118 lines
3.7 KiB
Scheme
118 lines
3.7 KiB
Scheme
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; Arithmetic that checks for overflow
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(define (carefully op)
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(lambda (x y succ fail)
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(let ((z (op (extract-fixnum x) (extract-fixnum y))))
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(if (or (too-big-for-fixnum? z)
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(too-small-for-fixnum? z))
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(goto fail x y)
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(goto succ (enter-fixnum z))))))
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(define add-carefully (carefully +))
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(define subtract-carefully (carefully -))
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(define half-word-size (quotient bits-per-cell 2))
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(define half-word-mask (- (ashl 1 half-word-size) 1))
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(define max-middle (ashl 1 (- (- bits-per-fixnum 1) half-word-size)))
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(define (multiply-carefully x y succ fail)
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(let* ((a (extract-fixnum x))
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(b (extract-fixnum y))
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(positive-result? (if (>= a 0)
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(>= b 0)
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(< b 0)))
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(a (abs a))
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(b (abs b))
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(lo-a (bitwise-and half-word-mask a))
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(lo-b (bitwise-and half-word-mask b))
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(hi-a (bitwise-and half-word-mask (high-bits a half-word-size)))
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(hi-b (bitwise-and half-word-mask (high-bits b half-word-size)))
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(lo-c (small* lo-a lo-b))
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(mid-c (+ (small* lo-a hi-b) (small* lo-b hi-a)))
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(c (+ lo-c (ashl mid-c half-word-size))))
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(cond ((or (and (> hi-a 0) (> hi-b 0))
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(too-big-for-fixnum? lo-c)
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(> 0 lo-c)
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(> mid-c max-middle))
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(goto fail x y))
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(positive-result?
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(if (too-big-for-fixnum? c)
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(goto fail x y)
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(goto succ (enter-fixnum c))))
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(else
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(if (too-small-for-fixnum? (- 0 c))
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(goto fail x y)
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(goto succ (enter-fixnum (- 0 c))))))))
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; Test cases for bits-per-cell = 28, bits-per-fixnum = 26
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; (do ((i 2 (* i 2))
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; (j (* -2 (expt 2 23)) (/ j 2)))
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; ((>= j 0) 'ok)
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; (write `((* ,i ,j) ?=? ,(* i j)))
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; (newline))
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(define (divide-carefully x y succ fail)
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(quotient-carefully x y
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(lambda (q)
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(remainder-carefully x y
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(lambda (r)
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(if (= r (enter-fixnum 0))
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(goto succ q)
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(goto fail x y)))
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fail))
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fail))
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; Watch out for (quotient least-fixnum -1)
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(define (quotient-carefully x y succ fail)
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(if (= y (enter-fixnum 0))
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(fail x y)
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(let* ((a (extract-fixnum x))
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(b (extract-fixnum y))
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(positive-result? (if (>= a 0)
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(>= b 0)
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(< b 0)))
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(a (abs a))
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(b (abs b))
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(c (quotient a b)))
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(cond ((not positive-result?)
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(goto succ (enter-fixnum (- 0 c))))
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((too-big-for-fixnum? c) ; (quotient least-fixnum -1)
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(goto fail x y))
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(else
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(goto succ (enter-fixnum c)))))))
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; Overflow check not necessary
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(define (remainder-carefully x y succ fail)
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(if (= y (enter-fixnum 0))
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(goto fail x y)
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(let* ((a (extract-fixnum x))
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(b (extract-fixnum y))
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(positive-result? (>= a 0))
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(a (abs a))
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(b (abs b))
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(c (remainder a b)))
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(goto succ (enter-fixnum (if positive-result? c (- 0 c)))))))
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(define (shift-carefully value+tag count+tag succ fail)
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(let ((value (extract-fixnum value+tag))
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(count (extract-fixnum count+tag)))
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(if (< count 0)
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(goto succ (enter-fixnum (ashr value (- 0 count))))
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(let ((result (extract-fixnum (enter-fixnum (ashl value count)))))
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(if (and (= value (ashr result count))
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(if (>= value 0)
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(>= result 0)
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(< result 0)))
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(goto succ (enter-fixnum result))
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(goto fail value+tag count+tag))))))
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; beware of (abs least-fixnum)
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(define (abs-carefully n succ fail)
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(let ((r (abs n)))
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(if (too-big-for-fixnum? r)
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(goto fail n)
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(goto succ (enter-fixnum r)))))
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