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rational.c

Parent

Numeric

Methods

#*
#**
#+
#-
#-@
#/
#<=>
#==
#abs
#ceil
#denominator
#fdiv
#floor
#inspect
#magnitude
#negative?
#numerator
#positive?
#quo
#rationalize
#round
#to_f
#to_i
#to_r
#to_s
#truncate

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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.

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)

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

 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, '*');
 }
}

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) #=> (0.0+2.0i)
Rational(1, 2) ** 0 #=> (1/1)
Rational(1, 2) ** 0.0 #=> 1.0

 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("**"));
 }
}

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

 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, '+');
 }
}

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_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, '-');
 }
}

-rat → rational click to toggle source

Negates rat.

 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);
}

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_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, '/');
 }
}

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

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

 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("<=>"));
 }
}

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_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 click to toggle source

Returns the absolute value of rat.

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

#magnitude is an alias for #abs.

 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 or rational click to toggle source

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

 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

 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)
{
 VALUE div;
 if (f_zero_p(other))
 return nurat_div(self, rb_float_new(0.0));
 if (FIXNUM_P(other) && other == LONG2FIX(1))
 return nurat_to_f(self);
 div = nurat_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 or rational click to toggle source

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

 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;
}

magnitude → rational click to toggle source

Returns the absolute value of rat.

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

#magnitude is an alias for #abs.

 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;
}

negative? → true or false click to toggle source

Returns true if rat is less than 0.

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

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;
}

positive? → true or false click to toggle source

Returns true if rat is greater than 0.

 static VALUE
nurat_positive_p(VALUE self)
{
 get_dat1(self);
 return f_boolcast(INT_POSITIVE_P(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_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, '/');
 }
}

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 (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 or rational click to toggle source

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)

 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 click to toggle source

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

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

to_i → integer click to toggle source

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

 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 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([ndigits]) → integer or rational click to toggle source

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

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

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