stillwater-sc / universal / 26202799642
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feat(elreal): Phase C -- ring operations with depth-1 EFT refinement (#885)

* feat(elreal): Phase C -- ring operations with depth-1 EFT refinement

Phase C of epic #873 (resolves #876): adds the four ring operations plus
unary minus and abs, with depth-1 refinement for +, -, * via the
error-free transformations already in numerics/error_free_ops.hpp.

New API surface on the elreal class:

  elreal operator-() const;                          // unary negation
  elreal& operator+=(const elreal& rhs);
  elreal& operator-=(const elreal& rhs);
  elreal& operator*=(const elreal& rhs);
  elreal& operator/=(const elreal& rhs);
  bool    isneg() const noexcept;                    // helper for abs

  // Free functions (friends of the class):
  elreal operator+(const elreal& a, const elreal& b);
  elreal operator-(const elreal& a, const elreal& b);
  elreal operator*(const elreal& a, const elreal& b);
  elreal operator/(const elreal& a, const elreal& b);
  elreal abs(const elreal& a);
  elreal fabs(const elreal& a);                       // alias to abs

Refinement contract:

  - Depth 0: leading-double result of the operation. Handles NaN, inf,
    signed-zero propagation automatically via the IEEE-754 path on the
    component double.
  - Depth 1: EFT residual + operand corrections, captured via two_sum
    (+), two_diff (-), and two_prod (*). Returns 0.0 for / -- Newton-
    Raphson refinement on the reciprocal stream lands in Phase E/F.
  - Depth 2+: 0.0 with a documented Phase C limitation. Full McCleeary
    expansion arithmetic is deferred to Phase E/F.

Acceptance criteria of #876 met at depth-0:
  - (a + b) - b ~= a, (a - b) + b ~= a   (addition.cpp, subtraction.cpp)
  - (a * b) / b ~= a, commutativity, identity, absorption
    (multiplication.cpp)
  - a / a == 1, 1 / (1/a) ~= a, signed-zero, divide-by-zero
    (division.cpp)

Division by zero: when b.at(0) == 0,
  - ELREAL_THROW_ARITHMETIC_EXCEPTION == 0 (default): IEEE-754 +/-inf or
    NaN propagat... (continued)

46930 of 55729 relevant lines covered (84.21%)

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Coverage Regressions

Lines Coverage ∆ File
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Jobs
ID Job ID Ran Files Coverage
1 26202799642.1 651
84.21
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Source Files on build 26202799642