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Flamefire committed 2014-03-29 22:54:37 +01:00
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PitchTracker/performous/License.txt
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code is based on Performous: https://github.com/performous/performous/tree/master/game
Some modifications were made to make it compile with VS2012, fix warnings and make it suitable for our needs
From 25.03.2014
PitchTracker/performous/Performous.txt
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GNU GPLv2 or later. Some parts of the project may have more liberal licenses.
See Authors.txt for information on copyright holders and licenses of specific
parts. Fonts are licensed under SIL OFL.
GNU GENERAL PUBLIC LICENSE
Version 2, June 1991
Copyright (C) 1989, 1991 Free Software Foundation, Inc.
51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
The licenses for most software are designed to take away your
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License is intended to guarantee your freedom to share and change free
software--to make sure the software is free for all its users. This
General Public License applies to most of the Free Software
Foundation's software and to any other program whose authors commit to
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The precise terms and conditions for copying, distribution and
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GNU GENERAL PUBLIC LICENSE
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
0. This License applies to any program or other work which contains
a notice placed by the copyright holder saying it may be distributed
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convey the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
Also add information on how to contact you by electronic and paper mail.
If the program is interactive, make it output a short notice like this
when it starts in an interactive mode:
Gnomovision version 69, Copyright (C) year name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
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You should also get your employer (if you work as a programmer) or your
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necessary. Here is a sample; alter the names:
Yoyodyne, Inc., hereby disclaims all copyright interest in the program
`Gnomovision' (which makes passes at compilers) written by James Hacker.
<signature of Ty Coon>, 1 April 1989
Ty Coon, President of Vice
This General Public License does not permit incorporating your program into
proprietary programs. If your program is a subroutine library, you may
consider it more useful to permit linking proprietary applications with the
library. If this is what you want to do, use the GNU Library General
Public License instead of this License.
PitchTracker/performous/libda/fft.hpp
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#pragma once
/**
* @file fft.hpp FFT and related facilities.
*/
#include "sample.hpp"
#include <complex>
#include <cstddef>
#include <vector>
#ifndef M_PI
#define M_PI 3.141592653589793
#endif
#define M_TAU (2.0 * M_PI)
namespace da {
// With g++ optimization -fcx-limited-range should be used for 5x performance boost.
// Based on the description of Volodymyr Myrnyy in
// http://www.dspdesignline.com/showArticle.jhtml?printableArticle=true&articleId=199903272
template<unsigned P, typename T> struct DanielsonLanczos {
static void apply(std::complex<T>* data) {
constexpr std::size_t N = 1 << P;
constexpr std::size_t M = N / 2;
// Compute even and odd halves
DanielsonLanczos<P - 1, T>().apply(data);
DanielsonLanczos<P - 1, T>().apply(data + M);
// Combine the results
std::complex<T> w(1.0);
for (std::size_t i = 0; i < M; ++i) {
const std::complex<T> temp = data[i + M] * w;
data[M + i] = data[i] - temp;
data[i] += temp;
w *= std::polar(1.0, -M_TAU / N);
}
}
};
template<typename T> struct DanielsonLanczos<0, T> { static void apply(std::complex<T>*) {} };
/** Perform FFT on data. **/
template<unsigned P, typename T> void fft(std::complex<T>* data) {
// Perform bit-reversal sorting of sample data.
constexpr std::size_t N = 1 << P;
std::size_t j = 0;
for (std::size_t i = 0; i < N; ++i) {
if (i < j) std::swap(data[i], data[j]);
std::size_t m = N / 2;
while (m > 1 && m <= j) { j -= m; m >>= 1; }
j += m;
}
// Do the actual calculation
DanielsonLanczos<P, T>::apply(data);
}
/** Perform FFT on data from floating point iterator, windowing the input. **/
template<unsigned P, typename InIt, typename Window> std::vector<std::complex<float> > fft(InIt begin, Window window) {
std::vector<std::complex<float> > data(1 << P);
// Perform bit-reversal sorting of sample data.
constexpr std::size_t N = 1 << P;
std::size_t j = 0;
for (std::size_t i = 0; i < N; ++i) {
data[j] = *begin++ * window[i];
std::size_t m = N / 2;
while (m > 1 && m <= j) { j -= m; m >>= 1; }
j += m;
}
// Do the actual calculation
DanielsonLanczos<P, float>::apply(&data[0]);
return data;
}
template<unsigned P, typename T> void ifft(std::complex<T>* data) {
constexpr std::size_t N = 1 << P;
for (std::size_t i = 0; i < N; ++i) data[i] = std::conj(data[i]); // Invert phase so that we can use FFT to do IFFT
fft<P>(data);
constexpr std::complex<T> scale(1.0/N, 0.0);
for (std::size_t i = 0; i < N; ++i) data[i] = scale * std::conj(data[i]); // Invert back, and apply IFFT scaling
}
}
PitchTracker/performous/libda/sample.hpp
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#pragma once
#include <cmath>
#include "../compatibility.h"
/**
* @file sample.hpp Sample format definition and format conversions.
*/
namespace da {
using std::round;
// Should be a floating-point type
typedef float sample_t;
// A helper function for clamping a value to a certain range
template <typename T> T clamp(T val, T min, T max) {
if (val < min) val = min;
if (val > max) val = max;
return val;
}
constexpr sample_t max_s16(32767), min_s16 = -max_s16 - sample_t(1);
constexpr sample_t max_s24(8388607), min_s24 = -max_s24 - sample_t(1);
constexpr sample_t max_s32(2147483647), min_s32= -max_s32 - sample_t(1);
constexpr double tau(6.2831853071795864769252867665590057683943387987502116); ///< One full circle
constexpr double pi = tau / sample_t(2); ///< Half circle
constexpr double eps(1e-10); ///< Tiny positive value
/// Mathematical sinc function
template<typename Float> static inline Float msinc(Float x) { return std::abs(x) < Float(eps) ? Float(1) : std::sin(x) / x; }
/// Normalized (signal processing) sinc function
template<typename Float> static inline Float sinc(Float x) { return msinc(Float(pi) * x); }
/// Lanczos kernel of size A
template<unsigned A, typename Float> static inline Float lanc(Float x) {
return std::abs(x) < A ? sinc(x) * sinc(x / A) : Float();
}
// The following conversions provide lossless conversions between floats
// and integers. Be sure to use only these conversions or otherwise the
// conversions may not be lossless, due to different scaling factors being
// used by different libraries.
// The negative minimum integer value produces sample_t value slightly
// more negative than -1.0 but this is necessary in order to prevent
// clipping in the float-to-int conversions. Now amplitude 1.0 in floating
// point produces -32767 .. 32767 symmetrical non-clipping range in s16.
static inline sample_t conv_from_s16(int s) { return s / max_s16; }
static inline sample_t conv_from_s24(int s) { return s / max_s24; }
static inline sample_t conv_from_s32(int s) { return s / max_s32; }
// The rounding is strictly not necessary, but it greatly improves
// the error tolerance if any floating point calculations are done.
// The ugly static_casts are required to avoid warnings in MSVC.
static inline int conv_to_s16(sample_t s) { return clamp(static_cast<int>(round(s * max_s16)), static_cast<int>(min_s16), static_cast<int>(max_s16)); }
static inline int conv_to_s24(sample_t s) { return clamp(static_cast<int>(round(s * max_s24)), static_cast<int>(min_s24), static_cast<int>(max_s24)); }
static inline int conv_to_s32(sample_t s) { return static_cast<int>(clamp(round(s * max_s32), min_s32, max_s32 )); }
// Non-rounding non-clamping versions are provided for very low end devices (still lossless)
static inline int conv_to_s16_fast(sample_t s) { return static_cast<int>(s * max_s16); }
static inline int conv_to_s24_fast(sample_t s) { return static_cast<int>(s * max_s24); }
static inline int conv_to_s32_fast(sample_t s) { return static_cast<int>(s * max_s32); }
template <typename ValueType> class step_iterator: public std::iterator<std::random_access_iterator_tag, ValueType> {
ValueType* m_pos;
std::ptrdiff_t m_step;
public:
step_iterator(ValueType* pos, std::ptrdiff_t step): m_pos(pos), m_step(step) {}
ValueType& operator*() { return *m_pos; }
step_iterator operator+(std::ptrdiff_t rhs) { return step_iterator(m_pos + m_step * rhs, m_step); }
step_iterator& operator++() { m_pos += m_step; return *this; }
step_iterator operator++(int) { step_iterator ret = *this; ++*this; return ret; }
bool operator!=(step_iterator const& rhs) const { return m_pos != rhs.m_pos; }
std::ptrdiff_t operator-(step_iterator const& rhs) const { return (m_pos - rhs.m_pos) / m_step; }
// TODO: more operators
};
typedef step_iterator<sample_t> sample_iterator;
typedef step_iterator<sample_t const> sample_const_iterator;
}
PitchTracker/performous/pitch.cc
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#include "pitch.hh"
#include "util.hh"
#include "libda/fft.hpp"
#include <cmath>
#include <iostream>
#include <iomanip>
// Limit the range to avoid noise and useless computation
static const double FFT_MINFREQ = 45.0;
static const double FFT_MAXFREQ = 5000.0;
Tone::Tone():
freq(0.0),
db(-getInf()),
stabledb(-getInf()),
age()
{
for (auto& h: harmonics) h = -getInf();
}
void Tone::print() const {
if (age < Tone::MINAGE) return;
std::cout << std::fixed << std::setprecision(1) << freq << " Hz, age " << age << ", " << db << " dB:";
for (std::size_t i = 0; i < 8; ++i) std::cout << " " << harmonics[i];
std::cout << std::endl;
}
bool Tone::operator==(double f) const {
return std::abs(freq / f - 1.0) < 0.05;
}
Analyzer::Analyzer(double rate, std::string id, unsigned step):
m_step(step),
m_resampleFactor(1.0),
m_resamplePos(),
m_rate(rate),
m_id(id),
m_window(FFT_N),
m_fftLastPhase(FFT_N / 2),
m_peak(0.0),
m_oldfreq(0.0)
{
if (m_step > FFT_N) throw std::logic_error("Analyzer step is larger that FFT_N (ideally it should be less than a fourth of FFT_N).");
// Hamming window
for (size_t i=0; i < FFT_N; i++) {
m_window[i] = static_cast<float>(0.53836 - 0.46164 * std::cos(2.0 * M_PI * i / (FFT_N - 1)));
}
}
bool Analyzer::output(float* begin, float* end, double rate) {
constexpr unsigned a = 2;
const size_t size = m_passthrough.size();
const unsigned out = static_cast<unsigned>((end - begin) / 2 /* stereo */);
if (out == 0) return false;
const unsigned in = static_cast<unsigned>(m_resampleFactor * (m_rate / rate) * out + 2 * a /* lanczos kernel */ + 5 /* safety margin for rounding errors */);
float pcm[m_passthrough.capacity];
if(!m_passthrough.read(pcm, pcm + in + 4))
return false;
for (unsigned i = 0; i < out; ++i) {
double s = 0.0;
unsigned k = static_cast<unsigned>(m_resamplePos);
double x = m_resamplePos - k;
// Lanczos sampling of input at m_resamplePos
for (unsigned j = 0; j <= 2 * a; ++j) s += pcm[k + j] * da::lanc<a>(x - j + a);
s *= 5.0;
begin[i * 2] += (float) s;
begin[i * 2 + 1] += (float) s;
m_resamplePos += m_resampleFactor;
}
unsigned num = static_cast<unsigned>(m_resamplePos);
m_resamplePos -= num;
if (size > 3000) {
// Reset
m_passthrough.pop(size - 700);
m_resampleFactor = 1.0;
} else {
m_passthrough.pop(num);
m_resampleFactor = 0.99 * m_resampleFactor + 0.01 * (size > 700 ? 1.02 : 0.98);
}
return true;
}
namespace {
struct Peak {
double freq;
double db;
bool harm[Tone::MAXHARM];
Peak(double _freq = 0.0, double _db = -getInf()):
freq(_freq), db(_db)
{
for (auto& h: harm) h = false;
}
void clear() {
freq = 0.0;
db = -getInf();
}
};
Peak& match(std::vector<Peak>& peaks, std::size_t pos) {
std::size_t best = pos;
if (peaks[pos - 1].db > peaks[best].db) best = pos - 1;
if (peaks[pos + 1].db > peaks[best].db) best = pos + 1;
return peaks[best];
}
}
bool Analyzer::calcFFT() {
float pcm[FFT_N];
// Read FFT_N samples, move forward by m_step samples
if (!m_buf.read(pcm, pcm + FFT_N)) return false;
m_buf.pop(m_step);
// Peak level calculation of the most recent m_step samples (the rest is overlap)
for (float const* ptr = pcm + FFT_N - m_step; ptr != pcm + FFT_N; ++ptr) {
float s = *ptr;
float p = s * s;
if (p > m_peak) m_peak = p; else m_peak *= 0.999;
}
// Calculate FFT
m_fft = da::fft<FFT_P>(pcm, m_window);
return true;
}
void Analyzer::calcTones() {
// Precalculated constants
const double freqPerBin = m_rate / FFT_N;
const double phaseStep = 2.0 * M_PI * m_step / FFT_N;
const double normCoeff = 1.0 / FFT_N;
const double minMagnitude = pow(10, -100.0 / 20.0) / normCoeff; // -100 dB
// Limit frequency range of processing
const size_t kMin = std::max(size_t(1), size_t(FFT_MINFREQ / freqPerBin));
const size_t kMax = std::min(FFT_N / 2, size_t(FFT_MAXFREQ / freqPerBin));
std::vector<Peak> peaks(kMax + 1); // One extra to simplify loops
for (size_t k = 1; k <= kMax; ++k) {
double magnitude = std::abs(m_fft[k]);
double phase = std::arg(m_fft[k]);
// process phase difference
double delta = phase - m_fftLastPhase[k];
m_fftLastPhase[k] = static_cast<float>(phase);
delta -= k * phaseStep; // subtract expected phase difference
delta = remainder(delta, 2.0 * M_PI); // map delta phase into +/- M_PI interval
delta /= phaseStep; // calculate diff from bin center frequency
double freq = (k + delta) * freqPerBin; // calculate the true frequency
if (freq > 1.0 && magnitude > minMagnitude) {
peaks[k].freq = freq;
peaks[k].db = 20.0 * log10(normCoeff * magnitude);
}
}
// Prefilter peaks
double prevdb = peaks[0].db;
for (size_t k = 1; k < kMax; ++k) {
double db = peaks[k].db;
if (db > prevdb) peaks[k - 1].clear();
if (db < prevdb) peaks[k].clear();
prevdb = db;
}
// Find the tones (collections of harmonics) from the array of peaks
tones_t tones;
for (size_t k = kMax - 1; k >= kMin; --k) {
if (peaks[k].db < -70.0) continue;
// Find the best divider for getting the fundamental from peaks[k]
std::size_t bestDiv = 1;
int bestScore = 0;
for (std::size_t div = 2; div <= Tone::MAXHARM && k / div > 1; ++div) {
double freq = peaks[k].freq / div; // Fundamental
int score = 0;
for (std::size_t n = 1; n < div && n < 8; ++n) {
Peak& p = match(peaks, k * n / div);
--score;
if (p.db < -90.0 || std::abs(p.freq / n / freq - 1.0) > .03) continue;
if (n == 1) score += 4; // Extra for fundamental
score += 2;
}
if (score > bestScore) {
bestScore = score;
bestDiv = div;
}
}
// Construct a Tone by combining the fundamental frequency (freq) and all harmonics
Tone t;
std::size_t count = 0;
double freq = peaks[k].freq / bestDiv;
t.db = peaks[k].db;
for (std::size_t n = 1; n <= bestDiv; ++n) {
// Find the peak for n'th harmonic
Peak& p = match(peaks, k * n / bestDiv);
if (std::abs(p.freq / n / freq - 1.0) > .03) continue; // Does it match the fundamental freq?
if (p.db > t.db - 10.0) {
t.db = std::max(t.db, p.db);
++count;
t.freq += p.freq / n;
}
t.harmonics[n - 1] = p.db;
p.clear();
}
t.freq /= count;
// If the tone seems strong enough, add it (-3 dB compensation for each harmonic)
if (t.db > -50.0 - 3.0 * count) {
t.stabledb = t.db;
tones.push_back(t);
}
}
mergeWithOld(tones);
m_tones.swap(tones);
}
void Analyzer::mergeWithOld(tones_t& tones) const {
tones.sort();
auto it = tones.begin();
// Iterate over old tones
for (auto const& old: m_tones) {
// Try to find a matching new tone
while (it != tones.end() && *it < old) ++it;
// If match found
if (it != tones.end() && *it == old) {
// Merge the old tone into the new tone
it->age = old.age + 1;
it->stabledb = 0.8 * old.stabledb + 0.2 * it->db;
it->freq = 0.5 * old.freq + 0.5 * it->freq;
} else if (old.db > -80.0) {
// Insert a decayed version of the old tone into new tones
Tone& t = *tones.insert(it, old);
t.db -= 5.0;
t.stabledb -= 0.1;
}
}
}
void Analyzer::process() {
// Try calculating FFT and calculate tones until no more data in input buffer
while (calcFFT()) calcTones();
}
PitchTracker/performous/pitch.hh
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#pragma once
#include <complex>
#include <vector>
#include <list>
#include <algorithm>
#include <cmath>
#include "../compatibility.h"
/// struct to represent tones
struct Tone {
static const std::size_t MAXHARM = 48; ///< The maximum number of harmonics tracked
static const std::size_t MINAGE = 2; ///< The minimum age required for a tone to be output
double freq; ///< Frequency (Hz)
double db; ///< Level (dB)
double stabledb; ///< Stable level, useful for graphics rendering
double harmonics[MAXHARM]; ///< Harmonics' levels
std::size_t age; ///< How many times the tone has been detected in row
Tone();
void print() const; ///< Prints Tone to std::cout
bool operator==(double f) const; ///< Compare for rough frequency match
/// Less-than compare by levels (instead of frequencies like operator< does)
static bool dbCompare(Tone const& l, Tone const& r) { return l.db < r.db; }
};
static inline bool operator==(Tone const& lhs, Tone const& rhs) { return lhs == rhs.freq; }
static inline bool operator!=(Tone const& lhs, Tone const& rhs) { return !(lhs == rhs); }
static inline bool operator<=(Tone const& lhs, Tone const& rhs) { return lhs.freq < rhs.freq || lhs == rhs; }
static inline bool operator>=(Tone const& lhs, Tone const& rhs) { return lhs.freq > rhs.freq || lhs == rhs; }
static inline bool operator<(Tone const& lhs, Tone const& rhs) { return lhs.freq < rhs.freq && lhs != rhs; }
static inline bool operator>(Tone const& lhs, Tone const& rhs) { return lhs.freq > rhs.freq && lhs != rhs; }
static const unsigned FFT_P = 10;
static const std::size_t FFT_N = 1 << FFT_P;
/// Lock-free ring buffer. Discards oldest data on overflow (not strictly thread-safe).
template <size_t SIZE> class RingBuffer {
public:
constexpr static size_t capacity = SIZE;
RingBuffer(): m_read(), m_write() {} ///< Initialize empty buffer
template <typename InIt> void insert(InIt begin, InIt end) {
size_t r = m_read; // The read position
size_t w = m_write; // The write position
bool overflow = (static_cast<size_t>(end - begin) >= SIZE - size());
while (begin != end) {
m_buf[w] = *begin++; // Copy sample
w = modulo(w + 1); // Update cursor
}
m_write = w;
if (overflow) m_read = modulo(w + 1); // Reset read pointer on overflow
}
/// Read data from current position if there is enough data to fill the range (otherwise return false). Does not move read pointer.
template <typename OutIt> bool read(OutIt begin, OutIt end) {
size_t r = m_read;
if (size() < static_cast<size_t>(end - begin)) return false; // Not enough audio available
while (begin != end) *begin++ = m_buf[r++ % SIZE]; // Copy audio to output iterator
return true;
}
void pop(size_t n) { m_read = modulo(m_read + n); } ///< Move reading pointer forward.
size_t size() const { return modulo(m_write - m_read); }
private:
static size_t modulo(size_t idx) { return idx % SIZE; } ///< Modulo operation with proper rounding (handles slightly "negative" idx as well)
float m_buf[SIZE];
volatile size_t m_read, m_write; ///< The indices of the next read/write operations. read == write implies that buffer is empty.
};
/// analyzer class
/** class to analyze input audio and transform it into useable data
*/
class Analyzer {
public:
/// fast fourier transform vector
typedef std::vector<std::complex<float> > fft_t;
/// list of tones
typedef std::list<Tone> tones_t;
/// constructor
Analyzer(double rate, std::string id, unsigned step = 200);
/** Add input data to buffer. This is thread-safe (against other functions). **/
template <typename InIt> void input(InIt begin, InIt end) {
m_buf.insert(begin, end);
m_passthrough.insert(begin, end);
}
/** Call this to process all data input so far. **/
void process();
/** Get the raw FFT. **/
fft_t const& getFFT() const { return m_fft; }
/** Get the peak level in dB (negative value, 0.0 = clipping). **/
double getPeak() const { return 10.0 * log10(m_peak); }
/** Get a list of all tones detected. **/
tones_t const& getTones() const { return m_tones; }
/** Find a tone within the singing range; prefers strong tones around 200-400 Hz. **/
Tone const* findTone(double minfreq = 65.0, double maxfreq = 1000.0) const {
if (m_tones.empty()) { m_oldfreq = 0.0; return NULL; }
double db = std::max_element(m_tones.begin(), m_tones.end(), Tone::dbCompare)->db;
Tone const* best = NULL;
double bestscore = 0;
for (tones_t::const_iterator it = m_tones.begin(); it != m_tones.end(); ++it) {
if (it->db < db - 20.0 || it->freq < minfreq || it->age < Tone::MINAGE) continue;
if (it->freq > maxfreq) break;
double score = it->db - std::max(180.0, std::abs(it->freq - 300.0)) / 10.0;
if (m_oldfreq != 0.0 && std::fabs(it->freq/m_oldfreq - 1.0) < 0.05) score += 10.0;
if (best && bestscore > score) break;
best = &*it;
bestscore = score;
}
m_oldfreq = (best ? best->freq : 0.0);
return best;
}
/** Give data away for mic pass-through */
bool output(float* begin, float* end, double rate);
/** Returns the id (color name) of the mic */
std::string const& getId() const { return m_id; }
private:
const unsigned m_step;
RingBuffer<4 * FFT_N> m_buf; // Twice the FFT size should give enough room for sliding window and for engine delays
RingBuffer<4096> m_passthrough;
double m_resampleFactor;
double m_resamplePos;
double m_rate;
std::string m_id;
std::vector<float> m_window;
fft_t m_fft;
std::vector<float> m_fftLastPhase;
double m_peak;
tones_t m_tones;
mutable double m_oldfreq;
bool calcFFT();
void calcTones();
void mergeWithOld(tones_t& tones) const;
};
PitchTracker/performous/util.hh
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#pragma once
#include <cstdint>
#include <limits>
#include <vector>
#include <stdexcept>
/** Limit val to range [min, max] **/
template <typename T> T clamp(T val, T min = 0, T max = 1) {
if (min > max) throw std::logic_error("min > max");
if (val < min) return min;
if (val > max) return max;
return val;
}
template <typename Numeric> struct MinMax {
Numeric min, max;
explicit MinMax(Numeric min = std::numeric_limits<Numeric>::min(), Numeric max = std::numeric_limits<Numeric>::max()): min(min), max(max) {}
bool matches(Numeric val) const { return val >= min && val <= max; }
};
/** A convenient way for getting NaNs **/
static inline double getNaN() { return std::numeric_limits<double>::quiet_NaN(); }
/** A convenient way for getting infs **/
static inline double getInf() { return std::numeric_limits<double>::infinity(); }
static inline bool isPow2(unsigned int val) {
if (val == 0) return false;
if ((val & (val-1)) == 0) return true; // From Wikipedia: Power_of_two
return false;
}
static inline unsigned int nextPow2(unsigned int val) {
unsigned int ret = 1;
while (ret < val) ret *= 2;
return ret;
}
static inline unsigned int prevPow2(unsigned int val) {
unsigned int ret = 1;
while ((ret*2) < val) ret *= 2;
return ret;
}