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Diffstat (limited to 'engine/src/android/jme3tools/android/Fixed.java')
| -rw-r--r-- | engine/src/android/jme3tools/android/Fixed.java | 431 |
1 files changed, 431 insertions, 0 deletions
diff --git a/engine/src/android/jme3tools/android/Fixed.java b/engine/src/android/jme3tools/android/Fixed.java new file mode 100644 index 0000000..4420999 --- /dev/null +++ b/engine/src/android/jme3tools/android/Fixed.java @@ -0,0 +1,431 @@ +package jme3tools.android; + +import java.util.Random; + +/** + * Fixed point maths class. This can be tailored for specific needs by + * changing the bits allocated to the 'fraction' part (see <code>FIXED_POINT + * </code>, which would also require <code>SIN_PRECALC</code> and <code> + * COS_PRECALC</code> updating). + * + * <p><a href="http://blog.numfum.com/2007/09/java-fixed-point-maths.html"> + * http://blog.numfum.com/2007/09/java-fixed-point-maths.html</a></p> + * + * @version 1.0 + * @author CW + * + * @deprecated Most devices with OpenGL ES 2.0 have an FPU. Please use + * floats instead of this class for decimal math. + */ +@Deprecated +public final class Fixed { + + /** + * Number of bits used for 'fraction'. + */ + public static final int FIXED_POINT = 16; + /** + * Decimal one as represented by the Fixed class. + */ + public static final int ONE = 1 << FIXED_POINT; + /** + * Half in fixed point. + */ + public static final int HALF = ONE >> 1; + /** + * Quarter circle resolution for trig functions (should be a power of + * two). This is the number of discrete steps in 90 degrees. + */ + public static final int QUARTER_CIRCLE = 64; + /** + * Mask used to limit angles to one revolution. If a quarter circle is 64 + * (i.e. 90 degrees is broken into 64 steps) then the mask is 255. + */ + public static final int FULL_CIRCLE_MASK = QUARTER_CIRCLE * 4 - 1; + /** + * The trig table is generated at a higher precision than the typical + * 16.16 format used for the rest of the fixed point maths. The table + * values are then shifted to match the actual fixed point used. + */ + private static final int TABLE_SHIFT = 30; + /** + * Equivalent to: sin((2 * PI) / (QUARTER_CIRCLE * 4)) + * <p> + * Note: if either QUARTER_CIRCLE or TABLE_SHIFT is changed this value + * will need recalculating (put the above formular into a calculator set + * radians, then shift the result by <code>TABLE_SHIFT</code>). + */ + private static final int SIN_PRECALC = 26350943; + /** + * Equivalent to: cos((2 * PI) / (QUARTER_CIRCLE * 4)) * 2 + * + * Note: if either QUARTER_CIRCLE or TABLE_SHIFT is changed this value + * will need recalculating ((put the above formular into a calculator set + * radians, then shift the result by <code>TABLE_SHIFT</code>). + */ + private static final int COS_PRECALC = 2146836866; + /** + * One quarter sine wave as fixed point values. + */ + private static final int[] SINE_TABLE = new int[QUARTER_CIRCLE + 1]; + /** + * Scale value for indexing ATAN_TABLE[]. + */ + private static final int ATAN_SHIFT; + /** + * Reverse atan lookup table. + */ + private static final byte[] ATAN_TABLE; + /** + * ATAN_TABLE.length + */ + private static final int ATAN_TABLE_LEN; + + /* + * Generates the tables and fills in any remaining static ints. + */ + static { + // Generate the sine table using recursive synthesis. + SINE_TABLE[0] = 0; + SINE_TABLE[1] = SIN_PRECALC; + for (int n = 2; n < QUARTER_CIRCLE + 1; n++) { + SINE_TABLE[n] = (int) (((long) SINE_TABLE[n - 1] * COS_PRECALC) >> TABLE_SHIFT) - SINE_TABLE[n - 2]; + } + // Scale the values to the fixed point format used. + for (int n = 0; n < QUARTER_CIRCLE + 1; n++) { + SINE_TABLE[n] = SINE_TABLE[n] + (1 << (TABLE_SHIFT - FIXED_POINT - 1)) >> TABLE_SHIFT - FIXED_POINT; + } + + // Calculate a shift used to scale atan lookups + int rotl = 0; + int tan0 = tan(0); + int tan1 = tan(1); + while (rotl < 32) { + if ((tan1 >>= 1) > (tan0 >>= 1)) { + rotl++; + } else { + break; + } + } + ATAN_SHIFT = rotl; + // Create the a table of tan values + int[] lut = new int[QUARTER_CIRCLE]; + for (int n = 0; n < QUARTER_CIRCLE; n++) { + lut[n] = tan(n) >> rotl; + } + ATAN_TABLE_LEN = lut[QUARTER_CIRCLE - 1]; + // Then from the tan values create a reverse lookup + ATAN_TABLE = new byte[ATAN_TABLE_LEN]; + for (byte n = 0; n < QUARTER_CIRCLE - 1; n++) { + int min = lut[n]; + int max = lut[n + 1]; + for (int i = min; i < max; i++) { + ATAN_TABLE[i] = n; + } + } + } + /** + * How many decimal places to use when converting a fixed point value to + * a decimal string. + * + * @see #toString + */ + private static final int STRING_DECIMAL_PLACES = 2; + /** + * Value to add in order to round down a fixed point number when + * converting to a string. + */ + private static final int STRING_DECIMAL_PLACES_ROUND; + + static { + int i = 10; + for (int n = 1; n < STRING_DECIMAL_PLACES; n++) { + i *= i; + } + if (STRING_DECIMAL_PLACES == 0) { + STRING_DECIMAL_PLACES_ROUND = ONE / 2; + } else { + STRING_DECIMAL_PLACES_ROUND = ONE / (2 * i); + } + } + /** + * Random number generator. The standard <code>java.utll.Random</code> is + * used since it is available to both J2ME and J2SE. If a guaranteed + * sequence is required this would not be adequate. + */ + private static Random rng = null; + + /** + * Fixed can't be instantiated. + */ + private Fixed() { + } + + /** + * Returns an integer as a fixed point value. + */ + public static int intToFixed(int n) { + return n << FIXED_POINT; + } + + /** + * Returns a fixed point value as a float. + */ + public static float fixedToFloat(int i) { + float fp = i; + fp = fp / ((float) ONE); + return fp; + } + + /** + * Returns a float as a fixed point value. + */ + public static int floatToFixed(float fp) { + return (int) (fp * ((float) ONE)); + } + + /** + * Converts a fixed point value into a decimal string. + */ + public static String toString(int n) { + StringBuffer sb = new StringBuffer(16); + sb.append((n += STRING_DECIMAL_PLACES_ROUND) >> FIXED_POINT); + sb.append('.'); + n &= ONE - 1; + for (int i = 0; i < STRING_DECIMAL_PLACES; i++) { + n *= 10; + sb.append((n / ONE) % 10); + } + return sb.toString(); + } + + /** + * Multiplies two fixed point values and returns the result. + */ + public static int mul(int a, int b) { + return (int) ((long) a * (long) b >> FIXED_POINT); + } + + /** + * Divides two fixed point values and returns the result. + */ + public static int div(int a, int b) { + return (int) (((long) a << FIXED_POINT * 2) / (long) b >> FIXED_POINT); + } + + /** + * Sine of an angle. + * + * @see #QUARTER_CIRCLE + */ + public static int sin(int n) { + n &= FULL_CIRCLE_MASK; + if (n < QUARTER_CIRCLE * 2) { + if (n < QUARTER_CIRCLE) { + return SINE_TABLE[n]; + } else { + return SINE_TABLE[QUARTER_CIRCLE * 2 - n]; + } + } else { + if (n < QUARTER_CIRCLE * 3) { + return -SINE_TABLE[n - QUARTER_CIRCLE * 2]; + } else { + return -SINE_TABLE[QUARTER_CIRCLE * 4 - n]; + } + } + } + + /** + * Cosine of an angle. + * + * @see #QUARTER_CIRCLE + */ + public static int cos(int n) { + n &= FULL_CIRCLE_MASK; + if (n < QUARTER_CIRCLE * 2) { + if (n < QUARTER_CIRCLE) { + return SINE_TABLE[QUARTER_CIRCLE - n]; + } else { + return -SINE_TABLE[n - QUARTER_CIRCLE]; + } + } else { + if (n < QUARTER_CIRCLE * 3) { + return -SINE_TABLE[QUARTER_CIRCLE * 3 - n]; + } else { + return SINE_TABLE[n - QUARTER_CIRCLE * 3]; + } + } + } + + /** + * Tangent of an angle. + * + * @see #QUARTER_CIRCLE + */ + public static int tan(int n) { + return div(sin(n), cos(n)); + } + + /** + * Returns the arc tangent of an angle. + */ + public static int atan(int n) { + n = n + (1 << (ATAN_SHIFT - 1)) >> ATAN_SHIFT; + if (n < 0) { + if (n <= -ATAN_TABLE_LEN) { + return -(QUARTER_CIRCLE - 1); + } + return -ATAN_TABLE[-n]; + } else { + if (n >= ATAN_TABLE_LEN) { + return QUARTER_CIRCLE - 1; + } + return ATAN_TABLE[n]; + } + } + + /** + * Returns the polar angle of a rectangular coordinate. + */ + public static int atan(int x, int y) { + int n = atan(div(x, abs(y) + 1)); // kludge to prevent ArithmeticException + if (y > 0) { + return n; + } + if (y < 0) { + if (x < 0) { + return -QUARTER_CIRCLE * 2 - n; + } + if (x > 0) { + return QUARTER_CIRCLE * 2 - n; + } + return QUARTER_CIRCLE * 2; + } + if (x > 0) { + return QUARTER_CIRCLE; + } + return -QUARTER_CIRCLE; + } + + /** + * Rough calculation of the hypotenuse. Whilst not accurate it is very fast. + * <p> + * Derived from a piece in Graphics Gems. + */ + public static int hyp(int x1, int y1, int x2, int y2) { + if ((x2 -= x1) < 0) { + x2 = -x2; + } + if ((y2 -= y1) < 0) { + y2 = -y2; + } + return x2 + y2 - (((x2 > y2) ? y2 : x2) >> 1); + } + + /** + * Fixed point square root. + * <p> + * Derived from a 1993 Usenet algorithm posted by Christophe Meessen. + */ + public static int sqrt(int n) { + if (n <= 0) { + return 0; + } + long sum = 0; + int bit = 0x40000000; + while (bit >= 0x100) { // lower values give more accurate results + long tmp = sum | bit; + if (n >= tmp) { + n -= tmp; + sum = tmp + bit; + } + bit >>= 1; + n <<= 1; + } + return (int) (sum >> 16 - (FIXED_POINT / 2)); + } + + /** + * Returns the absolute value. + */ + public static int abs(int n) { + return (n < 0) ? -n : n; + } + + /** + * Returns the sign of a value, -1 for negative numbers, otherwise 1. + */ + public static int sgn(int n) { + return (n < 0) ? -1 : 1; + } + + /** + * Returns the minimum of two values. + */ + public static int min(int a, int b) { + return (a < b) ? a : b; + } + + /** + * Returns the maximum of two values. + */ + public static int max(int a, int b) { + return (a > b) ? a : b; + } + + /** + * Clamps the value n between min and max. + */ + public static int clamp(int n, int min, int max) { + return (n < min) ? min : (n > max) ? max : n; + } + + /** + * Wraps the value n between 0 and the required limit. + */ + public static int wrap(int n, int limit) { + return ((n %= limit) < 0) ? limit + n : n; + } + + /** + * Returns the nearest int to a fixed point value. Equivalent to <code> + * Math.round()</code> in the standard library. + */ + public static int round(int n) { + return n + HALF >> FIXED_POINT; + } + + /** + * Returns the nearest int rounded down from a fixed point value. + * Equivalent to <code>Math.floor()</code> in the standard library. + */ + public static int floor(int n) { + return n >> FIXED_POINT; + } + + /** + * Returns the nearest int rounded up from a fixed point value. + * Equivalent to <code>Math.ceil()</code> in the standard library. + */ + public static int ceil(int n) { + return n + (ONE - 1) >> FIXED_POINT; + } + + /** + * Returns a fixed point value greater than or equal to decimal 0.0 and + * less than 1.0 (in 16.16 format this would be 0 to 65535 inclusive). + */ + public static int rand() { + if (rng == null) { + rng = new Random(); + } + return rng.nextInt() >>> (32 - FIXED_POINT); + } + + /** + * Returns a random number between 0 and <code>n</code> (exclusive). + */ + public static int rand(int n) { + return (rand() * n) >> FIXED_POINT; + } +}
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