Functions to perform bitwise operations on unsigned ints up to 53 bit (highest JS precision) without bigint libraries.

bitwise53bit.js

var POW31 = 0x80000000
var MSK31 = 0x7FFFFFFF

function checkBitSize(bs) {
    if (bs > 53 || bs < 1 || Math.floor(bs) !== bs) {
        throw new Error('Invalid Bit Size')
    }
}

function splitBits(val, size) {
    if (val >= Math.pow(2, size) || val < 0 || Math.floor(val) !== val) {
        throw new Error('Invalid value')
    }
    var upperSize = size > 31 ? size - 31 : 0
    var upperMask = Math.pow(2, upperSize) - 1
    return [
        Math.floor(val / POW31) & upperMask,
        val & MSK31,
    ]
}

function xor(a, b, bitsize) {
    bitsize = bitsize || 53
    checkBitSize(bitsize)
    var aS = splitBits(a, bitsize)
    var bS = splitBits(b, bitsize)
    aS[0] ^= bS[0]
    aS[1] ^= bS[1]
    return aS[0] * POW31 + aS[1]
}

function and(a, b, bitsize) {
    bitsize = bitsize || 53
    checkBitSize(bitsize)
    var aS = splitBits(a, bitsize)
    var bS = splitBits(b, bitsize)
    aS[0] &= bS[0]
    aS[1] &= bS[1]
    return aS[0] * POW31 + aS[1]
}

function or(a, b, bitsize) {
    bitsize = bitsize || 53
    checkBitSize(bitsize)
    var aS = splitBits(a, bitsize)
    var bS = splitBits(b, bitsize)
    aS[0] |= bS[0]
    aS[1] |= bS[1]
    return aS[0] * POW31 + aS[1]
}