109 lines
3.2 KiB
Scheme
109 lines
3.2 KiB
Scheme
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; Copyright (c) 1993-1999 by Richard Kelsey and Jonathan Rees. See file COPYING.
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; Inexact numbers as mere shells surrounding exact numbers.
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(define-extended-number-type :innum (:inexact)
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(make-innum exact)
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innum?
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(exact innum-exact))
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(define-method &exact? ((n :innum)) #f)
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(define-method &complex? ((n :innum)) (complex? (innum-exact n)))
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(define-method &real? ((n :innum)) (real? (innum-exact n)))
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(define-method &rational? ((n :innum)) (rational? (innum-exact n)))
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(define-method &integer? ((n :innum)) (integer? (innum-exact n)))
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(define-method &exact->inexact (n)
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(if (innum? n)
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(next-method)
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(make-innum n)))
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(define-method &inexact->exact ((n :innum)) (innum-exact n))
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(define (inexactify n)
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(if (exact? n)
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(exact->inexact n)
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n))
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(define (define-innum-method mtable proc)
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(define-method mtable ((m :innum) (n :number))
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(inexactify (proc (innum-exact m) n)))
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(define-method mtable ((m :number) (n :innum))
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(inexactify (proc m (innum-exact n)))))
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(define-innum-method &+ +)
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(define-innum-method &- -)
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(define-innum-method &* *)
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(define-innum-method &/ /)
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(define-innum-method "ient quotient)
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(define-innum-method &remainder remainder)
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(define (define-innum-comparison mtable proc)
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(define-method mtable ((m :innum) (n :number))
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(proc (innum-exact m) n))
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(define-method mtable ((m :number) (n :innum))
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(proc m (innum-exact n))))
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(define-innum-comparison &= =)
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(define-innum-comparison &< <)
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(define-method &numerator ((n :innum))
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(inexactify (numerator (innum-exact n))))
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(define-method &denominator ((n :innum))
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(inexactify (denominator (innum-exact n))))
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(define-method &floor ((n :innum))
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(inexactify (floor (innum-exact n))))
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(define-method &number->string ((i :innum) radix)
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(let ((n (innum-exact i)))
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(cond ((integer? n)
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(string-append (number->string n radix) "."))
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((rational? n)
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(let ((q (denominator n)))
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(if (= radix 10)
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(let ((foo (decimable? q)))
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(if foo
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(decimal-representation (numerator n) q foo)
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(string-append "#i" (number->string n radix))))
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(string-append "#i" (number->string n radix)))))
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(else
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(string-append "#i" (number->string n radix))))))
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; The Scheme report obligates us to print inexact rationals using
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; decimal points whenever this can be done without losing precision.
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(define (decimal-representation p q foo)
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(let ((kludge (number->string (* (car foo) (abs (remainder p q)))
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10)))
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(string-append (if (< p 0) "-" "")
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(number->string (quotient (abs p) q) 10)
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"."
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(string-append (do ((i (- (cdr foo) (string-length kludge))
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(- i 1))
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(l '() (cons #\0 l)))
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((<= i 0) (list->string l)))
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kludge))))
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(define (ratio-string p q radix)
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(string-append (number->string p radix)
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"/"
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(number->string q radix)))
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; (decimable? n) => non-#f iff n is a product of 2's and 5's.
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; The value returned is (k . i) such that 10^i divides n * k.
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(define (decimable? n)
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(let loop ((n n) (d 1) (i 0))
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(if (= n 1)
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(cons d i)
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(let ((q (quotient n 10))
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(r (remainder n 10)))
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(cond ((= r 0) (loop q d (+ i 1)))
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((= r 5) (loop (quotient n 5) (* d 2) (+ i 1)))
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((even? r) (loop (quotient n 2) (* d 5) (+ i 1)))
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(else #f))))))
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