Class
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)
Class Methods
ext/json/lib/json/add/rational.rb
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# File tmp/rubies/ruby-2.6.10/ext/json/lib/json/add/rational.rb, line 10
def self.json_create(object)
Rational(object['n'], object['d'])
end
Instance Methods
rational.c
View on GitHub
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, '*');
}
}
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
rational.c
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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(f_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_TYPE_P(other, T_BIGNUM)) {
rb_warn("in a**b, b may be too big");
return rb_float_pow(nurat_to_f(self), other);
}
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, rb_intern("**"));
}
}
Performs exponentiation.
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
rational.c
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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, '+');
}
}
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
rational.c
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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, '-');
}
}
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
rational.c
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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);
}
Negates rat.
rational.c
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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, '/');
}
}
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
rational.c
View on GitHub
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("<=>"));
}
}
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
rational.c
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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);
}
}
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
rational.c
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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)
Rational#magnitude is an alias for Rational#abs.
ext/json/lib/json/add/rational.rb
View on GitHub
# File tmp/rubies/ruby-2.6.10/ext/json/lib/json/add/rational.rb, line 16
def as_json(*)
{
JSON.create_id => self.class.name,
'n' => numerator,
'd' => denominator,
}
end
Returns a hash, that will be turned into a JSON object and represent this object.
rational.c
View on GitHub
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
rational.c
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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
rational.c
View on GitHub
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
rational.c
View on GitHub
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
rational.c
View on GitHub
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)"
rational.c
View on GitHub
static VALUE
nurat_negative_p(VALUE self)
{
get_dat1(self);
return f_boolcast(INT_NEGATIVE_P(dat->num));
}
Returns true if rat is less than 0.
rational.c
View on GitHub
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
rational.c
View on GitHub
static VALUE
nurat_positive_p(VALUE self)
{
get_dat1(self);
return f_boolcast(INT_POSITIVE_P(dat->num));
}
Returns true if rat is greater than 0.
rational.c
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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);
}
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)
rational.c
View on GitHub
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)
ext/bigdecimal/lib/bigdecimal/util.rb
View on GitHub
# File tmp/rubies/ruby-2.6.10/ext/bigdecimal/lib/bigdecimal/util.rb, line 126
def to_d(precision)
BigDecimal(self, precision)
end
Returns the value as a BigDecimal.
The required precision parameter is used to determine the number of significant digits for the result.
require 'bigdecimal' require 'bigdecimal/util' Rational(22, 7).to_d(3) # => 0.314e1
See also BigDecimal::new.
rational.c
View on GitHub
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
rational.c
View on GitHub
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
ext/json/lib/json/add/rational.rb
View on GitHub
# File tmp/rubies/ruby-2.6.10/ext/json/lib/json/add/rational.rb, line 25
def to_json(*)
as_json.to_json
end
rational.c
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static VALUE
nurat_to_r(VALUE self)
{
return self;
}
Returns self.
Rational(2).to_r #=> (2/1) Rational(-8, 6).to_r #=> (-4/3)
rational.c
View on GitHub
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"
rational.c
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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