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indexing |
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|
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description: |
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"Prime number properties" |
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|
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status: "See notice at end of class" |
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names: primes; |
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date: "$Date$" |
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revision: "$Revision$" |
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|
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class PRIMES inherit |
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|
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COUNTABLE_SEQUENCE [INTEGER] |
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rename |
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has as is_prime |
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redefine |
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is_prime |
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end |
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|
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feature -- Access |
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|
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Smallest_prime: INTEGER is 2 |
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|
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Smallest_odd_prime: INTEGER is 3 |
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|
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higher_prime (n: INTEGER): INTEGER is |
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-- Lowest prime greater than or equal to `n' |
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do |
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if n <= Smallest_prime then |
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Result := Smallest_prime |
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else |
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check |
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n > Smallest_prime |
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end |
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from |
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if n \\ Smallest_prime = 0 then |
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-- Make sure that `Result' is odd |
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Result := n + 1 |
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else |
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Result := n |
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end |
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until |
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is_prime (Result) |
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loop |
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Result := Result + Smallest_prime |
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end |
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end |
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end |
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|
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lower_prime (n: INTEGER): INTEGER is |
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-- Greatest prime lower than or equal to `n' |
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require |
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argument_big_enough: n >= Smallest_prime |
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do |
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if n = Smallest_prime then |
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Result := Smallest_prime |
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else |
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-- `n' > Smallest_prime |
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from |
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if n \\ Smallest_prime = 0 then |
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-- make sure that `Result' is odd |
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Result := n - 1 |
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else |
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Result := n |
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end |
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until |
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is_prime (Result) |
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loop |
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Result := Result - Smallest_prime |
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end |
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end |
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end |
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|
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all_lower_primes (n: INTEGER): ARRAY [BOOLEAN] is |
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-- Array of `n' boolean values, where the |
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-- value at index `i' is true if and only if |
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-- `i' is prime. |
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local |
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i, j: INTEGER |
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do |
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-- All odd numbers except 1 are candidates |
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from |
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create Result.make (1, n) |
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i := 3 |
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until |
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i > n |
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loop |
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Result.put (True, i) |
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i := i + Smallest_prime |
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end |
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-- `Smallest_prime' is the lowest prime number |
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if n >= Smallest_prime then |
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Result.put (True, Smallest_prime) |
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end |
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-- Remove all multiples of primes |
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from |
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i := Smallest_odd_prime |
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until |
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i * i > n |
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loop |
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if Result.item (i) then |
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from |
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j := i * i |
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until |
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j > n |
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loop |
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Result.put (False, j) |
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j := j + Smallest_prime * i |
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end |
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end |
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i := i + Smallest_prime |
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end |
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end |
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|
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is_prime (n: INTEGER): BOOLEAN is |
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-- Is `n' a prime number? |
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local |
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divisor: INTEGER |
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do |
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if n <= 1 then |
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Result := False |
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elseif n = Smallest_prime then |
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Result := True |
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elseif n \\ Smallest_prime /= 0 then |
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from |
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divisor := Smallest_odd_prime |
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until |
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(n \\ divisor = 0) or else (divisor * divisor >= n) |
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loop |
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divisor := divisor + Smallest_prime |
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end |
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if divisor * divisor > n then |
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Result := True |
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end |
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end |
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end |
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|
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i_th (i: INTEGER): INTEGER is |
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-- The `i'-th prime number |
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local |
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candidates: ARRAY [BOOLEAN] |
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found: INTEGER |
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do |
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candidates := all_lower_primes (i * i) |
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from |
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Result := 2; found := 1 |
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invariant |
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-- Between 1 and `Result' there are `found' primes. |
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variant |
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i * i - Result |
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until |
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found = i |
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loop |
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Result := Result + 1 |
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if candidates.item (Result) then |
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found := found + 1 |
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end |
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end |
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end |
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|
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indexing |
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|
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library: "[ |
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EiffelBase: Library of reusable components for Eiffel. |
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]" |
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|
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status: "[ |
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--| Copyright (c) 1993-2006 University of Southern California and contributors. |
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For ISE customers the original versions are an ISE product |
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covered by the ISE Eiffel license and support agreements. |
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]" |
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|
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license: "[ |
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EiffelBase may now be used by anyone as FREE SOFTWARE to |
| 175 |
develop any product, public-domain or commercial, without |
| 176 |
payment to ISE, under the terms of the ISE Free Eiffel Library |
| 177 |
License (IFELL) at http://eiffel.com/products/base/license.html. |
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]" |
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|
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source: "[ |
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Interactive Software Engineering Inc. |
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ISE Building |
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360 Storke Road, Goleta, CA 93117 USA |
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Telephone 805-685-1006, Fax 805-685-6869 |
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Electronic mail <info@eiffel.com> |
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Customer support http://support.eiffel.com |
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]" |
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|
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info: "[ |
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For latest info see award-winning pages: http://eiffel.com |
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]" |
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|
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end -- class PRIMES |
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|
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|
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