41 lines
1.2 KiB
Scheme
41 lines
1.2 KiB
Scheme
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(load "stream.scm")
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;
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; Given a continued fraction in the form of a stream of
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; integers, return the stream of convergents. (The stream
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; actually returns a list (num denom quotient) ).
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;
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(define (cf->convergents cf-stream)
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(define (produce n-2 n-1 rest)
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(let ((nextval (+ (* n-1 (stream-car rest)) n-2)))
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(cons-stream nextval (produce n-1 nextval (stream-cdr rest)))))
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(define (cf-num cf-stream)
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(let* ((a0 (stream-car cf-stream))
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(a1 (stream-car (stream-cdr cf-stream)))
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(n1 (+ (* a0 a1) 1))
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(rest (stream-cdr (stream-cdr cf-stream))))
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(cons-stream a0 (cons-stream n1 (produce a0 n1 rest)))))
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(define (cf-denom cf-stream)
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(let ((a0 1)
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(a1 (stream-car (stream-cdr cf-stream)))
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(rest (stream-cdr (stream-cdr cf-stream))))
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(cons-stream a0 (cons-stream a1 (produce a0 a1 rest)))))
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(stream-map (lambda (n d) (list n d (/ n d)))
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(cf-num cf-stream)
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(cf-denom cf-stream)))
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(define ones (cons-stream 1 ones))
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(define twos (cons-stream 2 twos))
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(define onetwo (interleave ones twos))
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(display-stream-n ones 5)
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(display-stream-n (cf->convergents ones) 40)
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(display (/ (+ 1 (sqrt 5)) 2))
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(display-stream-n (cf->convergents twos) 10)
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(display-stream-n (cf->convergents onetwo) 10)
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