note

	description:
		"Prime number properties"

	status: "See notice at end of class"
	names: primes;
	date: "$Date$"
	revision: "$Revision$"

class PRIMES inherit

	COUNTABLE_SEQUENCE [INTEGER]
		rename
			has as is_prime
		redefine
			is_prime
		end

feature -- Access

	Smallest_prime: INTEGER = 2

	Smallest_odd_prime: INTEGER = 3

	higher_prime (n: INTEGER): INTEGER
			-- Lowest prime greater than or equal to `n'
		do
			if n <= Smallest_prime then
				Result := Smallest_prime
			else
					check
						n > Smallest_prime
					end
				from
					if n \\ Smallest_prime = 0 then
							-- Make sure that `Result' is odd
						Result := n + 1
					else
						Result := n
					end
				until
					is_prime (Result)
				loop
					Result := Result + Smallest_prime
				end
			end
		end

	lower_prime (n: INTEGER): INTEGER
			-- Greatest prime lower than or equal to `n'
		require
			argument_big_enough: n >= Smallest_prime
		do
			if n = Smallest_prime then
				Result := Smallest_prime
			else
					-- `n' > Smallest_prime
				from
					if n \\ Smallest_prime = 0 then
							-- make sure that `Result' is odd
						Result := n - 1
					else
						Result := n
					end
				until
					is_prime (Result)
				loop
					Result := Result - Smallest_prime
				end
			end
		end

	all_lower_primes (n: INTEGER): ARRAY [BOOLEAN]
			-- Array of `n' boolean values, where the
			-- value at index `i' is true if and only if
			-- `i' is prime.
		local
			i, j: INTEGER
		do
				-- All odd numbers except 1 are candidates
			from
				create Result.make (1, n)
				i := 3
			until
				i > n
			loop
				Result.put (True, i)
				i := i + Smallest_prime
			end
				-- `Smallest_prime' is the lowest prime number
			if n >= Smallest_prime then
				Result.put (True, Smallest_prime)
			end
				-- Remove all multiples of primes
			from
				i := Smallest_odd_prime
			until
				i * i > n
			loop
				if Result.item (i) then
					from
						j := i * i
					until
						j > n
					loop
						Result.put (False, j)
						j := j + Smallest_prime * i
					end
				end
				i := i + Smallest_prime
			end
		end

	is_prime (n: INTEGER): BOOLEAN
			-- Is `n' a prime number?
		local
			divisor: INTEGER
		do
			if n <= 1 then
				Result := False
			elseif n = Smallest_prime then
				Result := True
			elseif n \\ Smallest_prime /= 0 then
				from
					divisor := Smallest_odd_prime
				until
					(n \\ divisor = 0) or else (divisor * divisor >= n)
				loop
					divisor := divisor + Smallest_prime
				end
				if divisor * divisor > n then
					Result := True
				end
			end
		end

	i_th (i: INTEGER): INTEGER
			-- The `i'-th prime number
		local
			candidates: ARRAY [BOOLEAN]
			found: INTEGER
		do
			candidates := all_lower_primes (i * i)
			from
				Result := 2; found := 1
			invariant
				-- Between 1 and `Result' there are `found' primes.
			variant
				i * i - Result
			until
				found = i
			loop
				Result := Result + 1
				if candidates.item (Result) then
					found := found + 1
				end
			end
		end

note

	library: "[
			EiffelBase: Library of reusable components for Eiffel.
			]"

	status: "[
--| Copyright (c) 1993-2006 University of Southern California and contributors.
			For ISE customers the original versions are an ISE product
			covered by the ISE Eiffel license and support agreements.
			]"

	license: "[
			EiffelBase may now be used by anyone as FREE SOFTWARE to
			develop any product, public-domain or commercial, without
			payment to ISE, under the terms of the ISE Free Eiffel Library
			License (IFELL) at http://eiffel.com/products/base/license.html.
			]"

	source: "[
			Interactive Software Engineering Inc.
			ISE Building
			360 Storke Road, Goleta, CA 93117 USA
			Telephone 805-685-1006, Fax 805-685-6869
			Electronic mail <info@eiffel.com>
			Customer support http://support.eiffel.com
			]"

	info: "[
			For latest info see award-winning pages: http://eiffel.com
			]"

end -- class PRIMES