142 lines
3.7 KiB
Scheme
142 lines
3.7 KiB
Scheme
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; Copyright (c) 1993-1999 by Richard Kelsey and Jonathan Rees. See file COPYING.
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; This is file ratnum.scm.
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; Rational arithmetic
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; Assumes that +, -, etc. perform integer arithmetic.
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(define-simple-type :exact-rational (:rational :exact)
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(lambda (n) (and (rational? n) (exact? n))))
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(define-extended-number-type :ratnum (:exact-rational :exact) ;?
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(make-ratnum num den)
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ratnum?
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(num ratnum-numerator)
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(den ratnum-denominator))
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(define (integer/ m n)
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(cond ((< n 0)
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(integer/ (- 0 m) (- 0 n)))
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((= n 0)
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(error "rational division by zero" m))
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((and (exact? m) (exact? n))
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(let ((g (gcd m n)))
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(let ((m (quotient m g))
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(n (quotient n g)))
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(if (= n 1)
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m
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(make-ratnum m n)))))
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(else (/ m n)))) ;In case we get flonums
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(define (rational-numerator p)
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(if (ratnum? p)
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(ratnum-numerator p)
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(numerator p)))
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(define (rational-denominator p)
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(if (ratnum? p)
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(ratnum-denominator p)
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(denominator p)))
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; a/b * c/d = a*c / b*d
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(define (rational* p q)
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(integer/ (* (rational-numerator p) (rational-numerator q))
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(* (rational-denominator p) (rational-denominator q))))
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; a/b / c/d = a*d / b*c
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(define (rational/ p q)
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(integer/ (* (rational-numerator p) (rational-denominator q))
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(* (rational-denominator p) (rational-numerator q))))
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; a/b + c/d = (a*d + b*c)/(b*d)
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(define (rational+ p q)
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(let ((b (rational-denominator p))
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(d (rational-denominator q)))
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(integer/ (+ (* (rational-numerator p) d)
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(* b (rational-numerator q)))
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(* b d))))
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; a/b - c/d = (a*d - b*c)/(b*d)
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(define (rational- p q)
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(let ((b (rational-denominator p))
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(d (rational-denominator q)))
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(integer/ (- (* (rational-numerator p) d)
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(* b (rational-numerator q)))
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(* b d))))
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; a/b < c/d when a*d < b*c
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(define (rational< p q)
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(< (* (rational-numerator p) (rational-denominator q))
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(* (rational-denominator p) (rational-numerator q))))
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; a/b = c/d when a = b and c = d (always lowest terms)
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(define (rational= p q)
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(and (= (rational-numerator p) (rational-numerator q))
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(= (rational-denominator p) (rational-denominator q))))
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; (rational-truncate p) = integer of largest magnitude <= (abs p)
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(define (rational-truncate p)
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(quotient (rational-numerator p) (rational-denominator p)))
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; (floor p) = greatest integer <= p
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(define (rational-floor p)
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(let* ((n (numerator p))
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(q (quotient n (denominator p))))
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(if (>= n 0)
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q
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(- q 1))))
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; Extend the generic number procedures
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(define-method &rational? ((n :ratnum)) #t)
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(define-method &numerator ((n :ratnum)) (ratnum-numerator n))
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(define-method &denominator ((n :ratnum)) (ratnum-denominator n))
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(define-method &exact? ((n :ratnum)) #t)
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;(define-method &exact->inexact ((n :ratnum))
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; (/ (exact->inexact (numerator n))
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; (exact->inexact (denominator n))))
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;(define-method &inexact->exact ((n :rational)) ;?
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; (/ (inexact->exact (numerator n))
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; (inexact->exact (denominator n))))
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(define-method &/ ((m :exact-integer) (n :exact-integer))
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(integer/ m n))
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(define (define-ratnum-method mtable proc)
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(define-method mtable ((m :ratnum) (n :exact-rational)) (proc m n))
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(define-method mtable ((m :exact-rational) (n :ratnum)) (proc m n)))
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(define-ratnum-method &+ rational+)
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(define-ratnum-method &- rational-)
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(define-ratnum-method &* rational*)
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(define-ratnum-method &/ rational/)
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(define-ratnum-method &= rational=)
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(define-ratnum-method &< rational<)
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(define-method &floor ((m :ratnum)) (rational-floor m))
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;(define-method &sqrt ((p :ratnum))
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; (if (< p 0)
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; (next-method)
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; (integer/ (sqrt (numerator p))
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; (sqrt (denominator p)))))
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(define-method &number->string ((p :ratnum) radix)
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(string-append (number->string (ratnum-numerator p) radix)
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"/"
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(number->string (ratnum-denominator p) radix)))
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