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	description: "Prime number properties"
	status: "See notice at end of class"
	names: primes
	date: "$Date: 2001-11-16 20:32:23 +0000 (Fri, 16 Nov 2001) $"
	revision: "$Revision: 51435 $"

class 
	PRIMES

feature -- Access

	all_lower_primes (n: INTEGER): ARRAY [BOOLEAN] is
			-- 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
			from
				create Result.make (1, n)
				i := 3
			until
				i > n
			loop
				Result.put (True, i)
				i := i + smallest_prime
			end
			if n >= smallest_prime then
				Result.put (True, smallest_prime)
			end
			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

	higher_prime (n: INTEGER): INTEGER is
			-- 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
						Result := n + 1
					else
						Result := n
					end
				until
					is_prime (Result)
				loop
					Result := Result + smallest_prime
				end
			end
		end

	i_th (i: INTEGER): INTEGER is
			-- The i-th prime number
		require -- from COUNTABLE
			positive_argument: i > 0
		local
			candidates: ARRAY [BOOLEAN]
			found: INTEGER
		do
			candidates := all_lower_primes (i * i)
			from
				Result := 2
				found := 1
			variant
				i * i - Result
			until
				found = i
			loop
				Result := Result + 1
				if candidates.item (Result) then
					found := found + 1
				end
			end
		end

	index: INTEGER
			-- Index of current position
			-- (from COUNTABLE_SEQUENCE)

	index_of (v: like item; i: INTEGER): INTEGER is
			-- Index of i-th occurrence of v.
			-- 0 if none.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from LINEAR)
		require -- from LINEAR
			positive_occurrences: i > 0
		local
			occur, pos: INTEGER
		do
			if object_comparison and v /= void then
				from
					start
					pos := 1
				until
					off or (occur = i)
				loop
					if item /= void and then v.is_equal (item) then
						occur := occur + 1
					end
					forth
					pos := pos + 1
				end
			else
				from
					start
					pos := 1
				until
					off or (occur = i)
				loop
					if item = v then
						occur := occur + 1
					end
					forth
					pos := pos + 1
				end
			end
			if occur = i then
				Result := pos - 1
			end
		ensure -- from LINEAR
			non_negative_result: Result >= 0
		end

	is_prime (n: INTEGER): BOOLEAN is
			-- 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
		ensure -- from CONTAINER
			not_found_in_empty: Result implies not is_empty
		end

	item: INTEGER is
			-- Item at current position
			-- (from COUNTABLE_SEQUENCE)
		require -- from TRAVERSABLE
			not_off: not off
		require -- from ACTIVE
			readable: readable
		do
			Result := i_th (index)
		end

	lower_prime (n: INTEGER): INTEGER is
			-- 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
				from
					if n \\ smallest_prime = 0 then
						Result := n - 1
					else
						Result := n
					end
				until
					is_prime (Result)
				loop
					Result := Result - smallest_prime
				end
			end
		end

	occurrences (v: INTEGER): INTEGER is
			-- Number of times v appears.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from LINEAR)
		do
			from
				start
				search (v)
			until
				exhausted
			loop
				Result := Result + 1
				forth
				search (v)
			end
		ensure -- from BAG
			non_negative_occurrences: Result >= 0
		end

	search (v: like item) is
			-- Move to first position (at or after current
			-- position) where item and v are equal.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- If no such position ensure that exhausted will be true.
			-- (from LINEAR)
		do
			if object_comparison and v /= void then
				from
				until
					exhausted or else (item /= void and then v.is_equal (item))
				loop
					forth
				end
			else
				from
				until
					exhausted or else v = item
				loop
					forth
				end
			end
		ensure -- from LINEAR
			object_found: (not exhausted and object_comparison) implies equal (v, item)
			item_found: (not exhausted and not object_comparison) implies v = item
		end

	Smallest_odd_prime: INTEGER is 3

	Smallest_prime: INTEGER is 2
	
feature -- Status report

	After: BOOLEAN is False
			-- Is current position past last item? (Answer: no.)
			-- (from COUNTABLE_SEQUENCE)

	changeable_comparison_criterion: BOOLEAN is
			-- May object_comparison be changed?
			-- (Answer: yes by default.)
			-- (from CONTAINER)
		do
			Result := True
		end

	empty: BOOLEAN is
		obsolete "ELKS 2000: Use `is_empty' instead"
			-- Is there no element?
			-- (from CONTAINER)
		do
			Result := is_empty
		end

	exhausted: BOOLEAN is
			-- Has structure been completely explored?
			-- (from LINEAR)
		do
			Result := off
		ensure -- from LINEAR
			exhausted_when_off: off implies Result
		end

	Extendible: BOOLEAN is False
			-- May items be added? (Answer: no.)
			-- (from COUNTABLE_SEQUENCE)

	Full: BOOLEAN is True
			-- The structure is complete
			-- (from INFINITE)

	Is_empty: BOOLEAN is False
			-- Is structure empty? (Answer: no.)
			-- (from INFINITE)

	is_inserted (v: INTEGER): BOOLEAN is
			-- Has v been inserted by the most recent insertion?
			-- (By default, the value returned is equivalent to calling
			-- `has (v)'. However, descendants might be able to provide more
			-- efficient implementations.)
			-- (from COLLECTION)
		do
			Result := is_prime (v)
		end

	object_comparison: BOOLEAN
			-- Must search operations use equal rather than =
			-- for comparing references? (Default: no, use =.)
			-- (from CONTAINER)

	off: BOOLEAN is
			-- Is there no current item?
			-- (from LINEAR)
		do
			Result := is_empty or after
		end

	Prunable: BOOLEAN is False
			-- May items be removed? (Answer: no.)
			-- (from COUNTABLE_SEQUENCE)

	Readable: BOOLEAN is True
			-- Is there a current item that may be read?
			-- (Answer: yes.)
			-- (from COUNTABLE_SEQUENCE)

	Writable: BOOLEAN is False
			-- Is there a current item that may be written?
			-- (Answer: no.)
			-- (from COUNTABLE_SEQUENCE)
	
feature -- Status setting

	compare_objects is
			-- Ensure that future search operations will use equal
			-- rather than = for comparing references.
			-- (from CONTAINER)
		require -- from CONTAINER
			changeable_comparison_criterion
		do
			object_comparison := True
		ensure -- from CONTAINER
			object_comparison
		end

	compare_references is
			-- Ensure that future search operations will use =
			-- rather than equal for comparing references.
			-- (from CONTAINER)
		require -- from CONTAINER
			changeable_comparison_criterion
		do
			object_comparison := False
		ensure -- from CONTAINER
			reference_comparison: not object_comparison
		end
	
feature -- Cursor movement

	forth is
			-- Move to next position.
			-- (from COUNTABLE_SEQUENCE)
		require -- from LINEAR
			not_after: not after
		do
			index := index + 1
		end

	start is
			-- Move to first position.
			-- (from COUNTABLE_SEQUENCE)
		do
			index := 1
		end
	
feature {NONE} -- Element change

	fill (other: CONTAINER [INTEGER]) is
			-- Fill with as many items of other as possible.
			-- The representations of other and current structure
			-- need not be the same.
			-- (from COLLECTION)
		require -- from COLLECTION
			other_not_void: other /= void
			extendible
		local
			lin_rep: LINEAR [INTEGER]
		do
			lin_rep := other.linear_representation
			from
				lin_rep.start
			until
				not extendible or else lin_rep.off
			loop
				extend (lin_rep.item)
				lin_rep.forth
			end
		end
	
feature {NONE} -- Removal

	prune_all (v: INTEGER) is
			-- Remove all occurrences of v.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from COLLECTION)
		require -- from COLLECTION
			prunable
		do
			from
			until
				not is_prime (v)
			loop
				prune (v)
			end
		ensure -- from COLLECTION
			no_more_occurrences: not is_prime (v)
		end
	
feature {NONE} -- Inapplicable

	extend (v: INTEGER) is
			-- Add v at end.
			-- (from COUNTABLE_SEQUENCE)
		require -- from COLLECTION
			extendible: extendible
		do
		ensure -- from COLLECTION
			item_inserted: is_inserted (v)
		ensure then -- from BAG
			one_more_occurrence: occurrences (v) = old (occurrences (v)) + 1
		end

	finish is
			-- Move to last position.
			-- (from COUNTABLE_SEQUENCE)
		do
		ensure then -- from COUNTABLE_SEQUENCE
			failure: False
		end

	linear_representation: LINEAR [INTEGER] is
			-- Representation as a linear structure
			-- (from COUNTABLE_SEQUENCE)
		do
		end

	prune (v: INTEGER) is
			-- Remove first occurrence of v, if any.
			-- (from COUNTABLE_SEQUENCE)
		require -- from COLLECTION
			prunable: prunable
		do
		end

	put (v: INTEGER) is
			-- Add v to the right of current position.
			-- (from COUNTABLE_SEQUENCE)
		require -- from COLLECTION
			extendible: extendible
		do
		ensure -- from COLLECTION
			item_inserted: is_inserted (v)
		end

	remove is
			-- Remove item to the right of current position.
			-- (from COUNTABLE_SEQUENCE)
		require -- from ACTIVE
			prunable: prunable
			writable: writable
		do
		end

	replace (v: INTEGER) is
			-- Replace by v item at current position.
			-- (from COUNTABLE_SEQUENCE)
		require -- from ACTIVE
			writable: writable
		do
		ensure -- from ACTIVE
			item_replaced: item = v
		end

	wipe_out is
			-- Remove all items.
			-- (from COUNTABLE_SEQUENCE)
		require -- from COLLECTION
			prunable
		do
		ensure -- from COLLECTION
			wiped_out: is_empty
		end
	
feature -- Iteration

	do_all (action: PROCEDURE [ANY, TUPLE [INTEGER]]) is
			-- Apply action to every item.
			-- Semantics not guaranteed if action changes the structure;
			-- in such a case, apply iterator to clone of structure instead.
			-- (from LINEAR)
		require -- from TRAVERSABLE
			action_exists: action /= void
		local
			t: TUPLE [INTEGER]
		do
			create t.make
			from
				start
			until
				after
			loop
				t.put (item, 1)
				action.call (t)
				forth
			end
		end

	do_if (action: PROCEDURE [ANY, TUPLE [INTEGER]]; test: FUNCTION [ANY, TUPLE [INTEGER], BOOLEAN]) is
			-- Apply action to every item that satisfies test.
			-- Semantics not guaranteed if action or test changes the structure;
			-- in such a case, apply iterator to clone of structure instead.
			-- (from LINEAR)
		require -- from TRAVERSABLE
			action_exists: action /= void
			test_exits: test /= void
		local
			t: TUPLE [INTEGER]
		do
			create t.make
			from
				start
			until
				after
			loop
				t.put (item, 1)
				if test.item (t) then
					action.call (t)
				end
				forth
			end
		end

	for_all (test: FUNCTION [ANY, TUPLE [INTEGER], BOOLEAN]): BOOLEAN is
			-- Is test true for all items?
			-- (from LINEAR)
		require -- from TRAVERSABLE
			test_exits: test /= void
		local
			cs: CURSOR_STRUCTURE [INTEGER]
			c: CURSOR
			t: TUPLE [INTEGER]
		do
			create t.make
			cs ?= Current
			if cs /= void then
				c := cs.cursor
			end
			from
				start
				Result := True
			until
				after or not Result
			loop
				t.put (item, 1)
				Result := test.item (t)
				forth
			end
			if cs /= void then
				cs.go_to (c)
			end
		end

	there_exists (test: FUNCTION [ANY, TUPLE [INTEGER], BOOLEAN]): BOOLEAN is
			-- Is test true for at least one item?
			-- (from LINEAR)
		require -- from TRAVERSABLE
			test_exits: test /= void
		local
			cs: CURSOR_STRUCTURE [INTEGER]
			c: CURSOR
			t: TUPLE [INTEGER]
		do
			create t.make
			cs ?= Current
			if cs /= void then
				c := cs.cursor
			end
			from
				start
			until
				after or Result
			loop
				t.put (item, 1)
				Result := test.item (t)
				forth
			end
			if cs /= void then
				cs.go_to (c)
			end
		end
	
invariant

		-- from ANY
	reflexive_equality: standard_is_equal (Current)
	reflexive_conformance: conforms_to (Current)
		-- from INFINITE
	never_empty: not is_empty
	always_full: full
		-- from ACTIVE
	writable_constraint: writable implies readable
	empty_constraint: is_empty implies (not readable) and (not writable)
		-- from LINEAR
	after_constraint: after implies off
		-- from TRAVERSABLE
	empty_constraint: is_empty implies off

indexing
	library: "[
			EiffelBase: Library of reusable components for Eiffel.
	]"
	status: "[
			Copyright 1986-2001 Interactive Software Engineering (ISE).
			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


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