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Edit File: numeric.rbs

# 
# Numeric is the class from which all higher-level numeric classes should
# inherit.
#
# Numeric allows instantiation of heap-allocated objects. Other core numeric
# classes such as Integer are implemented as immediates, which means that each
# Integer is a single immutable object which is always passed by value.
#
# a = 1
# 1.object_id == a.object_id #=> true
#
# There can only ever be one instance of the integer `1`, for example. Ruby
# ensures this by preventing instantiation. If duplication is attempted, the
# same instance is returned.
#
# Integer.new(1) #=> NoMethodError: undefined method `new' for Integer:Class
# 1.dup #=> 1
# 1.object_id == 1.dup.object_id #=> true
#
# For this reason, Numeric should be used when defining other numeric classes.
#
# Classes which inherit from Numeric must implement `coerce`, which returns a
# two-member Array containing an object that has been coerced into an instance
# of the new class and `self` (see #coerce).
#
# Inheriting classes should also implement arithmetic operator methods (`+`,
# `-`, `*` and `/`) and the `<=>` operator (see Comparable). These methods may
# rely on `coerce` to ensure interoperability with instances of other numeric
# classes.
#
# class Tally < Numeric
# def initialize(string)
# @string = string
# end
#
# def to_s
# @string
# end
#
# def to_i
# @string.size
# end
#
# def coerce(other)
# [self.class.new('|' * other.to_i), self]
# end
#
# def <=>(other)
# to_i <=> other.to_i
# end
#
# def +(other)
# self.class.new('|' * (to_i + other.to_i))
# end
#
# def -(other)
# self.class.new('|' * (to_i - other.to_i))
# end
#
# def *(other)
# self.class.new('|' * (to_i * other.to_i))
# end
#
# def /(other)
# self.class.new('|' * (to_i / other.to_i))
# end
# end
#
# tally = Tally.new('||')
# puts tally * 2 #=> "||||"
# puts tally > 1 #=> true
#
# ## What's Here
#
# First, what's elsewhere. Class Numeric:
#
# * Inherits from [class
# Object](Object.html#class-Object-label-What-27s+Here).
# * Includes [module
# Comparable](Comparable.html#module-Comparable-label-What-27s+Here).
#
#
# Here, class Numeric provides methods for:
#
# * [Querying](#class-Numeric-label-Querying)
# * [Comparing](#class-Numeric-label-Comparing)
# * [Converting](#class-Numeric-label-Converting)
# * [Other](#class-Numeric-label-Other)
#
#
# ### Querying
#
# #finite?
# : Returns true unless `self` is infinite or not a number.
#
# #infinite?
# : Returns -1, `nil` or +1, depending on whether `self` is
# `-Infinity<tt>, finite, or <tt>+Infinity`.
#
# #integer?
# : Returns whether `self` is an integer.
#
# #negative?
# : Returns whether `self` is negative.
#
# #nonzero?
# : Returns whether `self` is not zero.
#
# #positive?
# : Returns whether `self` is positive.
#
# #real?
# : Returns whether `self` is a real value.
#
# #zero?
# : Returns whether `self` is zero.
#
#
#
# ### Comparing
#
# [<=>](#method-i-3C-3D-3E)
# : Returns:
#
# * -1 if `self` is less than the given value.
# * 0 if `self` is equal to the given value.
# * 1 if `self` is greater than the given value.
# * `nil` if `self` and the given value are not comparable.
#
# #eql?
# : Returns whether `self` and the given value have the same value and
# type.
#
#
#
# ### Converting
#
# #% (aliased as #modulo)
# : Returns the remainder of `self` divided by the given value.
#
# #-@
# : Returns the value of `self`, negated.
#
# #abs (aliased as #magnitude)
# : Returns the absolute value of `self`.
#
# #abs2
# : Returns the square of `self`.
#
# #angle (aliased as #arg and #phase)
# : Returns 0 if `self` is positive, Math::PI otherwise.
#
# #ceil
# : Returns the smallest number greater than or equal to `self`, to a
# given precision.
#
# #coerce
# : Returns array `[coerced_self, coerced_other]` for the given other
# value.
#
# #conj (aliased as #conjugate)
# : Returns the complex conjugate of `self`.
#
# #denominator
# : Returns the denominator (always positive) of the Rational
# representation of `self`.
#
# #div
# : Returns the value of `self` divided by the given value and converted
# to an integer.
#
# #divmod
# : Returns array `[quotient, modulus]` resulting from dividing `self` the
# given divisor.
#
# #fdiv
# : Returns the Float result of dividing `self` by the given divisor.
#
# #floor
# : Returns the largest number less than or equal to `self`, to a given
# precision.
#
# #i
# : Returns the Complex object `Complex(0, self)`. the given value.
#
# #imaginary (aliased as #imag)
# : Returns the imaginary part of the `self`.
#
# #numerator
# : Returns the numerator of the Rational representation of `self`; has
# the same sign as `self`.
#
# #polar
# : Returns the array `[self.abs, self.arg]`.
#
# #quo
# : Returns the value of `self` divided by the given value.
#
# #real
# : Returns the real part of `self`.
#
# #rect (aliased as #rectangular)
# : Returns the array `[self, 0]`.
#
# #remainder
# : Returns `self-arg*(self/arg).truncate` for the given `arg`.
#
# #round
# : Returns the value of `self` rounded to the nearest value for the given
# a precision.
#
# #to_c
# : Returns the Complex representation of `self`.
#
# #to_int
# : Returns the Integer representation of `self`, truncating if necessary.
#
# #truncate
# : Returns `self` truncated (toward zero) to a given precision.
#
#
#
# ### Other
#
# #clone
# : Returns `self`; does not allow freezing.
#
# #dup (aliased as #+@)
# : Returns `self`.
#
# #step
# : Invokes the given block with the sequence of specified numbers.
#
class Numeric
 include Comparable

public

# 
 # Returns `self` modulo `other` as a real number.
 #
 # Of the Core and Standard Library classes, only Rational uses this
 # implementation.
 #
 # For Rational `r` and real number `n`, these expressions are equivalent:
 #
 # c % n
 # c-n*(c/n).floor
 # c.divmod(n)[1]
 #
 # See Numeric#divmod.
 #
 # Examples:
 #
 # r = Rational(1, 2) # => (1/2)
 # r2 = Rational(2, 3) # => (2/3)
 # r % r2 # => (1/2)
 # r % 2 # => (1/2)
 # r % 2.0 # => 0.5
 #
 # r = Rational(301,100) # => (301/100)
 # r2 = Rational(7,5) # => (7/5)
 # r % r2 # => (21/100)
 # r % -r2 # => (-119/100)
 # (-r) % r2 # => (119/100)
 # (-r) %-r2 # => (-21/100)
 #
 # Numeric#modulo is an alias for Numeric#%.
 #
 def %: (Numeric) -> Numeric

# Performs addition: the class of the resulting object depends on the class of
  # `numeric`.
  #
  def +: (Numeric) -> Numeric

# 
 # Returns `self`.
 #
 def +@: () -> Numeric

# Performs subtraction: the class of the resulting object depends on the class
  # of `numeric`.
  #
  def -: (Numeric) -> Numeric

# 
 # Unary Minus---Returns the receiver, negated.
 #
 def -@: () -> Numeric

# 
 # Returns zero if `self` is the same as `other`, `nil` otherwise.
 #
 # No subclass in the Ruby Core or Standard Library uses this implementation.
 #
 def <=>: (Numeric other) -> Integer

# 
 # Returns the absolute value of `self`.
 #
 # 12.abs #=> 12
 # (-34.56).abs #=> 34.56
 # -34.56.abs #=> 34.56
 #
 # Numeric#magnitude is an alias for Numeric#abs.
 #
 def abs: () -> Numeric

# 
 # Returns square of self.
 #
 def abs2: () -> Numeric

# 
 # Returns 0 if the value is positive, pi otherwise.
 #
 def angle: () -> Numeric

# 
 # Returns 0 if the value is positive, pi otherwise.
 #
 alias arg angle

# 
 # Returns the smallest number that is greater than or equal to `self` with a
 # precision of `digits` decimal digits.
 #
 # Numeric implements this by converting `self` to a Float and invoking
 # Float#ceil.
 #
 def ceil: () -> Integer
 | (Integer digits) -> (Integer | Numeric)

# 
 # Returns a 2-element array containing two numeric elements, formed from the two
 # operands `self` and `other`, of a common compatible type.
 #
 # Of the Core and Standard Library classes, Integer, Rational, and Complex use
 # this implementation.
 #
 # Examples:
 #
 # i = 2 # => 2
 # i.coerce(3) # => [3, 2]
 # i.coerce(3.0) # => [3.0, 2.0]
 # i.coerce(Rational(1, 2)) # => [0.5, 2.0]
 # i.coerce(Complex(3, 4)) # Raises RangeError.
 #
 # r = Rational(5, 2) # => (5/2)
 # r.coerce(2) # => [(2/1), (5/2)]
 # r.coerce(2.0) # => [2.0, 2.5]
 # r.coerce(Rational(2, 3)) # => [(2/3), (5/2)]
 # r.coerce(Complex(3, 4)) # => [(3+4i), ((5/2)+0i)]
 #
 # c = Complex(2, 3) # => (2+3i)
 # c.coerce(2) # => [(2+0i), (2+3i)]
 # c.coerce(2.0) # => [(2.0+0i), (2+3i)]
 # c.coerce(Rational(1, 2)) # => [((1/2)+0i), (2+3i)]
 # c.coerce(Complex(3, 4)) # => [(3+4i), (2+3i)]
 #
 # Raises an exception if any type conversion fails.
 #
 def coerce: (Numeric) -> [ Numeric, Numeric ]

# 
 # Returns self.
 #
 def conj: () -> Numeric

# 
 # Returns self.
 #
 def conjugate: () -> Numeric

# 
 # Returns the denominator (always positive).
 #
 def denominator: () -> Integer

# 
 # Returns the quotient `self/other` as an integer (via `floor`), using method
 # `/` in the derived class of `self`. (Numeric itself does not define method
 # `/`.)
 #
 # Of the Core and Standard Library classes, Float, Rational, and Complex use
 # this implementation.
 #
 def div: (Numeric) -> Integer

# 
 # Returns a 2-element array `[q, r]`, where
 #
 # q = (self/other).floor # Quotient
 # r = self % other # Remainder
 #
 # Of the Core and Standard Library classes, only Rational uses this
 # implementation.
 #
 # Examples:
 #
 # Rational(11, 1).divmod(4) # => [2, (3/1)]
 # Rational(11, 1).divmod(-4) # => [-3, (-1/1)]
 # Rational(-11, 1).divmod(4) # => [-3, (1/1)]
 # Rational(-11, 1).divmod(-4) # => [2, (-3/1)]
 #
 # Rational(12, 1).divmod(4) # => [3, (0/1)]
 # Rational(12, 1).divmod(-4) # => [-3, (0/1)]
 # Rational(-12, 1).divmod(4) # => [-3, (0/1)]
 # Rational(-12, 1).divmod(-4) # => [3, (0/1)]
 #
 # Rational(13, 1).divmod(4.0) # => [3, 1.0]
 # Rational(13, 1).divmod(Rational(4, 11)) # => [35, (3/11)]
 #
 def divmod: (Numeric) -> [ Numeric, Numeric ]

# 
 # Returns `true` if `self` and `other` are the same type and have equal values.
 #
 # Of the Core and Standard Library classes, only Integer, Rational, and Complex
 # use this implementation.
 #
 # Examples:
 #
 # 1.eql?(1) # => true
 # 1.eql?(1.0) # => false
 # 1.eql?(Rational(1, 1)) # => false
 # 1.eql?(Complex(1, 0)) # => false
 #
 # Method `eql?` is different from +==+ in that `eql?` requires matching types,
 # while +==+ does not.
 #
 def eql?: (untyped) -> bool

# 
 # Returns the quotient `self/other` as a float, using method `/` in the derived
 # class of `self`. (Numeric itself does not define method `/`.)
 #
 # Of the Core and Standard Library classes, only BigDecimal uses this
 # implementation.
 #
 def fdiv: (Numeric) -> Numeric

# 
 # Returns `true` if `num` is a finite number, otherwise returns `false`.
 #
 def finite?: () -> bool

# 
 # Returns the largest number that is less than or equal to `self` with a
 # precision of `digits` decimal digits.
 #
 # Numeric implements this by converting `self` to a Float and invoking
 # Float#floor.
 #
 def floor: () -> Integer
 | (Integer digits) -> Numeric

# 
 # Returns `Complex(0, self)`:
 #
 # 2.i # => (0+2i)
 # -2.i # => (0-2i)
 # 2.0.i # => (0+2.0i)
 # Rational(1, 2).i # => (0+(1/2)*i)
 # Complex(3, 4).i # Raises NoMethodError.
 #
 def i: () -> Complex

# 
 # Returns zero.
 #
 def imag: () -> Numeric

# 
 # Returns zero.
 #
 def imaginary: () -> Numeric

# 
 # Returns `nil`, -1, or 1 depending on whether the value is finite, `-Infinity`,
 # or `+Infinity`.
 #
 def infinite?: () -> Integer?

# 
 # Returns `true` if `num` is an Integer.
 #
 # 1.0.integer? #=> false
 # 1.integer? #=> true
 #
 def integer?: () -> bool

# 
 # Returns the absolute value of `self`.
 #
 # 12.abs #=> 12
 # (-34.56).abs #=> 34.56
 # -34.56.abs #=> 34.56
 #
 # Numeric#magnitude is an alias for Numeric#abs.
 #
 alias magnitude abs

# 
 # Returns `self` modulo `other` as a real number.
 #
 # Of the Core and Standard Library classes, only Rational uses this
 # implementation.
 #
 # For Rational `r` and real number `n`, these expressions are equivalent:
 #
 # c % n
 # c-n*(c/n).floor
 # c.divmod(n)[1]
 #
 # See Numeric#divmod.
 #
 # Examples:
 #
 # r = Rational(1, 2) # => (1/2)
 # r2 = Rational(2, 3) # => (2/3)
 # r % r2 # => (1/2)
 # r % 2 # => (1/2)
 # r % 2.0 # => 0.5
 #
 # r = Rational(301,100) # => (301/100)
 # r2 = Rational(7,5) # => (7/5)
 # r % r2 # => (21/100)
 # r % -r2 # => (-119/100)
 # (-r) % r2 # => (119/100)
 # (-r) %-r2 # => (-21/100)
 #
 # Numeric#modulo is an alias for Numeric#%.
 #
 def modulo: (Numeric) -> Numeric

# 
 # Returns `true` if `self` is less than 0, `false` otherwise.
 #
 def negative?: () -> bool

# 
 # Returns `self` if `self` is not a zero value, `nil` otherwise; uses method
 # `zero?` for the evaluation.
 #
 # The returned `self` allows the method to be chained:
 #
 # a = %w[z Bb bB bb BB a aA Aa AA A]
 # a.sort {|a, b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
 # # => ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]
 #
 # Of the Core and Standard Library classes, Integer, Float, Rational, and
 # Complex use this implementation.
 #
 def nonzero?: () -> self?

# 
 # Returns the numerator.
 #
 def numerator: () -> Numeric

# 
 # Returns 0 if the value is positive, pi otherwise.
 #
 alias phase angle

# 
 # Returns an array; [num.abs, num.arg].
 #
 def polar: () -> [ Numeric, Numeric ]

# 
 # Returns `true` if `self` is greater than 0, `false` otherwise.
 #
 def positive?: () -> bool

# 
 # Returns the most exact division (rational for integers, float for floats).
 #
 def quo: (Numeric) -> Numeric

# 
 # Returns self.
 #
 def real: () -> Numeric

# 
 # Returns `true` if `num` is a real number (i.e. not Complex).
 #
 def real?: () -> bool

# 
 # Returns an array; [num, 0].
 #
 def rect: () -> [ Numeric, Numeric ]

# 
 # Returns an array; [num, 0].
 #
 alias rectangular rect

# 
 # Returns the remainder after dividing `self` by `other`.
 #
 # Of the Core and Standard Library classes, only Float and Rational use this
 # implementation.
 #
 # Examples:
 #
 # 11.0.remainder(4) # => 3.0
 # 11.0.remainder(-4) # => 3.0
 # -11.0.remainder(4) # => -3.0
 # -11.0.remainder(-4) # => -3.0
 #
 # 12.0.remainder(4) # => 0.0
 # 12.0.remainder(-4) # => 0.0
 # -12.0.remainder(4) # => -0.0
 # -12.0.remainder(-4) # => -0.0
 #
 # 13.0.remainder(4.0) # => 1.0
 # 13.0.remainder(Rational(4, 1)) # => 1.0
 #
 # Rational(13, 1).remainder(4) # => (1/1)
 # Rational(13, 1).remainder(-4) # => (1/1)
 # Rational(-13, 1).remainder(4) # => (-1/1)
 # Rational(-13, 1).remainder(-4) # => (-1/1)
 #
 def remainder: (Numeric) -> Numeric

# 
 # Returns `self` rounded to the nearest value with a precision of `digits`
 # decimal digits.
 #
 # Numeric implements this by converting `self` to a Float and invoking
 # Float#round.
 #
 def round: () -> Integer
 | (Integer digits) -> Numeric

# 
 # Generates a sequence of numbers; with a block given, traverses the sequence.
 #
 # Of the Core and Standard Library classes,
 # Integer, Float, and Rational use this implementation.
 #
 # A quick example:
 #
 # squares = []
 # 1.step(by: 2, to: 10) {|i| squares.push(i*i) }
 # squares # => [1, 9, 25, 49, 81]
 #
 # The generated sequence:
 #
 # - Begins with +self+.
 # - Continues at intervals of +step+ (which may not be zero).
 # - Ends with the last number that is within or equal to +limit+;
 # that is, less than or equal to +limit+ if +step+ is positive,
 # greater than or equal to +limit+ if +step+ is negative.
 # If +limit+ is not given, the sequence is of infinite length.
 #
 # If a block is given, calls the block with each number in the sequence;
 # returns +self+. If no block is given, returns an Enumerator::ArithmeticSequence.
 #
 # Keyword Arguments
 #
 # With keyword arguments +by+ and +to+,
 # their values (or defaults) determine the step and limit:
 #
 # # Both keywords given.
 # squares = []
 # 4.step(by: 2, to: 10) {|i| squares.push(i*i) } # => 4
 # squares # => [16, 36, 64, 100]
 # cubes = []
 # 3.step(by: -1.5, to: -3) {|i| cubes.push(i*i*i) } # => 3
 # cubes # => [27.0, 3.375, 0.0, -3.375, -27.0]
 # squares = []
 # 1.2.step(by: 0.2, to: 2.0) {|f| squares.push(f*f) }
 # squares # => [1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
 #
 # squares = []
 # Rational(6/5).step(by: 0.2, to: 2.0) {|r| squares.push(r*r) }
 # squares # => [1.0, 1.44, 1.9599999999999997, 2.5600000000000005, 3.24, 4.0]
 #
 # # Only keyword to given.
 # squares = []
 # 4.step(to: 10) {|i| squares.push(i*i) } # => 4
 # squares # => [16, 25, 36, 49, 64, 81, 100]
 # # Only by given.
 #
 # # Only keyword by given
 # squares = []
 # 4.step(by:2) {|i| squares.push(i*i); break if i > 10 }
 # squares # => [16, 36, 64, 100, 144]
 #
 # # No block given.
 # e = 3.step(by: -1.5, to: -3) # => (3.step(by: -1.5, to: -3))
 # e.class # => Enumerator::ArithmeticSequence
 #
 # Positional Arguments
 #
 # With optional positional arguments +limit+ and +step+,
 # their values (or defaults) determine the step and limit:
 #
 # squares = []
 # 4.step(10, 2) {|i| squares.push(i*i) } # => 4
 # squares # => [16, 36, 64, 100]
 # squares = []
 # 4.step(10) {|i| squares.push(i*i) }
 # squares # => [16, 25, 36, 49, 64, 81, 100]
 # squares = []
 # 4.step {|i| squares.push(i*i); break if i > 10 } # => nil
 # squares # => [16, 25, 36, 49, 64, 81, 100, 121]
 #
 # **Implementation Notes**
 #
 # If all the arguments are integers, the loop operates using an integer
 # counter.
 #
 # If any of the arguments are floating point numbers, all are converted
 # to floats, and the loop is executed
 # floor(n + n*Float::EPSILON) + 1 times,
 # where n = (limit - self)/step.
 #
 def step: (?Numeric limit, ?Numeric step) { (Numeric) -> void } -> self
 | (?Numeric limit, ?Numeric step) -> Enumerator[Numeric, self]
 | (?by: Numeric, ?to: Numeric) { (Numeric) -> void } -> self
 | (?by: Numeric, ?to: Numeric) -> Enumerator[Numeric, self]

# 
 # Returns the value as a complex.
 #
 def to_c: () -> Complex

# 
 # Returns `self` as an integer; converts using method `to_i` in the derived
 # class.
 #
 # Of the Core and Standard Library classes, only Rational and Complex use this
 # implementation.
 #
 # Examples:
 #
 # Rational(1, 2).to_int # => 0
 # Rational(2, 1).to_int # => 2
 # Complex(2, 0).to_int # => 2
 # Complex(2, 1) # Raises RangeError (non-zero imaginary part)
 #
 def to_int: () -> Integer

# 
 # Returns `self` truncated (toward zero) to a precision of `digits` decimal
 # digits.
 #
 # Numeric implements this by converting `self` to a Float and invoking
 # Float#truncate.
 #
 def truncate: () -> Integer
 | (Integer ndigits) -> (Integer | Numeric)

# 
 # Returns `true` if `zero` has a zero value, `false` otherwise.
 #
 # Of the Core and Standard Library classes, only Rational and Complex use this
 # implementation.
 #
 def zero?: () -> bool

# 
 # Returns `self`.
 #
 # Raises an exception if the value for `freeze` is neither `true` nor `nil`.
 #
 # Related: Numeric#dup.
 #
 def clone: (?freeze: true?) -> self
end

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