note
	description: "[
				An arbitrary precision library for integer numbers.
				
				Creation
					make_from_string,
					make_from_integer64,
					make_from_integer32,
		
				Queries
					absolute: BIG_INTEGER
					as_integer32: INTEGER
					as_integer64: INTEGER
					divide (other: BIG_INTEGER): BIG_INTEGER
					gcd (other: BIG_INTEGER): BIG_INTEGER
					is_equal (other: BIG_INTEGER): BOOLEAN
					is_greater alias ">" (other: [like Current] BIG_INTEGER): BOOLEAN
					is_greater_equal alias ">=" (other: [like Current] BIG_INTEGER): BOOLEAN
					is_less alias "<" (other: BIG_INTEGER): BOOLEAN
					is_less_equal alias "<=" (other: [like Current] BIG_INTEGER): BOOLEAN
					max (other: [like Current] BIG_INTEGER): [like Current] BIG_INTEGER
					min (other: [like Current] BIG_INTEGER): [like Current] BIG_INTEGER
					minus alias "-" (other: BIG_INTEGER): BIG_INTEGER
					opposite alias "-": BIG_INTEGER
					out: STRING
					plus alias "+" (other: BIG_INTEGER): BIG_INTEGER
					power alias "^" (other: INTEGER): BIG_INTEGER
					product alias "*" (other: BIG_INTEGER): BIG_INTEGER
					quotient alias "//" (other: BIG_INTEGER): BIG_INTEGER
					remainder alias "\\" (other: BIG_INTEGER): BIG_INTEGER
					square: BIG_INTEGER
	]"
	author: "JSO"
	date: "$17 July, 2018$"
	revision: "$0.91$"

class interface
	BIG_INTEGER

create 
	make_from_string,
	make_from_integer64,
	make_from_integer32,
	default_create

convert
	make_from_string ({STRING_8}),
	make_from_integer64 ({INTEGER_64}),
	make_from_integer32 ({INTEGER_32}),
	as_integer64: {INTEGER_64},
	as_integer32: {INTEGER_32},
	out: {STRING_8}

feature -- comparison

	is_equal (other: BIG_INTEGER): BOOLEAN
			-- Is other equal to Current?

	is_less alias "<" (other: BIG_INTEGER): BOOLEAN
			-- Is Current less than other?
	
feature -- operations

	plus alias "+" (other: BIG_INTEGER): BIG_INTEGER
			-- Returns the result of adding other to Current

	minus alias "-" (other: BIG_INTEGER): BIG_INTEGER
			-- Returns the result of subtracting other from Current
			-- Was declared in BIG_INTEGER as synonym of subtract.

	subtract (other: BIG_INTEGER): BIG_INTEGER
			-- Returns the result of subtracting other from Current
			-- Was declared in BIG_INTEGER as synonym of minus.

	product alias "*" (other: BIG_INTEGER): BIG_INTEGER
			-- Returns the result of multiplying Current with other

	quotient alias "//" (other: BIG_INTEGER): BIG_INTEGER
			-- Returns the result of dividing Current from other
			-- Was declared in BIG_INTEGER as synonym of divide.
		require
			denominator_non_zero: other /~ zero

	divide (other: BIG_INTEGER): BIG_INTEGER
			-- Returns the result of dividing Current from other
			-- Was declared in BIG_INTEGER as synonym of quotient.
		require
			denominator_non_zero: other /~ zero

	square: BIG_INTEGER
			-- Returns the result of Current * Current

	power alias "^" (other: INTEGER_32): BIG_INTEGER
			-- Returns the result of raising Current to the power other
			-- Was declared in BIG_INTEGER as synonym of exp.
		require
			power_non_zero: other >= 0

	exp (other: INTEGER_32): BIG_INTEGER
			-- Returns the result of raising Current to the power other
			-- Was declared in BIG_INTEGER as synonym of power.
		require
			power_non_zero: other >= 0

	remainder alias "\\" (other: BIG_INTEGER): BIG_INTEGER
			-- Return the result of Current mod other (Consistent with WolframAlpha's mod)
		require
			non_zero: other /~ zero

	gcd (other: BIG_INTEGER): BIG_INTEGER
			-- Return the positive greatest common divisor of Current and other
		require
			both_not_zero: Current /~ zero or other /~ zero

	negate
			-- negates the number

	absolute: BIG_INTEGER
			-- Returns the absolute value of Current
		ensure
				Result >= Result.zero
	
feature -- conversion

	as_integer64: INTEGER_64
			-- represent as a integer 64
		require
			valid_int64: out.is_integer_64

	as_integer32: INTEGER_32
			-- represent as a integer 32
		require
			valid_int32: out.is_integer_32
	
feature -- queries

	out: STRING_8
			-- New string containing terse printable representation
			-- of current object

	opposite alias "-": BIG_INTEGER
			-- unary minus

	identity alias "+": BIG_INTEGER
			-- unary plus

	zero: BIG_INTEGER
			-- neutral element for "+" and "-"

	one: BIG_INTEGER
			-- neutral element for "*" and "/"

	divisible (other: BIG_INTEGER): BOOLEAN
			-- may current object be divided by other?

	is_natural: BOOLEAN
			-- Is Current a natural number?

	is_natural1: BOOLEAN
			-- Is `Current a Natural1 number?

	is_integer: BOOLEAN
			-- Is string representation item an int?
	
feature -- is_string_int

	is_string_int (s: STRING_8): BOOLEAN
			-- Is the given string a representation of big integer?
		require
			non_empty: not s.is_empty
	
invariant
		Default_precision = 0
		is_integer

note
	copyright: "Copyright (c) SEL, York University"
	license: "MIT"
	todo: "[
		integer division \\ is veru ineficient. Fpr js algorithm see:
		www.javascripter.net/math/calculators/100digitbigintcalculator.htm
		and {TEST_INT_JSO}t51.
		To generate large random numbers:
		python3
		import random
		random.getrandbits(128) -- 128 bits
	]"

end -- class BIG_INTEGER

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