2.34.scm

;;;; 2.34
;; Evaluating a polynomial in $x$ at a given value of $x$ can be formulated as an accumulation. We evaluate the polynomial
;;
;; $$
;; a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0
;; $$
;;
;; using a well-known algorithm called *Horner's rule*, which structures the computation as
;;
;; $$
;; (\dots (a_n x + a_{n-1}) x + \dots + a_1) x + a_0
;; $$
;;
;; In other words, we start with $a_n$, multiply by $x$, add $a_{n-1}$, multiply by $x$, and so on, until we reach $a_0$. Fill in the following template to produce a procedure that evaluates a polynomial using Horner's rule. Assume that the coefficients of the polynomial are arranged in a sequence, from $a_0$ through $a_n$.
;;
;; (define (horner-eval x coefficient-sequence)
;;   (accumulate (lambda (this-coeff higher-terms) <??>)
;;               0
;;               coefficient-sequence))

;;; Answer
(load "0.efma.scm")
(define (horner-eval x coefficient-sequence)
  (accumulate (lambda (this-coeff higher-terms) (+ (* higher-terms x) this-coeff))
              0
              coefficient-sequence))

;; Test
(load "0.util.scm")
(test (horner-eval 2 (list 1 3 0 5 0 1)) 79)