal scale of one pixel per signal sample is a
mathematically pleasing reference point, this reference scale is not
used in practice because it would result in spectrogram that is much
too stretched out horizontally. A more typical scale factor might be
2<sup>10</sup> = 1024, yielding one pixel for every 1024 signal
samples, which is about one pixel per 23 milliseconds of signal at a
sample rate of 44.1 kHz.</p>
<pre>
int x_scale_exp = 10;
</pre>
<p>To ensure that the spectrogram will fit on the screen even in the
case of a long audio file, let's auto-scale it down further until
it is no more than 1000 pixels wide:</p>
<pre>
while ((n_frames &gt;&gt; x_scale_exp) &gt; 1000)
x_scale_exp++;
</pre>
<p>In the vertical, the reference scale factor of one pixel per
frequency band is reasonable, so we will use it as-is. In other words,
the vertical scale factor will be 2<sup>0</sup>.</p>
<pre>
int y_scale_exp = 0;
</pre>
<p>Next, we need to define the rectangular region of the image
coordinate space to render. Since we are rendering the entire
spectrogram rather than a tile, the top left corner of the
rectangle will have an origin of (0, 0).
</p>
<pre>
int64_t x0 = 0;
int64_t y0 = 0;
</pre>
<p>The coordinates of the bottom right corner are determined by the
length of the signal and the number of bands, respectively, taking the
scale factors into account.
The length of the signal in samples is <code>n_frames</code>,
and we get the number of bands as the difference of the end points of
the range of band numbers:
<code>analyzer.bandpass_bands_end() - analyzer.bandpass_bands_begin()</code>.
The scale factor is taken into account by right shifting by the
scale exponent.
</p>
<pre>
int64_t x1 = n_frames &gt;&gt; x_scale_exp;
int64_t y1 = (analyzer.bandpass_bands_end() - analyzer.bandpass_bands_begin()) &gt;&gt; y_scale_exp;
</pre>
<p>The right shift by <code>y_scale_exp</code> above doesn't actually
do anything because <code>y_scale_exp</code> is zero, but it would be
needed if, for example, you were to change <code>y_scale_exp</code> to
1 to get a spectrogram scaled to half the height. You could also make a
double-height spectrogram by setting <code>y_scale_exp</code> to -1,
but then you also need to change the
<code>&gt;&gt; y_scale_exp</code> to
<code>&lt;&lt; -y_scale_exp</code> since you can't shift by
a negative number.
</p>
<p>We are now ready to render the spectrogram, producing
a vector of floating-point amplitude values, one per pixel.
Although this is stored as a 1-dimensional vector of floats, its
contents should be interpreted as a 2-dimensional rectangular array of
<code>(y1 - y0)</code> rows of <code>(x1 - x0)</code> columns
each, with the row indices increasing towards lower
frequencies and column indices increasing towards later
sampling times.
</p>
<pre>
std::vector&lt;float&gt; amplitudes((x1 - x0) * (y1 - y0));
gaborator::render_p2scale(
analyzer,
coefs,
x_origin, y_origin,
x0, x1, x_scale_exp,
y0, y1, y_scale_exp,
amplitudes.data());
</pre>
<h2>Writing the Image File</h2>
<p>To keep the code simple and to avoid additional library
dependencies, the image is stored in
<code>pgm</code> (Portable GreyMap) format, which is simple
enough to be generated with just a few lines of inline code.
Each amplitude value in <code>amplitudes</code> is converted into an 8-bit
gamma corrected pixel value by calling <code>gaborator::float2pixel_8bit()</code>.
To control the brightness of the resulting image, each
amplitude value is multiplied by a gain; this may have to be adjusted
depending on the type of signal and the amount of headroom in the
recording, but a gain of about 15 often works well for typical music
signals.</p>
<pre>
float gain = 15;
std::ofstream f;
f.open(argv[2], std::ios::out | std::ios::binary);
f << "P5\n" << (x1 - x0) << ' ' << (y1 - y0) << "\n255\n";
for (size_t i = 0; i < amplitudes.size(); i++)
f.put(gaborator::float2pixel_8bit(amplitudes[i] * gain));
f.close();
</pre>
<h2>Postamble</h2>
<p>
To make the example code a complete program,
we just need to finish <code>main()</code>:
</p>
<pre>
return 0;
}
</pre>
<h2>Compiling</h2>
<p>
If you are using macOS, Linux, NetBSD, or a similar system, you can build
the example by running the following command in the <code>examples</code>
subdirectory.
You need to have <i>libsndfile</i> is installed and supported by
<code>pkg-config</code>.
</p>
<pre class="build Darwin Linux NetBSD">
c++ -std=c++11 -I.. -O3 -ffast-math `pkg-config --cflags sndfile` render.cc `pkg-config --libs sndfile` -o render
</pre>
<h2>Compiling for Speed</h2>
<p>The above build command uses the Gaborator's built-in FFT implementation,
which is simple and portable but rather slow. Performance can be
significantly improved by using a faster FFT library. On macOS, you
can use the FFT from Apple's vDSP library by defining
<code>GABORATOR_USE_VDSP</code> and linking with the <code>Accelerate</code>
framework:
</p>
<pre class="build Darwin">
c++ -std=c++11 -I.. -O3 -ffast-math -DGABORATOR_USE_VDSP `pkg-config --cflags sndfile` render.cc `pkg-config --libs sndfile` -framework Accelerate -o render
</pre>
<p>On Linux and NetBSD, you can use the PFFFT (Pretty Fast FFT) library.
You can get the latest version from
<a href="https://bitbucket.org/jpommier/pffft">https://bitbucket.org/jpommier/pffft</a>,
or the exact version that was used for testing from gaborator.com:
</p>
<!-- ftp https://bitbucket.org/jpommier/pffft/get/29e4f76ac53b.zip -->
<pre class="build Linux NetBSD">
wget http://download.gaborator.com/mirror/pffft/29e4f76ac53b.zip
unzip 29e4f76ac53b.zip
mv jpommier-pffft-29e4f76ac53b pffft
</pre>
<p>Then, compile it:</p>
<pre class="build Linux NetBSD">
cc -c -O3 -ffast-math pffft/pffft.c -o pffft/pffft.o
</pre>
<p>PFFFT is single precision only, but it comes with a copy of FFTPACK which can
be used for double-precision FFTs. Let's compile that, too:</p>
<pre class="build Linux NetBSD">
cc -c -O3 -ffast-math -DFFTPACK_DOUBLE_PRECISION pffft/fftpack.c -o pffft/fftpack.o
</pre>
<p>Then build the example and link it with both PFFFT and FFTPACK:</p>
<pre class="build Linux NetBSD">
c++ -std=c++11 -I.. -Ipffft -O3 -ffast-math -DGABORATOR_USE_PFFFT `pkg-config --cflags sndfile` render.cc pffft/pffft.o pffft/fftpack.o `pkg-config --libs sndfile` -o render
</pre>
<h2>Running</h2>
<p>Running the following shell commands will download a short example
audio file (of picking each string on an acoustic guitar), generate
a spectrogram from it as a <code>.pgm</code> image, and then convert
the <code>.pgm</code> image into a <code>JPEG</code> image:
<pre class="run">
wget http://download.gaborator.com/audio/guitar.wav
./render guitar.wav guitar.pgm
cjpeg &lt;guitar.pgm &gt;guitar.jpg
</pre>
<h2>Example Output</h2>
<p>The JPEG file produced by the above will look like this:</p>
<img src="spectrogram.jpg" alt="Spectrogram">
</body>
</html>

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// See ../doc/filter.html for commentary
#include <memory.h>
#include <iostream>
#include <sndfile.h>
#include <gaborator/gaborator.h>
int main(int argc, char **argv) {
if (argc < 3) {
std::cerr << "usage: filter input.wav output.wav\n";
exit(1);
}
SF_INFO sfinfo;
memset(&sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &sfinfo);
if (! sf_in) {
std::cerr << "could not open input audio file\n";
exit(1);
}
double fs = sfinfo.samplerate;
sf_count_t n_frames = sfinfo.frames;
sf_count_t n_samples = sfinfo.frames * sfinfo.channels;
std::vector<float> audio(n_samples);
sf_count_t n_read = sf_readf_float(sf_in, audio.data(), n_frames);
if (n_read != n_frames) {
std::cerr << "read error\n";
exit(1);
}
sf_close(sf_in);
gaborator::parameters params(100, 20.0 / fs);
gaborator::analyzer<float> analyzer(params);
std::vector<float> band_gains(analyzer.bands_end());
for (int band = analyzer.bandpass_bands_begin(); band < analyzer.bandpass_bands_end(); band++) {
float f_hz = analyzer.band_ff(band) * fs;
band_gains[band] = 1.0 / sqrt(f_hz / 20.0);
}
band_gains[analyzer.band_lowpass()] = band_gains[analyzer.bandpass_bands_end() - 1];
for (sf_count_t ch = 0; ch < sfinfo.channels; ch++) {
std::vector<float> channel(n_frames);
for (sf_count_t i = 0; i < n_frames; i++)
channel[i] = audio[i * sfinfo.channels + ch];
gaborator::coefs<float> coefs(analyzer);
analyzer.analyze(channel.data(), 0, channel.size(), coefs);
gaborator::apply(analyzer, coefs,
[&](std::complex<float> &coef, int band, int64_t) {
coef *= band_gains[band];
});
analyzer.synthesize(coefs, 0, channel.size(), channel.data());
for (sf_count_t i = 0; i < n_frames; i++)
audio[i * sfinfo.channels + ch] = channel[i];
}
SNDFILE *sf_out = sf_open(argv[2], SFM_WRITE, &sfinfo);
if (! sf_out) {
std::cerr << "could not output audio file\n";
exit(1);
}
sf_command(sf_out, SFC_SET_CLIPPING, NULL, SF_TRUE);
sf_count_t n_written = sf_writef_float(sf_out, audio.data(), n_frames);
if (n_written != n_frames) {
std::cerr << "write error\n";
exit(1);
}
sf_close(sf_out);
return 0;
}

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// See ../doc/render.html for commentary
#include <memory.h>
#include <iostream>
#include <fstream>
#include <sndfile.h>
#include <gaborator/gaborator.h>
#include <gaborator/render.h>
int main(int argc, char **argv) {
if (argc < 3) {
std::cerr << "usage: render input.wav output.pgm\n";
exit(1);
}
SF_INFO sfinfo;
memset(&sfinfo, 0, sizeof(sfinfo));
SNDFILE *sf_in = sf_open(argv[1], SFM_READ, &sfinfo);
if (! sf_in) {
std::cerr << "could not open input audio file\n";
exit(1);
}
double fs = sfinfo.samplerate;
sf_count_t n_frames = sfinfo.frames;
sf_count_t n_samples = sfinfo.frames * sfinfo.channels;
std::vector<float> audio(n_samples);
sf_count_t n_read = sf_readf_float(sf_in, audio.data(), n_frames);
if (n_read != n_frames) {
std::cerr << "read error\n";
exit(1);
}
sf_close(sf_in);
std::vector<float> mono(n_frames);
for (size_t i = 0; i < (size_t)n_frames; i++) {
float v = 0;
for (size_t c = 0; c < (size_t)sfinfo.channels; c++)
v += audio[i * sfinfo.channels + c];
mono[i] = v;
}
gaborator::parameters params(48, 20.0 / fs, 440.0 / fs);
gaborator::analyzer<float> analyzer(params);
gaborator::coefs<float> coefs(analyzer);
analyzer.analyze(mono.data(), 0, mono.size(), coefs);
int64_t x_origin = 0;
int64_t y_origin = analyzer.bandpass_bands_begin();
int x_scale_exp = 10;
while ((n_frames >> x_scale_exp) > 1000)
x_scale_exp++;
int y_scale_exp = 0;
int64_t x0 = 0;
int64_t y0 = 0;
int64_t x1 = n_frames >> x_scale_exp;
int64_t y1 = (analyzer.bandpass_bands_end() - analyzer.bandpass_bands_begin()) >> y_scale_exp;
std::vector<float> amplitudes((x1 - x0) * (y1 - y0));
gaborator::render_p2scale(
analyzer,
coefs,
x_origin, y_origin,
x0, x1, x_scale_exp,
y0, y1, y_scale_exp,
amplitudes.data());
float gain = 15;
std::ofstream f;
f.open(argv[2], std::ios::out | std::ios::binary);
f << "P5\n" << (x1 - x0) << ' ' << (y1 - y0) << "\n255\n";
for (size_t i = 0; i < amplitudes.size(); i++)
f.put(gaborator::float2pixel_8bit(amplitudes[i] * gain));
f.close();
return 0;
}

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//
// Fast Fourier transform
//
// Copyright (C) 2016-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_FFT_H
#define _GABORATOR_FFT_H
#include "gaborator/fft_naive.h"
#if GABORATOR_USE_VDSP
#include "gaborator/fft_vdsp.h"
#elif GABORATOR_USE_PFFFT
#include "gaborator/fft_pffft.h"
#endif
#endif

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//
// Fast Fourier transform, naive reference implementations
//
// Copyright (C) 1992-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
// Based on the module "fft" used in audsl/test, audsl/mls,
// scope/core, whitesig
#ifndef _GABORATOR_FFT_NAIVE_H
#define _GABORATOR_FFT_NAIVE_H
#include <algorithm>
#include <complex>
#include <iterator>
#include <vector>
#include <memory.h>
namespace gaborator {
template <class I>
struct fft {
typedef typename std::iterator_traits<I>::value_type C; // complex
typedef typename C::value_type T; // float/double
typedef typename std::vector<C> twiddle_vector;
fft(unsigned int n): n_(n), wtab(n / 2) { init_wtab(); }
~fft() { }
unsigned int size() { return n_; }
// Transform the contents of the array "a", leaving results in
// bit-reversed order.
void
br_transform(I a) {
unsigned int i, j, m, n;
typename twiddle_vector::iterator wp; // twiddle factor pointer
I p, q;
// n is the number of points in each subtransform (butterfly group)
// m is the number of subtransforms (butterfly groups), = n_ / n
// i is the index of the first point in the current butterfly group
// j is the number of the butterfly within the group
for (n = 2, m = n_ / 2; n <= n_; n *= 2 , m /= 2) // each stage
for (i = 0; i < n_; i += n) // each butterfly group
for (j = 0, wp = wtab.begin(), p = a + i, q = a + i + n / 2;
j < n / 2;
j++, wp += m, p++, q++) // each butterfly
{
C temp((*q) * (*wp));
*q = *p - temp;
*p += temp;
}
}
void
bit_reverse(I a) {
unsigned int i, j;
for (i = 0, j = 0; i < n_; i++, j = bitrev_inc(j)) {
if (i < j)
std::swap(*(a + i), *(a + j));
}
}
void
reverse(I a) {
for (unsigned int i = 1; i < n_ / 2; i++)
std::swap(*(a + i), *(a + n_ - i));
}
// in-place
void
transform(I a) {
bit_reverse(a);
br_transform(a);
}
void
itransform(I a) {
reverse(a);
transform(a);
}
// out-of-place
// XXX const
void
transform(I in, I out) {
std::copy(in, in + n_, out);
transform(out);
}
void
itransform(I in, I out) {
std::copy(in, in + n_, out);
itransform(out);
}
private:
// Initialize twiddle factor array
void init_wtab() {
unsigned int wt_size = wtab.size();
for (unsigned int i = 0; i < wt_size; ++i) {
double arg = (-2.0 * M_PI / n_) * i;
wtab[i] = C(cos(arg), sin(arg));
}
}
unsigned int
bitrev_inc(unsigned int i) {
unsigned int carry = n_;
do {
carry >>= 1;
unsigned int new_i = i ^ carry;
carry &= i;
i = new_i;
} while(carry);
return i;
}
// Size of the transform
unsigned int n_;
// Twiddle factor array (size n / 2)
twiddle_vector wtab;
};
#if GABORATOR_USE_REAL_FFT
// Real FFT
//
// This is a trivial implementation offering no performance advantage
// over a complex FFT. It is intended as a placeholder to be
// overridden with a specialization, and as a reference implementation
// to compare the results of specializations against.
//
template <class CI>
struct rfft {
typedef typename std::iterator_traits<CI>::value_type C; // complex
typedef typename C::value_type T; // float/double
typedef T *RI; // Real iterator
typedef const T *CONST_RI;
rfft(unsigned int n): cf(n) { }
~rfft() { }
void
transform(CONST_RI in, CI out) {
size_t n = cf.size();
C *tmp = new C[n];
C *out_tmp = new C[n];
std::copy(in, in + cf.size(), tmp); // Real to complex
cf.transform(tmp, out_tmp);
delete [] tmp;
#if GABORATOR_REAL_FFT_NEGATIVE_FQS
std::copy(out_tmp, out_tmp + n, out);
#else
std::copy(out_tmp, out_tmp + n / 2 + 1, out);
#endif
delete [] out_tmp;
}
void
itransform(CI in, RI out) {
size_t n = cf.size();
// Make sure not to use the negative frequency part of "in",
// because it may not be valid.
C *in_tmp = new C[n];
for (size_t i = 0; i < n / 2 + 1; i++) {
in_tmp[i] = in[i];
}
for (size_t i = 1; i < n / 2; i++) {
in_tmp[n - i] = conj(in[i]);
}
C *tmp = new C[n];
cf.itransform(in_tmp, tmp);
for (size_t i = 0; i < n; i++) {
*out++ = tmp[i].real();
}
delete [] tmp;
delete [] in_tmp;
}
fft<CI> cf;
};
#endif
} // Namespace
#endif

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//
// Fast Fourier transform using PFFFT
//
// Copyright (C) 2017-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_FFT_PFFFT_H
#define _GABORATOR_FFT_PFFFT_H
#include <assert.h>
#include <complex>
#include <iterator>
#include <vector>
#include "pffft.h"
// XXX disable in production
#ifdef __x86_64__
#define GABORATOR_PFFFT_CHECK_ALIGN(p) assert((((uint64_t)(p)) & 0xF) == 0)
#else
#define GABORATOR_PFFFT_CHECK_ALIGN(p) do {} while (0)
#endif
namespace gaborator {
template <>
struct fft<std::complex<float> *> {
typedef std::complex<float> *I;
typedef const std::complex<float> *CONST_I;
typedef std::iterator_traits<I>::value_type C; // complex
typedef C::value_type T; // float/double
fft(unsigned int n_): n(n_) {
setup = pffft_new_setup(n, PFFFT_COMPLEX);
assert(setup);
}
~fft() {
pffft_destroy_setup(setup);
}
unsigned int size() { return n; }
// in-place
void
transform(I a) {
pffft_transform_ordered(setup, (float *)a, (float *)a, NULL, PFFFT_FORWARD);
}
void
itransform(I a) {
pffft_transform_ordered(setup, (float *)a, (float *)a, NULL, PFFFT_BACKWARD);
}
// out-of-place
void
transform(CONST_I in, I out) {
GABORATOR_PFFFT_CHECK_ALIGN(in);
GABORATOR_PFFFT_CHECK_ALIGN(out);
pffft_transform_ordered(setup, (const float *)in, (float *)out, NULL, PFFFT_FORWARD);
}
void
itransform(CONST_I in, I out) {
GABORATOR_PFFFT_CHECK_ALIGN(in);
GABORATOR_PFFFT_CHECK_ALIGN(out);
pffft_transform_ordered(setup, (const float *)in, (float *)out, NULL, PFFFT_BACKWARD);
}
private:
// Size of the transform
unsigned int n;
PFFFT_Setup *setup;
};
// Support transforming std::vector<std::complex<float> >::iterator
template <>
struct fft<std::vector<std::complex<float> >::iterator>:
public fft<std::complex<float> *>
{
typedef fft<std::complex<float> *> base;
typedef std::vector<std::complex<float> >::iterator I;
fft(unsigned int n_): fft<std::complex<float> *>(n_) { }
void
transform(I a) {
base::transform(&(*a));
}
void
itransform(I a) {
base::itransform(&(*a));
}
void
transform(I in, I out) {
base::transform(&(*in), &(*out));
}
void
itransform(I in, I out) {
base::itransform(&(*in), &(*out));
}
};
// Use fftpack for double precision
#define FFTPACK_DOUBLE_PRECISION 1
#include "fftpack.h"
#undef FFTPACK_DOUBLE_PRECISION
template <>
struct fft<std::complex<double> *> {
typedef std::complex<double> *I;
typedef const std::complex<double> *CONST_I;
typedef std::iterator_traits<I>::value_type C; // complex
typedef C::value_type T; // float/double
fft(unsigned int n_): n(n_), wsave(4 * n_ + 15) {
cffti(n, wsave.data());
}
~fft() {
}
unsigned int size() { return n; }
// in-place
void
transform(I a) {
cfftf(n, (double *)a, wsave.data());
}
void
itransform(I a) {
cfftb(n, (double *)a, wsave.data());
}
// out-of-place
void
transform(CONST_I in, I out) {
std::copy(in, in + n, out);
transform(out);
}
void
itransform(CONST_I in, I out) {
std::copy(in, in + n, out);
itransform(out);
}
private:
// Size of the transform
unsigned int n;
std::vector<double> wsave;
};
#if GABORATOR_USE_REAL_FFT
// Real FFT
template <>
struct rfft<std::complex<float> *> {
typedef std::complex<float> *CI; // Complex iterator
typedef const std::complex<float> *CONST_CI;
typedef typename std::iterator_traits<CI>::value_type C; // complex
typedef typename C::value_type T; // float/double
typedef T *RI; // Real iterator
typedef const T *CONST_RI;
rfft(unsigned int n_): n(n_) {
setup = pffft_new_setup(n, PFFFT_REAL);
assert(setup);
}
~rfft() {
pffft_destroy_setup(setup);
}
unsigned int size() { return n; }
// out-of-place only
void
transform(CONST_RI in, CI out) {
GABORATOR_PFFFT_CHECK_ALIGN(in);
GABORATOR_PFFFT_CHECK_ALIGN(out);
pffft_transform_ordered(setup, in, (float *) out, NULL, PFFFT_FORWARD);
C tmp = out[0];
#if GABORATOR_REAL_FFT_NEGATIVE_FQS
for (unsigned int i = 1; i < (n >> 1); i++)
out[n - i] = conj(out[i]);
#endif
out[0] = C(tmp.real(), 0);
out[n >> 1] = C(tmp.imag(), 0);
}
// Note: this temporarily modifies in[0], in spite of the const
void
itransform(CONST_CI in, RI out) {
GABORATOR_PFFFT_CHECK_ALIGN(in);
GABORATOR_PFFFT_CHECK_ALIGN(out);
C tmp = in[0];
const_cast<CI>(in)[0] = C(tmp.real(), in[n >> 1].real());
pffft_transform_ordered(setup, (const float *) in, out, NULL, PFFFT_BACKWARD);
const_cast<CI>(in)[0] = tmp;
}
private:
// Size of the transform
unsigned int n;
PFFFT_Setup *setup;
};
#endif
#undef GABORATOR_PFFFT_CHECK_ALIGN
} // namespace
#endif

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//
// Fast Fourier transform using the Apple vDSP framework
//
// Copyright (C) 2013-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_FFT_VDSP_H
#define _GABORATOR_FFT_VDSP_H
#include <assert.h>
#include <iterator>
#include <vector>
#include <memory.h>
#include <mach/mach.h>
#include <mach/task.h>
#include <mach/task_info.h>
#include <mach/vm_map.h>
#include <Accelerate/Accelerate.h>
namespace gaborator {
static inline int log2_int_exact(int n) {
// n must be a power of two
assert(n != 0 && ((n & (n >> 1)) == 0));
int r = 0;
for (;;) {
n >>= 1;
if (n == 0)
break;
r++;
}
return r;
}
template <>
struct fft<std::complex<float> *> {
typedef std::complex<float> *I;
typedef typename std::iterator_traits<I>::value_type C; // complex
typedef typename C::value_type T; // float/double
fft(unsigned int n_): n(n_), log2n(log2_int_exact(n)) {
setup = vDSP_create_fftsetup(log2n, kFFTRadix2);
}
~fft() {
vDSP_destroy_fftsetup(setup);
}
unsigned int size() { return n; }
// in-place
void
transform(I a) {
DSPSplitComplex s;
// XXX this result in disoptimal alignment
s.realp = (float *) a;
s.imagp = (float *) a + 1;
vDSP_fft_zip(setup, &s, 2, log2n, kFFTDirection_Forward);
}
void
itransform(I a) {
DSPSplitComplex s;
s.realp = (float *) a;
s.imagp = (float *) a + 1;
vDSP_fft_zip(setup, &s, 2, log2n, kFFTDirection_Inverse);
}
// out-of-place
// XXX const
void
transform(I in, I out) {
DSPSplitComplex si;
si.realp = (float *) in;
si.imagp = (float *) in + 1;
DSPSplitComplex so;
so.realp = (float *) out;
so.imagp = (float *) out + 1;
vDSP_fft_zop(setup,
&si, 2,
&so, 2,
log2n, kFFTDirection_Forward);
}
void
itransform(I in, I out) {
DSPSplitComplex si;
si.realp = (float *) in;
si.imagp = (float *) in + 1;
DSPSplitComplex so;
so.realp = (float *) out;
so.imagp = (float *) out + 1;
vDSP_fft_zop(setup,
&si, 2,
&so, 2,
log2n, kFFTDirection_Inverse);
}
private:
// Size of the transform
unsigned int n;
unsigned int log2n;
FFTSetup setup;
};
// Support transforming std::vector<std::complex<float> >::iterator
template <>
struct fft<typename std::vector<std::complex<float> >::iterator>:
public fft<std::complex<float> *>
{
typedef fft<std::complex<float> *> base;
typedef typename std::vector<std::complex<float> >::iterator I;
fft(unsigned int n_): fft<std::complex<float> *>(n_) { }
void
transform(I a) {
base::transform(&(*a));
}
void
itransform(I a) {
base::itransform(&(*a));
}
void
transform(I in, I out) {
base::transform(&(*in), &(*out));
}
void
itransform(I in, I out) {
base::itransform(&(*in), &(*out));
}
};
} // Namespace
#endif

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//
// The Gaussian and related functions
//
// Copyright (C) 2015-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_GAUSSIAN_H
#define _GABORATOR_GAUSSIAN_H
#include <math.h>
namespace gaborator {
// A rough approximation of erfc_inv(), the inverse complementary
// error function. This is good for arguments in the range 1e-8 to 1,
// to within a few percent.
inline float erfc_inv(float x) {
return sqrtf(-logf(x)) - 0.3f;
}
// Gaussian with peak = 1
inline double norm_gaussian(double sd, double x) {
return exp(-(x * x) / (2 * sd * sd));
}
// Gaussian with integral = 1
inline double gaussian(double sd, double x) {
double a = 1.0 / (sd * sqrt(2.0 * M_PI));
return a * norm_gaussian(sd, x);
}
// The convolution of a Heaviside step function with a Gaussian of
// standard deviation sd. Goes smoothly from 0 to 1, with the 0.5
// point at x=0.
static inline
double gaussian_edge(double sd, double x) {
double erf_arg = x / (sd * M_SQRT2);
if (erf_arg < -7)
return 0; // error < 5e-23
if (erf_arg > 7)
return 1; // error < 5e-23
return (erf(erf_arg) + 1) * 0.5;
}
// Translate the time-domain standard deviation of a gaussian
// (in samples) into the corresponding frequency-domain standard
// deviation (as a fractional frequency), or vice versa.
static inline double sd_t2f(double st_sd) {
return 1.0 / (2.0 * M_PI * st_sd);
}
static inline double sd_f2t(double ff_sd) {
return sd_t2f(ff_sd);
}
// Given a gaussian with standard deviation "sd" and a maximum error
// "max_error", calculate the support needed on each side to keep the
// area below the curve within max_error of the exact value.
static inline double gaussian_support(double sd, double max_error) {
return sd * M_SQRT2 * erfc_inv(max_error);
}
// Inverse of the above: given a support and maximum error, calculate
// the standard deviation.
static inline double gaussian_support_inv(double support, double max_error) {
return support / (M_SQRT2 * erfc_inv(max_error));
}
} // namespace
#endif

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//
// A vector class without default-initialization, for "plain old data"
//
// Copyright (C) 2016-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_POD_VECTOR_H
#define _GABORATOR_POD_VECTOR_H
#include <stdlib.h> // size_t
#include <algorithm> // std::swap
namespace gaborator {
template <class T>
struct pod_vector {
typedef T *iterator;
pod_vector() {
b = e = 0;
}
pod_vector(size_t size_) {
b = static_cast<T *>(::operator new(size_ * sizeof(T)));
e = b + size_;
}
~pod_vector()
#if __cplusplus >= 201103L
noexcept
#endif
{
_free();
}
void swap(pod_vector &x) {
std::swap(b, x.b);
std::swap(e, x.e);
}
iterator begin() const { return b; }
iterator end() const { return e; }
T *data() { return b; }
const T *data() const { return b; }
T &operator[](size_t i) { return b[i]; }
const T &operator[](size_t i) const { return b[i]; }
size_t size() const { return e - b; }
void resize(size_t new_size) {
if (new_size == size())
return;
T *n = static_cast<T *>(::operator new(new_size * sizeof(T)));
size_t ncopy = std::min(size(), new_size);
std::copy(b, b + ncopy, n);
_free();
b = n;
e = n + new_size;
}
pod_vector(const pod_vector &a)
{
b = new T[a.size()];
e = b + a.size();
std::copy(a.b, a.e, b);
//if (size()) fprintf(stderr, "pod_vector cc %d\n", (int)size());
}
void clear() {
_free();
b = e = 0;
}
#if __cplusplus >= 201103L
pod_vector(pod_vector&& x) noexcept:
b(x.b), e(x.e)
{
x.b = x.e = 0;
//if (size()) fprintf(stderr, "pod_vector mv %d\n", (int)size());
}
#endif
pod_vector &operator=(const pod_vector &a) {
if (&a == this)
return *this;
_free();
b = new T[a.size()];
e = b + a.size();
std::copy(a.b, a.e, b);
//if (size()) fprintf(stderr, "pod_vector = %d\n", (int)size());
return *this;
}
#if __cplusplus >= 201103L
pod_vector &operator=(pod_vector &&x) noexcept {
if (&x == this)
return *this;
b = x.b;
e = x.e;
x.b = x.e = 0;
return *this;
}
#endif
private:
void _free() {
::operator delete(b);
}
T *b;
T *e;
};
} // namespace
#endif

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//
// Pool of shared objects
//
// Copyright (C) 2015-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_POOL_H
#define _GABORATOR_POOL_H
#include <map>
namespace gaborator {
// The "pool" class is for sharing FFT objects so that we don't
// create multiple FFTs of the same size. It could also be used
// to share objects of some other class T where we don't want to
// create multiple Ts with the same K.
template <class T, class K>
struct pool {
typedef std::map<K, T *> m_t;
~pool() {
for (typename m_t::iterator it = m.begin(); it != m.end(); it++) {
delete (*it).second;
}
}
T *get(const K &k) {
std::pair<typename m_t::iterator, bool> r = m.insert(std::make_pair(k, (T *)0));
if (r.second) {
// New element was inserted
assert((*(r.first)).second == 0);
(*r.first).second = new T(k);
}
return (*r.first).second;
}
m_t m;
static pool shared;
};
template <class T, class K>
pool<T, K> pool<T, K>::shared;
} // namespace
#endif

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//
// Intrusive reference counting smart pointer
//
// Copyright (C) 2016-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_REF_H
#define _GABORATOR_REF_H
namespace gaborator {
template <class T> struct ref;
struct refcounted {
refcounted() { refcount = 0; }
unsigned int refcount;
};
template <class T>
struct ref {
ref(): p(0) { }
ref(T *p_): p(p_) {
incref();
}
ref(const ref &o): p(o.p) {
incref();
}
ref &operator=(const ref &o) { reset(o.p); return *this; }
~ref() { reset(); }
void reset() {
decref();
p = 0;
}
void reset(T *n) {
if (n == p)
return;
decref();
p = n;
incref();
}
T *get() const { return p; }
T *operator->() const { return p; }
T &operator*() const { return *p; }
operator bool() const { return p; }
private:
void incref() {
if (! p)
return;
p->refcount++;
}
void decref() {
if (! p)
return;
p->refcount--;
if (p->refcount == 0)
delete p;
}
T *p;
};
} // namespace
#endif

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//
// Rendering of spectrogram images
//
// Copyright (C) 2015-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_RENDER_H
#define _GABORATOR_RENDER_H
#include "gaborator/gaborator.h"
#include "gaborator/resample2.h"
namespace gaborator {
// Convert a floating-point linear brightness value in the range 0..1
// into an 8-bit pixel value, with clamping and (rough) gamma
// correction. This nominally uses the sRGB gamma curve, but the
// current implementation cheats and uses a gamma of 2 because it can
// be calculated quickly using a square root.
template <class T>
unsigned int float2pixel_8bit(T val) {
// Clamp before gamma correction so we don't take the square root
// of a negative number; those can arise from bicubic
// interpolation. While we're at it, let's also skip the gamma
// correction for small numbers that will round to zero anyway,
// and especially denormals which could rigger GCC bug target/83240.
static const T almost_zero = 1.0 / 65536;
if (val < almost_zero)
val = 0;
if (val > 1)
val = 1;
return (unsigned int)(sqrtf(val) * 255.0f);
}
// Magnitude
template<class T>
struct complex_abs_fob {
T operator()(const complex<T> &c) {
return complex_abs(c);
}
};
// A source object for resample2() that provides the absolute
// values of a row of spectrogram coordinates.
template <class T, class OI, class NORMF>
struct abs_row_source {
typedef complex<T> C;
typedef transform_output_iterator<NORMF, OI, C> abs_writer_t;
abs_row_source(const analyzer<T> &frs_,
const sliced_coefs<C> &sc_,
int oct_, unsigned int obno_,
NORMF normf_):
rs(frs_, sc_, oct_, obno_),
normf(normf_)
{ }
OI operator()(sample_index_t i0, sample_index_t i1, OI output) const {
abs_writer_t abswriter(normf, output);
abs_writer_t abswriter_end = rs(i0, i1, abswriter);
return abswriter_end.output;
}
row_source<T, abs_writer_t> rs;
NORMF normf;
};
// Helper class for abs_row_source specialization below
template <class C, class OI>
struct abs_writer_dest {
abs_writer_dest(OI output_): output(output_) { }
void process_existing_slice(C *bv, size_t len) {
complex_magnitude(bv, output, len);
output += len;
}
void process_missing_slice(size_t len) {
for (size_t i = 0; i < len; i++)
*output++ = 0;
}
OI output;
};
// Partial specialization of class abs_row_source for NORMF = complex_abs_fob,
// for vectorization.
template <class T, class OI>
struct abs_row_source<T, OI, struct complex_abs_fob<T> > {
typedef complex<T> C;
// Note unused last arg
abs_row_source(const analyzer<T> &frs_,
const sliced_coefs<C> &sc_,
int oct_, unsigned int obno_,
complex_abs_fob<T>):
slicer(frs_, sc_, oct_, obno_)
{ }
OI operator()(coef_index_t i0, coef_index_t i1, OI output) const {
abs_writer_dest<C, OI> dest(output);
slicer(i0, i1, dest);
return dest.output;
}
row_foreach_slice<T, abs_writer_dest<C, OI>, C> slicer;
};
// Render a single line (single frequency band), with scaling by
// powers of two in the horizontal (time) dimension, and filtering to
// avoid aliasing when minifying.
template <class OI, class T, class NORMF>
OI render_p2scale_line(const analyzer<T> &frs,
const coefs<T> &msc,
int gbno,
int64_t xorigin,
sample_index_t i0, sample_index_t i1, int e,
bool interpolate,
OI output,
NORMF normf)
{
int oct;
unsigned int obno; // Band number within octave
bool clip = ! frs.bno_split(gbno, oct, obno, false);
if (clip) {
for (sample_index_t i = i0; i < i1; i++)
*output++ = (T)0;
return output;
}
abs_row_source<T, T *, NORMF>
abs_rowsource(frs, msc.octaves[oct], oct, obno, normf);
// Scale by the downsampling factor of the band
int scale_exp = frs.band_scale_exp(oct, obno);
output = resample2(abs_rowsource, xorigin,
i0, i1, e - scale_exp,
interpolate, output);
return output;
}
// Render a two-dimensional image with scaling by powers of two in the
// horizontal direction only. In the vertical direction, there is
// always a one-to-one correspondence between bands and pixels.
// yi0 and yi1 already have the yorigin applied, so there is no
// yorigin argument.
template <class OI, class T, class NORMF>
OI render_p2scale_noyscale(const analyzer<T> &frs,
const coefs<T> &msc,
int64_t xorigin,
int64_t xi0, int64_t xi1, int xe,
int64_t yi0, int64_t yi1,
bool interpolate,
OI output,
NORMF normf)
{
assert(xi1 >= xi0);
int w = xi1 - xi0;
int gbno0 = yi0;
int gbno1 = yi1;
for (int gbno = gbno0; gbno < gbno1; gbno++) {
int oct;
unsigned int obno; // Band number within octave
bool clip = ! frs.bno_split(gbno, oct, obno, false);
if (clip) {
for (int x = 0; x < w; x++)
*output++ = (T)0;
} else {
output = render_p2scale_line(frs, msc, gbno, xorigin,
xi0, xi1, xe,
interpolate, output, normf);
}
}
return output;
}
// Source data from a column of a row-major two-dimensional array.
// data points to the beginning of a row-major array with an x
// range of x0..x1 and an y range from y0..y1, and operator()
// returns data from column x (where x is within the range x0..x1).
template <class OI>
struct transverse_source {
transverse_source(float *data_,
int64_t x0_, int64_t x1_, int64_t y0_, int64_t y1_,
int64_t x_):
data(data_),
x0(x0_), x1(x1_), y0(y0_), y1(y1_),
x(x_),
stride(x1 - x0)
{ }
OI operator()(int64_t i0, int64_t i1, OI out) const {
assert(x >= x0);
assert(x <= x1);
assert(i1 >= i0);
assert(i0 >= y0);
assert(i1 <= y1);
float *p = data + (x - x0) + (i0 - y0) * stride;
while (i0 != i1) {
*out++ = *p;
p += stride;
++i0;
}
return out;
}
float *data;
int64_t x0, x1, y0, y1, x;
size_t stride;
};
template <class I, class T>
struct stride_iterator: public std::iterator<std::forward_iterator_tag, T> {
stride_iterator(I it_, size_t stride_): it(it_), stride(stride_) { }
T& operator*() { return *it; }
stride_iterator<I, T>& operator++() {
it += stride;
return *this;
}
stride_iterator operator++(int) {
stride_iterator old = *this;
it += stride;
return old;
}
I it;
size_t stride;
};
// Render a two-dimensional image with scaling by powers of two in
// both the horizontal (time) and vertical (frequency) directions.
// The output may be written through "output" out of order, so
// "output" must be a random access iterator.
// Note the default template argument for NORMF. This is needed
// because the compiler won't deduce the type of NORMF from the
// default function argument "NORMF normf = complex_abs_fob<T>()"
// when the normf argument is omitted; it is considered a "non-deduced
// context", being "a template parameter used in the parameter type of
// a function parameter that has a default argument that is being used
// in the call for which argument deduction is being done".
// Unfortuantely, this work-around of providing a default template
// argument requires C++11.
template <class OI, class T, class NORMF = complex_abs_fob<T> >
void render_p2scale(const analyzer<T> &frs,
const coefs<T> &msc,
int64_t xorigin, int64_t yorigin,
int64_t xi0, int64_t xi1, int xe,
int64_t yi0, int64_t yi1, int ye,
OI output,
bool interpolate = true,
NORMF normf = complex_abs_fob<T>())
{
// Construct a temporary float image of the right width,
// but still needing scaling of the height. Include
// extra scanlines at the top and bottom for interpolation.
// Find the image bounds in the spectrogram coordinate system,
// including the interpolation margin. The Y bounds are in
// bands and are used both to determine what to render into the
// temporary image and for short-circuiting; the X bounds are in
// samples, and are only used for short-circuiting.
int64_t ysi0, ysi1;
resample2_support(yorigin, yi0, yi1, ye, ysi0, ysi1);
int64_t xsi0, xsi1;
resample2_support(xorigin, xi0, xi1, xe, xsi0, xsi1);
// Short-circuiting: if the image to be rendered falls entirely
// outside the data, just set it to zero instead of resampling down
// (potentially) high-resolution zeros to the display resolution.
// This makes a difference when zooming out by a large factor, for
// example such that the entire spectrogram falls within a single
// tile; that tile will necessarily be expensive to calculate, but
// the other tiles need not be, and mustn't be if we are going to
// keep the total amount of work bounded by O(L) with respect
// to the signal length L regardless of zoom.
int64_t cxi0, cxi1;
frs.get_coef_bounds(msc, cxi0, cxi1);
if (ysi1 < 0 || // Entirely above
ysi0 >= frs.n_bands_total - 1 || // Entirely below
xsi1 < cxi0 || // Entirely to the left
xsi0 >= cxi1) // Entirely to the right
{
size_t n = (yi1 - yi0) * (xi1 - xi0);
for (size_t i = 0; i < n; i++)
output[i] = (T)0;
return;
}
// Allocate buffer for temporary image resampled in the X
// direction but not yet in the Y direction
size_t n_pixels = (ysi1 - ysi0) * (xi1 - xi0);
pod_vector<float> render_data(n_pixels);
// Render data resampled in the X direction
float *p = render_data.data();
render_p2scale_noyscale(frs, msc, xorigin, xi0, xi1, xe,
ysi0, ysi1, interpolate, p, normf);
// Resample in the Y direction
for (int64_t xi = xi0; xi < xi1; xi++) {
transverse_source<OI> src(render_data.data(),
xi0, xi1, ysi0, ysi1,
xi);
stride_iterator<OI, float> dest(output + (xi - xi0), (xi1 - xi0));
resample2(src, yorigin, yi0, yi1, ye, interpolate, dest);
}
}
} // namespace
#endif

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//
// Fast resampling by powers of two
//
// Copyright (C) 2016-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
// Uses a two-lobe Lanczos kernel. Good enough for image data, not
// intended for audio.
#ifndef _GABORATOR_RESAMPLE2_H
#define _GABORATOR_RESAMPLE2_H
#include <assert.h>
#include <inttypes.h>
#include <algorithm> // std::copy
#include "gaborator/pod_vector.h"
namespace gaborator {
//
// There are two ways to look at this.
//
// In one point of view, there is only one coordinate space, and
// coordinates are floating-point numbers. The various sub- and
// supersampled views differ in step sizes and the number of
// fractional coordinate bits, but any given coordinates refer to the
// same point in the image at any scale. Steps are powers of two,
// with integer exponents that may be negative. A step size > 1
// implies downsampling (antialias lowpass filtering and subsampling),
// and a step size < 1 implies upsampling (aka interpolation).
//
// The coordinates are always integer multiples of the step size.
//
// e.g.,
// x0 = 33.5, xstep = 0.5
// x0 = 12, xstep = 4
//
// In the other point of view, we introduce an integer exponent e and
// substitute x0 = i0 * 2^e and xstep = 2^e. Now instead of floating
// point coordinates, we use integer "indices". The above example
// now looks like his:
//
// i0 = 67, e = -1
// i0 = 3, e = 2
//
// This latter point of view is how the code actually works.
//
// Resample data from "source", generating a view between indices
// i0 and i1 of the scale determined by exponent e, and storing
// i1 - i0 samples starting at *out.
//
// The source must implement an operator() taking the arguments
// (int64_t i0, int64_t i1, T *out) and generating data for the base
// resolution (e=0).
//
// S is the type of the data source
// OI is the output iterator type
template <class S, class T>
T *resample2_ptr(const S &source, int64_t origin,
int64_t i0, int64_t i1, int e,
bool interpolate, T *out)
{
assert(i1 >= i0);
if (e > 0) {
// Downsample
// Calculate super-octave coordinates
// margin is the support of the resampling kernel (on each side,
// not counting the center sample)
int margin = interpolate ? 1 : 0;
// When margin = 1, we use three samples, at 2i-1, 2i, 2i+1
// and the corresponding half-open inverval is 2i-1...2i+1+1
int64_t si0 = 2 * i0 - margin;
int64_t si1 = 2 * i1 + margin + 1;
// Get super-octave data
gaborator::pod_vector<T> super_data(si1 - si0);
T *p = super_data.data();
p = resample2_ptr(source, origin, si0, si1, e - 1, interpolate, p);
assert(p == super_data.data() + si1 - si0);
for (int64_t i = i0; i < i1; i++) {
int64_t si = 2 * i - si0;
T val;
if (!interpolate) {
// Point sampling
val = super_data[si];
} else {
// Triangular kernel
T v1 = super_data[si - 1];
T v0 = super_data[si];
v1 += super_data[si + 1];
val =
v0 * (T)0.5 +
v1 * (T)0.25;
#if 0 // Lanczos2 is overkill when downsampling.
} else {
// Two-lobe Lanczos kernel, needs margin = 2
// Always aligned
T v3 = super_data[si - 3];
// There is no v2
T v1 = super_data[si - 1];
T v0 = super_data[si];
// There is still no v2
v1 += super_data[si + 1];
v3 += super_data[si + 3];
val =
v0 * (T)0.49530706 +
v1 * (T)0.28388978 +
v3 * (T)-0.03154331;
#endif
}
*out++ = val;
}
} else if (e < 0) {
// Upsample
if (! interpolate) {
// Return nearest neighbor. If the pixel lies
// exactly at the midpoint between the neighbors,
// return their average.
int sh = -e;
int64_t si0 = i0 >> sh;
int64_t si1 = ((i1 - 1) >> sh) + 1 + 1;
gaborator::pod_vector<T> source_data(si1 - si0);
source(origin + si0, origin + si1, source_data.data());
for (int64_t i = i0; i < i1; i++) {
int64_t si = (i >> sh) - si0;
T val;
int rem = i & ((1 << sh) - 1);
int half = (1 << sh) >> 1;
if (rem < half) {
val = source_data[si];
} else if (rem == half) {
val = (source_data[si] + source_data[si + 1]) * (T)0.5;
} else { // rem > half
val = source_data[si + 1];
}
*out++ = val;
}
} else {
// Interpolate
// Calculate sub-octave coordinates
int margin = 2;
int64_t si0 = (i0 >> 1) - margin;
int64_t si1 = ((i1 - 1) >> 1) + margin + 1;
// Get sub-octave data
gaborator::pod_vector<T> sub_data(si1 - si0);
T *p = sub_data.data();
p = resample2_ptr(source, origin, si0, si1, e + 1, interpolate, p);
assert(p == sub_data.data() + si1 - si0);
for (int64_t i = i0; i < i1; i++) {
int64_t si = (i >> 1) - si0;
T val;
if (i & 1) {
T v1 = sub_data[si - 1];
T v0 = sub_data[si];
v0 += sub_data[si + 1];
v1 += sub_data[si + 2];
val =
v0 * (T)0.5625 +
v1 * (T)-0.0625;
} else {
val = sub_data[si];
}
*out++ = val;
}
}
} else {
// e == 0
out = source(origin + i0, origin + i1, out);
}
return out;
}
template <class S, class OI>
OI resample2(const S &source, int64_t origin,
int64_t i0, int64_t i1, int e,
bool interpolate, OI out)
{
typedef typename std::iterator_traits<OI>::value_type T;
gaborator::pod_vector<T> data(i1 - i0);
T *p = data.data();
p = resample2_ptr(source, origin, i0, i1, e, interpolate, p);
return std::copy(data.data(), data.data() + (i1 - i0), out);
}
// Calculate the range of source indices that will be accessed
// by a call to resample2(source, i0, i1, e) and return it
// through si0_ret and si1_ret.
// XXX this should take an "interpolate" argument so we don't
// return an unnecessarily large support when interpolation is off
inline void
resample2_support(int64_t origin, int64_t i0, int64_t i1, int e,
int64_t &si0_ret, int64_t &si1_ret)
{
// Conservative
int margin = 2;
if (e > 0) {
// Note code duplication wrt resample2_ptr().
// Also note tail recursion.
int64_t si0 = i0 * 2 - margin * 2 + 1;
int64_t si1 = i1 * 2 + margin * 2;
resample2_support(origin, si0, si1, e - 1, si0_ret, si1_ret);
} else if (e < 0) {
int64_t si0 = (i0 >> 1) - margin;
int64_t si1 = ((i1 - 1) >> 1) + margin + 1;
resample2_support(origin, si0, si1, e + 1, si0_ret, si1_ret);
} else {
si0_ret = origin + i0;
si1_ret = origin + i1;
}
}
} // namespace
#endif

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//
// Vector math operations
//
// Copyright (C) 2016-2018 Andreas Gustafsson. This file is part of
// the Gaborator library source distribution. See the file LICENSE at
// the top level of the distribution for license information.
//
#ifndef _GABORATOR_VECTOR_MATH_H
#define _GABORATOR_VECTOR_MATH_H
#include <assert.h>
#if GABORATOR_USE_SSE3_INTRINSICS
#include <pmmintrin.h>
#endif
#include <complex>
namespace gaborator {
// The _naive versions are used when SSE is not available, and as
// references when testing the SSE versions
// Naive or not, this is faster than the macOS std::complex
// multiplication operator, which checks for infinities even with
// -ffast-math.
template <class T>
std::complex<T> complex_mul_naive(std::complex<T> a,
std::complex<T> b)
{
return std::complex<T>(a.real() * b.real() - a.imag() * b.imag(),
a.real() * b.imag() + a.imag() * b.real());
}
#if GABORATOR_USE_SSE3_INTRINSICS
// Note: this is sometimes slower than the naive code.
static inline
std::complex<double> complex_mul(std::complex<double> a_,
std::complex<double> b_)
{
__v2df a = _mm_setr_pd(a_.real(), a_.imag());
__v2df b = _mm_setr_pd(b_.real(), b_.imag());
__v2df as = (__v2df) _mm_shuffle_pd(a, a, 0x1);
__v2df t0 = _mm_mul_pd(a, _mm_shuffle_pd(b, b, 0x0));
__v2df t1 = _mm_mul_pd(as, _mm_shuffle_pd(b, b, 0x3));
__v2df c = __builtin_ia32_addsubpd(t0, t1); // SSE3
return std::complex<double>(c[0], c[1]);
}
#else
static inline
std::complex<double> complex_mul(std::complex<double> a_,
std::complex<double> b_)
{
return complex_mul_naive(a_, b_);
}
#endif
static inline
std::complex<float> complex_mul(std::complex<float> a_,
std::complex<float> b_)
{
return complex_mul_naive(a_, b_);
}
template <class T, class U, class V>
static inline void
elementwise_product_naive(T *r,
U *a,
V *b,
int n)
{
for (int i = 0; i < n; i++)
r[i] = complex_mul(a[i], b[i]);
}
template <class T, class U, class V, class S>
static inline void
elementwise_product_times_scalar_naive(T *r,
U *a,
V *b,
S s,
int n)
{
for (int i = 0; i < n; i++)
r[i] = a[i] * b[i] * s;
}
// I is the input complex data type, O is the output data type
template <class I, class O>
static inline void
complex_magnitude_naive(I *inv,
O *outv,
int n)
{
for (int i = 0; i < n; i++)
outv[i] = std::sqrt(inv[i].real() * inv[i].real() + inv[i].imag() * inv[i].imag());
}
#if GABORATOR_USE_SSE3_INTRINSICS
#include <pmmintrin.h>
// Perform two complex float multiplies in parallel
static inline
__v4sf complex_mul_vec2(__v4sf aa, __v4sf bb) {
__v4sf aas =_mm_shuffle_ps(aa, aa, 0xb1);
__v4sf t0 = _mm_mul_ps(aa, _mm_moveldup_ps(bb));
__v4sf t1 = _mm_mul_ps(aas, _mm_movehdup_ps(bb));
return __builtin_ia32_addsubps(t0, t1); // SSE3
}
// Calculate the elementwise product of a complex float vector
// and another complex float vector.
static inline void
elementwise_product(std::complex<float> *cv,
const std::complex<float> *av,
const std::complex<float> *bv,
int n)
{
assert((n & 1) == 0);
n >>= 1;
__v4sf *c = (__v4sf *) cv;
const __v4sf *a = (const __v4sf *) av;
const __v4sf *b = (const __v4sf *) bv;
while (n--) {
__v4sf aa = *a++;
__v4sf bb = *b++;
*c++ = complex_mul_vec2(aa, bb);
}
}
// Calculate the elementwise product of a complex float vector
// and real float vector.
//
// The input "a" may be unaligned; the output "c" must be aligned.
static inline void
elementwise_product(std::complex<float> *cv,
const std::complex<float> *av,
const float *bv,
int n)
{
assert((n & 3) == 0);
n >>= 2;
__v4sf *c = (__v4sf *) cv;
const __v4sf *a = (const __v4sf *) av;
const __v4sf *b = (const __v4sf *) bv;
while (n--) {
__v4sf a0 = (__v4sf) _mm_loadu_si128((const __m128i *) a++);
__v4sf a1 = (__v4sf) _mm_loadu_si128((const __m128i *) a++);
__v4sf bb = *b++;
*c++ = _mm_mul_ps(a0, _mm_unpacklo_ps(bb, bb));
*c++ = _mm_mul_ps(a1, _mm_unpackhi_ps(bb, bb));
}
}
static inline void
elementwise_product_times_scalar(std::complex<float> *cv,
const std::complex<float> *av,
const std::complex<float> *bv,
std::complex<float> d,
int n)
{
assert((n & 1) == 0);
n >>= 1;
const __v4sf *a = (const __v4sf *) av;
const __v4sf *b = (const __v4sf *) bv;
const __v4sf dd = (__v4sf) { d.real(), d.imag(), d.real(), d.imag() };
__v4sf *c = (__v4sf *) cv;
while (n--) {
__v4sf aa = *a++;
__v4sf bb = *b++;
*c++ = complex_mul_vec2(complex_mul_vec2(aa, bb), dd);
}
}
// XXX arguments reversed wrt others
static inline void
complex_magnitude(std::complex<float> *inv,
float *outv,
int n)
{
// Processes four complex values (32 bytes) at a time ,
// outputting four scalar magnitudes (16 bytes) at a time.
while ((((uintptr_t) inv) & 0x1F) && n) {
std::complex<float> v = *inv++;
*outv++ = std::sqrt(v.real() * v.real() + v.imag() * v.imag());
n--;
}
const __v4sf *in = (const __v4sf *) inv;
__v4sf *out = (__v4sf *) outv;
while (n >= 4) {
__v4sf aa = *in++; // c0re c0im c1re c1im
__v4sf aa2 = _mm_mul_ps(aa, aa); // c0re^2 c0im^2 c1re^2 c1im^2
__v4sf bb = *in++; // c2re c2im c3re c3im
__v4sf bb2 = _mm_mul_ps(bb, bb); // etc
// Gather the real parts: x0 x2 y0 y2
// 10 00 10 00 = 0x88
__v4sf re2 =_mm_shuffle_ps(aa2, bb2, 0x88);
__v4sf im2 =_mm_shuffle_ps(aa2, bb2, 0xdd);
__v4sf mag2 = _mm_add_ps(re2, im2);
__v4sf mag = __builtin_ia32_sqrtps(mag2);
// Unaligned store
_mm_storeu_si128((__m128i *)out, (__m128i)mag);
out++;
n -= 4;
}
inv = (std::complex<float> *) in;
outv = (float *)out;
while (n) {
std::complex<float> v = *inv++;
*outv++ = std::sqrt(v.real() * v.real() + v.imag() * v.imag());
n--;
}
}
// Double-precision version is unoptimized
static inline void
elementwise_product(std::complex<double> *c,
const std::complex<double> *a,
const std::complex<double> *b,
int n)
{
elementwise_product_naive(c, a, b, n);
}
static inline void
elementwise_product(std::complex<double> *c,
const std::complex<double> *a,
const double *b,
int n)
{
elementwise_product_naive(c, a, b, n);
}
template <class T, class U, class V, class S>
static inline void
elementwise_product_times_scalar(T *r,
U *a,
V *b,
S s,
int n)
{
elementwise_product_times_scalar_naive(r, a, b, s, n);
}
template <class O>
static inline void
complex_magnitude(std::complex<double> *inv,
O *outv,
int n)
{
complex_magnitude_naive(inv, outv, n);
}
#else // ! GABORATOR_USE_SSE3_INTRINSICS
// Forward to the naive implementations. These are inline functions
// rather than #defines to avoid namespace pollution.
template <class T, class U, class V>
static inline void
elementwise_product(T *r,
U *a,
V *b,
int n)
{
elementwise_product_naive(r, a, b, n);
}
template <class T, class U, class V, class S>
static inline void
elementwise_product_times_scalar(T *r,
U *a,
V *b,
S s,
int n)
{
elementwise_product_times_scalar_naive(r, a, b, s, n);
}
template <class I, class O>
static inline void
complex_magnitude(I *inv,
O *outv,
int n)
{
complex_magnitude_naive(inv, outv, n);
}
#endif // ! USE_SSE3_INTINSICS
} // namespace
#endif