/sci/ - Science & Math

[GOMADWarrior No.5160579]

rate this algorithm to find arctg

function arctg(t, dtheta)
{ for (theta=0; tan(theta) < t; theta += dtheta) ;
return theta;
}

[Anonymous No.5160615]

>>5160579
Pretty poor, you have O(1/dtheta) computations of tan(theta) for a O(dtheta) relative precision, and relative precision is useless near -1 and 1 because you'd want a relative precision of the distance to -1 (or 1). For instance, if arctan(t) = 1 - 10^(-100), then you will need dtheta around 10^(-100) to have a good idea of arctan(t), and the program will terminate in 10^100 steps. If you take a smaller precision, you will only know that arctan(t) is close to 1, but not how close to 1 it is. The least you could do if you want to use this kind of algorithm is make the precision parameter decay exponentially as you get closer to -1 or 1.

[Anonymous No.5160661]

>>5160615

This.

[Anonymous No.5160666]

Bad.
Learn about series expansion.