rdb_safe_math Module

Single point of control the math functions that break bitwise reproducibility across compilers, GPU vendors, and optimization levels would route through IF adopted: exp, log, sin, cos, sqrt, pow.

Status (PR-8): the safe_* wrappers (safe_exp, safe_log, safe_sin, safe_cos, safe_sqrt, safe_pow) are plain elemental inlines around the bare intrinsic — zero overhead, codegen identical to writing exp(x) directly. This module used to carry a second “safe” mode, selected by the RDB_BITWISE_REPRO build option, that dispatched the wrappers to the *_polynomial implementations below instead. That option was removed in PR-8: grep across src//app/ found zero call sites of any safe_* wrapper from a production kernel (one stale comment, no calls) — the option changed nothing at all, so it was a lie about a capability nothing used.

What SURVIVES this PR: every *_polynomial function and its coefficients are correct, unit-tested (tests/test_safe_math.F90, unconditionally compiled — no #ifdef), and are the raw material for a future bitwise-reproducibility PR. This module is a library with no production consumer today — adopting safe_* in kernels (which would first require re-adding a build-time or run-time dispatch) is future work, not a promise this module currently keeps.

Would-be convention (not currently enforced by any build path): a kernel wanting repro-safety would call the safe_* wrapper instead of the bare intrinsic. For integer exponents, a**2 / a**3 etc. compile to multiplications and are already deterministic — don’t wrap those.

Coverage: safe_exp, safe_log, safe_sin, safe_cos each have real polynomial paths (Cody-Waite reduction + Horner Taylor). safe_sqrt is IEEE-correctly-rounded by mandate so the intrinsic path is already deterministic. safe_pow’s polynomial path is unused by safe_pow itself (which is the bare intrinsic **) — it exists for a future safe_exp(b * safe_log(a)) decomposition.