Re: definition of complex norm

From: lums_at_[hidden]
Date: 2001-11-01 15:25:43

--- In boost_at_y..., nbecker_at_f... wrote:
> In the current gcc, norm of complex is defined in terms of abs.  I
> believe the definition should be changed to:
> 
> norm(z) = sqr(real(z)) + sqr (imag (z))
> 
> My reasons are:
> 
> 1. More efficient
> 2. Works for complex<int> (important in DSP)
> 3. Possibly more accurate
> 
> I have started a discussion on gcc_at_g... on this subject.  I'm
> wondering if any of you have an opinion.

This definition doesn't look correct (and has accuracy problems).

Mathematically, the norm of a complex number should be

norm(z) = sqrt( sqr(real(z)) + sqr(imag(z)) )

For maximal accuracy, the standard approach is something like the 
following:

if (abs(real(z)) > abs(imag(z))) {
  norm(z) = real(z) * sqrt(1 + sqr(imag(z))/sqr(real(z)))
} else {
  norm(z) = imag(z) * sqrt(1 + sqr(real(z))/sqr(imag(z)))
}

(This is all to be taken as pseudo code.)