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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 thirtyone)
#:export (product product-iter factorial factorial-iter pi pi-iter))
(define (product term a next b)
(if (> a b)
1
(* (term a)
(product term (next a) next b))))
(define (product-iter term a next b)
(define (iter a result)
(if (> a b)
result
(iter (next a) (* (term a) result))))
(iter a 1))
(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 (pi precision)
(let* ((n (lambda (x) (* (+ (quotient x 2) 1) 2))) ; numerator of term.
(d (lambda (x) (+ (* (quotient (1+ x) 2) 2) 1))) ; denominator of term.
(term (lambda (x) (/ (* (n x) 1.0) (* (d x) 1.0))))
(next (lambda (x) (1+ x))))
(* (product term 1 next precision) 4)))
(define (pi-iter precision)
(let* ((n (lambda (x) (* (+ (quotient x 2) 1) 2))) ; numerator of term.
(d (lambda (x) (+ (* (quotient (1+ x) 2) 2) 1))) ; denominator of term.
(term (lambda (x) (/ (* (n x) 1.0) (* (d x) 1.0))))
(next (lambda (x) (1+ x))))
(* (product-iter term 1 next precision) 4)))
;;; Guile REPL
;;; scheme@(guile-user)> ,use (net ricketyspace sicp one thirtyone)
;;; scheme@(guile-user)> (factorial 5)
;;; $19 = 120
;;; scheme@(guile-user)> (factorial-iter 5)
;;; $20 = 120
;;; scheme@(guile-user)> (factorial 10)
;;; $21 = 3628800
;;; scheme@(guile-user)> (factorial-iter 10)
;;; $22 = 3628800
;;; scheme@(guile-user)> (factorial 20)
;;; $23 = 2432902008176640000
;;; scheme@(guile-user)> (factorial-iter 20)
;;; $24 = 2432902008176640000
;;; scheme@(guile-user)> (pi 1000)
;;; $25 = 3.143160705532257
;;; scheme@(guile-user)> (pi-iter 1000)
;;; $26 = 3.1431607055322552
;;; scheme@(guile-user)> (pi 10000)
;;; $27 = 3.1417497057379635
;;; scheme@(guile-user)> (pi-iter 10000)
;;; $28 = 3.1417497057380084
;;; scheme@(guile-user)> (pi 100000)
;;; $29 = 3.1416083612780903
;;; scheme@(guile-user)> (pi-iter 100000)
;;; $30 = 3.141608361277941
;;; scheme@(guile-user)> (pi 1000000)
;;; $31 = 3.1415942243828017
;;; scheme@(guile-user)> (pi-iter 1000000)
;;; $32 = 3.141594224382854
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