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choelzl
2022-04-07 18:33:05 +02:00
commit 091ba18f50
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cs420-acc/l3-warmup/examples/bignums.l3 Normal file
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;; In Emacs, open this file in -*- Scheme -*- mode.
;; Basic computations (addition, multiplication and factorial) on big
;; numbers. These are represented as lists of "digits" in the base
;; specified below, in order of increasing weight.
(def %base 10000)
(def int->bignum list-make@1)
(def bignum-print
(fun (b)
(let ((rev-b (list-reverse b)))
(int-print (list-head rev-b))
(list-for-each (fun (d)
(if (< d 1000) (int-print 0))
(if (< d 100) (int-print 0))
(if (< d 10) (int-print 0))
(int-print d))
(list-tail rev-b)))))
(def bignum-+
(fun (b1 b2)
(rec loop ((b1 b1) (b2 b2) (carry 0))
(cond ((list-empty? b1)
(if (= 0 carry) b2 (loop (int->bignum carry) b2 0)))
((list-empty? b2)
(if (= 0 carry) b1 (loop b1 (int->bignum carry) 0)))
(#t
(let ((res (+ (list-head b1) (list-head b2) carry)))
(list-prepend (%t res %base)
(loop (list-tail b1)
(list-tail b2)
(/t res %base)))))))))
(def bignum-scale
(fun (b n)
(rec loop ((b b) (n n) (carry 0))
(if (list-empty? b)
(if (= 0 carry) list-empty (int->bignum carry))
(let ((sh (+ (* (list-head b) n) carry)))
(list-prepend (%t sh %base)
(loop (list-tail b) n (/t sh %base))))))))
(defrec bignum-*
(fun (b1 b2)
(if (list-empty? b1)
list-empty
(bignum-+ (bignum-scale b2 (list-head b1))
(bignum-scale (bignum-* (list-tail b1) b2) %base)))))
(def bignum-zero? list-empty?)
(defrec bignum-fact
(fun (n)
(if (= 0 n)
(int->bignum 1)
(bignum-* (int->bignum n) (bignum-fact (- n 1))))))
(string-print "Factorial of? ")
(let ((n (int-read)))
(int-print n)
(string-print "! = ")
(bignum-print (bignum-fact n))
(newline-print))