bitset.js

/**
 * @license BitSet v5.2.3 10/9/2024
 * https://raw.org/article/javascript-bit-array/
 *
 * Copyright (c) 2024, Robert Eisele (https://raw.org/)
 * Licensed under the MIT license.
 **/

/**
 * The number of bits of a word
 * @const
 * @type number
 */
var WORD_LENGTH = 32;

/**
 * The log base 2 of WORD_LENGTH
 * @const
 * @type number
 */
var WORD_LOG = 5;

/**
 * Calculates the number of set bits
 *
 * @param {number} v
 * @returns {number}
 */
function popCount(v) {

  // Warren, H. (2009). Hacker`s Delight. New York, NY: Addison-Wesley

  v -= ((v >>> 1) & 0x55555555);
  v = (v & 0x33333333) + ((v >>> 2) & 0x33333333);
  return (((v + (v >>> 4) & 0xF0F0F0F) * 0x1010101) >>> 24);
}

/**
 * Divide a number in base two by B
 *
 * @param {Array} arr
 * @param {number} B
 * @returns {number}
 */
function divide(arr, B) {

  var r = 0;

  for (var i = 0; i < arr.length; i++) {
    r *= 2;
    var d = (arr[i] + r) / B | 0;
    r = (arr[i] + r) % B;
    arr[i] = d;
  }
  return r;
}

/**
 * Parses the parameters and set variable P
 *
 * @param {Object} P
 * @param {string|BitSet|Array|Uint8Array|number=} val
 */
function parse(P, val) {

  if (val == null) {
    P['data'] = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
    P['_'] = 0;
    return;
  }

  if (val instanceof BitSet) {
    P['data'] = val['data'];
    P['_'] = val['_'];
    return;
  }

  switch (typeof val) {

    case 'number':
      P['data'] = [val | 0];
      P['_'] = 0;
      break;

    case 'string':

      var base = 2;
      var len = WORD_LENGTH;

      if (val.indexOf('0b') === 0) {
        val = val.substr(2);
      } else if (val.indexOf('0x') === 0) {
        val = val.substr(2);
        base = 16;
        len = 8;
      }

      P['data'] = [];
      P['_'] = 0;

      var a = val.length - len;
      var b = val.length;

      do {

        var num = parseInt(val.slice(a > 0 ? a : 0, b), base);

        if (isNaN(num)) {
          throw SyntaxError('Invalid param');
        }

        P['data'].push(num | 0);

        if (a <= 0)
          break;

        a -= len;
        b -= len;
      } while (1);

      break;

    default:

      P['data'] = [0];
      var data = P['data'];

      if (val instanceof Array) {

        for (var i = val.length - 1; i >= 0; i--) {

          var ndx = val[i];

          if (ndx === Infinity) {
            P['_'] = -1;
          } else {
            scale(P, ndx);
            data[ndx >>> WORD_LOG] |= 1 << ndx;
          }
        }
        break;
      }

      if (Uint8Array && val instanceof Uint8Array) {

        var bits = 8;

        scale(P, val.length * bits);

        for (var i = 0; i < val.length; i++) {

          var n = val[i];

          for (var j = 0; j < bits; j++) {

            var k = i * bits + j;

            data[k >>> WORD_LOG] |= (n >> j & 1) << k;
          }
        }
        break;
      }
      throw SyntaxError('Invalid param');
  }
}

/**
 * Module entry point
 *
 * @constructor
 * @param {string|BitSet|number=} param
 * @returns {BitSet}
 */
function BitSet(param) {

  if (!(this instanceof BitSet)) {
    return new BitSet(param);
  }
  parse(this, param);
  this['data'] = this['data'].slice();
}

function scale(dst, ndx) {

  var l = ndx >>> WORD_LOG;
  var d = dst['data'];
  var v = dst['_'];

  for (var i = d.length; l >= i; l--) {
    d.push(v);
  }
}

var P = {
  'data': [], // Holds the actual bits in form of a 32bit integer array.
  '_': 0 // Holds the MSB flag information to make indefinitely large bitsets inversion-proof
};

BitSet.prototype = {
  'data': [],
  '_': 0,
  /**
   * Set a single bit flag
   *
   * Ex:
   * bs1 = new BitSet(10);
   *
   * bs1.set(3, 1);
   *
   * @param {number} ndx The index of the bit to be set
   * @param {number=} value Optional value that should be set on the index (0 or 1)
   * @returns {BitSet} this
   */
  'set': function (ndx, value) {

    ndx |= 0;

    scale(this, ndx);

    if (value === undefined || value) {
      this['data'][ndx >>> WORD_LOG] |= (1 << ndx);
    } else {
      this['data'][ndx >>> WORD_LOG] &= ~(1 << ndx);
    }
    return this;
  },
  /**
   * Get a single bit flag of a certain bit position
   *
   * Ex:
   * bs1 = new BitSet();
   * var isValid = bs1.get(12);
   *
   * @param {number} ndx the index to be fetched
   * @returns {number} The binary flag
   */
  'get': function (ndx) {

    ndx |= 0;

    var d = this['data'];
    var n = ndx >>> WORD_LOG;

    if (n >= d.length) {
      return this['_'] & 1;
    }
    return (d[n] >>> ndx) & 1;
  },
  /**
   * Creates the bitwise NOT of a set.
   *
   * Ex:
   * bs1 = new BitSet(10);
   *
   * res = bs1.not();
   *
   * @returns {BitSet} A new BitSet object, containing the bitwise NOT of this
   */
  'not': function () { // invert()

    var t = this['clone']();
    var d = t['data'];
    for (var i = 0; i < d.length; i++) {
      d[i] = ~d[i];
    }

    t['_'] = ~t['_'];

    return t;
  },
  /**
   * Creates the bitwise AND of two sets.
   *
   * Ex:
   * bs1 = new BitSet(10);
   * bs2 = new BitSet(10);
   *
   * res = bs1.and(bs2);
   *
   * @param {BitSet} value A bitset object
   * @returns {BitSet} A new BitSet object, containing the bitwise AND of this and value
   */
  'and': function (value) {// intersection

    parse(P, value);

    var T = this['clone']();
    var t = T['data'];
    var p = P['data'];

    var pl = p.length;
    var p_ = P['_'];
    var t_ = T['_'];

    // If this is infinite, we need all bits from P
    if (t_ !== 0) {
      scale(T, pl * WORD_LENGTH - 1);
    }

    var tl = t.length;
    var l = Math.min(pl, tl);
    var i = 0;

    for (; i < l; i++) {
      t[i] &= p[i];
    }

    for (; i < tl; i++) {
      t[i] &= p_;
    }

    T['_'] &= p_;

    return T;
  },
  /**
   * Creates the bitwise OR of two sets.
   *
   * Ex:
   * bs1 = new BitSet(10);
   * bs2 = new BitSet(10);
   *
   * res = bs1.or(bs2);
   *
   * @param {BitSet} val A bitset object
   * @returns {BitSet} A new BitSet object, containing the bitwise OR of this and val
   */
  'or': function (val) { // union

    parse(P, val);

    var t = this['clone']();
    var d = t['data'];
    var p = P['data'];

    var pl = p.length - 1;
    var tl = d.length - 1;

    var minLength = Math.min(tl, pl);

    // Append backwards, extend array only once
    for (var i = pl; i > minLength; i--) {
      d[i] = p[i];
    }

    for (; i >= 0; i--) {
      d[i] |= p[i];
    }

    t['_'] |= P['_'];

    return t;
  },
  /**
   * Creates the bitwise XOR of two sets.
   *
   * Ex:
   * bs1 = new BitSet(10);
   * bs2 = new BitSet(10);
   *
   * res = bs1.xor(bs2);
   *
   * @param {BitSet} val A bitset object
   * @returns {BitSet} A new BitSet object, containing the bitwise XOR of this and val
   */
  'xor': function (val) { // symmetric difference

    parse(P, val);

    var t = this['clone']();
    var d = t['data'];
    var p = P['data'];

    var t_ = t['_'];
    var p_ = P['_'];

    var i = 0;

    var tl = d.length - 1;
    var pl = p.length - 1;

    // Cut if tl > pl
    for (i = tl; i > pl; i--) {
      d[i] ^= p_;
    }

    // Cut if pl > tl
    for (i = pl; i > tl; i--) {
      d[i] = t_ ^ p[i];
    }

    // XOR the rest
    for (; i >= 0; i--) {
      d[i] ^= p[i];
    }

    // XOR infinity
    t['_'] ^= p_;

    return t;
  },
  /**
   * Creates the bitwise AND NOT (not confuse with NAND!) of two sets.
   *
   * Ex:
   * bs1 = new BitSet(10);
   * bs2 = new BitSet(10);
   *
   * res = bs1.notAnd(bs2);
   *
   * @param {BitSet} val A bitset object
   * @returns {BitSet} A new BitSet object, containing the bitwise AND NOT of this and other
   */
  'andNot': function (val) { // difference

    return this['and'](new BitSet(val)['flip']());
  },
  /**
   * Flip/Invert a range of bits by setting
   *
   * Ex:
   * bs1 = new BitSet();
   * bs1.flip(); // Flip entire set
   * bs1.flip(5); // Flip single bit
   * bs1.flip(3,10); // Flip a bit range
   *
   * @param {number=} from The start index of the range to be flipped
   * @param {number=} to The end index of the range to be flipped
   * @returns {BitSet} this
   */
  'flip': function (from, to) {

    if (from === undefined) {

      var d = this['data'];
      for (var i = 0; i < d.length; i++) {
        d[i] = ~d[i];
      }

      this['_'] = ~this['_'];

    } else if (to === undefined) {

      scale(this, from);

      this['data'][from >>> WORD_LOG] ^= (1 << from);

    } else if (0 <= from && from <= to) {

      scale(this, to);

      for (var i = from; i <= to; i++) {
        this['data'][i >>> WORD_LOG] ^= (1 << i);
      }
    }
    return this;
  },
  /**
   * Clear a range of bits by setting it to 0
   *
   * Ex:
   * bs1 = new BitSet();
   * bs1.clear(); // Clear entire set
   * bs1.clear(5); // Clear single bit
   * bs1.clear(3,10); // Clear a bit range
   *
   * @param {number=} from The start index of the range to be cleared
   * @param {number=} to The end index of the range to be cleared
   * @returns {BitSet} this
   */
  'clear': function (from, to) {

    var data = this['data'];

    if (from === undefined) {

      for (var i = data.length - 1; i >= 0; i--) {
        data[i] = 0;
      }
      this['_'] = 0;

    } else if (to === undefined) {

      from |= 0;

      scale(this, from);

      data[from >>> WORD_LOG] &= ~(1 << from);

    } else if (from <= to) {

      scale(this, to);

      for (var i = from; i <= to; i++) {
        data[i >>> WORD_LOG] &= ~(1 << i);
      }
    }
    return this;
  },
  /**
   * Gets an entire range as a new bitset object
   *
   * Ex:
   * bs1 = new BitSet();
   * bs1.slice(4, 8);
   *
   * @param {number=} from The start index of the range to be get
   * @param {number=} to The end index of the range to be get
   * @returns {BitSet} A new smaller bitset object, containing the extracted range
   */
  'slice': function (from, to) {

    if (from === undefined) {
      return this['clone']();
    } else if (to === undefined) {

      to = this['data'].length * WORD_LENGTH;

      var im = Object.create(BitSet.prototype);

      im['_'] = this['_'];
      im['data'] = [0];

      for (var i = from; i <= to; i++) {
        im['set'](i - from, this['get'](i));
      }
      return im;

    } else if (from <= to && 0 <= from) {

      var im = Object.create(BitSet.prototype);
      im['data'] = [0];

      for (var i = from; i <= to; i++) {
        im['set'](i - from, this['get'](i));
      }
      return im;
    }
    return null;
  },
  /**
   * Set a range of bits
   *
   * Ex:
   * bs1 = new BitSet();
   *
   * bs1.setRange(10, 15, 1);
   *
   * @param {number} from The start index of the range to be set
   * @param {number} to The end index of the range to be set
   * @param {number} value Optional value that should be set on the index (0 or 1)
   * @returns {BitSet} this
   */
  'setRange': function (from, to, value) {

    for (var i = from; i <= to; i++) {
      this['set'](i, value);
    }
    return this;
  },
  /**
   * Clones the actual object
   *
   * Ex:
   * bs1 = new BitSet(10);
   * bs2 = bs1.clone();
   *
   * @returns {BitSet|Object} A new BitSet object, containing a copy of the actual object
   */
  'clone': function () {

    var im = Object.create(BitSet.prototype);
    im['data'] = this['data'].slice();
    im['_'] = this['_'];

    return im;
  },
  /**
   * Gets a list of set bits
   *
   * @returns {Array}
   */
  'toArray': Math['clz32'] ?
    function () {

      var ret = [];
      var data = this['data'];

      for (var i = data.length - 1; i >= 0; i--) {

        var num = data[i];

        while (num !== 0) {
          var t = 31 - Math['clz32'](num);
          num ^= 1 << t;
          ret.unshift((i * WORD_LENGTH) + t);
        }
      }

      if (this['_'] !== 0)
        ret.push(Infinity);

      return ret;
    } :
    function () {

      var ret = [];
      var data = this['data'];

      for (var i = 0; i < data.length; i++) {

        var num = data[i];

        while (num !== 0) {
          var t = num & -num;
          num ^= t;
          ret.push((i * WORD_LENGTH) + popCount(t - 1));
        }
      }

      if (this['_'] !== 0)
        ret.push(Infinity);

      return ret;
    },
  /**
   * Overrides the toString method to get a binary representation of the BitSet
   *
   * @param {number=} base
   * @returns string A binary string
   */
  'toString': function (base) {

    var data = this['data'];

    if (!base)
      base = 2;

    // If base is power of two
    if ((base & (base - 1)) === 0 && base < 36) {

      var ret = '';
      var len = 2 + Math.log(4294967295/*Math.pow(2, WORD_LENGTH)-1*/) / Math.log(base) | 0;

      for (var i = data.length - 1; i >= 0; i--) {

        var cur = data[i];

        // Make the number unsigned
        if (cur < 0)
          cur += 4294967296 /*Math.pow(2, WORD_LENGTH)*/;

        var tmp = cur.toString(base);

        if (ret !== '') {
          // Fill small positive numbers with leading zeros. The +1 for array creation is added outside already
          ret += '0'.repeat(len - tmp.length - 1);
        }
        ret += tmp;
      }

      if (this['_'] === 0) {

        ret = ret.replace(/^0+/, '');

        if (ret === '')
          ret = '0';
        return ret;

      } else {
        // Pad the string with ones
        ret = '1111' + ret;
        return ret.replace(/^1+/, '...1111');
      }

    } else {

      if ((2 > base || base > 36))
        throw SyntaxError('Invalid base');

      var ret = [];
      var arr = [];

      // Copy every single bit to a new array
      for (var i = data.length; i--;) {

        for (var j = WORD_LENGTH; j--;) {

          arr.push(data[i] >>> j & 1);
        }
      }

      do {
        ret.unshift(divide(arr, base).toString(base));
      } while (!arr.every(function (x) {
        return x === 0;
      }));

      return ret.join('');
    }
  },
  /**
   * Check if the BitSet is empty, means all bits are unset
   *
   * Ex:
   * bs1 = new BitSet(10);
   *
   * bs1.isEmpty() ? 'yes' : 'no'
   *
   * @returns {boolean} Whether the bitset is empty
   */
  'isEmpty': function () {

    if (this['_'] !== 0)
      return false;

    var d = this['data'];

    for (var i = d.length - 1; i >= 0; i--) {
      if (d[i] !== 0)
        return false;
    }
    return true;
  },
  /**
   * Calculates the number of bits set
   *
   * Ex:
   * bs1 = new BitSet(10);
   *
   * var num = bs1.cardinality();
   *
   * @returns {number} The number of bits set
   */
  'cardinality': function () {

    if (this['_'] !== 0) {
      return Infinity;
    }

    var s = 0;
    var d = this['data'];
    for (var i = 0; i < d.length; i++) {
      var n = d[i];
      if (n !== 0)
        s += popCount(n);
    }
    return s;
  },
  /**
   * Calculates the Most Significant Bit / log base two
   *
   * Ex:
   * bs1 = new BitSet(10);
   *
   * var logbase2 = bs1.msb();
   *
   * var truncatedTwo = Math.pow(2, logbase2); // May overflow!
   *
   * @returns {number} The index of the highest bit set
   */
  'msb': Math['clz32'] ?
    function () {

      if (this['_'] !== 0) {
        return Infinity;
      }

      var data = this['data'];

      for (var i = data.length; i-- > 0;) {

        var c = Math['clz32'](data[i]);

        if (c !== WORD_LENGTH) {
          return (i * WORD_LENGTH) + WORD_LENGTH - 1 - c;
        }
      }
      return Infinity;
    } :
    function () {

      if (this['_'] !== 0) {
        return Infinity;
      }

      var data = this['data'];

      for (var i = data.length; i-- > 0;) {

        var v = data[i];
        var c = 0;

        if (v) {

          for (; (v >>>= 1) > 0; c++) {
          }
          return (i * WORD_LENGTH) + c;
        }
      }
      return Infinity;
    },
  /**
   * Calculates the number of trailing zeros
   *
   * Ex:
   * bs1 = new BitSet(10);
   *
   * var ntz = bs1.ntz();
   *
   * @returns {number} The index of the lowest bit set
   */
  'ntz': function () {

    var data = this['data'];

    for (var j = 0; j < data.length; j++) {
      var v = data[j];

      if (v !== 0) {

        v = (v ^ (v - 1)) >>> 1; // Set v's trailing 0s to 1s and zero rest

        return (j * WORD_LENGTH) + popCount(v);
      }
    }
    return Infinity;
  },
  /**
   * Calculates the Least Significant Bit
   *
   * Ex:
   * bs1 = new BitSet(10);
   *
   * var lsb = bs1.lsb();
   *
   * @returns {number} The index of the lowest bit set
   */
  'lsb': function () {

    var data = this['data'];

    for (var i = 0; i < data.length; i++) {

      var v = data[i];
      var c = 0;

      if (v) {

        var bit = (v & -v);

        for (; (bit >>>= 1); c++) {

        }
        return WORD_LENGTH * i + c;
      }
    }
    return this['_'] & 1;
  },
  /**
   * Compares two BitSet objects
   *
   * Ex:
   * bs1 = new BitSet(10);
   * bs2 = new BitSet(10);
   *
   * bs1.equals(bs2) ? 'yes' : 'no'
   *
   * @param {BitSet} val A bitset object
   * @returns {boolean} Whether the two BitSets have the same bits set (valid for indefinite sets as well)
   */
  'equals': function (val) {

    parse(P, val);

    var t = this['data'];
    var p = P['data'];

    var t_ = this['_'];
    var p_ = P['_'];

    var tl = t.length - 1;
    var pl = p.length - 1;

    if (p_ !== t_) {
      return false;
    }

    var minLength = tl < pl ? tl : pl;
    var i = 0;

    for (; i <= minLength; i++) {
      if (t[i] !== p[i])
        return false;
    }

    for (i = tl; i > pl; i--) {
      if (t[i] !== p_)
        return false;
    }

    for (i = pl; i > tl; i--) {
      if (p[i] !== t_)
        return false;
    }
    return true;
  },
  [Symbol.iterator]: function () {

    var d = this['data'];
    var ndx = 0;

    if (this['_'] === 0) {

      // Find highest index with something meaningful
      var highest = 0;
      for (var i = d.length - 1; i >= 0; i--) {
        if (d[i] !== 0) {
          highest = i;
          break;
        }
      }

      return {
        'next': function () {
          var n = ndx >>> WORD_LOG;

          return {
            'done': n > highest || n === highest && (d[n] >>> ndx) === 0,
            'value': n > highest ? 0 : (d[n] >>> ndx++) & 1
          };
        }
      };

    } else {
      // Endless iterator!
      return {
        'next': function () {
          var n = ndx >>> WORD_LOG;

          return {
            'done': false,
            'value': n < d.length ? (d[n] >>> ndx++) & 1 : 1,
          };
        }
      };
    }
  }
};

BitSet['fromBinaryString'] = function (str) {

  return new BitSet('0b' + str);
};

BitSet['fromHexString'] = function (str) {

  return new BitSet('0x' + str);
};

BitSet['Random'] = function (n) {

  if (n === undefined || n < 0) {
    n = WORD_LENGTH;
  }

  var m = n % WORD_LENGTH;

  // Create an array, large enough to hold the random bits
  var t = [];
  var len = Math.ceil(n / WORD_LENGTH);

  // Create an bitset instance
  var s = Object.create(BitSet.prototype);

  // Fill the vector with random data, uniformly distributed
  for (var i = 0; i < len; i++) {
    t.push(Math.random() * 4294967296 | 0);
  }

  // Mask out unwanted bits
  if (m > 0) {
    t[len - 1] &= (1 << m) - 1;
  }

  s['data'] = t;
  s['_'] = 0;
  return s;
};