How to resolve the algorithm Horner's rule for polynomial evaluation step by step in the Lambdatalk programming language

Published on 12 May 2024 09:40 PM
#Lambdatalk

How to resolve the algorithm Horner's rule for polynomial evaluation step by step in the Lambdatalk programming language

Table of Contents

Problem Statement

A fast scheme for evaluating a polynomial such as: when is to arrange the computation as follows: And compute the result from the innermost brackets outwards as in this pseudocode: Task Description Cf. Formal power series

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Horner's rule for polynomial evaluation step by step in the Lambdatalk programming language

Source code in the lambdatalk programming language

{def horner
 {def horner.r
  {lambda {:p :x :r}
   {if {A.empty? :p}
    then :r
    else {horner.r {A.rest :p} :x {+ {A.first :p} {* :x :r}}}}}}
 {lambda {:p :x}
  {horner.r {A.reverse :p} :x 0}}}

{horner {A.new -19 7 -4 6} 3}
-> 128

{def φ {/ {+ 1 {sqrt 5}} 2}} = 1.618033988749895
{horner {A.new -1 -1 1} φ}
-> 2.220446049250313e-16 ~ 0

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