lean4-code-actions/libs/utils/bigint/sqrtNewton.ts

Refactorings and snippets for Lean 4

export const sqrtNewton = function (value: bigint) {
  if (value < 2n) return value

  if (value < 16n) return BigInt(Math.sqrt(Number(value)) | 0)

  let x0, x1
  if (value < 4503599627370496n) { // 1n<<52n
    x1 = BigInt(Math.sqrt(Number(value)) | 0) - 3n
  } else {
    const len = value.toString().length
    if (!(len & 1)) {
      x1 = 10n ** (BigInt(len / 2))
    } else {
      x1 = 4n * 10n ** (BigInt((len / 2) | 0))
    }
  }

  do {
    x0 = x1
    x1 = ((value / x0) + x0) >> 1n
  } while ((x0 !== x1 && x0 !== (x1 - 1n)))

  return x0
}