Class: Numeric

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 self.

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

Returns true if num has a zero value.

Unary Plus—Returns the receiver's value.

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

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

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.

Returns square of self.

Alias for #arg.

Returns 0 if the value is positive, pi otherwise.

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

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]

Returns self.

Alias for #conj.

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 #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 -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 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

Returns float division.

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

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

Returns zero.

Alias for #imag.

Numerics are immutable values, which should not be copied.

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

Alias for #abs.

Alias for #%.

Returns the numerator.

Alias for #arg.

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

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

Returns an array; [num, 0].

Alias for #rect.

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

See #divmod.

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.

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

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

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

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 => Fixnum
1.0.to_i.class => Fixnum

Returns num truncated to an ::Integer.

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