stillwater-sc / universal / 26203636807
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feat(elreal): Phase D -- sign, compare, ordering with refinement budget (#886)

* feat(elreal): Phase D -- sign, compare, ordering with refinement budget

Phase D of epic #873 (resolves #877): comparison and sign determination
on the lazy stream, with a per-call refinement budget that controls how
many components to materialise before declaring the value indistinguishable
from zero.

New API surface in include/sw/universal/number/elreal/elreal_impl.hpp:

  inline constexpr std::size_t elreal_default_budget = 8;

  int sign(const elreal& v, std::size_t budget = elreal_default_budget);
  int compare(const elreal& a, const elreal& b,
              std::size_t budget = elreal_default_budget);

  bool operator< (const elreal& a, const elreal& b);
  bool operator<=(const elreal& a, const elreal& b);
  bool operator> (const elreal& a, const elreal& b);
  bool operator>=(const elreal& a, const elreal& b);
  bool operator==(const elreal& a, const elreal& b);
  bool operator!=(const elreal& a, const elreal& b);

Sign determination algorithm (McCleeary 2019, dissertation Sec. 4.2):

For a normalized elreal with components c_0, c_1, ..., c_{N-1} satisfying
the non-overlapping property |c_{i+1}| <= ulp(c_i)/2, the sign of the
true value equals the sign of the first non-zero component. The remaining
components are corrections smaller than the leading non-zero by at least
one bit each, so their sum cannot flip the sign. The algorithm walks
at(k) for k = 0..budget-1 and returns the sign of the first non-zero
component found; if all are zero, the value is treated as zero "within
budget" (the canonical undecidable case is collapsed to a budgeted
answer the caller can tighten).

Special values:
  NaN  -- sign() returns 0 (unordered); ordering operators all return
          false; != returns true (matching IEEE-754).
  +/-inf -- sign returns +/-1 without consulting the budget.

IEEE-754 ordering: NaN is unordered, so <, <=, >, >=, == all return
false when either operand ... (continued)

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