See http://en.wikipedia.org/wiki/Continued_fraction:

"Every finite continued fraction represents a rational number, and every rational number can be represented in precisely two different ways as a finite continued fraction, with the conditions that the first coefficient is an integer and other coefficients being positive integers."

Also, "To calculate a continued fraction representation of a number r, write down the integer part (technically the *floor*) of r. Subtract this integer part from r..."  [emphasis added].

The canonical representation of a continued fraction puts all the negative in the first element.  The other CF functions here will work fine with nonpositive elements, and even non-integer elements.