# 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

### 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 `Numeric#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

`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;
    }

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 `Numeric#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

`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;
    }

modulo(numeric) → real click to toggle source

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

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

See `Numeric#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_FLOAT_TYPE_P(y)) {
            return rb_funcall(x, rb_intern("fdiv"), 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 `Numeric#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, argc, argv, 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;
    }