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

What’s Here

First, what’s elsewhere. Class Numeric:

Here, class Numeric provides methods for:

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

  • #<=>: 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.

Instance Methods

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#%.

Returns self.

Unary Minus—Returns the receiver, negated.

Returns zero if self is the same as other, nil otherwise.

No subclass in the Ruby Core or Standard Library uses this implementation.

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.

Returns square of self.

Returns 0 if the value is positive, pi otherwise.

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.

Returns self.

Raises an exception if the value for freeze is neither true nor nil.

Related: Numeric#dup.

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.

Returns self.

Returns the denominator (always positive).

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.

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)]

Returns self.

Related: Numeric#clone.

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.

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.

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

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.

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.

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
An alias for abs
An alias for %

Returns true if self is less than 0, false otherwise.

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.

Returns the numerator.

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

Returns true if self is greater than 0, false otherwise.

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].

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)

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.

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.

<b>Keyword Arguments</b>

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

<b>Positional Arguments</b>

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
<i>floor(n + n*Float::EPSILON) + 1</i> times,
where <i>n = (limit - self)/step</i>.

Returns the value as a 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)

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.

Returns true if zero has a zero value, false otherwise.

Of the Core and Standard Library classes, only Rational and Complex use this implementation.