Backdoor / mega-backdoor Roth (pro-rata rule)

Two Roth accumulation moves for earners over the direct-Roth income limits. The backdoor Roth applies the §408(d)(2) pro-rata rule: a nondeductible traditional-IRA contribution converted to Roth is taxed by basis across all traditional/SEP/SIMPLE IRAs, so a pre-tax balance makes part of the "backdoor" taxable (e.g. $93k pre-tax + $7k basis → 93% taxable). The mega-backdoor computes the after-tax 401(k) room under the §415(c) annual-additions limit (limit − elective deferrals − employer contributions, optionally capped by the plan). Returns the taxable/nontaxable split of the conversion, the basis and pre-tax left afterward, and the §415(c) room. Reuses the grounded contribution-limit tables; deterministic; not tax advice.