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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.

Methods
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Included Modules

Instance Public methods

self % other → real_numeric

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 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)
Also aliased as: modulo

Source: show 

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 → self

Returns self.

Source: show 

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

-self → numeric

Unary Minus—Returns the receiver, negated.

Source: show 

static VALUE
num_uminus(VALUE num)
{
    VALUE zero;

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

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

self <=> other → zero or nil

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

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

Source: show 

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

abs → numeric

Returns the absolute value of self.

12.abs        #=> 12
(-34.56).abs  #=> 34.56
-34.56.abs    #=> 34.56
Also aliased as: magnitude

Source: show 

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

abs2 → real

Returns the square of self.

Source: show 

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

angle()

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

Alias for: arg

arg → 0 or Math::PI

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

Also aliased as: angle, phase

Source: show 

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

ceil(digits = 0) → integer or 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.

Source: show 

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: Numeric#dup.

Source: show 

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.

Source: show 

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 → self

Alias for: conjugate

conjugate()

Returns self.

Also aliased as: conj

Source: show | on GitHub 

# File ruby/numeric.rb, line 68
def conjugate
  self
end

num.denominator → integer

Returns the denominator (always positive).

Source: show 

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.

Source: show 

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)]

Source: show 

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: Numeric#clone.

Source: show 

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

eql?(other) → true or false

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.

Source: show 

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.

Source: show 

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

finite? → true or false

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

Source: show | on GitHub 

# File ruby/numeric.rb, line 38
def finite?
  true
end

floor(digits = 0) → integer or 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.

Source: show 

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.

Source: show 

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

imag → 0

Alias for: imaginary

imaginary()

Returns zero.

Also aliased as: imag

Source: show | on GitHub 

# File ruby/numeric.rb, line 57
def imaginary
  0
end

infinite? → -1, 1, or nil

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

Source: show | on GitHub 

# File ruby/numeric.rb, line 48
def infinite?
  nil
end

integer? → true or false

Returns true if self is an Integer.

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

Source: show | on GitHub 

# File ruby/numeric.rb, line 29
def integer?
  false
end

magnitude()

Returns the absolute value of self.

12.abs        #=> 12
(-34.56).abs  #=> 34.56
-34.56.abs    #=> 34.56
Alias for: abs

modulo(p1)

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 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)
Alias for: %

negative? → true or false

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

Source: show 

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

nonzero? → self or nil

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.

Source: show 

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

num.numerator → integer

Returns the numerator.

Source: show 

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

phase()

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

Alias for: arg

polar → array

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

Source: show 

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);
}

positive? → true or false

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

Source: show 

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);
}

num.quo(int_or_rat) → rat
num.quo(flo) → flo

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

Source: show 

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

Returns self.

Source: show | on GitHub 

# File ruby/numeric.rb, line 17
def real
  self
end

real? → true or false

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

Source: show | on GitHub 

# File ruby/numeric.rb, line 8
def real?
  true
end

rect → array

Returns array [self, 0].

Alias for: rectangular

rectangular()

Returns array [self, 0].

Also aliased as: rect

Source: show 

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

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)

Source: show 

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 or 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.

Source: show 

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

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.

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

Source: show 

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.

Source: show 

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)

Source: show 

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

truncate(digits = 0) → integer or 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.

Source: show 

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

zero? → true or false

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

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

Source: show 

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