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|
#lang racket
(provide install-rational)
(require "../../../shared/data-directed-programming.rkt")
(define (install-rational get put apply-fn)
;; import generic methods
(define (=zero? a)
(apply-fn '=zero? a))
(define (equ? a b)
(apply-fn 'equ? a b))
(define (add a b)
(apply-fn 'add a b))
(define (neg a)
(apply-fn 'neg a))
(define (sub a b)
(apply-fn 'sub a b))
(define (mul a b)
(apply-fn 'mul a b))
(define (div a b)
(apply-fn 'div a b))
(define (cos a)
(apply-fn 'cos a))
(define (sin a)
(apply-fn 'sin a))
(define (sqr a)
(apply-fn 'sqr a))
(define (sqrt a)
(apply-fn 'sqrt a))
(define (atan a b)
(apply-fn 'atan a b))
;; constructor and selectors
(define (make-rat n d) (list n d))
(define (numer x) (car x))
(define (denom x) (cadr x))
;; ops
(define (add-rat x y)
(make-rat (add (mul (numer x) (denom y))
(mul (numer y) (denom x)))
(mul (denom x) (denom y))))
(define (neg-rat rat)
(make-rat (neg (numer rat))
(denom rat)))
(define (sub-rat x y)
(make-rat (sub (mul (numer x) (denom y))
(mul (numer y) (denom x)))
(mul (denom x) (denom y))))
(define (mul-rat x y)
(make-rat (mul (numer x) (numer y))
(mul (denom x) (denom y))))
(define (div-rat x y)
(make-rat (mul (numer x) (denom y))
(mul (denom x) (numer y))))
(define (equ?-rat x y)
(and (equ? (numer x) (numer y))
(equ? (denom x) (denom y))))
(define (=zero?-rat x)
(=zero? (numer x)))
(define (make-rat-reduce-lowest-terms n d)
(define (sign x)
(cond
((and (< x 0) (< d 0)) (* -1 x))
((and (< 0 x) (< d 0)) (* -1 x))
(else x)))
(let ((g (gcd n d)))
(cons (sign (/ n g)) (abs (/ d g)))))
(define (raiseme rat)
((get 'make 'real) (/ (numer rat) (denom rat))))
;; constructor
(put 'make 'rational
(lambda (x y) (tagme (make-rat x y))))
;; interface
(define (tagme x) (attach-tag 'rational x))
(put 'add '(rational rational)
(lambda (x y) (tagme (add-rat x y))))
(put 'neg '(rational)
(lambda (rat) (tagme (neg-rat rat))))
(put 'sub '(rational rational)
(lambda (x y) (tagme (sub-rat x y))))
(put 'mul '(rational rational)
(lambda (x y) (tagme (mul-rat x y))))
(put 'div '(rational rational)
(lambda (x y) (tagme (div-rat x y))))
(put 'raise '(rational) raiseme)
(put 'project '(rational) (lambda (rat)
((get 'make 'integer) (/ (numer rat) (denom rat)))))
;; sqrt and trig methods for complex nums
(put 'sqr '(rational) (lambda (r) (sqr (raiseme r))))
(put 'sqrt '(rational) (lambda (r) (sqrt (raiseme r))))
(put 'cos '(rational) (lambda (r) (cos (raiseme r))))
(put 'sin '(rational) (lambda (r) (sin (raiseme r))))
(put 'atan '(rational rational) (lambda (r1 r2) (atan (raiseme r1) (raiseme r2))))
;; predicates
(put 'equ? '(rational rational)
(lambda (x y) (equ?-rat x y)))
(put '=zero? '(rational)
(lambda (x) (=zero?-rat x)))
'done)
|
