  A solution for Smale's 17th problem, for the case of systems with bounded
degree was recently given. This solution, an algorithm computing approximate
zeros of complex polynomial systems in average polynomial time, assumed
infinite precision. In this paper we describe a finite-precision version of
this algorithm. Our main result shows that this version works within the same
time bounds and requires a precision which, on the average, amounts to a
polynomial amount of bits in the mantissa of the intervening floating-point
numbers.
