/*******************************************************************************
* 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;
import com.badlogic.gdx.utils.NumberUtils;
/**
* Utility and fast math functions.
* <p>
* Thanks to Riven on JavaGaming.org for the basis of sin/cos/atan2/floor/ceil.
*
* @author Nathan Sweet
*/
public class MathUtils {
static public final float nanoToSec = 1 / 1000000000f;
// ---
static public final float PI = 3.1415927f;
static private final int SIN_BITS = 13; // 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;
static public final float radiansToDegrees = 180f / PI;
static public final float radDeg = radiansToDegrees;
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);
}
}
static private class Cos {
static final float[] table = new float[SIN_COUNT];
static {
for (int i = 0; i < SIN_COUNT; i++)
table[i] = (float) Math.cos((i + 0.5f) / SIN_COUNT * radFull);
for (int i = 0; i < 360; i += 90)
table[(int) (i * degToIndex) & SIN_MASK] = (float) Math.cos(i * degreesToRadians);
}
}
/** Returns the sine in radians. */
static public final float sin(float radians) {
return Sin.table[(int) (radians * radToIndex) & SIN_MASK];
}
/** Returns the cosine in radians. */
static public final float cos(float radians) {
return Cos.table[(int) (radians * radToIndex) & SIN_MASK];
}
/** Returns the sine in radians. */
static public final float sinDeg(float degrees) {
return Sin.table[(int) (degrees * degToIndex) & SIN_MASK];
}
/** Returns the cosine in radians. */
static public final float cosDeg(float degrees) {
return Cos.table[(int) (degrees * degToIndex) & SIN_MASK];
}
// ---
static private final int ATAN2_BITS = 7; // Adjust for accuracy.
static private final int ATAN2_BITS2 = ATAN2_BITS << 1;
static private final int ATAN2_MASK = ~(-1 << ATAN2_BITS2);
static private final int ATAN2_COUNT = ATAN2_MASK + 1;
static final int ATAN2_DIM = (int) Math.sqrt(ATAN2_COUNT);
static private final float INV_ATAN2_DIM_MINUS_1 = 1.0f / (ATAN2_DIM - 1);
static private class Atan2 {
static final float[] table = new float[ATAN2_COUNT];
static {
for (int i = 0; i < ATAN2_DIM; i++) {
for (int j = 0; j < ATAN2_DIM; j++) {
float x0 = (float) i / ATAN2_DIM;
float y0 = (float) j / ATAN2_DIM;
table[j * ATAN2_DIM + i] = (float) Math.atan2(y0, x0);
}
}
}
}
/** Returns atan2 in radians from a lookup table. */
static public final float atan2(float y, float x) {
float add, mul;
if (x < 0) {
if (y < 0) {
y = -y;
mul = 1;
} else
mul = -1;
x = -x;
add = -PI;
} else {
if (y < 0) {
y = -y;
mul = -1;
} else
mul = 1;
add = 0;
}
float invDiv = 1 / ((x < y ? y : x) * INV_ATAN2_DIM_MINUS_1);
int xi = (int) (x * invDiv);
int yi = (int) (y * invDiv);
return (Atan2.table[yi * ATAN2_DIM + xi] + add) * mul;
}
// ---
static public Random random = new Random();
/** Returns a random number between 0 (inclusive) and the specified value (inclusive). */
static public final int random(int range) {
return random.nextInt(range + 1);
}
/** Returns a random number between start (inclusive) and end (inclusive). */
static public final int random(int start, int end) {
return start + random.nextInt(end - start + 1);
}
static public final boolean randomBoolean() {
return random.nextBoolean();
}
static public final float random() {
return random.nextFloat();
}
/** Returns a random number between 0 (inclusive) and the specified value (inclusive). */
static public final float random(float range) {
return random.nextFloat() * range;
}
/** Returns a random number between start (inclusive) and end (inclusive). */
static public final float random(float start, float end) {
return start + random.nextFloat() * (end - start);
}
// ---
/** 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 int clamp(int value, int min, int max) {
if (value < min)
return min;
if (value > max)
return max;
return value;
}
static public short clamp(short value, short min, short 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 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 = NumberUtils.longBitsToDouble(NumberUtils
.doubleToLongBits(BIG_ENOUGH_INT + 1) - 1);
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 x) {
return (int) (x + 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 x) {
return (int) x;
}
/**
* 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 x) {
return (int) (x + BIG_ENOUGH_CEIL) - BIG_ENOUGH_INT;
}
/**
* 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 x) {
return (int) (x + 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 x) {
return (int) (x + 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 x) {
return (int) (x + 0.5f);
}
}