Horner's rule for polynomial evaluation: Difference between revisions

Horner's rule for polynomial evaluation (view source)

267 bytes added , 8 years ago

→‎{{header|Perl 6}}: showing a version with potentially infinite list of coefficients

1,935

edits

Revision as of 18:43, 5 October 2015 (view source) Grondilu (talk \| contribs) (→‎{{header\|Perl 6}}: restoring alternate solution using composition operator) ← Older edit		Revision as of 19:13, 6 October 2015 (view source) Grondilu (talk \| contribs) (→‎{{header\|Perl 6}}: showing a version with potentially infinite list of coefficients) Newer edit →
Line 1,143: say horner( [ -19, 7, -4, 6 ], 3 );</lang> A recursive version would spare us the need for reversing the list of ~~coeffcients (and thus possibly allowing progressive evaluation with lazy lists?)~~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 [http://doc.perl6.org/type/Pair Pairs] and the reduction meta-operator: <lang perl6>multi horner(Numeric $c, $) { $c } Line 1,161: {{out}} <pre>128</pre> One advantage of using the composition operator is that it allows for the use of an infinite list of coefficients. <lang perl6>sub horner ( @coeffs, $x ) { map { .(0) }, [\o] map { $_ + $x * * }, @coeffs; } say horner( [ 1 X/ (1, \|[\] 1 .. ) ], i*pi )[20]; </lang> {{out}} <pre>-0.999999999924349-5.28918515954219e-10i</pre> =={{header\|PHP}}==