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In commit 8d6647548f7d005 I added the Hats grid type to Loopy, and
mentioned in the commit message that I was very pleased with the
algorithm I came up with.
In fact, I was so pleased with it that I've decided it deserves a
proper public writeup. So I've spent the Easter weekend producing one:
https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperiodic-tilings/
In this commit I adjust the header comments in both penrose.c and
hat.c to refer to the article (replacing a previous comment in
penrose.c to a much less polished page containing a copy of my
jotting-grade personal notes that I sent James Harvey once). Also,
added some code to hatgen.c to output Python hat descriptions in a
similar style to hat-test, which I used to generate a couple of the
more difficult diagrams in the new article, and didn't want to lose.
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This fixes a build failure introduced by commit 2e48ce132e011e8
yesterday.
When I saw that commit I expected the most likely problem would be in
the NestedVM build, which is currently the thing with the most most
out-of-date C implementation. And indeed the NestedVM toolchain
doesn't have <tgmath.h> - but much more surprisingly, our _Windows_
builds failed too, with a compile error inside <tgmath.h> itself!
I haven't looked closely into the problem yet. Our Windows builds are
done with clang, which comes with its own <tgmath.h> superseding the
standard Windows one. So you'd _hope_ that clang could make sense of
its own header! But perhaps the problem is that this is an unusual
compile mode and hasn't been tested.
My fix is to simply add a cmake check for <tgmath.h> - which doesn't
just check the file's existence, it actually tries compiling a file
that #includes it, so it will detect 'file exists but is mysteriously
broken' just as easily as 'not there at all'. So this makes the builds
start working again, precisely on Ben's theory of opportunistically
using <tgmath.h> where possible and falling back to <math.h>
otherwise.
It looks ugly, though! I'm half tempted to make a new header file
whose job is to include a standard set of system headers, just so that
that nasty #ifdef doesn't have to sit at the top of almost all the
source files. But for the moment this at least gets the build working
again.
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C89 provided only double-precision mathematical functions (sin() etc),
and so despite using single-precision elsewhere, those are what Puzzles
has traditionally used. C99 introduced single-precision equivalents
(sinf() etc), and I hope it's been long enough that we can safely use
them. Maybe they'll even be faster.
Rather than directly use the single-precision functions, though, we use
the magic macros from <tgmath.h> that automatically choose the precision
of mathematical functions based on their arguments. This has the
advantage that we only need to change which header we include, and thus
that we can switch back again if some platform has trouble with the new
header.
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This tweak improves the uniformity of the generated patches of hat
tiling, by selecting from (the closest 32-bit approximation I can get
to) the limiting probability distribution of finite patches in the
whole plane.
This shouldn't invalidate any grid description that contains enough
coordinates to uniquely specify a piece of tiling - in particular, any
generated by the game itself. But if anyone's been brave enough to
hand-type a grid description in the last two days and left off some of
the coordinates, then those might be invalidated.
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I renamed it in a hurry this morning after the first report of a git
error message on Windows. Now I realise that several source files
referred to the old name, and also need fixing.
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James Harvey points out that Windows still forbids calling a file
'aux' in any context. Even a directory. Gaaah.
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