Enhancement request 13022: add std.complex.abs2

[JLTastet]

Add std.complex.abs2, which returns the squared modulus of a
Complex or real number.

Rationale:

• It is common to need the squared modulus of a complex number,
  and using abs(z)*abs(z) would be inefficient due to the
  computation of the square root. Moreover, z*conj(z) returns a
  complex number, usually with nonzero imaginary part due to
  rounding, and cannot be used in a generic algorithm that can work
  with real numbers as well.
• The name abs2 has been chosen for consistency with abs, and
  for being mathematically more correct than norm, used by C++ STL
  for the equivalent function.
• For genericity, the function abs2 is also declared for real
  floating point numbers, in which case it simply returns its
  square.

UPDATE: use sqAbs instead of abs2.

https://issues.dlang.org/show_bug.cgi?id=13022

[JLTastet]

A trivial improvement, but it was missing.
I would like to hear your opinion about the name of the squared modulus function, since we won't be able to change it once it is released. As said in the commit message, I particularly dislike C++'s norm, but we could use sqAbs, sqMod, sqNorm as well.
I also think that some algorithms may benefit from having abs2 declared for real numbers.

[Safety0ff]

I would prefer either prefix or postfix sq over 2 to denote squaring.
Even prefix squared would be preferable to me, though I don't know how cumbersome it is.
2 suggests it is a different version of the function, e.g. atan versus atan2

[JLTastet]

The use of 2 to denote another version was actually what was worrying me. sqAbs seems perfectly fine to me. Ideally the name should be kept short, like most other mathematical functions, so I would avoid squaredAbs.
I would like to hear opinions from more people before changing it (especially from those who use Complex a lot !).

[JLTastet]

Rebased and changed the name for sqAbs.

[quickfur]

LGTM.

[JLTastet]

I just searched how this function is called in other languages.
Julia calls it abs2, while SciPy and MATLAB don't have it, and there is no such intrinsic function in Fortran or R (at least in package base where complex is defined).

[mihails-strasuns]

LGTM. sqAbs is much more clear than abs2

[mihails-strasuns]

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