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, rationalize method or suffixing r to a literal. 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)
2/3r             #=> (2/3)

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)

Defined Under Namespace

Classes: compatible

Instance Method Summary collapse

Methods inherited from Numeric

#%, #[email protected], #[email protected], #abs, #abs2, #angle, #arg, #conj, #conjugate, #div, #divmod, #eql?, #i, #imag, #imaginary, #initialize_copy, #integer?, #magnitude, #modulo, #negative?, #nonzero?, #phase, #polar, #positive?, #real, #real?, #rect, #rectangular, #remainder, #singleton_method_added, #step, #to_c, #to_int, #zero?

Methods included from Comparable

#<, #<=, #>, #>=, #between?

Instance Method Details

#*(numeric) ⇒ Numeric

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

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# File 'rational.c', line 868

static VALUE
nurat_mul(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
	{
	    get_dat1(self);

	    return f_muldiv(self,
			    dat->num, dat->den,
			    other, ONE, '*');
	}
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
	return f_mul(f_to_f(self), 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, '*');
    }
}

#**(numeric) ⇒ Numeric

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

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# File 'rational.c', line 986

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 */
    if (RB_TYPE_P(other, 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);
	}
    }
    else if (RB_TYPE_P(other, T_BIGNUM)) {
	rb_warn("in a**b, b may be too big");
	return f_expt(f_to_f(self), other);
    }
    else if (RB_TYPE_P(other, T_FLOAT) || RB_TYPE_P(other, T_RATIONAL)) {
	return f_expt(f_to_f(self), other);
    }
    else {
	return rb_num_coerce_bin(self, other, id_expt);
    }
}

#+(numeric) ⇒ Numeric

Performs addition.

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

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# File 'rational.c', line 747

static VALUE
nurat_add(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
	{
	    get_dat1(self);

	    return f_addsub(self,
			    dat->num, dat->den,
			    other, ONE, '+');
	}
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
	return f_add(f_to_f(self), 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, '+');
    }
}

#-(numeric) ⇒ Numeric

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

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# File 'rational.c', line 788

static VALUE
nurat_sub(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
	{
	    get_dat1(self);

	    return f_addsub(self,
			    dat->num, dat->den,
			    other, ONE, '-');
	}
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
	return f_sub(f_to_f(self), 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, '-');
    }
}

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

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

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# File 'rational.c', line 910

static VALUE
nurat_div(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
	if (f_zero_p(other))
	    rb_raise_zerodiv();
	{
	    get_dat1(self);

	    return f_muldiv(self,
			    dat->num, dat->den,
			    other, ONE, '/');
	}
    }
    else if (RB_TYPE_P(other, T_FLOAT))
	return rb_funcall(f_to_f(self), '/', 1, other);
    else if (RB_TYPE_P(other, 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,
			    adat->num, adat->den,
			    bdat->num, bdat->den, '/');
	}
    }
    else {
	return rb_num_coerce_bin(self, other, '/');
    }
}

#<=>(numeric) ⇒ -1, ...

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

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# File 'rational.c', line 1070

static VALUE
nurat_cmp(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, 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));
	}
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
	return f_cmp(f_to_f(self), other);
    }
    else if (RB_TYPE_P(other, 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 = f_mul(adat->num, bdat->den);
		num2 = f_mul(bdat->num, adat->den);
	    }
	    return f_cmp(f_sub(num1, num2), ZERO);
	}
    }
    else {
	return rb_num_coerce_cmp(self, other, id_cmp);
    }
}

#==(object) ⇒ Boolean

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

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# File 'rational.c', line 1120

static VALUE
nurat_eqeq_p(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, 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;
	}
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
	return f_eqeq_p(f_to_f(self), other);
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
	{
	    get_dat2(self, other);

	    if (f_zero_p(adat->num) && f_zero_p(bdat->num))
		return Qtrue;

	    return f_boolcast(f_eqeq_p(adat->num, bdat->num) &&
			      f_eqeq_p(adat->den, bdat->den));
	}
    }
    else {
	return f_eqeq_p(other, self);
    }
}

#ceilInteger #ceil(precision = 0) ⇒ Object

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"

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# File 'rational.c', line 1357

static VALUE
nurat_ceil_n(int argc, VALUE *argv, VALUE self)
{
    return f_round_common(argc, argv, self, nurat_ceil);
}

#coerce(other) ⇒ Object

:nodoc:


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# File 'rational.c', line 1159

static VALUE
nurat_coerce(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
	return rb_assoc_new(f_rational_new_bang1(CLASS_OF(self), other), self);
    }
    else if (RB_TYPE_P(other, T_FLOAT)) {
	return rb_assoc_new(other, f_to_f(self));
    }
    else if (RB_TYPE_P(other, T_RATIONAL)) {
	return rb_assoc_new(other, self);
    }
    else if (RB_TYPE_P(other, 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)));
    }

    rb_raise(rb_eTypeError, "%s can't be coerced into %s",
	     rb_obj_classname(other), rb_obj_classname(self));
    return Qnil;
}

#denominatorInteger

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

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# File 'rational.c', line 644

static VALUE
nurat_denominator(VALUE self)
{
    get_dat1(self);
    return dat->den;
}

#exact?Boolean

:nodoc:


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# File 'rational.c', line 1210

static VALUE
nurat_true(VALUE self)
{
    return Qtrue;
}

#fdiv(numeric) ⇒ Float

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

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# File 'rational.c', line 956

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));
}

#floorInteger #floor(precision = 0) ⇒ Object

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"

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# File 'rational.c', line 1333

static VALUE
nurat_floor_n(int argc, VALUE *argv, VALUE self)
{
    return f_round_common(argc, argv, self, nurat_floor);
}

#hashObject

:nodoc:


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# File 'rational.c', line 1579

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);
}

#inspectString

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)"

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# File 'rational.c', line 1633

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_dumpObject (private)

:nodoc:


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# File 'rational.c', line 1665

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;
}

#numeratorInteger

Returns the numerator.

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

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# File 'rational.c', line 625

static VALUE
nurat_numerator(VALUE self)
{
    get_dat1(self);
    return dat->num;
}

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

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

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# File 'rational.c', line 910

static VALUE
nurat_div(VALUE self, VALUE other)
{
    if (RB_TYPE_P(other, T_FIXNUM) || RB_TYPE_P(other, T_BIGNUM)) {
	if (f_zero_p(other))
	    rb_raise_zerodiv();
	{
	    get_dat1(self);

	    return f_muldiv(self,
			    dat->num, dat->den,
			    other, ONE, '/');
	}
    }
    else if (RB_TYPE_P(other, T_FLOAT))
	return rb_funcall(f_to_f(self), '/', 1, other);
    else if (RB_TYPE_P(other, 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,
			    adat->num, adat->den,
			    bdat->num, bdat->den, '/');
	}
    }
    else {
	return rb_num_coerce_bin(self, other, '/');
    }
}

#quot(other) ⇒ Object

:nodoc:


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# File 'rational.c', line 1193

static VALUE
nurat_quot(VALUE self, VALUE other)
{
    return f_truncate(f_div(self, other));
}

#quotrem(other) ⇒ Object

:nodoc:


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# File 'rational.c', line 1200

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?Boolean

:nodoc:


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# File 'rational.c', line 1210

static VALUE
nurat_true(VALUE self)
{
    return Qtrue;
}

#rationalizeself #rationalize(eps) ⇒ Object

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)

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# File 'rational.c', line 1555

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);
}

#roundInteger #round(precision = 0) ⇒ Object

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"

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# File 'rational.c', line 1406

static VALUE
nurat_round_n(int argc, VALUE *argv, VALUE self)
{
    return f_round_common(argc, argv, self, nurat_round);
}

#to_fFloat

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

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# File 'rational.c', line 1423

static VALUE
nurat_to_f(VALUE self)
{
    get_dat1(self);
    return f_fdiv(dat->num, dat->den);
}

#to_iInteger

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

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# File 'rational.c', line 1246

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_rself

Returns self.

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

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# File 'rational.c', line 1439

static VALUE
nurat_to_r(VALUE self)
{
    return self;
}

#to_sString

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"

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# File 'rational.c', line 1617

static VALUE
nurat_to_s(VALUE self)
{
    return f_format(self, f_to_s);
}

#truncateInteger #truncate(precision = 0) ⇒ Object

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"

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# File 'rational.c', line 1381

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