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 (s: STRING_8) -- Create a BIG_INTEGER from string s require non_empty: not s.is_empty has_correct_format: is_string_int (s) make_from_integer64 (int: INTEGER_64) -- Create a BIG_INTEGER from int make_from_integer32 (int: INTEGER_32) -- Create a BIG_INTEGER from int default_create -- Create BIG_INTEGER 0 require -- from ANY True ensure then item.is_equal ("0") convert default_create ({STRING_8}), default_create ({INTEGER_64}), default_create ({INTEGER_32}), default_create: {INTEGER_64}, default_create: {INTEGER_32}, default_create: {STRING_8} feature -- Access generating_type: TYPE [detachable BIG_INTEGER] -- 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 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 (other: BIG_INTEGER): 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_greater alias ">" (other: BIG_INTEGER): BOOLEAN -- Is current object greater than other? -- (from COMPARABLE) require -- from PART_COMPARABLE other_exists: other /= Void ensure then -- from COMPARABLE definition: Result = (other < Current) is_greater_equal alias ">=" (other: BIG_INTEGER): BOOLEAN -- Is current object greater than or equal to other? -- (from COMPARABLE) require -- from PART_COMPARABLE other_exists: other /= Void ensure then -- from COMPARABLE definition: Result = (other <= Current) is_less_equal alias "<=" (other: BIG_INTEGER): BOOLEAN -- Is current object less than or equal to other? -- (from COMPARABLE) require -- from PART_COMPARABLE other_exists: other /= Void ensure then -- from COMPARABLE definition: Result = ((Current < other) or (Current ~ other)) max (other: BIG_INTEGER): BIG_INTEGER -- The greater of current object and other -- (from COMPARABLE) require -- from COMPARABLE other_exists: other /= Void ensure -- from COMPARABLE current_if_not_smaller: Current >= other implies Result = Current other_if_smaller: Current < other implies Result = other min (other: BIG_INTEGER): BIG_INTEGER -- The smaller of current object and other -- (from COMPARABLE) require -- from COMPARABLE other_exists: other /= Void ensure -- from COMPARABLE current_if_not_greater: Current <= other implies Result = Current other_if_greater: Current > other implies Result = other 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 (other: BIG_INTEGER): 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) three_way_comparison (other: BIG_INTEGER): INTEGER_32 -- If current object equal to other, 0; -- if smaller, -1; if greater, 1 -- (from COMPARABLE) require -- from COMPARABLE other_exists: other /= Void ensure -- from COMPARABLE equal_zero: (Result = 0) = (Current ~ other) smaller_negative: (Result = -1) = (Current < other) greater_positive: (Result = 1) = (Current > other) feature -- Status report 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 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)) feature -- Duplication copy (other: BIG_INTEGER) -- 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: BIG_INTEGER) -- 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: BIG_INTEGER -- 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: BIG_INTEGER) -- 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: BIG_INTEGER -- 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: BIG_INTEGER -- 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 BIG_INTEGER -- 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 -- Output Io: STD_FILES -- Handle to standard file setup -- (from ANY) ensure -- from ANY instance_free: class io_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 feature -- comparison is_equal (other: BIG_INTEGER): BOOLEAN -- Is other equal to Current? require -- from ANY other_not_void: other /= Void ensure -- from ANY symmetric: Result implies other ~ Current consistent: standard_is_equal (other) implies Result ensure then -- from COMPARABLE trichotomy: Result = (not (Current < other) and not (other < Current)) is_less alias "<" (other: BIG_INTEGER): BOOLEAN -- Is Current less than other? require -- from PART_COMPARABLE other_exists: other /= Void ensure then -- from COMPARABLE asymmetric: Result implies not (other < Current) feature -- conversion as_integer32: INTEGER_32 -- represent as a integer 32 require valid_int32: out.is_integer_32 as_integer64: INTEGER_64 -- represent as a integer 64 require valid_int64: out.is_integer_64 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 feature -- operations absolute: BIG_INTEGER -- Returns the absolute value of Current ensure Result >= Result.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 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 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 minus alias "-" (other: BIG_INTEGER): BIG_INTEGER -- Returns the result of subtracting other from Current -- Was declared in BIG_INTEGER as synonym of subtract. negate -- negates the number plus alias "+" (other: BIG_INTEGER): BIG_INTEGER -- Returns the result of adding other to 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 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 remainder alias "\\" (other: BIG_INTEGER): BIG_INTEGER -- Return the result of Current mod other (Consistent with WolframAlpha's mod) require non_zero: other /~ zero square: BIG_INTEGER -- Returns the result of Current * Current subtract (other: BIG_INTEGER): BIG_INTEGER -- Returns the result of subtracting other from Current -- Was declared in BIG_INTEGER as synonym of minus. feature -- queries divisible (other: BIG_INTEGER): BOOLEAN -- may current object be divided by other? identity alias "+": BIG_INTEGER -- unary plus is_integer: BOOLEAN -- Is string representation item an int? is_natural: BOOLEAN -- Is Current a natural number? is_natural1: BOOLEAN -- Is `Current a Natural1 number? one: BIG_INTEGER -- neutral element for "*" and "/" opposite alias "-": BIG_INTEGER -- unary minus out: STRING_8 -- New string containing terse printable representation -- of current object ensure -- from ANY out_not_void: Result /= Void zero: BIG_INTEGER -- neutral element for "+" and "-" invariant Default_precision = 0 is_integer -- from COMPARABLE irreflexive_comparison: not (Current < Current) -- from ANY reflexive_equality: standard_is_equal (Current) reflexive_conformance: conforms_to (Current) 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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