The floating-point implementation of a function on an interval often reduces
to polynomial approximation, the polynomial being typically provided by Remez
algorithm. However, the floating-point evaluation of a Remez polynomial
sometimes leads to catastrophic cancellations. This happens when some of the
polynomial coefficients are very small in magnitude with respects to others. In
this case, it is better to force these coefficients to zero, which also reduces
the operation count. This technique, classically used for odd or even
functions, may be generalized to a much larger class of functions. An algorithm
is presented that forces to zero the smaller coefficients of the initial
polynomial thanks to a modified Remez algorithm targeting an incomplete
monomial basis. One advantage of this technique is that it is purely numerical,
the function being used as a numerical black box. This algorithm is implemented
within a larger polynomial implementation tool that is demonstrated on a range
of examples, resulting in polynomials with less coefficients than those
obtained the usual way.Comment: 12 page
