Class: Complex

Inherits:
Numeric show all
Defined in:
complex.c

Overview

A complex number can be represented as a paired real number with imaginary unit; a+bi. Where a is real part, b is imaginary part and i is imaginary unit. Real a equals complex a+0i mathematically.

In ruby, you can create complex object with Complex, Complex::rect, Complex::polar or to_c method.

Complex(1)           #=> (1+0i)
Complex(2, 3)        #=> (2+3i)
Complex.polar(2, 3)  #=> (-1.9799849932008908+0.2822400161197344i)
3.to_c               #=> (3+0i)

You can also create complex object from floating-point numbers or strings.

Complex(0.3)         #=> (0.3+0i)
Complex('0.3-0.5i')  #=> (0.3-0.5i)
Complex('2/3+3/4i')  #=> ((2/3)+(3/4)*i)
Complex('[email protected]')       #=> (-0.4161468365471424+0.9092974268256817i)

0.3.to_c             #=> (0.3+0i)
'0.3-0.5i'.to_c      #=> (0.3-0.5i)
'2/3+3/4i'.to_c      #=> ((2/3)+(3/4)*i)
'[email protected]'.to_c           #=> (-0.4161468365471424+0.9092974268256817i)

A complex object is either an exact or an inexact number.

Complex(1, 1) / 2    #=> ((1/2)+(1/2)*i)
Complex(1, 1) / 2.0  #=> (0.5+0.5i)

Defined Under Namespace

Classes: compatible

Constant Summary collapse

I =

The imaginary unit.

f_complex_new_bang2(rb_cComplex, ZERO, ONE)

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from Numeric

#%, #[email protected], #<=>, #ceil, #div, #divmod, #floor, #i, #initialize_copy, #integer?, #modulo, #nonzero?, #remainder, #round, #singleton_method_added, #step, #to_int, #truncate, #zero?

Methods included from Comparable

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

Class Method Details

.polar(abs[, arg]) ⇒ Object

Returns a complex object which denotes the given polar form.

Complex.polar(3, 0)            #=> (3.0+0.0i)
Complex.polar(3, Math::PI/2)   #=> (1.836909530733566e-16+3.0i)
Complex.polar(3, Math::PI)     #=> (-3.0+3.673819061467132e-16i)
Complex.polar(3, -Math::PI/2)  #=> (1.836909530733566e-16-3.0i)

600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
# File 'complex.c', line 600

static VALUE
nucomp_s_polar(int argc, VALUE *argv, VALUE klass)
{
    VALUE abs, arg;

    switch (rb_scan_args(argc, argv, "11", &abs, &arg)) {
      case 1:
	nucomp_real_check(abs);
	arg = ZERO;
	break;
      default:
	nucomp_real_check(abs);
	nucomp_real_check(arg);
	break;
    }
    return f_complex_polar(klass, abs, arg);
}

.rect(real[, imag]) ⇒ Object .rectangular(real[, imag]) ⇒ Object

Returns a complex object which denotes the given rectangular form.

Complex.rectangular(1, 2)  #=> (1+2i)

445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
# File 'complex.c', line 445

static VALUE
nucomp_s_new(int argc, VALUE *argv, VALUE klass)
{
    VALUE real, imag;

    switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
      case 1:
	nucomp_real_check(real);
	imag = ZERO;
	break;
      default:
	nucomp_real_check(real);
	nucomp_real_check(imag);
	break;
    }

    return nucomp_s_canonicalize_internal(klass, real, imag);
}

.rect(real[, imag]) ⇒ Object .rectangular(real[, imag]) ⇒ Object

Returns a complex object which denotes the given rectangular form.

Complex.rectangular(1, 2)  #=> (1+2i)

445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
# File 'complex.c', line 445

static VALUE
nucomp_s_new(int argc, VALUE *argv, VALUE klass)
{
    VALUE real, imag;

    switch (rb_scan_args(argc, argv, "11", &real, &imag)) {
      case 1:
	nucomp_real_check(real);
	imag = ZERO;
	break;
      default:
	nucomp_real_check(real);
	nucomp_real_check(imag);
	break;
    }

    return nucomp_s_canonicalize_internal(klass, real, imag);
}

Instance Method Details

#*(numeric) ⇒ Object

Performs multiplication.

Complex(2, 3)  * Complex(2, 3)   #=> (-5+12i)
Complex(900)   * Complex(1)      #=> (900+0i)
Complex(-2, 9) * Complex(-9, 2)  #=> (0-85i)
Complex(9, 8)  * 4               #=> (36+32i)
Complex(20, 9) * 9.8             #=> (196.0+88.2i)

738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
# File 'complex.c', line 738

static VALUE
nucomp_mul(VALUE self, VALUE other)
{
    if (k_complex_p(other)) {
	VALUE real, imag;

	get_dat2(self, other);

	real = f_sub(f_mul(adat->real, bdat->real),
		     f_mul(adat->imag, bdat->imag));
	imag = f_add(f_mul(adat->real, bdat->imag),
		     f_mul(adat->imag, bdat->real));

	return f_complex_new2(CLASS_OF(self), real, imag);
    }
    if (k_numeric_p(other) && f_real_p(other)) {
	get_dat1(self);

	return f_complex_new2(CLASS_OF(self),
			      f_mul(dat->real, other),
			      f_mul(dat->imag, other));
    }
    return rb_num_coerce_bin(self, other, '*');
}

#**(numeric) ⇒ Object

Performs exponentiation.

Complex('i') ** 2              #=> (-1+0i)
Complex(-8) ** Rational(1, 3)  #=> (1.0000000000000002+1.7320508075688772i)

867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
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
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
# File 'complex.c', line 867

static VALUE
nucomp_expt(VALUE self, VALUE other)
{
    if (k_numeric_p(other) && k_exact_zero_p(other))
	return f_complex_new_bang1(CLASS_OF(self), ONE);

    if (k_rational_p(other) && f_one_p(f_denominator(other)))
	other = f_numerator(other); /* c14n */

    if (k_complex_p(other)) {
	get_dat1(other);

	if (k_exact_zero_p(dat->imag))
	    other = dat->real; /* c14n */
    }

    if (k_complex_p(other)) {
	VALUE r, theta, nr, ntheta;

	get_dat1(other);

	r = f_abs(self);
	theta = f_arg(self);

	nr = m_exp_bang(f_sub(f_mul(dat->real, m_log_bang(r)),
			      f_mul(dat->imag, theta)));
	ntheta = f_add(f_mul(theta, dat->real),
		       f_mul(dat->imag, m_log_bang(r)));
	return f_complex_polar(CLASS_OF(self), nr, ntheta);
    }
    if (k_fixnum_p(other)) {
	if (f_gt_p(other, ZERO)) {
	    VALUE x, z;
	    long n;

	    x = self;
	    z = x;
	    n = FIX2LONG(other) - 1;

	    while (n) {
		long q, r;

		while (1) {
		    get_dat1(x);

		    q = n / 2;
		    r = n % 2;

		    if (r)
			break;

		    x = nucomp_s_new_internal(CLASS_OF(self),
				       f_sub(f_mul(dat->real, dat->real),
					     f_mul(dat->imag, dat->imag)),
				       f_mul(f_mul(TWO, dat->real), dat->imag));
		    n = q;
		}
		z = f_mul(z, x);
		n--;
	    }
	    return z;
	}
	return f_expt(f_reciprocal(self), f_negate(other));
    }
    if (k_numeric_p(other) && f_real_p(other)) {
	VALUE r, theta;

	if (k_bignum_p(other))
	    rb_warn("in a**b, b may be too big");

	r = f_abs(self);
	theta = f_arg(self);

	return f_complex_polar(CLASS_OF(self), f_expt(r, other),
			       f_mul(theta, other));
    }
    return rb_num_coerce_bin(self, other, id_expt);
}

#+(numeric) ⇒ Object

Performs addition.

Complex(2, 3)  + Complex(2, 3)   #=> (4+6i)
Complex(900)   + Complex(1)      #=> (901+0i)
Complex(-2, 9) + Complex(-9, 2)  #=> (-11+11i)
Complex(9, 8)  + 4               #=> (13+8i)
Complex(20, 9) + 9.8             #=> (29.8+9i)

702
703
704
705
706
# File 'complex.c', line 702

static VALUE
nucomp_add(VALUE self, VALUE other)
{
    return f_addsub(self, other, f_add, '+');
}

#-(numeric) ⇒ Object

Performs subtraction.

Complex(2, 3)  - Complex(2, 3)   #=> (0+0i)
Complex(900)   - Complex(1)      #=> (899+0i)
Complex(-2, 9) - Complex(-9, 2)  #=> (7+7i)
Complex(9, 8)  - 4               #=> (5+8i)
Complex(20, 9) - 9.8             #=> (10.2+9i)

720
721
722
723
724
# File 'complex.c', line 720

static VALUE
nucomp_sub(VALUE self, VALUE other)
{
    return f_addsub(self, other, f_sub, '-');
}

#-Object

Returns negation of the value.

-Complex(1, 2)  #=> (-1-2i)

659
660
661
662
663
664
665
# File 'complex.c', line 659

static VALUE
nucomp_negate(VALUE self)
{
  get_dat1(self);
  return f_complex_new2(CLASS_OF(self),
			f_negate(dat->real), f_negate(dat->imag));
}

#/(numeric) ⇒ Object #quo(numeric) ⇒ Object

Performs division.

Complex(2, 3)  / Complex(2, 3)   #=> ((1/1)+(0/1)*i)
Complex(900)   / Complex(1)      #=> ((900/1)+(0/1)*i)
Complex(-2, 9) / Complex(-9, 2)  #=> ((36/85)-(77/85)*i)
Complex(9, 8)  / 4               #=> ((9/4)+(2/1)*i)
Complex(20, 9) / 9.8             #=> (2.0408163265306123+0.9183673469387754i)

830
831
832
833
834
# File 'complex.c', line 830

static VALUE
nucomp_div(VALUE self, VALUE other)
{
    return f_divide(self, other, f_quo, id_quo);
}

#==(object) ⇒ Boolean

Returns true if cmp equals object numerically.

Complex(2, 3)  == Complex(2, 3)   #=> true
Complex(5)     == 5               #=> true
Complex(0)     == 0.0             #=> true
Complex('1/3') == 0.33            #=> false
Complex('1/2') == '1/2'           #=> false

Returns:

  • (Boolean)

958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
# File 'complex.c', line 958

static VALUE
nucomp_eqeq_p(VALUE self, VALUE other)
{
    if (k_complex_p(other)) {
	get_dat2(self, other);

	return f_boolcast(f_eqeq_p(adat->real, bdat->real) &&
			  f_eqeq_p(adat->imag, bdat->imag));
    }
    if (k_numeric_p(other) && f_real_p(other)) {
	get_dat1(self);

	return f_boolcast(f_eqeq_p(dat->real, other) && f_zero_p(dat->imag));
    }
    return f_eqeq_p(other, self);
}

#absObject #magnitudeObject

Returns the absolute part of its polar form.

Complex(-1).abs         #=> 1
Complex(3.0, -4.0).abs  #=> 5.0

999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
# File 'complex.c', line 999

static VALUE
nucomp_abs(VALUE self)
{
    get_dat1(self);

    if (f_zero_p(dat->real)) {
	VALUE a = f_abs(dat->imag);
	if (k_float_p(dat->real) && !k_float_p(dat->imag))
	    a = f_to_f(a);
	return a;
    }
    if (f_zero_p(dat->imag)) {
	VALUE a = f_abs(dat->real);
	if (!k_float_p(dat->real) && k_float_p(dat->imag))
	    a = f_to_f(a);
	return a;
    }
    return m_hypot(dat->real, dat->imag);
}

#abs2Object

Returns square of the absolute value.

Complex(-1).abs2         #=> 1
Complex(3.0, -4.0).abs2  #=> 25.0

1028
1029
1030
1031
1032
1033
1034
# File 'complex.c', line 1028

static VALUE
nucomp_abs2(VALUE self)
{
    get_dat1(self);
    return f_add(f_mul(dat->real, dat->real),
		 f_mul(dat->imag, dat->imag));
}

#argFloat #angleFloat #phaseFloat

Returns the angle part of its polar form.

Complex.polar(3, Math::PI/2).arg  #=> 1.5707963267948966

Overloads:


1046
1047
1048
1049
1050
1051
# File 'complex.c', line 1046

static VALUE
nucomp_arg(VALUE self)
{
    get_dat1(self);
    return m_atan2_bang(dat->imag, dat->real);
}

#argFloat #angleFloat #phaseFloat

Returns the angle part of its polar form.

Complex.polar(3, Math::PI/2).arg  #=> 1.5707963267948966

Overloads:


1046
1047
1048
1049
1050
1051
# File 'complex.c', line 1046

static VALUE
nucomp_arg(VALUE self)
{
    get_dat1(self);
    return m_atan2_bang(dat->imag, dat->real);
}

#coerceObject

:nodoc:


976
977
978
979
980
981
982
983
984
985
986
987
# File 'complex.c', line 976

static VALUE
nucomp_coerce(VALUE self, VALUE other)
{
    if (k_numeric_p(other) && f_real_p(other))
	return rb_assoc_new(f_complex_new_bang1(CLASS_OF(self), other), self);
    if (RB_TYPE_P(other, T_COMPLEX))
	return rb_assoc_new(other, self);

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

#complex?Boolean

:nodoc:

Returns:

  • (Boolean)

1101
1102
1103
1104
1105
# File 'complex.c', line 1101

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

#conjObject #conjugateObject

Returns the complex conjugate.

Complex(1, 2).conjugate  #=> (1-2i)

1092
1093
1094
1095
1096
1097
# File 'complex.c', line 1092

static VALUE
nucomp_conj(VALUE self)
{
    get_dat1(self);
    return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}

#conjObject #conjugateObject

Returns the complex conjugate.

Complex(1, 2).conjugate  #=> (1-2i)

1092
1093
1094
1095
1096
1097
# File 'complex.c', line 1092

static VALUE
nucomp_conj(VALUE self)
{
    get_dat1(self);
    return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}

#denominatorInteger

Returns the denominator (lcm of both denominator - real and imag).

See numerator.

Returns:


1145
1146
1147
1148
1149
1150
# File 'complex.c', line 1145

static VALUE
nucomp_denominator(VALUE self)
{
    get_dat1(self);
    return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
}

#eql?Boolean

:nodoc:

Returns:

  • (Boolean)

1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
# File 'complex.c', line 1202

static VALUE
nucomp_eql_p(VALUE self, VALUE other)
{
    if (k_complex_p(other)) {
	get_dat2(self, other);

	return f_boolcast((CLASS_OF(adat->real) == CLASS_OF(bdat->real)) &&
			  (CLASS_OF(adat->imag) == CLASS_OF(bdat->imag)) &&
			  f_eqeq_p(self, other));

    }
    return Qfalse;
}

#exact?Boolean

:nodoc:

Returns:

  • (Boolean)

1122
1123
1124
1125
1126
1127
# File 'complex.c', line 1122

static VALUE
nucomp_exact_p(VALUE self)
{
    get_dat1(self);
    return f_boolcast(k_exact_p(dat->real) && k_exact_p(dat->imag));
}

#fdiv(numeric) ⇒ Object

Performs division as each part is a float, never returns a float.

Complex(11, 22).fdiv(3)  #=> (3.6666666666666665+7.333333333333333i)

846
847
848
849
850
# File 'complex.c', line 846

static VALUE
nucomp_fdiv(VALUE self, VALUE other)
{
    return f_divide(self, other, f_fdiv, id_fdiv);
}

#hashObject

:nodoc:


1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
# File 'complex.c', line 1186

static VALUE
nucomp_hash(VALUE self)
{
    st_index_t v, h[2];
    VALUE n;

    get_dat1(self);
    n = rb_hash(dat->real);
    h[0] = NUM2LONG(n);
    n = rb_hash(dat->imag);
    h[1] = NUM2LONG(n);
    v = rb_memhash(h, sizeof(h));
    return LONG2FIX(v);
}

#imagObject #imaginaryObject

Returns the imaginary part.

Complex(7).imaginary      #=> 0
Complex(9, -4).imaginary  #=> -4

644
645
646
647
648
649
# File 'complex.c', line 644

static VALUE
nucomp_imag(VALUE self)
{
    get_dat1(self);
    return dat->imag;
}

#imagObject #imaginaryObject

Returns the imaginary part.

Complex(7).imaginary      #=> 0
Complex(9, -4).imaginary  #=> -4

644
645
646
647
648
649
# File 'complex.c', line 644

static VALUE
nucomp_imag(VALUE self)
{
    get_dat1(self);
    return dat->imag;
}

#inexact?Boolean

:nodoc:

Returns:

  • (Boolean)

1130
1131
1132
1133
1134
# File 'complex.c', line 1130

static VALUE
nucomp_inexact_p(VALUE self)
{
    return f_boolcast(!nucomp_exact_p(self));
}

#inspectString

Returns the value as a string for inspection.

Complex(2).inspect                       #=> "(2+0i)"
Complex('-8/6').inspect                  #=> "((-4/3)+0i)"
Complex('1/2i').inspect                  #=> "(0+(1/2)*i)"
Complex(0, Float::INFINITY).inspect      #=> "(0+Infinity*i)"
Complex(Float::NAN, Float::NAN).inspect  #=> "(NaN+NaN*i)"

Returns:


1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
# File 'complex.c', line 1288

static VALUE
nucomp_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;
}

#absObject #magnitudeObject

Returns the absolute part of its polar form.

Complex(-1).abs         #=> 1
Complex(3.0, -4.0).abs  #=> 5.0

999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
# File 'complex.c', line 999

static VALUE
nucomp_abs(VALUE self)
{
    get_dat1(self);

    if (f_zero_p(dat->real)) {
	VALUE a = f_abs(dat->imag);
	if (k_float_p(dat->real) && !k_float_p(dat->imag))
	    a = f_to_f(a);
	return a;
    }
    if (f_zero_p(dat->imag)) {
	VALUE a = f_abs(dat->real);
	if (!k_float_p(dat->real) && k_float_p(dat->imag))
	    a = f_to_f(a);
	return a;
    }
    return m_hypot(dat->real, dat->imag);
}

#marshal_dumpObject (private)

:nodoc:


1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
# File 'complex.c', line 1320

static VALUE
nucomp_marshal_dump(VALUE self)
{
    VALUE a;
    get_dat1(self);

    a = rb_assoc_new(dat->real, dat->imag);
    rb_copy_generic_ivar(a, self);
    return a;
}

#numeratorNumeric

Returns the numerator.

    1   2       3+4i  <-  numerator
    - + -i  ->  ----
    2   3        6    <-  denominator

c = Complex('1/2+2/3i')  #=> ((1/2)+(2/3)*i)
n = c.numerator          #=> (3+4i)
d = c.denominator        #=> 6
n / d                    #=> ((1/2)+(2/3)*i)
Complex(Rational(n.real, d), Rational(n.imag, d))
                         #=> ((1/2)+(2/3)*i)

See denominator.

Returns:


1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
# File 'complex.c', line 1170

static VALUE
nucomp_numerator(VALUE self)
{
    VALUE cd;

    get_dat1(self);

    cd = f_denominator(self);
    return f_complex_new2(CLASS_OF(self),
			  f_mul(f_numerator(dat->real),
				f_div(cd, f_denominator(dat->real))),
			  f_mul(f_numerator(dat->imag),
				f_div(cd, f_denominator(dat->imag))));
}

#argFloat #angleFloat #phaseFloat

Returns the angle part of its polar form.

Complex.polar(3, Math::PI/2).arg  #=> 1.5707963267948966

Overloads:


1046
1047
1048
1049
1050
1051
# File 'complex.c', line 1046

static VALUE
nucomp_arg(VALUE self)
{
    get_dat1(self);
    return m_atan2_bang(dat->imag, dat->real);
}

#polarArray

Returns an array; [cmp.abs, cmp.arg].

Complex(1, 2).polar  #=> [2.23606797749979, 1.1071487177940904]

Returns:


1077
1078
1079
1080
1081
# File 'complex.c', line 1077

static VALUE
nucomp_polar(VALUE self)
{
    return rb_assoc_new(f_abs(self), f_arg(self));
}

#quoObject

#rationalize([eps]) ⇒ Object

Returns the value as a rational if possible (the imaginary part should be exactly zero).

Complex(1.0/3, 0).rationalize  #=> (1/3)
Complex(1, 0.0).rationalize    # RangeError
Complex(1, 2).rationalize      # RangeError

See to_r.


1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
# File 'complex.c', line 1461

static VALUE
nucomp_rationalize(int argc, VALUE *argv, VALUE self)
{
    get_dat1(self);

    rb_scan_args(argc, argv, "01", NULL);

    if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) {
       VALUE s = f_to_s(self);
       rb_raise(rb_eRangeError, "can't convert %s into Rational",
                StringValuePtr(s));
    }
    return rb_funcall2(dat->real, rb_intern("rationalize"), argc, argv);
}

#realObject

Returns the real part.

Complex(7).real      #=> 7
Complex(9, -4).real  #=> 9

627
628
629
630
631
632
# File 'complex.c', line 627

static VALUE
nucomp_real(VALUE self)
{
    get_dat1(self);
    return dat->real;
}

#real?false

Returns false.

Returns:

  • (false)

Returns:

  • (Boolean)

1114
1115
1116
1117
1118
# File 'complex.c', line 1114

static VALUE
nucomp_false(VALUE self)
{
    return Qfalse;
}

#rectArray #rectangularArray

Returns an array; [cmp.real, cmp.imag].

Complex(1, 2).rectangular  #=> [1, 2]

Overloads:


1062
1063
1064
1065
1066
1067
# File 'complex.c', line 1062

static VALUE
nucomp_rect(VALUE self)
{
    get_dat1(self);
    return rb_assoc_new(dat->real, dat->imag);
}

#rectArray #rectangularArray

Returns an array; [cmp.real, cmp.imag].

Complex(1, 2).rectangular  #=> [1, 2]

Overloads:


1062
1063
1064
1065
1066
1067
# File 'complex.c', line 1062

static VALUE
nucomp_rect(VALUE self)
{
    get_dat1(self);
    return rb_assoc_new(dat->real, dat->imag);
}

#to_cself

Returns self.

Complex(2).to_c      #=> (2+0i)
Complex(-8, 6).to_c  #=> (-8+6i)

Returns:

  • (self)

1485
1486
1487
1488
1489
# File 'complex.c', line 1485

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

#to_fFloat

Returns the value as a float if possible (the imaginary part should be exactly zero).

Complex(1, 0).to_f    #=> 1.0
Complex(1, 0.0).to_f  # RangeError
Complex(1, 2).to_f    # RangeError

Returns:


1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
# File 'complex.c', line 1409

static VALUE
nucomp_to_f(VALUE self)
{
    get_dat1(self);

    if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) {
	VALUE s = f_to_s(self);
	rb_raise(rb_eRangeError, "can't convert %s into Float",
		 StringValuePtr(s));
    }
    return f_to_f(dat->real);
}

#to_iInteger

Returns the value as an integer if possible (the imaginary part should be exactly zero).

Complex(1, 0).to_i    #=> 1
Complex(1, 0.0).to_i  # RangeError
Complex(1, 2).to_i    # RangeError

Returns:


1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
# File 'complex.c', line 1385

static VALUE
nucomp_to_i(VALUE self)
{
    get_dat1(self);

    if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) {
	VALUE s = f_to_s(self);
	rb_raise(rb_eRangeError, "can't convert %s into Integer",
		 StringValuePtr(s));
    }
    return f_to_i(dat->real);
}

#to_rObject

Returns the value as a rational if possible (the imaginary part should be exactly zero).

Complex(1, 0).to_r    #=> (1/1)
Complex(1, 0.0).to_r  # RangeError
Complex(1, 2).to_r    # RangeError

See rationalize.


1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
# File 'complex.c', line 1435

static VALUE
nucomp_to_r(VALUE self)
{
    get_dat1(self);

    if (k_inexact_p(dat->imag) || f_nonzero_p(dat->imag)) {
	VALUE s = f_to_s(self);
	rb_raise(rb_eRangeError, "can't convert %s into Rational",
		 StringValuePtr(s));
    }
    return f_to_r(dat->real);
}

#to_sString

Returns the value as a string.

Complex(2).to_s                       #=> "2+0i"
Complex('-8/6').to_s                  #=> "-4/3+0i"
Complex('1/2i').to_s                  #=> "0+1/2i"
Complex(0, Float::INFINITY).to_s      #=> "0+Infinity*i"
Complex(Float::NAN, Float::NAN).to_s  #=> "NaN+NaN*i"

Returns:


1270
1271
1272
1273
1274
# File 'complex.c', line 1270

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

#conjObject #conjugateObject

Returns the complex conjugate.

Complex(1, 2).conjugate  #=> (1-2i)

1092
1093
1094
1095
1096
1097
# File 'complex.c', line 1092

static VALUE
nucomp_conj(VALUE self)
{
    get_dat1(self);
    return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
}