Partially Addresses #100 - #111
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The tabulated solid-angle grids are declared
template <typename T> struct lebedev_laikov_N {
static constexpr std::array<cartesian_pt_t<T>,N> points = {...};
static constexpr std::array<T,N> weights = {...};
};
`constexpr` requires a literal type, so instantiating any of these over a type
that is not literal -- an interval type wrapping boost::numeric::interval, or an
uncertainty-propagating scalar holding a map of dependencies -- fails to
compile. That is the mechanical barrier to using the library with such types.
This commit adds the machinery to store the tables in a fixed type and convert
them to the quadrature's value type on read; the tables themselves are rewritten
in a following commit.
config.hpp defines `ixx_int` and `ixx_real`, the `IXX_INT` / `IXX_REAL` macros
that denote which kind a literal is, and the `INTEGRATORXX_ENABLE_STRING_REALS`
build option. types.hpp includes it, so the macros reach every table file
through the existing `*_grids.hpp` umbrellas with no new include lines.
The split between the two kinds is integer vs. non-integer rather than exactly-
representable vs. not. Measured across all 231 tables, of 1,919,804 literals
1,913,026 are non-integral and *none* of those is exactly representable as a
double; the only exactly-representable values in the corpus are the 6,778
occurrences of 0 and +/-1 at the axis points. So integrality is the distinction
that carries information, which is what `from_integer` / `from_real` capture.
`divide_integer` covers the case of a constant that is the ratio of two
integers, so the division is the only rounding rather than being inherited from
a constant the compiler already rounded.
fp_traits is the single seam through which every operation whose meaning depends
on the value type is routed, so that supporting a new type is a matter of
specializing one class rather than auditing every quadrature. It carries only
the conversions here; the math functions arrive with the quadratures that call
them.
Under ENABLE_STRING_REALS `ixx_real` becomes a `std::string_view` and IXX_REAL
captures its argument's source text rather than a double. A double literal has
already lost precision by the time any code can inspect it, so a type more
precise than double -- or one that must bound its own error -- cannot recover
the intended value from it; carrying the decimal text lets such a type parse it
directly. The default `from_real` still parses via double, so the option is
inert until a type specializes it. It is applied to the `integratorxx` target
rather than to a directory because it changes the type of a table entry: in the
non-header-only build the library's own TUs in src/ and its consumers must agree
on what `ixx_real` is.
copy_grid, the tables' only consumer, does the conversion. It also grows a
branch for equal-weight grids, which record a point count in place of a weight
table; the Womersley tables take that form in the following commit.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Performs the rewrite of the 231 tabulated solid-angle grids to the ixx_real literal policy: element type `T` -> `ixx_real`, every table entry wrapped in `IXX_REAL(...)`, and the Womersley grids' computed weights replaced by the point count they are derived from. A script rather than a hand edit because the change touches ~1.9 million literals, and because it is idempotent: the transformation can be replayed after syncing tables from upstream instead of being reapplied by hand across 231 files. `--check` reports what would change without writing, so CI or a reviewer can confirm the committed tables are what the script produces. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Generated by
python3 scripts/retype_s2_tables.py
and reproducible from this commit's parent by re-running it; the script is
idempotent, so `--check` reports no changes against the result.
The 231 tables switch to `ixx_real` elements with every entry wrapped in
IXX_REAL, which is what lifts the literal-type requirement that `constexpr`
imposes on them. The surrounding `template <typename T>` is left in place though
T is no longer used by the table itself, so that none of the ~30 dispatch
branches in each of the four family headers has to change.
Entries whose value is integral (0 and +/-1 at the axis points) are wrapped in
IXX_REAL too, despite the rule that integral literals are spelled IXX_INT: a
std::array is homogeneous, so they must share their neighbours' element type.
They convert exactly either way.
The 125 Womersley tables did not tabulate weights at all -- they built them with
`create_array<N, T>(4.0 * M_PI / N.0)`, which is templated on T (so it breaks
for non-literal types), pre-divides in double, and materializes N identical
values. They now record only the point count, and copy_grid forms the weight as
pi times the exact rational 4/N: one rounding instead of two, correct under
ENABLE_STRING_REALS, and a true enclosure for types that bound their own error.
That reassociation moves the weight by one ulp for 29 of the 125 sizes -- it is
strictly the more accurate of the two -- and by nothing at all for the other 96.
The Lebedev-Laikov, Delley, and Ahrens-Beylkin grids are unchanged bitwise.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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Accomplishes:
N.B. Conflicts with the approach in #110.