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Continued fraction/Arithmetic/Construct from rational number: Difference between revisions
Continued fraction/Arithmetic/Construct from rational number (view source)
Revision as of 20:44, 27 June 2022
, 1 year agoAdded a Scheme implementation.
(→{{header|ALGOL 68}}: Let's use the Algol 68 MOD operator after all) |
(Added a Scheme implementation.) |
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[3, 7, 476190, 3]
[3, 7, 7142857]
</pre>
=={{header|Scheme}}==
{{works with|Chez Scheme}}
'''The Implementation'''
<lang scheme>; Create a terminating Continued Fraction generator for the given rational number.
; Returns one term per call; returns #f when no more terms remaining.
(define make-continued-fraction-gen
(lambda (rat)
(let ((num (numerator rat)) (den (denominator rat)))
(lambda ()
(if (= den 0)
#f
(let ((ret (quotient num den))
(rem (modulo num den)))
(set! num den)
(set! den rem)
ret))))))
; Return the continued fraction representation of a rational number as a string.
(define rat->cf-string
(lambda (rat)
(let* ((cf (make-continued-fraction-gen rat))
(str (string-append "[" (format "~a" (cf))))
(sep ";"))
(let loop ((term (cf)))
(when term
(set! str (string-append str (format "~a ~a" sep term)))
(set! sep ",")
(loop (cf))))
(string-append str "]"))))
; Return the continued fraction representation of a rational number as a list of terms.
(define rat->cf-list
(lambda (rat)
(let ((cf (make-continued-fraction-gen rat))
(lst '()))
(let loop ((term (cf)))
(when term
(set! lst (append lst (list term)))
(loop (cf))))
lst)))</lang>
'''The Task'''
<br />
Each continued fraction is displayed in both the conventional written form and as a list of terms.
<lang scheme>(printf "~%Basic examples:~%")
(for-each
(lambda (rat)
(printf "~a = ~a~%" rat (rat->cf-string rat))
(printf "~a : ~a~%" rat (rat->cf-list rat)))
'(1/2 3 23/8 13/11 22/7 -151/77 0))
(printf "~%Root2 approximations:~%")
(for-each
(lambda (rat)
(printf "~a = ~a~%" rat (rat->cf-string rat))
(printf "~a : ~a~%" rat (rat->cf-list rat)))
'(14142/10000 141421/100000 1414214/1000000 14142136/10000000 141421356237/100000000000))
(printf "~%Pi approximations:~%")
(for-each
(lambda (rat)
(printf "~a = ~a~%" rat (rat->cf-string rat))
(printf "~a : ~a~%" rat (rat->cf-list rat)))
'(31/10 314/100 3142/1000 31428/10000 314285/100000 3142857/1000000
31428571/10000000 314285714/100000000 31415926535898/10000000000000))</lang>
{{out}}
<pre>
Basic examples:
1/2 = [0; 2]
1/2 : (0 2)
3 = [3]
3 : (3)
23/8 = [2; 1, 7]
23/8 : (2 1 7)
13/11 = [1; 5, 2]
13/11 : (1 5 2)
22/7 = [3; 7]
22/7 : (3 7)
-151/77 = [-1; 25, 1, 2]
-151/77 : (-1 25 1 2)
0 = [0]
0 : (0)
Root2 approximations:
7071/5000 = [1; 2, 2, 2, 2, 2, 1, 1, 29]
7071/5000 : (1 2 2 2 2 2 1 1 29)
141421/100000 = [1; 2, 2, 2, 2, 2, 2, 3, 1, 1, 3, 1, 7, 2]
141421/100000 : (1 2 2 2 2 2 2 3 1 1 3 1 7 2)
707107/500000 = [1; 2, 2, 2, 2, 2, 2, 2, 3, 6, 1, 2, 1, 12]
707107/500000 : (1 2 2 2 2 2 2 2 3 6 1 2 1 12)
1767767/1250000 = [1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 1, 2, 4, 1, 1, 2]
1767767/1250000 : (1 2 2 2 2 2 2 2 2 2 6 1 2 4 1 1 2)
141421356237/100000000000 = [1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 4, 1, 2, 1, 63, 2, 1, 1, 1, 4, 2]
141421356237/100000000000 : (1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 4 1 2 1 63 2 1 1 1 4 2)
Pi approximations:
31/10 = [3; 10]
31/10 : (3 10)
157/50 = [3; 7, 7]
157/50 : (3 7 7)
1571/500 = [3; 7, 23, 1, 2]
1571/500 : (3 7 23 1 2)
7857/2500 = [3; 7, 357]
7857/2500 : (3 7 357)
62857/20000 = [3; 7, 2857]
62857/20000 : (3 7 2857)
3142857/1000000 = [3; 7, 142857]
3142857/1000000 : (3 7 142857)
31428571/10000000 = [3; 7, 476190, 3]
31428571/10000000 : (3 7 476190 3)
157142857/50000000 = [3; 7, 7142857]
157142857/50000000 : (3 7 7142857)
15707963267949/5000000000000 = [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 21, 17, 1, 1, 1, 1, 8, 1, 7, 2, 1, 2, 2]
15707963267949/5000000000000 : (3 7 15 1 292 1 1 1 2 1 3 1 21 17 1 1 1 1 8 1 7 2 1 2 2)
</pre>
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