Round down Integer to odd number.

Should this also apply to zero and negative integers?

At least that's  what your description demands and what Terry's solution provides.

BTW, if your inputs are only integers, you may also omit the "floor" functions:

If you intend to use the function for positive integers only, you may also try this:

Note the capital "R" in "Round". You see that the result for negative odd inputs is 'wrong'.

In case you rather intend to round "in the direction of zero" (basically apply the rounding to the absolute value of the input) you may use

Of course you get the same result with

And at last here is an alternative function doing exactly what you demanded (and what Terry's function also provides)