Types of rounding in coefficients quantization
The various rounding methods have a computation vs. quantization error tradeoff.

Truncate

Truncation is the simplest method.  Everything after the decimal point is simply lopped off.  For instance, both 2.1 and 2.9 become 2.  This is very simple, but is the worst method in terms of quantization error.  It is particularly bad because when you are dealing with non-negative numbers it introduces a strong negative bias.  In some algorithms that can be bad.

Round/Convergent Rounding

Simply saying "Round" doesn't tell you enough to know what is meant.  What kind of rounding?  People usually mean convergent rounding when they say "round", so I will assume that that is what is meant.

Convergent rounding rounds down when the decimal place is $\le .499\overline{9}$ and rounds up when the decimal place is $\ge .500\overline{0}1$.  The question remains- what to do when you have exactly $.5$?  Some rounding algorithms always round down (this is called "round-to-zero"), but that introduces a very small amount of bias.  Convergent rounding tries to eliminate the bias by rounding to the nearest even number, the assumption being that around half the time that will be up and half the time it will be down.

This is the best algorithm in terms of quantization noise, but is the most computationally intense.  In many situations though, you don't care how computationally intense it is since the calculation isn't done at run-time.

Round-to-Zero

As mentioned previously, round-to-zero is the same as convergent rounding except it always rounds towards zero when the decimal portion is $.5$.  This is a compromise between truncation (easy computationally) and convergent rounding (low quantization error).