class 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)

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));
}

Returns self.

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

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);
}

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

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

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

Returns the absolute value of self.

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

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

Returns the square of self.

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

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

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

Returns the smallest float or integer that is greater than or equal to self, as specified by the given ‘ndigits`, which must be an integer-convertible object.

Equivalent to self.to_f.ceil(ndigits).

Related: floor, Float#ceil.

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

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);
}

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);
}

Returns the denominator (always positive).

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

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.

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);
}

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));
}

Returns self.

Related: Numeric#clone.

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

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.

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);
}

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);
}

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

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

Returns the largest float or integer that is less than or equal to self, as specified by the given ‘ndigits`, which must be an integer-convertible object.

Equivalent to self.to_f.floor(ndigits).

Related: ceil, Float#floor.

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

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);
}

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

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

Returns true if self is an Integer.

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

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

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));
}

Returns +self+ if +self+ is not a zero value, +nil+ otherwise;
uses method <tt>zero?</tt> 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.

Related: zero?

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

Returns the numerator.

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

Returns array [self.abs, self.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);
}

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);
}

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);
}

Returns self.

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

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

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

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)
{
    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;
}

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.

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

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.

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;
}

Returns self as a Complex object.

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

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);
}

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.

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

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));
}