diff options
Diffstat (limited to 'net')
| -rw-r--r-- | net/ricketyspace/sicp/one/thirtytwo.scm | 33 |
1 files changed, 32 insertions, 1 deletions
diff --git a/net/ricketyspace/sicp/one/thirtytwo.scm b/net/ricketyspace/sicp/one/thirtytwo.scm index 6287353..f76b2ed 100644 --- a/net/ricketyspace/sicp/one/thirtytwo.scm +++ b/net/ricketyspace/sicp/one/thirtytwo.scm @@ -3,7 +3,7 @@ ;;;; <https://creativecommons.org/licenses/by-sa/4.0/>. (define-module (net ricketyspace sicp one thirtytwo) - #:export (factorial simpson)) + #:export (factorial factorial-iter simpson simpson-iter)) (define (accumulate combiner null-value term a next b) (if (> a b) @@ -11,17 +11,35 @@ (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)))) @@ -34,3 +52,16 @@ (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)))) |