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livetrax/libs/evoral/Curve.cc
Paul Davis 4fb3e24bd6 evoral: tentative fix for problems with Curve::multipoint_eval()
Now that we use superclock_t for audio time, it is possible for the square of an audio time value to overflow int64_t quite easily.
This change fixes that (and cleans up other code a little), but probably a different solution would be a good idea
2021-08-30 14:29:11 -06:00

487 lines
12 KiB
C++

/*
* Copyright (C) 2008-2013 Paul Davis <paul@linuxaudiosystems.com>
* Copyright (C) 2008-2016 David Robillard <d@drobilla.net>
* Copyright (C) 2010-2012 Carl Hetherington <carl@carlh.net>
* Copyright (C) 2012-2018 Robin Gareus <robin@gareus.org>
*
* 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 along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*/
#include <iostream>
#include <float.h>
#include <cmath>
#include <climits>
#include <cfloat>
#include <cmath>
#include <vector>
#include <glibmm/threads.h>
#include "pbd/control_math.h"
#include "evoral/Curve.h"
#include "evoral/ControlList.h"
using namespace std;
using namespace sigc;
namespace Evoral {
Curve::Curve (const ControlList& cl)
: _dirty (true)
, _list (cl)
{
}
void
Curve::solve () const
{
uint32_t npoints;
if (!_dirty) {
return;
}
if ((npoints = _list.events().size()) > 2) {
/* Compute coefficients needed to efficiently compute a constrained spline
curve. See "Constrained Cubic Spline Interpolation" by CJC Kruger
(www.korf.co.uk/spline.pdf) for more details.
*/
vector<Temporal::timepos_t> x (npoints);
vector<double> y(npoints);
uint32_t i;
ControlList::EventList::const_iterator xx;
for (i = 0, xx = _list.events().begin(); xx != _list.events().end(); ++xx, ++i) {
x[i] = (*xx)->when;
y[i] = (*xx)->value;
}
double lp0, lp1, fpone;
double xd;
xd = x[0].distance (x[1]).magnitude();
lp0 = xd/(y[1] - y[0]);
xd = x[1].distance (x[2]).magnitude();
lp1 = xd/(y[2] - y[1]);
if (lp0*lp1 < 0) {
fpone = 0;
} else {
fpone = 2 / (lp1 + lp0);
}
double fplast = 0;
for (i = 0, xx = _list.events().begin(); xx != _list.events().end(); ++xx, ++i) {
double xi = x[i].val();
if (i == 0) {
/* first segment */
fplast = ((3 * (y[1] - y[0]) / (2 * (x[1].val() - x[0].val()))) - (fpone * 0.5));
/* we don't store coefficients for i = 0 */
continue;
}
double xdelta; /* gcc is wrong about possible uninitialized use */
double xdelta2; /* ditto */
double ydelta; /* ditto */
double fppL, fppR;
double fpi;
double xim1;
xim1 = x[i-1].val();
xdelta = xi - xim1;
xdelta2 = xdelta * xdelta;
ydelta = y[i] - y[i-1];
/* compute (constrained) first derivatives */
if (i == npoints - 1) {
/* last segment */
fpi = ((3 * ydelta) / (2 * xdelta)) - (fplast * 0.5);
} else {
/* all other segments */
double slope_before = (x[i+1].val() - xi) / (y[i+1] - y[i]);
double slope_after = (xdelta / ydelta);
if (slope_after * slope_before < 0.0) {
/* slope changed sign */
fpi = 0.0;
} else {
fpi = 2 / (slope_before + slope_after);
}
}
/* compute second derivative for either side of control point `i' */
fppL = (((-2 * (fpi + (2 * fplast))) / (xdelta))) +
((6 * ydelta) / xdelta2);
fppR = (2 * ((2 * fpi) + fplast) / xdelta) -
((6 * ydelta) / xdelta2);
/* compute polynomial coefficients */
double b, c, d;
d = (fppR - fppL) / (6 * xdelta);
c = ((xi * fppL) - (xim1 * fppR))/(2 * xdelta);
double xim12, xim13;
double xi2, xi3;
xim12 = xim1 * xim1; /* "x[i-1] squared" */
xim13 = xim12 * xim1; /* "x[i-1] cubed" */
xi2 = xi * xi; /* "x[i] squared" */
xi3 = xi2 * xi; /* "x[i] cubed" */
b = (ydelta - (c * (xi2 - xim12)) - (d * (xi3 - xim13))) / xdelta;
/* store */
(*xx)->create_coeffs();
(*xx)->coeff[0] = y[i-1] - (b * xim1) - (c * xim12) - (d * xim13);
(*xx)->coeff[1] = b;
(*xx)->coeff[2] = c;
(*xx)->coeff[3] = d;
fplast = fpi;
}
}
_dirty = false;
}
bool
Curve::rt_safe_get_vector (Temporal::timepos_t const & x0, Temporal::timepos_t const & x1, float *vec, int32_t veclen) const
{
Glib::Threads::RWLock::ReaderLock lm(_list.lock(), Glib::Threads::TRY_LOCK);
if (!lm.locked()) {
return false;
} else {
_get_vector (x0, x1, vec, veclen);
return true;
}
}
void
Curve::get_vector (Temporal::timepos_t const & x0, Temporal::timepos_t const & x1, float *vec, int32_t veclen) const
{
Glib::Threads::RWLock::ReaderLock lm(_list.lock());
_get_vector (x0, x1, vec, veclen);
}
void
Curve::_get_vector (Temporal::timepos_t const & x0, Temporal::timepos_t const & x1, float *vec, int32_t veclen) const
{
double rx, lx, hx;
const double start = x0.val();
const double end = x1.val();
double max_x;
double min_x;
int32_t i;
int32_t original_veclen;
int32_t npoints;
if (veclen == 0) {
return;
}
if ((npoints = _list.events().size()) == 0) {
/* no events in list, so just fill the entire array with the default value */
for (int32_t i = 0; i < veclen; ++i) {
vec[i] = _list.descriptor().normal;
}
return;
}
if (npoints == 1) {
for (int32_t i = 0; i < veclen; ++i) {
vec[i] = _list.events().front()->value;
}
return;
}
/* events is now known not to be empty */
max_x = _list.events().back()->when.val();
min_x = _list.events().front()->when.val();
if (start > max_x) {
/* totally past the end - just fill the entire array with the final value */
for (int32_t i = 0; i < veclen; ++i) {
vec[i] = _list.events().back()->value;
}
return;
}
if (end < min_x) {
/* totally before the first event - fill the entire array with
* the initial value.
*/
for (int32_t i = 0; i < veclen; ++i) {
vec[i] = _list.events().front()->value;
}
return;
}
original_veclen = veclen;
if (start < min_x) {
/* fill some beginning section of the array with the
initial (used to be default) value
*/
double frac = (min_x - start) / (end - start);
int64_t fill_len = (int64_t) floor (veclen * frac);
fill_len = min (fill_len, (int64_t)veclen);
for (i = 0; i < fill_len; ++i) {
vec[i] = _list.events().front()->value;
}
veclen -= fill_len;
vec += fill_len;
}
if (veclen && end > max_x) {
/* fill some end section of the array with the default or final value */
double frac = (end - max_x) / (end - start);
int64_t fill_len = (int64_t) floor (original_veclen * frac);
float val;
fill_len = min (fill_len, (int64_t)veclen);
val = _list.events().back()->value;
for (i = veclen - fill_len; i < veclen; ++i) {
vec[i] = val;
}
veclen -= fill_len;
}
lx = max (min_x, start);
hx = min (max_x, end);
if (npoints == 2) {
const double lpos = _list.events().front()->when.val();
const double lval = _list.events().front()->value;
const double upos = _list.events().back()->when.val();
const double uval = _list.events().back()->value;
/* dx that we are using */
if (veclen > 1) {
const double dx_num = hx - lx;
const double dx_den = veclen - 1;
const double lower = _list.descriptor().lower;
const double upper = _list.descriptor().upper;
/* gradient of the line */
const double m_num = uval - lval;
const double m_den = upos - lpos;
/* y intercept of the line */
const double c = uval - (m_num * upos / m_den);
switch (_list.interpolation()) {
case ControlList::Logarithmic:
for (int i = 0; i < veclen; ++i) {
const double fraction = (lx - lpos + i * dx_num / dx_den) / m_den;
vec[i] = interpolate_logarithmic (lval, uval, fraction, lower, upper);
}
break;
case ControlList::Exponential:
for (int i = 0; i < veclen; ++i) {
const double fraction = (lx - lpos + i * dx_num / dx_den) / m_den;
vec[i] = interpolate_gain (lval, uval, fraction, upper);
}
break;
case ControlList::Discrete:
// any discrete vector curves somewhere?
assert (0);
case ControlList::Curved:
/* no 2 point spline */
/* fallthrough */
default: // Linear:
for (int i = 0; i < veclen; ++i) {
vec[i] = (lx * (m_num / m_den) + m_num * i * dx_num / (m_den * dx_den)) + c;
}
break;
}
} else {
double fraction = (lx - lpos) / (upos - lpos);
switch (_list.interpolation()) {
case ControlList::Logarithmic:
vec[0] = interpolate_logarithmic (lval, uval, fraction, _list.descriptor().lower, _list.descriptor().upper);
break;
case ControlList::Exponential:
vec[0] = interpolate_gain (lval, uval, fraction, _list.descriptor().upper);
break;
case ControlList::Discrete:
// any discrete vector curves somewhere?
assert (0);
case ControlList::Curved:
/* no 2 point spline */
/* fallthrough */
default: // Linear:
vec[0] = interpolate_linear (lval, uval, fraction);
break;
}
}
return;
}
if (_dirty) {
solve ();
}
rx = lx;
double dx = 0.;
if (veclen > 1) {
dx = (hx - lx) / (veclen - 1);
}
for (i = 0; i < veclen; ++i, rx += dx) {
vec[i] = multipoint_eval (x0.is_beats() ? Temporal::timepos_t::from_ticks (rx) : Temporal::timepos_t::from_superclock (rx));
}
}
double
Curve::multipoint_eval (Temporal::timepos_t const & x) const
{
pair<ControlList::EventList::const_iterator,ControlList::EventList::const_iterator> range;
ControlList::LookupCache& lookup_cache = _list.lookup_cache();
if ((lookup_cache.left == Temporal::timepos_t::max (_list.time_domain())) ||
((lookup_cache.left > x) ||
(lookup_cache.range.first == _list.events().end()) ||
((*lookup_cache.range.second)->when < x))) {
ControlEvent cp (x, 0.0);
lookup_cache.range = equal_range (_list.events().begin(), _list.events().end(), &cp, ControlList::time_comparator);
}
range = lookup_cache.range;
/* EITHER
a) x is an existing control point, so first == existing point, second == next point
OR
b) x is between control points, so range is empty (first == second, points to where
to insert x)
*/
if (range.first == range.second) {
/* x does not exist within the list as a control point */
lookup_cache.left = x;
if (range.first == _list.events().begin()) {
/* we're before the first point */
// return default_value;
return _list.events().front()->value;
}
if (range.second == _list.events().end()) {
/* we're after the last point */
return _list.events().back()->value;
}
ControlEvent* after = (*range.second);
range.second--;
ControlEvent* before = (*range.second);
double vdelta = after->value - before->value;
if (vdelta == 0.0) {
return before->value;
}
double aw = after->when.val();
double bw = before->when.val();
double tdelta = x.val() - bw;
double trange = aw - bw;
switch (_list.interpolation()) {
case ControlList::Discrete:
return before->value;
case ControlList::Logarithmic:
return interpolate_logarithmic (before->value, after->value, tdelta / trange, _list.descriptor().lower, _list.descriptor().upper);
case ControlList::Exponential:
return interpolate_gain (before->value, after->value, tdelta / trange, _list.descriptor().upper);
case ControlList::Curved:
if (after->coeff) {
ControlEvent* ev = after;
/* As of Jan 2020, we only use Curved
* for fade in/out curves (of audio
* regions).
*
* This means that x is a relatively
* small value (an offset into the
* fade) amd we do not need to worry
* about the square or cube overflowing
* a double type. They can overflow an
* int64_t by around 6 seconds.
*/
const double xv = x.val();
double xv2 = xv * xv;
return ev->coeff[0] + (ev->coeff[1] * xv) + (ev->coeff[2] * xv2) + (ev->coeff[3] * xv2 * xv);
}
/* fallthrough */
case ControlList::Linear:
return before->value + (vdelta * (tdelta / trange));
}
}
/* x is a control point in the data */
/* invalidate the cached range because its not usable */
lookup_cache.left = Temporal::timepos_t::max (_list.time_domain());
return (*range.first)->value;
}
} // namespace Evoral