{
  "id": "ch12-deterministic",
  "categoryId": "ifp-deterministic",
  "paperId": "ch12",
  "date": "2012-01-10",
  "datePrecision": "day",
  "time": {
    "coefficient": 0.25,
    "expression": "O(M_int(N^{1/4} log N) / sqrt(log log N))"
  },
  "space": {
    "coefficient": null,
    "expression": "Not extracted from the source"
  },
  "tags": [],
  "review": {
    "status": "source-checked"
  },
  "certificate": {
    "status": "not-provided",
    "lean": null
  },
  "notes": "The exact improvement is a sqrt(log log N) factor over the Bostan–Gaudry–Schost bound. The normalized exponent is still 1/4. M_int(k) denotes k-bit integer multiplication cost.",
  "extra": {
    "coefficientExact": "1/4"
  },
  "evidence": {
    "url": "https://arxiv.org/abs/1201.2116",
    "locator": "Abstract",
    "sourceVersion": "Version available at the cited URL; bibliographic metadata and stated bound checked on 2026-11-08"
  }
}