note description: "[ An arbitrary precision library for Rational numbers. Creation make, make_from_ints, make_from_string, make_from_real32, make_from_real64, Queries absolute: RATIONAL add (other: RATIONAL): RATIONAL as_real32: REAL_32 as_real64: REAL_64 divide alias "//" (other: RATIONAL): RATIONAL is_equal (other: RATIONAL): BOOLEAN is_greater alias ">" (other: RATIONAL): BOOLEAN is_greater_equal alias ">=" (other: RATIONAL): BOOLEAN is_less alias "<" (other: RATIONAL): BOOLEAN is_less_equal alias "<=" (other: RATIONAL): BOOLEAN is_valid_real_32: BOOLEAN is_valid_real_64: BOOLEAN max (other: [like Current] RATIONAL): RATIONAL min (other: [like Current] RATIONAL): RATIONAL minus alias "-" (other: RATIONAL): RATIONAL multiply (other: RATIONAL): RATIONAL negate: RATIONAL opposite alias "-": RATIONAL out: STRING_8 plus alias "+" (other: RATIONAL): RATIONAL power alias "^" (other: INTEGER): RATIONAL product alias "*" (other: RATIONAL): RATIONAL quotient alias "/" (other: RATIONAL): RATIONAL reciprocal: RATIONAL round_to (digits: INTEGER): STRING square: RATIONAL string_is_float (s: STRING): BOOLEAN string_is_fraction (s: STRING): BOOLEAN string_is_rational (s: STRING): BOOLEAN subtract (other: RATIONAL): RATIONAL Commands canonicalize ]" author: "JSO and AB" date: "$Date$" revision: "$Revision$" class interface RATIONAL create make (a_p, a_q: INTEGER_64) -- Initialization for Current. require q_non_zero: a_q /= 0 make_from_ints (a_p, a_q: BIG_INTEGER) -- Create by specifying the pand q values require q_non_zero: a_q /~ a_q.zero make_from_string (s: STRING_8) -- Create from string s require has_correct_format: string_is_rational (s) make_from_real32 (r: REAL_32) -- Create from a REAL_32, r make_from_real64 (r: REAL_64) -- Create from a REAL_64 default_create -- Process instances of classes with no creation clause. -- (Default: do nothing.) convert default_create ({STRING_8}), default_create ({REAL_32}), default_create ({REAL_64}), default_create: {REAL_32}, default_create: {REAL_64}, default_create: {STRING_8} feature -- Access generating_type: TYPE [detachable RATIONAL] -- 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: RATIONAL): 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: RATIONAL): 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: RATIONAL): 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: RATIONAL): 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: RATIONAL): RATIONAL -- 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: RATIONAL): RATIONAL -- 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: RATIONAL): 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: RATIONAL): 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: RATIONAL) -- 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: RATIONAL) -- 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: RATIONAL -- 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: RATIONAL) -- 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: RATIONAL -- 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: RATIONAL -- 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 RATIONAL -- 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 -- Commands canonicalize -- Canonicalize the current rational by dividing its numerator -- and denominator by their GCD. feature -- Internal queries get_p_q (s: STRING_8): TUPLE [a_p: like s; a_q: like s] -- Returns the numerator and denominator parsed from s. require string_is_rational (s) feature -- Operations abs: like Current -- Absolute value of Current -- Was declared in RATIONAL as synonym of absolute. absolute: like Current -- Absolute value of Current -- Was declared in RATIONAL as synonym of abs. add (other: like Current): like Current -- Return the result of adding Current to other -- Was declared in RATIONAL as synonym of plus. divide alias "//" (other: like Current): like Current -- Return the result of dividing Curent by other -- Was declared in RATIONAL as synonym of quotient. require denominator_non_zero: other /~ zero exp (other: INTEGER_32): RATIONAL -- Return the value of Current raised to the power other -- Was declared in RATIONAL as synonym of power. minus alias "-" (other: like Current): like Current -- Return the result of subtracting other from Current -- Was declared in RATIONAL as synonym of subtract. multiply (other: like Current): like Current -- Return the result of multiplying Current by other -- Was declared in RATIONAL as synonym of product. negate: like Current -- Negate Current -- Was declared in RATIONAL as synonym of opposite. opposite alias "-": like Current -- Negate Current -- Was declared in RATIONAL as synonym of negate. plus alias "+" (other: like Current): like Current -- Return the result of adding Current to other -- Was declared in RATIONAL as synonym of add. power alias "^" (other: INTEGER_32): RATIONAL -- Return the value of Current raised to the power other -- Was declared in RATIONAL as synonym of exp. product alias "*" (other: like Current): like Current -- Return the result of multiplying Current by other -- Was declared in RATIONAL as synonym of multiply. quotient alias "/" (other: like Current): like Current -- Return the result of dividing Curent by other -- Was declared in RATIONAL as synonym of divide. require denominator_non_zero: other /~ zero reciprocal: like Current -- Return 1 / Current square: RATIONAL -- Return the value of Current * Current subtract (other: like Current): like Current -- Return the result of subtracting other from Current -- Was declared in RATIONAL as synonym of minus. 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 -- Queries as_real32: REAL_32 -- Represent Current as a REAL_32 require is_valid_real_32 as_real64: REAL_64 -- Represent Current as a REAL_64 require is_valid_real_64 debug_output: STRING_8 -- Debut output for Current ensure -- from DEBUG_OUTPUT result_not_void: Result /= Void divisible (other: like Current): BOOLEAN -- May current object be divided by other? exponentiable (other: NUMERIC): BOOLEAN -- May current object be elevated to the power other? identity alias "+": like Current -- Unary plus int_zero: BIG_INTEGER -- Returns an Integer with value 0 for creation is_canonical: BOOLEAN -- Is Current in canonical form? is_equal (other: like Current): BOOLEAN -- Is other value 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: like Current): BOOLEAN -- Is current object less than other? require -- from PART_COMPARABLE other_exists: other /= Void ensure then -- from COMPARABLE asymmetric: Result implies not (other < Current) is_valid_real_32: BOOLEAN -- Is Current a valid REAL_32? is_valid_real_64: BOOLEAN -- Is Current a valid REAL_64? one: like Current -- Neutral element for "*" and "/" out: STRING_8 -- Return a string representation of Current ensure -- from ANY out_not_void: Result /= Void string_is_float (s: STRING_8): BOOLEAN -- Does s represent a valid and well-defined decimal number -- with potentially a floating point? This function was copied -- from {INT}.ensureValid, which came from mathmodels' VALUE. require non_void: s /= Void non_empty: not s.is_empty string_is_fraction (s: STRING_8): BOOLEAN -- Does s represent a valid and well-defined fraction? -- It must contain at most one '/', which separates the numerator -- from the denominator (no whitespace allowed). Also, either -- the numerator or denominator must be non-zero. Further, if '/' -- is present, what comes before and after it must be valid INTs. -- If s doesn't contain a '/', a denominator of 1 is assumed. string_is_rational (s: STRING_8): BOOLEAN -- Does s represent a fraction or a decimal with a floating -- point? zero: like Current -- Neutral element for "+" and "-" feature -- rounding round_to (digits: INTEGER_32): STRING_8 -- Round Current to digits number of digits. Uses half-up rounding. invariant well_defined: q /~ q.zero -- from ANY reflexive_equality: standard_is_equal (Current) reflexive_conformance: conforms_to (Current) -- from COMPARABLE irreflexive_comparison: not (Current < Current) end -- class RATIONAL
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