Fast gaussian kernel function
Fragment of a discussion from User talk:Rednaxela/FastTrig
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That "get rid of divisions" tip doubled the speed of my bot. O.o'
And for a mathematical purism, returning the value at the boundaries as minimum to keep the function smooth:
private static final double SQRT_2_PI_INVERSE = 1 / Math.sqrt(2 * Math.PI);
private static final double EXP_LIMIT = 700;
private static final double GAUSSIAN_LIMIT = Math.sqrt(EXP_LIMIT * 2);
private static final double MIN_GAUSSIAN_VALUE = gaussian(GAUSSIAN_LIMIT);
public static double gaussian(final double u) {
if (u > GAUSSIAN_LIMIT || u < -GAUSSIAN_LIMIT) {
return MIN_GAUSSIAN_VALUE;
}
return exp(u * u * -0.5) * SQRT_2_PI_INVERSE;
}
public static double exp(final double val) {
final long tmp = (long) (1512775 * val + 1072632447);
return Double.longBitsToDouble(tmp << 32);
}MN
