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fix(core): BigInt-length ranges and full BigFloat precision in integrate and the cubic cache - #223
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…e integrate
Ranges parameterized by a BigInt (`big.(0:16) ./ 16`, `big(0):big(16)`,
`big(0):big(2):big(32)`, `StepRange{Rational{BigInt}}`, `OneTo(big(17))`)
report a BigInt `length`; every method must build them like the Vector
twin (1D, one-shot, ND, `_CachedRange` slicing).
Every Hermite-family slope rule reproduces linear data exactly, so its
integral of x/3 + 1/7 must match the closed form at BigFloat precision
(1D bounded + cumulative, and the ND cubic bounded integrate that shares
the antiderivative basis). Today these sit at ~1e-18.
…ery precision `_cached_range` pinned `len::Int`, so any range whose `length` follows a BigInt type parameter threw a MethodError at normalization. The factory now takes `len::Integer` and stores `Int(len)` (checked), covering fresh conversion and slicing alike. The Hermite antiderivative basis `_IH10`/`_IH11` used the Float64 literals `-2/3` and `-1/3`, capping BigFloat integrals at ~1e-18 for PCHIP/Cardinal/Akima/user-slope 1D integrate and the ND cubic bounded integrate. Coefficients are now built from `one(t)`: Float64 folds to the same constants (bit-identical, no fdiv), BigFloat keeps full precision, and Float32 computes in Float32 instead of widening to Float64.
BigFloat precision is global state outside the type, and `isequal`
ignores it: on a dyadic grid (equal across precisions) a factorization
built at 256 bits is served to a 512-bit build, capping the spline at
~1e-78 instead of ~1e-155. Pin that each precision keeps and reuses its
own entry, for Vector BigFloat grids, Int grids with BigFloat data
(Vector{BigFloat} bank), and the periodic pool.
Float16/32/64 carry their precision in the type, so they never share a
bank. BigFloat is one type for every precision, so 256- and 512-bit
grids landed in the same bank and the `isequal` lookup handed out a
factorization built at the wrong precision.
`_rcu_lookup` now also requires `_verify_build_context(entry.cache)`:
`true` for every cache type (folds away — Float/Range/Periodic/Unitful/
Dual lookup IR is unchanged), and for `CubicSplineCache{BigFloat}`
compares the precision of the build-time `inv_d` with the current
default. A mismatch is a miss that inserts a new entry, so each
precision keeps and reuses its own factorization like the other floats
do. Kept separate from `_verify_cache_match`: that hook dispatches on
(cache, bc), and a BigFloat-cache method there is ambiguous with its
`PeriodicBC{:exclusive}` method.
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Codecov Report✅ All modified and coverable lines are covered by tests. Additional details and impacted files@@ Coverage Diff @@
## master #223 +/- ##
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Coverage 96.31% 96.31%
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Files 173 173
Lines 15560 15562 +2
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+ Hits 14986 14988 +2
Misses 574 574
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Summary
Problem: arbitrary-precision inputs either failed or silently lost precision in three places.
big.(0:16) ./ 16,big(0):big(16),big(0):big(2):big(32),OneTo(big(17))gridsMethodErrorVectortwinintegrate, ND cubic boundedintegrate(BigFloat)cubic_interpon the same grid aftersetprecision(BigFloat, 512)BigIntlength, but_cached_rangetooklen::Int; (2) the Hermite antiderivative basis_IH10/_IH11used the Float64 literals-2/3,-1/3; (3) BigFloat precision lives outside the type andisequalignores it, so 256- and 512-bit grids matched the same cubic cache entry.Fix: one targeted change each. Float64 is unaffected: bit-identical results, unchanged cache-lookup code.
Changes
_cached_rangetakeslen::Integerand storesInt(len)(checked), covering conversion and slicing._IH00…_IH11build their coefficients fromone(t): Float64 folds to the same constants (bit-identical, nofdiv); Float32 now computes in Float32 instead of widening to Float64 (±1–2 ulp)._rcu_lookupalso requires_verify_build_context(cache)—truefor every cache type (folded away), and forCubicSplineCache{BigFloat}a check of the build-time precision. Each precision keeps and reuses its own entry, as Float32/Float64 do via separate banks.Performance
No change on the non-BigFloat path: the LLVM IR of
_get_*_cache_impl/_lookup_or_insert!is identical before/after for Float64/32/16 (Vector, Range, Periodic), Int grids, Unitful, and Dual; an interleaved BenchmarkTools A/B is within noise with the same allocations (Apple M1 Pro, Julia 1.13). BigFloat keeps the cache's ~1.9× build speedup.Not covered
Rational{BigInt}→ BigFloat), as documented intype_promotion_rules.md.Tests
test/test_bigfloat_support.jl(fails on master): BigInt-length grids vs theVectortwin across methods, one-shot, ND, and slicing; Hermite-family 1D integrate/cumulative and ND cubic bounded integrate at BigFloat precision; per-precision cubic cache entries (Vector, Int grid + BigFloat data, periodic). Passes on Julia 1.10 and 1.13.