JezK
Edit File: rational.rbs
# <!-- rdoc-file=rational.c --> # A rational number can be represented as a pair of integer numbers: a/b (b>0), # where a is the numerator and b is the denominator. Integer a equals rational # a/1 mathematically. # # You can create a Rational object explicitly with: # # * A [rational # literal](doc/syntax/literals_rdoc.html#label-Rational+Literals). # # # You can convert certain objects to Rationals with: # # * Method [Rational](Kernel.html#method-i-Rational). # # # Examples # # Rational(1) #=> (1/1) # Rational(2, 3) #=> (2/3) # Rational(4, -6) #=> (-2/3) # Reduced. # 3.to_r #=> (3/1) # 2/3r #=> (2/3) # # You can also create rational objects from floating-point numbers or strings. # # Rational(0.3) #=> (5404319552844595/18014398509481984) # Rational('0.3') #=> (3/10) # Rational('2/3') #=> (2/3) # # 0.3.to_r #=> (5404319552844595/18014398509481984) # '0.3'.to_r #=> (3/10) # '2/3'.to_r #=> (2/3) # 0.3.rationalize #=> (3/10) # # A rational object is an exact number, which helps you to write programs # without any rounding errors. # # 10.times.inject(0) {|t| t + 0.1 } #=> 0.9999999999999999 # 10.times.inject(0) {|t| t + Rational('0.1') } #=> (1/1) # # However, when an expression includes an inexact component (numerical value or # operation), it will produce an inexact result. # # Rational(10) / 3 #=> (10/3) # Rational(10) / 3.0 #=> 3.3333333333333335 # # Rational(-8) ** Rational(1, 3) # #=> (1.0000000000000002+1.7320508075688772i) # class Rational < Numeric public def %: (Integer) -> Rational | (Float) -> Float | (Rational) -> Rational | (Numeric) -> Numeric # <!-- # rdoc-file=rational.c # - rat * numeric -> numeric # --> # Performs multiplication. # # Rational(2, 3) * Rational(2, 3) #=> (4/9) # Rational(900) * Rational(1) #=> (900/1) # Rational(-2, 9) * Rational(-9, 2) #=> (1/1) # Rational(9, 8) * 4 #=> (9/2) # Rational(20, 9) * 9.8 #=> 21.77777777777778 # def *: (Float) -> Float | (Complex) -> Complex | (Numeric) -> Numeric # <!-- # rdoc-file=rational.c # - rat ** numeric -> numeric # --> # Performs exponentiation. # # Rational(2) ** Rational(3) #=> (8/1) # Rational(10) ** -2 #=> (1/100) # Rational(10) ** -2.0 #=> 0.01 # Rational(-4) ** Rational(1, 2) #=> (0.0+2.0i) # Rational(1, 2) ** 0 #=> (1/1) # Rational(1, 2) ** 0.0 #=> 1.0 # def **: (Complex) -> Complex | (Numeric) -> Numeric # <!-- # rdoc-file=rational.c # - rat + numeric -> numeric # --> # Performs addition. # # Rational(2, 3) + Rational(2, 3) #=> (4/3) # Rational(900) + Rational(1) #=> (901/1) # Rational(-2, 9) + Rational(-9, 2) #=> (-85/18) # Rational(9, 8) + 4 #=> (41/8) # Rational(20, 9) + 9.8 #=> 12.022222222222222 # def +: (Float) -> Float | (Complex) -> Complex | (Numeric) -> Rational def +@: () -> Rational # <!-- # rdoc-file=rational.c # - rat - numeric -> numeric # --> # Performs subtraction. # # Rational(2, 3) - Rational(2, 3) #=> (0/1) # Rational(900) - Rational(1) #=> (899/1) # Rational(-2, 9) - Rational(-9, 2) #=> (77/18) # Rational(9, 8) - 4 #=> (-23/8) # Rational(20, 9) - 9.8 #=> -7.577777777777778 # def -: (Float) -> Float | (Complex) -> Complex | (Numeric) -> Rational # <!-- # rdoc-file=rational.c # - -rat -> rational # --> # Negates `rat`. # def -@: () -> Rational # <!-- # rdoc-file=rational.c # - rat / numeric -> numeric # - rat.quo(numeric) -> numeric # --> # Performs division. # # Rational(2, 3) / Rational(2, 3) #=> (1/1) # Rational(900) / Rational(1) #=> (900/1) # Rational(-2, 9) / Rational(-9, 2) #=> (4/81) # Rational(9, 8) / 4 #=> (9/32) # Rational(20, 9) / 9.8 #=> 0.22675736961451246 # def /: (Float) -> Float | (Complex) -> Complex | (Numeric) -> Rational # <!-- # rdoc-file=rational.c # - rational <=> numeric -> -1, 0, +1, or nil # --> # Returns -1, 0, or +1 depending on whether `rational` is less than, equal to, # or greater than `numeric`. # # `nil` is returned if the two values are incomparable. # # Rational(2, 3) <=> Rational(2, 3) #=> 0 # Rational(5) <=> 5 #=> 0 # Rational(2, 3) <=> Rational(1, 3) #=> 1 # Rational(1, 3) <=> 1 #=> -1 # Rational(1, 3) <=> 0.3 #=> 1 # # Rational(1, 3) <=> "0.3" #=> nil # def <=>: (Integer | Rational) -> Integer | (untyped) -> Integer? # <!-- # rdoc-file=rational.c # - rat == object -> true or false # --> # Returns `true` if `rat` equals `object` numerically. # # Rational(2, 3) == Rational(2, 3) #=> true # Rational(5) == 5 #=> true # Rational(0) == 0.0 #=> true # Rational('1/3') == 0.33 #=> false # Rational('1/2') == '1/2' #=> false # def ==: (untyped) -> bool # <!-- # rdoc-file=rational.c # - rat.abs -> rational # - rat.magnitude -> rational # --> # Returns the absolute value of `rat`. # # (1/2r).abs #=> (1/2) # (-1/2r).abs #=> (1/2) # # Rational#magnitude is an alias for Rational#abs. # def abs: () -> Rational def abs2: () -> Rational def angle: () -> (Integer | Float) alias arg angle # <!-- # rdoc-file=rational.c # - rat.ceil([ndigits]) -> integer or rational # --> # Returns the smallest number greater than or equal to `rat` with a precision of # `ndigits` decimal digits (default: 0). # # When the precision is negative, the returned value is an integer with at least # `ndigits.abs` trailing zeros. # # Returns a rational when `ndigits` is positive, otherwise returns an integer. # # Rational(3).ceil #=> 3 # Rational(2, 3).ceil #=> 1 # Rational(-3, 2).ceil #=> -1 # # # decimal - 1 2 3 . 4 5 6 # # ^ ^ ^ ^ ^ ^ # # precision -3 -2 -1 0 +1 +2 # # Rational('-123.456').ceil(+1).to_f #=> -123.4 # Rational('-123.456').ceil(-1) #=> -120 # def ceil: () -> Integer | (Integer digits) -> (Integer | Rational) def coerce: (Numeric) -> [ Numeric, Numeric ] def conj: () -> Rational def conjugate: () -> Rational # <!-- # rdoc-file=rational.c # - rat.denominator -> integer # --> # Returns the denominator (always positive). # # Rational(7).denominator #=> 1 # Rational(7, 1).denominator #=> 1 # Rational(9, -4).denominator #=> 4 # Rational(-2, -10).denominator #=> 5 # def denominator: () -> Integer def div: (Numeric) -> Integer def divmod: (Numeric) -> [ Numeric, Numeric ] def dup: () -> self def eql?: (untyped) -> bool # <!-- # rdoc-file=rational.c # - rat.fdiv(numeric) -> float # --> # Performs division and returns the value as a Float. # # Rational(2, 3).fdiv(1) #=> 0.6666666666666666 # Rational(2, 3).fdiv(0.5) #=> 1.3333333333333333 # Rational(2).fdiv(3) #=> 0.6666666666666666 # def fdiv: (Numeric) -> Float def finite?: () -> bool # <!-- # rdoc-file=rational.c # - rat.floor([ndigits]) -> integer or rational # --> # Returns the largest number less than or equal to `rat` with a precision of # `ndigits` decimal digits (default: 0). # # When the precision is negative, the returned value is an integer with at least # `ndigits.abs` trailing zeros. # # Returns a rational when `ndigits` is positive, otherwise returns an integer. # # Rational(3).floor #=> 3 # Rational(2, 3).floor #=> 0 # Rational(-3, 2).floor #=> -2 # # # decimal - 1 2 3 . 4 5 6 # # ^ ^ ^ ^ ^ ^ # # precision -3 -2 -1 0 +1 +2 # # Rational('-123.456').floor(+1).to_f #=> -123.5 # Rational('-123.456').floor(-1) #=> -130 # def floor: () -> Integer | (Integer digits) -> (Integer | Rational) # <!-- # rdoc-file=rational.c # - hash() # --> # def hash: () -> Integer def i: () -> Complex def imag: () -> Integer def imaginary: () -> Integer def infinite?: () -> Integer? # <!-- # rdoc-file=rational.c # - rat.inspect -> string # --> # Returns the value as a string for inspection. # # Rational(2).inspect #=> "(2/1)" # Rational(-8, 6).inspect #=> "(-4/3)" # Rational('1/2').inspect #=> "(1/2)" # def inspect: () -> String def integer?: () -> bool # <!-- rdoc-file=rational.c --> # Returns the absolute value of `rat`. # # (1/2r).abs #=> (1/2) # (-1/2r).abs #=> (1/2) # # Rational#magnitude is an alias for Rational#abs. # alias magnitude abs def modulo: (Float) -> Float | (Numeric) -> Rational # <!-- # rdoc-file=rational.c # - rat.negative? -> true or false # --> # Returns `true` if `rat` is less than 0. # def negative?: () -> bool def nonzero?: () -> self? # <!-- # rdoc-file=rational.c # - rat.numerator -> integer # --> # Returns the numerator. # # Rational(7).numerator #=> 7 # Rational(7, 1).numerator #=> 7 # Rational(9, -4).numerator #=> -9 # Rational(-2, -10).numerator #=> 1 # def numerator: () -> Integer alias phase angle def polar: () -> [ Rational, Integer | Float ] # <!-- # rdoc-file=rational.c # - rat.positive? -> true or false # --> # Returns `true` if `rat` is greater than 0. # def positive?: () -> bool # <!-- rdoc-file=rational.c --> # Performs division. # # Rational(2, 3) / Rational(2, 3) #=> (1/1) # Rational(900) / Rational(1) #=> (900/1) # Rational(-2, 9) / Rational(-9, 2) #=> (4/81) # Rational(9, 8) / 4 #=> (9/32) # Rational(20, 9) / 9.8 #=> 0.22675736961451246 # def quo: (Float) -> Float | (Complex) -> Complex | (Numeric) -> Rational # <!-- # rdoc-file=rational.c # - rat.rationalize -> self # - rat.rationalize(eps) -> rational # --> # Returns a simpler approximation of the value if the optional argument `eps` is # given (rat-|eps| <= result <= rat+|eps|), self otherwise. # # r = Rational(5033165, 16777216) # r.rationalize #=> (5033165/16777216) # r.rationalize(Rational('0.01')) #=> (3/10) # r.rationalize(Rational('0.1')) #=> (1/3) # def rationalize: (?Numeric eps) -> Rational def real: () -> Rational def real?: () -> true def rect: () -> [ Rational, Numeric ] alias rectangular rect def remainder: (Float) -> Float | (Numeric) -> Rational # <!-- # rdoc-file=rational.c # - rat.round([ndigits] [, half: mode]) -> integer or rational # --> # Returns `rat` rounded to the nearest value with a precision of `ndigits` # decimal digits (default: 0). # # When the precision is negative, the returned value is an integer with at least # `ndigits.abs` trailing zeros. # # Returns a rational when `ndigits` is positive, otherwise returns an integer. # # Rational(3).round #=> 3 # Rational(2, 3).round #=> 1 # Rational(-3, 2).round #=> -2 # # # decimal - 1 2 3 . 4 5 6 # # ^ ^ ^ ^ ^ ^ # # precision -3 -2 -1 0 +1 +2 # # Rational('-123.456').round(+1).to_f #=> -123.5 # Rational('-123.456').round(-1) #=> -120 # # The optional `half` keyword argument is available similar to Float#round. # # Rational(25, 100).round(1, half: :up) #=> (3/10) # Rational(25, 100).round(1, half: :down) #=> (1/5) # Rational(25, 100).round(1, half: :even) #=> (1/5) # Rational(35, 100).round(1, half: :up) #=> (2/5) # Rational(35, 100).round(1, half: :down) #=> (3/10) # Rational(35, 100).round(1, half: :even) #=> (2/5) # Rational(-25, 100).round(1, half: :up) #=> (-3/10) # Rational(-25, 100).round(1, half: :down) #=> (-1/5) # Rational(-25, 100).round(1, half: :even) #=> (-1/5) # def round: (?half: :up | :down | :even) -> Integer | (Integer digits, ?half: :up | :down | :even) -> (Integer | Rational) def step: (?Numeric limit, ?Numeric step) { (Rational) -> void } -> self | (?Numeric limit, ?Numeric step) -> Enumerator[Rational, self] | (?by: Numeric, ?to: Numeric) { (Rational) -> void } -> self | (?by: Numeric, ?to: Numeric) -> Enumerator[Rational, self] def to_c: () -> Complex # <!-- # rdoc-file=rational.c # - rat.to_f -> float # --> # Returns the value as a Float. # # Rational(2).to_f #=> 2.0 # Rational(9, 4).to_f #=> 2.25 # Rational(-3, 4).to_f #=> -0.75 # Rational(20, 3).to_f #=> 6.666666666666667 # def to_f: () -> Float # <!-- # rdoc-file=rational.c # - rat.to_i -> integer # --> # Returns the truncated value as an integer. # # Equivalent to Rational#truncate. # # Rational(2, 3).to_i #=> 0 # Rational(3).to_i #=> 3 # Rational(300.6).to_i #=> 300 # Rational(98, 71).to_i #=> 1 # Rational(-31, 2).to_i #=> -15 # def to_i: () -> Integer alias to_int to_i # <!-- # rdoc-file=rational.c # - rat.to_r -> self # --> # Returns self. # # Rational(2).to_r #=> (2/1) # Rational(-8, 6).to_r #=> (-4/3) # def to_r: () -> Rational # <!-- # rdoc-file=rational.c # - rat.to_s -> string # --> # Returns the value as a string. # # Rational(2).to_s #=> "2/1" # Rational(-8, 6).to_s #=> "-4/3" # Rational('1/2').to_s #=> "1/2" # def to_s: () -> String # <!-- # rdoc-file=rational.c # - rat.truncate([ndigits]) -> integer or rational # --> # Returns `rat` truncated (toward zero) to a precision of `ndigits` decimal # digits (default: 0). # # When the precision is negative, the returned value is an integer with at least # `ndigits.abs` trailing zeros. # # Returns a rational when `ndigits` is positive, otherwise returns an integer. # # Rational(3).truncate #=> 3 # Rational(2, 3).truncate #=> 0 # Rational(-3, 2).truncate #=> -1 # # # decimal - 1 2 3 . 4 5 6 # # ^ ^ ^ ^ ^ ^ # # precision -3 -2 -1 0 +1 +2 # # Rational('-123.456').truncate(+1).to_f #=> -123.4 # Rational('-123.456').truncate(-1) #=> -120 # def truncate: () -> Integer | (Integer ndigits) -> (Integer | Rational) def zero?: () -> bool end