class Rational
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.
You can create a Rational object explicitly with:
You can convert certain objects to Rationals with:
-
Method
Rational.
Examples
Rational(1) #=> (1/1) Rational(2, 3) #=> (2/3) Rational(4, -6) #=> (-2/3) # Reduced. 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)
Public Class Methods
Source
# File ext/json/lib/json/add/rational.rb, line 9 def self.json_create(object) Rational(object['n'], object['d']) end
See as_json.
Public Instance Methods
Source
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, '*');
}
}
Returns the numeric product of self and other:
Rational(9, 8) * 4 #=> (9/2) Rational(20, 9) * 9.8 #=> 21.77777777777778 Rational(9, 8) * Complex(1, 2) # => ((9/8)+(9/4)*i) Rational(2, 3) * Rational(2, 3) #=> (4/9) Rational(900) * Rational(1) #=> (900/1) Rational(-2, 9) * Rational(-9, 2) #=> (1/1)
Source
VALUE
rb_rational_pow(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) && RB_INTEGER_TYPE_P(other)) {
return f_rational_new_bang1(CLASS_OF(self), INT2FIX(rb_int_odd_p(other) ? -1 : 1));
}
else if (INT_ZERO_P(dat->num)) {
if (rb_num_negative_p(other)) {
rb_num_zerodiv();
}
else {
return f_rational_new_bang1(CLASS_OF(self), ZERO);
}
}
}
}
/* General case */
if (FIXNUM_P(other)) {
{
VALUE num, den;
get_dat1(self);
if (INT_POSITIVE_P(other)) {
num = rb_int_pow(dat->num, other);
den = rb_int_pow(dat->den, other);
}
else if (INT_NEGATIVE_P(other)) {
num = rb_int_pow(dat->den, rb_int_uminus(other));
den = rb_int_pow(dat->num, rb_int_uminus(other));
}
else {
num = ONE;
den = ONE;
}
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_BIGNUM_TYPE_P(other)) {
rb_raise(rb_eArgError, "exponent is too large");
}
else if (RB_FLOAT_TYPE_P(other) || RB_TYPE_P(other, T_RATIONAL)) {
return rb_float_pow(nurat_to_f(self), other);
}
else {
return rb_num_coerce_bin(self, other, idPow);
}
}
Returns self raised to the power exponent:
Rational(2) ** Rational(3) #=> (8/1) Rational(10) ** -2 #=> (1/100) Rational(10) ** -2.0 #=> 0.01 Rational(-4) ** Rational(1, 2) #=> (0.0+2.0i) Rational(1, 2) ** 0 #=> (1/1) Rational(1, 2) ** 0.0 #=> 1.0
Source
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, '+');
}
}
Returns the sum of self and other:
Rational(2, 3) + 0 # => (2/3) Rational(2, 3) + 1 # => (5/3) Rational(2, 3) + -1 # => (-1/3) Rational(2, 3) + Complex(1, 0) # => ((5/3)+0i) Rational(2, 3) + Rational(1, 1) # => (5/3) Rational(2, 3) + Rational(3, 2) # => (13/6) Rational(2, 3) + Rational(3.0, 2.0) # => (13/6) Rational(2, 3) + Rational(3.1, 2.1) # => (30399297484750849/14186338826217063)
For a computation involving Floats, the result may be inexact (see Float#+):
Rational(2, 3) + 1.0 # => 1.6666666666666665 Rational(2, 3) + Complex(1.0, 0.0) # => (1.6666666666666665+0.0i)
Source
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, '-');
}
}
Returns the difference of self and other:
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
Source
VALUE
rb_rational_uminus(VALUE self)
{
const int unused = (RUBY_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);
}
Returns self, negated:
-(1/3r) # => (-1/3) -(-1/3r) # => (1/3)
Source
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, '/');
}
}
Returns the quotient of self and other:
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
Also aliased as: quo
Source
VALUE
rb_rational_cmp(VALUE self, VALUE other)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
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);
/* FALLTHROUGH */
}
case 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 = 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);
}
case T_FLOAT:
return rb_dbl_cmp(nurat_to_double(self), RFLOAT_VALUE(other));
default:
return rb_num_coerce_cmp(self, other, idCmp);
}
}
Compares self and other.
Returns:
-
-1, ifselfis less thanother. -
0, if the two values are the same. -
1, ifselfis greater thanother. -
nil, if the two values are incomparable.
Examples:
Rational(2, 3) <=> Rational(4, 3) # => -1 Rational(2, 1) <=> Rational(2, 1) # => 0 Rational(2, 1) <=> 2 # => 0 Rational(2, 1) <=> 2.0 # => 0 Rational(2, 1) <=> Complex(2, 0) # => 0 Rational(4, 3) <=> Rational(2, 3) # => 1 Rational(4, 3) <=> :foo # => nil
Class Rational includes module Comparable, each of whose methods uses Rational#<=> for comparison.
Source
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 RBOOL(FIXNUM_ZERO_P(rb_dbl_cmp(d, NUM2DBL(other))));
}
}
else if (RB_FLOAT_TYPE_P(other)) {
const double d = nurat_to_double(self);
return RBOOL(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 RBOOL(rb_int_equal(adat->num, bdat->num) &&
rb_int_equal(adat->den, bdat->den));
}
}
else {
return rb_equal(other, self);
}
}
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
Source
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;
}
Returns the absolute value of rat.
(1/2r).abs #=> (1/2) (-1/2r).abs #=> (1/2)
Also aliased as: magnitude
Source
# File ext/json/lib/json/add/rational.rb, line 29 def as_json(*) { JSON.create_id => self.class.name, 'n' => numerator, 'd' => denominator, } end
Methods Rational#as_json and Rational.json_create may be used to serialize and deserialize a Rational object; see Marshal.
Method Rational#as_json serializes self, returning a 2-element hash representing self:
require 'json/add/rational' x = Rational(2, 3).as_json # => {"json_class"=>"Rational", "n"=>2, "d"=>3}
Method JSON.create deserializes such a hash, returning a Rational object:
Rational.json_create(x) # => (2/3)
Source
static VALUE
nurat_ceil_n(int argc, VALUE *argv, VALUE self)
{
return f_round_common(argc, argv, self, nurat_ceil);
}
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
Source
static VALUE
nurat_denominator(VALUE self)
{
get_dat1(self);
return dat->den;
}
Returns the denominator (always positive).
Rational(7).denominator #=> 1 Rational(7, 1).denominator #=> 1 Rational(9, -4).denominator #=> 4 Rational(-2, -10).denominator #=> 5
Source
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);
}
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
Source
static VALUE
nurat_floor_n(int argc, VALUE *argv, VALUE self)
{
return f_round_common(argc, argv, self, nurat_floor);
}
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
Source
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;
}
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)"
Returns the absolute value of rat.
(1/2r).abs #=> (1/2) (-1/2r).abs #=> (1/2)
Alias for: abs
Source
static VALUE
nurat_negative_p(VALUE self)
{
get_dat1(self);
return RBOOL(INT_NEGATIVE_P(dat->num));
}
Returns true if rat is less than 0.
Source
static VALUE
nurat_numerator(VALUE self)
{
get_dat1(self);
return dat->num;
}
Returns the numerator.
Rational(7).numerator #=> 7 Rational(7, 1).numerator #=> 7 Rational(9, -4).numerator #=> -9 Rational(-2, -10).numerator #=> 1
Source
static VALUE
nurat_positive_p(VALUE self)
{
get_dat1(self);
return RBOOL(INT_POSITIVE_P(dat->num));
}
Returns true if rat is greater than 0.
Source
static VALUE
nurat_rationalize(int argc, VALUE *argv, VALUE self)
{
VALUE e, a, b, p, q;
VALUE rat = self;
get_dat1(self);
if (rb_check_arity(argc, 0, 1) == 0)
return self;
e = f_abs(argv[0]);
if (INT_NEGATIVE_P(dat->num)) {
rat = f_rational_new2(RBASIC_CLASS(self), rb_int_uminus(dat->num), dat->den);
}
a = FIXNUM_ZERO_P(e) ? rat : rb_rational_minus(rat, e);
b = FIXNUM_ZERO_P(e) ? rat : rb_rational_plus(rat, e);
if (f_eqeq_p(a, b))
return self;
nurat_rationalize_internal(a, b, &p, &q);
if (rat != self) {
RATIONAL_SET_NUM(rat, rb_int_uminus(p));
RATIONAL_SET_DEN(rat, q);
return rat;
}
return f_rational_new2(CLASS_OF(self), p, q);
}
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)
Source
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);
}
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)
Source
# File bundled-src/bigdecimal-4.0.1/lib/bigdecimal/util.rb, line 135 def to_d(precision=0) BigDecimal(self, precision) end
Returns the value as a BigDecimal.
The precision parameter is used to determine the number of significant digits for the result. When precision is set to 0, the number of digits to represent the float being converted is determined automatically. The default precision is 0.
require 'bigdecimal' require 'bigdecimal/util' Rational(22, 7).to_d(3) # => 0.314e1
See also Kernel.BigDecimal.
Source
static VALUE
nurat_to_f(VALUE self)
{
return DBL2NUM(nurat_to_double(self));
}
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
Source
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);
}
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(-31, 2).to_i #=> -15
Source
# File ext/json/lib/json/add/rational.rb, line 46 def to_json(*args) as_json.to_json(*args) end
Returns a JSON string representing self:
require 'json/add/rational' puts Rational(2, 3).to_json
Output:
{"json_class":"Rational","n":2,"d":3}
Source
static VALUE
nurat_to_r(VALUE self)
{
return self;
}
Returns self.
Rational(2).to_r #=> (2/1) Rational(-8, 6).to_r #=> (-4/3)
Source
static VALUE
nurat_to_s(VALUE self)
{
return f_format(self, f_to_s);
}
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"
Source
static VALUE
nurat_truncate_n(int argc, VALUE *argv, VALUE self)
{
return f_round_common(argc, argv, self, nurat_truncate);
}
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