libs/input/tests/VelocityTracker_test.cpp

/*
 * Copyright (C) 2017 The Android Open Source Project
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#define LOG_TAG "VelocityTracker_test"

#include <array>
#include <chrono>
#include <math.h>

#include <android-base/stringprintf.h>
#include <gtest/gtest.h>
#include <input/VelocityTracker.h>

using namespace std::chrono_literals;
using android::base::StringPrintf;

namespace android {

constexpr int32_t DISPLAY_ID = ADISPLAY_ID_DEFAULT; // default display id

constexpr int32_t DEFAULT_POINTER_ID = 0; // pointer ID used for manually defined tests

// velocity must be in the range (1-tol)*EV <= velocity <= (1+tol)*EV
// here EV = expected value, tol = VELOCITY_TOLERANCE
constexpr float VELOCITY_TOLERANCE = 0.2;

// estimate coefficients must be within 0.001% of the target value
constexpr float COEFFICIENT_TOLERANCE = 0.00001;

// --- VelocityTrackerTest ---
class VelocityTrackerTest : public testing::Test { };

/*
 * Similar to EXPECT_NEAR, but ensures that the difference between the two float values
 * is at most a certain fraction of the target value.
 * If fraction is zero, require exact match.
 */
static void EXPECT_NEAR_BY_FRACTION(float actual, float target, float fraction) {
    float tolerance = fabsf(target * fraction);

    if (target == 0 && fraction != 0) {
        // If target is zero, this would force actual == target, which is too harsh.
        // Relax this requirement a little. The value is determined empirically from the
        // coefficients computed by the quadratic least squares algorithms.
        tolerance = 1E-6;
    }
    EXPECT_NEAR(actual, target, tolerance);
}

static void checkVelocity(float Vactual, float Vtarget) {
    EXPECT_NEAR_BY_FRACTION(Vactual, Vtarget, VELOCITY_TOLERANCE);
}

static void checkCoefficient(float actual, float target) {
    EXPECT_NEAR_BY_FRACTION(actual, target, COEFFICIENT_TOLERANCE);
}

struct Position {
    float x;
    float y;

    /**
     * If both values are NAN, then this is considered to be an empty entry (no pointer data).
     * If only one of the values is NAN, this is still a valid entry,
     * because we may only care about a single axis.
     */
    bool isValid() const {
        return !(isnan(x) && isnan(y));
    }
};

struct MotionEventEntry {
    std::chrono::nanoseconds eventTime;
    std::vector<Position> positions;
};

static BitSet32 getValidPointers(const std::vector<Position>& positions) {
    BitSet32 pointers;
    for (size_t i = 0; i < positions.size(); i++) {
        if (positions[i].isValid()) {
            pointers.markBit(i);
        }
    }
    return pointers;
}

static uint32_t getChangingPointerId(BitSet32 pointers, BitSet32 otherPointers) {
    BitSet32 difference(pointers.value ^ otherPointers.value);
    uint32_t pointerId = difference.clearFirstMarkedBit();
    EXPECT_EQ(0U, difference.value) << "Only 1 pointer can enter or leave at a time";
    return pointerId;
}

static int32_t resolveAction(const std::vector<Position>& lastPositions,
        const std::vector<Position>& currentPositions,
        const std::vector<Position>& nextPositions) {
    BitSet32 pointers = getValidPointers(currentPositions);
    const uint32_t pointerCount = pointers.count();

    BitSet32 lastPointers = getValidPointers(lastPositions);
    const uint32_t lastPointerCount = lastPointers.count();
    if (lastPointerCount < pointerCount) {
        // A new pointer is down
        uint32_t pointerId = getChangingPointerId(pointers, lastPointers);
        return AMOTION_EVENT_ACTION_POINTER_DOWN |
                (pointerId << AMOTION_EVENT_ACTION_POINTER_INDEX_SHIFT);
    }

    BitSet32 nextPointers = getValidPointers(nextPositions);
    const uint32_t nextPointerCount = nextPointers.count();
    if (pointerCount > nextPointerCount) {
        // An existing pointer is leaving
        uint32_t pointerId = getChangingPointerId(pointers, nextPointers);
        return AMOTION_EVENT_ACTION_POINTER_UP |
                (pointerId << AMOTION_EVENT_ACTION_POINTER_INDEX_SHIFT);
    }

    return AMOTION_EVENT_ACTION_MOVE;
}

static std::vector<MotionEvent> createMotionEventStream(
        const std::vector<MotionEventEntry>& motions) {
    if (motions.empty()) {
        ADD_FAILURE() << "Need at least 1 sample to create a MotionEvent. Received empty vector.";
    }

    std::vector<MotionEvent> events;
    for (size_t i = 0; i < motions.size(); i++) {
        const MotionEventEntry& entry = motions[i];
        BitSet32 pointers = getValidPointers(entry.positions);
        const uint32_t pointerCount = pointers.count();

        int32_t action;
        if (i == 0) {
            action = AMOTION_EVENT_ACTION_DOWN;
            EXPECT_EQ(1U, pointerCount) << "First event should only have 1 pointer";
        } else if (i == motions.size() - 1) {
            EXPECT_EQ(1U, pointerCount) << "Last event should only have 1 pointer";
            action = AMOTION_EVENT_ACTION_UP;
        } else {
            const MotionEventEntry& previousEntry = motions[i-1];
            const MotionEventEntry& nextEntry = motions[i+1];
            action = resolveAction(previousEntry.positions, entry.positions, nextEntry.positions);
        }

        PointerCoords coords[pointerCount];
        PointerProperties properties[pointerCount];
        uint32_t pointerIndex = 0;
        while(!pointers.isEmpty()) {
            uint32_t pointerId = pointers.clearFirstMarkedBit();

            coords[pointerIndex].clear();
            // We are treating column positions as pointerId
            EXPECT_TRUE(entry.positions[pointerId].isValid()) <<
                    "The entry at pointerId must be valid";
            coords[pointerIndex].setAxisValue(AMOTION_EVENT_AXIS_X, entry.positions[pointerId].x);
            coords[pointerIndex].setAxisValue(AMOTION_EVENT_AXIS_Y, entry.positions[pointerId].y);

            properties[pointerIndex].id = pointerId;
            properties[pointerIndex].toolType = AMOTION_EVENT_TOOL_TYPE_FINGER;
            pointerIndex++;
        }
        EXPECT_EQ(pointerIndex, pointerCount);

        MotionEvent event;
        ui::Transform identityTransform;
        event.initialize(InputEvent::nextId(), 0 /*deviceId*/, AINPUT_SOURCE_TOUCHSCREEN,
                         DISPLAY_ID, INVALID_HMAC, action, 0 /*actionButton*/, 0 /*flags*/,
                         AMOTION_EVENT_EDGE_FLAG_NONE, AMETA_NONE, 0 /*buttonState*/,
                         MotionClassification::NONE, identityTransform, 0 /*xPrecision*/,
                         0 /*yPrecision*/, AMOTION_EVENT_INVALID_CURSOR_POSITION,
                         AMOTION_EVENT_INVALID_CURSOR_POSITION, 0 /*downTime*/,
                         entry.eventTime.count(), pointerCount, properties, coords);

        events.emplace_back(event);
    }

    return events;
}

static void computeAndCheckVelocity(const VelocityTracker::Strategy strategy,
                                    const std::vector<MotionEventEntry>& motions, int32_t axis,
                                    float targetVelocity) {
    VelocityTracker vt(strategy);
    float Vx, Vy;

    std::vector<MotionEvent> events = createMotionEventStream(motions);
    for (MotionEvent event : events) {
        vt.addMovement(&event);
    }

    vt.getVelocity(DEFAULT_POINTER_ID, &Vx, &Vy);

    switch (axis) {
    case AMOTION_EVENT_AXIS_X:
        checkVelocity(Vx, targetVelocity);
        break;
    case AMOTION_EVENT_AXIS_Y:
        checkVelocity(Vy, targetVelocity);
        break;
    default:
        FAIL() << "Axis must be either AMOTION_EVENT_AXIS_X or AMOTION_EVENT_AXIS_Y";
    }
}

static void computeAndCheckQuadraticEstimate(const std::vector<MotionEventEntry>& motions,
        const std::array<float, 3>& coefficients) {
    VelocityTracker vt(VelocityTracker::Strategy::LSQ2);
    std::vector<MotionEvent> events = createMotionEventStream(motions);
    for (MotionEvent event : events) {
        vt.addMovement(&event);
    }
    VelocityTracker::Estimator estimator;
    EXPECT_TRUE(vt.getEstimator(0, &estimator));
    for (size_t i = 0; i< coefficients.size(); i++) {
        checkCoefficient(estimator.xCoeff[i], coefficients[i]);
        checkCoefficient(estimator.yCoeff[i], coefficients[i]);
    }
}

/*
 * ================== VelocityTracker tests generated manually =====================================
 */
TEST_F(VelocityTrackerTest, ThreePointsPositiveVelocityTest) {
    // Same coordinate is reported 2 times in a row
    // It is difficult to determine the correct answer here, but at least the direction
    // of the reported velocity should be positive.
    std::vector<MotionEventEntry> motions = {
            {0ms, {{273, 0}}},
            {12585us, {{293, 0}}},
            {14730us, {{293, 0}}},
            {14730us, {{293, 0}}}, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            1600);
}

TEST_F(VelocityTrackerTest, ThreePointsZeroVelocityTest) {
    // Same coordinate is reported 3 times in a row
    std::vector<MotionEventEntry> motions = {
            {0ms, {{293, 0}}},
            {6132us, {{293, 0}}},
            {11283us, {{293, 0}}},
            {11283us, {{293, 0}}}, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X, 0);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X, 0);
}

TEST_F(VelocityTrackerTest, ThreePointsLinearVelocityTest) {
    // Fixed velocity at 5 points per 10 milliseconds
    std::vector<MotionEventEntry> motions = {
            {0ms, {{0, 0}}}, {10ms, {{5, 0}}}, {20ms, {{10, 0}}}, {20ms, {{10, 0}}}, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X, 500);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X, 500);
}


/**
 * ================== VelocityTracker tests generated by recording real events =====================
 *
 * To add a test, record the input coordinates and event times to all calls
 * to void VelocityTracker::addMovement(const MotionEvent* event).
 * Also record all calls to VelocityTracker::clear().
 * Finally, record the output of VelocityTracker::getVelocity(...)
 * This will give you the necessary data to create a new test.
 *
 * Another good way to generate this data is to use 'dumpsys input' just after the event has
 * occurred.
 */

// --------------- Recorded by hand on swordfish ---------------------------------------------------
TEST_F(VelocityTrackerTest, SwordfishFlingDown) {
    // Recording of a fling on Swordfish that could cause a fling in the wrong direction
    std::vector<MotionEventEntry> motions = {
        { 0ms, {{271, 96}} },
        { 16071042ns, {{269.786346, 106.922775}} },
        { 35648403ns, {{267.983063, 156.660034}} },
        { 52313925ns, {{262.638397, 220.339081}} },
        { 68976522ns, {{266.138824, 331.581116}} },
        { 85639375ns, {{274.79245, 428.113159}} },
        { 96948871ns, {{274.79245, 428.113159}} },
        { 96948871ns, {{274.79245, 428.113159}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            623.577637);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            5970.7309);
}

// --------------- Recorded by hand on sailfish, generated by a script -----------------------------
// For some of these tests, the X-direction velocity checking has been removed, because the lsq2
// and the impulse VelocityTrackerStrategies did not agree within 20%.
// Since the flings were recorded in the Y-direction, the intentional user action should only
// be relevant for the Y axis.
// There have been also cases where lsq2 and impulse disagreed more than 20% in the Y-direction.
// Those recordings have been discarded because we didn't feel one strategy's interpretation was
// more correct than another's but didn't want to increase the tolerance for the entire test suite.
//
// There are 18 tests total below: 9 in the positive Y direction and 9 in the opposite.
// The recordings were loosely binned into 3 categories - slow, faster, and fast, which roughly
// characterizes the velocity of the finger motion.
// These can be treated approximately as:
// slow - less than 1 page gets scrolled
// faster - more than 1 page gets scrolled, but less than 3
// fast - entire list is scrolled (fling is done as hard as possible)

TEST_F(VelocityTrackerTest, SailfishFlingUpSlow1) {
    // Sailfish - fling up - slow - 1
    std::vector<MotionEventEntry> motions = {
        { 235089067457000ns, {{528.00, 983.00}} },
        { 235089084684000ns, {{527.00, 981.00}} },
        { 235089093349000ns, {{527.00, 977.00}} },
        { 235089095677625ns, {{527.00, 975.93}} },
        { 235089101859000ns, {{527.00, 970.00}} },
        { 235089110378000ns, {{528.00, 960.00}} },
        { 235089112497111ns, {{528.25, 957.51}} },
        { 235089118760000ns, {{531.00, 946.00}} },
        { 235089126686000ns, {{535.00, 931.00}} },
        { 235089129316820ns, {{536.33, 926.02}} },
        { 235089135199000ns, {{540.00, 914.00}} },
        { 235089144297000ns, {{546.00, 896.00}} },
        { 235089146136443ns, {{547.21, 892.36}} },
        { 235089152923000ns, {{553.00, 877.00}} },
        { 235089160784000ns, {{559.00, 851.00}} },
        { 235089162955851ns, {{560.66, 843.82}} },
        { 235089162955851ns, {{560.66, 843.82}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            872.794617);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X,
                            951.698181);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            -3604.819336);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            -3044.966064);
}


TEST_F(VelocityTrackerTest, SailfishFlingUpSlow2) {
    // Sailfish - fling up - slow - 2
    std::vector<MotionEventEntry> motions = {
        { 235110560704000ns, {{522.00, 1107.00}} },
        { 235110575764000ns, {{522.00, 1107.00}} },
        { 235110584385000ns, {{522.00, 1107.00}} },
        { 235110588421179ns, {{521.52, 1106.52}} },
        { 235110592830000ns, {{521.00, 1106.00}} },
        { 235110601385000ns, {{520.00, 1104.00}} },
        { 235110605088160ns, {{519.14, 1102.27}} },
        { 235110609952000ns, {{518.00, 1100.00}} },
        { 235110618353000ns, {{517.00, 1093.00}} },
        { 235110621755146ns, {{516.60, 1090.17}} },
        { 235110627010000ns, {{517.00, 1081.00}} },
        { 235110634785000ns, {{518.00, 1063.00}} },
        { 235110638422450ns, {{518.87, 1052.58}} },
        { 235110643161000ns, {{520.00, 1039.00}} },
        { 235110651767000ns, {{524.00, 1011.00}} },
        { 235110655089581ns, {{525.54, 1000.19}} },
        { 235110660368000ns, {{530.00, 980.00}} },
        { 235110660368000ns, {{530.00, 980.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            -4096.583008);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            -3455.094238);
}


TEST_F(VelocityTrackerTest, SailfishFlingUpSlow3) {
    // Sailfish - fling up - slow - 3
    std::vector<MotionEventEntry> motions = {
        { 792536237000ns, {{580.00, 1317.00}} },
        { 792541538987ns, {{580.63, 1311.94}} },
        { 792544613000ns, {{581.00, 1309.00}} },
        { 792552301000ns, {{583.00, 1295.00}} },
        { 792558362309ns, {{585.13, 1282.92}} },
        { 792560828000ns, {{586.00, 1278.00}} },
        { 792569446000ns, {{589.00, 1256.00}} },
        { 792575185095ns, {{591.54, 1241.41}} },
        { 792578491000ns, {{593.00, 1233.00}} },
        { 792587044000ns, {{597.00, 1211.00}} },
        { 792592008172ns, {{600.28, 1195.92}} },
        { 792594616000ns, {{602.00, 1188.00}} },
        { 792603129000ns, {{607.00, 1167.00}} },
        { 792608831290ns, {{609.48, 1155.83}} },
        { 792612321000ns, {{611.00, 1149.00}} },
        { 792620768000ns, {{615.00, 1131.00}} },
        { 792625653873ns, {{617.32, 1121.73}} },
        { 792629200000ns, {{619.00, 1115.00}} },
        { 792629200000ns, {{619.00, 1115.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            574.33429);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X,
                            617.40564);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            -2361.982666);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            -2500.055664);
}


TEST_F(VelocityTrackerTest, SailfishFlingUpFaster1) {
    // Sailfish - fling up - faster - 1
    std::vector<MotionEventEntry> motions = {
        { 235160420675000ns, {{610.00, 1042.00}} },
        { 235160428220000ns, {{609.00, 1026.00}} },
        { 235160436544000ns, {{609.00, 1024.00}} },
        { 235160441852394ns, {{609.64, 1020.82}} },
        { 235160444878000ns, {{610.00, 1019.00}} },
        { 235160452673000ns, {{613.00, 1006.00}} },
        { 235160458519743ns, {{617.18, 992.06}} },
        { 235160461061000ns, {{619.00, 986.00}} },
        { 235160469798000ns, {{627.00, 960.00}} },
        { 235160475186713ns, {{632.22, 943.02}} },
        { 235160478051000ns, {{635.00, 934.00}} },
        { 235160486489000ns, {{644.00, 906.00}} },
        { 235160491853697ns, {{649.56, 890.56}} },
        { 235160495177000ns, {{653.00, 881.00}} },
        { 235160504148000ns, {{662.00, 858.00}} },
        { 235160509231495ns, {{666.81, 845.37}} },
        { 235160512603000ns, {{670.00, 837.00}} },
        { 235160520366000ns, {{679.00, 814.00}} },
        { 235160520366000ns, {{679.00, 814.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            1274.141724);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X,
                            1438.53186);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            -3001.4348);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            -3695.859619);
}


TEST_F(VelocityTrackerTest, SailfishFlingUpFaster2) {
    // Sailfish - fling up - faster - 2
    std::vector<MotionEventEntry> motions = {
        { 847153808000ns, {{576.00, 1264.00}} },
        { 847171174000ns, {{576.00, 1262.00}} },
        { 847179640000ns, {{576.00, 1257.00}} },
        { 847185187540ns, {{577.41, 1249.22}} },
        { 847187487000ns, {{578.00, 1246.00}} },
        { 847195710000ns, {{581.00, 1227.00}} },
        { 847202027059ns, {{583.93, 1209.40}} },
        { 847204324000ns, {{585.00, 1203.00}} },
        { 847212672000ns, {{590.00, 1176.00}} },
        { 847218861395ns, {{594.36, 1157.11}} },
        { 847221190000ns, {{596.00, 1150.00}} },
        { 847230484000ns, {{602.00, 1124.00}} },
        { 847235701400ns, {{607.56, 1103.83}} },
        { 847237986000ns, {{610.00, 1095.00}} },
        { 847237986000ns, {{610.00, 1095.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            -4280.07959);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            -4241.004395);
}


TEST_F(VelocityTrackerTest, SailfishFlingUpFaster3) {
    // Sailfish - fling up - faster - 3
    std::vector<MotionEventEntry> motions = {
        { 235200532789000ns, {{507.00, 1084.00}} },
        { 235200549221000ns, {{507.00, 1083.00}} },
        { 235200557841000ns, {{507.00, 1081.00}} },
        { 235200558051189ns, {{507.00, 1080.95}} },
        { 235200566314000ns, {{507.00, 1078.00}} },
        { 235200574876586ns, {{508.97, 1070.12}} },
        { 235200575006000ns, {{509.00, 1070.00}} },
        { 235200582900000ns, {{514.00, 1054.00}} },
        { 235200591276000ns, {{525.00, 1023.00}} },
        { 235200591701829ns, {{525.56, 1021.42}} },
        { 235200600064000ns, {{542.00, 976.00}} },
        { 235200608519000ns, {{563.00, 911.00}} },
        { 235200608527086ns, {{563.02, 910.94}} },
        { 235200616933000ns, {{590.00, 844.00}} },
        { 235200616933000ns, {{590.00, 844.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            -8715.686523);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            -7639.026367);
}


TEST_F(VelocityTrackerTest, SailfishFlingUpFast1) {
    // Sailfish - fling up - fast - 1
    std::vector<MotionEventEntry> motions = {
        { 920922149000ns, {{561.00, 1412.00}} },
        { 920930185000ns, {{559.00, 1377.00}} },
        { 920930262463ns, {{558.98, 1376.66}} },
        { 920938547000ns, {{559.00, 1371.00}} },
        { 920947096857ns, {{562.91, 1342.68}} },
        { 920947302000ns, {{563.00, 1342.00}} },
        { 920955502000ns, {{577.00, 1272.00}} },
        { 920963931021ns, {{596.87, 1190.54}} },
        { 920963987000ns, {{597.00, 1190.00}} },
        { 920972530000ns, {{631.00, 1093.00}} },
        { 920980765511ns, {{671.31, 994.68}} },
        { 920980906000ns, {{672.00, 993.00}} },
        { 920989261000ns, {{715.00, 903.00}} },
        { 920989261000ns, {{715.00, 903.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            5670.329102);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X,
                            5991.866699);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            -13021.101562);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            -15093.995117);
}


TEST_F(VelocityTrackerTest, SailfishFlingUpFast2) {
    // Sailfish - fling up - fast - 2
    std::vector<MotionEventEntry> motions = {
        { 235247153233000ns, {{518.00, 1168.00}} },
        { 235247170452000ns, {{517.00, 1167.00}} },
        { 235247178908000ns, {{515.00, 1159.00}} },
        { 235247179556213ns, {{514.85, 1158.39}} },
        { 235247186821000ns, {{515.00, 1125.00}} },
        { 235247195265000ns, {{521.00, 1051.00}} },
        { 235247196389476ns, {{521.80, 1041.15}} },
        { 235247203649000ns, {{538.00, 932.00}} },
        { 235247212253000ns, {{571.00, 794.00}} },
        { 235247213222491ns, {{574.72, 778.45}} },
        { 235247220736000ns, {{620.00, 641.00}} },
        { 235247220736000ns, {{620.00, 641.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            -20286.958984);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            -20494.587891);
}


TEST_F(VelocityTrackerTest, SailfishFlingUpFast3) {
    // Sailfish - fling up - fast - 3
    std::vector<MotionEventEntry> motions = {
        { 235302568736000ns, {{529.00, 1167.00}} },
        { 235302576644000ns, {{523.00, 1140.00}} },
        { 235302579395063ns, {{520.91, 1130.61}} },
        { 235302585140000ns, {{522.00, 1130.00}} },
        { 235302593615000ns, {{527.00, 1065.00}} },
        { 235302596207444ns, {{528.53, 1045.12}} },
        { 235302602102000ns, {{559.00, 872.00}} },
        { 235302610545000ns, {{652.00, 605.00}} },
        { 235302613019881ns, {{679.26, 526.73}} },
        { 235302613019881ns, {{679.26, 526.73}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            -39295.941406);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            -36461.421875);
}


TEST_F(VelocityTrackerTest, SailfishFlingDownSlow1) {
    // Sailfish - fling down - slow - 1
    std::vector<MotionEventEntry> motions = {
        { 235655749552755ns, {{582.00, 432.49}} },
        { 235655750638000ns, {{582.00, 433.00}} },
        { 235655758865000ns, {{582.00, 440.00}} },
        { 235655766221523ns, {{581.16, 448.43}} },
        { 235655767594000ns, {{581.00, 450.00}} },
        { 235655776044000ns, {{580.00, 462.00}} },
        { 235655782890696ns, {{579.18, 474.35}} },
        { 235655784360000ns, {{579.00, 477.00}} },
        { 235655792795000ns, {{578.00, 496.00}} },
        { 235655799559531ns, {{576.27, 515.04}} },
        { 235655800612000ns, {{576.00, 518.00}} },
        { 235655809535000ns, {{574.00, 542.00}} },
        { 235655816988015ns, {{572.17, 564.86}} },
        { 235655817685000ns, {{572.00, 567.00}} },
        { 235655825981000ns, {{569.00, 595.00}} },
        { 235655833808653ns, {{566.26, 620.60}} },
        { 235655834541000ns, {{566.00, 623.00}} },
        { 235655842893000ns, {{563.00, 649.00}} },
        { 235655842893000ns, {{563.00, 649.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            -419.749695);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X,
                            -398.303894);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            3309.016357);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            3969.099854);
}


TEST_F(VelocityTrackerTest, SailfishFlingDownSlow2) {
    // Sailfish - fling down - slow - 2
    std::vector<MotionEventEntry> motions = {
        { 235671152083370ns, {{485.24, 558.28}} },
        { 235671154126000ns, {{485.00, 559.00}} },
        { 235671162497000ns, {{484.00, 566.00}} },
        { 235671168750511ns, {{483.27, 573.29}} },
        { 235671171071000ns, {{483.00, 576.00}} },
        { 235671179390000ns, {{482.00, 588.00}} },
        { 235671185417210ns, {{481.31, 598.98}} },
        { 235671188173000ns, {{481.00, 604.00}} },
        { 235671196371000ns, {{480.00, 624.00}} },
        { 235671202084196ns, {{479.27, 639.98}} },
        { 235671204235000ns, {{479.00, 646.00}} },
        { 235671212554000ns, {{478.00, 673.00}} },
        { 235671219471011ns, {{476.39, 697.12}} },
        { 235671221159000ns, {{476.00, 703.00}} },
        { 235671229592000ns, {{474.00, 734.00}} },
        { 235671236281462ns, {{472.43, 758.38}} },
        { 235671238098000ns, {{472.00, 765.00}} },
        { 235671246532000ns, {{470.00, 799.00}} },
        { 235671246532000ns, {{470.00, 799.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            -262.80426);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X,
                            -243.665344);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            4215.682129);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            4587.986816);
}


TEST_F(VelocityTrackerTest, SailfishFlingDownSlow3) {
    // Sailfish - fling down - slow - 3
    std::vector<MotionEventEntry> motions = {
        { 170983201000ns, {{557.00, 533.00}} },
        { 171000668000ns, {{556.00, 534.00}} },
        { 171007359750ns, {{554.73, 535.27}} },
        { 171011197000ns, {{554.00, 536.00}} },
        { 171017660000ns, {{552.00, 540.00}} },
        { 171024201831ns, {{549.97, 544.73}} },
        { 171027333000ns, {{549.00, 547.00}} },
        { 171034603000ns, {{545.00, 557.00}} },
        { 171041043371ns, {{541.98, 567.55}} },
        { 171043147000ns, {{541.00, 571.00}} },
        { 171051052000ns, {{536.00, 586.00}} },
        { 171051052000ns, {{536.00, 586.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            -723.413513);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X,
                            -651.038452);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            2091.502441);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            1934.517456);
}


TEST_F(VelocityTrackerTest, SailfishFlingDownFaster1) {
    // Sailfish - fling down - faster - 1
    std::vector<MotionEventEntry> motions = {
        { 235695280333000ns, {{558.00, 451.00}} },
        { 235695283971237ns, {{558.43, 454.45}} },
        { 235695289038000ns, {{559.00, 462.00}} },
        { 235695297388000ns, {{561.00, 478.00}} },
        { 235695300638465ns, {{561.83, 486.25}} },
        { 235695305265000ns, {{563.00, 498.00}} },
        { 235695313591000ns, {{564.00, 521.00}} },
        { 235695317305492ns, {{564.43, 532.68}} },
        { 235695322181000ns, {{565.00, 548.00}} },
        { 235695330709000ns, {{565.00, 577.00}} },
        { 235695333972227ns, {{565.00, 588.10}} },
        { 235695339250000ns, {{565.00, 609.00}} },
        { 235695347839000ns, {{565.00, 642.00}} },
        { 235695351313257ns, {{565.00, 656.18}} },
        { 235695356412000ns, {{565.00, 677.00}} },
        { 235695364899000ns, {{563.00, 710.00}} },
        { 235695368118682ns, {{562.24, 722.52}} },
        { 235695373403000ns, {{564.00, 744.00}} },
        { 235695373403000ns, {{564.00, 744.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            4254.639648);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            4698.415039);
}


TEST_F(VelocityTrackerTest, SailfishFlingDownFaster2) {
    // Sailfish - fling down - faster - 2
    std::vector<MotionEventEntry> motions = {
        { 235709624766000ns, {{535.00, 579.00}} },
        { 235709642256000ns, {{534.00, 580.00}} },
        { 235709643350278ns, {{533.94, 580.06}} },
        { 235709650760000ns, {{532.00, 584.00}} },
        { 235709658615000ns, {{530.00, 593.00}} },
        { 235709660170495ns, {{529.60, 594.78}} },
        { 235709667095000ns, {{527.00, 606.00}} },
        { 235709675616000ns, {{524.00, 628.00}} },
        { 235709676983261ns, {{523.52, 631.53}} },
        { 235709684289000ns, {{521.00, 652.00}} },
        { 235709692763000ns, {{518.00, 682.00}} },
        { 235709693804993ns, {{517.63, 685.69}} },
        { 235709701438000ns, {{515.00, 709.00}} },
        { 235709709830000ns, {{512.00, 739.00}} },
        { 235709710626776ns, {{511.72, 741.85}} },
        { 235709710626776ns, {{511.72, 741.85}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            -430.440247);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X,
                            -447.600311);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            3953.859375);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            4316.155273);
}


TEST_F(VelocityTrackerTest, SailfishFlingDownFaster3) {
    // Sailfish - fling down - faster - 3
    std::vector<MotionEventEntry> motions = {
        { 235727628927000ns, {{540.00, 440.00}} },
        { 235727636810000ns, {{537.00, 454.00}} },
        { 235727646176000ns, {{536.00, 454.00}} },
        { 235727653586628ns, {{535.12, 456.65}} },
        { 235727654557000ns, {{535.00, 457.00}} },
        { 235727663024000ns, {{534.00, 465.00}} },
        { 235727670410103ns, {{533.04, 479.45}} },
        { 235727670691000ns, {{533.00, 480.00}} },
        { 235727679255000ns, {{531.00, 501.00}} },
        { 235727687233704ns, {{529.09, 526.73}} },
        { 235727687628000ns, {{529.00, 528.00}} },
        { 235727696113000ns, {{526.00, 558.00}} },
        { 235727704057546ns, {{523.18, 588.98}} },
        { 235727704576000ns, {{523.00, 591.00}} },
        { 235727713099000ns, {{520.00, 626.00}} },
        { 235727720880776ns, {{516.33, 655.36}} },
        { 235727721580000ns, {{516.00, 658.00}} },
        { 235727721580000ns, {{516.00, 658.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            4484.617676);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            4927.92627);
}


TEST_F(VelocityTrackerTest, SailfishFlingDownFast1) {
    // Sailfish - fling down - fast - 1
    std::vector<MotionEventEntry> motions = {
        { 235762352849000ns, {{467.00, 286.00}} },
        { 235762360250000ns, {{443.00, 344.00}} },
        { 235762362787412ns, {{434.77, 363.89}} },
        { 235762368807000ns, {{438.00, 359.00}} },
        { 235762377220000ns, {{425.00, 423.00}} },
        { 235762379608561ns, {{421.31, 441.17}} },
        { 235762385698000ns, {{412.00, 528.00}} },
        { 235762394133000ns, {{406.00, 648.00}} },
        { 235762396429369ns, {{404.37, 680.67}} },
        { 235762396429369ns, {{404.37, 680.67}} }, //ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            14227.0224);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            16064.685547);
}


TEST_F(VelocityTrackerTest, SailfishFlingDownFast2) {
    // Sailfish - fling down - fast - 2
    std::vector<MotionEventEntry> motions = {
        { 235772487188000ns, {{576.00, 204.00}} },
        { 235772495159000ns, {{553.00, 236.00}} },
        { 235772503568000ns, {{551.00, 240.00}} },
        { 235772508192247ns, {{545.55, 254.17}} },
        { 235772512051000ns, {{541.00, 266.00}} },
        { 235772520794000ns, {{520.00, 337.00}} },
        { 235772525015263ns, {{508.92, 394.43}} },
        { 235772529174000ns, {{498.00, 451.00}} },
        { 235772537635000ns, {{484.00, 589.00}} },
        { 235772537635000ns, {{484.00, 589.00}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            18660.048828);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            16918.439453);
}


TEST_F(VelocityTrackerTest, SailfishFlingDownFast3) {
    // Sailfish - fling down - fast - 3
    std::vector<MotionEventEntry> motions = {
        { 507650295000ns, {{628.00, 233.00}} },
        { 507658234000ns, {{605.00, 269.00}} },
        { 507666784000ns, {{601.00, 274.00}} },
        { 507669660483ns, {{599.65, 275.68}} },
        { 507675427000ns, {{582.00, 308.00}} },
        { 507683740000ns, {{541.00, 404.00}} },
        { 507686506238ns, {{527.36, 435.95}} },
        { 507692220000ns, {{487.00, 581.00}} },
        { 507700707000ns, {{454.00, 792.00}} },
        { 507703352649ns, {{443.71, 857.77}} },
        { 507703352649ns, {{443.71, 857.77}} }, // ACTION_UP
    };
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X,
                            -4111.8173);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X,
                            -6388.48877);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y,
                            29765.908203);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y,
                            28354.796875);
}

/**
 * ================== Multiple pointers ============================================================
 *
 * Three fingers quickly tap the screen. Since this is a tap, the velocities should be zero.
 * If the events with POINTER_UP or POINTER_DOWN are not handled correctly (these should not be
 * part of the fitted data), this can cause large velocity values to be reported instead.
 */
TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_ThreeFingerTap) {
    std::vector<MotionEventEntry> motions = {
        { 0us,      {{1063, 1128}, {NAN, NAN}, {NAN, NAN}} },
        { 10800us,  {{1063, 1128}, {682, 1318}, {NAN, NAN}} }, // POINTER_DOWN
        { 10800us,  {{1063, 1128}, {682, 1318}, {397, 1747}} }, // POINTER_DOWN
        { 267300us, {{1063, 1128}, {682, 1318}, {397, 1747}} }, // POINTER_UP
        { 267300us, {{1063, 1128}, {NAN, NAN}, {397, 1747}} }, // POINTER_UP
        { 272700us, {{1063, 1128}, {NAN, NAN}, {NAN, NAN}} },
    };

    // Velocity should actually be zero, but we expect 0.016 here instead.
    // This is close enough to zero, and is likely caused by division by a very small number.
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_X, -0.016);
    computeAndCheckVelocity(VelocityTracker::Strategy::LSQ2, motions, AMOTION_EVENT_AXIS_Y, -0.016);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_X, 0);
    computeAndCheckVelocity(VelocityTracker::Strategy::IMPULSE, motions, AMOTION_EVENT_AXIS_Y, 0);
}

/**
 * ================== Tests for least squares fitting ==============================================
 *
 * Special care must be taken when constructing tests for LeastSquaresVelocityTrackerStrategy
 * getEstimator function. In particular:
 * - inside the function, time gets converted from nanoseconds to seconds
 *   before being used in the fit.
 * - any values that are older than 100 ms are being discarded.
 * - the newest time gets subtracted from all of the other times before being used in the fit.
 * So these tests have to be designed with those limitations in mind.
 *
 * General approach for the tests below:
 * We only used timestamps in milliseconds, 0 ms, 1 ms, and 2 ms, to be sure that
 * we are well within the HORIZON range.
 * When specifying the expected values of the coefficients, we treat the x values as if
 * they were in ms. Then, to adjust for the time units, the coefficients get progressively
 * multiplied by powers of 1E3.
 * For example:
 * data: t(ms), x
 *        1 ms, 1
 *        2 ms, 4
 *        3 ms, 9
 * The coefficients are (0, 0, 1).
 * In the test, we would convert these coefficients to (0*(1E3)^0, 0*(1E3)^1, 1*(1E3)^2).
 */
TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Constant) {
    std::vector<MotionEventEntry> motions = {
        { 0ms, {{1, 1}} }, // 0 s
        { 1ms, {{1, 1}} }, // 0.001 s
        { 2ms, {{1, 1}} }, // 0.002 s
        { 2ms, {{1, 1}} }, // ACTION_UP
    };
    // The data used for the fit will be as follows:
    // time(s), position
    // -0.002, 1
    // -0.001, 1
    // -0.ms, 1
    computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({1, 0, 0}));
}

/*
 * Straight line y = x :: the constant and quadratic coefficients are zero.
 */
TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Linear) {
    std::vector<MotionEventEntry> motions = {
        { 0ms, {{-2, -2}} },
        { 1ms, {{-1, -1}} },
        { 2ms, {{-0, -0}} },
        { 2ms, {{-0, -0}} }, // ACTION_UP
    };
    // The data used for the fit will be as follows:
    // time(s), position
    // -0.002, -2
    // -0.001, -1
    // -0.000,  0
    computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({0, 1E3, 0}));
}

/*
 * Parabola
 */
TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Parabolic) {
    std::vector<MotionEventEntry> motions = {
        { 0ms, {{1, 1}} },
        { 1ms, {{4, 4}} },
        { 2ms, {{8, 8}} },
        { 2ms, {{8, 8}} }, // ACTION_UP
    };
    // The data used for the fit will be as follows:
    // time(s), position
    // -0.002, 1
    // -0.001, 4
    // -0.000, 8
    computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({8, 4.5E3, 0.5E6}));
}

/*
 * Parabola
 */
TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Parabolic2) {
    std::vector<MotionEventEntry> motions = {
        { 0ms, {{1, 1}} },
        { 1ms, {{4, 4}} },
        { 2ms, {{9, 9}} },
        { 2ms, {{9, 9}} }, // ACTION_UP
    };
    // The data used for the fit will be as follows:
    // time(s), position
    // -0.002, 1
    // -0.001, 4
    // -0.000, 9
    computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({9, 6E3, 1E6}));
}

/*
 * Parabola :: y = x^2 :: the constant and linear coefficients are zero.
 */
TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Parabolic3) {
    std::vector<MotionEventEntry> motions = {
        { 0ms, {{4, 4}} },
        { 1ms, {{1, 1}} },
        { 2ms, {{0, 0}} },
        { 2ms, {{0, 0}} }, // ACTION_UP
    };
    // The data used for the fit will be as follows:
    // time(s), position
    // -0.002, 4
    // -0.001, 1
    // -0.000, 0
    computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({0, 0E3, 1E6}));
}

} // namespace android