[maximumError, roundTypeStr, independentFlag]=AlphaMultiplicationAccuracyTest([screenNumber])

Test the accuracy of alpha blending multiplication. OpenGL guarantees
perfect accuracy of alpha multiplication for values 0 and 1 only.
AlphaMultiplicationAccuracyTest measures accuracy of intermediate values.

Return argument “maximumError” is the maximum unsigned difference between
OpenGL alpha multiplication and simulated alpha blending in MATLAB using
double-precisions floating point multiplication.

Values of maximumError fall into three categories:

0 <= maximumError < 0.5 : OpenGL rounds to nearest integer. No
accuracy loss for a single multiplication.

0.5 <= maximumError < 1 : OpenGL truncates or rounds up. For a single
multiplication, Accuracy is off 0.5 parts
in 255 more than would multiplying luminances
using floating-point values and rounding.

maximumError >= 1 : Something is wrong.

AlphaMultiplicationAccuracyTest tries to determine whether OpenGL alpha
multiplication rounds to the nearest integer, rounds down or rounds up
and returns in “roundTypeStr” a string indicating which, either, “round”
“floor”, or “ceil”. If AlphaMultiplicationAccuracyTest can not determine
the rounding method, then it returns “unknown”.

AlphaMultiplicationAccuracyTest also tests that multiplication errors are
independent of the choice of blending factor string and the blending
surface, setting return argument “independentFlag” accordingly.

Because in OpenGL pixel color components are ultimately encoded as 8-bit
integers in video RAM, the results of OpenGL alpha multiplicaion will be
less accurate than those predicted by floating-point calculations. If
OpenGL rounds to the nearest integer then the alpha multiply error will
be less than 0.5. This is the limit of precision of the color components
of a pixel. Therefore, when alpha blending rounds to the nearest integer,
no more accuracy is lost with OpenGL alpha blending than by calculating
pixel values in MATLAB with floating point precision then rounding them
to integer pixel values for display.

Note that errors are cumulative and iterative alpha multiplication, in
which a product of a prevoius multiplication becomes a factor in a
subsequent multiplication, can produce large errors, even in the best
case of rounding where 0 <= maximumError < 0.5. Note also that A single
alpha blending operation may result in two multipliations, because both
source and destination surfaces may be multiplied before they are added.

We test blending accuracy becasue OpenGL makes no gurantees. The OpenGL
policy on alpha multiplician is summarized here:

    "Despite the apparent precision of the above equations, blending  
    arithmetic is not exactly specified, because blending operates with  
    imprecise integer color values. However, a blend factor that should be  
    equal to one is guaranteed not to modify its multiplicand, and a blend  
    factor equal to zero reduces its multiplicand to zero."   

See also: AlphaBlendingTest, PsychAlphaBlending

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