Class: Rational

Relationships & Source Files
Namespace Children
Classes: `compatible`
Super Chains via Extension / Inclusion / Inheritance
Class Chain: self, `::Numeric`
Instance Chain: self, `::Numeric`, `::Comparable`
Inherits:	Numeric `::Object` Numeric Rational
Defined in:	rational.c

Overview

A rational number can be represented as a pair of integer numbers: a/b (b>0), where a is the numerator and b is the denominator. ::Integer a equals rational a/1 mathematically.

In Ruby, you can create rational objects with the Kernel.Rational, to_r, or rationalize methods or by suffixing r to a literal. The return values will be irreducible fractions.

Rational(1)      #=> (1/1)
Rational(2, 3)   #=> (2/3)
Rational(4, -6)  #=> (-2/3)
3.to_r           #=> (3/1)
2/3r             #=> (2/3)

You can also create rational objects from floating-point numbers or strings.

Rational(0.3)    #=> (5404319552844595/18014398509481984)
Rational('0.3')  #=> (3/10)
Rational('2/3')  #=> (2/3)

0.3.to_r         #=> (5404319552844595/18014398509481984)
'0.3'.to_r       #=> (3/10)
'2/3'.to_r       #=> (2/3)
0.3.rationalize  #=> (3/10)

A rational object is an exact number, which helps you to write programs without any rounding errors.

10.times.inject(0) {|t| t + 0.1 }              #=> 0.9999999999999999
10.times.inject(0) {|t| t + Rational('0.1') }  #=> (1/1)

However, when an expression includes an inexact component (numerical value or operation), it will produce an inexact result.

Rational(10) / 3   #=> (10/3)
Rational(10) / 3.0 #=> 3.3333333333333335

Rational(-8) ** Rational(1, 3)
                   #=> (1.0000000000000002+1.7320508075688772i)

Instance Attribute Summary

#negative? ⇒ Boolean readonly

Returns true if rat is less than 0.
#positive? ⇒ Boolean readonly

Returns true if rat is greater than 0.

`::Numeric` - Inherited

#finite?	Returns `true` if `num` is a finite number, otherwise returns `false`.
#infinite?	Returns `nil`, -1, or 1 depending on whether the value is finite, `-Infinity`, or `+Infinity`.
#integer?	Returns `true` if `num` is an `::Integer`.
#negative?	Returns `true` if `num` is less than 0.
#nonzero?	Returns `self` if `num` is not zero, `nil` otherwise.
#positive?	Returns `true` if `num` is greater than 0.
#real	Returns self.
#real?	Returns `true` if `num` is a real number (i.e.
#zero?	Returns `true` if `num` has a zero value.

Instance Method Summary

#*(numeric) ⇒ Numeric

Performs multiplication.
#**
#+(numeric) ⇒ Numeric

Performs addition.
#-(numeric) ⇒ Numeric

Performs subtraction.
#- ⇒ Rational

Negates rat.
#/(numeric) ⇒ Numeric (also: #quo)

Performs division.
#<=>(numeric) ⇒ 1, ...

Returns -1, 0, or +1 depending on whether rational is less than, equal to, or greater than numeric.
#==(object) ⇒ Boolean

Returns true if rat equals object numerically.
#abs ⇒ Rational (also: #magnitude)

Returns the absolute value of rat.
#ceil([ndigits]) ⇒ Integer, Rational

Returns the smallest number greater than or equal to rat with a precision of ndigits decimal digits (default: 0).
#denominator ⇒ Integer

Returns the denominator (always positive).
#fdiv(numeric) ⇒ Float

Performs division and returns the value as a ::Float.
#floor([ndigits]) ⇒ Integer, Rational

Returns the largest number less than or equal to rat with a precision of ndigits decimal digits (default: 0).
#inspect ⇒ String

Returns the value as a string for inspection.
#magnitude ⇒ Rational

Alias for #abs.
#numerator ⇒ Integer

Returns the numerator.
#quo(numeric) ⇒ Numeric

Alias for #/.
#rationalize ⇒ self

Returns a simpler approximation of the value if the optional argument eps is given (rat-|eps| <= result <= rat+|eps|), self otherwise.
#round([ndigits] [, half: mode]) ⇒ Integer, Rational

Returns rat rounded to the nearest value with a precision of ndigits decimal digits (default: 0).
#to_f ⇒ Float

Returns the value as a ::Float.
#to_i ⇒ Integer

Returns the truncated value as an integer.
#to_r ⇒ self

Returns self.
#to_s ⇒ String

Returns the value as a string.
#truncate([ndigits]) ⇒ Integer, Rational

Returns rat truncated (toward zero) to a precision of ndigits decimal digits (default: 0).
#coerce(other) Internal use only
#hash Internal use only
#marshal_dump private Internal use only

`::Numeric` - Inherited

#%	`x.modulo(y)` means `x-y*(x/y).floor`.
#+@	Unary Plus—Returns the receiver.
#-@	Unary Minus—Returns the receiver, negated.
#<=>	Returns zero if `number` equals `other`, otherwise returns `nil`.
#abs	Returns the absolute value of `num`.
#abs2	Returns square of self.
#angle	Alias for Numeric#arg.
#arg	Returns 0 if the value is positive, pi otherwise.
#ceil	Returns the smallest number greater than or equal to `num` with a precision of `ndigits` decimal digits (default: 0).
#clone	Returns the receiver.
#coerce	If `numeric` is the same type as `num`, returns an array `[numeric, num]`.
#conj	Returns self.
#conjugate	Alias for Numeric#conj.
#denominator	Returns the denominator (always positive).
#div	Uses `/` to perform division, then converts the result to an integer.
#divmod	Returns an array containing the quotient and modulus obtained by dividing `num` by `numeric`.
#dup	Returns the receiver.
#eql?	Returns `true` if `num` and `numeric` are the same type and have equal values.
#fdiv	Returns float division.
#floor	Returns the largest number less than or equal to `num` with a precision of `ndigits` decimal digits (default: 0).
#i	Returns the corresponding imaginary number.
#imag	Returns zero.
#imaginary	Alias for Numeric#imag.
#magnitude	Alias for Numeric#abs.
#modulo	Alias for Numeric#%.
#numerator	Returns the numerator.
#phase	Alias for Numeric#arg.
#polar	Returns an array; [num.abs, num.arg].
#quo	Returns the most exact division (rational for integers, float for floats).
#rect	Returns an array; [num, 0].
#rectangular	Alias for Numeric#rect.
#remainder	`x.remainder(y)` means `x-y*(x/y).truncate`.
#round	Returns `num` rounded to the nearest value with a precision of `ndigits` decimal digits (default: 0).
#step	Invokes the given block with the sequence of numbers starting at `num`, incremented by `step` (defaulted to `1`) on each call.
#to_c	Returns the value as a complex.
#to_int	Invokes the child class’s #to_i method to convert `num` to an integer.
#truncate	Returns `num` truncated (toward zero) to a precision of `ndigits` decimal digits (default: 0).
#singleton_method_added	Trap attempts to add methods to `::Numeric` objects.

`::Comparable` - Included

#<	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value less than 0.
#<=	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value less than or equal to 0.
#==	Compares two objects based on the receiver’s #<=> method, returning true if it returns 0.
#>	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value greater than 0.
#>=	Compares two objects based on the receiver’s #<=> method, returning true if it returns a value greater than or equal to 0.
#between?	Returns `false` if obj #<=> min is less than zero or if obj #<=> max is greater than zero, `true` otherwise.
#clamp	In `(min, max)` form, returns min if obj #<=> min is less than zero, max if obj #<=> max is greater than zero, and obj otherwise.

Instance Attribute Details

#negative? ⇒ `Boolean` (readonly)

Returns true if rat is less than 0.

[ GitHub ]

# File 'rational.c', line 1234


static VALUE
nurat_negative_p(VALUE self)
{
    get_dat1(self);
    return f_boolcast(INT_NEGATIVE_P(dat->num));
}

#positive? ⇒ `Boolean` (readonly)

Returns true if rat is greater than 0.

[ GitHub ]

# File 'rational.c', line 1221


static VALUE
nurat_positive_p(VALUE self)
{
    get_dat1(self);
    return f_boolcast(INT_POSITIVE_P(dat->num));
}

Instance Method Details

#*(numeric) ⇒ Numeric

Performs multiplication.

Rational(2, 3)  * Rational(2, 3)   #=> (4/9)
Rational(900)   * Rational(1)      #=> (900/1)
Rational(-2, 9) * Rational(-9, 2)  #=> (1/1)
Rational(9, 8)  * 4                #=> (9/2)
Rational(20, 9) * 9.8              #=> 21.77777777777778

[ GitHub ]

# File 'rational.c', line 873


VALUE
rb_rational_mul(VALUE self, VALUE other)
{
    if (RB_INTEGER_TYPE_P(other)) {
	{
	    get_dat1(self);

	    return f_muldiv(self,
			    dat->num, dat->den,
			    other, ONE, '*');
	}
    }
    else if (RB_FLOAT_TYPE_P(other)) {
	return DBL2NUM(nurat_to_double(self) * RFLOAT_VALUE(other));
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
	{
	    get_dat2(self, other);

	    return f_muldiv(self,
			    adat->num, adat->den,
			    bdat->num, bdat->den, '*');
	}
    }
    else {
	return rb_num_coerce_bin(self, other, '*');
    }
}

#**

[ GitHub ]

#+(numeric) ⇒ Numeric

Performs addition.

Rational(2, 3)  + Rational(2, 3)   #=> (4/3)
Rational(900)   + Rational(1)      #=> (901/1)
Rational(-2, 9) + Rational(-9, 2)  #=> (-85/18)
Rational(9, 8)  + 4                #=> (41/8)
Rational(20, 9) + 9.8              #=> 12.022222222222222

[ GitHub ]

# File 'rational.c', line 736


VALUE
rb_rational_plus(VALUE self, VALUE other)
{
    if (RB_INTEGER_TYPE_P(other)) {
	{
	    get_dat1(self);

	    return f_rational_new_no_reduce2(CLASS_OF(self),
					     rb_int_plus(dat->num, rb_int_mul(other, dat->den)),
					     dat->den);
	}
    }
    else if (RB_FLOAT_TYPE_P(other)) {
	return DBL2NUM(nurat_to_double(self) + RFLOAT_VALUE(other));
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
	{
	    get_dat2(self, other);

	    return f_addsub(self,
			    adat->num, adat->den,
			    bdat->num, bdat->den, '+');
	}
    }
    else {
	return rb_num_coerce_bin(self, other, '+');
    }
}

#-(numeric) ⇒ Numeric

Performs subtraction.

Rational(2, 3)  - Rational(2, 3)   #=> (0/1)
Rational(900)   - Rational(1)      #=> (899/1)
Rational(-2, 9) - Rational(-9, 2)  #=> (77/18)
Rational(9, 8)  - 4                #=> (-23/8)
Rational(20, 9) - 9.8              #=> -7.577777777777778

[ GitHub ]

# File 'rational.c', line 777


VALUE
rb_rational_minus(VALUE self, VALUE other)
{
    if (RB_INTEGER_TYPE_P(other)) {
	{
	    get_dat1(self);

	    return f_rational_new_no_reduce2(CLASS_OF(self),
					     rb_int_minus(dat->num, rb_int_mul(other, dat->den)),
					     dat->den);
	}
    }
    else if (RB_FLOAT_TYPE_P(other)) {
	return DBL2NUM(nurat_to_double(self) - RFLOAT_VALUE(other));
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
	{
	    get_dat2(self, other);

	    return f_addsub(self,
			    adat->num, adat->den,
			    bdat->num, bdat->den, '-');
	}
    }
    else {
	return rb_num_coerce_bin(self, other, '-');
    }
}

#- ⇒ `Rational`

Negates rat.

[ GitHub ]

# File 'rational.c', line 623


VALUE
rb_rational_uminus(VALUE self)
{
    const int unused = (assert(RB_TYPE_P(self, T_RATIONAL)), 0);
    get_dat1(self);
    (void)unused;
    return f_rational_new2(CLASS_OF(self), rb_int_uminus(dat->num), dat->den);
}

#/(numeric) ⇒ Numeric #quo(numeric) ⇒ Numeric
Also known as: #quo

Performs division.

Rational(2, 3)  / Rational(2, 3)   #=> (1/1)
Rational(900)   / Rational(1)      #=> (900/1)
Rational(-2, 9) / Rational(-9, 2)  #=> (4/81)
Rational(9, 8)  / 4                #=> (9/32)
Rational(20, 9) / 9.8              #=> 0.22675736961451246

[ GitHub ]

# File 'rational.c', line 915


VALUE
rb_rational_div(VALUE self, VALUE other)
{
    if (RB_INTEGER_TYPE_P(other)) {
	if (f_zero_p(other))
            rb_num_zerodiv();
	{
	    get_dat1(self);

	    return f_muldiv(self,
			    dat->num, dat->den,
			    other, ONE, '/');
	}
    }
    else if (RB_FLOAT_TYPE_P(other)) {
        VALUE v = nurat_to_f(self);
        return rb_flo_div_flo(v, other);
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
	if (f_zero_p(other))
            rb_num_zerodiv();
	{
	    get_dat2(self, other);

	    if (f_one_p(self))
		return f_rational_new_no_reduce2(CLASS_OF(self),
						 bdat->den, bdat->num);

	    return f_muldiv(self,
			    adat->num, adat->den,
			    bdat->num, bdat->den, '/');
	}
    }
    else {
	return rb_num_coerce_bin(self, other, '/');
    }
}

#<=>(numeric) ⇒ `1`, ...

Returns -1, 0, or +1 depending on whether rational is less than, equal to, or greater than numeric.

nil is returned if the two values are incomparable.

Rational(2, 3) <=> Rational(2, 3)  #=> 0
Rational(5)    <=> 5               #=> 0
Rational(2, 3) <=> Rational(1, 3)  #=> 1
Rational(1, 3) <=> 1               #=> -1
Rational(1, 3) <=> 0.3             #=> 1

Rational(1, 3) <=> "0.3"           #=> nil

[ GitHub ]

# File 'rational.c', line 1096


VALUE
rb_rational_cmp(VALUE self, VALUE other)
{
    if (RB_INTEGER_TYPE_P(other)) {
	{
	    get_dat1(self);

	    if (dat->den == LONG2FIX(1))
		return rb_int_cmp(dat->num, other); /* c14n */
	    other = f_rational_new_bang1(CLASS_OF(self), other);
	    goto other_is_rational;
	}
    }
    else if (RB_FLOAT_TYPE_P(other)) {
	return rb_dbl_cmp(nurat_to_double(self), RFLOAT_VALUE(other));
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
	other_is_rational:
	{
	    VALUE num1, num2;

	    get_dat2(self, other);

	    if (FIXNUM_P(adat->num) && FIXNUM_P(adat->den) &&
		FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) {
		num1 = f_imul(FIX2LONG(adat->num), FIX2LONG(bdat->den));
		num2 = f_imul(FIX2LONG(bdat->num), FIX2LONG(adat->den));
	    }
	    else {
		num1 = rb_int_mul(adat->num, bdat->den);
		num2 = rb_int_mul(bdat->num, adat->den);
	    }
	    return rb_int_cmp(rb_int_minus(num1, num2), ZERO);
	}
    }
    else {
	return rb_num_coerce_cmp(self, other, rb_intern("<=>"));
    }
}

#==(object) ⇒ `Boolean`

Returns true if rat equals object numerically.

Rational(2, 3)  == Rational(2, 3)   #=> true
Rational(5)     == 5                #=> true
Rational(0)     == 0.0              #=> true
Rational('1/3') == 0.33             #=> false
Rational('1/2') == '1/2'            #=> false

[ GitHub ]

# File 'rational.c', line 1148


static VALUE
nurat_eqeq_p(VALUE self, VALUE other)
{
    if (RB_INTEGER_TYPE_P(other)) {
        get_dat1(self);

        if (RB_INTEGER_TYPE_P(dat->num) && RB_INTEGER_TYPE_P(dat->den)) {
	    if (INT_ZERO_P(dat->num) && INT_ZERO_P(other))
		return Qtrue;

	    if (!FIXNUM_P(dat->den))
		return Qfalse;
	    if (FIX2LONG(dat->den) != 1)
		return Qfalse;
	    return rb_int_equal(dat->num, other);
	}
        else {
            const double d = nurat_to_double(self);
            return f_boolcast(FIXNUM_ZERO_P(rb_dbl_cmp(d, NUM2DBL(other))));
        }
    }
    else if (RB_FLOAT_TYPE_P(other)) {
	const double d = nurat_to_double(self);
	return f_boolcast(FIXNUM_ZERO_P(rb_dbl_cmp(d, RFLOAT_VALUE(other))));
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
	{
	    get_dat2(self, other);

	    if (INT_ZERO_P(adat->num) && INT_ZERO_P(bdat->num))
		return Qtrue;

	    return f_boolcast(rb_int_equal(adat->num, bdat->num) &&
			      rb_int_equal(adat->den, bdat->den));
	}
    }
    else {
	return rb_equal(other, self);
    }
}

#abs ⇒ `Rational` #magnitude ⇒ `Rational`
Also known as: #magnitude

Returns the absolute value of rat.

(1/2r).abs    #=> (1/2)
(-1/2r).abs   #=> (1/2)

#magnitude is an alias for abs.

[ GitHub ]

# File 'rational.c', line 1254


VALUE
rb_rational_abs(VALUE self)
{
    get_dat1(self);
    if (INT_NEGATIVE_P(dat->num)) {
        VALUE num = rb_int_abs(dat->num);
        return nurat_s_canonicalize_internal_no_reduce(CLASS_OF(self), num, dat->den);
    }
    return self;
}

#ceil([ndigits]) ⇒ Integer, `Rational`

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

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns a rational when ndigits is positive, otherwise returns an integer.

Rational(3).ceil      #=> 3
Rational(2, 3).ceil   #=> 1
Rational(-3, 2).ceil  #=> -1

  #    decimal      -  1  2  3 . 4  5  6
  #                   ^  ^  ^  ^   ^  ^
  #   precision      -3 -2 -1  0  +1 +2

Rational('-123.456').ceil(+1).to_f  #=> -123.4
Rational('-123.456').ceil(-1)       #=> -120

[ GitHub ]

# File 'rational.c', line 1480


static VALUE
nurat_ceil_n(int argc, VALUE *argv, VALUE self)
{
    return f_round_common(argc, argv, self, nurat_ceil);
}

#coerce(other)

This method is for internal use only.

[ GitHub ]

# File 'rational.c', line 1190


static VALUE
nurat_coerce(VALUE self, VALUE other)
{
    if (RB_INTEGER_TYPE_P(other)) {
	return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self);
    }
    else if (RB_FLOAT_TYPE_P(other)) {
        return rb_assoc_new(other, nurat_to_f(self));
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
	return rb_assoc_new(other, self);
    }
    else if (RB_TYPE_P(other, T_COMPLEX)) {
	if (k_exact_zero_p(RCOMPLEX(other)->imag))
	    return rb_assoc_new(f_rational_new_bang1
				(CLASS_OF(self), RCOMPLEX(other)->real), self);
	else
	    return rb_assoc_new(other, rb_Complex(self, INT2FIX(0)));
    }

    rb_raise(rb_eTypeError, "%s can't be coerced into %s",
	     rb_obj_classname(other), rb_obj_classname(self));
    return Qnil;
}

#denominator ⇒ Integer

Returns the denominator (always positive).

Rational(7).denominator             #=> 1
Rational(7, 1).denominator          #=> 1
Rational(9, -4).denominator         #=> 4
Rational(-2, -10).denominator       #=> 5

[ GitHub ]

# File 'rational.c', line 610


static VALUE
nurat_denominator(VALUE self)
{
    get_dat1(self);
    return dat->den;
}

#fdiv(numeric) ⇒ Float

Performs division and returns the value as a ::Float.

Rational(2, 3).fdiv(1)       #=> 0.6666666666666666
Rational(2, 3).fdiv(0.5)     #=> 1.3333333333333333
Rational(2).fdiv(3)          #=> 0.6666666666666666

[ GitHub ]

# File 'rational.c', line 963


static VALUE
nurat_fdiv(VALUE self, VALUE other)
{
    VALUE div;
    if (f_zero_p(other))
        return rb_rational_div(self, rb_float_new(0.0));
    if (FIXNUM_P(other) && other == LONG2FIX(1))
	return nurat_to_f(self);
    div = rb_rational_div(self, other);
    if (RB_TYPE_P(div, T_RATIONAL))
	return nurat_to_f(div);
    if (RB_FLOAT_TYPE_P(div))
	return div;
    return rb_funcall(div, idTo_f, 0);
}

#floor([ndigits]) ⇒ Integer, `Rational`

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

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns a rational when ndigits is positive, otherwise returns an integer.

Rational(3).floor      #=> 3
Rational(2, 3).floor   #=> 0
Rational(-3, 2).floor  #=> -2

  #    decimal      -  1  2  3 . 4  5  6
  #                   ^  ^  ^  ^   ^  ^
  #   precision      -3 -2 -1  0  +1 +2

Rational('-123.456').floor(+1).to_f  #=> -123.5
Rational('-123.456').floor(-1)       #=> -130

[ GitHub ]

# File 'rational.c', line 1450


static VALUE
nurat_floor_n(int argc, VALUE *argv, VALUE self)
{
    return f_round_common(argc, argv, self, nurat_floor);
}

#hash

This method is for internal use only.

[ GitHub ]

# File 'rational.c', line 1757


static VALUE
nurat_hash(VALUE self)
{
    st_index_t v, h[2];
    VALUE n;

    get_dat1(self);
    n = rb_hash(dat->num);
    h[0] = NUM2LONG(n);
    n = rb_hash(dat->den);
    h[1] = NUM2LONG(n);
    v = rb_memhash(h, sizeof(h));
    return ST2FIX(v);
}

#inspect ⇒ String

Returns the value as a string for inspection.

Rational(2).inspect      #=> "(2/1)"
Rational(-8, 6).inspect  #=> "(-4/3)"
Rational('1/2').inspect  #=> "(1/2)"

[ GitHub ]

# File 'rational.c', line 1811


static VALUE
nurat_inspect(VALUE self)
{
    VALUE s;

    s = rb_usascii_str_new2("(");
    rb_str_concat(s, f_format(self, f_inspect));
    rb_str_cat2(s, ")");

    return s;
}

#abs ⇒ `Rational` #magnitude ⇒ `Rational`

Alias for #abs.

#marshal_dump (private)

This method is for internal use only.

[ GitHub ]

# File 'rational.c', line 1850


static VALUE
nurat_marshal_dump(VALUE self)
{
    VALUE a;
    get_dat1(self);

    a = rb_assoc_new(dat->num, dat->den);
    rb_copy_generic_ivar(a, self);
    return a;
}

#numerator ⇒ Integer

Returns the numerator.

Rational(7).numerator        #=> 7
Rational(7, 1).numerator     #=> 7
Rational(9, -4).numerator    #=> -9
Rational(-2, -10).numerator  #=> 1

[ GitHub ]

# File 'rational.c', line 592


static VALUE
nurat_numerator(VALUE self)
{
    get_dat1(self);
    return dat->num;
}

#/(numeric) ⇒ Numeric #quo(numeric) ⇒ Numeric

Alias for #/.

#rationalize ⇒ `self` #rationalize(eps) ⇒ `Rational`

Returns a simpler approximation of the value if the optional argument eps is given (rat-|eps| <= result <= rat+|eps|), self otherwise.

r = Rational(5033165, 16777216)
r.rationalize                    #=> (5033165/16777216)
r.rationalize(Rational('0.01'))  #=> (3/10)
r.rationalize(Rational('0.1'))   #=> (1/3)

[ GitHub ]

# File 'rational.c', line 1734


static VALUE
nurat_rationalize(int argc, VALUE *argv, VALUE self)
{
    VALUE e, a, b, p, q;

    if (rb_check_arity(argc, 0, 1) == 0)
	return self;

    if (nurat_negative_p(self))
	return rb_rational_uminus(nurat_rationalize(argc, argv, rb_rational_uminus(self)));

    e = f_abs(argv[0]);
    a = f_sub(self, e);
    b = f_add(self, e);

    if (f_eqeq_p(a, b))
	return self;

    nurat_rationalize_internal(a, b, &p, &q);
    return f_rational_new2(CLASS_OF(self), p, q);
}

#round([ndigits] [, half: mode]) ⇒ Integer, `Rational`

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

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns a rational when ndigits is positive, otherwise returns an integer.

Rational(3).round      #=> 3
Rational(2, 3).round   #=> 1
Rational(-3, 2).round  #=> -2

  #    decimal      -  1  2  3 . 4  5  6
  #                   ^  ^  ^  ^   ^  ^
  #   precision      -3 -2 -1  0  +1 +2

Rational('-123.456').round(+1).to_f  #=> -123.5
Rational('-123.456').round(-1)       #=> -120

The optional half keyword argument is available similar to Float#round.

Rational(25, 100).round(1, half: :up)    #=> (3/10)
Rational(25, 100).round(1, half: :down)  #=> (1/5)
Rational(25, 100).round(1, half: :even)  #=> (1/5)
Rational(35, 100).round(1, half: :up)    #=> (2/5)
Rational(35, 100).round(1, half: :down)  #=> (3/10)
Rational(35, 100).round(1, half: :even)  #=> (2/5)
Rational(-25, 100).round(1, half: :up)   #=> (-3/10)
Rational(-25, 100).round(1, half: :down) #=> (-1/5)
Rational(-25, 100).round(1, half: :even) #=> (-1/5)

[ GitHub ]

# File 'rational.c', line 1553


static VALUE
nurat_round_n(int argc, VALUE *argv, VALUE self)
{
    VALUE opt;
    enum ruby_num_rounding_mode mode = (
        argc = rb_scan_args(argc, argv, "*:", NULL, &opt),
	rb_num_get_rounding_option(opt));
    VALUE (*round_func)(VALUE) = ROUND_FUNC(mode, nurat_round);
    return f_round_common(argc, argv, self, round_func);
}

#to_f ⇒ Float

Returns the value as a ::Float.

Rational(2).to_f      #=> 2.0
Rational(9, 4).to_f   #=> 2.25
Rational(-3, 4).to_f  #=> -0.75
Rational(20, 3).to_f  #=> 6.666666666666667

[ GitHub ]

# File 'rational.c', line 1585


static VALUE
nurat_to_f(VALUE self)
{
    return DBL2NUM(nurat_to_double(self));
}

#to_i ⇒ Integer

Returns the truncated value as an integer.

Equivalent to #truncate.

Rational(2, 3).to_i    #=> 0
Rational(3).to_i       #=> 3
Rational(300.6).to_i   #=> 300
Rational(98, 71).to_i  #=> 1
Rational(-31, 2).to_i  #=> -15

[ GitHub ]

# File 'rational.c', line 1293


static VALUE
nurat_truncate(VALUE self)
{
    get_dat1(self);
    if (INT_NEGATIVE_P(dat->num))
	return rb_int_uminus(rb_int_idiv(rb_int_uminus(dat->num), dat->den));
    return rb_int_idiv(dat->num, dat->den);
}

#to_r ⇒ `self`

Returns self.

Rational(2).to_r      #=> (2/1)
Rational(-8, 6).to_r  #=> (-4/3)

[ GitHub ]

# File 'rational.c', line 1600


static VALUE
nurat_to_r(VALUE self)
{
    return self;
}

#to_s ⇒ String

Returns the value as a string.

Rational(2).to_s      #=> "2/1"
Rational(-8, 6).to_s  #=> "-4/3"
Rational('1/2').to_s  #=> "1/2"

[ GitHub ]

# File 'rational.c', line 1795


static VALUE
nurat_to_s(VALUE self)
{
    return f_format(self, f_to_s);
}

#truncate([ndigits]) ⇒ Integer, `Rational`

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

When the precision is negative, the returned value is an integer with at least ndigits.abs trailing zeros.

Returns a rational when ndigits is positive, otherwise returns an integer.

Rational(3).truncate      #=> 3
Rational(2, 3).truncate   #=> 0
Rational(-3, 2).truncate  #=> -1

  #    decimal      -  1  2  3 . 4  5  6
  #                   ^  ^  ^  ^   ^  ^
  #   precision      -3 -2 -1  0  +1 +2

Rational('-123.456').truncate(+1).to_f  #=> -123.4
Rational('-123.456').truncate(-1)       #=> -120

[ GitHub ]

# File 'rational.c', line 1510


static VALUE
nurat_truncate_n(int argc, VALUE *argv, VALUE self)
{
    return f_round_common(argc, argv, self, nurat_truncate);
}

Class: Rational

Overview

Instance Attribute Summary

::Numeric - Inherited

Instance Method Summary

::Numeric - Inherited

::Comparable - Included

Instance Attribute Details

#negative? ⇒ Boolean (readonly)

#positive? ⇒ Boolean (readonly)

Instance Method Details

#*(numeric) ⇒ Numeric

#**

#+(numeric) ⇒ Numeric

#-(numeric) ⇒ Numeric

#- ⇒ Rational

#/(numeric) ⇒ Numeric #quo(numeric) ⇒ Numeric Also known as: #quo

#<=>(numeric) ⇒ 1, ...

#==(object) ⇒ Boolean

#abs ⇒ Rational #magnitude ⇒ Rational Also known as: #magnitude

#ceil([ndigits]) ⇒ Integer, Rational

#coerce(other)

#denominator ⇒ Integer

#fdiv(numeric) ⇒ Float

#floor([ndigits]) ⇒ Integer, Rational

#hash

#inspect ⇒ String

#abs ⇒ Rational #magnitude ⇒ Rational

#marshal_dump (private)

#numerator ⇒ Integer

#/(numeric) ⇒ Numeric #quo(numeric) ⇒ Numeric

#rationalize ⇒ self #rationalize(eps) ⇒ Rational

#round([ndigits] [, half: mode]) ⇒ Integer, Rational

#to_f ⇒ Float

#to_i ⇒ Integer

#to_r ⇒ self

#to_s ⇒ String

#truncate([ndigits]) ⇒ Integer, Rational

`::Numeric` - Inherited

`::Numeric` - Inherited

`::Comparable` - Included

#negative? ⇒ `Boolean` (readonly)

#positive? ⇒ `Boolean` (readonly)

#- ⇒ `Rational`

#/(numeric) ⇒ Numeric #quo(numeric) ⇒ Numeric
Also known as: #quo

#<=>(numeric) ⇒ `1`, ...

#==(object) ⇒ `Boolean`

#abs ⇒ `Rational` #magnitude ⇒ `Rational`
Also known as: #magnitude

#ceil([ndigits]) ⇒ Integer, `Rational`

#floor([ndigits]) ⇒ Integer, `Rational`

#abs ⇒ `Rational` #magnitude ⇒ `Rational`

#rationalize ⇒ `self` #rationalize(eps) ⇒ `Rational`

#round([ndigits] [, half: mode]) ⇒ Integer, `Rational`

#to_r ⇒ `self`

#truncate([ndigits]) ⇒ Integer, `Rational`