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;;;; Under Creative Commons Attribution-ShareAlike 4.0
;;;; International. See
;;;; <https://creativecommons.org/licenses/by-sa/4.0/>.
(define-module (net ricketyspace sicp one twentynine)
#:export (simpson))
(define (sum term a next b)
(if (> a b)
0
(+ (term a)
(sum term (next a) next b))))
(define (simpson f a b n)
(let* ((h (/ (- b a) (* 1.0 n)))
(y (lambda (k) (+ a (* k h))))
(ce (lambda (k) ;coefficient
(cond ((or (= k 0) (= k n)) 1)
((even? k) 2)
(else 4))))
(term (lambda (k)
(* (ce k) (f (y k)))))
(next (lambda (k) (1+ k))))
(* (/ h 3.0)
(sum term 0 next n))))
;;; Guile REPL
;;; scheme@(guile-user)> ,use (net ricketyspace sicp one twentynine)
;;; scheme@(guile-user)> (define (cube x) (* x x x))
;;; scheme@(guile-user)> (simpson cube 0 1 100)
;;; $23 = 0.24999999999999992
;;; scheme@(guile-user)> (simpson cube 0 1 1000)
;;; $24 = 0.2500000000000003
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