Consider a DISJOINT_ATOP operation with the following pixels:
- source: 0xff (8 bits)
- source alpha: 0x01 (8 bits)
- mask alpha: 0x7b (8 bits)
- dest: 0x00 (8 bits)
- dest alpha: 0xff (8 bits)
When (src IN mask) is computed in 8 bits, the resulting alpha channel
is 0 due to rounding:
floor ((0x01 * 0x7b) / 255.0 + 0.5) = floor (0.9823) = 0
which means that since Render defines any division by zero as
infinity, the Fa and Fb for this operator end up as follows:
Fa = max (1 - (1 - 1) / 0, 0) = 0
Fb = min (1, (1 - 0) / 1) = 1
and so since dest is 0x00, the overall result is 0.
However, when computed in full precision, the alpha value no longer
rounds to 0, and so Fa ends up being
Fa = max (1 - (1 - 1) / 0.0001, 0) = 1
and so the result is now
s * ma * Fa + d * Fb
= (1.0 * (0x7b / 255.0) * 1) + d * 0
= 0x7b / 255.0
= 0.4823
so the error in this case ends up being 0.48235294, which is clearly
not something that can be considered acceptable.
In order to avoid this problem, we need to do all arithmetic in such a
way that a multiplication of two tiny numbers can never end up being
zero unless one of the input numbers is itself zero.
This patch makes all computations that involve divisions take place in
floating point, which is sufficient to fix the test cases
This brings the number of failures in pixel-test down to 14.
This commit fixes four separate bugs:
1. In the computation
(1 - sa) * d + (1 - da) * s + sa * da * B(s, d)
we were using regular addition for all four channels, but for
superluminescent pixels, the addition could overflow causing
nonsensical results.
2. The variables and return types used for the results of the blend
mode calculations were unsigned, but for various blend modes (and
especially with superluminescent pixels), the blend mode
calculations could be negative, resulting in underflows.
3. The blend mode computations were returned as 8-bit values, which is
not sufficient precision (especially considering that we need
signed results).
4. The value before the final division by 255 was not properly clamped
to [0, 255].
This patch fixes all those bugs. The blend mode computations are now
returned as signed 16 bit values with 1 represented as 255 * 255.
With these fixes, the number of failing pixels in pixel-test goes down
from 431 to 384.
For superluminescent destinations, the old code could underflow in
uint32_t r = (ad - d) * as / s;
when (ad - d) was negative. The new code avoids this problem (and
therefore causes changes in the checksums of thread-test and
blitters-test), but it is likely still buggy due to the use of
unsigned variables and other issues in the blend mode code.
Change blend_color_dodge() to follow the math in the comment more
closely.
Note, the new code here is in some sense worse than the old code
because it can now underflow the unsigned variables when the source is
superluminescent and (as - s) is therefore negative. The old code was
careful to clamp to 0.
But for superluminescent variables we really need the ability for the
blend function to become negative, and so the solution the underflow
problem is to just use signed variables. The use of unsigned variables
is a general problem in all of the blend mode code that will have to
be solved later.
The CRC32 values in thread-test and blitters-test are updated to
account for the changes in output.
The non-reentrant versions of prng_* functions are thread-safe only in
OpenMP-enabled builds.
Fixes thread-test failing when compiled with Clang (both on Linux and
on MacOS).
This test program allocates an array of 16 * 7 uint32_ts and spawns 16
threads that each use 7 of the allocated uint32_ts as a destination
image for a large number of composite operations. Each thread then
computes and returns a checksum for the image. Finally, the main
thread computes a checksum of the checksums and verifies that it
matches expectations.
The purpose of this test is catch errors where memory outside images
is read and then written back. Such out-of-bounds accesses are broken
when multiple threads are involved, because the threads will race to
read and write the shared memory.
V2:
- Incorporate fixes from Siarhei for endianness and undefined behavior
regarding argument evaluation
- Make the images 7 pixels wide since the bug only happens when the
composite width is greater than 4.
- Compute a checksum of the checksums so that you don't have to
update 16 values if something changes.
V3: Remove stray dollar sign
