stillwater-sc / universal / 29886492854

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feat(elreal): Phase 8 real floating-point conversion -- round_to<double|float|dd|qd> (#932) (#1181)

Adds round_to<Target>(ZBCL<FpType> x, RoundingMode = RoundToNearest) -> Target,
the primitive that hands an exact-real elreal intermediate to the rest of the
library as a correctly-rounded double, float, dd, or qd.

Method (dissertation 4.3): a ZBCL is a 0-overlap (non-overlapping) expansion, so
its blocks widened to double form a Shewchuk expansion of the exact value. To
round to P significand bits, split each block at the cut bit e0-P+1 into a kept
part (>= cut) and a round-off part (< cut); renormalise the round-off so
opposite-sign cancellation collapses to its true leading magnitude; classify it
against the half-ulp 2^(cut-1); then apply the mode and renormalise the kept
expansion. double/float take one limb (P=53/24); dd/qd take two/four (106/212)
via their raw limb constructors. Reuses sw::universal::RoundingMode; no new enum.

The subtle case is the SIGNED non-overlapping tail: block[1] can be negative, so
the value sits below the leading block -- the round-off must be renormalised
before the half-ulp comparison, else an opposite-sign sub-half tail is misread
as > half.

All four modes (nearest ties-to-even, toward zero, toward +inf, toward -inf)
validated exhaustively against an independent exact einteger-dyadic oracle:
320,000 roundings across the four targets x four modes, 0 mismatches.

New elastic/elreal/rounding/round_to.cpp covers the issue's acceptance criteria:
correctly-rounded (vs the dyadic oracle), idempotence, monotonicity across the
nested pairs (double,float)/(dd,double)/(qd,dd) -- i.e. no double-rounding --
lossless roundtrip round_to<double>(from_native(x))==x, and path-independent
determinism. Fast (~0.2s), runs at every regression level. gcc + clang,
warning/cppcheck/ASCII clean.

cfloat<N,E> (bit-level construction + arbitrary exponent-range handling) is a
distinct sub-problem, scoped to a follow-up.

Resolves #932
Relates ... (continued)

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