How to implement unsigned right shift for BigInt in JavaScript?

Question

I tried this sort of implementation, but it doesn't appear to be working.

function urs32(n, amount) {
  const mask = (1 << (32 - amount)) - 1
  return (n >> amount) & mask
}

function flip32(n) {
  const mask = (1 << 32) - 1
  return ~n & mask
}

log(~0b10101010 >>> 0, urs32(~0b10101010, 0))
log(~0b10101010 >>> 0, flip32(0b10101010))

function log(a, b) {
  console.log(a.toString(2), b.toString(2))
}

I would expect for a to equal b in both cases, if done right. Basically I am trying to flip 32-bits (so 1's become 0s, 0's become 1s). I see that 1 << 32 === 0, so to get the value, I do 2 ** 32, but still doesn't work.

How do you implement the equivalent of ~n >>> 0 on a BigInt?

Basically what I am trying to do is create the countLeadingOnes functions (out of the countLeadingZeroes functions), like so:

const LEADING_ZERO_BIT_TABLE = makeLeadingZeroTable()

function makeLeadingZeroTable() {
  let i = 0
  const table = new Uint8Array(256).fill(0)
  while (i < 256) {
    let count = 8
    let index = i
    while (index > 0) {
      index = (index / 2) | 0
      count--
    }
    table[i] = count
    i++
  }
  return table
}

function countLeadingZeroes32JS(n)
{
  let accum = LEADING_ZERO_BIT_TABLE[n >>> 24];

  if (accum === 8) {
    accum += LEADING_ZERO_BIT_TABLE[(n >>> 16)]
  }
  if (accum === 16) {
    accum += LEADING_ZERO_BIT_TABLE[(n >>>  8)]
  }
  if (accum === 24) {
    accum += LEADING_ZERO_BIT_TABLE[ n       ]
  }

  return accum;
}

function countLeadingZeroes16JS(n)
{
  let accum = LEADING_ZERO_BIT_TABLE[n >>> 8]

  if (accum === 8) {
    accum += LEADING_ZERO_BIT_TABLE[n]
  }

  return accum;
}

function countLeadingZeroes8JS(n)
{
  return LEADING_ZERO_BIT_TABLE[n]
}

console.log('countLeadingZeroes32JS', countLeadingZeroes32JS(0b10100010001000100010001000100010))
console.log('countLeadingZeroes32JS', countLeadingZeroes32JS(0b00100010001000100010001000100010))
console.log('countLeadingZeroes32JS', countLeadingZeroes32JS(0b00000010001000100010001000100010))
console.log('countLeadingZeroes16JS', countLeadingZeroes16JS(0b1010001000100010))
console.log('countLeadingZeroes16JS', countLeadingZeroes16JS(0b0010001000100010))
console.log('countLeadingZeroes16JS', countLeadingZeroes16JS(0b0000001000100010))
console.log('countLeadingZeroes16JS', countLeadingZeroes16JS(0b0000000000100010))
console.log('countLeadingZeroes8JS', countLeadingZeroes8JS(0b10100010))
console.log('countLeadingZeroes8JS', countLeadingZeroes8JS(0b00100010))
console.log('countLeadingZeroes8JS', countLeadingZeroes8JS(0b00000010))

function countLeadingOnes32JS(n) {
  return countLeadingZeroes32JS(~n >>> 0)
}

function countLeadingOnes16JS(n) {
  return countLeadingZeroes16JS(~n >>> 0)
}

function countLeadingOnes8JS(n) {
  return countLeadingZeroes8JS(~n >>> 0)
}

console.log('countLeadingOnes32JS', countLeadingZeroes32JS(0b00100010001000100010001000100010))
console.log('countLeadingOnes32JS', countLeadingZeroes32JS(0b11100010001000100010001000100010))
console.log('countLeadingOnes32JS', countLeadingZeroes32JS(0b11111100001000100010001000100010))
console.log('countLeadingOnes16JS', countLeadingOnes16JS(0b0100001000100010))
console.log('countLeadingOnes16JS', countLeadingOnes16JS(0b1111110000100010))
console.log('countLeadingOnes16JS', countLeadingOnes16JS(0b1111111111000010))
console.log('countLeadingOnes8JS', countLeadingOnes8JS(0b01000010))
console.log('countLeadingOnes8JS', countLeadingOnes8JS(0b11000010))
console.log('countLeadingOnes8JS', countLeadingOnes8JS(0b11111100))

But it appears that ~n >>> 0 doesn't work on 32-bit integers. How to get this working properly?

Where in that code are you using a `BigInt`? I'm not seeing it... — T.J. Crowder, Apr 20 '22 at 09:42

score 1 · Accepted Answer · answered Apr 26 '22 at 11:58

How to implement unsigned right shift for BigInt in JavaScript?

Unsigned right-shift is difficult to define meaningfully for arbitrary-size integers, so before you (or anyone) can implement it, you'll have to decide how you want it to behave.
That said, considering the rest of this question, I don't see why you would even need this.

I would expect for a to equal b in both cases

Why would it? Unsigned right-shift and bit flipping are different operations and produce different results.

I see that 1 << 32 === 0

Nope, 1 << 32 === 1. JavaScript (like x86 CPUs) performs an implicit &31 on the shift amount, so since 32 & 31 === 0, ... << 32 is the same as ... << 0.

How do you implement the equivalent of ~n >>> 0 on a BigInt?

The equivalent of ~n is ~n. (That's not a typo. It's literally the same thing.)
The equivalent of ... >>> 0 is BigInt.asUintN(32, ...). (Note that neither the Number version nor the BigInt version shifts anything, so this doesn't answer your headline question "how to implement USR for BigInt".)

it appears that ~n >>> 0 doesn't work on 32-bit integers.

It sure does work. In fact, it only works on 32-bit integers.

The >>> 0 part is completely unnecessary though, you could just drop it.
The reason why this line:

console.log('countLeadingOnes32JS', countLeadingZeroes32JS(0b00100010001000100010001000100010))

isn't producing the number of leading ones is because the function it's calling is ...Zeroes...; an apparent copy-paste bug.
The reason why countLeadingOnes16JS isn't working correctly is because ~ in JavaScript always flips 32 bits. Since a 16-bit number's 32-bit representation has (at least) 16 leading zeros, those all become ones after flipping, and countLeadingZeroes16JS gets an input that's far bigger than it can handle: LEADING_ZERO_BIT_TABLE[n >>> 8] looks up an element that doesn't exist in the table, because the result of n >>> 8 is a 24-bit number in this case, not an 8-bit number. The solution is to use a mask after flipping; a valid implementation of clo16 might be:

function countLeadingOnes16(n) {
  return countLeadingZeroes16(~n & 0xFFFF);
}

No BigInts and no >>> 0 required.
countLeadingOnes8 is similar.

You may want to read https://en.wikipedia.org/wiki/Two%27s_complement (or some other description of that concept) to understand what's going on with bitwise operations on negative numbers.

You may also want to learn how to debug your own code. There's a range of techniques: for example, you could have:

inserted console.log statements for intermediate results,
or stepped through execution in a debugger,
or simply evaluated small snippets in the console,

any of which would have made it very easy for you to see what's happening on the path from input number to end result.

For anyone else reading this: there's Math.clz32, which is highly efficient because it gets compiled to a machine instruction, so implementing countLeadingZeros by hand is unnecessary and wasteful. For smaller widths, just subtract: function clz8(n) { return Math.clz32(n) - 24; }

How to implement unsigned right shift for BigInt in JavaScript?

1 Answers1