dynamic-animation/src/android/support/animation/SpringForce.java - platform/frameworks/support - Git at Google

 /*
  * 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.
  */

 package android.support.animation;

 import android.support.annotation.FloatRange;

 /**
  * Spring Force defines the characteristics of the spring being used in the animation.
  * <p>
  * By configuring the stiffness and damping ratio, callers can create a spring with the look and
  * feel suits their use case. Stiffness corresponds to the spring constant. The stiffer the spring
  * is, the harder it is to stretch it, the faster it undergoes dampening.
  * <p>
  * Spring damping ratio describes how oscillations in a system decay after a disturbance.
  * When damping ratio > 1* (i.e. over-damped), the object will quickly return to the rest position
  * without overshooting. If damping ratio equals to 1 (i.e. critically damped), the object will
  * return to equilibrium within the shortest amount of time. When damping ratio is less than 1
  * (i.e. under-damped), the mass tends to overshoot, and return, and overshoot again. Without any
  * damping (i.e. damping ratio = 0), the mass will oscillate forever.
  */
 public final class SpringForce implements Force {
     /**
      * Stiffness constant for extremely stiff spring.
      */
     public static final float STIFFNESS_HIGH = 10_000f;
     /**
      * Stiffness constant for medium stiff spring. This is the default stiffness for spring force.
      */
     public static final float STIFFNESS_MEDIUM = 1500f;
     /**
      * Stiffness constant for a spring with low stiffness.
      */
     public static final float STIFFNESS_LOW = 200f;
     /**
      * Stiffness constant for a spring with very low stiffness.
      */
     public static final float STIFFNESS_VERY_LOW = 50f;

     /**
      * Damping ratio for a very bouncy spring. Note for under-damped springs
      * (i.e. damping ratio < 1), the lower the damping ratio, the more bouncy the spring.
      */
     public static final float DAMPING_RATIO_HIGH_BOUNCY = 0.2f;
     /**
      * Damping ratio for a medium bouncy spring. This is also the default damping ratio for spring
      * force. Note for under-damped springs (i.e. damping ratio < 1), the lower the damping ratio,
      * the more bouncy the spring.
      */
     public static final float DAMPING_RATIO_MEDIUM_BOUNCY = 0.5f;
     /**
      * Damping ratio for a spring with low bounciness. Note for under-damped springs
      * (i.e. damping ratio < 1), the lower the damping ratio, the higher the bounciness.
      */
     public static final float DAMPING_RATIO_LOW_BOUNCY = 0.75f;
     /**
      * Damping ratio for a spring with no bounciness. This damping ratio will create a critically
      * damped spring that returns to equilibrium within the shortest amount of time without
      * oscillating.
      */
     public static final float DAMPING_RATIO_NO_BOUNCY = 1f;

     // This multiplier is used to calculate the velocity threshold given a certain value threshold.
     // The idea is that if it takes >= 1 frame to move the value threshold amount, then the velocity
     // is a reasonable threshold.
     private static final double VELOCITY_THRESHOLD_MULTIPLIER = 1000.0 / 16.0;

     // Natural frequency
     double mNaturalFreq = Math.sqrt(STIFFNESS_MEDIUM);
     // Damping ratio.
     double mDampingRatio = DAMPING_RATIO_MEDIUM_BOUNCY;

     // Value to indicate an unset state.
     private static final double UNSET = Double.MAX_VALUE;

     // Indicates whether the spring has been initialized
     private boolean mInitialized = false;

     // Threshold for velocity and value to determine when it's reasonable to assume that the spring
     // is approximately at rest.
     private double mValueThreshold;
     private double mVelocityThreshold;

     // Intermediate values to simplify the spring function calculation per frame.
     private double mGammaPlus;
     private double mGammaMinus;
     private double mDampedFreq;

     // Final position of the spring. This must be set before the start of the animation.
     private double mFinalPosition = UNSET;

     // Internal state to hold a value/velocity pair.
     private final DynamicAnimation.MassState mMassState = new DynamicAnimation.MassState();

     /**
      * Creates a spring force. Note that final position of the spring must be set through
      * {@link #setFinalPosition(float)} before the spring animation starts.
      */
     public SpringForce() {
         // No op.
     }

     /**
      * Creates a spring with a given final rest position.
      *
      * @param finalPosition final position of the spring when it reaches equilibrium
      */
     public SpringForce(float finalPosition) {
         mFinalPosition = finalPosition;
     }

     /**
      * Sets the stiffness of a spring. The more stiff a spring is, the more force it applies to
      * the object attached when the spring is not at the final position. Default stiffness is
      * {@link #STIFFNESS_MEDIUM}.
      *
      * @param stiffness non-negative stiffness constant of a spring
      * @return the spring force that the given stiffness is set on
      * @throws IllegalArgumentException if the given spring stiffness is not positive
      */
     public SpringForce setStiffness(
             @FloatRange(from = 0.0, fromInclusive = false) float stiffness) {
         if (stiffness <= 0) {
             throw new IllegalArgumentException("Spring stiffness constant must be positive.");
         }
         mNaturalFreq = Math.sqrt(stiffness);
         // All the intermediate values need to be recalculated.
         mInitialized = false;
         return this;
     }

     /**
      * Gets the stiffness of the spring.
      *
      * @return the stiffness of the spring
      */
     public float getStiffness() {
         return (float) (mNaturalFreq * mNaturalFreq);
     }

     /**
      * Spring damping ratio describes how oscillations in a system decay after a disturbance.
      * <p>
      * When damping ratio > 1 (over-damped), the object will quickly return to the rest position
      * without overshooting. If damping ratio equals to 1 (i.e. critically damped), the object will
      * return to equilibrium within the shortest amount of time. When damping ratio is less than 1
      * (i.e. under-damped), the mass tends to overshoot, and return, and overshoot again. Without
      * any damping (i.e. damping ratio = 0), the mass will oscillate forever.
      * <p>
      * Default damping ratio is {@link #DAMPING_RATIO_MEDIUM_BOUNCY}.
      *
      * @param dampingRatio damping ratio of the spring, it should be non-negative
      * @return the spring force that the given damping ratio is set on
      * @throws IllegalArgumentException if the {@param dampingRatio} is negative.
      */
     public SpringForce setDampingRatio(@FloatRange(from = 0.0) float dampingRatio) {
         if (dampingRatio < 0) {
             throw new IllegalArgumentException("Damping ratio must be non-negative");
         }
         mDampingRatio = dampingRatio;
         // All the intermediate values need to be recalculated.
         mInitialized = false;
         return this;
     }

     /**
      * Returns the damping ratio of the spring.
      *
      * @return damping ratio of the spring
      */
     public float getDampingRatio() {
         return (float) mDampingRatio;
     }

     /**
      * Sets the rest position of the spring.
      *
      * @param finalPosition rest position of the spring
      * @return the spring force that the given final position is set on
      */
     public SpringForce setFinalPosition(float finalPosition) {
         mFinalPosition = finalPosition;
         return this;
     }

     /**
      * Returns the rest position of the spring.
      *
      * @return rest position of the spring
      */
     public float getFinalPosition() {
         return (float) mFinalPosition;
     }

     /*********************** Below are private APIs *********************/

     /**
      * @hide
      */
     @Override
     public float getAcceleration(float lastDisplacement, float lastVelocity) {

         lastDisplacement -= getFinalPosition();

         double k = mNaturalFreq * mNaturalFreq;
         double c = 2 * mNaturalFreq * mDampingRatio;

         return (float) (-k * lastDisplacement - c * lastVelocity);
     }

     /**
      * @hide
      */
     @Override
     public boolean isAtEquilibrium(float value, float velocity) {
         if (Math.abs(velocity) < mVelocityThreshold
                 && Math.abs(value - getFinalPosition()) < mValueThreshold) {
             return true;
         }
         return false;
     }

     /**
      * Initialize the string by doing the necessary pre-calculation as well as some sanity check
      * on the setup.
      *
      * @throws IllegalStateException if the final position is not yet set by the time the spring
      *                               animation has started
      */
     private void init() {
         if (mInitialized) {
             return;
         }

         if (mFinalPosition == UNSET) {
             throw new IllegalStateException("Error: Final position of the spring must be"
                     + " set before the animation starts");
         }

         if (mDampingRatio > 1) {
             // Over damping
             mGammaPlus = -mDampingRatio * mNaturalFreq
                     + mNaturalFreq * Math.sqrt(mDampingRatio * mDampingRatio - 1);
             mGammaMinus = -mDampingRatio * mNaturalFreq
                     - mNaturalFreq * Math.sqrt(mDampingRatio * mDampingRatio - 1);
         } else if (mDampingRatio >= 0 && mDampingRatio < 1) {
             // Under damping
             mDampedFreq = mNaturalFreq * Math.sqrt(1 - mDampingRatio * mDampingRatio);
         }

         mInitialized = true;
     }

     /**
      * Internal only call for Spring to calculate the spring position/velocity using
      * an analytical approach.
      */
     DynamicAnimation.MassState updateValues(double lastDisplacement, double lastVelocity,
             long timeElapsed) {
         init();

         double deltaT = timeElapsed / 1000d; // unit: seconds
         lastDisplacement -= mFinalPosition;
         double displacement;
         double currentVelocity;
         if (mDampingRatio > 1) {
             // Overdamped
             double coeffA =  lastDisplacement - (mGammaMinus * lastDisplacement - lastVelocity)
                     / (mGammaMinus - mGammaPlus);
             double coeffB =  (mGammaMinus * lastDisplacement - lastVelocity)
                     / (mGammaMinus - mGammaPlus);
             displacement = coeffA * Math.pow(Math.E, mGammaMinus * deltaT)
                     + coeffB * Math.pow(Math.E, mGammaPlus * deltaT);
             currentVelocity = coeffA * mGammaMinus * Math.pow(Math.E, mGammaMinus * deltaT)
                     + coeffB * mGammaPlus * Math.pow(Math.E, mGammaPlus * deltaT);
         } else if (mDampingRatio == 1) {
             // Critically damped
             double coeffA = lastDisplacement;
             double coeffB = lastVelocity + mNaturalFreq * lastDisplacement;
             displacement = (coeffA + coeffB * deltaT) * Math.pow(Math.E, -mNaturalFreq * deltaT);
             currentVelocity = (coeffA + coeffB * deltaT) * Math.pow(Math.E, -mNaturalFreq * deltaT)
                     * (-mNaturalFreq) + coeffB * Math.pow(Math.E, -mNaturalFreq * deltaT);
         } else {
             // Underdamped
             double cosCoeff = lastDisplacement;
             double sinCoeff = (1 / mDampedFreq) * (mDampingRatio * mNaturalFreq
                     * lastDisplacement + lastVelocity);
             displacement = Math.pow(Math.E, -mDampingRatio * mNaturalFreq * deltaT)
                     * (cosCoeff * Math.cos(mDampedFreq * deltaT)
                     + sinCoeff * Math.sin(mDampedFreq * deltaT));
             currentVelocity = displacement * (-mNaturalFreq) * mDampingRatio
                     + Math.pow(Math.E, -mDampingRatio * mNaturalFreq * deltaT)
                     * (-mDampedFreq * cosCoeff * Math.sin(mDampedFreq * deltaT)
                     + mDampedFreq * sinCoeff * Math.cos(mDampedFreq * deltaT));
         }

         mMassState.mValue = (float) (displacement + mFinalPosition);
         mMassState.mVelocity = (float) currentVelocity;
         return mMassState;
     }

     /**
      * This threshold defines how close the animation value needs to be before the animation can
      * finish. This default value is based on the property being animated, e.g. animations on alpha,
      * scale, translation or rotation would have different thresholds. This value should be small
      * enough to avoid visual glitch of "jumping to the end". But it shouldn't be so small that
      * animations take seconds to finish.
      *
      * @param threshold the difference between the animation value and final spring position that
      *                  is allowed to end the animation when velocity is very low
      */
     void setValueThreshold(double threshold) {
         mValueThreshold = Math.abs(threshold);
         mVelocityThreshold = mValueThreshold * VELOCITY_THRESHOLD_MULTIPLIER;
     }
 }
	/*
	* 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.
	*/

	package android.support.animation;

	import android.support.annotation.FloatRange;

	/**
	* Spring Force defines the characteristics of the spring being used in the animation.
	* <p>
	* By configuring the stiffness and damping ratio, callers can create a spring with the look and
	* feel suits their use case. Stiffness corresponds to the spring constant. The stiffer the spring
	* is, the harder it is to stretch it, the faster it undergoes dampening.
	* <p>
	* Spring damping ratio describes how oscillations in a system decay after a disturbance.
	* When damping ratio > 1* (i.e. over-damped), the object will quickly return to the rest position
	* without overshooting. If damping ratio equals to 1 (i.e. critically damped), the object will
	* return to equilibrium within the shortest amount of time. When damping ratio is less than 1
	* (i.e. under-damped), the mass tends to overshoot, and return, and overshoot again. Without any
	* damping (i.e. damping ratio = 0), the mass will oscillate forever.
	*/
	public final class SpringForce implements Force {
	/**
	* Stiffness constant for extremely stiff spring.
	*/
	public static final float STIFFNESS_HIGH = 10_000f;
	/**
	* Stiffness constant for medium stiff spring. This is the default stiffness for spring force.
	*/
	public static final float STIFFNESS_MEDIUM = 1500f;
	/**
	* Stiffness constant for a spring with low stiffness.
	*/
	public static final float STIFFNESS_LOW = 200f;
	/**
	* Stiffness constant for a spring with very low stiffness.
	*/
	public static final float STIFFNESS_VERY_LOW = 50f;

	/**
	* Damping ratio for a very bouncy spring. Note for under-damped springs
	* (i.e. damping ratio < 1), the lower the damping ratio, the more bouncy the spring.
	*/
	public static final float DAMPING_RATIO_HIGH_BOUNCY = 0.2f;
	/**
	* Damping ratio for a medium bouncy spring. This is also the default damping ratio for spring
	* force. Note for under-damped springs (i.e. damping ratio < 1), the lower the damping ratio,
	* the more bouncy the spring.
	*/
	public static final float DAMPING_RATIO_MEDIUM_BOUNCY = 0.5f;
	/**
	* Damping ratio for a spring with low bounciness. Note for under-damped springs
	* (i.e. damping ratio < 1), the lower the damping ratio, the higher the bounciness.
	*/
	public static final float DAMPING_RATIO_LOW_BOUNCY = 0.75f;
	/**
	* Damping ratio for a spring with no bounciness. This damping ratio will create a critically
	* damped spring that returns to equilibrium within the shortest amount of time without
	* oscillating.
	*/
	public static final float DAMPING_RATIO_NO_BOUNCY = 1f;

	// This multiplier is used to calculate the velocity threshold given a certain value threshold.
	// The idea is that if it takes >= 1 frame to move the value threshold amount, then the velocity
	// is a reasonable threshold.
	private static final double VELOCITY_THRESHOLD_MULTIPLIER = 1000.0 / 16.0;

	// Natural frequency
	double mNaturalFreq = Math.sqrt(STIFFNESS_MEDIUM);
	// Damping ratio.
	double mDampingRatio = DAMPING_RATIO_MEDIUM_BOUNCY;

	// Value to indicate an unset state.
	private static final double UNSET = Double.MAX_VALUE;

	// Indicates whether the spring has been initialized
	private boolean mInitialized = false;

	// Threshold for velocity and value to determine when it's reasonable to assume that the spring
	// is approximately at rest.
	private double mValueThreshold;
	private double mVelocityThreshold;

	// Intermediate values to simplify the spring function calculation per frame.
	private double mGammaPlus;
	private double mGammaMinus;
	private double mDampedFreq;

	// Final position of the spring. This must be set before the start of the animation.
	private double mFinalPosition = UNSET;

	// Internal state to hold a value/velocity pair.
	private final DynamicAnimation.MassState mMassState = new DynamicAnimation.MassState();

	/**
	* Creates a spring force. Note that final position of the spring must be set through
	* {@link #setFinalPosition(float)} before the spring animation starts.
	*/
	public SpringForce() {
	// No op.
	}

	/**
	* Creates a spring with a given final rest position.
	*
	* @param finalPosition final position of the spring when it reaches equilibrium
	*/
	public SpringForce(float finalPosition) {
	mFinalPosition = finalPosition;
	}

	/**
	* Sets the stiffness of a spring. The more stiff a spring is, the more force it applies to
	* the object attached when the spring is not at the final position. Default stiffness is
	* {@link #STIFFNESS_MEDIUM}.
	*
	* @param stiffness non-negative stiffness constant of a spring
	* @return the spring force that the given stiffness is set on
	* @throws IllegalArgumentException if the given spring stiffness is not positive
	*/
	public SpringForce setStiffness(
	@FloatRange(from = 0.0, fromInclusive = false) float stiffness) {
	if (stiffness <= 0) {
	throw new IllegalArgumentException("Spring stiffness constant must be positive.");
	}
	mNaturalFreq = Math.sqrt(stiffness);
	// All the intermediate values need to be recalculated.
	mInitialized = false;
	return this;
	}

	/**
	* Gets the stiffness of the spring.
	*
	* @return the stiffness of the spring
	*/
	public float getStiffness() {
	return (float) (mNaturalFreq * mNaturalFreq);
	}

	/**
	* Spring damping ratio describes how oscillations in a system decay after a disturbance.
	* <p>
	* When damping ratio > 1 (over-damped), the object will quickly return to the rest position
	* without overshooting. If damping ratio equals to 1 (i.e. critically damped), the object will
	* return to equilibrium within the shortest amount of time. When damping ratio is less than 1
	* (i.e. under-damped), the mass tends to overshoot, and return, and overshoot again. Without
	* any damping (i.e. damping ratio = 0), the mass will oscillate forever.
	* <p>
	* Default damping ratio is {@link #DAMPING_RATIO_MEDIUM_BOUNCY}.
	*
	* @param dampingRatio damping ratio of the spring, it should be non-negative
	* @return the spring force that the given damping ratio is set on
	* @throws IllegalArgumentException if the {@param dampingRatio} is negative.
	*/
	public SpringForce setDampingRatio(@FloatRange(from = 0.0) float dampingRatio) {
	if (dampingRatio < 0) {
	throw new IllegalArgumentException("Damping ratio must be non-negative");
	}
	mDampingRatio = dampingRatio;
	// All the intermediate values need to be recalculated.
	mInitialized = false;
	return this;
	}

	/**
	* Returns the damping ratio of the spring.
	*
	* @return damping ratio of the spring
	*/
	public float getDampingRatio() {
	return (float) mDampingRatio;
	}

	/**
	* Sets the rest position of the spring.
	*
	* @param finalPosition rest position of the spring
	* @return the spring force that the given final position is set on
	*/
	public SpringForce setFinalPosition(float finalPosition) {
	mFinalPosition = finalPosition;
	return this;
	}

	/**
	* Returns the rest position of the spring.
	*
	* @return rest position of the spring
	*/
	public float getFinalPosition() {
	return (float) mFinalPosition;
	}

	/********************* Below are private APIs *******************/

	/**
	* @hide
	*/
	@Override
	public float getAcceleration(float lastDisplacement, float lastVelocity) {

	lastDisplacement -= getFinalPosition();

	double k = mNaturalFreq * mNaturalFreq;
	double c = 2 * mNaturalFreq * mDampingRatio;

	return (float) (-k * lastDisplacement - c * lastVelocity);
	}

	/**
	* @hide
	*/
	@Override
	public boolean isAtEquilibrium(float value, float velocity) {
	if (Math.abs(velocity) < mVelocityThreshold
	&& Math.abs(value - getFinalPosition()) < mValueThreshold) {
	return true;
	}
	return false;
	}

	/**
	* Initialize the string by doing the necessary pre-calculation as well as some sanity check
	* on the setup.
	*
	* @throws IllegalStateException if the final position is not yet set by the time the spring
	* animation has started
	*/
	private void init() {
	if (mInitialized) {
	return;
	}

	if (mFinalPosition == UNSET) {
	throw new IllegalStateException("Error: Final position of the spring must be"
	+ " set before the animation starts");
	}

	if (mDampingRatio > 1) {
	// Over damping
	mGammaPlus = -mDampingRatio * mNaturalFreq
	+ mNaturalFreq * Math.sqrt(mDampingRatio * mDampingRatio - 1);
	mGammaMinus = -mDampingRatio * mNaturalFreq
	- mNaturalFreq * Math.sqrt(mDampingRatio * mDampingRatio - 1);
	} else if (mDampingRatio >= 0 && mDampingRatio < 1) {
	// Under damping
	mDampedFreq = mNaturalFreq * Math.sqrt(1 - mDampingRatio * mDampingRatio);
	}

	mInitialized = true;
	}

	/**
	* Internal only call for Spring to calculate the spring position/velocity using
	* an analytical approach.
	*/
	DynamicAnimation.MassState updateValues(double lastDisplacement, double lastVelocity,
	long timeElapsed) {
	init();

	double deltaT = timeElapsed / 1000d; // unit: seconds
	lastDisplacement -= mFinalPosition;
	double displacement;
	double currentVelocity;
	if (mDampingRatio > 1) {
	// Overdamped
	double coeffA = lastDisplacement - (mGammaMinus * lastDisplacement - lastVelocity)
	/ (mGammaMinus - mGammaPlus);
	double coeffB = (mGammaMinus * lastDisplacement - lastVelocity)
	/ (mGammaMinus - mGammaPlus);
	displacement = coeffA * Math.pow(Math.E, mGammaMinus * deltaT)
	+ coeffB * Math.pow(Math.E, mGammaPlus * deltaT);
	currentVelocity = coeffA * mGammaMinus * Math.pow(Math.E, mGammaMinus * deltaT)
	+ coeffB * mGammaPlus * Math.pow(Math.E, mGammaPlus * deltaT);
	} else if (mDampingRatio == 1) {
	// Critically damped
	double coeffA = lastDisplacement;
	double coeffB = lastVelocity + mNaturalFreq * lastDisplacement;
	displacement = (coeffA + coeffB * deltaT) * Math.pow(Math.E, -mNaturalFreq * deltaT);
	currentVelocity = (coeffA + coeffB * deltaT) * Math.pow(Math.E, -mNaturalFreq * deltaT)
	* (-mNaturalFreq) + coeffB * Math.pow(Math.E, -mNaturalFreq * deltaT);
	} else {
	// Underdamped
	double cosCoeff = lastDisplacement;
	double sinCoeff = (1 / mDampedFreq) * (mDampingRatio * mNaturalFreq
	* lastDisplacement + lastVelocity);
	displacement = Math.pow(Math.E, -mDampingRatio * mNaturalFreq * deltaT)
	* (cosCoeff * Math.cos(mDampedFreq * deltaT)
	+ sinCoeff * Math.sin(mDampedFreq * deltaT));
	currentVelocity = displacement * (-mNaturalFreq) * mDampingRatio
	+ Math.pow(Math.E, -mDampingRatio * mNaturalFreq * deltaT)
	* (-mDampedFreq * cosCoeff * Math.sin(mDampedFreq * deltaT)
	+ mDampedFreq * sinCoeff * Math.cos(mDampedFreq * deltaT));
	}

	mMassState.mValue = (float) (displacement + mFinalPosition);
	mMassState.mVelocity = (float) currentVelocity;
	return mMassState;
	}

	/**
	* This threshold defines how close the animation value needs to be before the animation can
	* finish. This default value is based on the property being animated, e.g. animations on alpha,
	* scale, translation or rotation would have different thresholds. This value should be small
	* enough to avoid visual glitch of "jumping to the end". But it shouldn't be so small that
	* animations take seconds to finish.
	*
	* @param threshold the difference between the animation value and final spring position that
	* is allowed to end the animation when velocity is very low
	*/
	void setValueThreshold(double threshold) {
	mValueThreshold = Math.abs(threshold);
	mVelocityThreshold = mValueThreshold * VELOCITY_THRESHOLD_MULTIPLIER;
	}
	}