1 /*
2  * Copyright (C) 2017 The Android Open Source Project
3  *
4  * Licensed under the Apache License, Version 2.0 (the "License");
5  * you may not use this file except in compliance with the License.
6  * You may obtain a copy of the License at
7  *
8  *      http://www.apache.org/licenses/LICENSE-2.0
9  *
10  * Unless required by applicable law or agreed to in writing, software
11  * distributed under the License is distributed on an "AS IS" BASIS,
12  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13  * See the License for the specific language governing permissions and
14  * limitations under the License.
15  */
16 
17 #define LOG_TAG "VelocityTracker_test"
18 
19 #include <array>
20 #include <chrono>
21 #include <math.h>
22 
23 #include <android-base/stringprintf.h>
24 #include <gtest/gtest.h>
25 #include <input/VelocityTracker.h>
26 
27 using namespace std::chrono_literals;
28 using android::base::StringPrintf;
29 
30 namespace android {
31 
32 constexpr int32_t DISPLAY_ID = ADISPLAY_ID_DEFAULT; // default display id
33 
34 constexpr int32_t DEFAULT_POINTER_ID = 0; // pointer ID used for manually defined tests
35 
36 // velocity must be in the range (1-tol)*EV <= velocity <= (1+tol)*EV
37 // here EV = expected value, tol = VELOCITY_TOLERANCE
38 constexpr float VELOCITY_TOLERANCE = 0.2;
39 
40 // estimate coefficients must be within 0.001% of the target value
41 constexpr float COEFFICIENT_TOLERANCE = 0.00001;
42 
43 // --- VelocityTrackerTest ---
44 class VelocityTrackerTest : public testing::Test { };
45 
46 /*
47  * Similar to EXPECT_NEAR, but ensures that the difference between the two float values
48  * is at most a certain fraction of the target value.
49  * If fraction is zero, require exact match.
50  */
EXPECT_NEAR_BY_FRACTION(float actual,float target,float fraction)51 static void EXPECT_NEAR_BY_FRACTION(float actual, float target, float fraction) {
52     float tolerance = fabsf(target * fraction);
53 
54     if (target == 0 && fraction != 0) {
55         // If target is zero, this would force actual == target, which is too harsh.
56         // Relax this requirement a little. The value is determined empirically from the
57         // coefficients computed by the quadratic least squares algorithms.
58         tolerance = 1E-6;
59     }
60     EXPECT_NEAR(actual, target, tolerance);
61 }
62 
checkVelocity(float Vactual,float Vtarget)63 static void checkVelocity(float Vactual, float Vtarget) {
64     EXPECT_NEAR_BY_FRACTION(Vactual, Vtarget, VELOCITY_TOLERANCE);
65 }
66 
checkCoefficient(float actual,float target)67 static void checkCoefficient(float actual, float target) {
68     EXPECT_NEAR_BY_FRACTION(actual, target, COEFFICIENT_TOLERANCE);
69 }
70 
71 struct Position {
72     float x;
73     float y;
74 
75     /**
76      * If both values are NAN, then this is considered to be an empty entry (no pointer data).
77      * If only one of the values is NAN, this is still a valid entry,
78      * because we may only care about a single axis.
79      */
isValidandroid::Position80     bool isValid() const {
81         return !(isnan(x) && isnan(y));
82     }
83 };
84 
85 struct MotionEventEntry {
86     std::chrono::nanoseconds eventTime;
87     std::vector<Position> positions;
88 };
89 
getValidPointers(const std::vector<Position> & positions)90 static BitSet32 getValidPointers(const std::vector<Position>& positions) {
91     BitSet32 pointers;
92     for (size_t i = 0; i < positions.size(); i++) {
93         if (positions[i].isValid()) {
94             pointers.markBit(i);
95         }
96     }
97     return pointers;
98 }
99 
getChangingPointerId(BitSet32 pointers,BitSet32 otherPointers)100 static uint32_t getChangingPointerId(BitSet32 pointers, BitSet32 otherPointers) {
101     BitSet32 difference(pointers.value ^ otherPointers.value);
102     uint32_t pointerId = difference.clearFirstMarkedBit();
103     EXPECT_EQ(0U, difference.value) << "Only 1 pointer can enter or leave at a time";
104     return pointerId;
105 }
106 
resolveAction(const std::vector<Position> & lastPositions,const std::vector<Position> & currentPositions,const std::vector<Position> & nextPositions)107 static int32_t resolveAction(const std::vector<Position>& lastPositions,
108         const std::vector<Position>& currentPositions,
109         const std::vector<Position>& nextPositions) {
110     BitSet32 pointers = getValidPointers(currentPositions);
111     const uint32_t pointerCount = pointers.count();
112 
113     BitSet32 lastPointers = getValidPointers(lastPositions);
114     const uint32_t lastPointerCount = lastPointers.count();
115     if (lastPointerCount < pointerCount) {
116         // A new pointer is down
117         uint32_t pointerId = getChangingPointerId(pointers, lastPointers);
118         return AMOTION_EVENT_ACTION_POINTER_DOWN |
119                 (pointerId << AMOTION_EVENT_ACTION_POINTER_INDEX_SHIFT);
120     }
121 
122     BitSet32 nextPointers = getValidPointers(nextPositions);
123     const uint32_t nextPointerCount = nextPointers.count();
124     if (pointerCount > nextPointerCount) {
125         // An existing pointer is leaving
126         uint32_t pointerId = getChangingPointerId(pointers, nextPointers);
127         return AMOTION_EVENT_ACTION_POINTER_UP |
128                 (pointerId << AMOTION_EVENT_ACTION_POINTER_INDEX_SHIFT);
129     }
130 
131     return AMOTION_EVENT_ACTION_MOVE;
132 }
133 
createMotionEventStream(const std::vector<MotionEventEntry> & motions)134 static std::vector<MotionEvent> createMotionEventStream(
135         const std::vector<MotionEventEntry>& motions) {
136     if (motions.empty()) {
137         ADD_FAILURE() << "Need at least 1 sample to create a MotionEvent. Received empty vector.";
138     }
139 
140     std::vector<MotionEvent> events;
141     for (size_t i = 0; i < motions.size(); i++) {
142         const MotionEventEntry& entry = motions[i];
143         BitSet32 pointers = getValidPointers(entry.positions);
144         const uint32_t pointerCount = pointers.count();
145 
146         int32_t action;
147         if (i == 0) {
148             action = AMOTION_EVENT_ACTION_DOWN;
149             EXPECT_EQ(1U, pointerCount) << "First event should only have 1 pointer";
150         } else if (i == motions.size() - 1) {
151             EXPECT_EQ(1U, pointerCount) << "Last event should only have 1 pointer";
152             action = AMOTION_EVENT_ACTION_UP;
153         } else {
154             const MotionEventEntry& previousEntry = motions[i-1];
155             const MotionEventEntry& nextEntry = motions[i+1];
156             action = resolveAction(previousEntry.positions, entry.positions, nextEntry.positions);
157         }
158 
159         PointerCoords coords[pointerCount];
160         PointerProperties properties[pointerCount];
161         uint32_t pointerIndex = 0;
162         while(!pointers.isEmpty()) {
163             uint32_t pointerId = pointers.clearFirstMarkedBit();
164 
165             coords[pointerIndex].clear();
166             // We are treating column positions as pointerId
167             EXPECT_TRUE(entry.positions[pointerId].isValid()) <<
168                     "The entry at pointerId must be valid";
169             coords[pointerIndex].setAxisValue(AMOTION_EVENT_AXIS_X, entry.positions[pointerId].x);
170             coords[pointerIndex].setAxisValue(AMOTION_EVENT_AXIS_Y, entry.positions[pointerId].y);
171 
172             properties[pointerIndex].id = pointerId;
173             properties[pointerIndex].toolType = AMOTION_EVENT_TOOL_TYPE_FINGER;
174             pointerIndex++;
175         }
176         EXPECT_EQ(pointerIndex, pointerCount);
177 
178         MotionEvent event;
179         event.initialize(0 /*deviceId*/, AINPUT_SOURCE_TOUCHSCREEN, DISPLAY_ID,
180                 action, 0 /*actionButton*/, 0 /*flags*/,
181                 AMOTION_EVENT_EDGE_FLAG_NONE, AMETA_NONE, 0 /*buttonState*/,
182                 MotionClassification::NONE,
183                 0 /*xOffset*/, 0 /*yOffset*/, 0 /*xPrecision*/, 0 /*yPrecision*/,
184                 0 /*downTime*/, entry.eventTime.count(), pointerCount, properties, coords);
185 
186         events.emplace_back(event);
187     }
188 
189     return events;
190 }
191 
computeAndCheckVelocity(const char * strategy,const std::vector<MotionEventEntry> & motions,int32_t axis,float targetVelocity)192 static void computeAndCheckVelocity(const char* strategy,
193         const std::vector<MotionEventEntry>& motions, int32_t axis, float targetVelocity) {
194     VelocityTracker vt(strategy);
195     float Vx, Vy;
196 
197     std::vector<MotionEvent> events = createMotionEventStream(motions);
198     for (MotionEvent event : events) {
199         vt.addMovement(&event);
200     }
201 
202     vt.getVelocity(DEFAULT_POINTER_ID, &Vx, &Vy);
203 
204     switch (axis) {
205     case AMOTION_EVENT_AXIS_X:
206         checkVelocity(Vx, targetVelocity);
207         break;
208     case AMOTION_EVENT_AXIS_Y:
209         checkVelocity(Vy, targetVelocity);
210         break;
211     default:
212         FAIL() << "Axis must be either AMOTION_EVENT_AXIS_X or AMOTION_EVENT_AXIS_Y";
213     }
214 }
215 
computeAndCheckQuadraticEstimate(const std::vector<MotionEventEntry> & motions,const std::array<float,3> & coefficients)216 static void computeAndCheckQuadraticEstimate(const std::vector<MotionEventEntry>& motions,
217         const std::array<float, 3>& coefficients) {
218     VelocityTracker vt("lsq2");
219     std::vector<MotionEvent> events = createMotionEventStream(motions);
220     for (MotionEvent event : events) {
221         vt.addMovement(&event);
222     }
223     VelocityTracker::Estimator estimator;
224     EXPECT_TRUE(vt.getEstimator(0, &estimator));
225     for (size_t i = 0; i< coefficients.size(); i++) {
226         checkCoefficient(estimator.xCoeff[i], coefficients[i]);
227         checkCoefficient(estimator.yCoeff[i], coefficients[i]);
228     }
229 }
230 
231 /*
232  * ================== VelocityTracker tests generated manually =====================================
233  */
TEST_F(VelocityTrackerTest,ThreePointsPositiveVelocityTest)234 TEST_F(VelocityTrackerTest, ThreePointsPositiveVelocityTest) {
235     // Same coordinate is reported 2 times in a row
236     // It is difficult to determine the correct answer here, but at least the direction
237     // of the reported velocity should be positive.
238     std::vector<MotionEventEntry> motions = {
239         {0ms, {{ 273, NAN}}},
240         {12585us, {{293, NAN}}},
241         {14730us, {{293, NAN}}},
242         {14730us, {{293, NAN}}}, // ACTION_UP
243     };
244     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, 1600);
245 }
246 
TEST_F(VelocityTrackerTest,ThreePointsZeroVelocityTest)247 TEST_F(VelocityTrackerTest, ThreePointsZeroVelocityTest) {
248     // Same coordinate is reported 3 times in a row
249     std::vector<MotionEventEntry> motions = {
250         { 0ms, {{293, NAN}} },
251         { 6132us, {{293, NAN}} },
252         { 11283us, {{293, NAN}} },
253         { 11283us, {{293, NAN}} }, // ACTION_UP
254     };
255     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, 0);
256     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, 0);
257 }
258 
TEST_F(VelocityTrackerTest,ThreePointsLinearVelocityTest)259 TEST_F(VelocityTrackerTest, ThreePointsLinearVelocityTest) {
260     // Fixed velocity at 5 points per 10 milliseconds
261     std::vector<MotionEventEntry> motions = {
262         { 0ms, {{0, NAN}} },
263         { 10ms, {{5, NAN}} },
264         { 20ms, {{10, NAN}} },
265         { 20ms, {{10, NAN}} }, // ACTION_UP
266     };
267     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, 500);
268     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, 500);
269 }
270 
271 
272 /**
273  * ================== VelocityTracker tests generated by recording real events =====================
274  *
275  * To add a test, record the input coordinates and event times to all calls
276  * to void VelocityTracker::addMovement(const MotionEvent* event).
277  * Also record all calls to VelocityTracker::clear().
278  * Finally, record the output of VelocityTracker::getVelocity(...)
279  * This will give you the necessary data to create a new test.
280  *
281  * Another good way to generate this data is to use 'dumpsys input' just after the event has
282  * occurred.
283  */
284 
285 // --------------- Recorded by hand on swordfish ---------------------------------------------------
TEST_F(VelocityTrackerTest,SwordfishFlingDown)286 TEST_F(VelocityTrackerTest, SwordfishFlingDown) {
287     // Recording of a fling on Swordfish that could cause a fling in the wrong direction
288     std::vector<MotionEventEntry> motions = {
289         { 0ms, {{271, 96}} },
290         { 16071042ns, {{269.786346, 106.922775}} },
291         { 35648403ns, {{267.983063, 156.660034}} },
292         { 52313925ns, {{262.638397, 220.339081}} },
293         { 68976522ns, {{266.138824, 331.581116}} },
294         { 85639375ns, {{274.79245, 428.113159}} },
295         { 96948871ns, {{274.79245, 428.113159}} },
296         { 96948871ns, {{274.79245, 428.113159}} }, // ACTION_UP
297     };
298     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, 623.577637);
299     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 5970.7309);
300 }
301 
302 // --------------- Recorded by hand on sailfish, generated by a script -----------------------------
303 // For some of these tests, the X-direction velocity checking has been removed, because the lsq2
304 // and the impulse VelocityTrackerStrategies did not agree within 20%.
305 // Since the flings were recorded in the Y-direction, the intentional user action should only
306 // be relevant for the Y axis.
307 // There have been also cases where lsq2 and impulse disagreed more than 20% in the Y-direction.
308 // Those recordings have been discarded because we didn't feel one strategy's interpretation was
309 // more correct than another's but didn't want to increase the tolerance for the entire test suite.
310 //
311 // There are 18 tests total below: 9 in the positive Y direction and 9 in the opposite.
312 // The recordings were loosely binned into 3 categories - slow, faster, and fast, which roughly
313 // characterizes the velocity of the finger motion.
314 // These can be treated approximately as:
315 // slow - less than 1 page gets scrolled
316 // faster - more than 1 page gets scrolled, but less than 3
317 // fast - entire list is scrolled (fling is done as hard as possible)
318 
TEST_F(VelocityTrackerTest,SailfishFlingUpSlow1)319 TEST_F(VelocityTrackerTest, SailfishFlingUpSlow1) {
320     // Sailfish - fling up - slow - 1
321     std::vector<MotionEventEntry> motions = {
322         { 235089067457000ns, {{528.00, 983.00}} },
323         { 235089084684000ns, {{527.00, 981.00}} },
324         { 235089093349000ns, {{527.00, 977.00}} },
325         { 235089095677625ns, {{527.00, 975.93}} },
326         { 235089101859000ns, {{527.00, 970.00}} },
327         { 235089110378000ns, {{528.00, 960.00}} },
328         { 235089112497111ns, {{528.25, 957.51}} },
329         { 235089118760000ns, {{531.00, 946.00}} },
330         { 235089126686000ns, {{535.00, 931.00}} },
331         { 235089129316820ns, {{536.33, 926.02}} },
332         { 235089135199000ns, {{540.00, 914.00}} },
333         { 235089144297000ns, {{546.00, 896.00}} },
334         { 235089146136443ns, {{547.21, 892.36}} },
335         { 235089152923000ns, {{553.00, 877.00}} },
336         { 235089160784000ns, {{559.00, 851.00}} },
337         { 235089162955851ns, {{560.66, 843.82}} },
338         { 235089162955851ns, {{560.66, 843.82}} }, // ACTION_UP
339     };
340     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, 872.794617);
341     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, 951.698181);
342     computeAndCheckVelocity("impulse",motions, AMOTION_EVENT_AXIS_Y, -3604.819336);
343     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -3044.966064);
344 }
345 
346 
TEST_F(VelocityTrackerTest,SailfishFlingUpSlow2)347 TEST_F(VelocityTrackerTest, SailfishFlingUpSlow2) {
348     // Sailfish - fling up - slow - 2
349     std::vector<MotionEventEntry> motions = {
350         { 235110560704000ns, {{522.00, 1107.00}} },
351         { 235110575764000ns, {{522.00, 1107.00}} },
352         { 235110584385000ns, {{522.00, 1107.00}} },
353         { 235110588421179ns, {{521.52, 1106.52}} },
354         { 235110592830000ns, {{521.00, 1106.00}} },
355         { 235110601385000ns, {{520.00, 1104.00}} },
356         { 235110605088160ns, {{519.14, 1102.27}} },
357         { 235110609952000ns, {{518.00, 1100.00}} },
358         { 235110618353000ns, {{517.00, 1093.00}} },
359         { 235110621755146ns, {{516.60, 1090.17}} },
360         { 235110627010000ns, {{517.00, 1081.00}} },
361         { 235110634785000ns, {{518.00, 1063.00}} },
362         { 235110638422450ns, {{518.87, 1052.58}} },
363         { 235110643161000ns, {{520.00, 1039.00}} },
364         { 235110651767000ns, {{524.00, 1011.00}} },
365         { 235110655089581ns, {{525.54, 1000.19}} },
366         { 235110660368000ns, {{530.00, 980.00}} },
367         { 235110660368000ns, {{530.00, 980.00}} }, // ACTION_UP
368     };
369     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, -4096.583008);
370     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -3455.094238);
371 }
372 
373 
TEST_F(VelocityTrackerTest,SailfishFlingUpSlow3)374 TEST_F(VelocityTrackerTest, SailfishFlingUpSlow3) {
375     // Sailfish - fling up - slow - 3
376     std::vector<MotionEventEntry> motions = {
377         { 792536237000ns, {{580.00, 1317.00}} },
378         { 792541538987ns, {{580.63, 1311.94}} },
379         { 792544613000ns, {{581.00, 1309.00}} },
380         { 792552301000ns, {{583.00, 1295.00}} },
381         { 792558362309ns, {{585.13, 1282.92}} },
382         { 792560828000ns, {{586.00, 1278.00}} },
383         { 792569446000ns, {{589.00, 1256.00}} },
384         { 792575185095ns, {{591.54, 1241.41}} },
385         { 792578491000ns, {{593.00, 1233.00}} },
386         { 792587044000ns, {{597.00, 1211.00}} },
387         { 792592008172ns, {{600.28, 1195.92}} },
388         { 792594616000ns, {{602.00, 1188.00}} },
389         { 792603129000ns, {{607.00, 1167.00}} },
390         { 792608831290ns, {{609.48, 1155.83}} },
391         { 792612321000ns, {{611.00, 1149.00}} },
392         { 792620768000ns, {{615.00, 1131.00}} },
393         { 792625653873ns, {{617.32, 1121.73}} },
394         { 792629200000ns, {{619.00, 1115.00}} },
395         { 792629200000ns, {{619.00, 1115.00}} }, // ACTION_UP
396     };
397     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, 574.33429);
398     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, 617.40564);
399     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, -2361.982666);
400     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -2500.055664);
401 }
402 
403 
TEST_F(VelocityTrackerTest,SailfishFlingUpFaster1)404 TEST_F(VelocityTrackerTest, SailfishFlingUpFaster1) {
405     // Sailfish - fling up - faster - 1
406     std::vector<MotionEventEntry> motions = {
407         { 235160420675000ns, {{610.00, 1042.00}} },
408         { 235160428220000ns, {{609.00, 1026.00}} },
409         { 235160436544000ns, {{609.00, 1024.00}} },
410         { 235160441852394ns, {{609.64, 1020.82}} },
411         { 235160444878000ns, {{610.00, 1019.00}} },
412         { 235160452673000ns, {{613.00, 1006.00}} },
413         { 235160458519743ns, {{617.18, 992.06}} },
414         { 235160461061000ns, {{619.00, 986.00}} },
415         { 235160469798000ns, {{627.00, 960.00}} },
416         { 235160475186713ns, {{632.22, 943.02}} },
417         { 235160478051000ns, {{635.00, 934.00}} },
418         { 235160486489000ns, {{644.00, 906.00}} },
419         { 235160491853697ns, {{649.56, 890.56}} },
420         { 235160495177000ns, {{653.00, 881.00}} },
421         { 235160504148000ns, {{662.00, 858.00}} },
422         { 235160509231495ns, {{666.81, 845.37}} },
423         { 235160512603000ns, {{670.00, 837.00}} },
424         { 235160520366000ns, {{679.00, 814.00}} },
425         { 235160520366000ns, {{679.00, 814.00}} }, // ACTION_UP
426     };
427     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, 1274.141724);
428     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, 1438.53186);
429     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, -3001.4348);
430     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -3695.859619);
431 }
432 
433 
TEST_F(VelocityTrackerTest,SailfishFlingUpFaster2)434 TEST_F(VelocityTrackerTest, SailfishFlingUpFaster2) {
435     // Sailfish - fling up - faster - 2
436     std::vector<MotionEventEntry> motions = {
437         { 847153808000ns, {{576.00, 1264.00}} },
438         { 847171174000ns, {{576.00, 1262.00}} },
439         { 847179640000ns, {{576.00, 1257.00}} },
440         { 847185187540ns, {{577.41, 1249.22}} },
441         { 847187487000ns, {{578.00, 1246.00}} },
442         { 847195710000ns, {{581.00, 1227.00}} },
443         { 847202027059ns, {{583.93, 1209.40}} },
444         { 847204324000ns, {{585.00, 1203.00}} },
445         { 847212672000ns, {{590.00, 1176.00}} },
446         { 847218861395ns, {{594.36, 1157.11}} },
447         { 847221190000ns, {{596.00, 1150.00}} },
448         { 847230484000ns, {{602.00, 1124.00}} },
449         { 847235701400ns, {{607.56, 1103.83}} },
450         { 847237986000ns, {{610.00, 1095.00}} },
451         { 847237986000ns, {{610.00, 1095.00}} }, // ACTION_UP
452     };
453     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, -4280.07959);
454     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -4241.004395);
455 }
456 
457 
TEST_F(VelocityTrackerTest,SailfishFlingUpFaster3)458 TEST_F(VelocityTrackerTest, SailfishFlingUpFaster3) {
459     // Sailfish - fling up - faster - 3
460     std::vector<MotionEventEntry> motions = {
461         { 235200532789000ns, {{507.00, 1084.00}} },
462         { 235200549221000ns, {{507.00, 1083.00}} },
463         { 235200557841000ns, {{507.00, 1081.00}} },
464         { 235200558051189ns, {{507.00, 1080.95}} },
465         { 235200566314000ns, {{507.00, 1078.00}} },
466         { 235200574876586ns, {{508.97, 1070.12}} },
467         { 235200575006000ns, {{509.00, 1070.00}} },
468         { 235200582900000ns, {{514.00, 1054.00}} },
469         { 235200591276000ns, {{525.00, 1023.00}} },
470         { 235200591701829ns, {{525.56, 1021.42}} },
471         { 235200600064000ns, {{542.00, 976.00}} },
472         { 235200608519000ns, {{563.00, 911.00}} },
473         { 235200608527086ns, {{563.02, 910.94}} },
474         { 235200616933000ns, {{590.00, 844.00}} },
475         { 235200616933000ns, {{590.00, 844.00}} }, // ACTION_UP
476     };
477     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, -8715.686523);
478     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -7639.026367);
479 }
480 
481 
TEST_F(VelocityTrackerTest,SailfishFlingUpFast1)482 TEST_F(VelocityTrackerTest, SailfishFlingUpFast1) {
483     // Sailfish - fling up - fast - 1
484     std::vector<MotionEventEntry> motions = {
485         { 920922149000ns, {{561.00, 1412.00}} },
486         { 920930185000ns, {{559.00, 1377.00}} },
487         { 920930262463ns, {{558.98, 1376.66}} },
488         { 920938547000ns, {{559.00, 1371.00}} },
489         { 920947096857ns, {{562.91, 1342.68}} },
490         { 920947302000ns, {{563.00, 1342.00}} },
491         { 920955502000ns, {{577.00, 1272.00}} },
492         { 920963931021ns, {{596.87, 1190.54}} },
493         { 920963987000ns, {{597.00, 1190.00}} },
494         { 920972530000ns, {{631.00, 1093.00}} },
495         { 920980765511ns, {{671.31, 994.68}} },
496         { 920980906000ns, {{672.00, 993.00}} },
497         { 920989261000ns, {{715.00, 903.00}} },
498         { 920989261000ns, {{715.00, 903.00}} }, // ACTION_UP
499     };
500     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, 5670.329102);
501     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, 5991.866699);
502     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, -13021.101562);
503     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -15093.995117);
504 }
505 
506 
TEST_F(VelocityTrackerTest,SailfishFlingUpFast2)507 TEST_F(VelocityTrackerTest, SailfishFlingUpFast2) {
508     // Sailfish - fling up - fast - 2
509     std::vector<MotionEventEntry> motions = {
510         { 235247153233000ns, {{518.00, 1168.00}} },
511         { 235247170452000ns, {{517.00, 1167.00}} },
512         { 235247178908000ns, {{515.00, 1159.00}} },
513         { 235247179556213ns, {{514.85, 1158.39}} },
514         { 235247186821000ns, {{515.00, 1125.00}} },
515         { 235247195265000ns, {{521.00, 1051.00}} },
516         { 235247196389476ns, {{521.80, 1041.15}} },
517         { 235247203649000ns, {{538.00, 932.00}} },
518         { 235247212253000ns, {{571.00, 794.00}} },
519         { 235247213222491ns, {{574.72, 778.45}} },
520         { 235247220736000ns, {{620.00, 641.00}} },
521         { 235247220736000ns, {{620.00, 641.00}} }, // ACTION_UP
522     };
523     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, -20286.958984);
524     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -20494.587891);
525 }
526 
527 
TEST_F(VelocityTrackerTest,SailfishFlingUpFast3)528 TEST_F(VelocityTrackerTest, SailfishFlingUpFast3) {
529     // Sailfish - fling up - fast - 3
530     std::vector<MotionEventEntry> motions = {
531         { 235302568736000ns, {{529.00, 1167.00}} },
532         { 235302576644000ns, {{523.00, 1140.00}} },
533         { 235302579395063ns, {{520.91, 1130.61}} },
534         { 235302585140000ns, {{522.00, 1130.00}} },
535         { 235302593615000ns, {{527.00, 1065.00}} },
536         { 235302596207444ns, {{528.53, 1045.12}} },
537         { 235302602102000ns, {{559.00, 872.00}} },
538         { 235302610545000ns, {{652.00, 605.00}} },
539         { 235302613019881ns, {{679.26, 526.73}} },
540         { 235302613019881ns, {{679.26, 526.73}} }, // ACTION_UP
541     };
542     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, -39295.941406);
543     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -36461.421875);
544 }
545 
546 
TEST_F(VelocityTrackerTest,SailfishFlingDownSlow1)547 TEST_F(VelocityTrackerTest, SailfishFlingDownSlow1) {
548     // Sailfish - fling down - slow - 1
549     std::vector<MotionEventEntry> motions = {
550         { 235655749552755ns, {{582.00, 432.49}} },
551         { 235655750638000ns, {{582.00, 433.00}} },
552         { 235655758865000ns, {{582.00, 440.00}} },
553         { 235655766221523ns, {{581.16, 448.43}} },
554         { 235655767594000ns, {{581.00, 450.00}} },
555         { 235655776044000ns, {{580.00, 462.00}} },
556         { 235655782890696ns, {{579.18, 474.35}} },
557         { 235655784360000ns, {{579.00, 477.00}} },
558         { 235655792795000ns, {{578.00, 496.00}} },
559         { 235655799559531ns, {{576.27, 515.04}} },
560         { 235655800612000ns, {{576.00, 518.00}} },
561         { 235655809535000ns, {{574.00, 542.00}} },
562         { 235655816988015ns, {{572.17, 564.86}} },
563         { 235655817685000ns, {{572.00, 567.00}} },
564         { 235655825981000ns, {{569.00, 595.00}} },
565         { 235655833808653ns, {{566.26, 620.60}} },
566         { 235655834541000ns, {{566.00, 623.00}} },
567         { 235655842893000ns, {{563.00, 649.00}} },
568         { 235655842893000ns, {{563.00, 649.00}} }, // ACTION_UP
569     };
570     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, -419.749695);
571     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, -398.303894);
572     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 3309.016357);
573     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, 3969.099854);
574 }
575 
576 
TEST_F(VelocityTrackerTest,SailfishFlingDownSlow2)577 TEST_F(VelocityTrackerTest, SailfishFlingDownSlow2) {
578     // Sailfish - fling down - slow - 2
579     std::vector<MotionEventEntry> motions = {
580         { 235671152083370ns, {{485.24, 558.28}} },
581         { 235671154126000ns, {{485.00, 559.00}} },
582         { 235671162497000ns, {{484.00, 566.00}} },
583         { 235671168750511ns, {{483.27, 573.29}} },
584         { 235671171071000ns, {{483.00, 576.00}} },
585         { 235671179390000ns, {{482.00, 588.00}} },
586         { 235671185417210ns, {{481.31, 598.98}} },
587         { 235671188173000ns, {{481.00, 604.00}} },
588         { 235671196371000ns, {{480.00, 624.00}} },
589         { 235671202084196ns, {{479.27, 639.98}} },
590         { 235671204235000ns, {{479.00, 646.00}} },
591         { 235671212554000ns, {{478.00, 673.00}} },
592         { 235671219471011ns, {{476.39, 697.12}} },
593         { 235671221159000ns, {{476.00, 703.00}} },
594         { 235671229592000ns, {{474.00, 734.00}} },
595         { 235671236281462ns, {{472.43, 758.38}} },
596         { 235671238098000ns, {{472.00, 765.00}} },
597         { 235671246532000ns, {{470.00, 799.00}} },
598         { 235671246532000ns, {{470.00, 799.00}} }, // ACTION_UP
599     };
600     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, -262.80426);
601     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, -243.665344);
602     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 4215.682129);
603     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, 4587.986816);
604 }
605 
606 
TEST_F(VelocityTrackerTest,SailfishFlingDownSlow3)607 TEST_F(VelocityTrackerTest, SailfishFlingDownSlow3) {
608     // Sailfish - fling down - slow - 3
609     std::vector<MotionEventEntry> motions = {
610         { 170983201000ns, {{557.00, 533.00}} },
611         { 171000668000ns, {{556.00, 534.00}} },
612         { 171007359750ns, {{554.73, 535.27}} },
613         { 171011197000ns, {{554.00, 536.00}} },
614         { 171017660000ns, {{552.00, 540.00}} },
615         { 171024201831ns, {{549.97, 544.73}} },
616         { 171027333000ns, {{549.00, 547.00}} },
617         { 171034603000ns, {{545.00, 557.00}} },
618         { 171041043371ns, {{541.98, 567.55}} },
619         { 171043147000ns, {{541.00, 571.00}} },
620         { 171051052000ns, {{536.00, 586.00}} },
621         { 171051052000ns, {{536.00, 586.00}} }, // ACTION_UP
622     };
623     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, -723.413513);
624     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, -651.038452);
625     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 2091.502441);
626     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, 1934.517456);
627 }
628 
629 
TEST_F(VelocityTrackerTest,SailfishFlingDownFaster1)630 TEST_F(VelocityTrackerTest, SailfishFlingDownFaster1) {
631     // Sailfish - fling down - faster - 1
632     std::vector<MotionEventEntry> motions = {
633         { 235695280333000ns, {{558.00, 451.00}} },
634         { 235695283971237ns, {{558.43, 454.45}} },
635         { 235695289038000ns, {{559.00, 462.00}} },
636         { 235695297388000ns, {{561.00, 478.00}} },
637         { 235695300638465ns, {{561.83, 486.25}} },
638         { 235695305265000ns, {{563.00, 498.00}} },
639         { 235695313591000ns, {{564.00, 521.00}} },
640         { 235695317305492ns, {{564.43, 532.68}} },
641         { 235695322181000ns, {{565.00, 548.00}} },
642         { 235695330709000ns, {{565.00, 577.00}} },
643         { 235695333972227ns, {{565.00, 588.10}} },
644         { 235695339250000ns, {{565.00, 609.00}} },
645         { 235695347839000ns, {{565.00, 642.00}} },
646         { 235695351313257ns, {{565.00, 656.18}} },
647         { 235695356412000ns, {{565.00, 677.00}} },
648         { 235695364899000ns, {{563.00, 710.00}} },
649         { 235695368118682ns, {{562.24, 722.52}} },
650         { 235695373403000ns, {{564.00, 744.00}} },
651         { 235695373403000ns, {{564.00, 744.00}} }, // ACTION_UP
652     };
653     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 4254.639648);
654     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, 4698.415039);
655 }
656 
657 
TEST_F(VelocityTrackerTest,SailfishFlingDownFaster2)658 TEST_F(VelocityTrackerTest, SailfishFlingDownFaster2) {
659     // Sailfish - fling down - faster - 2
660     std::vector<MotionEventEntry> motions = {
661         { 235709624766000ns, {{535.00, 579.00}} },
662         { 235709642256000ns, {{534.00, 580.00}} },
663         { 235709643350278ns, {{533.94, 580.06}} },
664         { 235709650760000ns, {{532.00, 584.00}} },
665         { 235709658615000ns, {{530.00, 593.00}} },
666         { 235709660170495ns, {{529.60, 594.78}} },
667         { 235709667095000ns, {{527.00, 606.00}} },
668         { 235709675616000ns, {{524.00, 628.00}} },
669         { 235709676983261ns, {{523.52, 631.53}} },
670         { 235709684289000ns, {{521.00, 652.00}} },
671         { 235709692763000ns, {{518.00, 682.00}} },
672         { 235709693804993ns, {{517.63, 685.69}} },
673         { 235709701438000ns, {{515.00, 709.00}} },
674         { 235709709830000ns, {{512.00, 739.00}} },
675         { 235709710626776ns, {{511.72, 741.85}} },
676         { 235709710626776ns, {{511.72, 741.85}} }, // ACTION_UP
677     };
678     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, -430.440247);
679     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, -447.600311);
680     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 3953.859375);
681     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, 4316.155273);
682 }
683 
684 
TEST_F(VelocityTrackerTest,SailfishFlingDownFaster3)685 TEST_F(VelocityTrackerTest, SailfishFlingDownFaster3) {
686     // Sailfish - fling down - faster - 3
687     std::vector<MotionEventEntry> motions = {
688         { 235727628927000ns, {{540.00, 440.00}} },
689         { 235727636810000ns, {{537.00, 454.00}} },
690         { 235727646176000ns, {{536.00, 454.00}} },
691         { 235727653586628ns, {{535.12, 456.65}} },
692         { 235727654557000ns, {{535.00, 457.00}} },
693         { 235727663024000ns, {{534.00, 465.00}} },
694         { 235727670410103ns, {{533.04, 479.45}} },
695         { 235727670691000ns, {{533.00, 480.00}} },
696         { 235727679255000ns, {{531.00, 501.00}} },
697         { 235727687233704ns, {{529.09, 526.73}} },
698         { 235727687628000ns, {{529.00, 528.00}} },
699         { 235727696113000ns, {{526.00, 558.00}} },
700         { 235727704057546ns, {{523.18, 588.98}} },
701         { 235727704576000ns, {{523.00, 591.00}} },
702         { 235727713099000ns, {{520.00, 626.00}} },
703         { 235727720880776ns, {{516.33, 655.36}} },
704         { 235727721580000ns, {{516.00, 658.00}} },
705         { 235727721580000ns, {{516.00, 658.00}} }, // ACTION_UP
706     };
707     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 4484.617676);
708     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, 4927.92627);
709 }
710 
711 
TEST_F(VelocityTrackerTest,SailfishFlingDownFast1)712 TEST_F(VelocityTrackerTest, SailfishFlingDownFast1) {
713     // Sailfish - fling down - fast - 1
714     std::vector<MotionEventEntry> motions = {
715         { 235762352849000ns, {{467.00, 286.00}} },
716         { 235762360250000ns, {{443.00, 344.00}} },
717         { 235762362787412ns, {{434.77, 363.89}} },
718         { 235762368807000ns, {{438.00, 359.00}} },
719         { 235762377220000ns, {{425.00, 423.00}} },
720         { 235762379608561ns, {{421.31, 441.17}} },
721         { 235762385698000ns, {{412.00, 528.00}} },
722         { 235762394133000ns, {{406.00, 648.00}} },
723         { 235762396429369ns, {{404.37, 680.67}} },
724         { 235762396429369ns, {{404.37, 680.67}} }, //ACTION_UP
725     };
726     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 14227.0224);
727     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, 16064.685547);
728 }
729 
730 
TEST_F(VelocityTrackerTest,SailfishFlingDownFast2)731 TEST_F(VelocityTrackerTest, SailfishFlingDownFast2) {
732     // Sailfish - fling down - fast - 2
733     std::vector<MotionEventEntry> motions = {
734         { 235772487188000ns, {{576.00, 204.00}} },
735         { 235772495159000ns, {{553.00, 236.00}} },
736         { 235772503568000ns, {{551.00, 240.00}} },
737         { 235772508192247ns, {{545.55, 254.17}} },
738         { 235772512051000ns, {{541.00, 266.00}} },
739         { 235772520794000ns, {{520.00, 337.00}} },
740         { 235772525015263ns, {{508.92, 394.43}} },
741         { 235772529174000ns, {{498.00, 451.00}} },
742         { 235772537635000ns, {{484.00, 589.00}} },
743         { 235772537635000ns, {{484.00, 589.00}} }, // ACTION_UP
744     };
745     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 18660.048828);
746     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, 16918.439453);
747 }
748 
749 
TEST_F(VelocityTrackerTest,SailfishFlingDownFast3)750 TEST_F(VelocityTrackerTest, SailfishFlingDownFast3) {
751     // Sailfish - fling down - fast - 3
752     std::vector<MotionEventEntry> motions = {
753         { 507650295000ns, {{628.00, 233.00}} },
754         { 507658234000ns, {{605.00, 269.00}} },
755         { 507666784000ns, {{601.00, 274.00}} },
756         { 507669660483ns, {{599.65, 275.68}} },
757         { 507675427000ns, {{582.00, 308.00}} },
758         { 507683740000ns, {{541.00, 404.00}} },
759         { 507686506238ns, {{527.36, 435.95}} },
760         { 507692220000ns, {{487.00, 581.00}} },
761         { 507700707000ns, {{454.00, 792.00}} },
762         { 507703352649ns, {{443.71, 857.77}} },
763         { 507703352649ns, {{443.71, 857.77}} }, // ACTION_UP
764     };
765     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, -4111.8173);
766     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, -6388.48877);
767     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 29765.908203);
768     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, 28354.796875);
769 }
770 
771 /**
772  * ================== Multiple pointers ============================================================
773  *
774  * Three fingers quickly tap the screen. Since this is a tap, the velocities should be zero.
775  * If the events with POINTER_UP or POINTER_DOWN are not handled correctly (these should not be
776  * part of the fitted data), this can cause large velocity values to be reported instead.
777  */
TEST_F(VelocityTrackerTest,LeastSquaresVelocityTrackerStrategyEstimator_ThreeFingerTap)778 TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_ThreeFingerTap) {
779     std::vector<MotionEventEntry> motions = {
780         { 0us,      {{1063, 1128}, {NAN, NAN}, {NAN, NAN}} },
781         { 10800us,  {{1063, 1128}, {682, 1318}, {NAN, NAN}} }, // POINTER_DOWN
782         { 10800us,  {{1063, 1128}, {682, 1318}, {397, 1747}} }, // POINTER_DOWN
783         { 267300us, {{1063, 1128}, {682, 1318}, {397, 1747}} }, // POINTER_UP
784         { 267300us, {{1063, 1128}, {NAN, NAN}, {397, 1747}} }, // POINTER_UP
785         { 272700us, {{1063, 1128}, {NAN, NAN}, {NAN, NAN}} },
786     };
787 
788     // Velocity should actually be zero, but we expect 0.016 here instead.
789     // This is close enough to zero, and is likely caused by division by a very small number.
790     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_X, -0.016);
791     computeAndCheckVelocity("lsq2", motions, AMOTION_EVENT_AXIS_Y, -0.016);
792     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_X, 0);
793     computeAndCheckVelocity("impulse", motions, AMOTION_EVENT_AXIS_Y, 0);
794 }
795 
796 /**
797  * ================== Tests for least squares fitting ==============================================
798  *
799  * Special care must be taken when constructing tests for LeastSquaresVelocityTrackerStrategy
800  * getEstimator function. In particular:
801  * - inside the function, time gets converted from nanoseconds to seconds
802  *   before being used in the fit.
803  * - any values that are older than 100 ms are being discarded.
804  * - the newest time gets subtracted from all of the other times before being used in the fit.
805  * So these tests have to be designed with those limitations in mind.
806  *
807  * General approach for the tests below:
808  * We only used timestamps in milliseconds, 0 ms, 1 ms, and 2 ms, to be sure that
809  * we are well within the HORIZON range.
810  * When specifying the expected values of the coefficients, we treat the x values as if
811  * they were in ms. Then, to adjust for the time units, the coefficients get progressively
812  * multiplied by powers of 1E3.
813  * For example:
814  * data: t(ms), x
815  *        1 ms, 1
816  *        2 ms, 4
817  *        3 ms, 9
818  * The coefficients are (0, 0, 1).
819  * In the test, we would convert these coefficients to (0*(1E3)^0, 0*(1E3)^1, 1*(1E3)^2).
820  */
TEST_F(VelocityTrackerTest,LeastSquaresVelocityTrackerStrategyEstimator_Constant)821 TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Constant) {
822     std::vector<MotionEventEntry> motions = {
823         { 0ms, {{1, 1}} }, // 0 s
824         { 1ms, {{1, 1}} }, // 0.001 s
825         { 2ms, {{1, 1}} }, // 0.002 s
826         { 2ms, {{1, 1}} }, // ACTION_UP
827     };
828     // The data used for the fit will be as follows:
829     // time(s), position
830     // -0.002, 1
831     // -0.001, 1
832     // -0.ms, 1
833     computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({1, 0, 0}));
834 }
835 
836 /*
837  * Straight line y = x :: the constant and quadratic coefficients are zero.
838  */
TEST_F(VelocityTrackerTest,LeastSquaresVelocityTrackerStrategyEstimator_Linear)839 TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Linear) {
840     std::vector<MotionEventEntry> motions = {
841         { 0ms, {{-2, -2}} },
842         { 1ms, {{-1, -1}} },
843         { 2ms, {{-0, -0}} },
844         { 2ms, {{-0, -0}} }, // ACTION_UP
845     };
846     // The data used for the fit will be as follows:
847     // time(s), position
848     // -0.002, -2
849     // -0.001, -1
850     // -0.000,  0
851     computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({0, 1E3, 0}));
852 }
853 
854 /*
855  * Parabola
856  */
TEST_F(VelocityTrackerTest,LeastSquaresVelocityTrackerStrategyEstimator_Parabolic)857 TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Parabolic) {
858     std::vector<MotionEventEntry> motions = {
859         { 0ms, {{1, 1}} },
860         { 1ms, {{4, 4}} },
861         { 2ms, {{8, 8}} },
862         { 2ms, {{8, 8}} }, // ACTION_UP
863     };
864     // The data used for the fit will be as follows:
865     // time(s), position
866     // -0.002, 1
867     // -0.001, 4
868     // -0.000, 8
869     computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({8, 4.5E3, 0.5E6}));
870 }
871 
872 /*
873  * Parabola
874  */
TEST_F(VelocityTrackerTest,LeastSquaresVelocityTrackerStrategyEstimator_Parabolic2)875 TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Parabolic2) {
876     std::vector<MotionEventEntry> motions = {
877         { 0ms, {{1, 1}} },
878         { 1ms, {{4, 4}} },
879         { 2ms, {{9, 9}} },
880         { 2ms, {{9, 9}} }, // ACTION_UP
881     };
882     // The data used for the fit will be as follows:
883     // time(s), position
884     // -0.002, 1
885     // -0.001, 4
886     // -0.000, 9
887     computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({9, 6E3, 1E6}));
888 }
889 
890 /*
891  * Parabola :: y = x^2 :: the constant and linear coefficients are zero.
892  */
TEST_F(VelocityTrackerTest,LeastSquaresVelocityTrackerStrategyEstimator_Parabolic3)893 TEST_F(VelocityTrackerTest, LeastSquaresVelocityTrackerStrategyEstimator_Parabolic3) {
894     std::vector<MotionEventEntry> motions = {
895         { 0ms, {{4, 4}} },
896         { 1ms, {{1, 1}} },
897         { 2ms, {{0, 0}} },
898         { 2ms, {{0, 0}} }, // ACTION_UP
899     };
900     // The data used for the fit will be as follows:
901     // time(s), position
902     // -0.002, 4
903     // -0.001, 1
904     // -0.000, 0
905     computeAndCheckQuadraticEstimate(motions, std::array<float, 3>({0, 0E3, 1E6}));
906 }
907 
908 } // namespace android
909