Yes, xicclu is part of ArgyllCMS. ArgyllCMS code is very reliable and very accurate. ArgyllCMS is actually an entire ICC profile Color Management System, specializing in delivering accurate results for making device ICC profiles, among other things.
You ask an important question: How do you decide which software to trust for which particular application?
As an example, back in 2014 I wrote a patch for the babl code (extensions/CIE.c) that does LAB/LCH conversions for GIMP. To write this patch, I started with Lindbloom’s equations for converting from RGB to XYZ to LAB and LCH and back again. I set up spreadsheets and tracked sample colors forwards and backwards, and compared GIMP output using my code modifications with what my spreadsheet said should result, and also with ArgyllCMS xicclu output.
I also compared results with output from Lindbloom’s own online calculators (I’m not sure if those still are available and functioning). Lindbloom’s values do differ slightly from ArgyllCMS values and from my spreadsheet values even though the spreadsheet used Lindbloom’s equations. Why? Because Lindbloom uses ASTM values for D50 and D65, and ArgyllCMS uses the D50 values given in the ICC profile specifications and the D65 values used in various color space specifications.
So I trust Lindbloom’s equations for LAB/LCH and for Bradford chromatic adaptations. But I don’t trust his output, or rather I trust that his output is accurate given the input values he uses for D50 and D65. But he doesn’t use the values that are actually used in ICC profile color space conversions.
So obviously my own “chain of trust” includes relying on the Lindbloom equations to be accurate, and relying on output from ArgyllCMS utilities to be accurate, which trust was reinforced by the closeness of ArgyllCMS results to results from my spreadsheet equations, after setting up a spreadsheet to do the calculations given on Lindbloom’s website.
I haven’t only relied on these sources, I’ve read fairly widely, though not particularly deeply, on the efforts of color scientists to mathematically capture how we see colors, and I’ve never seen anything that makes me think “Oh, gee, maybe all these people who’s work I rely on are getting it wrong”.
I will leave it up to you and the gmic devs to determine how accurate gmic results are. I seldom use gmic, partly because it’s hard-coded to use the sRGB color space, and I don’t usually edit in the sRGB color space. On the other hand, a while back I picked an image and experimented with all the then-available gmic algorithms, and did “bookmark” one particular algorithm to come back to someday, at least for use with that particular image. Also I really like some of the gmic blurring algorithms.
If you like results of using gmic algorithms for image editing, then the accuracy of underlying calculations doesn’t really matter, does it? But if you are using gmic to determine accurate LCH values, it’s the wrong tool for the task.
Yes, the larger the RGB working space color gamut, the greater the chroma will be for the primaries. See Figure 3 on this page, comparing chromas of a selected swath of sRGB and Rec.2020 colors:
“Using LCH to pick complementary colors and for making hue-based color harmonies”: https://ninedegreesbelow.com/photography/lch-complements-and-color-harmonies.html
And compare the available ranges of chroma for given hues in sRGB and Rec.2020, with the chromas of pigments used in painting as given on the handprint.com website color wheels:
LAB: handprint : CIELAB ab plane
CIECAM: handprint : artist's color wheel (CIECAM version)
Yes, that is a drawback of using LCH - it’s very easy to produce out of gamut colors at floating point precision, and clipped colors at integer precision.
I’m not sure what you mean by under-delivering.
I’m looking forward to the day when Rec.2020 monitors are affordable and people are able to use larger color gamuts even for images posted to the web. But I’m not looking forward to the avalanche of oversaturated images that I sort of expect people will starting producing and posting.
With respect to using LCH, the “win” of editing in larger RGB color spaces isn’t that hues located near the primaries will have higher available maximum chromas. The “win” is that the hues in between the primaries will have higher available maximum chromas, allowing for example for a wider range of green-blues and blue-greens. From a “chroma” point of view, sRGB is very weak in these colors, compared not just to Rec.2020 but also to colors that can be printed using good quality photographic printers, to the pigments used in painting, and to the surface colors that are out there in the real world.