[ruby-core:109622] [Ruby master Bug#18937] Inconsistent definitions of Complex#<=> and Numeric#<=> with others

Issue #18937 has been updated by nobu (Nobuyoshi Nakada).


I agree that `Complex#<=>` should coerce the argument as well as other methods/classes.
https://github.com/ruby/ruby/pull/6269

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Bug #18937: Inconsistent definitions of Complex#<=> and Numeric#<=> with others
https://bugs.ruby-lang.org/issues/18937#change-98806

* Author: msnm (Masahiro Nomoto)
* Status: Open
* Priority: Normal
* ruby -v: 3.1.2
* Backport: 2.7: UNKNOWN, 3.0: UNKNOWN, 3.1: UNKNOWN
----------------------------------------
Object#<=> says "Returns 0 if `obj` and `other` are the same object or `obj == other`" .
https://ruby-doc.org/core-3.1.2/Object.html#method-i-3C-3D-3E

However, neither Complex#<=> nor Numeric#<=> satisfies that definition.

```ruby
num1 = Complex(0, 42)
num2 = Complex(0, 42)
p num1.equal?(num2)  #=> false
p num1 == num2       #=> true

# using Complex#<=>
p num1 <=> num2  #=> nil

# using Numeric#<=>
Complex.remove_method(:<=>)
p num1 <=> num2  #=> nil

# using Object#<=> (Kernel#<=>)
Numeric.remove_method(:<=>)
p num1 <=> num2  #=> 0
```

Complex#<=> has another problem that it does not coerce numeric objects while Integer#<=> and Float#<=> do.
This prevents users from adding yet another complex class having #<=>.

---

Here is my proposal of Complex#<=> behavior (in Ruby).
This considers #15857, complex numbers are comparable when their imaginary parts are 0.

```ruby
class Complex
  def <=>(other)
    return (self == other ? 0 : nil) if self.imag != 0

    if other.kind_of?(Complex)
      if other.imag == 0
        return self.real <=> other.real
      else
        return nil
      end
    elsif other.kind_of?(Numeric) && other.real?
      return self.real <=> other
    elsif other.respond_to?(:coerce)
      num1, num2 = other.coerce(self)
      return num1 <=> num2
    else
      return nil
    end
  end
end
``` 




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