note
	description: "Prime number properties"
	library: "Free implementation of ELKS library"
	status: "See notice at end of class."
	legal: "See notice at end of class."
	names: primes
	date: "$Date: 2018-10-03 13:41:17 +0000 (Wed, 03 Oct 2018) $"
	revision: "$Revision: 102260 $"

class interface
	PRIMES

create 
	default_create
			-- Process instances of classes with no creation clause.
			-- (Default: do nothing.)
			-- (from ANY)

feature -- Access

	all_lower_primes (n: INTEGER_32): ARRAY [BOOLEAN]
			-- Array of n boolean values, where the
			-- value at index i is true if and only if
			-- i is prime.
		ensure
			instance_free: class

	generating_type: TYPE [detachable PRIMES]
			-- Type of current object
			-- (type of which it is a direct instance)
			-- (from ANY)
		ensure -- from ANY
			generating_type_not_void: Result /= Void

	generator: STRING_8
			-- Name of current object's generating class
			-- (base class of the type of which it is a direct instance)
			-- (from ANY)
		ensure -- from ANY
			generator_not_void: Result /= Void
			generator_not_empty: not Result.is_empty

	higher_prime (n: INTEGER_32): INTEGER_32
			-- Lowest prime greater than or equal to n
		ensure
			instance_free: class

	i_th (i: INTEGER_32): INTEGER_32
			-- The i-th prime number
		require -- from COUNTABLE
			positive_argument: i > 0
		ensure then
			instance_free: class

	index: INTEGER_32
			-- Index of current position
			-- (from COUNTABLE_SEQUENCE)

	index_of (v: like item; i: INTEGER_32): INTEGER_32
			-- 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
		ensure -- from LINEAR
			non_negative_result: Result >= 0

	is_prime (n: INTEGER_32): BOOLEAN
			-- Is n a prime number?
		require -- from  CONTAINER
			True
		ensure -- from CONTAINER
			not_found_in_empty: Result implies not Is_empty
		ensure then
			instance_free: class

	item: INTEGER_32
			-- Item at current position
			-- (from COUNTABLE_SEQUENCE)
		require -- from ACTIVE
			readable: Readable
		require -- from TRAVERSABLE
			not_off: not off
		require -- from ITERATION_CURSOR
			valid_position: not After

	item_for_iteration: INTEGER_32
			-- Item at current position
			-- (from LINEAR)
		require -- from LINEAR
			not_off: not off

	lower_prime (n: INTEGER_32): INTEGER_32
			-- Greatest prime lower than or equal to n
		require
			argument_big_enough: n >= Smallest_prime
		ensure
			instance_free: class

	occurrences (v: like item): INTEGER_32
			-- Number of times v appears.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from LINEAR)
		require -- from  BAG
			True
		ensure -- from BAG
			non_negative_occurrences: Result >= 0

	search (v: like item)
			-- 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)
		ensure -- from LINEAR
			object_found: (not exhausted and object_comparison) implies v ~ item
			item_found: (not exhausted and not object_comparison) implies v = item

	Smallest_odd_prime: INTEGER_32 = 3

	Smallest_prime: INTEGER_32 = 2
	
feature -- Comparison

	frozen deep_equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void
			-- or attached to isomorphic object structures?
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			shallow_implies_deep: standard_equal (a, b) implies Result
			both_or_none_void: (a = Void) implies (Result = (b = Void))
			same_type: (Result and (a /= Void)) implies (b /= Void and then a.same_type (b))
			symmetric: Result implies deep_equal (b, a)

	frozen equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void or attached
			-- to objects considered equal?
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.is_equal (b))

	frozen is_deep_equal alias "≡≡≡" (other: PRIMES): BOOLEAN
			-- Are Current and other attached to isomorphic object structures?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			shallow_implies_deep: standard_is_equal (other) implies Result
			same_type: Result implies same_type (other)
			symmetric: Result implies other.is_deep_equal (Current)

	is_equal (other: PRIMES): BOOLEAN
			-- Is other attached to an object considered
			-- equal to current object?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			symmetric: Result implies other ~ Current
			consistent: standard_is_equal (other) implies Result

	frozen standard_equal (a: detachable ANY; b: like arg #1): BOOLEAN
			-- Are a and b either both void or attached to
			-- field-by-field identical objects of the same type?
			-- Always uses default object comparison criterion.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			definition: Result = (a = Void and b = Void) or else ((a /= Void and b /= Void) and then a.standard_is_equal (b))

	frozen standard_is_equal alias "≜" (other: PRIMES): BOOLEAN
			-- Is other attached to an object of the same type
			-- as current object, and field-by-field identical to it?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			same_type: Result implies same_type (other)
			symmetric: Result implies other.standard_is_equal (Current)
	
feature -- Status report

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

	changeable_comparison_criterion: BOOLEAN
			-- May object_comparison be changed?
			-- (Answer: yes by default.)
			-- (from CONTAINER)

	conforms_to (other: ANY): BOOLEAN
			-- Does type of current object conform to type
			-- of other (as per Eiffel: The Language, chapter 13)?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void

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

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

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

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

	is_inserted (v: INTEGER_32): BOOLEAN
			-- 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)

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

	off: BOOLEAN
			-- Is there no current item?
			-- (from LINEAR)

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

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

	Replaceable: BOOLEAN = False
			-- Can current item be replaced?
			-- (from COUNTABLE_SEQUENCE)

	same_type (other: ANY): BOOLEAN
			-- Is type of current object identical to type of other?
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			definition: Result = (conforms_to (other) and other.conforms_to (Current))

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

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

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

	forth
			-- Move to next position.
			-- (from COUNTABLE_SEQUENCE)
		require -- from LINEAR
			not_after: not After
		require -- from ITERATION_CURSOR
			valid_position: not After

	start
			-- Move to first position.
			-- (from COUNTABLE_SEQUENCE)
	
feature -- Element change

	fill (other: CONTAINER [INTEGER_32])
			-- 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: Extendible
	
feature -- Removal

	prune_all (v: INTEGER_32)
			-- Remove all occurrences of v.
			-- (Reference or object equality,
			-- based on object_comparison.)
			-- (from COLLECTION)
		require -- from COLLECTION
			prunable: Prunable
		ensure -- from COLLECTION
			no_more_occurrences: not is_prime (v)
	
feature -- Duplication

	copy (other: PRIMES)
			-- Update current object using fields of object attached
			-- to other, so as to yield equal objects.
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
			type_identity: same_type (other)
		ensure -- from ANY
			is_equal: Current ~ other

	frozen deep_copy (other: PRIMES)
			-- Effect equivalent to that of:
			--		copy (other . deep_twin)
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
		ensure -- from ANY
			deep_equal: deep_equal (Current, other)

	frozen deep_twin: PRIMES
			-- New object structure recursively duplicated from Current.
			-- (from ANY)
		ensure -- from ANY
			deep_twin_not_void: Result /= Void
			deep_equal: deep_equal (Current, Result)

	frozen standard_copy (other: PRIMES)
			-- Copy every field of other onto corresponding field
			-- of current object.
			-- (from ANY)
		require -- from ANY
			other_not_void: other /= Void
			type_identity: same_type (other)
		ensure -- from ANY
			is_standard_equal: standard_is_equal (other)

	frozen standard_twin: PRIMES
			-- New object field-by-field identical to other.
			-- Always uses default copying semantics.
			-- (from ANY)
		ensure -- from ANY
			standard_twin_not_void: Result /= Void
			equal: standard_equal (Result, Current)

	frozen twin: PRIMES
			-- New object equal to Current
			-- twin calls copy; to change copying/twinning semantics, redefine copy.
			-- (from ANY)
		ensure -- from ANY
			twin_not_void: Result /= Void
			is_equal: Result ~ Current
	
feature -- Basic operations

	frozen default: detachable PRIMES
			-- Default value of object's type
			-- (from ANY)

	frozen default_pointer: POINTER
			-- Default value of type POINTER
			-- (Avoid the need to write p.default for
			-- some p of type POINTER.)
			-- (from ANY)
		ensure -- from ANY
			instance_free: class

	default_rescue
			-- Process exception for routines with no Rescue clause.
			-- (Default: do nothing.)
			-- (from ANY)

	frozen do_nothing
			-- Execute a null action.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
	
feature -- Inapplicable

	extend (v: INTEGER_32)
			-- Add v at end.
			-- (from COUNTABLE_SEQUENCE)
		require -- from COLLECTION
			extendible: Extendible
		ensure -- from COLLECTION
			item_inserted: is_inserted (v)

	finish
			-- Move to last position.
			-- (from COUNTABLE_SEQUENCE)
		require -- from  LINEAR
			True
		ensure then -- from COUNTABLE_SEQUENCE
			failure: False

	linear_representation: LINEAR [INTEGER_32]
			-- Representation as a linear structure
			-- (from COUNTABLE_SEQUENCE)
		require -- from  CONTAINER
			True

	prune (v: INTEGER_32)
			-- Remove first occurrence of v, if any.
			-- (from COUNTABLE_SEQUENCE)
		require -- from COLLECTION
			prunable: Prunable

	put (v: INTEGER_32)
			-- Add v to the right of current position.
			-- (from COUNTABLE_SEQUENCE)
		require -- from COLLECTION
			extendible: Extendible
		ensure -- from COLLECTION
			item_inserted: is_inserted (v)

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

	replace (v: INTEGER_32)
			-- Replace by v item at current position.
			-- (from COUNTABLE_SEQUENCE)
		require -- from ACTIVE
			writable: Writable
			replaceable: Replaceable
		ensure -- from ACTIVE
			item_replaced: item = v

	wipe_out
			-- Remove all items.
			-- (from COUNTABLE_SEQUENCE)
		require -- from COLLECTION
			prunable: Prunable
		ensure -- from COLLECTION
			wiped_out: Is_empty
	
feature -- Iteration

	do_all (action: PROCEDURE [INTEGER_32])
			-- 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

	do_if (action: PROCEDURE [INTEGER_32]; test: FUNCTION [INTEGER_32, BOOLEAN])
			-- 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_exists: test /= Void

	for_all (test: FUNCTION [INTEGER_32, BOOLEAN]): BOOLEAN
			-- Is test true for all items?
			-- Semantics not guaranteed if test changes the structure;
			-- in such a case, apply iterator to clone of structure instead.
			-- (from LINEAR)
		require -- from TRAVERSABLE
			test_exists: test /= Void
		ensure then -- from LINEAR
			empty: Is_empty implies Result

	new_cursor: PRIMES
			-- Fresh cursor associated with current structure
		require -- from  ITERABLE
			True
		ensure -- from ITERABLE
			result_attached: Result /= Void
		ensure then
			instance_free: class

	there_exists (test: FUNCTION [INTEGER_32, BOOLEAN]): BOOLEAN
			-- Is test true for at least one item?
			-- Semantics not guaranteed if test changes the structure;
			-- in such a case, apply iterator to clone of structure instead.
			-- (from LINEAR)
		require -- from TRAVERSABLE
			test_exists: test /= Void
	
feature -- Output

	Io: STD_FILES
			-- Handle to standard file setup
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			io_not_void: Result /= Void

	out: STRING_8
			-- New string containing terse printable representation
			-- of current object
			-- (from ANY)
		ensure -- from ANY
			out_not_void: Result /= Void

	print (o: detachable ANY)
			-- Write terse external representation of o
			-- on standard output.
			-- (from ANY)
		ensure -- from ANY
			instance_free: class

	frozen tagged_out: STRING_8
			-- New string containing terse printable representation
			-- of current object
			-- (from ANY)
		ensure -- from ANY
			tagged_out_not_void: Result /= Void
	
feature -- Platform

	Operating_environment: OPERATING_ENVIRONMENT
			-- Objects available from the operating system
			-- (from ANY)
		ensure -- from ANY
			instance_free: class
			operating_environment_not_void: Result /= Void
	
invariant
		-- from INFINITE
	never_empty: not Is_empty
	always_full: Full

		-- from ANY
	reflexive_equality: standard_is_equal (Current)
	reflexive_conformance: conforms_to (Current)

		-- 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

note
	copyright: "Copyright (c) 1984-2018, Eiffel Software and others"
	license: "Eiffel Forum License v2 (see http://www.eiffel.com/licensing/forum.txt)"
	source: "[
		Eiffel Software
		5949 Hollister Ave., Goleta, CA 93117 USA
		Telephone 805-685-1006, Fax 805-685-6869
		Website http://www.eiffel.com
		Customer support http://support.eiffel.com
	]"

end -- class PRIMES

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