Difference between revisions of "User:WillNess"
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primes = 2 : g (fix g) |
primes = 2 : g (fix g) |
||
where |
where |
||
− | g |
+ | g xs = 3 : gaps 5 (foldi (\(c:cs) -> (c:) . union cs) |
− | [[ |
+ | [[x*x, x*x+2*x..] | x <- xs]) |
− | gaps k s@(c:t) |
+ | gaps k s@(c:t) |
− | | k < c = k : gaps (k+2) s -- |
+ | | k < c = k : gaps (k+2) s -- minus [k,k+2..] (c:t), k<=c |
| True = gaps (k+2) t -- fused to avoid a space leak |
| True = gaps (k+2) t -- fused to avoid a space leak |
||
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<code>foldi</code> is on [[Fold#Tree-like_folds|Tree-like folds]] page. <code>union</code> and more at [[Prime numbers#Sieve_of_Eratosthenes|Prime numbers]]. |
<code>foldi</code> is on [[Fold#Tree-like_folds|Tree-like folds]] page. <code>union</code> and more at [[Prime numbers#Sieve_of_Eratosthenes|Prime numbers]]. |
||
− | + | The math formula for Sieve of Eratosthenes, |
|
::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{n p:n \in \mathbb{N}_{p}\}</math> |
::::<math>\textstyle\mathbb{S} = \mathbb{N}_{2} \setminus \bigcup_{p\in \mathbb{S}} \{n p:n \in \mathbb{N}_{p}\}</math> |
Revision as of 10:06, 29 August 2011
I'm interested in Haskell.
I like this:
-- inifinte folding idea due to Richard Bird
-- double staged production idea due to Melissa O'Neill
-- tree folding idea Dave Bayer / simplified formulation Will Ness
primes = 2 : g (fix g)
where
g xs = 3 : gaps 5 (foldi (\(c:cs) -> (c:) . union cs)
[[x*x, x*x+2*x..] | x <- xs])
gaps k s@(c:t)
| k < c = k : gaps (k+2) s -- minus [k,k+2..] (c:t), k<=c
| True = gaps (k+2) t -- fused to avoid a space leak
fix g = xs where xs = g xs -- global defn to avoid space leak
foldi
is on Tree-like folds page. union
and more at Prime numbers.
The math formula for Sieve of Eratosthenes,
where
- . . . or, :) :) .
Trial division sieve: