                C++ Toolbox for Verified Computing I
                       Basic Numerical Problems

    Copyright (c) 1995 Rolf Hammer, Matthias Hocks, Dietmar Ratz

The function RPolyeval(p,t) evaluates the real polynomial p at t at maximum
accuracy, even in the neighborhood of a root where cancellation dooms an
ordinary floating-point evaluation. 

The function returns a vector with the entries [y;iy;it;err] where y is the
result of a Horner scheme evaluation, iy represents a maximum accuracy
enclosure, it the number of iterations needed and err an eventual error
message. The function rpeval(p,t) just returns the resulting interval.

  >X=poly("X");
  >p=(X-2)^4
   X^4-8*X^3+24*X^2-32*X+16
  >p(2.0001)
   -3.5527136788E-015
  >RPolyEval(p,2.0001)
   [-3.5527136788E-015;[1.0000000000E-016,1.0000000001E-016];2;""]
  >rpeval(p,2.0001)
   [1.0000000000E-016,1.0000000001E-016]