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feat(routes-f): fibonacci sequence generator with bigint #744

@davedumto

Description

@davedumto

Summary

Add a Fibonacci generator at app/api/routes-f/fibonacci/route.ts. Generate the sequence up to N terms or up to a max value.

Requirements

  • POST body { mode: count|until, n?: number, max?: number, format?: array|nth }
  • count mode: first n Fibonacci numbers
  • until mode: all Fibonacci numbers <= max
  • format nth returns just the nth value (with closed-form Binet formula for small n, BigInt iteration for large)
  • Use BigInt for n > 78 (where number precision fails)
  • Validate n in [1, 10000], max positive
  • Return as strings to preserve precision
  • Tests: known values, BigInt boundary, both modes

Scope Constraint - READ BEFORE STARTING

All files for this task must live inside app/api/routes-f/. This includes the route handler, helpers/utilities, types, and tests. Do NOT modify, import from, or add files to lib/, utils/, types/, components/, or anywhere else outside app/api/routes-f/. If you need shared logic, duplicate it inside your subfolder. Keeping everything scoped to this folder is intentional - it keeps these tasks independent and mergeable in any order.

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