here is what I was thinking prior to this: locally a torus is a square.
Assume that (p,p), where p=(1,0) is regular value.
So we can apply local degree theorem here.
Take a chart (t,s)|--->(exp(it), exp(is))
Calculations would give restriction on a,b,c,d. More precisely, a^2+b^2=1, c^2+d^2=1.
So Jac determinant of the composition chart \circ f\circ chart inverse is +1 or -1 depending upon the cases.
So degree (f) should be 1 or -1 depending upong a,b,c,d where a,b,c,d lie in {-1,0,1}.
but this is wrong because a,b,c,d are not restricted.