Søren Sandmann Pedersen 98fef3cef2 _cairo_color_double_to_short(): Use standard rounding algorithm ...

The _cairo_color_double_to_short() function converts a double
precision floating point value in the range of [0.0, 1.0] to a
uint16_t integer by dividing the [0.0, 1.0] range into 65536
equal-sized intervals and then associating each interval with an
integer.

Under the assumption that an integer i corresponds to the real value i
/ 65535.0 this algorithm introduces more error than necessary as can
be seen from the following picture showing the analogous
transformation for two-bit integers:

    +-----------+-----------+-----------+-----------+
   0b00         |  0b01     |      0b10 |          0b11
    +-----------+-----------+-----------+-----------+

which shows that some floating point values are not converted to the
integer that would minimize the error in value that that integer
corresponds to.

Instead, this patch uses standard rounding, which makes the diagram
look like this:

    +-------+---------------+---------------+-------+
   0b00     |      0b01     |      0b10     |      0b11
    +-------+---------------+---------------+-------+

It's clear that if the values corresponding to the given integers are
fixed, then it's not possible to decrease the resulting error by
moving any of the interval boundaries.

See this thread for more information:

    http://lists.freedesktop.org/archives/cairo/2013-October/024691.html

Reference images updated:

  pthread-similar.ref.png
  record-paint-alpha.ref.png
  record90-paint-alpha.argb32.ref
  record90-paint-alpha.rgb24.ref.png
  xcb-huge-image-shm.ref.png
  xcb-huge-subimage.ref.png

All of these have only one-step differences to the old images.

2013-10-22 14:27:43 -04:00

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