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Rational

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)

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)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);

return f_muldiv(self,
dat->num, dat->den,
other, ONE, '*');
}
case T_FLOAT:
return f_mul(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);

return f_muldiv(self,
bdat->num, bdat->den, '*');
}
default:
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 */
switch (TYPE(other)) {
case 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;
}
return f_rational_new2(CLASS_OF(self), num, den);
}
case T_BIGNUM:
rb_warn("in a**b, b may be too big");
/* fall through */
case T_FLOAT:
case T_RATIONAL:
return f_expt(f_to_f(self), other);
default:
return rb_num_coerce_bin(self, other, id_expt);
}
}

rat + numeric → numeric click to toggle source

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

static VALUE
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);

dat->num, dat->den,
other, ONE, '+');
}
case T_FLOAT:
case T_RATIONAL:
{
get_dat2(self, other);

bdat->num, bdat->den, '+');
}
default:
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)
{
switch (TYPE(other)) {
case T_FIXNUM:
case T_BIGNUM:
{
get_dat1(self);

dat->num, dat->den,
other, ONE, '-');
}
case T_FLOAT:
return f_sub(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);

bdat->num, bdat->den, '-');
}
default:
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)
{
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, '/');
}
case T_FLOAT:
{
double x = RFLOAT_VALUE(other), den;
get_dat1(self);

if (isnan(x)) return DBL2NUM(NAN);
if (isinf(x)) return INT2FIX(0);
if (x != 0.0 && modf(x, &den) == 0.0) {
return rb_rational_raw2(dat->num, f_mul(rb_dbl2big(den), dat->den));
}
}
return rb_funcall(f_to_f(self), '/', 1, other);
case 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,
bdat->num, bdat->den, '/');
}
default:
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)
{
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));
}
case T_FLOAT:
return f_cmp(f_to_f(self), other);
case T_RATIONAL:
{
VALUE num1, num2;

get_dat2(self, other);

FIXNUM_P(bdat->num) && FIXNUM_P(bdat->den)) {
}
else {
}
return f_cmp(f_sub(num1, num2), ZERO);
}
default:
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)
{
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;
}
case T_FLOAT:
return f_eqeq_p(f_to_f(self), other);
case T_RATIONAL:
{
get_dat2(self, other);

return Qtrue;

}
default:
return f_eqeq_p(other, self);
}
}

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)
{
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, '/');
}
case T_FLOAT:
{
double x = RFLOAT_VALUE(other), den;
get_dat1(self);

if (isnan(x)) return DBL2NUM(NAN);
if (isinf(x)) return INT2FIX(0);
if (x != 0.0 && modf(x, &den) == 0.0) {
return rb_rational_raw2(dat->num, f_mul(rb_dbl2big(den), dat->den));
}
}
return rb_funcall(f_to_f(self), '/', 1, other);
case 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,
bdat->num, bdat->den, '/');
}
default:
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);

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_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

rat.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_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);
}

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