Re: [boost] Re: definition of complex norm

From: nbecker_at_[hidden]
Date: 2001-11-01 15:28:44

>>>>> "lums" == lums  <lums_at_[hidden]> writes:

    lums> --- 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.

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

    lums> Mathematically, the norm of a complex number should be

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

Mathematically, you're correct.  Unfortunately, since day 1 the C++
library has used abs() to mean sqrt(sum of squares), and has used
norm() to mean (sum of squares).