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)

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, #nonzero?, #phase, #polar, #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

Returns:


897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
# File 'rational.c', line 897

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

Returns:


1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
# File 'rational.c', line 1015

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

Returns:


776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
# File 'rational.c', line 776

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

Returns:


817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
# File 'rational.c', line 817

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

Overloads:


939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
# File 'rational.c', line 939

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, '/');
    }
}

#//Object

:nodoc:


1215
1216
1217
1218
1219
# File 'rational.c', line 1215

static VALUE
nurat_idiv(VALUE self, VALUE other)
{
    return f_idiv(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

Returns:

  • (-1, 0, +1, nil)

1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
# File 'rational.c', line 1099

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

Returns:

  • (Boolean)

1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
# File 'rational.c', line 1149

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"

Overloads:


1386
1387
1388
1389
1390
# File 'rational.c', line 1386

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

#coerceObject

:nodoc:


1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
# File 'rational.c', line 1188

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

Returns:


673
674
675
676
677
678
# File 'rational.c', line 673

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

#exact?Boolean

:nodoc:

Returns:

  • (Boolean)

1239
1240
1241
1242
1243
# File 'rational.c', line 1239

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

Returns:


985
986
987
988
989
990
991
# File 'rational.c', line 985

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"

Overloads:


1362
1363
1364
1365
1366
# File 'rational.c', line 1362

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

#hashObject

:nodoc:


1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
# File 'rational.c', line 1608

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)"

Returns:


1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
# File 'rational.c', line 1662

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:


1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
# File 'rational.c', line 1694

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

Returns:


654
655
656
657
658
659
# File 'rational.c', line 654

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

Overloads:


939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
# File 'rational.c', line 939

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, '/');
    }
}

#quotObject

:nodoc:


1222
1223
1224
1225
1226
# File 'rational.c', line 1222

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

#quotremObject

:nodoc:


1229
1230
1231
1232
1233
1234
# File 'rational.c', line 1229

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:

Returns:

  • (Boolean)

1239
1240
1241
1242
1243
# File 'rational.c', line 1239

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)

Overloads:

  • #rationalizeself

    Returns:

    • (self)

1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
# File 'rational.c', line 1584

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"

Overloads:


1435
1436
1437
1438
1439
# File 'rational.c', line 1435

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

Returns:


1452
1453
1454
1455
1456
1457
# File 'rational.c', line 1452

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

Returns:


1275
1276
1277
1278
1279
1280
1281
1282
# File 'rational.c', line 1275

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)

Returns:

  • (self)

1468
1469
1470
1471
1472
# File 'rational.c', line 1468

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"

Returns:


1646
1647
1648
1649
1650
# File 'rational.c', line 1646

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"

Overloads:


1410
1411
1412
1413
1414
# File 'rational.c', line 1410

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