Class

# Numeric

Inheritance
< Object
Included Modules
Comparable

Numeric is a built-in class on which Fixnum, Bignum, etc., are based. Here some methods are added so that all number types can be treated to some extent as Complex numbers.

## Methods

### Instance

Visibility Signature
public +@ ()
public -@ ()
public <=> (p1)
public abs ()
public angle ()
public arg ()
public ceil ()
public coerce (p1)
public conj ()
public conjugate ()
public div (p1)
public divmod (p1)
public eql? (p1)
public fdiv (p1)
public floor ()
public im ()
public imag ()
public image ()
public integer? ()
public modulo (p1)
public nonzero? ()
public polar ()
public quo (p1)
public real ()
public remainder (p1)
public round ()
public step (...)
public to_int ()
public truncate ()
public zero? ()

## Instance Method Detail

#### -num => numeric

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

#### num <=> other → 0 or nil

Returns zero if num equals other, nil otherwise.

#### num.abs => num or numeric

Returns the absolute value of num.

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

Alias for arg

#### num.ceil => integer

Returns the smallest Integer greater than or equal to num. Class 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
```

#### num.coerce(numeric) => array

If aNumeric is the same type as num, returns an array containing aNumeric and num. Otherwise, returns an array with both aNumeric 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()

Alias for conjugate

#### conjugate()

See Complex#conjugate (short answer: returns self).

#### num.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.

#### num.divmod( aNumeric ) → anArray

Returns an array containing the quotient and modulus obtained by dividing num by aNumeric. If q, r = x.divmod(y), then

```    q = floor(float(x)/float(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     |  -3     |   -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]
```

#### num.eql?(numeric) => true or false

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
```

#### num.quo(numeric) => result num.fdiv(numeric) => result

Equivalent to Numeric#/, but overridden in subclasses.

#### num.floor => integer

Returns the largest integer less than or equal to num. Numeric implements this by converting anInteger to a Float and invoking Float#floor.

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

#### im()

Returns a Complex number (0,self).

Alias for image

#### image()

The imaginary part of a complex number, i.e. 0.

#### num.integer? → true or false

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

#### num.modulo(numeric) => result

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

#### num.nonzero? => num or nil

Returns num 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"]
```

#### num.quo(numeric) => result num.fdiv(numeric) => result

Equivalent to Numeric#/, but overridden in subclasses.

#### real()

The real part of a complex number, i.e. self.

#### num.remainder(numeric) => result

If num and numeric have different signs, returns mod-numeric; otherwise, returns mod. In both cases mod is the value num.modulo(numeric). The differences between remainder and modulo (%) are shown in the table under Numeric#divmod.

#### num.round => integer

Rounds num to the nearest integer. Numeric implements this by converting itself to a Float and invoking Float#round.

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

#### num.step(limit, step ) {|i| block } => num

Invokes block with the sequence of numbers starting at num, incremented by step 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). 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*epsilon)+ 1 times, where n = (limit - num)/step. Otherwise, the loop starts at num, uses either the < or > operator to compare the counter against limit, and increments itself using the + operator.

```   1.step(10, 2) { |i| print i, " " }
Math::E.step(Math::PI, 0.2) { |f| print f, " " }
```

produces:

```   1 3 5 7 9
2.71828182845905 2.91828182845905 3.11828182845905
```

#### num.to_int => integer

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

#### num.truncate => integer

Returns num truncated to an integer. Numeric implements this by converting its value to a float and invoking Float#truncate.

#### num.zero? => true or false

Returns true if num has a zero value.