class Numeric

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

Comparing

Converting

Other

Public Instance Methods

self % other → real_numeric click to toggle source

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#%.

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));
}
Also aliased as: modulo
+self → self click to toggle source

Returns self.

static VALUE
num_uplus(VALUE num)
{
    return num;
}
-self → numeric click to toggle source

Unary Minus—Returns the receiver, negated.

static VALUE
num_uminus(VALUE num)
{
    VALUE zero;

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

    return num_funcall1(zero, '-', num);
}
number <=> other → 0 or nil click to toggle source

Returns zero if number equals other, otherwise returns nil.

static VALUE
num_cmp(VALUE x, VALUE y)
{
    if (x == y) return INT2FIX(0);
    return Qnil;
}
abs → numeric click to toggle source

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.

static VALUE
num_abs(VALUE num)
{
    if (rb_num_negative_int_p(num)) {
        return num_funcall0(num, idUMinus);
    }
    return num;
}
Also aliased as: magnitude
abs2 → real click to toggle source

Returns square of self.

static VALUE
numeric_abs2(VALUE self)
{
    return f_mul(self, self);
}
angle → 0 or float

Returns 0 if the value is positive, pi otherwise.

Alias for: arg
arg → 0 or float click to toggle source

Returns 0 if the value is positive, pi otherwise.

static VALUE
numeric_arg(VALUE self)
{
    if (f_positive_p(self))
        return INT2FIX(0);
    return DBL2NUM(M_PI);
}
Also aliased as: angle, phase
ceil([ndigits]) → integer or float click to toggle source

Returns the smallest number greater than or equal to num with a precision of ndigits decimal digits (default: 0).

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

static VALUE
num_ceil(int argc, VALUE *argv, VALUE num)
{
    return flo_ceil(argc, argv, rb_Float(num));
}
clone(freeze: true) → self click to toggle source

Returns self.

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

Related: Numeric#dup.

static VALUE
num_clone(int argc, VALUE *argv, VALUE x)
{
    return rb_immutable_obj_clone(argc, argv, x);
}
coerce(other) → array click to toggle source

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.

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

Returns self.

Alias for: conjugate

Returns self.

static VALUE
numeric_conj(VALUE self)
{
    return self;
}
Also aliased as: conj
denominator → integer click to toggle source

Returns the denominator (always positive).

static VALUE
numeric_denominator(VALUE self)
{
    return f_denominator(f_to_r(self));
}
div(other) → integer click to toggle source

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.

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 click to toggle source

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)]
static VALUE
num_divmod(VALUE x, VALUE y)
{
    return rb_assoc_new(num_div(x, y), num_modulo(x, y));
}
dup → self click to toggle source

Returns self.

Related: Numeric#clone.

static VALUE
num_dup(VALUE x)
{
    return x;
}
eql?(numeric) → true or false click to toggle source

Returns true if num and numeric are the same type and have equal values. Contrast this with Numeric#==, which performs type conversions.

1 == 1.0        #=> true
1.eql?(1.0)     #=> false
1.0.eql?(1.0)   #=> true
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 click to toggle source

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.

static VALUE
num_fdiv(VALUE x, VALUE y)
{
    return rb_funcall(rb_Float(x), '/', 1, y);
}
finite? → true or false click to toggle source

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

# File numeric.rb, line 31
def finite?
  return true
end
floor([ndigits]) → integer or float click to toggle source

Returns the largest number less than or equal to num with a precision of ndigits decimal digits (default: 0).

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

static VALUE
num_floor(int argc, VALUE *argv, VALUE num)
{
    return flo_floor(argc, argv, rb_Float(num));
}
i → complex click to toggle source

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

Returns zero.

Alias for: imaginary

Returns zero.

static VALUE
numeric_imag(VALUE self)
{
    return INT2FIX(0);
}
Also aliased as: imag
infinite? → -1, 1, or nil click to toggle source

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

# File numeric.rb, line 42
def infinite?
  return nil
end
integer? → true or false click to toggle source

Returns true if num is an Integer.

1.0.integer?   #=> false
1.integer?     #=> true
# File numeric.rb, line 21
def integer?
  return false
end

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.

Alias for: abs

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#%.

Alias for: %
negative? → true or false click to toggle source

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

static VALUE
num_negative_p(VALUE num)
{
    return RBOOL(rb_num_negative_int_p(num));
}
nonzero? → self or nil click to toggle source

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.

static VALUE
num_nonzero_p(VALUE num)
{
    if (RTEST(num_funcall0(num, rb_intern("zero?")))) {
        return Qnil;
    }
    return num;
}
numerator → integer click to toggle source

Returns the numerator.

static VALUE
numeric_numerator(VALUE self)
{
    return f_numerator(f_to_r(self));
}
phase → 0 or float

Returns 0 if the value is positive, pi otherwise.

Alias for: arg
polar → array click to toggle source

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

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 click to toggle source

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

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);
}
quo(int_or_rat) → rat click to toggle source
quo(flo) → flo

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

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 click to toggle source

Returns self.

static VALUE
numeric_real(VALUE self)
{
    return self;
}
real? → true or false click to toggle source

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

# File numeric.rb, line 8
def real?
  return true
end
rect → array

Returns an array; [num, 0].

Alias for: rectangular

Returns an array; [num, 0].

static VALUE
numeric_rect(VALUE self)
{
    return rb_assoc_new(self, INT2FIX(0));
}
Also aliased as: rect
remainder(other) → real_number click to toggle source

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)
static VALUE
num_remainder(VALUE x, VALUE y)
{
    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([ndigits]) → integer or float click to toggle source

Returns num rounded to the nearest value with a precision of ndigits decimal digits (default: 0).

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

static VALUE
num_round(int argc, VALUE* argv, VALUE num)
{
    return flo_round(argc, argv, rb_Float(num));
}
step(by: step, to: limit) {|i| block } → self click to toggle source
step(by: step, to: limit) → an_enumerator
step(by: step, to: limit) → an_arithmetic_sequence
step(limit=nil, step=1) {|i| block } → self
step(limit=nil, step=1) → an_enumerator
step(limit=nil, step=1) → an_arithmetic_sequence

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 floor(n + n*Float::EPSILON) + 1 times, where 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. Especially, the enumerator is an Enumerator::ArithmeticSequence if both limit and step are kind of Numeric or nil.

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
2.718281828459045 2.9182818284590453 3.118281828459045
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 (by != Qundef) {
            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(from, 2, ((VALUE [2]){to, step}), num_step_size);
    }

    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 click to toggle source

Returns the value as a complex.

static VALUE
numeric_to_c(VALUE self)
{
    return rb_complex_new1(self);
}
to_int → integer click to toggle source

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)
static VALUE
num_to_int(VALUE num)
{
    return num_funcall0(num, id_to_i);
}
truncate([ndigits]) → integer or float click to toggle source

Returns num truncated (toward zero) to a precision of ndigits decimal digits (default: 0).

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

static VALUE
num_truncate(int argc, VALUE *argv, VALUE num)
{
    return flo_truncate(argc, argv, rb_Float(num));
}
zero? → true or false click to toggle source

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

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

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