Sieve of Eratosthenes: Difference between revisions

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Found 78498 primes to 1000000 in 192 milliseconds.</pre>

==~~{{header|~~Elm with immutable arrays}}==

===Elm with immutable arrays===

module PrimeArray exposing (main)

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import Html exposing (div, h1, p, text)

import Html.Attributes exposing (style)

{-

The Eratosthenes sieve task in Rosetta Code does not ~~allow~~

The Eratosthenes sieve task in Rosetta Code does not accept

the use of modulo function (modBy or remainderBy).

the use of modulo function (allthough Elm functions modBy and remainderBy work always correctly as they require type Int excluding type Float).

Thus the ~~work~~ ~~list is converted into~~ an indexed work array

Thus the solution needs an indexed work array

as Elm has no indexes for lists.

In this method we need no division remainder calculations,

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We need the indexes that we know, where the marking of the non-primes

shall be set.

Because everything is immutable in Elm, every change of array values will create a new array save the original array unchanged. That makes the program running slower or consuming more space of memory than with non-functional imperative languages. All conventional loops (for, while, until) are excluded in Elm because immutability requirement.

Live: https://ellie-app.com/pTHJyqXcHtpa1

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-- As Elm has no loops (for, while, until)

{- As Elm has no loops (for, while, until)

-- we must use recursion instead!

we must use recursion instead!

-- The ~~outer loop~~ of prime ~~search~~ ~~with~~ ~~increasing~~ ~~variable~~ i

The search of prime starts allways saving the

-- ~~The~~ ~~search~~ of ~~prime~~ ~~starts~~ ~~allways~~ ~~saving (not~~ setting zero)

first found value (not setting zero) and continues setting the multiples of prime to zero.

Zero is no integer and may thus be used as marking of non-prime numbers. At the end, only the primes remain in the array and the zeroes are removed from the resulted array to be shown in Html.

-- the first location of the found prime as the later found values are

-}

-- multiples and set zero

⚫

-- The ~~recursive~~ ~~loop of~~ variable i follows:

⚫

-- The recursion increasing variable i follows:

loopI : Int -> Int -> Array Int -> Array Int

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Found 35 primes

</pre>

=={{header|Emacs Lisp}}==