bjoli/wheel-utils
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Added skip-wheels.

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This commit is contained in:
Linus 2020-12-09 21:21:56 +01:00
parent 082082fcb9
commit bb786bb816
2 changed files with 56 additions and 28 deletions
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29
example.scm
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@ -18,11 +18,6 @@
;; Then we make our wheel circular so that we don't have to check any null.
(define actual-wheel (apply circular-list proto-wheel))
;; Here we loop from 1 to 99 and print every "opening" in the wheel
;; This _should_ be quite a lot faster than a solution that uses
;; division, and it should be quite extensible. We could easily add
;; a baz every 7 numbers.
(define (wheel-fizzbuzz n)
(let loop ((i 1) (wheel actual-wheel))
(if (> i n)
@ -41,3 +36,27 @@
(cons "buzz" (loop (+ i 1))))
(else
(cons i (loop (+ i 1)))))))
;;; Example: prime wheel
;; Here we create a skip wheel that we can use to skip multiples of 2 3 5 and 7.
;; It can be used when implementing, say, the sieve of erathostenes to skip numbers
;; that are already known to be divisors of primes. Removing the first 4 prime-multiples
;; drastically reduces the work that the program needs to do. The first false-positive
;; given by the prime wheel is 11² (121), making this an extremely efficient way to
;; reduce work when trying to find primes.
(define prime-wheel
(apply circular-list
(skip-wheel
(every-n-in 2)
(every-n-in 3)
(every-n-in 5)
(every-n-in 7))))
(display prime-wheel)
(cons* 2 3 5 7 (let loop ((n 11) (wheel (drop prime-wheel 1)))
(if (> n 200)
'()
(cons n (loop (+ n (car wheel)) (cdr wheel))))))