Compute base-10, base-2 and natural logarithms of JavaScript BigInts

biglog-0.js

import Decimal from 'decimal.js'

BigInt.log10 = x => Decimal.log(x, 10).toNumber()
BigInt.log2 = x => Decimal.log(x, 2).toNumber()
BigInt.log = x => Decimal.ln(x).toNumber() // `Decimal.log(x, Math.E)` gives incorrect results

biglog-simpler-worse.js

/*
  This alternate implementation requires no third-party dependencies.
  However, due to the limitations of floating point,
  the results are sometimes slightly inaccurate.

  For example, `BigInt.log2(16n)` evaluates to `3.9999999999999996`
*/

const embiggen = logB => {
  const logB10 = logB(10)
  return x => {
    if (typeof x !== 'bigint' || x < 0n) {
      return NaN
    }

    const s = x.toString(10)
    return logB(Number.parseFloat(`0.${s}`)) + s.length * logB10
  }
}

BigInt.log10 = embiggen(Math.log10)
BigInt.log2 = embiggen(Math.log2)
BigInt.log = embiggen(Math.log)

Usage:

import assert from 'node:assert/strict'
import './biglog-0.js'

assert.equal(BigInt.log10(1n), 0)
assert.equal(BigInt.log10(10n), 1)
assert.equal(BigInt.log10(100n), 2)
assert.equal(BigInt.log10(10n ** 1024n), 1024)

assert.equal(BigInt.log2(1n), 0)
assert.equal(BigInt.log2(2n), 1)
assert.equal(BigInt.log2(16n), 4)
assert.equal(BigInt.log2(2n ** 65536n), 65536)
assert.equal(BigInt.log2(2n ** 65536n / 3n), 65536 - Math.log2(3))