Class: Numeric

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

Inherits from class Object.
Includes module Comparable.

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 Attribute Summary

#finite? ⇒ Boolean readonly

Returns true if self is a finite number, false otherwise.
#infinite? ⇒ Boolean readonly

Returns nil, -1, or 1 depending on whether self is finite, -Infinity, or +Infinity.
#integer? ⇒ Boolean readonly

Returns true if self is an ::Integer.
#negative? ⇒ Boolean readonly

Returns true if self is less than 0, false otherwise.
#nonzero? ⇒ Boolean readonly

Returns self if self is not a zero value, nil otherwise; uses method #zero? for the evaluation.
#positive? ⇒ Boolean readonly

Returns true if self is greater than 0, false otherwise.
#real? ⇒ Boolean readonly

Returns true if self is a real number (i.e.
#zero? ⇒ Boolean readonly

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

Instance Method Summary

#%(other) ⇒ Numeric (also: #modulo)

Returns self modulo other as a real number.
#+ ⇒ self

Returns self.
#- ⇒ Numeric

Unary Minus—Returns the receiver, negated.
#<=>(other) ⇒ zero^?

Returns zero if self is the same as other, nil otherwise.
#abs ⇒ Numeric (also: #magnitude)

Returns the absolute value of self.
#abs2 ⇒ Numeric

Returns the square of self.
#angle ⇒ 0, Math::PI

Alias for #arg.
#arg ⇒ 0, Math::PI (also: #angle, #phase)

Returns zero if self is positive, Math::PI otherwise.
#ceil(digits = 0) ⇒ Integer, Float

Returns the smallest number that is greater than or equal to self with a precision of digits decimal digits.
#clone(freeze: true) ⇒ self

Returns self.
#coerce(other) ⇒ Array

Returns a 2-element array containing two numeric elements, formed from the two operands self and other, of a common compatible type.
#conj

Alias for #conjugate.
#conj ⇒ self (also: #conj)

Returns self.
#denominator ⇒ Integer

Returns the denominator (always positive).
#div(other) ⇒ Integer

Returns the quotient self/other as an integer (via #floor), using method / in the derived class of self.
#divmod(other) ⇒ Array

Returns a 2-element array [q, r], where.
#dup ⇒ self

Returns self.
#eql?(other) ⇒ Boolean

Returns true if self and other are the same type and have equal values.
#fdiv(other) ⇒ Float

Returns the quotient self/other as a float, using method / in the derived class of self.
#floor(digits = 0) ⇒ Integer, Float

Returns the largest number that is less than or equal to self with a precision of digits decimal digits.
#i ⇒ Complex

Returns Complex(0, self):
#imag

Alias for #imaginary.
#imag ⇒ 0 (also: #imag)

Returns zero.
#magnitude ⇒ Numeric

Alias for #abs.
#modulo(other) ⇒ Numeric

Alias for #%.
#numerator ⇒ Integer

Returns the numerator.
#phase ⇒ 0, Math::PI

Alias for #arg.
#polar ⇒ Array

Returns array [self.abs, self.arg].
#quo(int_or_rat) ⇒ rat

Returns the most exact division (rational for integers, float for floats).
#real ⇒ self readonly

Returns self.
#rect ⇒ Array (also: #rectangular)

Returns array [self, 0].
#rectangular ⇒ Array

Alias for #rect.
#remainder(other) ⇒ real_number

Returns the remainder after dividing self by other.
#round(digits = 0) ⇒ Integer, Float

Returns self rounded to the nearest value with a precision of digits decimal digits.
#step(to = nil, by = 1) {|n| ... } ⇒ self

Generates a sequence of numbers; with a block given, traverses the sequence.
#to_c ⇒ Complex

Returns self as a ::Complex object.
#to_int ⇒ Integer

Returns self as an integer; converts using method to_i in the derived class.
#truncate(digits = 0) ⇒ Integer, Float

Returns self truncated (toward zero) to a precision of digits decimal digits.
#singleton_method_added(name) Internal use only

Trap attempts to add methods to Numeric objects.

`::Comparable` - Included

#<	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value less than 0.
#<=	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value less than or equal to 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 a value greater than 0.
#>=	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value greater than or equal to 0.
#between?	Returns `false` if obj #<=> min is less than zero or if obj #<=> max is greater than zero, `true` otherwise.
#clamp	In `(min, max)` form, returns min if obj #<=> min is less than zero, max if obj #<=> max is greater than zero, and obj otherwise.

Instance Attribute Details

#finite? ⇒ `Boolean` (readonly)

Returns true if self is a finite number, false otherwise.

[ GitHub ]

# File 'numeric.rb', line 38


def finite?
  true
end

#infinite? ⇒ `Boolean` (readonly)

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

[ GitHub ]

# File 'numeric.rb', line 48


def infinite?
  nil
end

#integer? ⇒ `Boolean` (readonly)

Returns true if self is an ::Integer.

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

[ GitHub ]

# File 'numeric.rb', line 29


def integer?
  false
end

#negative? ⇒ `Boolean` (readonly)

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

[ GitHub ]

# File 'numeric.c', line 933


static VALUE
num_negative_p(VALUE num)
{
    return RBOOL(rb_num_negative_int_p(num));
}

#nonzero? ⇒ `Boolean` (readonly)

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.

[ GitHub ]

# File 'numeric.c', line 867


static VALUE
num_nonzero_p(VALUE num)
{
    if (RTEST(num_funcall0(num, rb_intern("zero?")))) {
        return Qnil;
    }
    return num;
}

#positive? ⇒ `Boolean` (readonly)

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

[ GitHub ]

# File 'numeric.c', line 909


static VALUE
num_positive_p(VALUE num)
{
    const ID mid = '>';

    if (FIXNUM_P(num)) {
        if (method_basic_p(rb_cInteger))
            return RBOOL((SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0));
    }
    else if (RB_BIGNUM_TYPE_P(num)) {
        if (method_basic_p(rb_cInteger))
            return RBOOL(BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num));
    }
    return rb_num_compare_with_zero(num, mid);
}

#real? ⇒ `Boolean` (readonly)

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

[ GitHub ]

# File 'numeric.rb', line 8


def real?
  true
end

#zero? ⇒ `Boolean` (readonly)

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

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

[ GitHub ]

# File 'numeric.c', line 827


static VALUE
num_zero_p(VALUE num)
{
    return rb_equal(num, INT2FIX(0));
}

Instance Method Details

#%(other) ⇒ `Numeric` Also known as: #modulo

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:

r % n
r-n*(r/n).floor
r.divmod(n)[1]

See #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)

[ GitHub ]

# File 'numeric.c', line 699


static VALUE
num_modulo(VALUE x, VALUE y)
{
    VALUE q = num_funcall1(x, id_div, y);
    return rb_funcall(x, '-', 1,
                      rb_funcall(y, '*', 1, q));
}

#+ ⇒ `self`

Returns self.

[ GitHub ]

# File 'numeric.c', line 582


static VALUE
num_uplus(VALUE num)
{
    return num;
}

#- ⇒ `Numeric`

Unary Minus—Returns the receiver, negated.

[ GitHub ]

# File 'numeric.c', line 615


static VALUE
num_uminus(VALUE num)
{
    VALUE zero;

    zero = INT2FIX(0);
    do_coerce(&zero, &num, TRUE);

    return num_funcall1(zero, '-', num);
}

#<=>(other) ⇒ `zero`^?

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

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

[ GitHub ]

# File 'numeric.c', line 1580


static VALUE
num_cmp(VALUE x, VALUE y)
{
    if (x == y) return INT2FIX(0);
    return Qnil;
}

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

Returns the absolute value of self.

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

[ GitHub ]

# File 'numeric.c', line 807


static VALUE
num_abs(VALUE num)
{
    if (rb_num_negative_int_p(num)) {
        return num_funcall0(num, idUMinus);
    }
    return num;
}

#abs2 ⇒ `Numeric`

Returns the square of self.

[ GitHub ]

# File 'complex.c', line 2376


static VALUE
numeric_abs2(VALUE self)
{
    return f_mul(self, self);
}

#arg ⇒ `0`, Math::PI #angle ⇒ `0`, Math::PI

Alias for #arg.

#arg ⇒ `0`, Math::PI Also known as: #angle, #phase

Returns zero if self is positive, Math::PI otherwise.

[ GitHub ]

# File 'complex.c', line 2388


static VALUE
numeric_arg(VALUE self)
{
    if (f_positive_p(self))
        return INT2FIX(0);
    return DBL2NUM(M_PI);
}

#ceil(digits = 0) ⇒ Integer, Float

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.

[ GitHub ]

# File 'numeric.c', line 2679


static VALUE
num_ceil(int argc, VALUE *argv, VALUE num)
{
    return flo_ceil(argc, argv, rb_Float(num));
}

#clone(freeze: true) ⇒ `self`

Returns self.

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

Related: #dup.

[ GitHub ]

# File 'numeric.c', line 546


static VALUE
num_clone(int argc, VALUE *argv, VALUE x)
{
    return rb_immutable_obj_clone(argc, argv, x);
}

#coerce(other) ⇒ Array

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.

[ GitHub ]

# File 'numeric.c', line 430


static VALUE
num_coerce(VALUE x, VALUE y)
{
    if (CLASS_OF(x) == CLASS_OF(y))
        return rb_assoc_new(y, x);
    x = rb_Float(x);
    y = rb_Float(y);
    return rb_assoc_new(y, x);
}

#conj

Alias for #conjugate.

[ GitHub ]

# File 'numeric.rb', line 72


alias conj conjugate

#conj ⇒ `self` Also known as: #conj

Returns self.

[ GitHub ]

# File 'numeric.rb', line 68


def conjugate
  self
end

#denominator ⇒ Integer

Returns the denominator (always positive).

[ GitHub ]

# File 'rational.c', line 2022


static VALUE
numeric_denominator(VALUE self)
{
    return f_denominator(f_to_r(self));
}

#div(other) ⇒ Integer

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, Only Float and ::Rational use this implementation.

[ GitHub ]

# File 'numeric.c', line 658


static VALUE
num_div(VALUE x, VALUE y)
{
    if (rb_equal(INT2FIX(0), y)) rb_num_zerodiv();
    return rb_funcall(num_funcall1(x, '/', y), rb_intern("floor"), 0);
}

#divmod(other) ⇒ Array

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)]

[ GitHub ]

# File 'numeric.c', line 789


static VALUE
num_divmod(VALUE x, VALUE y)
{
    return rb_assoc_new(num_div(x, y), num_modulo(x, y));
}

#dup ⇒ `self`

Returns self.

Related: #clone.

[ GitHub ]

# File 'numeric.c', line 565


static VALUE
num_dup(VALUE x)
{
    return x;
}

#eql?(other) ⇒ `Boolean`

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.

[ GitHub ]

# File 'numeric.c', line 1558


static VALUE
num_eql(VALUE x, VALUE y)
{
    if (TYPE(x) != TYPE(y)) return Qfalse;

    if (RB_BIGNUM_TYPE_P(x)) {
        return rb_big_eql(x, y);
    }

    return rb_equal(x, y);
}

#fdiv(other) ⇒ Float

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.

[ GitHub ]

# File 'numeric.c', line 639


static VALUE
num_fdiv(VALUE x, VALUE y)
{
    return rb_funcall(rb_Float(x), '/', 1, y);
}

#floor(digits = 0) ⇒ Integer, Float

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.

[ GitHub ]

# File 'numeric.c', line 2662


static VALUE
num_floor(int argc, VALUE *argv, VALUE num)
{
    return flo_floor(argc, argv, rb_Float(num));
}

#i ⇒ Complex

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.

[ GitHub ]

# File 'numeric.c', line 602


static VALUE
num_imaginary(VALUE num)
{
    return rb_complex_new(INT2FIX(0), num);
}

#imag

Alias for #imaginary.

[ GitHub ]

# File 'numeric.rb', line 61


alias imag imaginary

#imag ⇒ `0` Also known as: #imag

Returns zero.

[ GitHub ]

# File 'numeric.rb', line 57


def imaginary
  0
end

#abs ⇒ `Numeric` #magnitude ⇒ `Numeric`

Alias for #abs.

#%(other) ⇒ `Numeric` #modulo(other) ⇒ `Numeric`

Alias for #%.

#numerator ⇒ Integer

Returns the numerator.

[ GitHub ]

# File 'rational.c', line 2010


static VALUE
numeric_numerator(VALUE self)
{
    return f_numerator(f_to_r(self));
}

#arg ⇒ `0`, Math::PI #phase ⇒ `0`, Math::PI

Alias for #arg.

#polar ⇒ Array

Returns array [self.abs, self.arg].

[ GitHub ]

# File 'complex.c', line 2414


static VALUE
numeric_polar(VALUE self)
{
    VALUE abs, arg;

    if (RB_INTEGER_TYPE_P(self)) {
        abs = rb_int_abs(self);
        arg = numeric_arg(self);
    }
    else if (RB_FLOAT_TYPE_P(self)) {
        abs = rb_float_abs(self);
        arg = float_arg(self);
    }
    else if (RB_TYPE_P(self, T_RATIONAL)) {
        abs = rb_rational_abs(self);
        arg = numeric_arg(self);
    }
    else {
        abs = f_abs(self);
        arg = f_arg(self);
    }
    return rb_assoc_new(abs, arg);
}

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

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

[ GitHub ]

# File 'rational.c', line 2037


VALUE
rb_numeric_quo(VALUE x, VALUE y)
{
    if (RB_TYPE_P(x, T_COMPLEX)) {
        return rb_complex_div(x, y);
    }

    if (RB_FLOAT_TYPE_P(y)) {
        return rb_funcallv(x, idFdiv, 1, &y);
    }

    x = rb_convert_type(x, T_RATIONAL, "Rational", "to_r");
    return rb_rational_div(x, y);
}

#real ⇒ `self` (readonly)

Returns self.

[ GitHub ]

# File 'numeric.rb', line 17


def real
  self
end

#rect ⇒ Array Also known as: #rectangular

Returns array [self, 0].

[ GitHub ]

# File 'complex.c', line 2402


static VALUE
numeric_rect(VALUE self)
{
    return rb_assoc_new(self, INT2FIX(0));
}

#rect ⇒ Array #rectangular ⇒ Array

Alias for #rect.

#remainder(other) ⇒ `real_number`

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)

[ GitHub ]

# File 'numeric.c', line 738


static VALUE
num_remainder(VALUE x, VALUE y)
{
    if (!rb_obj_is_kind_of(y, rb_cNumeric)) {
        do_coerce(&x, &y, TRUE);
    }
    VALUE z = num_funcall1(x, '%', y);

    if ((!rb_equal(z, INT2FIX(0))) &&
        ((rb_num_negative_int_p(x) &&
          rb_num_positive_int_p(y)) ||
         (rb_num_positive_int_p(x) &&
          rb_num_negative_int_p(y)))) {
        if (RB_FLOAT_TYPE_P(y)) {
            if (isinf(RFLOAT_VALUE(y))) {
                return x;
            }
        }
        return rb_funcall(z, '-', 1, y);
    }
    return z;
}

#round(digits = 0) ⇒ Integer, Float

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.

[ GitHub ]

# File 'numeric.c', line 2696


static VALUE
num_round(int argc, VALUE* argv, VALUE num)
{
    return flo_round(argc, argv, rb_Float(num));
}

#singleton_method_added(name)

This method is for internal use only.

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

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

[ GitHub ]

# File 'numeric.c', line 520


static VALUE
num_sadded(VALUE x, VALUE name)
{
    ID mid = rb_to_id(name);
    /* ruby_frame = ruby_frame->prev; */ /* pop frame for "singleton_method_added" */
    rb_remove_method_id(rb_singleton_class(x), mid);
    rb_raise(rb_eTypeError,
             "can't define singleton method \"%"PRIsVALUE"\" for %"PRIsVALUE,
             rb_id2str(mid),
             rb_obj_class(x));

    UNREACHABLE_RETURN(Qnil);
}

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

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 by (which may not be zero).
Ends with the last number that is within or equal to to; that is, less than or equal to to if by is positive, greater than or equal to to if by is negative. If to is nil, 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.

Keyword Arguments

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

Positional Arguments

With optional positional arguments to and by, 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 floor(n + n*Float::EPSILON) + 1 times, where n = (limit - self)/step.

[ GitHub ]

# File 'numeric.c', line 3033


static VALUE
num_step(int argc, VALUE *argv, VALUE from)
{
    VALUE to, step;
    int desc, inf;

    if (!rb_block_given_p()) {
        VALUE by = Qundef;

        num_step_extract_args(argc, argv, &to, &step, &by);
        if (!UNDEF_P(by)) {
            step = by;
        }
        if (NIL_P(step)) {
            step = INT2FIX(1);
        }
        else if (rb_equal(step, INT2FIX(0))) {
            rb_raise(rb_eArgError, "step can't be 0");
        }
        if ((NIL_P(to) || rb_obj_is_kind_of(to, rb_cNumeric)) &&
            rb_obj_is_kind_of(step, rb_cNumeric)) {
            return rb_arith_seq_new(from, ID2SYM(rb_frame_this_func()), argc, argv,
                                    num_step_size, from, to, step, FALSE);
        }

        return SIZED_ENUMERATOR_KW(from, 2, ((VALUE [2]){to, step}), num_step_size, FALSE);
    }

    desc = num_step_scan_args(argc, argv, &to, &step, TRUE, FALSE);
    if (rb_equal(step, INT2FIX(0))) {
        inf = 1;
    }
    else if (RB_FLOAT_TYPE_P(to)) {
        double f = RFLOAT_VALUE(to);
        inf = isinf(f) && (signbit(f) ? desc : !desc);
    }
    else inf = 0;

    if (FIXNUM_P(from) && (inf || FIXNUM_P(to)) && FIXNUM_P(step)) {
        long i = FIX2LONG(from);
        long diff = FIX2LONG(step);

        if (inf) {
            for (;; i += diff)
                rb_yield(LONG2FIX(i));
        }
        else {
            long end = FIX2LONG(to);

            if (desc) {
                for (; i >= end; i += diff)
                    rb_yield(LONG2FIX(i));
            }
            else {
                for (; i <= end; i += diff)
                    rb_yield(LONG2FIX(i));
            }
        }
    }
    else if (!ruby_float_step(from, to, step, FALSE, FALSE)) {
        VALUE i = from;

        if (inf) {
            for (;; i = rb_funcall(i, '+', 1, step))
                rb_yield(i);
        }
        else {
            ID cmp = desc ? '<' : '>';

            for (; !RTEST(rb_funcall(i, cmp, 1, to)); i = rb_funcall(i, '+', 1, step))
                rb_yield(i);
        }
    }
    return from;
}

#to_c ⇒ Complex

Returns self as a ::Complex object.

[ GitHub ]

# File 'complex.c', line 1939


static VALUE
numeric_to_c(VALUE self)
{
    return rb_complex_new1(self);
}

#to_int ⇒ Integer

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)

[ GitHub ]

# File 'numeric.c', line 895


static VALUE
num_to_int(VALUE num)
{
    return num_funcall0(num, id_to_i);
}

#truncate(digits = 0) ⇒ Integer, Float

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.

[ GitHub ]

# File 'numeric.c', line 2713


static VALUE
num_truncate(int argc, VALUE *argv, VALUE num)
{
    return flo_truncate(argc, argv, rb_Float(num));
}

Class: Numeric

Overview

What’s Here

Querying

Comparing

Converting

Other

Instance Attribute Summary

Instance Method Summary

::Comparable - Included

Instance Attribute Details

#finite? ⇒ Boolean (readonly)

#infinite? ⇒ Boolean (readonly)

#integer? ⇒ Boolean (readonly)

#negative? ⇒ Boolean (readonly)

#nonzero? ⇒ Boolean (readonly)

#positive? ⇒ Boolean (readonly)

#real? ⇒ Boolean (readonly)

#zero? ⇒ Boolean (readonly)

Instance Method Details

#%(other) ⇒ Numeric Also known as: #modulo

#+ ⇒ self

#- ⇒ Numeric

#<=>(other) ⇒ zero?

#abs ⇒ Numeric Also known as: #magnitude

#abs2 ⇒ Numeric

#arg ⇒ 0, Math::PI #angle ⇒ 0, Math::PI

#arg ⇒ 0, Math::PI Also known as: #angle, #phase

#ceil(digits = 0) ⇒ Integer, Float

#clone(freeze: true) ⇒ self

#coerce(other) ⇒ Array

#conj

#conj ⇒ self Also known as: #conj

#denominator ⇒ Integer

#div(other) ⇒ Integer

#divmod(other) ⇒ Array

#dup ⇒ self

#eql?(other) ⇒ Boolean

#fdiv(other) ⇒ Float

#floor(digits = 0) ⇒ Integer, Float

#i ⇒ Complex

#imag

#imag ⇒ 0 Also known as: #imag

#abs ⇒ Numeric #magnitude ⇒ Numeric

#%(other) ⇒ Numeric #modulo(other) ⇒ Numeric

#numerator ⇒ Integer

#arg ⇒ 0, Math::PI #phase ⇒ 0, Math::PI

#polar ⇒ Array

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

#real ⇒ self (readonly)

#rect ⇒ Array Also known as: #rectangular

#rect ⇒ Array #rectangular ⇒ Array

#remainder(other) ⇒ real_number

#round(digits = 0) ⇒ Integer, Float

#singleton_method_added(name)

#to_c ⇒ Complex

#to_int ⇒ Integer

#truncate(digits = 0) ⇒ Integer, Float

`::Comparable` - Included

#finite? ⇒ `Boolean` (readonly)

#infinite? ⇒ `Boolean` (readonly)

#integer? ⇒ `Boolean` (readonly)

#negative? ⇒ `Boolean` (readonly)

#nonzero? ⇒ `Boolean` (readonly)

#positive? ⇒ `Boolean` (readonly)

#real? ⇒ `Boolean` (readonly)

#zero? ⇒ `Boolean` (readonly)

#%(other) ⇒ `Numeric` Also known as: #modulo

#+ ⇒ `self`

#- ⇒ `Numeric`

#<=>(other) ⇒ `zero`^?

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

#abs2 ⇒ `Numeric`

#arg ⇒ `0`, Math::PI #angle ⇒ `0`, Math::PI

#arg ⇒ `0`, Math::PI Also known as: #angle, #phase

#clone(freeze: true) ⇒ `self`

#conj ⇒ `self` Also known as: #conj

#dup ⇒ `self`

#eql?(other) ⇒ `Boolean`

#imag ⇒ `0` Also known as: #imag

#abs ⇒ `Numeric` #magnitude ⇒ `Numeric`

#%(other) ⇒ `Numeric` #modulo(other) ⇒ `Numeric`

#arg ⇒ `0`, Math::PI #phase ⇒ `0`, Math::PI

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

#real ⇒ `self` (readonly)

#remainder(other) ⇒ `real_number`