Fast sqrt in Java at the expense of accuracy

Question

I am looking for a fast square root implementation in Java for double values in the input range of [0, 2*10^12]. For any value in this range, the precision should be upto 5

Answer 1

Try this

double d = 289358932.0;
double sqrt = Double.longBitsToDouble( ( ( Double.doubleToLongBits( d )-(1l<<52) )>>1 ) + ( 1l<<61 ) );

I haven't benchmarked it, but I'd expect it to be faster. The accuracy isn't extremely good, but try it out and see if it meets your needs. I think you can add an additional bias term a to the end of the expression to make it more accurate.

EDIT: You can drastically improve the accuracy by passing it through a round or two of Newton's method

double better = (sqrt + d/sqrt)/2.0;
double evenbetter = (better + d/better)/2.0;

The second pass gives you almost the exact value of the square root.

sqrt            17022.533813476562
better          17010.557763511835
evenbetter      17010.553547724947
Math.sqrt()     17010.553547724423