math: gate transcendentals on snap, not real (allow non-real grids)#4
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A transcendental result is rounded onto the operand's grid, so the real requirement is `snap` (rounding permission), not `real` (double storage). - cmath.hpp: require_real → require_snap (has_flag(.., snap)) at all 22 sites. Backward compatible: `real` ⊃ round_nearest ⊃ snap, so existing code is unchanged. - New capability: transcendentals now work on any snap-capable grid — integer grids and non-dyadic grids (e.g. notch<1,100>) — not just `real` ones. - cmath_double.hpp: the double engine assumed `real` I/O (implicit bound→double, which is explicit for non-real). Add `dbl::store<Out>(double)` (direct store for `real`, rational-snap for non-real) and route every *_core + the inline sqrt/pow/pow_base/tan #else sites through it with explicit `static_cast<double>` inputs. Make cmath_double.hpp self-contained (include bound.hpp). - Tests: test_math_snap_grids.cpp pins exact special values on non-real integer and 1/100 grids (engine-agnostic). docs/math.md updated. Single header regen. Local: double 362/362, CORDIC 405/405. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Phase 1 of the math-engine plan. A transcendental's result is rounded onto the operand's grid, so the genuine requirement is
snap(rounding permission), notreal(double-backed storage).require_real→require_snapat all 22cmath.hppsites. Backward compatible (real ⊃ round_nearest ⊃ snap).bnd::mathtranscendentals now work on any snap-capable grid — plain integer grids and non-dyadic grids (e.g.notch<1,100>), not justrealones. Computed by the engine, snapped via exact rational rounding.realI/O (the implicitbound→doubleisexplicit(!real)). Addeddbl::store<Out>(double)(direct forreal, rational-snap for non-real) and routed every*_core+ the inlinesqrt/pow/pow_base/tansites through it with explicitstatic_cast<double>inputs.cmath_double.hppis now self-contained.realgrids — no change needed.tests/test_math_snap_grids.cpp: exact special values on non-realinteger and 1/100 grids (engine-agnostic, no margins).docs/math.mdupdated. Single header regenerated.Local: double 362/362, CORDIC 405/405.
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