raku-rosettacode/programming_tasks/H/Horner's_rule_for_polynomial_evaluation.md

Horner's rule for polynomial evaluation

sub horner ( @coeffs, $x ) {
    @coeffs.reverse.reduce: { $^a * $x + $^b };
}
 
say horner( [ -19, 7, -4, 6 ], 3 );

A recursive version would spare us the need for reversing the list of coefficients. However, special care must be taken in order to write it, because the way Perl 6 implements lists is not optimized for this kind of treatment. Lisp-style lists are, and fortunately it is possible to emulate them with Pairs and the reduction meta-operator:

multi horner(Numeric $c, $) { $c }
multi horner(Pair $c, $x) {
    $c.key + $x * horner( $c.value, $x ) 
}
 
say horner( [=>](-19, 7, -4, 6 ), 3 );

We can also use the composition operator:

sub horner ( @coeffs, $x ) {
    ([o] map { $_ + $x * * }, @coeffs)(0);
}
 
say horner( [ -19, 7, -4, 6 ], 3 );

Output:

128

One advantage of using the composition operator is that it allows for the use of an infinite list of coefficients.

sub horner ( @coeffs, $x ) {
    map { .(0) }, [\o] map { $_ + $x * * }, @coeffs;
}
 
say horner( [ 1 X/ (1, |[\*] 1 .. *) ], i*pi )[20];
 

Output:

-0.999999999924349-5.28918515954219e-10i