Class

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

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

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

See Numeric#divmod.

Unary Plus—Returns the receiver.

Unary Minus—Returns the receiver, negated.

Returns zero if number equals other, otherwise returns nil.

Returns the absolute value of num.

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

Numeric#magnitude is an alias for Numeric#abs.

Returns square of self.

Returns 0 if the value is positive, pi otherwise.

Returns 0 if the value is positive, pi otherwise.

Returns the smallest number greater than or equal to num with a precision of ndigits decimal digits (default: 0).

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

Returns the receiver. freeze cannot be false.

If numeric is the same type as num, returns an array [numeric, num]. Otherwise, returns an array with both 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]

Returns the denominator (always positive).

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 Numeric#divmod.

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 negative 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]

Returns the receiver.

Returns true if num and numeric are the same type and have equal values. Contrast this with Numeric#==, which performs type conversions.

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

Returns float division.

Returns true if num is a finite number, otherwise returns false.

Returns the largest number less than or equal to num with a precision of ndigits decimal digits (default: 0).

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

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

-42.i  #=> (0-42i)
2.0.i  #=> (0+2.0i)

Returns zero.

Returns nil, -1, or 1 depending on whether the value is finite, -Infinity, or +Infinity.

Returns true if num is an Integer.

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

Returns the absolute value of num.

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

Numeric#magnitude is an alias for Numeric#abs.

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

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

See Numeric#divmod.

Returns true if num is less than 0.

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"]

Returns the numerator.

Returns 0 if the value is positive, pi otherwise.

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

Returns true if num is greater than 0.

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

Returns self.

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

Returns an array; [num, 0].

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

See Numeric#divmod.

Returns num rounded to the nearest value with a precision of ndigits decimal digits (default: 0).

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

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 floor(n + n*Float::EPSILON) + 1 times, where 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. Especially, the enumerator is an Enumerator::ArithmeticSequence if both limit and step are kind of Numeric or nil.

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
2.718281828459045 2.9182818284590453 3.118281828459045

Returns the value as a complex.

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

1.0.class          #=> Float
1.0.to_int.class   #=> Integer
1.0.to_i.class     #=> Integer

Returns num truncated (toward zero) to a precision of ndigits decimal digits (default: 0).

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

Returns true if num has a zero value.