javascript - 获取 JavaScript 数字的精确十进制表示

Question

JavaScript 中的每个有限数都有一个精确的实数值。例如:

const x = Number.MAX_VALUE

这里，x 的精确值为 2¹⁰²⁴ - 2⁹⁷¹ =

179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368

我们可以通过在算术中使用 x 来证明这一点:

console.log(x % 10000) // 8368

但是我怎样才能得到所有这些十进制数字呢？

我希望解决方案也适用于非整数，例如 const y = Number.EPSILON 正好是 2^-52 =

0.0000000000000002220446049250313080847263336181640625

Answer 1

我发现最有效的方法是

• 将 float 写入ArrayBuffer，然后将其作为 64 位无符号 BigInt 读回
• 使用位运算提取符号、指数和尾数
• 计算所需的结果乘以 10 的大幂
• 对字符串化的 BigInt 使用字符串操作，在正确的位置插入小数点。

例如:

const SIGN_BITS = 1n
const EXPONENT_BITS = 11n
const MANTISSA_BITS = 52n
const BIAS = 1023n

export const stringify = value => {
  if (typeof value !== 'number') {
    throw Error('Not a number')
  }

  if (!Number.isFinite(value)) {
    return String(value)
  }

  const dataView = new DataView(new ArrayBuffer(8))
  dataView.setFloat64(0, value)
  const bigUint64 = dataView.getBigUint64(0)

  const mantissaBits = (bigUint64 >> 0n) & ((1n << MANTISSA_BITS) - 1n)
  const exponentBits = (bigUint64 >> MANTISSA_BITS) & ((1n << EXPONENT_BITS) - 1n)
  const signBits = (bigUint64 >> (MANTISSA_BITS + EXPONENT_BITS)) & ((1n << SIGN_BITS) - 1n)

  const sign = signBits === 0b0n ? '' : '-'

  const isSubnormal = exponentBits === 0b0n

  // So as to keep this in integers, multiply the fraction by 2 ** 52 while subtracting
  // that same power from the exponent
  const m = ((isSubnormal ? 0n : 1n) << MANTISSA_BITS) + mantissaBits
  const e = (isSubnormal ? 1n : exponentBits) - BIAS - MANTISSA_BITS

  if (e >= 0n) {
    // Pure integers, no problem
    return sign + String(m << e)
  }

  // Multiply by a large enough power of 10 that all possible decimal digits are preserved
  // when we then divide by the power of 2
  const power10 = 10n ** -e
  const f = (m * power10) >> -e
  const pre = f / power10
  const post = f % power10

  if (post === 0n) {
    return sign + String(pre)
  }

  return sign + String(pre) + '.' + String(post).padStart(Number(-e), '0').replace(/0+$/, '')
}

console.log(stringify(Number.MAX_VALUE))

这个输出:

179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368

类似地:

console.log(stringify(Number.EPSILON))

输出:

0.0000000000000002220446049250313080847263336181640625