The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Polynomial evaluation via the division algorithm the fast Fourier transform revisited
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
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The reverse of an nth degree polynomial p(x) is rev(p) (x) = xnp(x-1). We show that one can evaluate p and rev(p) in only n+0(log n) multiplications modulo {x-1}. The method uses an algorithm to evaluate reciprocal polynomials of degree n in only [n/2] + 1 + l([n/2]) multiplications modulo {x-1}, where l(k) denotes the length of a shortest addition chain for k.