elreal Phase E: Mathematical functions

[Ravenwater]

Part of #873. Blocked by Phase D.

Scope

The standard transcendental and root families, lazily implemented.

Sub-issues

Phase E is broken into 6 family-grouped sub-issues to keep PRs review-sized:

• E.1 -- Math constants as lazy streams (pi, e, ln2, ln10): elreal Phase E.1: math constants as lazy streams (pi, e, ln2, ln10) #887
• E.2 -- sqrt (+ hypot) via Newton-Raphson: elreal Phase E.2: sqrt via Newton-Raphson on the lazy stream #888
• E.3 -- exp / log / pow family: elreal Phase E.3: exp / log / pow family #889 (blocked by E.1 for ln2)
• E.4 -- Hyperbolic functions (sinh, cosh, tanh + inverses): elreal Phase E.4: hyperbolic functions (sinh, cosh, tanh + inverses) #890 (blocked by E.3)
• E.5 -- Inverse trigonometric (asin, acos, atan, atan2): elreal Phase E.5: inverse trigonometric functions (asin, acos, atan, atan2) #891 (blocked by E.2 for sqrt; E.1 for pi in atan2)
• E.6 -- Forward trig (sin, cos, tan) with Payne-Hanek range reduction: elreal Phase E.6: forward trig (sin, cos, tan) with Payne-Hanek range reduction #892 (blocked by E.1, the hardest sub-issue)

Deliverables (per sub-issue)

• sqrt, hypot (E.2)
• exp, log, exp2, log2, log10, expm1, log1p, pow (E.3)
• sin, cos, tan (E.6); asin, acos, atan, atan2 (E.5)
• sinh, cosh, tanh, asinh, acosh, atanh (E.4)
• Math constants pi, e, ln2, ln10 wired into numeric_limits<elreal> (E.1)
• Tests under elastic/elreal/math/*.cpp (test scaffolding from elastic/ereal/math/functions/ is the natural starting point)

Algorithmic notes

• Roots and the exp/log family are well-suited to lazy refinement (Newton, Taylor with adaptive truncation, AGM for log).
• Trig is the hard case: range reduction in exact arithmetic requires pulling arbitrarily many bits of pi. Document the strategy (e.g., Payne-Hanek with on-demand pi refinement).
• numeric_limits<elreal>::pi() etc. should themselves return elreal values (lazy streams of pi), not pre-rounded doubles.

Acceptance (Phase E as a whole)

• Each function passes round-trip identity tests at the refinement target (exp(log(x)) ~= x, sin^2 + cos^2 ~= 1, ...)
• Cross-validation against ereal::exp etc. at matched precision targets
• Range-reduction strategy for trig documented in a header comment

Dependency graph

E.1 (constants)
   |
   +-- E.3 (exp/log/pow)
   |       |
   |       +-- E.4 (hyperbolic)
   |
   +-- E.6 (forward trig, hardest)
   |
   +-- E.5 (inverse trig, also needs E.2 for sqrt)

E.2 (sqrt + hypot) -- independent