Class: Complex (Ruby 2.3.4)

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    • complex.c

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    Complex

    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.

    Complex object can be created as literal, and also by using Kernel#Complex, ::rect, ::polar or #to_c method.

    2+1i                 #=> (2+1i)
    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('1@2')       #=> (-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)
    '1@2'.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)
    

    Constants

    I

    The imaginary unit.

    Public Class Methods

    polar(abs[, arg]) → complex click to toggle source

    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)
    
     
                   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);
            if (canonicalization) return abs;
            return nucomp_s_new_internal(klass, abs, ZERO);
          default:
            nucomp_real_check(abs);
            nucomp_real_check(arg);
            break;
        }
        return f_complex_polar(klass, abs, arg);
    }
                
    rect(real[, imag]) → complex click to toggle source
    rectangular(real[, imag]) → complex

    Returns a complex object which denotes the given rectangular form.

    Complex.rectangular(1, 2)  #=> (1+2i)
    
     
                   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);
    }
                
    rectangular(real[, imag]) → complex click to toggle source

    Returns a complex object which denotes the given rectangular form.

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

    Public Instance Methods

    cmp * numeric → complex click to toggle source

    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)
    
     
                   VALUE
    rb_nucomp_mul(VALUE self, VALUE other)
    {
        if (k_complex_p(other)) {
            VALUE real, imag;
            VALUE areal, aimag, breal, bimag;
            int arzero, aizero, brzero, bizero;
    
            get_dat2(self, other);
    
            arzero = !!f_zero_p(areal = adat->real);
            aizero = !!f_zero_p(aimag = adat->imag);
            brzero = !!f_zero_p(breal = bdat->real);
            bizero = !!f_zero_p(bimag = bdat->imag);
            real = f_sub(safe_mul(areal, breal, arzero, brzero),
                         safe_mul(aimag, bimag, aizero, bizero));
            imag = f_add(safe_mul(areal, bimag, arzero, bizero),
                         safe_mul(aimag, breal, aizero, brzero));
    
            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, '*');
    }
                
    cmp ** numeric → complex click to toggle source

    Performs exponentiation.

    Complex('i') ** 2              #=> (-1+0i)
    Complex(-8) ** Rational(1, 3)  #=> (1.0000000000000002+1.7320508075688772i)
    
     
                   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);
    }
                
    cmp + numeric → complex click to toggle source

    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)
    
     
                   VALUE
    rb_nucomp_add(VALUE self, VALUE other)
    {
        return f_addsub(self, other, f_add, '+');
    }
                
    cmp - numeric → complex click to toggle source

    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)
    
     
                   static VALUE
    nucomp_sub(VALUE self, VALUE other)
    {
        return f_addsub(self, other, f_sub, '-');
    }
                
    -cmp → complex click to toggle source

    Returns negation of the value.

    -Complex(1, 2)  #=> (-1-2i)
    
     
                   static VALUE
    nucomp_negate(VALUE self)
    {
      get_dat1(self);
      return f_complex_new2(CLASS_OF(self),
                            f_negate(dat->real), f_negate(dat->imag));
    }
                
    cmp / numeric → complex click to toggle source
    quo(numeric) → complex

    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)
    
     
                   static VALUE
    nucomp_div(VALUE self, VALUE other)
    {
        return f_divide(self, other, f_quo, id_quo);
    }
                
    cmp == object → true or false click to toggle source

    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
    
     
                   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);
    }
                
    abs → real click to toggle source

    Returns the absolute part of its polar form.

    Complex(-1).abs         #=> 1
    Complex(3.0, -4.0).abs  #=> 5.0
    
     
                   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);
    }
                
    abs2 → real click to toggle source

    Returns square of the absolute value.

    Complex(-1).abs2         #=> 1
    Complex(3.0, -4.0).abs2  #=> 25.0
    
     
                   static VALUE
    nucomp_abs2(VALUE self)
    {
        get_dat1(self);
        return f_add(f_mul(dat->real, dat->real),
                     f_mul(dat->imag, dat->imag));
    }
                
    angle → float click to toggle source

    Returns the angle part of its polar form.

    Complex.polar(3, Math::PI/2).arg  #=> 1.5707963267948966
    
     
                   static VALUE
    nucomp_arg(VALUE self)
    {
        get_dat1(self);
        return m_atan2_bang(dat->imag, dat->real);
    }
                
    arg → float click to toggle source

    Returns the angle part of its polar form.

    Complex.polar(3, Math::PI/2).arg  #=> 1.5707963267948966
    
     
                   static VALUE
    nucomp_arg(VALUE self)
    {
        get_dat1(self);
        return m_atan2_bang(dat->imag, dat->real);
    }
                
    conj → complex click to toggle source
    conjugate → complex

    Returns the complex conjugate.

    Complex(1, 2).conjugate  #=> (1-2i)
    
     
                   static VALUE
    nucomp_conj(VALUE self)
    {
        get_dat1(self);
        return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
    }
                
    conjugate → complex click to toggle source

    Returns the complex conjugate.

    Complex(1, 2).conjugate  #=> (1-2i)
    
     
                   static VALUE
    nucomp_conj(VALUE self)
    {
        get_dat1(self);
        return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
    }
                
    denominator → integer click to toggle source

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

    See numerator.

     
                   static VALUE
    nucomp_denominator(VALUE self)
    {
        get_dat1(self);
        return rb_lcm(f_denominator(dat->real), f_denominator(dat->imag));
    }
                
    fdiv(numeric) → complex click to toggle source

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

    Complex(11, 22).fdiv(3)  #=> (3.6666666666666665+7.333333333333333i)
    
     
                   static VALUE
    nucomp_fdiv(VALUE self, VALUE other)
    {
        return f_divide(self, other, f_fdiv, id_fdiv);
    }
                
    imag → real click to toggle source
    imaginary → real

    Returns the imaginary part.

    Complex(7).imaginary      #=> 0
    Complex(9, -4).imaginary  #=> -4
    
     
                   static VALUE
    nucomp_imag(VALUE self)
    {
        get_dat1(self);
        return dat->imag;
    }
                
    imaginary → real click to toggle source

    Returns the imaginary part.

    Complex(7).imaginary      #=> 0
    Complex(9, -4).imaginary  #=> -4
    
     
                   static VALUE
    nucomp_imag(VALUE self)
    {
        get_dat1(self);
        return dat->imag;
    }
                
    inspect → string click to toggle source

    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)"
    
     
                   static VALUE
    nucomp_inspect(VALUE self)
    {
        VALUE s;
    
        s = rb_usascii_str_new2("(");
        rb_str_concat(s, f_format(self, rb_inspect));
        rb_str_cat2(s, ")");
    
        return s;
    }
                
    magnitude → real click to toggle source

    Returns the absolute part of its polar form.

    Complex(-1).abs         #=> 1
    Complex(3.0, -4.0).abs  #=> 5.0
    
     
                   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);
    }
                
    numerator → numeric click to toggle source

    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.

     
                   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))));
    }
                
    phase → float click to toggle source

    Returns the angle part of its polar form.

    Complex.polar(3, Math::PI/2).arg  #=> 1.5707963267948966
    
     
                   static VALUE
    nucomp_arg(VALUE self)
    {
        get_dat1(self);
        return m_atan2_bang(dat->imag, dat->real);
    }
                
    polar → array click to toggle source

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

    Complex(1, 2).polar  #=> [2.23606797749979, 1.1071487177940904]
    
     
                   static VALUE
    nucomp_polar(VALUE self)
    {
        return rb_assoc_new(f_abs(self), f_arg(self));
    }
                
    cmp / numeric → complex click to toggle source
    quo(numeric) → complex

    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)
    
     
                   static VALUE
    nucomp_div(VALUE self, VALUE other)
    {
        return f_divide(self, other, f_quo, id_quo);
    }
                
    rationalize([eps]) → rational click to toggle source

    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.

     
                   static VALUE
    nucomp_rationalize(int argc, VALUE *argv, VALUE self)
    {
        get_dat1(self);
    
        rb_scan_args(argc, argv, "01", NULL);
    
        if (!k_exact_zero_p(dat->imag)) {
           rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
                    self);
        }
        return rb_funcall2(dat->real, rb_intern("rationalize"), argc, argv);
    }
                
    real → real click to toggle source

    Returns the real part.

    Complex(7).real      #=> 7
    Complex(9, -4).real  #=> 9
    
     
                   static VALUE
    nucomp_real(VALUE self)
    {
        get_dat1(self);
        return dat->real;
    }
                
    real? → false click to toggle source

    Returns false.

     
                   static VALUE
    nucomp_false(VALUE self)
    {
        return Qfalse;
    }
                
    rect → array click to toggle source
    rectangular → array

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

    Complex(1, 2).rectangular  #=> [1, 2]
    
     
                   static VALUE
    nucomp_rect(VALUE self)
    {
        get_dat1(self);
        return rb_assoc_new(dat->real, dat->imag);
    }
                
    rect → array click to toggle source
    rectangular → array

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

    Complex(1, 2).rectangular  #=> [1, 2]
    
     
                   static VALUE
    nucomp_rect(VALUE self)
    {
        get_dat1(self);
        return rb_assoc_new(dat->real, dat->imag);
    }
                
    to_c → self click to toggle source

    Returns self.

    Complex(2).to_c      #=> (2+0i)
    Complex(-8, 6).to_c  #=> (-8+6i)
    
     
                   static VALUE
    nucomp_to_c(VALUE self)
    {
        return self;
    }
                
    to_f → float click to toggle source

    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
    
     
                   static VALUE
    nucomp_to_f(VALUE self)
    {
        get_dat1(self);
    
        if (!k_exact_zero_p(dat->imag)) {
            rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Float",
                     self);
        }
        return f_to_f(dat->real);
    }
                
    to_i → integer click to toggle source

    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
    
     
                   static VALUE
    nucomp_to_i(VALUE self)
    {
        get_dat1(self);
    
        if (!k_exact_zero_p(dat->imag)) {
            rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Integer",
                     self);
        }
        return f_to_i(dat->real);
    }
                
    to_r → rational click to toggle source

    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.

     
                   static VALUE
    nucomp_to_r(VALUE self)
    {
        get_dat1(self);
    
        if (!k_exact_zero_p(dat->imag)) {
            rb_raise(rb_eRangeError, "can't convert %"PRIsVALUE" into Rational",
                     self);
        }
        return f_to_r(dat->real);
    }
                
    to_s → string click to toggle source

    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"
    
     
                   static VALUE
    nucomp_to_s(VALUE self)
    {
        return f_format(self, rb_String);
    }
                
    conj → complex click to toggle source
    conjugate → complex

    Returns the complex conjugate.

    Complex(1, 2).conjugate  #=> (1-2i)
    
     
                   static VALUE
    nucomp_conj(VALUE self)
    {
        get_dat1(self);
        return f_complex_new2(CLASS_OF(self), dat->real, f_negate(dat->imag));
    }