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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 thirtytwo)
#:export (factorial factorial-iter simpson simpson-iter))
(define (accumulate combiner null-value term a next b)
(if (> a b)
null-value
(combiner (term a)
(accumulate combiner null-value term (next a) next b))))
(define (accumulate-iter combiner null-value term a next b)
(define (iter a result)
(if (> a b)
result
(iter (next a) (combiner (term a) result))))
(iter a null-value))
(define (product term a next b)
(accumulate * 1 term a next b))
(define (product-iter term a next b)
(accumulate-iter * 1 term a next b))
(define (factorial n)
(let ((term (lambda (x) x))
(next (lambda (x) (1+ x))))
(product term 1 next n)))
(define (factorial-iter n)
(let ((term (lambda (x) x))
(next (lambda (x) (1+ x))))
(product-iter term 1 next n)))
(define (sum term a next b)
(accumulate + 0 term a next b))
(define (sum-iter term a next b)
(accumulate-iter + 0 term 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))))
(define (simpson-iter 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-iter term 0 next n))))
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