gt:         boolean springback(int start, int min, int max) {
context: /*
   * Copyright (C) 2010 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.
   */
  
  package android.widget;
  
  import android.content.Context;
  import android.hardware.SensorManager;
  import android.util.Log;
  import android.view.ViewConfiguration;
  import android.view.animation.AnimationUtils;
  import android.view.animation.Interpolator;
  
  /**
   * This class encapsulates scrolling with the ability to overshoot the bounds
   * of a scrolling operation. This class is a drop-in replacement for
   * {@link android.widget.Scroller} in most cases.
   */
  public class OverScroller {
      private int mMode;
  
      private final SplineOverScroller mScrollerX;
      private final SplineOverScroller mScrollerY;
  
      private Interpolator mInterpolator;
  
      private final boolean mFlywheel;
  
      private static final int DEFAULT_DURATION = 250;
      private static final int SCROLL_MODE = 0;
      private static final int FLING_MODE = 1;
  
      /**
       * Creates an OverScroller with a viscous fluid scroll interpolator and flywheel.
       * @param context
       */
      public OverScroller(Context context) {
          this(context, null);
      }
  
      /**
       * Creates an OverScroller with flywheel enabled.
       * @param context The context of this application.
       * @param interpolator The scroll interpolator. If null, a default (viscous) interpolator will
       * be used.
       */
      public OverScroller(Context context, Interpolator interpolator) {
          this(context, interpolator, true);
      }
  
      /**
       * Creates an OverScroller.
       * @param context The context of this application.
       * @param interpolator The scroll interpolator. If null, a default (viscous) interpolator will
       * be used.
       * @param flywheel If true, successive fling motions will keep on increasing scroll speed.
       * @hide
       */
      public OverScroller(Context context, Interpolator interpolator, boolean flywheel) {
          if (interpolator == null) {
              mInterpolator = new Scroller.ViscousFluidInterpolator();
          } else {
              mInterpolator = interpolator;
          }
          mFlywheel = flywheel;
          mScrollerX = new SplineOverScroller(context);
          mScrollerY = new SplineOverScroller(context);
      }
  
      /**
       * Creates an OverScroller with flywheel enabled.
       * @param context The context of this application.
       * @param interpolator The scroll interpolator. If null, a default (viscous) interpolator will
       * be used.
       * @param bounceCoefficientX A value between 0 and 1 that will determine the proportion of the
       * velocity which is preserved in the bounce when the horizontal edge is reached. A null value
       * means no bounce. This behavior is no longer supported and this coefficient has no effect.
       * @param bounceCoefficientY Same as bounceCoefficientX but for the vertical direction. This
       * behavior is no longer supported and this coefficient has no effect.
       * !deprecated Use {!link #OverScroller(Context, Interpolator, boolean)} instead.
       */
      public OverScroller(Context context, Interpolator interpolator,
              float bounceCoefficientX, float bounceCoefficientY) {
          this(context, interpolator, true);
      }
  
      /**
       * Creates an OverScroller.
       * @param context The context of this application.
       * @param interpolator The scroll interpolator. If null, a default (viscous) interpolator will
       * be used.
       * @param bounceCoefficientX A value between 0 and 1 that will determine the proportion of the
       * velocity which is preserved in the bounce when the horizontal edge is reached. A null value
       * means no bounce. This behavior is no longer supported and this coefficient has no effect.
       * @param bounceCoefficientY Same as bounceCoefficientX but for the vertical direction. This
       * behavior is no longer supported and this coefficient has no effect.
       * @param flywheel If true, successive fling motions will keep on increasing scroll speed.
       * !deprecated Use {!link OverScroller(Context, Interpolator, boolean)} instead.
       */
      public OverScroller(Context context, Interpolator interpolator,
              float bounceCoefficientX, float bounceCoefficientY, boolean flywheel) {
          this(context, interpolator, flywheel);
      }
  
      void setInterpolator(Interpolator interpolator) {
          if (interpolator == null) {
              mInterpolator = new Scroller.ViscousFluidInterpolator();
          } else {
              mInterpolator = interpolator;
          }
      }
  
      /**
       * The amount of friction applied to flings. The default value
       * is {@link ViewConfiguration#getScrollFriction}.
       *
       * @param friction A scalar dimension-less value representing the coefficient of
       *         friction.
       */
      public final void setFriction(float friction) {
          mScrollerX.setFriction(friction);
          mScrollerY.setFriction(friction);
      }
  
      /**
       *
       * Returns whether the scroller has finished scrolling.
       *
       * @return True if the scroller has finished scrolling, false otherwise.
       */
      public final boolean isFinished() {
          return mScrollerX.mFinished && mScrollerY.mFinished;
      }
  
      /**
       * Force the finished field to a particular value. Contrary to
       * {@link #abortAnimation()}, forcing the animation to finished
       * does NOT cause the scroller to move to the final x and y
       * position.
       *
       * @param finished The new finished value.
       */
      public final void forceFinished(boolean finished) {
          mScrollerX.mFinished = mScrollerY.mFinished = finished;
      }
  
      /**
       * Returns the current X offset in the scroll.
       *
       * @return The new X offset as an absolute distance from the origin.
       */
      public final int getCurrX() {
          return mScrollerX.mCurrentPosition;
      }
  
      /**
       * Returns the current Y offset in the scroll.
       *
       * @return The new Y offset as an absolute distance from the origin.
       */
      public final int getCurrY() {
          return mScrollerY.mCurrentPosition;
      }
  
      /**
       * Returns the absolute value of the current velocity.
       *
       * @return The original velocity less the deceleration, norm of the X and Y velocity vector.
       */
      public float getCurrVelocity() {
          return (float) Math.hypot(mScrollerX.mCurrVelocity, mScrollerY.mCurrVelocity);
      }
  
      /**
       * Returns the start X offset in the scroll.
       *
       * @return The start X offset as an absolute distance from the origin.
       */
      public final int getStartX() {
          return mScrollerX.mStart;
      }
  
      /**
       * Returns the start Y offset in the scroll.
       *
       * @return The start Y offset as an absolute distance from the origin.
       */
      public final int getStartY() {
          return mScrollerY.mStart;
      }
  
      /**
       * Returns where the scroll will end. Valid only for "fling" scrolls.
       *
       * @return The final X offset as an absolute distance from the origin.
       */
      public final int getFinalX() {
          return mScrollerX.mFinal;
      }
  
      /**
       * Returns where the scroll will end. Valid only for "fling" scrolls.
       *
       * @return The final Y offset as an absolute distance from the origin.
       */
      public final int getFinalY() {
          return mScrollerY.mFinal;
      }
  
      /**
       * Returns how long the scroll event will take, in milliseconds.
       *
       * @return The duration of the scroll in milliseconds.
       *
       * @hide Pending removal once nothing depends on it
       * @deprecated OverScrollers don't necessarily have a fixed duration.
       *             This function will lie to the best of its ability.
       */
      @Deprecated
      public final int getDuration() {
          return Math.max(mScrollerX.mDuration, mScrollerY.mDuration);
      }
  
      /**
       * Extend the scroll animation. This allows a running animation to scroll
       * further and longer, when used with {@link #setFinalX(int)} or {@link #setFinalY(int)}.
       *
       * @param extend Additional time to scroll in milliseconds.
       * @see #setFinalX(int)
       * @see #setFinalY(int)
       *
       * @hide Pending removal once nothing depends on it
       * @deprecated OverScrollers don't necessarily have a fixed duration.
       *             Instead of setting a new final position and extending
       *             the duration of an existing scroll, use startScroll
       *             to begin a new animation.
       */
      @Deprecated
      public void extendDuration(int extend) {
          mScrollerX.extendDuration(extend);
          mScrollerY.extendDuration(extend);
      }
  
      /**
       * Sets the final position (X) for this scroller.
       *
       * @param newX The new X offset as an absolute distance from the origin.
       * @see #extendDuration(int)
       * @see #setFinalY(int)
       *
       * @hide Pending removal once nothing depends on it
       * @deprecated OverScroller's final position may change during an animation.
       *             Instead of setting a new final position and extending
       *             the duration of an existing scroll, use startScroll
       *             to begin a new animation.
       */
      @Deprecated
      public void setFinalX(int newX) {
          mScrollerX.setFinalPosition(newX);
      }
  
      /**
       * Sets the final position (Y) for this scroller.
       *
       * @param newY The new Y offset as an absolute distance from the origin.
       * @see #extendDuration(int)
       * @see #setFinalX(int)
       *
       * @hide Pending removal once nothing depends on it
       * @deprecated OverScroller's final position may change during an animation.
       *             Instead of setting a new final position and extending
       *             the duration of an existing scroll, use startScroll
       *             to begin a new animation.
       */
      @Deprecated
      public void setFinalY(int newY) {
          mScrollerY.setFinalPosition(newY);
      }
  
      /**
       * Call this when you want to know the new location. If it returns true, the
       * animation is not yet finished.
       */
      public boolean computeScrollOffset() {
          if (isFinished()) {
              return false;
          }
  
          switch (mMode) {
              case SCROLL_MODE:
                  long time = AnimationUtils.currentAnimationTimeMillis();
                  // Any scroller can be used for time, since they were started
                  // together in scroll mode. We use X here.
                  final long elapsedTime = time - mScrollerX.mStartTime;
  
                  final int duration = mScrollerX.mDuration;
                  if (elapsedTime < duration) {
                      final float q = mInterpolator.getInterpolation(elapsedTime / (float) duration);
                      mScrollerX.updateScroll(q);
                      mScrollerY.updateScroll(q);
                  } else {
                      abortAnimation();
                  }
                  break;
  
              case FLING_MODE:
                  if (!mScrollerX.mFinished) {
                      if (!mScrollerX.update()) {
                          if (!mScrollerX.continueWhenFinished()) {
                              mScrollerX.finish();
                          }
                      }
                  }
  
                  if (!mScrollerY.mFinished) {
                      if (!mScrollerY.update()) {
                          if (!mScrollerY.continueWhenFinished()) {
                              mScrollerY.finish();
                          }
                      }
                  }
  
                  break;
          }
  
          return true;
      }
  
      /**
       * Start scrolling by providing a starting point and the distance to travel.
       * The scroll will use the default value of 250 milliseconds for the
       * duration.
       *
       * @param startX Starting horizontal scroll offset in pixels. Positive
       *        numbers will scroll the content to the left.
       * @param startY Starting vertical scroll offset in pixels. Positive numbers
       *        will scroll the content up.
       * @param dx Horizontal distance to travel. Positive numbers will scroll the
       *        content to the left.
       * @param dy Vertical distance to travel. Positive numbers will scroll the
       *        content up.
       */
      public void startScroll(int startX, int startY, int dx, int dy) {
          startScroll(startX, startY, dx, dy, DEFAULT_DURATION);
      }
  
      /**
       * Start scrolling by providing a starting point and the distance to travel.
       *
       * @param startX Starting horizontal scroll offset in pixels. Positive
       *        numbers will scroll the content to the left.
       * @param startY Starting vertical scroll offset in pixels. Positive numbers
       *        will scroll the content up.
       * @param dx Horizontal distance to travel. Positive numbers will scroll the
       *        content to the left.
       * @param dy Vertical distance to travel. Positive numbers will scroll the
       *        content up.
       * @param duration Duration of the scroll in milliseconds.
       */
      public void startScroll(int startX, int startY, int dx, int dy, int duration) {
          mMode = SCROLL_MODE;
          mScrollerX.startScroll(startX, dx, duration);
          mScrollerY.startScroll(startY, dy, duration);
      }
  
      /**
       * Call this when you want to 'spring back' into a valid coordinate range.
       *
       * @param startX Starting X coordinate
       * @param startY Starting Y coordinate
       * @param minX Minimum valid X value
       * @param maxX Maximum valid X value
       * @param minY Minimum valid Y value
       * @param maxY Minimum valid Y value
       * @return true if a springback was initiated, false if startX and startY were
       *          already within the valid range.
       */
      public boolean springBack(int startX, int startY, int minX, int maxX, int minY, int maxY) {
          mMode = FLING_MODE;
  
          // Make sure both methods are called.
          final boolean spingbackX = mScrollerX.springback(startX, minX, maxX);
          final boolean spingbackY = mScrollerY.springback(startY, minY, maxY);
          return spingbackX || spingbackY;
      }
  
      public void fling(int startX, int startY, int velocityX, int velocityY,
              int minX, int maxX, int minY, int maxY) {
          fling(startX, startY, velocityX, velocityY, minX, maxX, minY, maxY, 0, 0);
      }
  
      /**
       * Start scrolling based on a fling gesture. The distance traveled will
       * depend on the initial velocity of the fling.
       *
       * @param startX Starting point of the scroll (X)
       * @param startY Starting point of the scroll (Y)
       * @param velocityX Initial velocity of the fling (X) measured in pixels per
       *            second.
       * @param velocityY Initial velocity of the fling (Y) measured in pixels per
       *            second
       * @param minX Minimum X value. The scroller will not scroll past this point
       *            unless overX > 0. If overfling is allowed, it will use minX as
       *            a springback boundary.
       * @param maxX Maximum X value. The scroller will not scroll past this point
       *            unless overX > 0. If overfling is allowed, it will use maxX as
       *            a springback boundary.
       * @param minY Minimum Y value. The scroller will not scroll past this point
       *            unless overY > 0. If overfling is allowed, it will use minY as
       *            a springback boundary.
       * @param maxY Maximum Y value. The scroller will not scroll past this point
       *            unless overY > 0. If overfling is allowed, it will use maxY as
       *            a springback boundary.
       * @param overX Overfling range. If > 0, horizontal overfling in either
       *            direction will be possible.
       * @param overY Overfling range. If > 0, vertical overfling in either
       *            direction will be possible.
       */
      public void fling(int startX, int startY, int velocityX, int velocityY,
              int minX, int maxX, int minY, int maxY, int overX, int overY) {
          // Continue a scroll or fling in progress
          if (mFlywheel && !isFinished()) {
              float oldVelocityX = mScrollerX.mCurrVelocity;
              float oldVelocityY = mScrollerY.mCurrVelocity;
              if (Math.signum(velocityX) == Math.signum(oldVelocityX) &&
                      Math.signum(velocityY) == Math.signum(oldVelocityY)) {
                  velocityX += oldVelocityX;
                  velocityY += oldVelocityY;
              }
          }
  
          mMode = FLING_MODE;
          mScrollerX.fling(startX, velocityX, minX, maxX, overX);
          mScrollerY.fling(startY, velocityY, minY, maxY, overY);
      }
  
      /**
       * Notify the scroller that we've reached a horizontal boundary.
       * Normally the information to handle this will already be known
       * when the animation is started, such as in a call to one of the
       * fling functions. However there are cases where this cannot be known
       * in advance. This function will transition the current motion and
       * animate from startX to finalX as appropriate.
       *
       * @param startX Starting/current X position
       * @param finalX Desired final X position
       * @param overX Magnitude of overscroll allowed. This should be the maximum
       *              desired distance from finalX. Absolute value - must be positive.
       */
      public void notifyHorizontalEdgeReached(int startX, int finalX, int overX) {
          mScrollerX.notifyEdgeReached(startX, finalX, overX);
      }
  
      /**
       * Notify the scroller that we've reached a vertical boundary.
       * Normally the information to handle this will already be known
       * when the animation is started, such as in a call to one of the
       * fling functions. However there are cases where this cannot be known
       * in advance. This function will animate a parabolic motion from
       * startY to finalY.
       *
       * @param startY Starting/current Y position
       * @param finalY Desired final Y position
       * @param overY Magnitude of overscroll allowed. This should be the maximum
       *              desired distance from finalY. Absolute value - must be positive.
       */
      public void notifyVerticalEdgeReached(int startY, int finalY, int overY) {
          mScrollerY.notifyEdgeReached(startY, finalY, overY);
      }
  
      /**
       * Returns whether the current Scroller is currently returning to a valid position.
       * Valid bounds were provided by the
       * {@link #fling(int, int, int, int, int, int, int, int, int, int)} method.
       *
       * One should check this value before calling
       * {@link #startScroll(int, int, int, int)} as the interpolation currently in progress
       * to restore a valid position will then be stopped. The caller has to take into account
       * the fact that the started scroll will start from an overscrolled position.
       *
       * @return true when the current position is overscrolled and in the process of
       *         interpolating back to a valid value.
       */
      public boolean isOverScrolled() {
          return ((!mScrollerX.mFinished &&
                  mScrollerX.mState != SplineOverScroller.SPLINE) ||
                  (!mScrollerY.mFinished &&
                          mScrollerY.mState != SplineOverScroller.SPLINE));
      }
  
      /**
       * Stops the animation. Contrary to {@link #forceFinished(boolean)},
       * aborting the animating causes the scroller to move to the final x and y
       * positions.
       *
       * @see #forceFinished(boolean)
       */
      public void abortAnimation() {
          mScrollerX.finish();
          mScrollerY.finish();
      }
  
      /**
       * Returns the time elapsed since the beginning of the scrolling.
       *
       * @return The elapsed time in milliseconds.
       *
       * @hide
       */
      public int timePassed() {
          final long time = AnimationUtils.currentAnimationTimeMillis();
          final long startTime = Math.min(mScrollerX.mStartTime, mScrollerY.mStartTime);
          return (int) (time - startTime);
      }
  
      /**
       * @hide
       */
      public boolean isScrollingInDirection(float xvel, float yvel) {
          final int dx = mScrollerX.mFinal - mScrollerX.mStart;
          final int dy = mScrollerY.mFinal - mScrollerY.mStart;
          return !isFinished() && Math.signum(xvel) == Math.signum(dx) &&
                  Math.signum(yvel) == Math.signum(dy);
      }
  
      static class SplineOverScroller {
          // Initial position
          private int mStart;
  
          // Current position
          private int mCurrentPosition;
  
          // Final position
          private int mFinal;
  
          // Initial velocity
          private int mVelocity;
  
          // Current velocity
          private float mCurrVelocity;
  
          // Constant current deceleration
          private float mDeceleration;
  
          // Animation starting time, in system milliseconds
          private long mStartTime;
  
          // Animation duration, in milliseconds
          private int mDuration;
  
          // Duration to complete spline component of animation
          private int mSplineDuration;
  
          // Distance to travel along spline animation
          private int mSplineDistance;
  
          // Whether the animation is currently in progress
          private boolean mFinished;
  
          // The allowed overshot distance before boundary is reached.
          private int mOver;
  
          // Fling friction
          private float mFlingFriction = ViewConfiguration.getScrollFriction();
  
          // Current state of the animation.
          private int mState = SPLINE;
  
          // Constant gravity value, used in the deceleration phase.
          private static final float GRAVITY = 2000.0f;
  
          // A context-specific coefficient adjusted to physical values.
          private float mPhysicalCoeff;
  
          private static float DECELERATION_RATE = (float) (Math.log(0.78) / Math.log(0.9));
          private static final float INFLEXION = 0.35f; // Tension lines cross at (INFLEXION, 1)
          private static final float START_TENSION = 0.5f;
          private static final float END_TENSION = 1.0f;
          private static final float P1 = START_TENSION * INFLEXION;
          private static final float P2 = 1.0f - END_TENSION * (1.0f - INFLEXION);
  
          private static final int NB_SAMPLES = 100;
          private static final float[] SPLINE_POSITION = new float[NB_SAMPLES + 1];
          private static final float[] SPLINE_TIME = new float[NB_SAMPLES + 1];
  
          private static final int SPLINE = 0;
          private static final int CUBIC = 1;
          private static final int BALLISTIC = 2;
  
          static {
              float x_min = 0.0f;
              float y_min = 0.0f;
              for (int i = 0; i < NB_SAMPLES; i++) {
                  final float alpha = (float) i / NB_SAMPLES;
  
                  float x_max = 1.0f;
                  float x, tx, coef;
                  while (true) {
                      x = x_min + (x_max - x_min) / 2.0f;
                      coef = 3.0f * x * (1.0f - x);
                      tx = coef * ((1.0f - x) * P1 + x * P2) + x * x * x;
                      if (Math.abs(tx - alpha) < 1E-5) break;
                      if (tx > alpha) x_max = x;
                      else x_min = x;
                  }
                  SPLINE_POSITION[i] = coef * ((1.0f - x) * START_TENSION + x) + x * x * x;
  
                  float y_max = 1.0f;
                  float y, dy;
                  while (true) {
                      y = y_min + (y_max - y_min) / 2.0f;
                      coef = 3.0f * y * (1.0f - y);
                      dy = coef * ((1.0f - y) * START_TENSION + y) + y * y * y;
                      if (Math.abs(dy - alpha) < 1E-5) break;
                      if (dy > alpha) y_max = y;
                      else y_min = y;
                  }
                  SPLINE_TIME[i] = coef * ((1.0f - y) * P1 + y * P2) + y * y * y;
              }
              SPLINE_POSITION[NB_SAMPLES] = SPLINE_TIME[NB_SAMPLES] = 1.0f;
          }
  
          void setFriction(float friction) {
              mFlingFriction = friction;
          }
  
          SplineOverScroller(Context context) {
              mFinished = true;
              final float ppi = context.getResources().getDisplayMetrics().density * 160.0f;
              mPhysicalCoeff = SensorManager.GRAVITY_EARTH // g (m/s^2)
                      * 39.37f // inch/meter
                      * ppi
                      * 0.84f; // look and feel tuning
          }
  
          void updateScroll(float q) {
              mCurrentPosition = mStart + Math.round(q * (mFinal - mStart));
          }
  
          /*
           * Get a signed deceleration that will reduce the velocity.
           */
          static private float getDeceleration(int velocity) {
              return velocity > 0 ? -GRAVITY : GRAVITY;
          }
  
          /*
           * Modifies mDuration to the duration it takes to get from start to newFinal using the
           * spline interpolation. The previous duration was needed to get to oldFinal.
           */
          private void adjustDuration(int start, int oldFinal, int newFinal) {
              final int oldDistance = oldFinal - start;
              final int newDistance = newFinal - start;
              final float x = Math.abs((float) newDistance / oldDistance);
              final int index = (int) (NB_SAMPLES * x);
              if (index < NB_SAMPLES) {
                  final float x_inf = (float) index / NB_SAMPLES;
                  final float x_sup = (float) (index + 1) / NB_SAMPLES;
                  final float t_inf = SPLINE_TIME[index];
                  final float t_sup = SPLINE_TIME[index + 1];
                  final float timeCoef = t_inf + (x - x_inf) / (x_sup - x_inf) * (t_sup - t_inf);
                  mDuration *= timeCoef;
              }
          }
  
          void startScroll(int start, int distance, int duration) {
              mFinished = false;
  
              mCurrentPosition = mStart = start;
              mFinal = start + distance;
  
              mStartTime = AnimationUtils.currentAnimationTimeMillis();
              mDuration = duration;
  
              // Unused
              mDeceleration = 0.0f;
              mVelocity = 0;
          }
  
          void finish() {
              mCurrentPosition = mFinal;
              // Not reset since WebView relies on this value for fast fling.
              // TODO: restore when WebView uses the fast fling implemented in this class.
              // mCurrVelocity = 0.0f;
              mFinished = true;
          }
  
          void setFinalPosition(int position) {
              mFinal = position;
              mFinished = false;
          }
  
          void extendDuration(int extend) {
              final long time = AnimationUtils.currentAnimationTimeMillis();
              final int elapsedTime = (int) (time - mStartTime);
              mDuration = elapsedTime + extend;
              mFinished = false;
          }
  
  