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Class: Numeric

Relationships & Source Files
Extension / Inclusion / Inheritance Descendants
Subclasses:
Bignum, Complex, Fixnum, Float, Integer, Rational
Super Chains via Extension / Inclusion / Inheritance
Instance Chain:
self, ::Comparable
Inherits: Object
Defined in: numeric.c,
complex.c,
rational.c

Overview

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
puts 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 and duplication.

Integer.new(1)   #=> NoMethodError: undefined method `new' for Integer:Class
1.dup            #=> TypeError: can't dup Fixnum

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

Instance Attribute Summary

Instance Method Summary

::Comparable - Included

#<

Compares two objects based on the receiver's #<=> method, returning true if it returns -1.
#<=

Compares two objects based on the receiver's #<=> method, returning true if it returns -1 or 0.
#==

Compares two objects based on the receiver's #<=> method, returning true if it returns 0.
#>

Compares two objects based on the receiver's #<=> method, returning true if it returns 1.
#>=

Compares two objects based on the receiver's #<=> method, returning true if it returns 0 or 1.
#between?

Returns false if obj #<=> min is less than zero or if anObject #<=> max is greater than zero, true otherwise.

Instance Attribute Details

#integer? ⇒ Boolean (readonly)

Returns true if num is an ::Integer (including ::Fixnum and ::Bignum).

(1.0).integer? #=> false
(1).integer?   #=> true

#negative? ⇒ Boolean (readonly)

Returns true if num is less than 0.

#nonzero? ⇒ Boolean (readonly)

Returns self if num is not zero, nil otherwise.

This behavior is useful when chaining comparisons:

a = %w( z Bb bB bb BB a aA Aa AA A )
b = a.sort {|a,b| (a.downcase <=> b.downcase).nonzero? || a <=> b }
b   #=> ["A", "a", "AA", "Aa", "aA", "BB", "Bb", "bB", "bb", "z"]

#positive? ⇒ Boolean (readonly)

Returns true if num is greater than 0.

#real ⇒ self (readonly)

Returns self.

#real? ⇒ Boolean (readonly)

Returns true if num is a Real number. (i.e. not ::Complex).

#zero? ⇒ Boolean (readonly)

Returns true if num has a zero value.

Instance Method Details

#modulo(numeric) ⇒ Numeric Also known as: #modulo

x.modulo(y) means x-y*(x/y).floor

Equivalent to num.divmod(numeric)[1].

See #divmod.

#+ ⇒ Numeric

Unary Plus—Returns the receiver's value.

#- ⇒ Numeric

Unary Minus—Returns the receiver's value, negated.

#<=>(other) ⇒ 0?

Returns zero if number equals other, otherwise nil is returned if the two values are incomparable.

#abs ⇒ Numeric #magnitude ⇒ Numeric
Also known as: #magnitude

Returns the absolute value of num.

12.abs         #=> 12
(-34.56).abs   #=> 34.56
-34.56.abs     #=> 34.56

#magnitude is an alias of abs.

#abs2 ⇒ Numeric

Returns square of self.

#arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

Alias for #arg.

#arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float
Also known as: #angle, #phase

Returns 0 if the value is positive, pi otherwise.

#ceil ⇒ Integer

Returns the smallest possible ::Integer that is greater than or equal to num.

Numeric achieves this by converting itself to a ::Float then invoking Float#ceil.

1.ceil        #=> 1
1.2.ceil      #=> 2
(-1.2).ceil   #=> -1
(-1.0).ceil   #=> -1

#coerce(numeric) ⇒ Array

If a numeric is the same type as num, returns an array containing numeric and num. Otherwise, returns an array with both a numeric and num represented as ::Float objects.

This coercion mechanism is used by Ruby to handle mixed-type numeric operations: it is intended to find a compatible common type between the two operands of the operator.

1.coerce(2.5)   #=> [2.5, 1.0]
1.2.coerce(3)   #=> [3.0, 1.2]
1.coerce(2)     #=> [2, 1]

#conj ⇒ self #conjugate ⇒ self
Also known as: #conjugate

Returns self.

#conj ⇒ self #conjugate ⇒ self

Alias for #conj.

#denominator ⇒ Integer

Returns the denominator (always positive).

#div(numeric) ⇒ Integer

Uses / to perform division, then converts the result to an integer. numeric does not define the / operator; this is left to subclasses.

Equivalent to num.divmod(numeric)[0].

See #divmod.

#divmod(numeric) ⇒ Array

Returns an array containing the quotient and modulus obtained by dividing num by numeric.

If q, r = * x.divmod(y), then

q = floor(x/y)
x = q*y+r

The quotient is rounded toward -infinity, as shown in the following table:

a    |  b  |  a.divmod(b)  |   a/b   | a.modulo(b) | a.remainder(b)
------------------------------------------------+---------------
 13   |  4  |   3,    1     |   3     |    1        |     1
------------------------------------------------+---------------
 13   | -4  |  -4,   -3     |  -4     |   -3        |     1
------------------------------------------------+---------------
-13   |  4  |  -4,    3     |  -4     |    3        |    -1
------------------------------------------------+---------------
-13   | -4  |   3,   -1     |   3     |   -1        |    -1
------------------------------------------------+---------------
 11.5 |  4  |   2,    3.5   |   2.875 |    3.5      |     3.5
------------------------------------------------+---------------
 11.5 | -4  |  -3,   -0.5   |  -2.875 |   -0.5      |     3.5
------------------------------------------------+---------------
-11.5 |  4  |  -3,    0.5   |  -2.875 |    0.5      |    -3.5
------------------------------------------------+---------------
-11.5 | -4  |   2,   -3.5   |   2.875 |   -3.5      |    -3.5

Examples

11.divmod(3)         #=> [3, 2]
11.divmod(-3)        #=> [-4, -1]
11.divmod(3.5)       #=> [3, 0.5]
(-11).divmod(3.5)    #=> [-4, 3.0]
(11.5).divmod(3.5)   #=> [3, 1.0]

#eql?(numeric) ⇒ Boolean

Returns true if num and numeric are the same type and have equal values.

1 == 1.0          #=> true
1.eql?(1.0)       #=> false
(1.0).eql?(1.0)   #=> true

#fdiv(numeric) ⇒ Float

Returns float division.

#floor ⇒ Integer

Returns the largest integer less than or equal to num.

Numeric implements this by converting an ::Integer to a ::Float and invoking Float#floor.

1.floor      #=> 1
(-1).floor   #=> -1

#i ⇒ Complex(0, num)

Returns the corresponding imaginary number. Not available for complex numbers.

#imag ⇒ 0 #imaginary ⇒ 0
Also known as: #imaginary

Returns zero.

#imag ⇒ 0 #imaginary ⇒ 0

Alias for #imag.

#initialize_copy(y)

Numerics are immutable values, which should not be copied.

Any attempt to use this method on a Numeric will raise a ::TypeError.

#abs ⇒ Numeric #magnitude ⇒ Numeric

Alias for #abs.

#modulo(numeric) ⇒ Numeric #modulo(numeric) ⇒ Numeric

Alias for #%.

#numerator ⇒ Integer

Returns the numerator.

#arg ⇒ 0, Float #angle ⇒ 0, Float #phase ⇒ 0, Float

Alias for #arg.

#polar ⇒ Array

Returns an array; [num.abs, num.arg].

#quo(int_or_rat) ⇒ rat #quo(flo) ⇒ flo

Returns most exact division (rational for integers, float for floats).

#rect ⇒ Array #rectangular ⇒ Array
Also known as: #rectangular

Returns an array; [num, 0].

#rect ⇒ Array #rectangular ⇒ Array

Alias for #rect.

#remainder(numeric) ⇒ Numeric

x.remainder(y) means x-y*(x/y).truncate

See #divmod.

#round([ndigits]) ⇒ Integer, Float

Rounds num to a given precision in decimal digits (default 0 digits).

Precision may be negative. Returns a floating point number when ndigits is more than zero.

Numeric implements this by converting itself to a ::Float and invoking Float#round.

#singleton_method_added(name)

Trap attempts to add methods to Numeric objects. Always raises a ::TypeError.

Numerics should be values; singleton_methods should not be added to them.

#step(by: step, to: limit) {|i| ... } ⇒ self #step(by: step, to: limit) ⇒ Enumerator #step(limit = nil, step = 1) {|i| ... } ⇒ self #step(limit = nil, step = 1) ⇒ Enumerator

Invokes the given block with the sequence of numbers starting at num, incremented by step (defaulted to 1) on each call.

The loop finishes when the value to be passed to the block is greater than limit (if step is positive) or less than limit (if step is negative), where limit is defaulted to infinity.

In the recommended keyword argument style, either or both of step and limit (default infinity) can be omitted. In the fixed position argument style, zero as a step (i.e. num.step(limit, 0)) is not allowed for historical compatibility reasons.

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 the following expression:

floor(n + n*epsilon)+ 1

Where the n is the following:

n = (limit - num)/step

Otherwise, the loop starts at num, uses either the less-than (<) or greater-than (>) operator to compare the counter against limit, and increments itself using the + operator.

If no block is given, an ::Enumerator is returned instead.

For example:

p 1.step.take(4)
p 10.step(by: -1).take(4)
3.step(to: 5) { |i| print i, " " }
1.step(10, 2) { |i| print i, " " }
Math::E.step(to: Math::PI, by: 0.2) { |f| print f, " " }

Will produce:

[1, 2, 3, 4]
[10, 9, 8, 7]
3 4 5
1 3 5 7 9
2.71828182845905 2.91828182845905 3.11828182845905

#to_c ⇒ Complex

Returns the value as a complex.

#to_int ⇒ Integer

Invokes the child class's to_i method to convert num to an integer.

1.0.class => Float
1.0.to_int.class => Fixnum
1.0.to_i.class => Fixnum

#truncate ⇒ Integer

Returns num truncated to an ::Integer.

Numeric implements this by converting its value to a ::Float and invoking Float#truncate.