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  • complex.c
  • numeric.c
  • rational.c

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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

Public Instance Methods

modulo(numeric) → real click to toggle source

x.modulo(y) means x-y*(x/y).floor.

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

See #divmod.

 
               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));
}
+num → num click to toggle source

Unary Plus—Returns the receiver.

 
               static VALUE
num_uplus(VALUE num)
{
    return num;
}
-num → 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 num.

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

#magnitude is an alias for #abs.

 
               static VALUE
num_abs(VALUE num)
{
    if (rb_num_negative_int_p(num)) {
        return num_funcall0(num, idUMinus);
    }
    return num;
}
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 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);
}
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);
}
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) → num click to toggle source

Returns the receiver. freeze cannot be false.

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

If numeric is the same type as num, returns an array [numeric, num]. Otherwise, returns an array with both 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]

 
               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 click to toggle source
conjugate → self

Returns self.

 
               static VALUE
numeric_conj(VALUE self)
{
    return self;
}
conjugate → self click to toggle source

Returns self.

 
               static VALUE
numeric_conj(VALUE self)
{
    return self;
}
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(numeric) → integer click to toggle source

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.

 
               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(numeric) → array click to toggle source

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 negative 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]

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

Returns the receiver.

 
               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_TYPE_P(x, T_BIGNUM)) {
        return rb_big_eql(x, y);
    }

    return rb_equal(x, y);
}
fdiv(numeric) → float click to toggle source

Returns float division.

 
               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.

 
               static VALUE
num_finite_p(VALUE num)
{
    return Qtrue;
}
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(0, num) click to toggle source

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

-42.i  #=> (0-42i)
2.0.i  #=> (0+2.0i)

 
               static VALUE
num_imaginary(VALUE num)
{
    return rb_complex_new(INT2FIX(0), num);
}
imag → 0 click to toggle source
imaginary → 0

Returns zero.

 
               static VALUE
numeric_imag(VALUE self)
{
    return INT2FIX(0);
}
imaginary → 0 click to toggle source

Returns zero.

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

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

 
               static VALUE
num_infinite_p(VALUE num)
{
    return Qnil;
}
integer? → true or false click to toggle source

Returns true if num is an Integer.

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

 
               static VALUE
num_int_p(VALUE num)
{
    return Qfalse;
}
magnitude → numeric click to toggle source

Returns the absolute value of num.

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

#magnitude is an alias for #abs.

 
               static VALUE
num_abs(VALUE num)
{
    if (rb_num_negative_int_p(num)) {
        return num_funcall0(num, idUMinus);
    }
    return num;
}
modulo(numeric) → real click to toggle source

x.modulo(y) means x-y*(x/y).floor.

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

See #divmod.

 
               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));
}
negative? → true or false click to toggle source

Returns true if num is less than 0.

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

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"]

 
               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 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);
}
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 num is greater than 0.

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

    if (FIXNUM_P(num)) {
        if (method_basic_p(rb_cInteger))
            return (SIGNED_VALUE)num > (SIGNED_VALUE)INT2FIX(0) ? Qtrue : Qfalse;
    }
    else if (RB_TYPE_P(num, T_BIGNUM)) {
        if (method_basic_p(rb_cInteger))
            return BIGNUM_POSITIVE_P(num) && !rb_bigzero_p(num) ? Qtrue : Qfalse;
    }
    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);
    }

    if (canonicalization) {
        x = rb_rational_raw1(x);
    }
    else {
        x = rb_convert_type(x, T_RATIONAL, "Rational", "to_r");
    }
    return nurat_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).

 
               static VALUE
num_real_p(VALUE num)
{
    return Qtrue;
}
rect → array click to toggle source
rectangular → array

Returns an array; [num, 0].

 
               static VALUE
numeric_rect(VALUE self)
{
    return rb_assoc_new(self, INT2FIX(0));
}
rectangular → array click to toggle source

Returns an array; [num, 0].

 
               static VALUE
numeric_rect(VALUE self)
{
    return rb_assoc_new(self, INT2FIX(0));
}
remainder(numeric) → real click to toggle source

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

See #divmod.

 
               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)))) {
        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);
        }
        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_TYPE_P(to, T_FLOAT)) {
        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

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

1.0.class          #=> Float
1.0.to_int.class   #=> Integer
1.0.to_i.class     #=> Integer

 
               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 num has a zero value.

 
               static VALUE
num_zero_p(VALUE num)
{
    if (FIXNUM_P(num)) {
        if (FIXNUM_ZERO_P(num)) {
            return Qtrue;
        }
    }
    else if (RB_TYPE_P(num, T_BIGNUM)) {
        if (rb_bigzero_p(num)) {
            /* this should not happen usually */
            return Qtrue;
        }
    }
    else if (rb_equal(num, INT2FIX(0))) {
        return Qtrue;
    }
    return Qfalse;
}