| … | |
… | |
| 29 | (apply (lambda ,(cdadr dform) ,@(cddr dform)) (cdr ,form)))))) |
29 | (apply (lambda ,(cdadr dform) ,@(cddr dform)) (cdr ,form)))))) |
| 30 | |
30 | |
| 31 | ; Utilities for math. Notice that inexact->exact is primitive, |
31 | ; Utilities for math. Notice that inexact->exact is primitive, |
| 32 | ; but exact->inexact is not. |
32 | ; but exact->inexact is not. |
| 33 | (define exact? integer?) |
33 | (define exact? integer?) |
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|
34 | (define exact-integer? integer?) |
| 34 | (define (inexact? x) (and (real? x) (not (integer? x)))) |
35 | (define (inexact? x) (and (real? x) (not (integer? x)))) |
| 35 | (define (even? n) (= (remainder n 2) 0)) |
36 | (define (even? n) (= (remainder n 2) 0)) |
| 36 | (define (odd? n) (not (= (remainder n 2) 0))) |
37 | (define (odd? n) (not (= (remainder n 2) 0))) |
| 37 | (define (zero? n) (= n 0)) |
38 | (define (zero? n) (= n 0)) |
| 38 | (define (positive? n) (> n 0)) |
39 | (define (positive? n) (> n 0)) |
| … | |
… | |
| 41 | (define rational? real?) |
42 | (define rational? real?) |
| 42 | (define (abs n) (if (>= n 0) n (- n))) |
43 | (define (abs n) (if (>= n 0) n (- n))) |
| 43 | (define (exact->inexact n) (* n 1.0)) |
44 | (define (exact->inexact n) (* n 1.0)) |
| 44 | (define (<> n1 n2) (not (= n1 n2))) |
45 | (define (<> n1 n2) (not (= n1 n2))) |
| 45 | |
46 | |
| 46 | ; min and max must return inexact if any arg is inexact; use (+ n 0.0) |
47 | ; min and max must return inexact if any arg is inexact |
| 47 | (define (max . lst) |
48 | (define (max . lst) |
| 48 | (foldr (lambda (a b) |
49 | (foldr (lambda (a b) |
| 49 | (if (> a b) |
50 | (if (> a b) |
| 50 | (if (exact? b) a (+ a 0.0)) |
51 | (if (exact? b) a (exact->inexact a)) |
| 51 | (if (exact? a) b (+ b 0.0)))) |
52 | (if (exact? a) b (exact->inexact b)))) |
| 52 | (car lst) (cdr lst))) |
53 | (car lst) (cdr lst))) |
| 53 | (define (min . lst) |
54 | (define (min . lst) |
| 54 | (foldr (lambda (a b) |
55 | (foldr (lambda (a b) |
| 55 | (if (< a b) |
56 | (if (< a b) |
| 56 | (if (exact? b) a (+ a 0.0)) |
57 | (if (exact? b) a (exact->inexact a)) |
| 57 | (if (exact? a) b (+ b 0.0)))) |
58 | (if (exact? a) b (exact->inexact b)))) |
| 58 | (car lst) (cdr lst))) |
59 | (car lst) (cdr lst))) |
| 59 | |
60 | |
| 60 | (define (succ x) (+ x 1)) |
61 | (define (succ x) (+ x 1)) |
| 61 | (define (pred x) (- x 1)) |
62 | (define (pred x) (- x 1)) |
| 62 | (define gcd |
63 | (define gcd |
