imsplit, imjoin

[John Denker <jsd av8n com>]

Hi Folks --

In the alpha 0.0.1 version of imfourier(...) I implemented the
following features:
 a) If the input consists of 1 column of N rows, the input is
  interpreted as N complex numbers in the obvious way.  As
  usual, floats are a subset of complex, and can be freely
  mixed in.
 b) If the input consists of 2 columns of N rows, each row is
  interpreted as a (real, imaginary) pair.

I wish to partially retract feature (b) ... not because the idea
is bad, but because it is too good.  The feature should not be
limited to the imfourier(...) function.  It should be more
widely available.

Therefore I have implemented imjoin(...) which takes an area
of N rows of M columns of real numbers, representing (real, 
imaginary) pairs.  It returns an area of N rows by (M+1)/2 
columns, representing complex numbers.

So now we write
       =imfourier(imjoin(A1:B4))

=============

As you might imagine, I also implemented imsplit(...) which
takes an area of N rows of M columns of complex numbers and
returns an area of N rows by 2M columns of floats.

===========================

FWIW I wrote a the C code for a collect_complex_values(...) function, 
rather closely analogous to collect_floats_value(...) function.
This makes it noticeably easier to implement spreadsheet features 
such as imsplit(...) and imjoin(...).

It also applies to things like imsumproduct(...) as mentioned in
the previous message.

==========================
Discussion:

I am quite aware that for one or two numbers, one can use
complex(...), imreal(...), and imaginary(...).  However, when
dealing with large two-dimensional arrays of complex numbers,
imsplit and imjoin are significantly easier to use.

In particular, routinely unpacking the CNS (complex number
string) representation to separate (real, imaginary) parts
solves all sorts of problems ... starting with the fact
that you can *format* the separate representation but
cannot format the CNS representation.

So, from a user-interface point of view, there is a premium
on making the packing and unpacking as simple as possible.