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/***
This file is part of PulseAudio.
Copyright 2007 Lennart Poettering
PulseAudio is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation; either version 2.1 of the
License, or (at your option) any later version.
PulseAudio 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
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with PulseAudio; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
USA.
***/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <stdio.h>
#include <pulse/sample.h>
#include <pulse/xmalloc.h>
#include <pulsecore/macro.h>
#include "time-smoother.h"
#define HISTORY_MAX 64
/*
* Implementation of a time smoothing algorithm to synchronize remote
* clocks to a local one. Evens out noise, adjusts to clock skew and
* allows cheap estimations of the remote time while clock updates may
* be seldom and recieved in non-equidistant intervals.
*
* Basically, we estimate the gradient of received clock samples in a
* certain history window (of size 'history_time') with linear
* regression. With that info we estimate the remote time in
* 'adjust_time' ahead and smoothen our current estimation function
* towards that point with a 3rd order polynomial interpolation with
* fitting derivatives. (more or less a b-spline)
*
* The larger 'history_time' is chosen the better we will surpress
* noise -- but we'll adjust to clock skew slower..
*
* The larger 'adjust_time' is chosen the smoother our estimation
* function will be -- but we'll adjust to clock skew slower, too.
*
* If 'monotonic' is TRUE the resulting estimation function is
* guaranteed to be monotonic.
*/
struct pa_smoother {
pa_usec_t adjust_time, history_time;
pa_usec_t time_offset;
pa_usec_t px, py; /* Point p, where we want to reach stability */
double dp; /* Gradient we want at point p */
pa_usec_t ex, ey; /* Point e, which we estimated before and need to smooth to */
double de; /* Gradient we estimated for point e */
pa_usec_t ry; /* The original y value for ex */
/* History of last measurements */
pa_usec_t history_x[HISTORY_MAX], history_y[HISTORY_MAX];
unsigned history_idx, n_history;
/* To even out for monotonicity */
pa_usec_t last_y, last_x;
/* Cached parameters for our interpolation polynomial y=ax^3+b^2+cx */
double a, b, c;
pa_bool_t abc_valid:1;
pa_bool_t monotonic:1;
pa_bool_t paused:1;
pa_bool_t smoothing:1; /* If FALSE we skip the polonyomial interpolation step */
pa_usec_t pause_time;
unsigned min_history;
};
pa_smoother* pa_smoother_new(
pa_usec_t adjust_time,
pa_usec_t history_time,
pa_bool_t monotonic,
pa_bool_t smoothing,
unsigned min_history,
pa_usec_t time_offset,
pa_bool_t paused) {
pa_smoother *s;
pa_assert(adjust_time > 0);
pa_assert(history_time > 0);
pa_assert(min_history >= 2);
pa_assert(min_history <= HISTORY_MAX);
s = pa_xnew(pa_smoother, 1);
s->adjust_time = adjust_time;
s->history_time = history_time;
s->min_history = min_history;
s->monotonic = monotonic;
s->smoothing = smoothing;
pa_smoother_reset(s, time_offset, paused);
return s;
}
void pa_smoother_free(pa_smoother* s) {
pa_assert(s);
pa_xfree(s);
}
#define REDUCE(x) \
do { \
x = (x) % HISTORY_MAX; \
} while(FALSE)
#define REDUCE_INC(x) \
do { \
x = ((x)+1) % HISTORY_MAX; \
} while(FALSE)
static void drop_old(pa_smoother *s, pa_usec_t x) {
/* Drop items from history which are too old, but make sure to
* always keep min_history in the history */
while (s->n_history > s->min_history) {
if (s->history_x[s->history_idx] + s->history_time >= x)
/* This item is still valid, and thus all following ones
* are too, so let's quit this loop */
break;
/* Item is too old, let's drop it */
REDUCE_INC(s->history_idx);
s->n_history --;
}
}
static void add_to_history(pa_smoother *s, pa_usec_t x, pa_usec_t y) {
unsigned j, i;
pa_assert(s);
/* First try to update an existing history entry */
i = s->history_idx;
for (j = s->n_history; j > 0; j--) {
if (s->history_x[i] == x) {
s->history_y[i] = y;
return;
}
REDUCE_INC(i);
}
/* Drop old entries */
drop_old(s, x);
/* Calculate position for new entry */
j = s->history_idx + s->n_history;
REDUCE(j);
/* Fill in entry */
s->history_x[j] = x;
s->history_y[j] = y;
/* Adjust counter */
s->n_history ++;
/* And make sure we don't store more entries than fit in */
if (s->n_history > HISTORY_MAX) {
s->history_idx += s->n_history - HISTORY_MAX;
REDUCE(s->history_idx);
s->n_history = HISTORY_MAX;
}
}
static double avg_gradient(pa_smoother *s, pa_usec_t x) {
unsigned i, j, c = 0;
int64_t ax = 0, ay = 0, k, t;
double r;
/* Too few measurements, assume gradient of 1 */
if (s->n_history < s->min_history)
return 1;
/* First, calculate average of all measurements */
i = s->history_idx;
for (j = s->n_history; j > 0; j--) {
ax += (int64_t) s->history_x[i];
ay += (int64_t) s->history_y[i];
c++;
REDUCE_INC(i);
}
pa_assert(c >= s->min_history);
ax /= c;
ay /= c;
/* Now, do linear regression */
k = t = 0;
i = s->history_idx;
for (j = s->n_history; j > 0; j--) {
int64_t dx, dy;
dx = (int64_t) s->history_x[i] - ax;
dy = (int64_t) s->history_y[i] - ay;
k += dx*dy;
t += dx*dx;
REDUCE_INC(i);
}
r = (double) k / (double) t;
return (s->monotonic && r < 0) ? 0 : r;
}
static void calc_abc(pa_smoother *s) {
pa_usec_t ex, ey, px, py;
int64_t kx, ky;
double de, dp;
pa_assert(s);
if (s->abc_valid)
return;
/* We have two points: (ex|ey) and (px|py) with two gradients at
* these points de and dp. We do a polynomial
* interpolation of degree 3 with these 6 values */
ex = s->ex; ey = s->ey;
px = s->px; py = s->py;
de = s->de; dp = s->dp;
pa_assert(ex < px);
/* To increase the dynamic range and symplify calculation, we
* move these values to the origin */
kx = (int64_t) px - (int64_t) ex;
ky = (int64_t) py - (int64_t) ey;
/* Calculate a, b, c for y=ax^3+bx^2+cx */
s->c = de;
s->b = (((double) (3*ky)/ (double) kx - dp - (double) (2*de))) / (double) kx;
s->a = (dp/(double) kx - 2*s->b - de/(double) kx) / (double) (3*kx);
s->abc_valid = TRUE;
}
static void estimate(pa_smoother *s, pa_usec_t x, pa_usec_t *y, double *deriv) {
pa_assert(s);
pa_assert(y);
if (x >= s->px) {
/* Linear interpolation right from px */
int64_t t;
/* The requested point is right of the point where we wanted
* to be on track again, thus just linearly estimate */
t = (int64_t) s->py + (int64_t) llrint(s->dp * (double) (x - s->px));
if (t < 0)
t = 0;
*y = (pa_usec_t) t;
if (deriv)
*deriv = s->dp;
} else if (x <= s->ex) {
/* Linear interpolation left from ex */
int64_t t;
t = (int64_t) s->ey - (int64_t) llrint(s->de * (double) (s->ex - x));
if (t < 0)
t = 0;
*y = (pa_usec_t) t;
if (deriv)
*deriv = s->de;
} else {
/* Spline interpolation between ex and px */
double tx, ty;
/* Ok, we're not yet on track, thus let's interpolate, and
* make sure that the first derivative is smooth */
calc_abc(s);
/* Move to origin */
tx = (double) (x - s->ex);
/* Horner scheme */
ty = (tx * (s->c + tx * (s->b + tx * s->a)));
/* Move back from origin */
ty += (double) s->ey;
*y = ty >= 0 ? (pa_usec_t) llrint(ty) : 0;
/* Horner scheme */
if (deriv)
*deriv = s->c + (tx * (s->b*2 + tx * s->a*3));
}
/* Guarantee monotonicity */
if (s->monotonic) {
if (deriv && *deriv < 0)
*deriv = 0;
}
}
void pa_smoother_put(pa_smoother *s, pa_usec_t x, pa_usec_t y) {
pa_usec_t ney;
double nde;
pa_bool_t is_new;
pa_assert(s);
/* Fix up x value */
if (s->paused)
x = s->pause_time;
x = PA_LIKELY(x >= s->time_offset) ? x - s->time_offset : 0;
is_new = x >= s->ex;
if (is_new) {
/* First, we calculate the position we'd estimate for x, so that
* we can adjust our position smoothly from this one */
estimate(s, x, &ney, &nde);
s->ex = x; s->ey = ney; s->de = nde;
s->ry = y;
}
/* Then, we add the new measurement to our history */
add_to_history(s, x, y);
/* And determine the average gradient of the history */
s->dp = avg_gradient(s, x);
/* And calculate when we want to be on track again */
if (s->smoothing) {
s->px = s->ex + s->adjust_time;
s->py = s->ry + (pa_usec_t) llrint(s->dp * (double) s->adjust_time);
} else {
s->px = s->ex;
s->py = s->ry;
}
s->abc_valid = FALSE;
#ifdef DEBUG_DATA
pa_log_debug("%p, put(%llu | %llu) = %llu", s, (unsigned long long) (x + s->time_offset), (unsigned long long) x, (unsigned long long) y);
#endif
}
pa_usec_t pa_smoother_get(pa_smoother *s, pa_usec_t x) {
pa_usec_t y;
pa_assert(s);
/* Fix up x value */
if (s->paused)
x = s->pause_time;
x = PA_LIKELY(x >= s->time_offset) ? x - s->time_offset : 0;
if (s->monotonic)
if (x <= s->last_x)
x = s->last_x;
estimate(s, x, &y, NULL);
if (s->monotonic) {
/* Make sure the querier doesn't jump forth and back. */
s->last_x = x;
if (y < s->last_y)
y = s->last_y;
else
s->last_y = y;
}
#ifdef DEBUG_DATA
pa_log_debug("%p, get(%llu | %llu) = %llu", s, (unsigned long long) (x + s->time_offset), (unsigned long long) x, (unsigned long long) y);
#endif
return y;
}
void pa_smoother_set_time_offset(pa_smoother *s, pa_usec_t offset) {
pa_assert(s);
s->time_offset = offset;
#ifdef DEBUG_DATA
pa_log_debug("offset(%llu)", (unsigned long long) offset);
#endif
}
void pa_smoother_pause(pa_smoother *s, pa_usec_t x) {
pa_assert(s);
if (s->paused)
return;
#ifdef DEBUG_DATA
pa_log_debug("pause(%llu)", (unsigned long long) x);
#endif
s->paused = TRUE;
s->pause_time = x;
}
void pa_smoother_resume(pa_smoother *s, pa_usec_t x, pa_bool_t fix_now) {
pa_assert(s);
if (!s->paused)
return;
if (x < s->pause_time)
x = s->pause_time;
#ifdef DEBUG_DATA
pa_log_debug("resume(%llu)", (unsigned long long) x);
#endif
s->paused = FALSE;
s->time_offset += x - s->pause_time;
if (fix_now)
pa_smoother_fix_now(s);
}
void pa_smoother_fix_now(pa_smoother *s) {
pa_assert(s);
s->px = s->ex;
s->py = s->ry;
}
pa_usec_t pa_smoother_translate(pa_smoother *s, pa_usec_t x, pa_usec_t y_delay) {
pa_usec_t ney;
double nde;
pa_assert(s);
/* Fix up x value */
if (s->paused)
x = s->pause_time;
x = PA_LIKELY(x >= s->time_offset) ? x - s->time_offset : 0;
estimate(s, x, &ney, &nde);
/* Play safe and take the larger gradient, so that we wakeup
* earlier when this is used for sleeping */
if (s->dp > nde)
nde = s->dp;
#ifdef DEBUG_DATA
pa_log_debug("translate(%llu) = %llu (%0.2f)", (unsigned long long) y_delay, (unsigned long long) ((double) y_delay / nde), nde);
#endif
return (pa_usec_t) llrint((double) y_delay / nde);
}
void pa_smoother_reset(pa_smoother *s, pa_usec_t time_offset, pa_bool_t paused) {
pa_assert(s);
s->px = s->py = 0;
s->dp = 1;
s->ex = s->ey = s->ry = 0;
s->de = 1;
s->history_idx = 0;
s->n_history = 0;
s->last_y = s->last_x = 0;
s->abc_valid = FALSE;
s->paused = paused;
s->time_offset = s->pause_time = time_offset;
#ifdef DEBUG_DATA
pa_log_debug("reset()");
#endif
}
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