class Rational

BigDecimal extends the native Rational class to provide the to_d method.

When you require BigDecimal in your application, this method will be available on Rational objects.

A rational number can be represented as a paired integer number; a/b (b>0). Where a is numerator and b is denominator. Integer a equals rational a/1 mathematically.

In ruby, you can create rational object with Rational, to_r, rationalize method or suffixing r to a literal. The return values will be irreducible.

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 object 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 program 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 has inexact factor (numerical value or operation), 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)

Public Class Methods

json_create(object) click to toggle source

Deserializes JSON string by converting numerator value n, denominator value d, to a Rational object.

# File ext/json/lib/json/add/rational.rb, line 10
def self.json_create(object)
  Rational(object['n'], object['d'])
end

Public Instance Methods

rat * numeric → numeric click to toggle source

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

static VALUE
nurat_mul(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
        {
            get_dat1(self);

            return f_muldiv(self,
                            dat->num, dat->den,
                            other, ONE, '*');
        }
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
        return f_mul(f_to_f(self), 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, '*');
    }
}

rat ** numeric → numeric click to toggle source

Performs exponentiation.

Rational(2)    ** Rational(3)    #=> (8/1)
Rational(10)   ** -2             #=> (1/100)
Rational(10)   ** -2.0           #=> 0.01
Rational(-4)   ** Rational(1,2)  #=> (1.2246063538223773e-16+2.0i)
Rational(1, 2) ** 0              #=> (1/1)
Rational(1, 2) ** 0.0            #=> 1.0

static VALUE
nurat_expt(VALUE self, VALUE other)
{
    if (k_numeric_p(other) && k_exact_zero_p(other))
        return f_rational_new_bang1(CLASS_OF(self), ONE);

    if (k_rational_p(other)) {
        get_dat1(other);

        if (f_one_p(dat->den))
            other = dat->num; /* c14n */
    }

    /* Deal with special cases of 0**n and 1**n */
    if (k_numeric_p(other) && k_exact_p(other)) {
        get_dat1(self);
        if (f_one_p(dat->den)) {
            if (f_one_p(dat->num)) {
                return f_rational_new_bang1(CLASS_OF(self), ONE);
            }
            else if (f_minus_one_p(dat->num) && k_integer_p(other)) {
                return f_rational_new_bang1(CLASS_OF(self), INT2FIX(f_odd_p(other) ? -1 : 1));
            }
            else if (f_zero_p(dat->num)) {
                if (FIX2INT(f_cmp(other, ZERO)) == -1) {
                    rb_raise_zerodiv();
                }
                else {
                    return f_rational_new_bang1(CLASS_OF(self), ZERO);
                }
            }
        }
    }

    /* General case */
    if (RB_TYPE_P(other, T_FIXNUM)) {
        {
            VALUE num, den;

            get_dat1(self);

            switch (FIX2INT(f_cmp(other, ZERO))) {
              case 1:
                num = f_expt(dat->num, other);
                den = f_expt(dat->den, other);
                break;
              case -1:
                num = f_expt(dat->den, f_negate(other));
                den = f_expt(dat->num, f_negate(other));
                break;
              default:
                num = ONE;
                den = ONE;
                break;
            }
            if (RB_FLOAT_TYPE_P(num)) { /* infinity due to overflow */
                if (RB_FLOAT_TYPE_P(den)) return DBL2NUM(NAN);
                return num;
            }
            if (RB_FLOAT_TYPE_P(den)) { /* infinity due to overflow */
                num = ZERO;
                den = ONE;
            }
            return f_rational_new2(CLASS_OF(self), num, den);
        }
    }
    else if (RB_TYPE_P(other, T_BIGNUM)) {
        rb_warn("in a**b, b may be too big");
        return f_expt(f_to_f(self), other);
    }
    else if (RB_TYPE_P(other, T_FLOAT) || RB_TYPE_P(other, T_RATIONAL)) {
        return f_expt(f_to_f(self), other);
    }
    else {
        return rb_num_coerce_bin(self, other, id_expt);
    }
}

rat + numeric → numeric click to toggle source

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

static VALUE
nurat_add(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
        {
            get_dat1(self);

            return f_addsub(self,
                            dat->num, dat->den,
                            other, ONE, '+');
        }
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
        return f_add(f_to_f(self), 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, '+');
    }
}

rat - numeric → numeric click to toggle source

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

static VALUE
nurat_sub(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
        {
            get_dat1(self);

            return f_addsub(self,
                            dat->num, dat->den,
                            other, ONE, '-');
        }
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
        return f_sub(f_to_f(self), 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, '-');
    }
}

rat / numeric → numeric click to toggle source

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

static VALUE
nurat_div(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
        if (f_zero_p(other))
            rb_raise_zerodiv();
        {
            get_dat1(self);

            return f_muldiv(self,
                            dat->num, dat->den,
                            other, ONE, '/');
        }
    }
    else if (RB_TYPE_P(other, T_FLOAT))
        return rb_funcall(f_to_f(self), '/', 1, other);
    else if (RB_TYPE_P(other, T_RATIONAL)) {
        if (f_zero_p(other))
            rb_raise_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, '/');
    }
}

rational <=> numeric → -1, 0, +1 or nil click to toggle source

Performs comparison and returns -1, 0, or +1.

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

static VALUE
nurat_cmp(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
        {
            get_dat1(self);

            if (FIXNUM_P(dat->den) && FIX2LONG(dat->den) == 1)
                return f_cmp(dat->num, other); /* c14n */
            return f_cmp(self, f_rational_new_bang1(CLASS_OF(self), other));
        }
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
        return f_cmp(f_to_f(self), other);
    }
    else if (RB_TYPE_P(other, T_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 = f_mul(adat->num, bdat->den);
                num2 = f_mul(bdat->num, adat->den);
            }
            return f_cmp(f_sub(num1, num2), ZERO);
        }
    }
    else {
        return rb_num_coerce_cmp(self, other, id_cmp);
    }
}

rat == object → true or false click to toggle source

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

static VALUE
nurat_eqeq_p(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
        {
            get_dat1(self);

            if (f_zero_p(dat->num) && f_zero_p(other))
                return Qtrue;

            if (!FIXNUM_P(dat->den))
                return Qfalse;
            if (FIX2LONG(dat->den) != 1)
                return Qfalse;
            if (f_eqeq_p(dat->num, other))
                return Qtrue;
            return Qfalse;
        }
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
        return f_eqeq_p(f_to_f(self), other);
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
        {
            get_dat2(self, other);

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

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

as_json(*) click to toggle source

Returns a hash, that will be turned into a JSON object and represent this object.

# File ext/json/lib/json/add/rational.rb, line 16
def as_json(*)
  {
    JSON.create_id => self.class.name,
    'n'            => numerator,
    'd'            => denominator,
  }
end

ceil → integer click to toggle source

ceil(precision=0) → rational

Returns the truncated value (toward positive infinity).

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

'%f' % Rational('-123.456').ceil(+1)  #=> "-123.400000"
'%f' % Rational('-123.456').ceil(-1)  #=> "-120.000000"

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

denominator → integer click to toggle source

Returns the denominator (always positive).

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

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

fdiv(numeric) → float click to toggle source

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

static VALUE
nurat_fdiv(VALUE self, VALUE other)
{
    if (f_zero_p(other))
        return f_div(self, f_to_f(other));
    return f_to_f(f_div(self, other));
}

floor → integer click to toggle source

floor(precision=0) → rational

Returns the truncated value (toward negative infinity).

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

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

'%f' % Rational('-123.456').floor(+1)  #=> "-123.500000"
'%f' % Rational('-123.456').floor(-1)  #=> "-130.000000"

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

inspect → string click to toggle source

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)"

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;
}

numerator → integer click to toggle source

Returns the numerator.

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

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

quo(numeric) → numeric click to toggle source

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

static VALUE
nurat_div(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
        if (f_zero_p(other))
            rb_raise_zerodiv();
        {
            get_dat1(self);

            return f_muldiv(self,
                            dat->num, dat->den,
                            other, ONE, '/');
        }
    }
    else if (RB_TYPE_P(other, T_FLOAT))
        return rb_funcall(f_to_f(self), '/', 1, other);
    else if (RB_TYPE_P(other, T_RATIONAL)) {
        if (f_zero_p(other))
            rb_raise_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, '/');
    }
}

rationalize → self click to toggle source

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)

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

    if (argc == 0)
        return self;

    if (f_negative_p(self))
        return f_negate(nurat_rationalize(argc, argv, f_abs(self)));

    rb_scan_args(argc, argv, "01", &e);
    e = f_abs(e);
    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 → integer click to toggle source

round(precision=0) → rational

Returns the truncated value (toward the nearest integer; 0.5 => 1; -0.5 => -1).

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

'%f' % Rational('-123.456').round(+1)  #=> "-123.500000"
'%f' % Rational('-123.456').round(-1)  #=> "-120.000000"

static VALUE
nurat_round_n(int argc, VALUE *argv, VALUE self)
{
    return f_round_common(argc, argv, self, nurat_round);
}

to_d(precision) → bigdecimal click to toggle source

Converts a Rational to a BigDecimal.

The required precision parameter is used to determine the amount of significant digits for the result. See BigDecimal#div for more information, as it is used along with the denominator and the precision for parameters.

r = (22/7.0).to_r
# => (7077085128725065/2251799813685248)
r.to_d(3)
# => #<BigDecimal:1a44d08,'0.314E1',18(36)>

# File ext/bigdecimal/lib/bigdecimal/util.rb, line 121
def to_d(precision)
  if precision <= 0
    raise ArgumentError, "negative precision"
  end
  num = self.numerator
  BigDecimal(num).div(self.denominator, precision)
end

to_f → float click to toggle source

Return 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

static VALUE
nurat_to_f(VALUE self)
{
    get_dat1(self);
    return f_fdiv(dat->num, dat->den);
}

to_i → integer click to toggle source

Returns the truncated value as an integer.

Equivalent to Rational#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(-30,2).to_i  #=> -15

static VALUE
nurat_truncate(VALUE self)
{
    get_dat1(self);
    if (f_negative_p(dat->num))
        return f_negate(f_idiv(f_negate(dat->num), dat->den));
    return f_idiv(dat->num, dat->den);
}

to_json(*) click to toggle source

Stores class name (Rational) along with numerator value n and denominator value d as JSON string

# File ext/json/lib/json/add/rational.rb, line 25
def to_json(*)
  as_json.to_json
end

to_r → self click to toggle source

Returns self.

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

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

to_s → string click to toggle source

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"

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

truncate → integer click to toggle source

truncate(precision=0) → rational

Returns the truncated value (toward zero).

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

'%f' % Rational('-123.456').truncate(+1)  #=>  "-123.400000"
'%f' % Rational('-123.456').truncate(-1)  #=>  "-120.000000"

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