The code in this directory implements optimized, filtered scaling
for pixmap data. 

This code is copyright Red Hat, Inc, 2000 and licensed under the terms
of the GNU Lesser General Public License (LGPL).

(If you want to use it in a project where that license is not
appropriate, please contact me, and most likely something can be
worked out.)

Owen Taylor <otaylor@redhat.com>

PRINCIPLES
==========

The general principle of this code is that it first computes a filter
matrix for the given filtering mode, and then calls a general driver
routine, passing in functions to composite pixels and lines.

(The pixel functions are used for handling edge cases, and the line
functions are simply used for the middle parts of the image.)

The system is designed so that the line functions can be simple, 
don't have to worry about special cases, can be selected to
be specific to the particular formats involved. This allows them
to be hyper-optimized. Since most of the compution time is 
spent in these functions, this results in an overall fast design.

MMX assembly code for Intel (and compatible) processors is included
for a number of the most common special cases:

 scaling from RGB to RGB
 compositing from RGBA to RGBx
 compositing against a color from RGBA and storing in a RGBx buffer

Alpha compositing 8 bit RGBAa onto RGB is defined in terms of
rounding the exact result (real values in [0,1]):

 cc = ca * aa + (1 - aa) * Cb

 Cc = ROUND [255. * (Ca/255. * Aa/255. + (1 - Aa/255.) * Cb/255.)]

ROUND(i / 255.) can be computed exactly for i in [0,255*255] as:

 t = i + 0x80; result = (t + (t >> 8)) >> 8;  [ call this as To8(i) ]

So, 
  
 t = Ca * Aa + (255 - Aa) * Cb + 0x80;
 Cc = (t + (t >> 8)) >> 8;

Alpha compositing 8 bit RaGaBaAa onto RbGbBbAa is a little harder, for
non-premultiplied alpha. The premultiplied result is simple:

 ac = aa + (1 - aa) * ab
 cc = ca + (1 - aa) * cb

Which can be computed in integers terms as:

 Cc = Ca + To8 ((255 - Aa) * Cb)
 Ac = Aa + To8 ((255 - Aa) * Ab)

For non-premultiplied alpha, we need divide the color components by 
the alpha:

       +- (ca * aa + (1 - aa) * ab * cb)) / ac; aa != 0
  cc = |
       +- cb; aa == 0

To calculate this as in integer, we note the alternate form:

 cc = cb + aa * (ca - cb) / ac

[ 'cc = ca + (ac - aa) * (cb - ca) / ac' can also be useful numerically,
  but isn't important here ]

We can express this as integers as:

 Ac_tmp = Aa * 255 + (255 - Aa) * Ab;
 
      +- Cb + (255 * Aa * (Ca - Cb) + Ac_tmp / 2) / Ac_tmp ; Ca > Cb
 Cc = | 
      +- Cb - (255 * Aa * (Cb - Ca) + Ac_tmp / 2) / Ac_tmp ; ca <= Cb

Or, playing bit tricks to avoid the conditional

 Cc = Cb + (255 * Aa * (Ca - Cb) + (((Ca - Cb) >> 8) ^ (Ac_tmp / 2)) ) / Ac_tmp

TODO
====

* ART_FILTER_HYPER is not correctly implemented. It is currently
  implemented as a filter that is derived by doing linear interpolation
  on the source image and then averaging that with a box filter.

  It should be defined as followed (see art_filterlevel.h)

   "HYPER is the highest quality reconstruction function. It is derived
    from the hyperbolic filters in Wolberg's "Digital Image Warping,"
    and is formally defined as the hyperbolic-filter sampling the ideal
    hyperbolic-filter interpolated image (the filter is designed to be
    idempotent for 1:1 pixel mapping). It is the slowest and highest
    quality."

  The current HYPER is probably as slow, but lower quality. Also, there
  are some subtle errors in the calculation current HYPER that show up as dark
  stripes if you scale a constant-color image.

* There are some roundoff errors in the compositing routines. 
  the _nearest() variants do it right, most of the other code 
  is wrong to some degree or another.

  For instance, in composite_line_22_4a4(), we have:

    dest[0] = ((0xff0000 - a) * dest[0] + r) >> 24;

   if a is 0 (implies r == 0), then we have:

    (0xff0000 * dest[0]) >> 24

   which gives results which are 1 to low:

       255 => 254,   1 => 0.

   So, this should be something like:

     ((0xff0000 - a) * dest[0] + r + 0xffffff) >> 24;

   (Not checked, caveat emptor)

   An alternatve formulation of this as:

     dest[0] + (r - a * dest[0] + 0xffffff) >> 24

   may be better numerically, but would need consideration for overflow.

* The generic functions could be sped up considerably by
  switching around conditionals and inner loops in various
  places.

* Right now, in several of the most common cases, there are
  optimized mmx routines, but no optimized C routines.

  For instance, there is a 

    pixops_composite_line_22_4a4_mmx()

  But no 
  
    pixops_composite_line_22_4a4()

  Also, it may be desirable to include a few more special cases - in particular:

    pixops_composite_line_22_4a3()

  May be desirable.

* Scaling down images by large scale factors is _slow_ since huge filter
  matrixes are computed. (e.g., to scale down by a factor of 100, we compute
  101x101 filter matrixes. At some point, it would be more efficent to
  switch over to subsampling when scaling down - one should never need a filter
  matrix bigger than 16x16.