# Class: Rational

Inherits:
Numeric
show all
Defined in:
rational.c

## Overview

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 or rationalize method. 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)
``````

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)
``````

## Instance Method Summary collapse

• Performs multiplication.

• Performs exponentiation.

• Performs subtraction.

• Performs division.

• :nodoc:.

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

• Returns true if rat equals object numerically.

• Returns the truncated value (toward positive infinity).

• :nodoc:.

• Returns the denominator (always positive).

• :nodoc:.

• Performs division and returns the value as a float.

• Returns the truncated value (toward negative infinity).

• :nodoc:.

• Returns the value as a string for inspection.

• :nodoc:.

• :nodoc:.

• Returns the numerator.

• Performs division.

• :nodoc:.

• :nodoc:.

• :nodoc:.

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

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

• Return the value as a float.

• Returns the truncated value as an integer.

• Returns self.

• Returns the value as a string.

• Returns the truncated value (toward zero).

## Instance Method Details

### #*(numeric) ⇒ Numeric

Performs multiplication.

For example:

``````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
``````

Returns:

 ``` ``` ```# File 'rational.c' static VALUE nurat_mul(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); return f_muldiv(self, dat->num, dat->den, other, ONE, '*'); }```

### #**(numeric) ⇒ Numeric

Performs exponentiation.

For example:

``````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
``````

Returns:

 ``` ``` ```# File 'rational.c' 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 */ }```

### #+(numeric) ⇒ Numeric

For example:

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

Returns:

 ``` ``` ```# File 'rational.c' static VALUE nurat_add(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); return f_addsub(self, dat->num, dat->den, other, ONE, '+'); }```

### #-(numeric) ⇒ Numeric

Performs subtraction.

For example:

``````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
``````

Returns:

 ``` ``` ```# File 'rational.c' static VALUE nurat_sub(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: { get_dat1(self); return f_addsub(self, dat->num, dat->den, other, ONE, '-'); }```

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

Performs division.

For example:

``````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
``````

 ``` ``` ```# File 'rational.c' static VALUE nurat_div(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: if (f_zero_p(other)) rb_raise_zerodiv(); { get_dat1(self); return f_muldiv(self, dat->num, dat->den, other, ONE, '/'); }```

### #// ⇒ Object

:nodoc:

 ``` ``` ```# File 'rational.c' static VALUE nurat_idiv(VALUE self, VALUE other) { return f_idiv(self, other); }```

### #<=>(numeric) ⇒ -1, ...

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

For example:

``````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
``````

Returns:

• (-1, 0, +1, nil)
 ``` ``` ```# File 'rational.c' static VALUE nurat_cmp(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case 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)); }```

### #==(object) ⇒ Boolean

Returns true if rat equals object numerically.

For example:

``````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
``````

Returns:

• (Boolean)
 ``` ``` ```# File 'rational.c' static VALUE nurat_eqeq_p(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case 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; }```

### #ceil ⇒ Integer #ceil(precision = 0) ⇒ Object

Returns the truncated value (toward positive infinity).

For example:

``````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"
``````

 ``` ``` ```# File 'rational.c' static VALUE nurat_ceil_n(int argc, VALUE *argv, VALUE self) { return f_round_common(argc, argv, self, nurat_ceil); }```

### #coerce ⇒ Object

:nodoc:

 ``` ``` ```# File 'rational.c' static VALUE nurat_coerce(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self); case T_FLOAT: return rb_assoc_new(other, f_to_f(self)); case T_RATIONAL: return rb_assoc_new(other, self); case 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))); }```

### #denominator ⇒ Integer

Returns the denominator (always positive).

For example:

``````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
``````

Returns:

 ``` ``` ```# File 'rational.c' static VALUE nurat_denominator(VALUE self) { get_dat1(self); return dat->den; }```

### #exact? ⇒ Object

:nodoc:

 ``` ``` ```# File 'rational.c' static VALUE nurat_true(VALUE self) { return Qtrue; }```

### #fdiv(numeric) ⇒ Float

Performs division and returns the value as a float.

For example:

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

Returns:

 ``` ``` ```# File 'rational.c' 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 #floor(precision = 0) ⇒ Object

Returns the truncated value (toward negative infinity).

For example:

``````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"
``````

 ``` ``` ```# File 'rational.c' static VALUE nurat_floor_n(int argc, VALUE *argv, VALUE self) { return f_round_common(argc, argv, self, nurat_floor); }```

### #hash ⇒ Object

:nodoc:

 ``` ``` ```# File 'rational.c' 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 LONG2FIX(v); }```

### #inspect ⇒ String

Returns the value as a string for inspection.

For example:

``````Rational(2).inspect      #=> "(2/1)"
Rational(-8, 6).inspect  #=> "(-4/3)"
Rational('0.5').inspect  #=> "(1/2)"
``````

Returns:

 ``` ``` ```# File 'rational.c' 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; }```

### #marshal_dump ⇒ Object

:nodoc:

 ``` ``` ```# File 'rational.c' 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; }```

:nodoc:

 ``` ``` ```# File 'rational.c' static VALUE nurat_marshal_load(VALUE self, VALUE a) { get_dat1(self); Check_Type(a, T_ARRAY); if (RARRAY_LEN(a) != 2) rb_raise(rb_eArgError, "marshaled rational must have an array whose length is 2 but %ld", RARRAY_LEN(a)); dat->num = RARRAY_PTR(a)[0]; dat->den = RARRAY_PTR(a)[1]; rb_copy_generic_ivar(self, a); if (f_zero_p(dat->den)) rb_raise_zerodiv(); return self; }```

### #numerator ⇒ Integer

Returns the numerator.

For example:

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

Returns:

 ``` ``` ```# File 'rational.c' static VALUE nurat_numerator(VALUE self) { get_dat1(self); return dat->num; }```

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

Performs division.

For example:

``````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
``````

 ``` ``` ```# File 'rational.c' static VALUE nurat_div(VALUE self, VALUE other) { switch (TYPE(other)) { case T_FIXNUM: case T_BIGNUM: if (f_zero_p(other)) rb_raise_zerodiv(); { get_dat1(self); return f_muldiv(self, dat->num, dat->den, other, ONE, '/'); }```

### #quot ⇒ Object

:nodoc:

 ``` ``` ```# File 'rational.c' static VALUE nurat_quot(VALUE self, VALUE other) { return f_truncate(f_div(self, other)); }```

### #quotrem ⇒ Object

:nodoc:

 ``` ``` ```# File 'rational.c' static VALUE nurat_quotrem(VALUE self, VALUE other) { VALUE val = f_truncate(f_div(self, other)); return rb_assoc_new(val, f_sub(self, f_mul(other, val))); }```

### #rational? ⇒ Object

:nodoc:

 ``` ``` ```# File 'rational.c' static VALUE nurat_true(VALUE self) { return Qtrue; }```

### #rationalize ⇒ Rational #rationalize(eps) ⇒ Object

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

For example:

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

 ``` ``` ```# File 'rational.c' 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 #round(precision = 0) ⇒ Object

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

For example:

``````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"
``````

 ``` ``` ```# File 'rational.c' static VALUE nurat_round_n(int argc, VALUE *argv, VALUE self) { return f_round_common(argc, argv, self, nurat_round); }```

### #to_f ⇒ Float

Return the value as a float.

For example:

``````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
``````

Returns:

 ``` ``` ```# File 'rational.c' static VALUE nurat_to_f(VALUE self) { get_dat1(self); return f_fdiv(dat->num, dat->den); }```

### #to_i ⇒ Integer

Returns the truncated value as an integer.

Equivalent to

``````rat.truncate.
``````

For example:

``````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
``````

Returns:

 ``` ``` ```# File 'rational.c' 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_r ⇒ Rational

Returns self.

For example:

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

Returns:

 ``` ``` ```# File 'rational.c' static VALUE nurat_to_r(VALUE self) { return self; }```

### #to_s ⇒ String

Returns the value as a string.

For example:

``````Rational(2).to_s      #=> "2/1"
Rational(-8, 6).to_s  #=> "-4/3"
Rational('0.5').to_s  #=> "1/2"
``````

Returns:

 ``` ``` ```# File 'rational.c' static VALUE nurat_to_s(VALUE self) { return f_format(self, f_to_s); }```

### #truncate ⇒ Integer #truncate(precision = 0) ⇒ Object

Returns the truncated value (toward zero).

For example:

``````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"
``````

 ``` ``` ```# File 'rational.c' static VALUE nurat_truncate_n(int argc, VALUE *argv, VALUE self) { return f_round_common(argc, argv, self, nurat_truncate); }```