Extend the NORM2 intrinsic function to COMPLEX argument

[nncarlson]

It would be useful to extend the norm2 intrinsic function to complex arrays, so that
norm2(z) returns sqrt(sum(conjg(z)* z)). Note that dot_product already appropriately handles the case of complex arrays so that in the case of a rank-1 array this is equivalent to sqrt(dot_product(z,z)).

This is such an obvious extension of norm2 that is is puzzling why it wasn't included in the first place. There must be implementation difficulties (e.g., the standard recommendation "that the processor compute the result without undue overflow or underflow") for it to have been omitted.

Edit: sqrt(sum(conjg(z),z)) --> sqrt(sum(conjg(z)*z))

[klausler]

Did you mean sqrt(sum(conjg(z) * z))?

[nncarlson]

Did you mean sqrt(sum(conjg(z) * z))?

Um, yeah... That was dumb of me.

[PierUgit]

There must be implementation difficulties (e.g., the standard recommendation "that the processor compute the result without undue overflow or underflow") for it to have been omitted.

I can't see which difficulties, actually. The complex array would be internally treated as a real array of twice the size:
$\sqrt{ \sum_i ( conjg(z_i)*z_i ) } = \sqrt{ \sum_i ( z_i\%re^2 ) + \sum_i ( z_i\%im^2 ) ) }$

So in practice the over/underflow protections could be applied the same way.

[klausler]

There must be implementation difficulties (e.g., the standard recommendation "that the processor compute the result without undue overflow or underflow") for it to have been omitted.

I can't see which difficulties, actually. The complex array would be internally treated as a real array of twice the size: ∑ i ( c o n j g ( z i ) ∗ z i ) = ∑ i ( z i % r e 2 ) + ∑ i ( z i % i m 2 ) )

So in practice the over/underflow protections could be applied the same way.

I agree.

The technique that I use in f18 is to make one pass over the data, keeping both the maximum magnitude element value and a running sum of (x(i)/currmax) squared, adjusting that as necessary when larger maxima are found. (Maybe I should make two passes, one to find the true maximum and another to compute the sum of squares of scaled values, but that's how it works today.). Seems easy to adapt this to COMPLEX arguments.