/*******************************************************************************
* Copyright 2011 See AUTHORS file.
*
* 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 com.badlogic.gdx.math;
import java.util.Random;
/** Utility and fast math functions.
* <p>
* Thanks to Riven on JavaGaming.org for the basis of sin/cos/floor/ceil.
* @author Nathan Sweet */
public final class MathUtils {
static public final float nanoToSec = 1 / 1000000000f;
// ---
static public final float FLOAT_ROUNDING_ERROR = 0.000001f; // 32 bits
static public final float PI = 3.1415927f;
static public final float PI2 = PI * 2;
static public final float E = 2.7182818f;
static private final int SIN_BITS = 14; // 16KB. Adjust for accuracy.
static private final int SIN_MASK = ~(-1 << SIN_BITS);
static private final int SIN_COUNT = SIN_MASK + 1;
static private final float radFull = PI * 2;
static private final float degFull = 360;
static private final float radToIndex = SIN_COUNT / radFull;
static private final float degToIndex = SIN_COUNT / degFull;
/** multiply by this to convert from radians to degrees */
static public final float radiansToDegrees = 180f / PI;
static public final float radDeg = radiansToDegrees;
/** multiply by this to convert from degrees to radians */
static public final float degreesToRadians = PI / 180;
static public final float degRad = degreesToRadians;
static private class Sin {
static final float[] table = new float[SIN_COUNT];
static {
for (int i = 0; i < SIN_COUNT; i++)
table[i] = (float)Math.sin((i + 0.5f) / SIN_COUNT * radFull);
for (int i = 0; i < 360; i += 90)
table[(int)(i * degToIndex) & SIN_MASK] = (float)Math.sin(i * degreesToRadians);
}
}
/** Returns the sine in radians from a lookup table. */
static public float sin (float radians) {
return Sin.table[(int)(radians * radToIndex) & SIN_MASK];
}
/** Returns the cosine in radians from a lookup table. */
static public float cos (float radians) {
return Sin.table[(int)((radians + PI / 2) * radToIndex) & SIN_MASK];
}
/** Returns the sine in radians from a lookup table. */
static public float sinDeg (float degrees) {
return Sin.table[(int)(degrees * degToIndex) & SIN_MASK];
}
/** Returns the cosine in radians from a lookup table. */
static public float cosDeg (float degrees) {
return Sin.table[(int)((degrees + 90) * degToIndex) & SIN_MASK];
}
// ---
/** Returns atan2 in radians, faster but less accurate than Math.atan2. Average error of 0.00231 radians (0.1323 degrees),
* largest error of 0.00488 radians (0.2796 degrees). */
static public float atan2 (float y, float x) {
if (x == 0f) {
if (y > 0f) return PI / 2;
if (y == 0f) return 0f;
return -PI / 2;
}
final float atan, z = y / x;
if (Math.abs(z) < 1f) {
atan = z / (1f + 0.28f * z * z);
if (x < 0f) return atan + (y < 0f ? -PI : PI);
return atan;
}
atan = PI / 2 - z / (z * z + 0.28f);
return y < 0f ? atan - PI : atan;
}
// ---
static public Random random = new RandomXS128();
/** Returns a random number between 0 (inclusive) and the specified value (inclusive). */
static public int random (int range) {
return random.nextInt(range + 1);
}
/** Returns a random number between start (inclusive) and end (inclusive). */
static public int random (int start, int end) {
return start + random.nextInt(end - start + 1);
}
/** Returns a random number between 0 (inclusive) and the specified value (inclusive). */
static public long random (long range) {
return (long)(random.nextDouble() * range);
}
/** Returns a random number between start (inclusive) and end (inclusive). */
static public long random (long start, long end) {
return start + (long)(random.nextDouble() * (end - start));
}
/** Returns a random boolean value. */
static public boolean randomBoolean () {
return random.nextBoolean();
}
/** Returns true if a random value between 0 and 1 is less than the specified value. */
static public boolean randomBoolean (float chance) {
return MathUtils.random() < chance;
}
/** Returns random number between 0.0 (inclusive) and 1.0 (exclusive). */
static public float random () {
return random.nextFloat();
}
/** Returns a random number between 0 (inclusive) and the specified value (exclusive). */
static public float random (float range) {
return random.nextFloat() * range;
}
/** Returns a random number between start (inclusive) and end (exclusive). */
static public float random (float start, float end) {
return start + random.nextFloat() * (end - start);
}
/** Returns -1 or 1, randomly. */
static public int randomSign () {
return 1 | (random.nextInt() >> 31);
}
/** Returns a triangularly distributed random number between -1.0 (exclusive) and 1.0 (exclusive), where values around zero are
* more likely.
* <p>
* This is an optimized version of {@link #randomTriangular(float, float, float) randomTriangular(-1, 1, 0)} */
public static float randomTriangular () {
return random.nextFloat() - random.nextFloat();
}
/** Returns a triangularly distributed random number between {@code -max} (exclusive) and {@code max} (exclusive), where values
* around zero are more likely.
* <p>
* This is an optimized version of {@link #randomTriangular(float, float, float) randomTriangular(-max, max, 0)}
* @param max the upper limit */
public static float randomTriangular (float max) {
return (random.nextFloat() - random.nextFloat()) * max;
}
/** Returns a triangularly distributed random number between {@code min} (inclusive) and {@code max} (exclusive), where the
* {@code mode} argument defaults to the midpoint between the bounds, giving a symmetric distribution.
* <p>
* This method is equivalent of {@link #randomTriangular(float, float, float) randomTriangular(min, max, (min + max) * .5f)}
* @param min the lower limit
* @param max the upper limit */
public static float randomTriangular (float min, float max) {
return randomTriangular(min, max, (min + max) * 0.5f);
}
/** Returns a triangularly distributed random number between {@code min} (inclusive) and {@code max} (exclusive), where values
* around {@code mode} are more likely.
* @param min the lower limit
* @param max the upper limit
* @param mode the point around which the values are more likely */
public static float randomTriangular (float min, float max, float mode) {
float u = random.nextFloat();
float d = max - min;
if (u <= (mode - min) / d) return min + (float)Math.sqrt(u * d * (mode - min));
return max - (float)Math.sqrt((1 - u) * d * (max - mode));
}
// ---
/** Returns the next power of two. Returns the specified value if the value is already a power of two. */
static public int nextPowerOfTwo (int value) {
if (value == 0) return 1;
value--;
value |= value >> 1;
value |= value >> 2;
value |= value >> 4;
value |= value >> 8;
value |= value >> 16;
return value + 1;
}
static public boolean isPowerOfTwo (int value) {
return value != 0 && (value & value - 1) == 0;
}
// ---
static public short clamp (short value, short min, short max) {
if (value < min) return min;
if (value > max) return max;
return value;
}
static public int clamp (int value, int min, int max) {
if (value < min) return min;
if (value > max) return max;
return value;
}
static public long clamp (long value, long min, long max) {
if (value < min) return min;
if (value > max) return max;
return value;
}
static public float clamp (float value, float min, float max) {
if (value < min) return min;
if (value > max) return max;
return value;
}
static public double clamp (double value, double min, double max) {
if (value < min) return min;
if (value > max) return max;
return value;
}
// ---
/** Linearly interpolates between fromValue to toValue on progress position. */
static public float lerp (float fromValue, float toValue, float progress) {
return fromValue + (toValue - fromValue) * progress;
}
/** Linearly interpolates between two angles in radians. Takes into account that angles wrap at two pi and always takes the
* direction with the smallest delta angle.
*
* @param fromRadians start angle in radians
* @param toRadians target angle in radians
* @param progress interpolation value in the range [0, 1]
* @return the interpolated angle in the range [0, PI2[ */
public static float lerpAngle (float fromRadians, float toRadians, float progress) {
float delta = ((toRadians - fromRadians + PI2 + PI) % PI2) - PI;
return (fromRadians + delta * progress + PI2) % PI2;
}
/** Linearly interpolates between two angles in degrees. Takes into account that angles wrap at 360 degrees and always takes
* the direction with the smallest delta angle.
*
* @param fromDegrees start angle in degrees
* @param toDegrees target angle in degrees
* @param progress interpolation value in the range [0, 1]
* @return the interpolated angle in the range [0, 360[ */
public static float lerpAngleDeg (float fromDegrees, float toDegrees, float progress) {
float delta = ((toDegrees - fromDegrees + 360 + 180) % 360) - 180;
return (fromDegrees + delta * progress + 360) % 360;
}
// ---
static private final int BIG_ENOUGH_INT = 16 * 1024;
static private final double BIG_ENOUGH_FLOOR = BIG_ENOUGH_INT;
static private final double CEIL = 0.9999999;
static private final double BIG_ENOUGH_CEIL = 16384.999999999996;
static private final double BIG_ENOUGH_ROUND = BIG_ENOUGH_INT + 0.5f;
/** Returns the largest integer less than or equal to the specified float. This method will only properly floor floats from
* -(2^14) to (Float.MAX_VALUE - 2^14). */
static public int floor (float value) {
return (int)(value + BIG_ENOUGH_FLOOR) - BIG_ENOUGH_INT;
}
/** Returns the largest integer less than or equal to the specified float. This method will only properly floor floats that are
* positive. Note this method simply casts the float to int. */
static public int floorPositive (float value) {
return (int)value;
}
/** Returns the smallest integer greater than or equal to the specified float. This method will only properly ceil floats from
* -(2^14) to (Float.MAX_VALUE - 2^14). */
static public int ceil (float value) {
return BIG_ENOUGH_INT - (int)(BIG_ENOUGH_FLOOR - value);
}
/** Returns the smallest integer greater than or equal to the specified float. This method will only properly ceil floats that
* are positive. */
static public int ceilPositive (float value) {
return (int)(value + CEIL);
}
/** Returns the closest integer to the specified float. This method will only properly round floats from -(2^14) to
* (Float.MAX_VALUE - 2^14). */
static public int round (float value) {
return (int)(value + BIG_ENOUGH_ROUND) - BIG_ENOUGH_INT;
}
/** Returns the closest integer to the specified float. This method will only properly round floats that are positive. */
static public int roundPositive (float value) {
return (int)(value + 0.5f);
}
/** Returns true if the value is zero (using the default tolerance as upper bound) */
static public boolean isZero (float value) {
return Math.abs(value) <= FLOAT_ROUNDING_ERROR;
}
/** Returns true if the value is zero.
* @param tolerance represent an upper bound below which the value is considered zero. */
static public boolean isZero (float value, float tolerance) {
return Math.abs(value) <= tolerance;
}
/** Returns true if a is nearly equal to b. The function uses the default floating error tolerance.
* @param a the first value.
* @param b the second value. */
static public boolean isEqual (float a, float b) {
return Math.abs(a - b) <= FLOAT_ROUNDING_ERROR;
}
/** Returns true if a is nearly equal to b.
* @param a the first value.
* @param b the second value.
* @param tolerance represent an upper bound below which the two values are considered equal. */
static public boolean isEqual (float a, float b, float tolerance) {
return Math.abs(a - b) <= tolerance;
}
/** @return the logarithm of value with base a */
static public float log (float a, float value) {
return (float)(Math.log(value) / Math.log(a));
}
/** @return the logarithm of value with base 2 */
static public float log2 (float value) {
return log(2, value);
}
}