xenocara/xserver/dix/ptrveloc.c

/*
 *
 * Copyright © 2006-2009 Simon Thum             simon dot thum at gmx dot de
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice (including the next
 * paragraph) shall be included in all copies or substantial portions of the
 * Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 * DEALINGS IN THE SOFTWARE.
 */

#ifdef HAVE_DIX_CONFIG_H
#include <dix-config.h>
#endif

#include <math.h>
#include <ptrveloc.h>
#include <exevents.h>
#include <X11/Xatom.h>
#include <os.h>

#include <xserver-properties.h>

/*****************************************************************************
 * Predictable pointer acceleration
 *
 * 2006-2009 by Simon Thum (simon [dot] thum [at] gmx de)
 *
 * Serves 3 complementary functions:
 * 1) provide a sophisticated ballistic velocity estimate to improve
 *    the relation between velocity (of the device) and acceleration
 * 2) make arbitrary acceleration profiles possible
 * 3) decelerate by two means (constant and adaptive) if enabled
 *
 * Important concepts are the
 *
 * - Scheme
 *      which selects the basic algorithm
 *      (see devices.c/InitPointerAccelerationScheme)
 * - Profile
 *      which returns an acceleration
 *      for a given velocity
 *
 *  The profile can be selected by the user at runtime.
 *  The classic profile is intended to cleanly perform old-style
 *  function selection (threshold =/!= 0)
 *
 ****************************************************************************/

/* fwds */
int
 SetAccelerationProfile(DeviceVelocityPtr vel, int profile_num);
static double

SimpleSmoothProfile(DeviceIntPtr dev, DeviceVelocityPtr vel, double velocity,
                    double threshold, double acc);
static PointerAccelerationProfileFunc
GetAccelerationProfile(DeviceVelocityPtr vel, int profile_num);
static BOOL
InitializePredictableAccelerationProperties(DeviceIntPtr,
                                            DeviceVelocityPtr,
                                            PredictableAccelSchemePtr);
static BOOL
DeletePredictableAccelerationProperties(DeviceIntPtr,
                                        PredictableAccelSchemePtr);

/*#define PTRACCEL_DEBUGGING*/

#ifdef PTRACCEL_DEBUGGING
#define DebugAccelF ErrorF
#else
#define DebugAccelF(...)        /* */
#endif

/********************************
 *  Init/Uninit
 *******************************/

/* some int which is not a profile number */
#define PROFILE_UNINITIALIZE (-100)

/**
 * Init DeviceVelocity struct so it should match the average case
 */
void
InitVelocityData(DeviceVelocityPtr vel)
{
    memset(vel, 0, sizeof(DeviceVelocityRec));

    vel->corr_mul = 10.0;       /* dots per 10 milisecond should be usable */
    vel->const_acceleration = 1.0;      /* no acceleration/deceleration  */
    vel->reset_time = 300;
    vel->use_softening = 1;
    vel->min_acceleration = 1.0;        /* don't decelerate */
    vel->max_rel_diff = 0.2;
    vel->max_diff = 1.0;
    vel->initial_range = 2;
    vel->average_accel = TRUE;
    SetAccelerationProfile(vel, AccelProfileClassic);
    InitTrackers(vel, 16);
}

/**
 * Clean up DeviceVelocityRec
 */
void
FreeVelocityData(DeviceVelocityPtr vel)
{
    free(vel->tracker);
    SetAccelerationProfile(vel, PROFILE_UNINITIALIZE);
}

/**
 * Init predictable scheme
 */
Bool
InitPredictableAccelerationScheme(DeviceIntPtr dev,
                                  ValuatorAccelerationPtr protoScheme)
{
    DeviceVelocityPtr vel;
    ValuatorAccelerationRec scheme;
    PredictableAccelSchemePtr schemeData;

    scheme = *protoScheme;
    vel = calloc(1, sizeof(DeviceVelocityRec));
    schemeData = calloc(1, sizeof(PredictableAccelSchemeRec));
    if (!vel || !schemeData)
        return FALSE;
    InitVelocityData(vel);
    schemeData->vel = vel;
    scheme.accelData = schemeData;
    if (!InitializePredictableAccelerationProperties(dev, vel, schemeData))
        return FALSE;
    /* all fine, assign scheme to device */
    dev->valuator->accelScheme = scheme;
    return TRUE;
}

/**
 *  Uninit scheme
 */
void
AccelerationDefaultCleanup(DeviceIntPtr dev)
{
    DeviceVelocityPtr vel = GetDevicePredictableAccelData(dev);

    if (vel) {
        /* the proper guarantee would be that we're not inside of
         * AccelSchemeProc(), but that seems impossible. Schemes don't get
         * switched often anyway.
         */
        OsBlockSignals();
        dev->valuator->accelScheme.AccelSchemeProc = NULL;
        FreeVelocityData(vel);
        free(vel);
        DeletePredictableAccelerationProperties(dev,
                                                (PredictableAccelSchemePtr)
                                                dev->valuator->accelScheme.
                                                accelData);
        free(dev->valuator->accelScheme.accelData);
        dev->valuator->accelScheme.accelData = NULL;
        OsReleaseSignals();
    }
}

/*************************
 * Input property support
 ************************/

/**
 * choose profile
 */
static int
AccelSetProfileProperty(DeviceIntPtr dev, Atom atom,
                        XIPropertyValuePtr val, BOOL checkOnly)
{
    DeviceVelocityPtr vel;
    int profile, *ptr = &profile;
    int rc;
    int nelem = 1;

    if (atom != XIGetKnownProperty(ACCEL_PROP_PROFILE_NUMBER))
        return Success;

    vel = GetDevicePredictableAccelData(dev);
    if (!vel)
        return BadValue;
    rc = XIPropToInt(val, &nelem, &ptr);

    if (checkOnly) {
        if (rc)
            return rc;

        if (GetAccelerationProfile(vel, profile) == NULL)
            return BadValue;
    }
    else
        SetAccelerationProfile(vel, profile);

    return Success;
}

static long
AccelInitProfileProperty(DeviceIntPtr dev, DeviceVelocityPtr vel)
{
    int profile = vel->statistics.profile_number;
    Atom prop_profile_number = XIGetKnownProperty(ACCEL_PROP_PROFILE_NUMBER);

    XIChangeDeviceProperty(dev, prop_profile_number, XA_INTEGER, 32,
                           PropModeReplace, 1, &profile, FALSE);
    XISetDevicePropertyDeletable(dev, prop_profile_number, FALSE);
    return XIRegisterPropertyHandler(dev, AccelSetProfileProperty, NULL, NULL);
}

/**
 * constant deceleration
 */
static int
AccelSetDecelProperty(DeviceIntPtr dev, Atom atom,
                      XIPropertyValuePtr val, BOOL checkOnly)
{
    DeviceVelocityPtr vel;
    float v, *ptr = &v;
    int rc;
    int nelem = 1;

    if (atom != XIGetKnownProperty(ACCEL_PROP_CONSTANT_DECELERATION))
        return Success;

    vel = GetDevicePredictableAccelData(dev);
    if (!vel)
        return BadValue;
    rc = XIPropToFloat(val, &nelem, &ptr);

    if (checkOnly) {
        if (rc)
            return rc;
        return (v >= 1.0f) ? Success : BadValue;
    }

    if (v >= 1.0f)
        vel->const_acceleration = 1 / v;

    return Success;
}

static long
AccelInitDecelProperty(DeviceIntPtr dev, DeviceVelocityPtr vel)
{
    float fval = 1.0 / vel->const_acceleration;
    Atom prop_const_decel =
        XIGetKnownProperty(ACCEL_PROP_CONSTANT_DECELERATION);
    XIChangeDeviceProperty(dev, prop_const_decel,
                           XIGetKnownProperty(XATOM_FLOAT), 32, PropModeReplace,
                           1, &fval, FALSE);
    XISetDevicePropertyDeletable(dev, prop_const_decel, FALSE);
    return XIRegisterPropertyHandler(dev, AccelSetDecelProperty, NULL, NULL);
}

/**
 * adaptive deceleration
 */
static int
AccelSetAdaptDecelProperty(DeviceIntPtr dev, Atom atom,
                           XIPropertyValuePtr val, BOOL checkOnly)
{
    DeviceVelocityPtr veloc;
    float v, *ptr = &v;
    int rc;
    int nelem = 1;

    if (atom != XIGetKnownProperty(ACCEL_PROP_ADAPTIVE_DECELERATION))
        return Success;

    veloc = GetDevicePredictableAccelData(dev);
    if (!veloc)
        return BadValue;
    rc = XIPropToFloat(val, &nelem, &ptr);

    if (checkOnly) {
        if (rc)
            return rc;
        return (v >= 1.0f) ? Success : BadValue;
    }

    if (v >= 1.0f)
        veloc->min_acceleration = 1 / v;

    return Success;
}

static long
AccelInitAdaptDecelProperty(DeviceIntPtr dev, DeviceVelocityPtr vel)
{
    float fval = 1.0 / vel->min_acceleration;
    Atom prop_adapt_decel =
        XIGetKnownProperty(ACCEL_PROP_ADAPTIVE_DECELERATION);

    XIChangeDeviceProperty(dev, prop_adapt_decel,
                           XIGetKnownProperty(XATOM_FLOAT), 32, PropModeReplace,
                           1, &fval, FALSE);
    XISetDevicePropertyDeletable(dev, prop_adapt_decel, FALSE);
    return XIRegisterPropertyHandler(dev, AccelSetAdaptDecelProperty, NULL,
                                     NULL);
}

/**
 * velocity scaling
 */
static int
AccelSetScaleProperty(DeviceIntPtr dev, Atom atom,
                      XIPropertyValuePtr val, BOOL checkOnly)
{
    DeviceVelocityPtr vel;
    float v, *ptr = &v;
    int rc;
    int nelem = 1;

    if (atom != XIGetKnownProperty(ACCEL_PROP_VELOCITY_SCALING))
        return Success;

    vel = GetDevicePredictableAccelData(dev);
    if (!vel)
        return BadValue;
    rc = XIPropToFloat(val, &nelem, &ptr);

    if (checkOnly) {
        if (rc)
            return rc;

        return (v > 0) ? Success : BadValue;
    }

    if (v > 0)
        vel->corr_mul = v;

    return Success;
}

static long
AccelInitScaleProperty(DeviceIntPtr dev, DeviceVelocityPtr vel)
{
    float fval = vel->corr_mul;
    Atom prop_velo_scale = XIGetKnownProperty(ACCEL_PROP_VELOCITY_SCALING);

    XIChangeDeviceProperty(dev, prop_velo_scale,
                           XIGetKnownProperty(XATOM_FLOAT), 32, PropModeReplace,
                           1, &fval, FALSE);
    XISetDevicePropertyDeletable(dev, prop_velo_scale, FALSE);
    return XIRegisterPropertyHandler(dev, AccelSetScaleProperty, NULL, NULL);
}

static BOOL
InitializePredictableAccelerationProperties(DeviceIntPtr dev,
                                            DeviceVelocityPtr vel,
                                            PredictableAccelSchemePtr
                                            schemeData)
{
    int num_handlers = 4;

    if (!vel)
        return FALSE;

    schemeData->prop_handlers = calloc(num_handlers, sizeof(long));
    if (!schemeData->prop_handlers)
        return FALSE;
    schemeData->num_prop_handlers = num_handlers;
    schemeData->prop_handlers[0] = AccelInitProfileProperty(dev, vel);
    schemeData->prop_handlers[1] = AccelInitDecelProperty(dev, vel);
    schemeData->prop_handlers[2] = AccelInitAdaptDecelProperty(dev, vel);
    schemeData->prop_handlers[3] = AccelInitScaleProperty(dev, vel);

    return TRUE;
}

BOOL
DeletePredictableAccelerationProperties(DeviceIntPtr dev,
                                        PredictableAccelSchemePtr scheme)
{
    DeviceVelocityPtr vel;
    Atom prop;
    int i;

    prop = XIGetKnownProperty(ACCEL_PROP_VELOCITY_SCALING);
    XIDeleteDeviceProperty(dev, prop, FALSE);
    prop = XIGetKnownProperty(ACCEL_PROP_ADAPTIVE_DECELERATION);
    XIDeleteDeviceProperty(dev, prop, FALSE);
    prop = XIGetKnownProperty(ACCEL_PROP_CONSTANT_DECELERATION);
    XIDeleteDeviceProperty(dev, prop, FALSE);
    prop = XIGetKnownProperty(ACCEL_PROP_PROFILE_NUMBER);
    XIDeleteDeviceProperty(dev, prop, FALSE);

    vel = GetDevicePredictableAccelData(dev);
    if (vel) {
        for (i = 0; i < scheme->num_prop_handlers; i++)
            if (scheme->prop_handlers[i])
                XIUnregisterPropertyHandler(dev, scheme->prop_handlers[i]);
    }

    free(scheme->prop_handlers);
    scheme->prop_handlers = NULL;
    scheme->num_prop_handlers = 0;
    return TRUE;
}

/*********************
 * Tracking logic
 ********************/

void
InitTrackers(DeviceVelocityPtr vel, int ntracker)
{
    if (ntracker < 1) {
        ErrorF("(dix ptracc) invalid number of trackers\n");
        return;
    }
    free(vel->tracker);
    vel->tracker = (MotionTrackerPtr) calloc(ntracker, sizeof(MotionTracker));
    vel->num_tracker = ntracker;
}

enum directions {
    N = (1 << 0),
    NE = (1 << 1),
    E = (1 << 2),
    SE = (1 << 3),
    S = (1 << 4),
    SW = (1 << 5),
    W = (1 << 6),
    NW = (1 << 7),
    UNDEFINED = 0xFF
};

/**
 * return a bit field of possible directions.
 * There's no reason against widening to more precise directions (<45 degrees),
 * should it not perform well. All this is needed for is sort out non-linear
 * motion, so precision isn't paramount. However, one should not flag direction
 * too narrow, since it would then cut the linear segment to zero size way too
 * often.
 *
 * @return A bitmask for N, NE, S, SE, etc. indicating the directions for
 * this movement.
 */
static int
DoGetDirection(int dx, int dy)
{
    int dir = 0;

    /* on insignificant mickeys, flag 135 degrees */
    if (abs(dx) < 2 && abs(dy) < 2) {
        /* first check diagonal cases */
        if (dx > 0 && dy > 0)
            dir = E | SE | S;
        else if (dx > 0 && dy < 0)
            dir = N | NE | E;
        else if (dx < 0 && dy < 0)
            dir = W | NW | N;
        else if (dx < 0 && dy > 0)
            dir = W | SW | S;
        /* check axis-aligned directions */
        else if (dx > 0)
            dir = NE | E | SE;
        else if (dx < 0)
            dir = NW | W | SW;
        else if (dy > 0)
            dir = SE | S | SW;
        else if (dy < 0)
            dir = NE | N | NW;
        else
            dir = UNDEFINED;    /* shouldn't happen */
    }
    else {                      /* compute angle and set appropriate flags */
        double r;
        int i1, i2;

        r = atan2(dy, dx);
        /* find direction.
         *
         * Add 360° to avoid r become negative since C has no well-defined
         * modulo for such cases. Then divide by 45° to get the octant
         * number,  e.g.
         *          0 <= r <= 1 is [0-45]°
         *          1 <= r <= 2 is [45-90]°
         *          etc.
         * But we add extra 90° to match up with our N, S, etc. defines up
         * there, rest stays the same.
         */
        r = (r + (M_PI * 2.5)) / (M_PI / 4);
        /* this intends to flag 2 directions (45 degrees),
         * except on very well-aligned mickeys. */
        i1 = (int) (r + 0.1) % 8;
        i2 = (int) (r + 0.9) % 8;
        if (i1 < 0 || i1 > 7 || i2 < 0 || i2 > 7)
            dir = UNDEFINED;    /* shouldn't happen */
        else
            dir = (1 << i1 | 1 << i2);
    }
    return dir;
}

#define DIRECTION_CACHE_RANGE 5
#define DIRECTION_CACHE_SIZE (DIRECTION_CACHE_RANGE*2+1)

/* cache DoGetDirection().
 * To avoid excessive use of direction calculation, cache the values for
 * [-5..5] for both x/y. Anything outside of that is calcualted on the fly.
 *
 * @return A bitmask for N, NE, S, SE, etc. indicating the directions for
 * this movement.
 */
static int
GetDirection(int dx, int dy)
{
    static int cache[DIRECTION_CACHE_SIZE][DIRECTION_CACHE_SIZE];
    int dir;

    if (abs(dx) <= DIRECTION_CACHE_RANGE && abs(dy) <= DIRECTION_CACHE_RANGE) {
        /* cacheable */
        dir = cache[DIRECTION_CACHE_RANGE + dx][DIRECTION_CACHE_RANGE + dy];
        if (dir == 0) {
            dir = DoGetDirection(dx, dy);
            cache[DIRECTION_CACHE_RANGE + dx][DIRECTION_CACHE_RANGE + dy] = dir;
        }
    }
    else {
        /* non-cacheable */
        dir = DoGetDirection(dx, dy);
    }

    return dir;
}

#undef DIRECTION_CACHE_RANGE
#undef DIRECTION_CACHE_SIZE

/* convert offset (age) to array index */
#define TRACKER_INDEX(s, d) (((s)->num_tracker + (s)->cur_tracker - (d)) % (s)->num_tracker)
#define TRACKER(s, d) &(s)->tracker[TRACKER_INDEX(s,d)]

/**
 * Add the delta motion to each tracker, then reset the latest tracker to
 * 0/0 and set it as the current one.
 */
static inline void
FeedTrackers(DeviceVelocityPtr vel, double dx, double dy, int cur_t)
{
    int n;

    for (n = 0; n < vel->num_tracker; n++) {
        vel->tracker[n].dx += dx;
        vel->tracker[n].dy += dy;
    }
    n = (vel->cur_tracker + 1) % vel->num_tracker;
    vel->tracker[n].dx = 0.0;
    vel->tracker[n].dy = 0.0;
    vel->tracker[n].time = cur_t;
    vel->tracker[n].dir = GetDirection(dx, dy);
    DebugAccelF("(dix prtacc) motion [dx: %i dy: %i dir:%i diff: %i]\n",
                dx, dy, vel->tracker[n].dir,
                cur_t - vel->tracker[vel->cur_tracker].time);
    vel->cur_tracker = n;
}

/**
 * calc velocity for given tracker, with
 * velocity scaling.
 * This assumes linear motion.
 */
static double
CalcTracker(const MotionTracker * tracker, int cur_t)
{
    double dist = sqrt(tracker->dx * tracker->dx + tracker->dy * tracker->dy);
    int dtime = cur_t - tracker->time;

    if (dtime > 0)
        return dist / dtime;
    else
        return 0;               /* synonymous for NaN, since we're not C99 */
}

/* find the most plausible velocity. That is, the most distant
 * (in time) tracker which isn't too old, the movement vector was
 * in the same octant, and where the velocity is within an
 * acceptable range to the inital velocity.
 *
 * @return The tracker's velocity or 0 if the above conditions are unmet
 */
static double
QueryTrackers(DeviceVelocityPtr vel, int cur_t)
{
    int offset, dir = UNDEFINED, used_offset = -1, age_ms;

    /* initial velocity: a low-offset, valid velocity */
    double initial_velocity = 0, result = 0, velocity_diff;
    double velocity_factor = vel->corr_mul * vel->const_acceleration;   /* premultiply */

    /* loop from current to older data */
    for (offset = 1; offset < vel->num_tracker; offset++) {
        MotionTracker *tracker = TRACKER(vel, offset);
        double tracker_velocity;

        age_ms = cur_t - tracker->time;

        /* bail out if data is too old and protect from overrun */
        if (age_ms >= vel->reset_time || age_ms < 0) {
            DebugAccelF("(dix prtacc) query: tracker too old\n");
            break;
        }

        /*
         * this heuristic avoids using the linear-motion velocity formula
         * in CalcTracker() on motion that isn't exactly linear. So to get
         * even more precision we could subdivide as a final step, so possible
         * non-linearities are accounted for.
         */
        dir &= tracker->dir;
        if (dir == 0) {         /* we've changed octant of movement (e.g. NE → NW) */
            DebugAccelF("(dix prtacc) query: no longer linear\n");
            /* instead of breaking it we might also inspect the partition after,
             * but actual improvement with this is probably rare. */
            break;
        }

        tracker_velocity = CalcTracker(tracker, cur_t) * velocity_factor;

        if ((initial_velocity == 0 || offset <= vel->initial_range) &&
            tracker_velocity != 0) {
            /* set initial velocity and result */
            result = initial_velocity = tracker_velocity;
            used_offset = offset;
        }
        else if (initial_velocity != 0 && tracker_velocity != 0) {
            velocity_diff = fabs(initial_velocity - tracker_velocity);

            if (velocity_diff > vel->max_diff &&
                velocity_diff / (initial_velocity + tracker_velocity) >=
                vel->max_rel_diff) {
                /* we're not in range, quit - it won't get better. */
                DebugAccelF("(dix prtacc) query: tracker too different:"
                            " old %2.2f initial %2.2f diff: %2.2f\n",
                            tracker_velocity, initial_velocity, velocity_diff);
                break;
            }
            /* we're in range with the initial velocity,
             * so this result is likely better
             * (it contains more information). */
            result = tracker_velocity;
            used_offset = offset;
        }
    }
    if (offset == vel->num_tracker) {
        DebugAccelF("(dix prtacc) query: last tracker in effect\n");
        used_offset = vel->num_tracker - 1;
    }
    if (used_offset >= 0) {
#ifdef PTRACCEL_DEBUGGING
        MotionTracker *tracker = TRACKER(vel, used_offset);

        DebugAccelF("(dix prtacc) result: offset %i [dx: %i dy: %i diff: %i]\n",
                    used_offset, tracker->dx, tracker->dy,
                    cur_t - tracker->time);
#endif
    }
    return result;
}

#undef TRACKER_INDEX
#undef TRACKER

/**
 * Perform velocity approximation based on 2D 'mickeys' (mouse motion delta).
 * return true if non-visible state reset is suggested
 */
BOOL
ProcessVelocityData2D(DeviceVelocityPtr vel, double dx, double dy, int time)
{
    double velocity;

    vel->last_velocity = vel->velocity;

    FeedTrackers(vel, dx, dy, time);

    velocity = QueryTrackers(vel, time);

    vel->velocity = velocity;
    return velocity == 0;
}

/**
 * this flattens significant ( > 1) mickeys a little bit for more steady
 * constant-velocity response
 */
static inline double
ApplySimpleSoftening(double prev_delta, double delta)
{
    double result = delta;

    if (delta < -1.0 || delta > 1.0) {
        if (delta > prev_delta)
            result -= 0.5;
        else if (delta < prev_delta)
            result += 0.5;
    }
    return result;
}

/**
 * Soften the delta based on previous deltas stored in vel.
 *
 * @param[in,out] fdx Delta X, modified in-place.
 * @param[in,out] fdx Delta Y, modified in-place.
 */
static void
ApplySoftening(DeviceVelocityPtr vel, double *fdx, double *fdy)
{
    if (vel->use_softening) {
        *fdx = ApplySimpleSoftening(vel->last_dx, *fdx);
        *fdy = ApplySimpleSoftening(vel->last_dy, *fdy);
    }
}

static void
ApplyConstantDeceleration(DeviceVelocityPtr vel, double *fdx, double *fdy)
{
    *fdx *= vel->const_acceleration;
    *fdy *= vel->const_acceleration;
}

/*
 * compute the acceleration for given velocity and enforce min_acceleartion
 */
double
BasicComputeAcceleration(DeviceIntPtr dev,
                         DeviceVelocityPtr vel,
                         double velocity, double threshold, double acc)
{

    double result;

    result = vel->Profile(dev, vel, velocity, threshold, acc);

    /* enforce min_acceleration */
    if (result < vel->min_acceleration)
        result = vel->min_acceleration;
    return result;
}

/**
 * Compute acceleration. Takes into account averaging, nv-reset, etc.
 * If the velocity has changed, an average is taken of 6 velocity factors:
 * current velocity, last velocity and 4 times the average between the two.
 */
static double
ComputeAcceleration(DeviceIntPtr dev,
                    DeviceVelocityPtr vel, double threshold, double acc)
{
    double result;

    if (vel->velocity <= 0) {
        DebugAccelF("(dix ptracc) profile skipped\n");
        /*
         * If we have no idea about device velocity, don't pretend it.
         */
        return 1;
    }

    if (vel->average_accel && vel->velocity != vel->last_velocity) {
        /* use simpson's rule to average acceleration between
         * current and previous velocity.
         * Though being the more natural choice, it causes a minor delay
         * in comparison, so it can be disabled. */
        result =
            BasicComputeAcceleration(dev, vel, vel->velocity, threshold, acc);
        result +=
            BasicComputeAcceleration(dev, vel, vel->last_velocity, threshold,
                                     acc);
        result +=
            4.0f * BasicComputeAcceleration(dev, vel,
                                            (vel->last_velocity +
                                             vel->velocity) / 2, threshold,
                                            acc);
        result /= 6.0f;
        DebugAccelF("(dix ptracc) profile average [%.2f ... %.2f] is %.3f\n",
                    vel->velocity, vel->last_velocity, result);
    }
    else {
        result = BasicComputeAcceleration(dev, vel,
                                          vel->velocity, threshold, acc);
        DebugAccelF("(dix ptracc) profile sample [%.2f] is %.3f\n",
                    vel->velocity, res);
    }

    return result;
}

/*****************************************
 *  Acceleration functions and profiles
 ****************************************/

/**
 * Polynomial function similar previous one, but with f(1) = 1
 */
static double
PolynomialAccelerationProfile(DeviceIntPtr dev,
                              DeviceVelocityPtr vel,
                              double velocity, double ignored, double acc)
{
    return pow(velocity, (acc - 1.0) * 0.5);
}

/**
 * returns acceleration for velocity.
 * This profile selects the two functions like the old scheme did
 */
static double
ClassicProfile(DeviceIntPtr dev,
               DeviceVelocityPtr vel,
               double velocity, double threshold, double acc)
{
    if (threshold > 0) {
        return SimpleSmoothProfile(dev, vel, velocity, threshold, acc);
    }
    else {
        return PolynomialAccelerationProfile(dev, vel, velocity, 0, acc);
    }
}

/**
 * Power profile
 * This has a completely smooth transition curve, i.e. no jumps in the
 * derivatives.
 *
 * This has the expense of overall response dependency on min-acceleration.
 * In effect, min_acceleration mimics const_acceleration in this profile.
 */
static double
PowerProfile(DeviceIntPtr dev,
             DeviceVelocityPtr vel,
             double velocity, double threshold, double acc)
{
    double vel_dist;

    acc = (acc - 1.0) * 0.1f + 1.0;     /* without this, acc of 2 is unuseable */

    if (velocity <= threshold)
        return vel->min_acceleration;
    vel_dist = velocity - threshold;
    return (pow(acc, vel_dist)) * vel->min_acceleration;
}

/**
 * just a smooth function in [0..1] -> [0..1]
 *  - point symmetry at 0.5
 *  - f'(0) = f'(1) = 0
 *  - starts faster than a sinoid
 *  - smoothness C1 (Cinf if you dare to ignore endpoints)
 */
static inline double
CalcPenumbralGradient(double x)
{
    x *= 2.0f;
    x -= 1.0f;
    return 0.5f + (x * sqrt(1.0 - x * x) + asin(x)) / M_PI;
}

/**
 * acceleration function similar to classic accelerated/unaccelerated,
 * but with smooth transition in between (and towards zero for adaptive dec.).
 */
static double
SimpleSmoothProfile(DeviceIntPtr dev,
                    DeviceVelocityPtr vel,
                    double velocity, double threshold, double acc)
{
    if (velocity < 1.0f)
        return CalcPenumbralGradient(0.5 + velocity * 0.5) * 2.0f - 1.0f;
    if (threshold < 1.0f)
        threshold = 1.0f;
    if (velocity <= threshold)
        return 1;
    velocity /= threshold;
    if (velocity >= acc)
        return acc;
    else
        return 1.0f + (CalcPenumbralGradient(velocity / acc) * (acc - 1.0f));
}

/**
 * This profile uses the first half of the penumbral gradient as a start
 * and then scales linearly.
 */
static double
SmoothLinearProfile(DeviceIntPtr dev,
                    DeviceVelocityPtr vel,
                    double velocity, double threshold, double acc)
{
    double res, nv;

    if (acc > 1.0f)
        acc -= 1.0f;            /*this is so acc = 1 is no acceleration */
    else
        return 1.0f;

    nv = (velocity - threshold) * acc * 0.5f;

    if (nv < 0) {
        res = 0;
    }
    else if (nv < 2) {
        res = CalcPenumbralGradient(nv * 0.25f) * 2.0f;
    }
    else {
        nv -= 2.0f;
        res = nv * 2.0f / M_PI  /* steepness of gradient at 0.5 */
            + 1.0f;             /* gradient crosses 2|1 */
    }
    res += vel->min_acceleration;
    return res;
}

/**
 * From 0 to threshold, the response graduates smoothly from min_accel to
 * acceleration. Beyond threshold it is exactly the specified acceleration.
 */
static double
SmoothLimitedProfile(DeviceIntPtr dev,
                     DeviceVelocityPtr vel,
                     double velocity, double threshold, double acc)
{
    double res;

    if (velocity >= threshold || threshold == 0.0f)
        return acc;

    velocity /= threshold;      /* should be [0..1[ now */

    res = CalcPenumbralGradient(velocity) * (acc - vel->min_acceleration);

    return vel->min_acceleration + res;
}

static double
LinearProfile(DeviceIntPtr dev,
              DeviceVelocityPtr vel,
              double velocity, double threshold, double acc)
{
    return acc * velocity;
}

static double
NoProfile(DeviceIntPtr dev,
          DeviceVelocityPtr vel, double velocity, double threshold, double acc)
{
    return 1.0f;
}

static PointerAccelerationProfileFunc
GetAccelerationProfile(DeviceVelocityPtr vel, int profile_num)
{
    switch (profile_num) {
    case AccelProfileClassic:
        return ClassicProfile;
    case AccelProfileDeviceSpecific:
        return vel->deviceSpecificProfile;
    case AccelProfilePolynomial:
        return PolynomialAccelerationProfile;
    case AccelProfileSmoothLinear:
        return SmoothLinearProfile;
    case AccelProfileSimple:
        return SimpleSmoothProfile;
    case AccelProfilePower:
        return PowerProfile;
    case AccelProfileLinear:
        return LinearProfile;
    case AccelProfileSmoothLimited:
        return SmoothLimitedProfile;
    case AccelProfileNone:
        return NoProfile;
    default:
        return NULL;
    }
}

/**
 * Set the profile by number.
 * Intended to make profiles exchangeable at runtime.
 * If you created a profile, give it a number here and in the header to
 * make it selectable. In case some profile-specific init is needed, here
 * would be a good place, since FreeVelocityData() also calls this with
 * PROFILE_UNINITIALIZE.
 *
 * returns FALSE if profile number is unavailable, TRUE otherwise.
 */
int
SetAccelerationProfile(DeviceVelocityPtr vel, int profile_num)
{
    PointerAccelerationProfileFunc profile;

    profile = GetAccelerationProfile(vel, profile_num);

    if (profile == NULL && profile_num != PROFILE_UNINITIALIZE)
        return FALSE;

    /* Here one could free old profile-private data */
    free(vel->profile_private);
    vel->profile_private = NULL;
    /* Here one could init profile-private data */
    vel->Profile = profile;
    vel->statistics.profile_number = profile_num;
    return TRUE;
}

/**********************************************
 * driver interaction
 **********************************************/

/**
 * device-specific profile
 *
 * The device-specific profile is intended as a hook for a driver
 * which may want to provide an own acceleration profile.
 * It should not rely on profile-private data, instead
 * it should do init/uninit in the driver (ie. with DEVICE_INIT and friends).
 * Users may override or choose it.
 */
void
SetDeviceSpecificAccelerationProfile(DeviceVelocityPtr vel,
                                     PointerAccelerationProfileFunc profile)
{
    if (vel)
        vel->deviceSpecificProfile = profile;
}

/**
 * Use this function to obtain a DeviceVelocityPtr for a device. Will return NULL if
 * the predictable acceleration scheme is not in effect.
 */
DeviceVelocityPtr
GetDevicePredictableAccelData(DeviceIntPtr dev)
{
    /*sanity check */
    if (!dev) {
        ErrorF("[dix] accel: DeviceIntPtr was NULL");
        return NULL;
    }
    if (dev->valuator &&
        dev->valuator->accelScheme.AccelSchemeProc ==
        acceleratePointerPredictable &&
        dev->valuator->accelScheme.accelData != NULL) {

        return ((PredictableAccelSchemePtr)
                dev->valuator->accelScheme.accelData)->vel;
    }
    return NULL;
}

/********************************
 *  acceleration schemes
 *******************************/

/**
 * Modifies valuators in-place.
 * This version employs a velocity approximation algorithm to
 * enable fine-grained predictable acceleration profiles.
 */
void
acceleratePointerPredictable(DeviceIntPtr dev, ValuatorMask *val, CARD32 evtime)
{
    double dx = 0, dy = 0;
    DeviceVelocityPtr velocitydata = GetDevicePredictableAccelData(dev);
    Bool soften = TRUE;

    if (valuator_mask_num_valuators(val) == 0 || !velocitydata)
        return;

    if (velocitydata->statistics.profile_number == AccelProfileNone &&
        velocitydata->const_acceleration == 1.0f) {
        return;                 /*we're inactive anyway, so skip the whole thing. */
    }

    if (valuator_mask_isset(val, 0)) {
        dx = valuator_mask_get_double(val, 0);
    }

    if (valuator_mask_isset(val, 1)) {
        dy = valuator_mask_get_double(val, 1);
    }

    if (dx != 0.0 || dy != 0.0) {
        /* reset non-visible state? */
        if (ProcessVelocityData2D(velocitydata, dx, dy, evtime)) {
            soften = FALSE;
        }

        if (dev->ptrfeed && dev->ptrfeed->ctrl.num) {
            double mult;

            /* invoke acceleration profile to determine acceleration */
            mult = ComputeAcceleration(dev, velocitydata,
                                       dev->ptrfeed->ctrl.threshold,
                                       (double) dev->ptrfeed->ctrl.num /
                                       (double) dev->ptrfeed->ctrl.den);

            if (mult != 1.0f || velocitydata->const_acceleration != 1.0f) {
                if (mult > 1.0f && soften)
                    ApplySoftening(velocitydata, &dx, &dy);
                ApplyConstantDeceleration(velocitydata, &dx, &dy);

                if (dx != 0.0)
                    valuator_mask_set_double(val, 0, mult * dx);
                if (dy != 0.0)
                    valuator_mask_set_double(val, 1, mult * dy);
                DebugAccelF("pos (%i | %i) delta x:%.3f y:%.3f\n", mult * dx,
                            mult * dy);
            }
        }
    }
    /* remember last motion delta (for softening/slow movement treatment) */
    velocitydata->last_dx = dx;
    velocitydata->last_dy = dy;
}

/**
 * Originally a part of xf86PostMotionEvent; modifies valuators
 * in-place. Retained mostly for embedded scenarios.
 */
void
acceleratePointerLightweight(DeviceIntPtr dev,
                             ValuatorMask *val, CARD32 ignored)
{
    double mult = 0.0, tmpf;
    double dx = 0.0, dy = 0.0;

    if (valuator_mask_isset(val, 0)) {
        dx = valuator_mask_get(val, 0);
    }

    if (valuator_mask_isset(val, 1)) {
        dy = valuator_mask_get(val, 1);
    }

    if (valuator_mask_num_valuators(val) == 0)
        return;

    if (dev->ptrfeed && dev->ptrfeed->ctrl.num) {
        /* modeled from xf86Events.c */
        if (dev->ptrfeed->ctrl.threshold) {
            if ((fabs(dx) + fabs(dy)) >= dev->ptrfeed->ctrl.threshold) {
                if (dx != 0.0) {
                    tmpf = (dx * (double) (dev->ptrfeed->ctrl.num)) /
                        (double) (dev->ptrfeed->ctrl.den);
                    valuator_mask_set_double(val, 0, tmpf);
                }

                if (dy != 0.0) {
                    tmpf = (dy * (double) (dev->ptrfeed->ctrl.num)) /
                        (double) (dev->ptrfeed->ctrl.den);
                    valuator_mask_set_double(val, 1, tmpf);
                }
            }
        }
        else {
            mult = pow(dx * dx + dy * dy,
                       ((double) (dev->ptrfeed->ctrl.num) /
                        (double) (dev->ptrfeed->ctrl.den) - 1.0) / 2.0) / 2.0;
            if (dx != 0.0)
                valuator_mask_set_double(val, 0, mult * dx);
            if (dy != 0.0)
                valuator_mask_set_double(val, 1, mult * dy);
        }
    }
}