Previously, we'd loop over the index of the output coordinate,
for example for a CMYK->RGB function, we'd loop over RGB. For
every output index, we'd then sample the function at the CMYK
input point.
Now, we sample at CMYK once and return a span for all outputs,
since they're stored in contiguous memory. And we then loop
over the outputs only to do weighting and mapping to the target
range at the end.
Reduces the runtime of
(cd Tests/LibPDF; \
../../Build/lagom/bin/BenchmarkPDF --benchmark_repetitions 5)
from 235.6±2.3ms to 103.2±3.3ms on my system, and makes
SampledFunction::evaluate() more similar to lerp_nd() in TagTypes.h.
Previously, if we wanted to to e.g. do linear interpolation in 2-D,
we'd get a sample point like (1.3, 4.4), then get 4 samples around
it at (1, 4), (2, 4), (1, 5), (2, 5), then reduce the 4 samples
to 2 samples by computing the combined samples
`0.3 * f(1, 4) + 0.7 * f(2, 4)` and `0.3 * f(1, 5) + 0.8 * f(2, 5)`,
and then 1-D linearly blending between these two samples with the
factor 0.4. In the end we'd multiply the first value by 0.3 * 0.4,
the second by 0.7 * 0.4, the third by 0.3 * 0.6, and the third by
0.7 * 0.6, and then sum them all up.
This requires computing and storing 2**N samples, followed by
another 2**N iterations to combine the 2**N sampls to a single value.
(N is in practice either 4 or 3, so 2**N isn't super huge.)
Instead, for every sample we can directly compute the product of
weights and sum them up directly. This lets us omit the second loop
and storing 2**N values, in exchange for doing an additional O(n)
work to compute the product.
Takes
Build/lagom/bin/image --no-output --invert-cmyk \
--assign-color-profile \
Build/lagom/Root/res/icc/Adobe/CMYK/USWebCoatedSWOP.icc \
--convert-to-color-profile serenity-sRGB.icc \
cmyk.jpg
form 3.42s to 3.08s on my machine, almost 10% faster (and less code).
Here cmyk.jpg is a 2253x3080 cmyk jpeg, and USWebCoatedSWOP.icc is an
mft2 profile with input tables with 256 samples and a 9x9x9x9 CLUT.
The LibPDF change is covered by TEST_CASE(sampled) in LibPDF.cpp,
and the LibGfx change is basically the same change as the one in
LibPDF (where the test results don't change) and the output
subjectively looks identical. So hopefully this causes indeed no
behavior change :^)
Instead of recomputing the left index and the float amount in that
interval for each coordinate all the time, do it once when we
preprocess the input coordinates.
One line less, faster, and arguably easier to read.
No behavior change.
Using `min()` to guarantee the left index is never == `size() - 1`,
even for an interpolation value of 1.0, is less code, and arguably
easier to understand as well.
No behavior change.
I didn't find example code for this and the AI assistant did very
poorly on this as well. So I had to write it all by myself!
It can be much more efficient I think, but I think the overall
shape is maybe roughly fine.
* SampledFunction now keeps the StreamObject it gets data from alive
(doesn't matter too much in practice, but does matter in the test,
where nothing else keeps the stream alive).
* If a sample is an integer, we would previously sample that value
twice and then divide by zero when interpolating. Make sure to
sample 1 unit apart.
