crowd-funder-for-time-pwa/sw_scripts/sw-bn.js

"use strict";

// Utils
function assert(val, msg) {
  if (!val) throw new Error(msg || "Assertion failed");
}

// Could use `inherits` module, but don't want to move from single file
// architecture yet.
function inherits(ctor, superCtor) {
  ctor.super_ = superCtor;
  var TempCtor = function () {};
  TempCtor.prototype = superCtor.prototype;
  ctor.prototype = new TempCtor();
  ctor.prototype.constructor = ctor;
}

// BN

function BN(number, base, endian) {
  if (BN.isBN(number)) {
    return number;
  }

  this.negative = 0;
  this.words = null;
  this.length = 0;

  // Reduction context
  this.red = null;

  if (number !== null) {
    if (base === "le" || base === "be") {
      endian = base;
      base = 10;
    }

    this._init(number || 0, base || 10, endian || "be");
  }
}
self.BN = BN;

BN.BN = BN;
BN.wordSize = 26;

var Buffer;
try {
  if (typeof window !== "undefined" && typeof window.Buffer !== "undefined") {
    Buffer = window.Buffer;
  } else {
    Buffer = require("buffer").Buffer;
  }
} catch (e) {}

BN.isBN = function isBN(num) {
  if (num instanceof BN) {
    return true;
  }

  return (
    num !== null &&
    typeof num === "object" &&
    num.constructor.wordSize === BN.wordSize &&
    Array.isArray(num.words)
  );
};

BN.max = function max(left, right) {
  if (left.cmp(right) > 0) return left;
  return right;
};

BN.min = function min(left, right) {
  if (left.cmp(right) < 0) return left;
  return right;
};

BN.prototype._init = function init(number, base, endian) {
  if (typeof number === "number") {
    return this._initNumber(number, base, endian);
  }

  if (typeof number === "object") {
    return this._initArray(number, base, endian);
  }

  if (base === "hex") {
    base = 16;
  }
  assert(base === (base | 0) && base >= 2 && base <= 36);

  number = number.toString().replace(/\s+/g, "");
  var start = 0;
  if (number[0] === "-") {
    start++;
    this.negative = 1;
  }

  if (start < number.length) {
    if (base === 16) {
      this._parseHex(number, start, endian);
    } else {
      this._parseBase(number, base, start);
      if (endian === "le") {
        this._initArray(this.toArray(), base, endian);
      }
    }
  }
};

BN.prototype._initNumber = function _initNumber(number, base, endian) {
  if (number < 0) {
    this.negative = 1;
    number = -number;
  }
  if (number < 0x4000000) {
    this.words = [number & 0x3ffffff];
    this.length = 1;
  } else if (number < 0x10000000000000) {
    this.words = [number & 0x3ffffff, (number / 0x4000000) & 0x3ffffff];
    this.length = 2;
  } else {
    assert(number < 0x20000000000000); // 2 ^ 53 (unsafe)
    this.words = [number & 0x3ffffff, (number / 0x4000000) & 0x3ffffff, 1];
    this.length = 3;
  }

  if (endian !== "le") return;

  // Reverse the bytes
  this._initArray(this.toArray(), base, endian);
};

BN.prototype._initArray = function _initArray(number, base, endian) {
  // Perhaps a Uint8Array
  assert(typeof number.length === "number");
  if (number.length <= 0) {
    this.words = [0];
    this.length = 1;
    return this;
  }

  this.length = Math.ceil(number.length / 3);
  this.words = new Array(this.length);
  for (var i = 0; i < this.length; i++) {
    this.words[i] = 0;
  }

  var j, w;
  var off = 0;
  if (endian === "be") {
    for (i = number.length - 1, j = 0; i >= 0; i -= 3) {
      w = number[i] | (number[i - 1] << 8) | (number[i - 2] << 16);
      this.words[j] |= (w << off) & 0x3ffffff;
      this.words[j + 1] = (w >>> (26 - off)) & 0x3ffffff;
      off += 24;
      if (off >= 26) {
        off -= 26;
        j++;
      }
    }
  } else if (endian === "le") {
    for (i = 0, j = 0; i < number.length; i += 3) {
      w = number[i] | (number[i + 1] << 8) | (number[i + 2] << 16);
      this.words[j] |= (w << off) & 0x3ffffff;
      this.words[j + 1] = (w >>> (26 - off)) & 0x3ffffff;
      off += 24;
      if (off >= 26) {
        off -= 26;
        j++;
      }
    }
  }
  return this._strip();
};

function parseHex4Bits(string, index) {
  var c = string.charCodeAt(index);
  // '0' - '9'
  if (c >= 48 && c <= 57) {
    return c - 48;
    // 'A' - 'F'
  } else if (c >= 65 && c <= 70) {
    return c - 55;
    // 'a' - 'f'
  } else if (c >= 97 && c <= 102) {
    return c - 87;
  } else {
    assert(false, "Invalid character in " + string);
  }
}

function parseHexByte(string, lowerBound, index) {
  var r = parseHex4Bits(string, index);
  if (index - 1 >= lowerBound) {
    r |= parseHex4Bits(string, index - 1) << 4;
  }
  return r;
}

BN.prototype._parseHex = function _parseHex(number, start, endian) {
  // Create possibly bigger array to ensure that it fits the number
  this.length = Math.ceil((number.length - start) / 6);
  this.words = new Array(this.length);
  for (var i = 0; i < this.length; i++) {
    this.words[i] = 0;
  }

  // 24-bits chunks
  var off = 0;
  var j = 0;

  var w;
  if (endian === "be") {
    for (i = number.length - 1; i >= start; i -= 2) {
      w = parseHexByte(number, start, i) << off;
      this.words[j] |= w & 0x3ffffff;
      if (off >= 18) {
        off -= 18;
        j += 1;
        this.words[j] |= w >>> 26;
      } else {
        off += 8;
      }
    }
  } else {
    var parseLength = number.length - start;
    for (
      i = parseLength % 2 === 0 ? start + 1 : start;
      i < number.length;
      i += 2
    ) {
      w = parseHexByte(number, start, i) << off;
      this.words[j] |= w & 0x3ffffff;
      if (off >= 18) {
        off -= 18;
        j += 1;
        this.words[j] |= w >>> 26;
      } else {
        off += 8;
      }
    }
  }

  this._strip();
};

function parseBase(str, start, end, mul) {
  var r = 0;
  var b = 0;
  var len = Math.min(str.length, end);
  for (var i = start; i < len; i++) {
    var c = str.charCodeAt(i) - 48;

    r *= mul;

    // 'a'
    if (c >= 49) {
      b = c - 49 + 0xa;

      // 'A'
    } else if (c >= 17) {
      b = c - 17 + 0xa;

      // '0' - '9'
    } else {
      b = c;
    }
    assert(c >= 0 && b < mul, "Invalid character");
    r += b;
  }
  return r;
}

BN.prototype._parseBase = function _parseBase(number, base, start) {
  // Initialize as zero
  this.words = [0];
  this.length = 1;

  // Find length of limb in base
  for (var limbLen = 0, limbPow = 1; limbPow <= 0x3ffffff; limbPow *= base) {
    limbLen++;
  }
  limbLen--;
  limbPow = (limbPow / base) | 0;

  var total = number.length - start;
  var mod = total % limbLen;
  var end = Math.min(total, total - mod) + start;

  var word = 0;
  for (var i = start; i < end; i += limbLen) {
    word = parseBase(number, i, i + limbLen, base);

    this.imuln(limbPow);
    if (this.words[0] + word < 0x4000000) {
      this.words[0] += word;
    } else {
      this._iaddn(word);
    }
  }

  if (mod !== 0) {
    var pow = 1;
    word = parseBase(number, i, number.length, base);

    for (i = 0; i < mod; i++) {
      pow *= base;
    }

    this.imuln(pow);
    if (this.words[0] + word < 0x4000000) {
      this.words[0] += word;
    } else {
      this._iaddn(word);
    }
  }

  this._strip();
};

BN.prototype.copy = function copy(dest) {
  dest.words = new Array(this.length);
  for (var i = 0; i < this.length; i++) {
    dest.words[i] = this.words[i];
  }
  dest.length = this.length;
  dest.negative = this.negative;
  dest.red = this.red;
};

function move(dest, src) {
  dest.words = src.words;
  dest.length = src.length;
  dest.negative = src.negative;
  dest.red = src.red;
}

BN.prototype._move = function _move(dest) {
  move(dest, this);
};

BN.prototype.clone = function clone() {
  var r = new BN(null);
  this.copy(r);
  return r;
};

BN.prototype._expand = function _expand(size) {
  while (this.length < size) {
    this.words[this.length++] = 0;
  }
  return this;
};

// Remove leading `0` from `this`
BN.prototype._strip = function strip() {
  while (this.length > 1 && this.words[this.length - 1] === 0) {
    this.length--;
  }
  return this._normSign();
};

BN.prototype._normSign = function _normSign() {
  // -0 = 0
  if (this.length === 1 && this.words[0] === 0) {
    this.negative = 0;
  }
  return this;
};

// Check Symbol.for because not everywhere where Symbol defined
// See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Symbol#Browser_compatibility
if (typeof Symbol !== "undefined" && typeof Symbol.for === "function") {
  try {
    BN.prototype[Symbol.for("nodejs.util.inspect.custom")] = inspect;
  } catch (e) {
    BN.prototype.inspect = inspect;
  }
} else {
  BN.prototype.inspect = inspect;
}

function inspect() {
  return (this.red ? "<BN-R: " : "<BN: ") + this.toString(16) + ">";
}

/*

  var zeros = [];
  var groupSizes = [];
  var groupBases = [];

  var s = '';
  var i = -1;
  while (++i < BN.wordSize) {
    zeros[i] = s;
    s += '0';
  }
  groupSizes[0] = 0;
  groupSizes[1] = 0;
  groupBases[0] = 0;
  groupBases[1] = 0;
  var base = 2 - 1;
  while (++base < 36 + 1) {
    var groupSize = 0;
    var groupBase = 1;
    while (groupBase < (1 << BN.wordSize) / base) {
      groupBase *= base;
      groupSize += 1;
    }
    groupSizes[base] = groupSize;
    groupBases[base] = groupBase;
  }

  */

var zeros = [
  "",
  "0",
  "00",
  "000",
  "0000",
  "00000",
  "000000",
  "0000000",
  "00000000",
  "000000000",
  "0000000000",
  "00000000000",
  "000000000000",
  "0000000000000",
  "00000000000000",
  "000000000000000",
  "0000000000000000",
  "00000000000000000",
  "000000000000000000",
  "0000000000000000000",
  "00000000000000000000",
  "000000000000000000000",
  "0000000000000000000000",
  "00000000000000000000000",
  "000000000000000000000000",
  "0000000000000000000000000",
];

var groupSizes = [
  0, 0, 25, 16, 12, 11, 10, 9, 8, 8, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5,
  5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
];

var groupBases = [
  0, 0, 33554432, 43046721, 16777216, 48828125, 60466176, 40353607, 16777216,
  43046721, 10000000, 19487171, 35831808, 62748517, 7529536, 11390625, 16777216,
  24137569, 34012224, 47045881, 64000000, 4084101, 5153632, 6436343, 7962624,
  9765625, 11881376, 14348907, 17210368, 20511149, 24300000, 28629151, 33554432,
  39135393, 45435424, 52521875, 60466176,
];

BN.prototype.toString = function toString(base, padding) {
  base = base || 10;
  padding = padding | 0 || 1;

  var out;
  if (base === 16 || base === "hex") {
    out = "";
    var off = 0;
    var carry = 0;
    for (var i = 0; i < this.length; i++) {
      var w = this.words[i];
      var word = (((w << off) | carry) & 0xffffff).toString(16);
      carry = (w >>> (24 - off)) & 0xffffff;
      off += 2;
      if (off >= 26) {
        off -= 26;
        i--;
      }
      if (carry !== 0 || i !== this.length - 1) {
        out = zeros[6 - word.length] + word + out;
      } else {
        out = word + out;
      }
    }
    if (carry !== 0) {
      out = carry.toString(16) + out;
    }
    while (out.length % padding !== 0) {
      out = "0" + out;
    }
    if (this.negative !== 0) {
      out = "-" + out;
    }
    return out;
  }

  if (base === (base | 0) && base >= 2 && base <= 36) {
    // var groupSize = Math.floor(BN.wordSize * Math.LN2 / Math.log(base));
    var groupSize = groupSizes[base];
    // var groupBase = Math.pow(base, groupSize);
    var groupBase = groupBases[base];
    out = "";
    var c = this.clone();
    c.negative = 0;
    while (!c.isZero()) {
      var r = c.modrn(groupBase).toString(base);
      c = c.idivn(groupBase);

      if (!c.isZero()) {
        out = zeros[groupSize - r.length] + r + out;
      } else {
        out = r + out;
      }
    }
    if (this.isZero()) {
      out = "0" + out;
    }
    while (out.length % padding !== 0) {
      out = "0" + out;
    }
    if (this.negative !== 0) {
      out = "-" + out;
    }
    return out;
  }

  assert(false, "Base should be between 2 and 36");
};

BN.prototype.toNumber = function toNumber() {
  var ret = this.words[0];
  if (this.length === 2) {
    ret += this.words[1] * 0x4000000;
  } else if (this.length === 3 && this.words[2] === 0x01) {
    // NOTE: at this stage it is known that the top bit is set
    ret += 0x10000000000000 + this.words[1] * 0x4000000;
  } else if (this.length > 2) {
    assert(false, "Number can only safely store up to 53 bits");
  }
  return this.negative !== 0 ? -ret : ret;
};

BN.prototype.toJSON = function toJSON() {
  return this.toString(16, 2);
};

if (Buffer) {
  BN.prototype.toBuffer = function toBuffer(endian, length) {
    return this.toArrayLike(Buffer, endian, length);
  };
}

BN.prototype.toArray = function toArray(endian, length) {
  return this.toArrayLike(Array, endian, length);
};

var allocate = function allocate(ArrayType, size) {
  if (ArrayType.allocUnsafe) {
    return ArrayType.allocUnsafe(size);
  }
  return new ArrayType(size);
};

BN.prototype.toArrayLike = function toArrayLike(ArrayType, endian, length) {
  this._strip();

  var byteLength = this.byteLength();
  var reqLength = length || Math.max(1, byteLength);
  assert(byteLength <= reqLength, "byte array longer than desired length");
  assert(reqLength > 0, "Requested array length <= 0");

  var res = allocate(ArrayType, reqLength);
  var postfix = endian === "le" ? "LE" : "BE";
  this["_toArrayLike" + postfix](res, byteLength);
  return res;
};

BN.prototype._toArrayLikeLE = function _toArrayLikeLE(res, byteLength) {
  var position = 0;
  var carry = 0;

  for (var i = 0, shift = 0; i < this.length; i++) {
    var word = (this.words[i] << shift) | carry;

    res[position++] = word & 0xff;
    if (position < res.length) {
      res[position++] = (word >> 8) & 0xff;
    }
    if (position < res.length) {
      res[position++] = (word >> 16) & 0xff;
    }

    if (shift === 6) {
      if (position < res.length) {
        res[position++] = (word >> 24) & 0xff;
      }
      carry = 0;
      shift = 0;
    } else {
      carry = word >>> 24;
      shift += 2;
    }
  }

  if (position < res.length) {
    res[position++] = carry;

    while (position < res.length) {
      res[position++] = 0;
    }
  }
};

BN.prototype._toArrayLikeBE = function _toArrayLikeBE(res, byteLength) {
  var position = res.length - 1;
  var carry = 0;

  for (var i = 0, shift = 0; i < this.length; i++) {
    var word = (this.words[i] << shift) | carry;

    res[position--] = word & 0xff;
    if (position >= 0) {
      res[position--] = (word >> 8) & 0xff;
    }
    if (position >= 0) {
      res[position--] = (word >> 16) & 0xff;
    }

    if (shift === 6) {
      if (position >= 0) {
        res[position--] = (word >> 24) & 0xff;
      }
      carry = 0;
      shift = 0;
    } else {
      carry = word >>> 24;
      shift += 2;
    }
  }

  if (position >= 0) {
    res[position--] = carry;

    while (position >= 0) {
      res[position--] = 0;
    }
  }
};

if (Math.clz32) {
  BN.prototype._countBits = function _countBits(w) {
    return 32 - Math.clz32(w);
  };
} else {
  BN.prototype._countBits = function _countBits(w) {
    var t = w;
    var r = 0;
    if (t >= 0x1000) {
      r += 13;
      t >>>= 13;
    }
    if (t >= 0x40) {
      r += 7;
      t >>>= 7;
    }
    if (t >= 0x8) {
      r += 4;
      t >>>= 4;
    }
    if (t >= 0x02) {
      r += 2;
      t >>>= 2;
    }
    return r + t;
  };
}

BN.prototype._zeroBits = function _zeroBits(w) {
  // Short-cut
  if (w === 0) return 26;

  var t = w;
  var r = 0;
  if ((t & 0x1fff) === 0) {
    r += 13;
    t >>>= 13;
  }
  if ((t & 0x7f) === 0) {
    r += 7;
    t >>>= 7;
  }
  if ((t & 0xf) === 0) {
    r += 4;
    t >>>= 4;
  }
  if ((t & 0x3) === 0) {
    r += 2;
    t >>>= 2;
  }
  if ((t & 0x1) === 0) {
    r++;
  }
  return r;
};

// Return number of used bits in a BN
BN.prototype.bitLength = function bitLength() {
  var w = this.words[this.length - 1];
  var hi = this._countBits(w);
  return (this.length - 1) * 26 + hi;
};

function toBitArray(num) {
  var w = new Array(num.bitLength());

  for (var bit = 0; bit < w.length; bit++) {
    var off = (bit / 26) | 0;
    var wbit = bit % 26;

    w[bit] = (num.words[off] >>> wbit) & 0x01;
  }

  return w;
}

// Number of trailing zero bits
BN.prototype.zeroBits = function zeroBits() {
  if (this.isZero()) return 0;

  var r = 0;
  for (var i = 0; i < this.length; i++) {
    var b = this._zeroBits(this.words[i]);
    r += b;
    if (b !== 26) break;
  }
  return r;
};

BN.prototype.byteLength = function byteLength() {
  return Math.ceil(this.bitLength() / 8);
};

BN.prototype.toTwos = function toTwos(width) {
  if (this.negative !== 0) {
    return this.abs().inotn(width).iaddn(1);
  }
  return this.clone();
};

BN.prototype.fromTwos = function fromTwos(width) {
  if (this.testn(width - 1)) {
    return this.notn(width).iaddn(1).ineg();
  }
  return this.clone();
};

BN.prototype.isNeg = function isNeg() {
  return this.negative !== 0;
};

// Return negative clone of `this`
BN.prototype.neg = function neg() {
  return this.clone().ineg();
};

BN.prototype.ineg = function ineg() {
  if (!this.isZero()) {
    this.negative ^= 1;
  }

  return this;
};

// Or `num` with `this` in-place
BN.prototype.iuor = function iuor(num) {
  while (this.length < num.length) {
    this.words[this.length++] = 0;
  }

  for (var i = 0; i < num.length; i++) {
    this.words[i] = this.words[i] | num.words[i];
  }

  return this._strip();
};

BN.prototype.ior = function ior(num) {
  assert((this.negative | num.negative) === 0);
  return this.iuor(num);
};

// Or `num` with `this`
BN.prototype.or = function or(num) {
  if (this.length > num.length) return this.clone().ior(num);
  return num.clone().ior(this);
};

BN.prototype.uor = function uor(num) {
  if (this.length > num.length) return this.clone().iuor(num);
  return num.clone().iuor(this);
};

// And `num` with `this` in-place
BN.prototype.iuand = function iuand(num) {
  // b = min-length(num, this)
  var b;
  if (this.length > num.length) {
    b = num;
  } else {
    b = this;
  }

  for (var i = 0; i < b.length; i++) {
    this.words[i] = this.words[i] & num.words[i];
  }

  this.length = b.length;

  return this._strip();
};

BN.prototype.iand = function iand(num) {
  assert((this.negative | num.negative) === 0);
  return this.iuand(num);
};

// And `num` with `this`
BN.prototype.and = function and(num) {
  if (this.length > num.length) return this.clone().iand(num);
  return num.clone().iand(this);
};

BN.prototype.uand = function uand(num) {
  if (this.length > num.length) return this.clone().iuand(num);
  return num.clone().iuand(this);
};

// Xor `num` with `this` in-place
BN.prototype.iuxor = function iuxor(num) {
  // a.length > b.length
  var a;
  var b;
  if (this.length > num.length) {
    a = this;
    b = num;
  } else {
    a = num;
    b = this;
  }

  for (var i = 0; i < b.length; i++) {
    this.words[i] = a.words[i] ^ b.words[i];
  }

  if (this !== a) {
    for (; i < a.length; i++) {
      this.words[i] = a.words[i];
    }
  }

  this.length = a.length;

  return this._strip();
};

BN.prototype.ixor = function ixor(num) {
  assert((this.negative | num.negative) === 0);
  return this.iuxor(num);
};

// Xor `num` with `this`
BN.prototype.xor = function xor(num) {
  if (this.length > num.length) return this.clone().ixor(num);
  return num.clone().ixor(this);
};

BN.prototype.uxor = function uxor(num) {
  if (this.length > num.length) return this.clone().iuxor(num);
  return num.clone().iuxor(this);
};

// Not ``this`` with ``width`` bitwidth
BN.prototype.inotn = function inotn(width) {
  assert(typeof width === "number" && width >= 0);

  var bytesNeeded = Math.ceil(width / 26) | 0;
  var bitsLeft = width % 26;

  // Extend the buffer with leading zeroes
  this._expand(bytesNeeded);

  if (bitsLeft > 0) {
    bytesNeeded--;
  }

  // Handle complete words
  for (var i = 0; i < bytesNeeded; i++) {
    this.words[i] = ~this.words[i] & 0x3ffffff;
  }

  // Handle the residue
  if (bitsLeft > 0) {
    this.words[i] = ~this.words[i] & (0x3ffffff >> (26 - bitsLeft));
  }

  // And remove leading zeroes
  return this._strip();
};

BN.prototype.notn = function notn(width) {
  return this.clone().inotn(width);
};

// Set `bit` of `this`
BN.prototype.setn = function setn(bit, val) {
  assert(typeof bit === "number" && bit >= 0);

  var off = (bit / 26) | 0;
  var wbit = bit % 26;

  this._expand(off + 1);

  if (val) {
    this.words[off] = this.words[off] | (1 << wbit);
  } else {
    this.words[off] = this.words[off] & ~(1 << wbit);
  }

  return this._strip();
};

// Add `num` to `this` in-place
BN.prototype.iadd = function iadd(num) {
  var r;

  // negative + positive
  if (this.negative !== 0 && num.negative === 0) {
    this.negative = 0;
    r = this.isub(num);
    this.negative ^= 1;
    return this._normSign();

    // positive + negative
  } else if (this.negative === 0 && num.negative !== 0) {
    num.negative = 0;
    r = this.isub(num);
    num.negative = 1;
    return r._normSign();
  }

  // a.length > b.length
  var a, b;
  if (this.length > num.length) {
    a = this;
    b = num;
  } else {
    a = num;
    b = this;
  }

  var carry = 0;
  for (var i = 0; i < b.length; i++) {
    r = (a.words[i] | 0) + (b.words[i] | 0) + carry;
    this.words[i] = r & 0x3ffffff;
    carry = r >>> 26;
  }
  for (; carry !== 0 && i < a.length; i++) {
    r = (a.words[i] | 0) + carry;
    this.words[i] = r & 0x3ffffff;
    carry = r >>> 26;
  }

  this.length = a.length;
  if (carry !== 0) {
    this.words[this.length] = carry;
    this.length++;
    // Copy the rest of the words
  } else if (a !== this) {
    for (; i < a.length; i++) {
      this.words[i] = a.words[i];
    }
  }

  return this;
};

// Add `num` to `this`
BN.prototype.add = function add(num) {
  var res;
  if (num.negative !== 0 && this.negative === 0) {
    num.negative = 0;
    res = this.sub(num);
    num.negative ^= 1;
    return res;
  } else if (num.negative === 0 && this.negative !== 0) {
    this.negative = 0;
    res = num.sub(this);
    this.negative = 1;
    return res;
  }

  if (this.length > num.length) return this.clone().iadd(num);

  return num.clone().iadd(this);
};

// Subtract `num` from `this` in-place
BN.prototype.isub = function isub(num) {
  // this - (-num) = this + num
  if (num.negative !== 0) {
    num.negative = 0;
    var r = this.iadd(num);
    num.negative = 1;
    return r._normSign();

    // -this - num = -(this + num)
  } else if (this.negative !== 0) {
    this.negative = 0;
    this.iadd(num);
    this.negative = 1;
    return this._normSign();
  }

  // At this point both numbers are positive
  var cmp = this.cmp(num);

  // Optimization - zeroify
  if (cmp === 0) {
    this.negative = 0;
    this.length = 1;
    this.words[0] = 0;
    return this;
  }

  // a > b
  var a, b;
  if (cmp > 0) {
    a = this;
    b = num;
  } else {
    a = num;
    b = this;
  }

  var carry = 0;
  for (var i = 0; i < b.length; i++) {
    r = (a.words[i] | 0) - (b.words[i] | 0) + carry;
    carry = r >> 26;
    this.words[i] = r & 0x3ffffff;
  }
  for (; carry !== 0 && i < a.length; i++) {
    r = (a.words[i] | 0) + carry;
    carry = r >> 26;
    this.words[i] = r & 0x3ffffff;
  }

  // Copy rest of the words
  if (carry === 0 && i < a.length && a !== this) {
    for (; i < a.length; i++) {
      this.words[i] = a.words[i];
    }
  }

  this.length = Math.max(this.length, i);

  if (a !== this) {
    this.negative = 1;
  }

  return this._strip();
};

// Subtract `num` from `this`
BN.prototype.sub = function sub(num) {
  return this.clone().isub(num);
};

function smallMulTo(self, num, out) {
  out.negative = num.negative ^ self.negative;
  var len = (self.length + num.length) | 0;
  out.length = len;
  len = (len - 1) | 0;

  // Peel one iteration (compiler can't do it, because of code complexity)
  var a = self.words[0] | 0;
  var b = num.words[0] | 0;
  var r = a * b;

  var lo = r & 0x3ffffff;
  var carry = (r / 0x4000000) | 0;
  out.words[0] = lo;

  for (var k = 1; k < len; k++) {
    // Sum all words with the same `i + j = k` and accumulate `ncarry`,
    // note that ncarry could be >= 0x3ffffff
    var ncarry = carry >>> 26;
    var rword = carry & 0x3ffffff;
    var maxJ = Math.min(k, num.length - 1);
    for (var j = Math.max(0, k - self.length + 1); j <= maxJ; j++) {
      var i = (k - j) | 0;
      a = self.words[i] | 0;
      b = num.words[j] | 0;
      r = a * b + rword;
      ncarry += (r / 0x4000000) | 0;
      rword = r & 0x3ffffff;
    }
    out.words[k] = rword | 0;
    carry = ncarry | 0;
  }
  if (carry !== 0) {
    out.words[k] = carry | 0;
  } else {
    out.length--;
  }

  return out._strip();
}

// TODO(indutny): it may be reasonable to omit it for users who don't need
// to work with 256-bit numbers, otherwise it gives 20% improvement for 256-bit
// multiplication (like elliptic secp256k1).
var comb10MulTo = function comb10MulTo(self, num, out) {
  var a = self.words;
  var b = num.words;
  var o = out.words;
  var c = 0;
  var lo;
  var mid;
  var hi;
  var a0 = a[0] | 0;
  var al0 = a0 & 0x1fff;
  var ah0 = a0 >>> 13;
  var a1 = a[1] | 0;
  var al1 = a1 & 0x1fff;
  var ah1 = a1 >>> 13;
  var a2 = a[2] | 0;
  var al2 = a2 & 0x1fff;
  var ah2 = a2 >>> 13;
  var a3 = a[3] | 0;
  var al3 = a3 & 0x1fff;
  var ah3 = a3 >>> 13;
  var a4 = a[4] | 0;
  var al4 = a4 & 0x1fff;
  var ah4 = a4 >>> 13;
  var a5 = a[5] | 0;
  var al5 = a5 & 0x1fff;
  var ah5 = a5 >>> 13;
  var a6 = a[6] | 0;
  var al6 = a6 & 0x1fff;
  var ah6 = a6 >>> 13;
  var a7 = a[7] | 0;
  var al7 = a7 & 0x1fff;
  var ah7 = a7 >>> 13;
  var a8 = a[8] | 0;
  var al8 = a8 & 0x1fff;
  var ah8 = a8 >>> 13;
  var a9 = a[9] | 0;
  var al9 = a9 & 0x1fff;
  var ah9 = a9 >>> 13;
  var b0 = b[0] | 0;
  var bl0 = b0 & 0x1fff;
  var bh0 = b0 >>> 13;
  var b1 = b[1] | 0;
  var bl1 = b1 & 0x1fff;
  var bh1 = b1 >>> 13;
  var b2 = b[2] | 0;
  var bl2 = b2 & 0x1fff;
  var bh2 = b2 >>> 13;
  var b3 = b[3] | 0;
  var bl3 = b3 & 0x1fff;
  var bh3 = b3 >>> 13;
  var b4 = b[4] | 0;
  var bl4 = b4 & 0x1fff;
  var bh4 = b4 >>> 13;
  var b5 = b[5] | 0;
  var bl5 = b5 & 0x1fff;
  var bh5 = b5 >>> 13;
  var b6 = b[6] | 0;
  var bl6 = b6 & 0x1fff;
  var bh6 = b6 >>> 13;
  var b7 = b[7] | 0;
  var bl7 = b7 & 0x1fff;
  var bh7 = b7 >>> 13;
  var b8 = b[8] | 0;
  var bl8 = b8 & 0x1fff;
  var bh8 = b8 >>> 13;
  var b9 = b[9] | 0;
  var bl9 = b9 & 0x1fff;
  var bh9 = b9 >>> 13;

  out.negative = self.negative ^ num.negative;
  out.length = 19;
  /* k = 0 */
  lo = Math.imul(al0, bl0);
  mid = Math.imul(al0, bh0);
  mid = (mid + Math.imul(ah0, bl0)) | 0;
  hi = Math.imul(ah0, bh0);
  var w0 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w0 >>> 26)) | 0;
  w0 &= 0x3ffffff;
  /* k = 1 */
  lo = Math.imul(al1, bl0);
  mid = Math.imul(al1, bh0);
  mid = (mid + Math.imul(ah1, bl0)) | 0;
  hi = Math.imul(ah1, bh0);
  lo = (lo + Math.imul(al0, bl1)) | 0;
  mid = (mid + Math.imul(al0, bh1)) | 0;
  mid = (mid + Math.imul(ah0, bl1)) | 0;
  hi = (hi + Math.imul(ah0, bh1)) | 0;
  var w1 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w1 >>> 26)) | 0;
  w1 &= 0x3ffffff;
  /* k = 2 */
  lo = Math.imul(al2, bl0);
  mid = Math.imul(al2, bh0);
  mid = (mid + Math.imul(ah2, bl0)) | 0;
  hi = Math.imul(ah2, bh0);
  lo = (lo + Math.imul(al1, bl1)) | 0;
  mid = (mid + Math.imul(al1, bh1)) | 0;
  mid = (mid + Math.imul(ah1, bl1)) | 0;
  hi = (hi + Math.imul(ah1, bh1)) | 0;
  lo = (lo + Math.imul(al0, bl2)) | 0;
  mid = (mid + Math.imul(al0, bh2)) | 0;
  mid = (mid + Math.imul(ah0, bl2)) | 0;
  hi = (hi + Math.imul(ah0, bh2)) | 0;
  var w2 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w2 >>> 26)) | 0;
  w2 &= 0x3ffffff;
  /* k = 3 */
  lo = Math.imul(al3, bl0);
  mid = Math.imul(al3, bh0);
  mid = (mid + Math.imul(ah3, bl0)) | 0;
  hi = Math.imul(ah3, bh0);
  lo = (lo + Math.imul(al2, bl1)) | 0;
  mid = (mid + Math.imul(al2, bh1)) | 0;
  mid = (mid + Math.imul(ah2, bl1)) | 0;
  hi = (hi + Math.imul(ah2, bh1)) | 0;
  lo = (lo + Math.imul(al1, bl2)) | 0;
  mid = (mid + Math.imul(al1, bh2)) | 0;
  mid = (mid + Math.imul(ah1, bl2)) | 0;
  hi = (hi + Math.imul(ah1, bh2)) | 0;
  lo = (lo + Math.imul(al0, bl3)) | 0;
  mid = (mid + Math.imul(al0, bh3)) | 0;
  mid = (mid + Math.imul(ah0, bl3)) | 0;
  hi = (hi + Math.imul(ah0, bh3)) | 0;
  var w3 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w3 >>> 26)) | 0;
  w3 &= 0x3ffffff;
  /* k = 4 */
  lo = Math.imul(al4, bl0);
  mid = Math.imul(al4, bh0);
  mid = (mid + Math.imul(ah4, bl0)) | 0;
  hi = Math.imul(ah4, bh0);
  lo = (lo + Math.imul(al3, bl1)) | 0;
  mid = (mid + Math.imul(al3, bh1)) | 0;
  mid = (mid + Math.imul(ah3, bl1)) | 0;
  hi = (hi + Math.imul(ah3, bh1)) | 0;
  lo = (lo + Math.imul(al2, bl2)) | 0;
  mid = (mid + Math.imul(al2, bh2)) | 0;
  mid = (mid + Math.imul(ah2, bl2)) | 0;
  hi = (hi + Math.imul(ah2, bh2)) | 0;
  lo = (lo + Math.imul(al1, bl3)) | 0;
  mid = (mid + Math.imul(al1, bh3)) | 0;
  mid = (mid + Math.imul(ah1, bl3)) | 0;
  hi = (hi + Math.imul(ah1, bh3)) | 0;
  lo = (lo + Math.imul(al0, bl4)) | 0;
  mid = (mid + Math.imul(al0, bh4)) | 0;
  mid = (mid + Math.imul(ah0, bl4)) | 0;
  hi = (hi + Math.imul(ah0, bh4)) | 0;
  var w4 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w4 >>> 26)) | 0;
  w4 &= 0x3ffffff;
  /* k = 5 */
  lo = Math.imul(al5, bl0);
  mid = Math.imul(al5, bh0);
  mid = (mid + Math.imul(ah5, bl0)) | 0;
  hi = Math.imul(ah5, bh0);
  lo = (lo + Math.imul(al4, bl1)) | 0;
  mid = (mid + Math.imul(al4, bh1)) | 0;
  mid = (mid + Math.imul(ah4, bl1)) | 0;
  hi = (hi + Math.imul(ah4, bh1)) | 0;
  lo = (lo + Math.imul(al3, bl2)) | 0;
  mid = (mid + Math.imul(al3, bh2)) | 0;
  mid = (mid + Math.imul(ah3, bl2)) | 0;
  hi = (hi + Math.imul(ah3, bh2)) | 0;
  lo = (lo + Math.imul(al2, bl3)) | 0;
  mid = (mid + Math.imul(al2, bh3)) | 0;
  mid = (mid + Math.imul(ah2, bl3)) | 0;
  hi = (hi + Math.imul(ah2, bh3)) | 0;
  lo = (lo + Math.imul(al1, bl4)) | 0;
  mid = (mid + Math.imul(al1, bh4)) | 0;
  mid = (mid + Math.imul(ah1, bl4)) | 0;
  hi = (hi + Math.imul(ah1, bh4)) | 0;
  lo = (lo + Math.imul(al0, bl5)) | 0;
  mid = (mid + Math.imul(al0, bh5)) | 0;
  mid = (mid + Math.imul(ah0, bl5)) | 0;
  hi = (hi + Math.imul(ah0, bh5)) | 0;
  var w5 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w5 >>> 26)) | 0;
  w5 &= 0x3ffffff;
  /* k = 6 */
  lo = Math.imul(al6, bl0);
  mid = Math.imul(al6, bh0);
  mid = (mid + Math.imul(ah6, bl0)) | 0;
  hi = Math.imul(ah6, bh0);
  lo = (lo + Math.imul(al5, bl1)) | 0;
  mid = (mid + Math.imul(al5, bh1)) | 0;
  mid = (mid + Math.imul(ah5, bl1)) | 0;
  hi = (hi + Math.imul(ah5, bh1)) | 0;
  lo = (lo + Math.imul(al4, bl2)) | 0;
  mid = (mid + Math.imul(al4, bh2)) | 0;
  mid = (mid + Math.imul(ah4, bl2)) | 0;
  hi = (hi + Math.imul(ah4, bh2)) | 0;
  lo = (lo + Math.imul(al3, bl3)) | 0;
  mid = (mid + Math.imul(al3, bh3)) | 0;
  mid = (mid + Math.imul(ah3, bl3)) | 0;
  hi = (hi + Math.imul(ah3, bh3)) | 0;
  lo = (lo + Math.imul(al2, bl4)) | 0;
  mid = (mid + Math.imul(al2, bh4)) | 0;
  mid = (mid + Math.imul(ah2, bl4)) | 0;
  hi = (hi + Math.imul(ah2, bh4)) | 0;
  lo = (lo + Math.imul(al1, bl5)) | 0;
  mid = (mid + Math.imul(al1, bh5)) | 0;
  mid = (mid + Math.imul(ah1, bl5)) | 0;
  hi = (hi + Math.imul(ah1, bh5)) | 0;
  lo = (lo + Math.imul(al0, bl6)) | 0;
  mid = (mid + Math.imul(al0, bh6)) | 0;
  mid = (mid + Math.imul(ah0, bl6)) | 0;
  hi = (hi + Math.imul(ah0, bh6)) | 0;
  var w6 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w6 >>> 26)) | 0;
  w6 &= 0x3ffffff;
  /* k = 7 */
  lo = Math.imul(al7, bl0);
  mid = Math.imul(al7, bh0);
  mid = (mid + Math.imul(ah7, bl0)) | 0;
  hi = Math.imul(ah7, bh0);
  lo = (lo + Math.imul(al6, bl1)) | 0;
  mid = (mid + Math.imul(al6, bh1)) | 0;
  mid = (mid + Math.imul(ah6, bl1)) | 0;
  hi = (hi + Math.imul(ah6, bh1)) | 0;
  lo = (lo + Math.imul(al5, bl2)) | 0;
  mid = (mid + Math.imul(al5, bh2)) | 0;
  mid = (mid + Math.imul(ah5, bl2)) | 0;
  hi = (hi + Math.imul(ah5, bh2)) | 0;
  lo = (lo + Math.imul(al4, bl3)) | 0;
  mid = (mid + Math.imul(al4, bh3)) | 0;
  mid = (mid + Math.imul(ah4, bl3)) | 0;
  hi = (hi + Math.imul(ah4, bh3)) | 0;
  lo = (lo + Math.imul(al3, bl4)) | 0;
  mid = (mid + Math.imul(al3, bh4)) | 0;
  mid = (mid + Math.imul(ah3, bl4)) | 0;
  hi = (hi + Math.imul(ah3, bh4)) | 0;
  lo = (lo + Math.imul(al2, bl5)) | 0;
  mid = (mid + Math.imul(al2, bh5)) | 0;
  mid = (mid + Math.imul(ah2, bl5)) | 0;
  hi = (hi + Math.imul(ah2, bh5)) | 0;
  lo = (lo + Math.imul(al1, bl6)) | 0;
  mid = (mid + Math.imul(al1, bh6)) | 0;
  mid = (mid + Math.imul(ah1, bl6)) | 0;
  hi = (hi + Math.imul(ah1, bh6)) | 0;
  lo = (lo + Math.imul(al0, bl7)) | 0;
  mid = (mid + Math.imul(al0, bh7)) | 0;
  mid = (mid + Math.imul(ah0, bl7)) | 0;
  hi = (hi + Math.imul(ah0, bh7)) | 0;
  var w7 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w7 >>> 26)) | 0;
  w7 &= 0x3ffffff;
  /* k = 8 */
  lo = Math.imul(al8, bl0);
  mid = Math.imul(al8, bh0);
  mid = (mid + Math.imul(ah8, bl0)) | 0;
  hi = Math.imul(ah8, bh0);
  lo = (lo + Math.imul(al7, bl1)) | 0;
  mid = (mid + Math.imul(al7, bh1)) | 0;
  mid = (mid + Math.imul(ah7, bl1)) | 0;
  hi = (hi + Math.imul(ah7, bh1)) | 0;
  lo = (lo + Math.imul(al6, bl2)) | 0;
  mid = (mid + Math.imul(al6, bh2)) | 0;
  mid = (mid + Math.imul(ah6, bl2)) | 0;
  hi = (hi + Math.imul(ah6, bh2)) | 0;
  lo = (lo + Math.imul(al5, bl3)) | 0;
  mid = (mid + Math.imul(al5, bh3)) | 0;
  mid = (mid + Math.imul(ah5, bl3)) | 0;
  hi = (hi + Math.imul(ah5, bh3)) | 0;
  lo = (lo + Math.imul(al4, bl4)) | 0;
  mid = (mid + Math.imul(al4, bh4)) | 0;
  mid = (mid + Math.imul(ah4, bl4)) | 0;
  hi = (hi + Math.imul(ah4, bh4)) | 0;
  lo = (lo + Math.imul(al3, bl5)) | 0;
  mid = (mid + Math.imul(al3, bh5)) | 0;
  mid = (mid + Math.imul(ah3, bl5)) | 0;
  hi = (hi + Math.imul(ah3, bh5)) | 0;
  lo = (lo + Math.imul(al2, bl6)) | 0;
  mid = (mid + Math.imul(al2, bh6)) | 0;
  mid = (mid + Math.imul(ah2, bl6)) | 0;
  hi = (hi + Math.imul(ah2, bh6)) | 0;
  lo = (lo + Math.imul(al1, bl7)) | 0;
  mid = (mid + Math.imul(al1, bh7)) | 0;
  mid = (mid + Math.imul(ah1, bl7)) | 0;
  hi = (hi + Math.imul(ah1, bh7)) | 0;
  lo = (lo + Math.imul(al0, bl8)) | 0;
  mid = (mid + Math.imul(al0, bh8)) | 0;
  mid = (mid + Math.imul(ah0, bl8)) | 0;
  hi = (hi + Math.imul(ah0, bh8)) | 0;
  var w8 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w8 >>> 26)) | 0;
  w8 &= 0x3ffffff;
  /* k = 9 */
  lo = Math.imul(al9, bl0);
  mid = Math.imul(al9, bh0);
  mid = (mid + Math.imul(ah9, bl0)) | 0;
  hi = Math.imul(ah9, bh0);
  lo = (lo + Math.imul(al8, bl1)) | 0;
  mid = (mid + Math.imul(al8, bh1)) | 0;
  mid = (mid + Math.imul(ah8, bl1)) | 0;
  hi = (hi + Math.imul(ah8, bh1)) | 0;
  lo = (lo + Math.imul(al7, bl2)) | 0;
  mid = (mid + Math.imul(al7, bh2)) | 0;
  mid = (mid + Math.imul(ah7, bl2)) | 0;
  hi = (hi + Math.imul(ah7, bh2)) | 0;
  lo = (lo + Math.imul(al6, bl3)) | 0;
  mid = (mid + Math.imul(al6, bh3)) | 0;
  mid = (mid + Math.imul(ah6, bl3)) | 0;
  hi = (hi + Math.imul(ah6, bh3)) | 0;
  lo = (lo + Math.imul(al5, bl4)) | 0;
  mid = (mid + Math.imul(al5, bh4)) | 0;
  mid = (mid + Math.imul(ah5, bl4)) | 0;
  hi = (hi + Math.imul(ah5, bh4)) | 0;
  lo = (lo + Math.imul(al4, bl5)) | 0;
  mid = (mid + Math.imul(al4, bh5)) | 0;
  mid = (mid + Math.imul(ah4, bl5)) | 0;
  hi = (hi + Math.imul(ah4, bh5)) | 0;
  lo = (lo + Math.imul(al3, bl6)) | 0;
  mid = (mid + Math.imul(al3, bh6)) | 0;
  mid = (mid + Math.imul(ah3, bl6)) | 0;
  hi = (hi + Math.imul(ah3, bh6)) | 0;
  lo = (lo + Math.imul(al2, bl7)) | 0;
  mid = (mid + Math.imul(al2, bh7)) | 0;
  mid = (mid + Math.imul(ah2, bl7)) | 0;
  hi = (hi + Math.imul(ah2, bh7)) | 0;
  lo = (lo + Math.imul(al1, bl8)) | 0;
  mid = (mid + Math.imul(al1, bh8)) | 0;
  mid = (mid + Math.imul(ah1, bl8)) | 0;
  hi = (hi + Math.imul(ah1, bh8)) | 0;
  lo = (lo + Math.imul(al0, bl9)) | 0;
  mid = (mid + Math.imul(al0, bh9)) | 0;
  mid = (mid + Math.imul(ah0, bl9)) | 0;
  hi = (hi + Math.imul(ah0, bh9)) | 0;
  var w9 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w9 >>> 26)) | 0;
  w9 &= 0x3ffffff;
  /* k = 10 */
  lo = Math.imul(al9, bl1);
  mid = Math.imul(al9, bh1);
  mid = (mid + Math.imul(ah9, bl1)) | 0;
  hi = Math.imul(ah9, bh1);
  lo = (lo + Math.imul(al8, bl2)) | 0;
  mid = (mid + Math.imul(al8, bh2)) | 0;
  mid = (mid + Math.imul(ah8, bl2)) | 0;
  hi = (hi + Math.imul(ah8, bh2)) | 0;
  lo = (lo + Math.imul(al7, bl3)) | 0;
  mid = (mid + Math.imul(al7, bh3)) | 0;
  mid = (mid + Math.imul(ah7, bl3)) | 0;
  hi = (hi + Math.imul(ah7, bh3)) | 0;
  lo = (lo + Math.imul(al6, bl4)) | 0;
  mid = (mid + Math.imul(al6, bh4)) | 0;
  mid = (mid + Math.imul(ah6, bl4)) | 0;
  hi = (hi + Math.imul(ah6, bh4)) | 0;
  lo = (lo + Math.imul(al5, bl5)) | 0;
  mid = (mid + Math.imul(al5, bh5)) | 0;
  mid = (mid + Math.imul(ah5, bl5)) | 0;
  hi = (hi + Math.imul(ah5, bh5)) | 0;
  lo = (lo + Math.imul(al4, bl6)) | 0;
  mid = (mid + Math.imul(al4, bh6)) | 0;
  mid = (mid + Math.imul(ah4, bl6)) | 0;
  hi = (hi + Math.imul(ah4, bh6)) | 0;
  lo = (lo + Math.imul(al3, bl7)) | 0;
  mid = (mid + Math.imul(al3, bh7)) | 0;
  mid = (mid + Math.imul(ah3, bl7)) | 0;
  hi = (hi + Math.imul(ah3, bh7)) | 0;
  lo = (lo + Math.imul(al2, bl8)) | 0;
  mid = (mid + Math.imul(al2, bh8)) | 0;
  mid = (mid + Math.imul(ah2, bl8)) | 0;
  hi = (hi + Math.imul(ah2, bh8)) | 0;
  lo = (lo + Math.imul(al1, bl9)) | 0;
  mid = (mid + Math.imul(al1, bh9)) | 0;
  mid = (mid + Math.imul(ah1, bl9)) | 0;
  hi = (hi + Math.imul(ah1, bh9)) | 0;
  var w10 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w10 >>> 26)) | 0;
  w10 &= 0x3ffffff;
  /* k = 11 */
  lo = Math.imul(al9, bl2);
  mid = Math.imul(al9, bh2);
  mid = (mid + Math.imul(ah9, bl2)) | 0;
  hi = Math.imul(ah9, bh2);
  lo = (lo + Math.imul(al8, bl3)) | 0;
  mid = (mid + Math.imul(al8, bh3)) | 0;
  mid = (mid + Math.imul(ah8, bl3)) | 0;
  hi = (hi + Math.imul(ah8, bh3)) | 0;
  lo = (lo + Math.imul(al7, bl4)) | 0;
  mid = (mid + Math.imul(al7, bh4)) | 0;
  mid = (mid + Math.imul(ah7, bl4)) | 0;
  hi = (hi + Math.imul(ah7, bh4)) | 0;
  lo = (lo + Math.imul(al6, bl5)) | 0;
  mid = (mid + Math.imul(al6, bh5)) | 0;
  mid = (mid + Math.imul(ah6, bl5)) | 0;
  hi = (hi + Math.imul(ah6, bh5)) | 0;
  lo = (lo + Math.imul(al5, bl6)) | 0;
  mid = (mid + Math.imul(al5, bh6)) | 0;
  mid = (mid + Math.imul(ah5, bl6)) | 0;
  hi = (hi + Math.imul(ah5, bh6)) | 0;
  lo = (lo + Math.imul(al4, bl7)) | 0;
  mid = (mid + Math.imul(al4, bh7)) | 0;
  mid = (mid + Math.imul(ah4, bl7)) | 0;
  hi = (hi + Math.imul(ah4, bh7)) | 0;
  lo = (lo + Math.imul(al3, bl8)) | 0;
  mid = (mid + Math.imul(al3, bh8)) | 0;
  mid = (mid + Math.imul(ah3, bl8)) | 0;
  hi = (hi + Math.imul(ah3, bh8)) | 0;
  lo = (lo + Math.imul(al2, bl9)) | 0;
  mid = (mid + Math.imul(al2, bh9)) | 0;
  mid = (mid + Math.imul(ah2, bl9)) | 0;
  hi = (hi + Math.imul(ah2, bh9)) | 0;
  var w11 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w11 >>> 26)) | 0;
  w11 &= 0x3ffffff;
  /* k = 12 */
  lo = Math.imul(al9, bl3);
  mid = Math.imul(al9, bh3);
  mid = (mid + Math.imul(ah9, bl3)) | 0;
  hi = Math.imul(ah9, bh3);
  lo = (lo + Math.imul(al8, bl4)) | 0;
  mid = (mid + Math.imul(al8, bh4)) | 0;
  mid = (mid + Math.imul(ah8, bl4)) | 0;
  hi = (hi + Math.imul(ah8, bh4)) | 0;
  lo = (lo + Math.imul(al7, bl5)) | 0;
  mid = (mid + Math.imul(al7, bh5)) | 0;
  mid = (mid + Math.imul(ah7, bl5)) | 0;
  hi = (hi + Math.imul(ah7, bh5)) | 0;
  lo = (lo + Math.imul(al6, bl6)) | 0;
  mid = (mid + Math.imul(al6, bh6)) | 0;
  mid = (mid + Math.imul(ah6, bl6)) | 0;
  hi = (hi + Math.imul(ah6, bh6)) | 0;
  lo = (lo + Math.imul(al5, bl7)) | 0;
  mid = (mid + Math.imul(al5, bh7)) | 0;
  mid = (mid + Math.imul(ah5, bl7)) | 0;
  hi = (hi + Math.imul(ah5, bh7)) | 0;
  lo = (lo + Math.imul(al4, bl8)) | 0;
  mid = (mid + Math.imul(al4, bh8)) | 0;
  mid = (mid + Math.imul(ah4, bl8)) | 0;
  hi = (hi + Math.imul(ah4, bh8)) | 0;
  lo = (lo + Math.imul(al3, bl9)) | 0;
  mid = (mid + Math.imul(al3, bh9)) | 0;
  mid = (mid + Math.imul(ah3, bl9)) | 0;
  hi = (hi + Math.imul(ah3, bh9)) | 0;
  var w12 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w12 >>> 26)) | 0;
  w12 &= 0x3ffffff;
  /* k = 13 */
  lo = Math.imul(al9, bl4);
  mid = Math.imul(al9, bh4);
  mid = (mid + Math.imul(ah9, bl4)) | 0;
  hi = Math.imul(ah9, bh4);
  lo = (lo + Math.imul(al8, bl5)) | 0;
  mid = (mid + Math.imul(al8, bh5)) | 0;
  mid = (mid + Math.imul(ah8, bl5)) | 0;
  hi = (hi + Math.imul(ah8, bh5)) | 0;
  lo = (lo + Math.imul(al7, bl6)) | 0;
  mid = (mid + Math.imul(al7, bh6)) | 0;
  mid = (mid + Math.imul(ah7, bl6)) | 0;
  hi = (hi + Math.imul(ah7, bh6)) | 0;
  lo = (lo + Math.imul(al6, bl7)) | 0;
  mid = (mid + Math.imul(al6, bh7)) | 0;
  mid = (mid + Math.imul(ah6, bl7)) | 0;
  hi = (hi + Math.imul(ah6, bh7)) | 0;
  lo = (lo + Math.imul(al5, bl8)) | 0;
  mid = (mid + Math.imul(al5, bh8)) | 0;
  mid = (mid + Math.imul(ah5, bl8)) | 0;
  hi = (hi + Math.imul(ah5, bh8)) | 0;
  lo = (lo + Math.imul(al4, bl9)) | 0;
  mid = (mid + Math.imul(al4, bh9)) | 0;
  mid = (mid + Math.imul(ah4, bl9)) | 0;
  hi = (hi + Math.imul(ah4, bh9)) | 0;
  var w13 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w13 >>> 26)) | 0;
  w13 &= 0x3ffffff;
  /* k = 14 */
  lo = Math.imul(al9, bl5);
  mid = Math.imul(al9, bh5);
  mid = (mid + Math.imul(ah9, bl5)) | 0;
  hi = Math.imul(ah9, bh5);
  lo = (lo + Math.imul(al8, bl6)) | 0;
  mid = (mid + Math.imul(al8, bh6)) | 0;
  mid = (mid + Math.imul(ah8, bl6)) | 0;
  hi = (hi + Math.imul(ah8, bh6)) | 0;
  lo = (lo + Math.imul(al7, bl7)) | 0;
  mid = (mid + Math.imul(al7, bh7)) | 0;
  mid = (mid + Math.imul(ah7, bl7)) | 0;
  hi = (hi + Math.imul(ah7, bh7)) | 0;
  lo = (lo + Math.imul(al6, bl8)) | 0;
  mid = (mid + Math.imul(al6, bh8)) | 0;
  mid = (mid + Math.imul(ah6, bl8)) | 0;
  hi = (hi + Math.imul(ah6, bh8)) | 0;
  lo = (lo + Math.imul(al5, bl9)) | 0;
  mid = (mid + Math.imul(al5, bh9)) | 0;
  mid = (mid + Math.imul(ah5, bl9)) | 0;
  hi = (hi + Math.imul(ah5, bh9)) | 0;
  var w14 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w14 >>> 26)) | 0;
  w14 &= 0x3ffffff;
  /* k = 15 */
  lo = Math.imul(al9, bl6);
  mid = Math.imul(al9, bh6);
  mid = (mid + Math.imul(ah9, bl6)) | 0;
  hi = Math.imul(ah9, bh6);
  lo = (lo + Math.imul(al8, bl7)) | 0;
  mid = (mid + Math.imul(al8, bh7)) | 0;
  mid = (mid + Math.imul(ah8, bl7)) | 0;
  hi = (hi + Math.imul(ah8, bh7)) | 0;
  lo = (lo + Math.imul(al7, bl8)) | 0;
  mid = (mid + Math.imul(al7, bh8)) | 0;
  mid = (mid + Math.imul(ah7, bl8)) | 0;
  hi = (hi + Math.imul(ah7, bh8)) | 0;
  lo = (lo + Math.imul(al6, bl9)) | 0;
  mid = (mid + Math.imul(al6, bh9)) | 0;
  mid = (mid + Math.imul(ah6, bl9)) | 0;
  hi = (hi + Math.imul(ah6, bh9)) | 0;
  var w15 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w15 >>> 26)) | 0;
  w15 &= 0x3ffffff;
  /* k = 16 */
  lo = Math.imul(al9, bl7);
  mid = Math.imul(al9, bh7);
  mid = (mid + Math.imul(ah9, bl7)) | 0;
  hi = Math.imul(ah9, bh7);
  lo = (lo + Math.imul(al8, bl8)) | 0;
  mid = (mid + Math.imul(al8, bh8)) | 0;
  mid = (mid + Math.imul(ah8, bl8)) | 0;
  hi = (hi + Math.imul(ah8, bh8)) | 0;
  lo = (lo + Math.imul(al7, bl9)) | 0;
  mid = (mid + Math.imul(al7, bh9)) | 0;
  mid = (mid + Math.imul(ah7, bl9)) | 0;
  hi = (hi + Math.imul(ah7, bh9)) | 0;
  var w16 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w16 >>> 26)) | 0;
  w16 &= 0x3ffffff;
  /* k = 17 */
  lo = Math.imul(al9, bl8);
  mid = Math.imul(al9, bh8);
  mid = (mid + Math.imul(ah9, bl8)) | 0;
  hi = Math.imul(ah9, bh8);
  lo = (lo + Math.imul(al8, bl9)) | 0;
  mid = (mid + Math.imul(al8, bh9)) | 0;
  mid = (mid + Math.imul(ah8, bl9)) | 0;
  hi = (hi + Math.imul(ah8, bh9)) | 0;
  var w17 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w17 >>> 26)) | 0;
  w17 &= 0x3ffffff;
  /* k = 18 */
  lo = Math.imul(al9, bl9);
  mid = Math.imul(al9, bh9);
  mid = (mid + Math.imul(ah9, bl9)) | 0;
  hi = Math.imul(ah9, bh9);
  var w18 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;
  c = (((hi + (mid >>> 13)) | 0) + (w18 >>> 26)) | 0;
  w18 &= 0x3ffffff;
  o[0] = w0;
  o[1] = w1;
  o[2] = w2;
  o[3] = w3;
  o[4] = w4;
  o[5] = w5;
  o[6] = w6;
  o[7] = w7;
  o[8] = w8;
  o[9] = w9;
  o[10] = w10;
  o[11] = w11;
  o[12] = w12;
  o[13] = w13;
  o[14] = w14;
  o[15] = w15;
  o[16] = w16;
  o[17] = w17;
  o[18] = w18;
  if (c !== 0) {
    o[19] = c;
    out.length++;
  }
  return out;
};

// Polyfill comb
if (!Math.imul) {
  comb10MulTo = smallMulTo;
}

function bigMulTo(self, num, out) {
  out.negative = num.negative ^ self.negative;
  out.length = self.length + num.length;

  var carry = 0;
  var hncarry = 0;
  for (var k = 0; k < out.length - 1; k++) {
    // Sum all words with the same `i + j = k` and accumulate `ncarry`,
    // note that ncarry could be >= 0x3ffffff
    var ncarry = hncarry;
    hncarry = 0;
    var rword = carry & 0x3ffffff;
    var maxJ = Math.min(k, num.length - 1);
    for (var j = Math.max(0, k - self.length + 1); j <= maxJ; j++) {
      var i = k - j;
      var a = self.words[i] | 0;
      var b = num.words[j] | 0;
      var r = a * b;

      var lo = r & 0x3ffffff;
      ncarry = (ncarry + ((r / 0x4000000) | 0)) | 0;
      lo = (lo + rword) | 0;
      rword = lo & 0x3ffffff;
      ncarry = (ncarry + (lo >>> 26)) | 0;

      hncarry += ncarry >>> 26;
      ncarry &= 0x3ffffff;
    }
    out.words[k] = rword;
    carry = ncarry;
    ncarry = hncarry;
  }
  if (carry !== 0) {
    out.words[k] = carry;
  } else {
    out.length--;
  }

  return out._strip();
}

function jumboMulTo(self, num, out) {
  // Temporary disable, see https://github.com/indutny/bn.js/issues/211
  // var fftm = new FFTM();
  // return fftm.mulp(self, num, out);
  return bigMulTo(self, num, out);
}

BN.prototype.mulTo = function mulTo(num, out) {
  var res;
  var len = this.length + num.length;
  if (this.length === 10 && num.length === 10) {
    res = comb10MulTo(this, num, out);
  } else if (len < 63) {
    res = smallMulTo(this, num, out);
  } else if (len < 1024) {
    res = bigMulTo(this, num, out);
  } else {
    res = jumboMulTo(this, num, out);
  }

  return res;
};

// Cooley-Tukey algorithm for FFT
// slightly revisited to rely on looping instead of recursion

function FFTM(x, y) {
  this.x = x;
  this.y = y;
}

FFTM.prototype.makeRBT = function makeRBT(N) {
  var t = new Array(N);
  var l = BN.prototype._countBits(N) - 1;
  for (var i = 0; i < N; i++) {
    t[i] = this.revBin(i, l, N);
  }

  return t;
};

// Returns binary-reversed representation of `x`
FFTM.prototype.revBin = function revBin(x, l, N) {
  if (x === 0 || x === N - 1) return x;

  var rb = 0;
  for (var i = 0; i < l; i++) {
    rb |= (x & 1) << (l - i - 1);
    x >>= 1;
  }

  return rb;
};

// Performs "tweedling" phase, therefore 'emulating'
// behaviour of the recursive algorithm
FFTM.prototype.permute = function permute(rbt, rws, iws, rtws, itws, N) {
  for (var i = 0; i < N; i++) {
    rtws[i] = rws[rbt[i]];
    itws[i] = iws[rbt[i]];
  }
};

FFTM.prototype.transform = function transform(rws, iws, rtws, itws, N, rbt) {
  this.permute(rbt, rws, iws, rtws, itws, N);

  for (var s = 1; s < N; s <<= 1) {
    var l = s << 1;

    var rtwdf = Math.cos((2 * Math.PI) / l);
    var itwdf = Math.sin((2 * Math.PI) / l);

    for (var p = 0; p < N; p += l) {
      var rtwdf_ = rtwdf;
      var itwdf_ = itwdf;

      for (var j = 0; j < s; j++) {
        var re = rtws[p + j];
        var ie = itws[p + j];

        var ro = rtws[p + j + s];
        var io = itws[p + j + s];

        var rx = rtwdf_ * ro - itwdf_ * io;

        io = rtwdf_ * io + itwdf_ * ro;
        ro = rx;

        rtws[p + j] = re + ro;
        itws[p + j] = ie + io;

        rtws[p + j + s] = re - ro;
        itws[p + j + s] = ie - io;

        /* jshint maxdepth : false */
        if (j !== l) {
          rx = rtwdf * rtwdf_ - itwdf * itwdf_;

          itwdf_ = rtwdf * itwdf_ + itwdf * rtwdf_;
          rtwdf_ = rx;
        }
      }
    }
  }
};

FFTM.prototype.guessLen13b = function guessLen13b(n, m) {
  var N = Math.max(m, n) | 1;
  var odd = N & 1;
  var i = 0;
  for (N = (N / 2) | 0; N; N = N >>> 1) {
    i++;
  }

  return 1 << (i + 1 + odd);
};

FFTM.prototype.conjugate = function conjugate(rws, iws, N) {
  if (N <= 1) return;

  for (var i = 0; i < N / 2; i++) {
    var t = rws[i];

    rws[i] = rws[N - i - 1];
    rws[N - i - 1] = t;

    t = iws[i];

    iws[i] = -iws[N - i - 1];
    iws[N - i - 1] = -t;
  }
};

FFTM.prototype.normalize13b = function normalize13b(ws, N) {
  var carry = 0;
  for (var i = 0; i < N / 2; i++) {
    var w =
      Math.round(ws[2 * i + 1] / N) * 0x2000 +
      Math.round(ws[2 * i] / N) +
      carry;

    ws[i] = w & 0x3ffffff;

    if (w < 0x4000000) {
      carry = 0;
    } else {
      carry = (w / 0x4000000) | 0;
    }
  }

  return ws;
};

FFTM.prototype.convert13b = function convert13b(ws, len, rws, N) {
  var carry = 0;
  for (var i = 0; i < len; i++) {
    carry = carry + (ws[i] | 0);

    rws[2 * i] = carry & 0x1fff;
    carry = carry >>> 13;
    rws[2 * i + 1] = carry & 0x1fff;
    carry = carry >>> 13;
  }

  // Pad with zeroes
  for (i = 2 * len; i < N; ++i) {
    rws[i] = 0;
  }

  assert(carry === 0);
  assert((carry & ~0x1fff) === 0);
};

FFTM.prototype.stub = function stub(N) {
  var ph = new Array(N);
  for (var i = 0; i < N; i++) {
    ph[i] = 0;
  }

  return ph;
};

FFTM.prototype.mulp = function mulp(x, y, out) {
  var N = 2 * this.guessLen13b(x.length, y.length);

  var rbt = this.makeRBT(N);

  var _ = this.stub(N);

  var rws = new Array(N);
  var rwst = new Array(N);
  var iwst = new Array(N);

  var nrws = new Array(N);
  var nrwst = new Array(N);
  var niwst = new Array(N);

  var rmws = out.words;
  rmws.length = N;

  this.convert13b(x.words, x.length, rws, N);
  this.convert13b(y.words, y.length, nrws, N);

  this.transform(rws, _, rwst, iwst, N, rbt);
  this.transform(nrws, _, nrwst, niwst, N, rbt);

  for (var i = 0; i < N; i++) {
    var rx = rwst[i] * nrwst[i] - iwst[i] * niwst[i];
    iwst[i] = rwst[i] * niwst[i] + iwst[i] * nrwst[i];
    rwst[i] = rx;
  }

  this.conjugate(rwst, iwst, N);
  this.transform(rwst, iwst, rmws, _, N, rbt);
  this.conjugate(rmws, _, N);
  this.normalize13b(rmws, N);

  out.negative = x.negative ^ y.negative;
  out.length = x.length + y.length;
  return out._strip();
};

// Multiply `this` by `num`
BN.prototype.mul = function mul(num) {
  var out = new BN(null);
  out.words = new Array(this.length + num.length);
  return this.mulTo(num, out);
};

// Multiply employing FFT
BN.prototype.mulf = function mulf(num) {
  var out = new BN(null);
  out.words = new Array(this.length + num.length);
  return jumboMulTo(this, num, out);
};

// In-place Multiplication
BN.prototype.imul = function imul(num) {
  return this.clone().mulTo(num, this);
};

BN.prototype.imuln = function imuln(num) {
  var isNegNum = num < 0;
  if (isNegNum) num = -num;

  assert(typeof num === "number");
  assert(num < 0x4000000);

  // Carry
  var carry = 0;
  for (var i = 0; i < this.length; i++) {
    var w = (this.words[i] | 0) * num;
    var lo = (w & 0x3ffffff) + (carry & 0x3ffffff);
    carry >>= 26;
    carry += (w / 0x4000000) | 0;
    // NOTE: lo is 27bit maximum
    carry += lo >>> 26;
    this.words[i] = lo & 0x3ffffff;
  }

  if (carry !== 0) {
    this.words[i] = carry;
    this.length++;
  }

  return isNegNum ? this.ineg() : this;
};

BN.prototype.muln = function muln(num) {
  return this.clone().imuln(num);
};

// `this` * `this`
BN.prototype.sqr = function sqr() {
  return this.mul(this);
};

// `this` * `this` in-place
BN.prototype.isqr = function isqr() {
  return this.imul(this.clone());
};

// Math.pow(`this`, `num`)
BN.prototype.pow = function pow(num) {
  var w = toBitArray(num);
  if (w.length === 0) return new BN(1);

  // Skip leading zeroes
  var res = this;
  for (var i = 0; i < w.length; i++, res = res.sqr()) {
    if (w[i] !== 0) break;
  }

  if (++i < w.length) {
    for (var q = res.sqr(); i < w.length; i++, q = q.sqr()) {
      if (w[i] === 0) continue;

      res = res.mul(q);
    }
  }

  return res;
};

// Shift-left in-place
BN.prototype.iushln = function iushln(bits) {
  assert(typeof bits === "number" && bits >= 0);
  var r = bits % 26;
  var s = (bits - r) / 26;
  var carryMask = (0x3ffffff >>> (26 - r)) << (26 - r);
  var i;

  if (r !== 0) {
    var carry = 0;

    for (i = 0; i < this.length; i++) {
      var newCarry = this.words[i] & carryMask;
      var c = ((this.words[i] | 0) - newCarry) << r;
      this.words[i] = c | carry;
      carry = newCarry >>> (26 - r);
    }

    if (carry) {
      this.words[i] = carry;
      this.length++;
    }
  }

  if (s !== 0) {
    for (i = this.length - 1; i >= 0; i--) {
      this.words[i + s] = this.words[i];
    }

    for (i = 0; i < s; i++) {
      this.words[i] = 0;
    }

    this.length += s;
  }

  return this._strip();
};

BN.prototype.ishln = function ishln(bits) {
  // TODO(indutny): implement me
  assert(this.negative === 0);
  return this.iushln(bits);
};

// Shift-right in-place
// NOTE: `hint` is a lowest bit before trailing zeroes
// NOTE: if `extended` is present - it will be filled with destroyed bits
BN.prototype.iushrn = function iushrn(bits, hint, extended) {
  assert(typeof bits === "number" && bits >= 0);
  var h;
  if (hint) {
    h = (hint - (hint % 26)) / 26;
  } else {
    h = 0;
  }

  var r = bits % 26;
  var s = Math.min((bits - r) / 26, this.length);
  var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r);
  var maskedWords = extended;

  h -= s;
  h = Math.max(0, h);

  // Extended mode, copy masked part
  if (maskedWords) {
    for (var i = 0; i < s; i++) {
      maskedWords.words[i] = this.words[i];
    }
    maskedWords.length = s;
  }

  if (s === 0) {
    // No-op, we should not move anything at all
  } else if (this.length > s) {
    this.length -= s;
    for (i = 0; i < this.length; i++) {
      this.words[i] = this.words[i + s];
    }
  } else {
    this.words[0] = 0;
    this.length = 1;
  }

  var carry = 0;
  for (i = this.length - 1; i >= 0 && (carry !== 0 || i >= h); i--) {
    var word = this.words[i] | 0;
    this.words[i] = (carry << (26 - r)) | (word >>> r);
    carry = word & mask;
  }

  // Push carried bits as a mask
  if (maskedWords && carry !== 0) {
    maskedWords.words[maskedWords.length++] = carry;
  }

  if (this.length === 0) {
    this.words[0] = 0;
    this.length = 1;
  }

  return this._strip();
};

BN.prototype.ishrn = function ishrn(bits, hint, extended) {
  // TODO(indutny): implement me
  assert(this.negative === 0);
  return this.iushrn(bits, hint, extended);
};

// Shift-left
BN.prototype.shln = function shln(bits) {
  return this.clone().ishln(bits);
};

BN.prototype.ushln = function ushln(bits) {
  return this.clone().iushln(bits);
};

// Shift-right
BN.prototype.shrn = function shrn(bits) {
  return this.clone().ishrn(bits);
};

BN.prototype.ushrn = function ushrn(bits) {
  return this.clone().iushrn(bits);
};

// Test if n bit is set
BN.prototype.testn = function testn(bit) {
  assert(typeof bit === "number" && bit >= 0);
  var r = bit % 26;
  var s = (bit - r) / 26;
  var q = 1 << r;

  // Fast case: bit is much higher than all existing words
  if (this.length <= s) return false;

  // Check bit and return
  var w = this.words[s];

  return !!(w & q);
};

// Return only lowers bits of number (in-place)
BN.prototype.imaskn = function imaskn(bits) {
  assert(typeof bits === "number" && bits >= 0);
  var r = bits % 26;
  var s = (bits - r) / 26;

  assert(this.negative === 0, "imaskn works only with positive numbers");

  if (this.length <= s) {
    return this;
  }

  if (r !== 0) {
    s++;
  }
  this.length = Math.min(s, this.length);

  if (r !== 0) {
    var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r);
    this.words[this.length - 1] &= mask;
  }

  return this._strip();
};

// Return only lowers bits of number
BN.prototype.maskn = function maskn(bits) {
  return this.clone().imaskn(bits);
};

// Add plain number `num` to `this`
BN.prototype.iaddn = function iaddn(num) {
  assert(typeof num === "number");
  assert(num < 0x4000000);
  if (num < 0) return this.isubn(-num);

  // Possible sign change
  if (this.negative !== 0) {
    if (this.length === 1 && (this.words[0] | 0) <= num) {
      this.words[0] = num - (this.words[0] | 0);
      this.negative = 0;
      return this;
    }

    this.negative = 0;
    this.isubn(num);
    this.negative = 1;
    return this;
  }

  // Add without checks
  return this._iaddn(num);
};

BN.prototype._iaddn = function _iaddn(num) {
  this.words[0] += num;

  // Carry
  for (var i = 0; i < this.length && this.words[i] >= 0x4000000; i++) {
    this.words[i] -= 0x4000000;
    if (i === this.length - 1) {
      this.words[i + 1] = 1;
    } else {
      this.words[i + 1]++;
    }
  }
  this.length = Math.max(this.length, i + 1);

  return this;
};

// Subtract plain number `num` from `this`
BN.prototype.isubn = function isubn(num) {
  assert(typeof num === "number");
  assert(num < 0x4000000);
  if (num < 0) return this.iaddn(-num);

  if (this.negative !== 0) {
    this.negative = 0;
    this.iaddn(num);
    this.negative = 1;
    return this;
  }

  this.words[0] -= num;

  if (this.length === 1 && this.words[0] < 0) {
    this.words[0] = -this.words[0];
    this.negative = 1;
  } else {
    // Carry
    for (var i = 0; i < this.length && this.words[i] < 0; i++) {
      this.words[i] += 0x4000000;
      this.words[i + 1] -= 1;
    }
  }

  return this._strip();
};

BN.prototype.addn = function addn(num) {
  return this.clone().iaddn(num);
};

BN.prototype.subn = function subn(num) {
  return this.clone().isubn(num);
};

BN.prototype.iabs = function iabs() {
  this.negative = 0;

  return this;
};

BN.prototype.abs = function abs() {
  return this.clone().iabs();
};

BN.prototype._ishlnsubmul = function _ishlnsubmul(num, mul, shift) {
  var len = num.length + shift;
  var i;

  this._expand(len);

  var w;
  var carry = 0;
  for (i = 0; i < num.length; i++) {
    w = (this.words[i + shift] | 0) + carry;
    var right = (num.words[i] | 0) * mul;
    w -= right & 0x3ffffff;
    carry = (w >> 26) - ((right / 0x4000000) | 0);
    this.words[i + shift] = w & 0x3ffffff;
  }
  for (; i < this.length - shift; i++) {
    w = (this.words[i + shift] | 0) + carry;
    carry = w >> 26;
    this.words[i + shift] = w & 0x3ffffff;
  }

  if (carry === 0) return this._strip();

  // Subtraction overflow
  assert(carry === -1);
  carry = 0;
  for (i = 0; i < this.length; i++) {
    w = -(this.words[i] | 0) + carry;
    carry = w >> 26;
    this.words[i] = w & 0x3ffffff;
  }
  this.negative = 1;

  return this._strip();
};

BN.prototype._wordDiv = function _wordDiv(num, mode) {
  var shift = this.length - num.length;

  var a = this.clone();
  var b = num;

  // Normalize
  var bhi = b.words[b.length - 1] | 0;
  var bhiBits = this._countBits(bhi);
  shift = 26 - bhiBits;
  if (shift !== 0) {
    b = b.ushln(shift);
    a.iushln(shift);
    bhi = b.words[b.length - 1] | 0;
  }

  // Initialize quotient
  var m = a.length - b.length;
  var q;

  if (mode !== "mod") {
    q = new BN(null);
    q.length = m + 1;
    q.words = new Array(q.length);
    for (var i = 0; i < q.length; i++) {
      q.words[i] = 0;
    }
  }

  var diff = a.clone()._ishlnsubmul(b, 1, m);
  if (diff.negative === 0) {
    a = diff;
    if (q) {
      q.words[m] = 1;
    }
  }

  for (var j = m - 1; j >= 0; j--) {
    var qj =
      (a.words[b.length + j] | 0) * 0x4000000 + (a.words[b.length + j - 1] | 0);

    // NOTE: (qj / bhi) is (0x3ffffff * 0x4000000 + 0x3ffffff) / 0x2000000 max
    // (0x7ffffff)
    qj = Math.min((qj / bhi) | 0, 0x3ffffff);

    a._ishlnsubmul(b, qj, j);
    while (a.negative !== 0) {
      qj--;
      a.negative = 0;
      a._ishlnsubmul(b, 1, j);
      if (!a.isZero()) {
        a.negative ^= 1;
      }
    }
    if (q) {
      q.words[j] = qj;
    }
  }
  if (q) {
    q._strip();
  }
  a._strip();

  // Denormalize
  if (mode !== "div" && shift !== 0) {
    a.iushrn(shift);
  }

  return {
    div: q || null,
    mod: a,
  };
};

// NOTE: 1) `mode` can be set to `mod` to request mod only,
//       to `div` to request div only, or be absent to
//       request both div & mod
//       2) `positive` is true if unsigned mod is requested
BN.prototype.divmod = function divmod(num, mode, positive) {
  assert(!num.isZero());

  if (this.isZero()) {
    return {
      div: new BN(0),
      mod: new BN(0),
    };
  }

  var div, mod, res;
  if (this.negative !== 0 && num.negative === 0) {
    res = this.neg().divmod(num, mode);

    if (mode !== "mod") {
      div = res.div.neg();
    }

    if (mode !== "div") {
      mod = res.mod.neg();
      if (positive && mod.negative !== 0) {
        mod.iadd(num);
      }
    }

    return {
      div: div,
      mod: mod,
    };
  }

  if (this.negative === 0 && num.negative !== 0) {
    res = this.divmod(num.neg(), mode);

    if (mode !== "mod") {
      div = res.div.neg();
    }

    return {
      div: div,
      mod: res.mod,
    };
  }

  if ((this.negative & num.negative) !== 0) {
    res = this.neg().divmod(num.neg(), mode);

    if (mode !== "div") {
      mod = res.mod.neg();
      if (positive && mod.negative !== 0) {
        mod.isub(num);
      }
    }

    return {
      div: res.div,
      mod: mod,
    };
  }

  // Both numbers are positive at this point

  // Strip both numbers to approximate shift value
  if (num.length > this.length || this.cmp(num) < 0) {
    return {
      div: new BN(0),
      mod: this,
    };
  }

  // Very short reduction
  if (num.length === 1) {
    if (mode === "div") {
      return {
        div: this.divn(num.words[0]),
        mod: null,
      };
    }

    if (mode === "mod") {
      return {
        div: null,
        mod: new BN(this.modrn(num.words[0])),
      };
    }

    return {
      div: this.divn(num.words[0]),
      mod: new BN(this.modrn(num.words[0])),
    };
  }

  return this._wordDiv(num, mode);
};

// Find `this` / `num`
BN.prototype.div = function div(num) {
  return this.divmod(num, "div", false).div;
};

// Find `this` % `num`
BN.prototype.mod = function mod(num) {
  return this.divmod(num, "mod", false).mod;
};

BN.prototype.umod = function umod(num) {
  return this.divmod(num, "mod", true).mod;
};

// Find Round(`this` / `num`)
BN.prototype.divRound = function divRound(num) {
  var dm = this.divmod(num);

  // Fast case - exact division
  if (dm.mod.isZero()) return dm.div;

  var mod = dm.div.negative !== 0 ? dm.mod.isub(num) : dm.mod;

  var half = num.ushrn(1);
  var r2 = num.andln(1);
  var cmp = mod.cmp(half);

  // Round down
  if (cmp < 0 || (r2 === 1 && cmp === 0)) return dm.div;

  // Round up
  return dm.div.negative !== 0 ? dm.div.isubn(1) : dm.div.iaddn(1);
};

BN.prototype.modrn = function modrn(num) {
  var isNegNum = num < 0;
  if (isNegNum) num = -num;

  assert(num <= 0x3ffffff);
  var p = (1 << 26) % num;

  var acc = 0;
  for (var i = this.length - 1; i >= 0; i--) {
    acc = (p * acc + (this.words[i] | 0)) % num;
  }

  return isNegNum ? -acc : acc;
};

// WARNING: DEPRECATED
BN.prototype.modn = function modn(num) {
  return this.modrn(num);
};

// In-place division by number
BN.prototype.idivn = function idivn(num) {
  var isNegNum = num < 0;
  if (isNegNum) num = -num;

  assert(num <= 0x3ffffff);

  var carry = 0;
  for (var i = this.length - 1; i >= 0; i--) {
    var w = (this.words[i] | 0) + carry * 0x4000000;
    this.words[i] = (w / num) | 0;
    carry = w % num;
  }

  this._strip();
  return isNegNum ? this.ineg() : this;
};

BN.prototype.divn = function divn(num) {
  return this.clone().idivn(num);
};

BN.prototype.egcd = function egcd(p) {
  assert(p.negative === 0);
  assert(!p.isZero());

  var x = this;
  var y = p.clone();

  if (x.negative !== 0) {
    x = x.umod(p);
  } else {
    x = x.clone();
  }

  // A * x + B * y = x
  var A = new BN(1);
  var B = new BN(0);

  // C * x + D * y = y
  var C = new BN(0);
  var D = new BN(1);

  var g = 0;

  while (x.isEven() && y.isEven()) {
    x.iushrn(1);
    y.iushrn(1);
    ++g;
  }

  var yp = y.clone();
  var xp = x.clone();

  while (!x.isZero()) {
    for (var i = 0, im = 1; (x.words[0] & im) === 0 && i < 26; ++i, im <<= 1);
    if (i > 0) {
      x.iushrn(i);
      while (i-- > 0) {
        if (A.isOdd() || B.isOdd()) {
          A.iadd(yp);
          B.isub(xp);
        }

        A.iushrn(1);
        B.iushrn(1);
      }
    }

    for (var j = 0, jm = 1; (y.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1);
    if (j > 0) {
      y.iushrn(j);
      while (j-- > 0) {
        if (C.isOdd() || D.isOdd()) {
          C.iadd(yp);
          D.isub(xp);
        }

        C.iushrn(1);
        D.iushrn(1);
      }
    }

    if (x.cmp(y) >= 0) {
      x.isub(y);
      A.isub(C);
      B.isub(D);
    } else {
      y.isub(x);
      C.isub(A);
      D.isub(B);
    }
  }

  return {
    a: C,
    b: D,
    gcd: y.iushln(g),
  };
};

// This is reduced incarnation of the binary EEA
// above, designated to invert members of the
// _prime_ fields F(p) at a maximal speed
BN.prototype._invmp = function _invmp(p) {
  assert(p.negative === 0);
  assert(!p.isZero());

  var a = this;
  var b = p.clone();

  if (a.negative !== 0) {
    a = a.umod(p);
  } else {
    a = a.clone();
  }

  var x1 = new BN(1);
  var x2 = new BN(0);

  var delta = b.clone();

  while (a.cmpn(1) > 0 && b.cmpn(1) > 0) {
    for (var i = 0, im = 1; (a.words[0] & im) === 0 && i < 26; ++i, im <<= 1);
    if (i > 0) {
      a.iushrn(i);
      while (i-- > 0) {
        if (x1.isOdd()) {
          x1.iadd(delta);
        }

        x1.iushrn(1);
      }
    }

    for (var j = 0, jm = 1; (b.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1);
    if (j > 0) {
      b.iushrn(j);
      while (j-- > 0) {
        if (x2.isOdd()) {
          x2.iadd(delta);
        }

        x2.iushrn(1);
      }
    }

    if (a.cmp(b) >= 0) {
      a.isub(b);
      x1.isub(x2);
    } else {
      b.isub(a);
      x2.isub(x1);
    }
  }

  var res;
  if (a.cmpn(1) === 0) {
    res = x1;
  } else {
    res = x2;
  }

  if (res.cmpn(0) < 0) {
    res.iadd(p);
  }

  return res;
};

BN.prototype.gcd = function gcd(num) {
  if (this.isZero()) return num.abs();
  if (num.isZero()) return this.abs();

  var a = this.clone();
  var b = num.clone();
  a.negative = 0;
  b.negative = 0;

  // Remove common factor of two
  for (var shift = 0; a.isEven() && b.isEven(); shift++) {
    a.iushrn(1);
    b.iushrn(1);
  }

  do {
    while (a.isEven()) {
      a.iushrn(1);
    }
    while (b.isEven()) {
      b.iushrn(1);
    }

    var r = a.cmp(b);
    if (r < 0) {
      // Swap `a` and `b` to make `a` always bigger than `b`
      var t = a;
      a = b;
      b = t;
    } else if (r === 0 || b.cmpn(1) === 0) {
      break;
    }

    a.isub(b);
  } while (true);

  return b.iushln(shift);
};

// Invert number in the field F(num)
BN.prototype.invm = function invm(num) {
  return this.egcd(num).a.umod(num);
};

BN.prototype.isEven = function isEven() {
  return (this.words[0] & 1) === 0;
};

BN.prototype.isOdd = function isOdd() {
  return (this.words[0] & 1) === 1;
};

// And first word and num
BN.prototype.andln = function andln(num) {
  return this.words[0] & num;
};

// Increment at the bit position in-line
BN.prototype.bincn = function bincn(bit) {
  assert(typeof bit === "number");
  var r = bit % 26;
  var s = (bit - r) / 26;
  var q = 1 << r;

  // Fast case: bit is much higher than all existing words
  if (this.length <= s) {
    this._expand(s + 1);
    this.words[s] |= q;
    return this;
  }

  // Add bit and propagate, if needed
  var carry = q;
  for (var i = s; carry !== 0 && i < this.length; i++) {
    var w = this.words[i] | 0;
    w += carry;
    carry = w >>> 26;
    w &= 0x3ffffff;
    this.words[i] = w;
  }
  if (carry !== 0) {
    this.words[i] = carry;
    this.length++;
  }
  return this;
};

BN.prototype.isZero = function isZero() {
  return this.length === 1 && this.words[0] === 0;
};

BN.prototype.cmpn = function cmpn(num) {
  var negative = num < 0;

  if (this.negative !== 0 && !negative) return -1;
  if (this.negative === 0 && negative) return 1;

  this._strip();

  var res;
  if (this.length > 1) {
    res = 1;
  } else {
    if (negative) {
      num = -num;
    }

    assert(num <= 0x3ffffff, "Number is too big");

    var w = this.words[0] | 0;
    res = w === num ? 0 : w < num ? -1 : 1;
  }
  if (this.negative !== 0) return -res | 0;
  return res;
};

// Compare two numbers and return:
// 1 - if `this` > `num`
// 0 - if `this` == `num`
// -1 - if `this` < `num`
BN.prototype.cmp = function cmp(num) {
  if (this.negative !== 0 && num.negative === 0) return -1;
  if (this.negative === 0 && num.negative !== 0) return 1;

  var res = this.ucmp(num);
  if (this.negative !== 0) return -res | 0;
  return res;
};

// Unsigned comparison
BN.prototype.ucmp = function ucmp(num) {
  // At this point both numbers have the same sign
  if (this.length > num.length) return 1;
  if (this.length < num.length) return -1;

  var res = 0;
  for (var i = this.length - 1; i >= 0; i--) {
    var a = this.words[i] | 0;
    var b = num.words[i] | 0;

    if (a === b) continue;
    if (a < b) {
      res = -1;
    } else if (a > b) {
      res = 1;
    }
    break;
  }
  return res;
};

BN.prototype.gtn = function gtn(num) {
  return this.cmpn(num) === 1;
};

BN.prototype.gt = function gt(num) {
  return this.cmp(num) === 1;
};

BN.prototype.gten = function gten(num) {
  return this.cmpn(num) >= 0;
};

BN.prototype.gte = function gte(num) {
  return this.cmp(num) >= 0;
};

BN.prototype.ltn = function ltn(num) {
  return this.cmpn(num) === -1;
};

BN.prototype.lt = function lt(num) {
  return this.cmp(num) === -1;
};

BN.prototype.lten = function lten(num) {
  return this.cmpn(num) <= 0;
};

BN.prototype.lte = function lte(num) {
  return this.cmp(num) <= 0;
};

BN.prototype.eqn = function eqn(num) {
  return this.cmpn(num) === 0;
};

BN.prototype.eq = function eq(num) {
  return this.cmp(num) === 0;
};

//
// A reduce context, could be using montgomery or something better, depending
// on the `m` itself.
//
BN.red = function red(num) {
  return new Red(num);
};

BN.prototype.toRed = function toRed(ctx) {
  assert(!this.red, "Already a number in reduction context");
  assert(this.negative === 0, "red works only with positives");
  return ctx.convertTo(this)._forceRed(ctx);
};

BN.prototype.fromRed = function fromRed() {
  assert(this.red, "fromRed works only with numbers in reduction context");
  return this.red.convertFrom(this);
};

BN.prototype._forceRed = function _forceRed(ctx) {
  this.red = ctx;
  return this;
};

BN.prototype.forceRed = function forceRed(ctx) {
  assert(!this.red, "Already a number in reduction context");
  return this._forceRed(ctx);
};

BN.prototype.redAdd = function redAdd(num) {
  assert(this.red, "redAdd works only with red numbers");
  return this.red.add(this, num);
};

BN.prototype.redIAdd = function redIAdd(num) {
  assert(this.red, "redIAdd works only with red numbers");
  return this.red.iadd(this, num);
};

BN.prototype.redSub = function redSub(num) {
  assert(this.red, "redSub works only with red numbers");
  return this.red.sub(this, num);
};

BN.prototype.redISub = function redISub(num) {
  assert(this.red, "redISub works only with red numbers");
  return this.red.isub(this, num);
};

BN.prototype.redShl = function redShl(num) {
  assert(this.red, "redShl works only with red numbers");
  return this.red.shl(this, num);
};

BN.prototype.redMul = function redMul(num) {
  assert(this.red, "redMul works only with red numbers");
  this.red._verify2(this, num);
  return this.red.mul(this, num);
};

BN.prototype.redIMul = function redIMul(num) {
  assert(this.red, "redMul works only with red numbers");
  this.red._verify2(this, num);
  return this.red.imul(this, num);
};

BN.prototype.redSqr = function redSqr() {
  assert(this.red, "redSqr works only with red numbers");
  this.red._verify1(this);
  return this.red.sqr(this);
};

BN.prototype.redISqr = function redISqr() {
  assert(this.red, "redISqr works only with red numbers");
  this.red._verify1(this);
  return this.red.isqr(this);
};

// Square root over p
BN.prototype.redSqrt = function redSqrt() {
  assert(this.red, "redSqrt works only with red numbers");
  this.red._verify1(this);
  return this.red.sqrt(this);
};

BN.prototype.redInvm = function redInvm() {
  assert(this.red, "redInvm works only with red numbers");
  this.red._verify1(this);
  return this.red.invm(this);
};

// Return negative clone of `this` % `red modulo`
BN.prototype.redNeg = function redNeg() {
  assert(this.red, "redNeg works only with red numbers");
  this.red._verify1(this);
  return this.red.neg(this);
};

BN.prototype.redPow = function redPow(num) {
  assert(this.red && !num.red, "redPow(normalNum)");
  this.red._verify1(this);
  return this.red.pow(this, num);
};

// Prime numbers with efficient reduction
var primes = {
  k256: null,
  p224: null,
  p192: null,
  p25519: null,
};

// Pseudo-Mersenne prime
function MPrime(name, p) {
  // P = 2 ^ N - K
  this.name = name;
  this.p = new BN(p, 16);
  this.n = this.p.bitLength();
  this.k = new BN(1).iushln(this.n).isub(this.p);

  this.tmp = this._tmp();
}

MPrime.prototype._tmp = function _tmp() {
  var tmp = new BN(null);
  tmp.words = new Array(Math.ceil(this.n / 13));
  return tmp;
};

MPrime.prototype.ireduce = function ireduce(num) {
  // Assumes that `num` is less than `P^2`
  // num = HI * (2 ^ N - K) + HI * K + LO = HI * K + LO (mod P)
  var r = num;
  var rlen;

  do {
    this.split(r, this.tmp);
    r = this.imulK(r);
    r = r.iadd(this.tmp);
    rlen = r.bitLength();
  } while (rlen > this.n);

  var cmp = rlen < this.n ? -1 : r.ucmp(this.p);
  if (cmp === 0) {
    r.words[0] = 0;
    r.length = 1;
  } else if (cmp > 0) {
    r.isub(this.p);
  } else {
    if (r.strip !== undefined) {
      // r is a BN v4 instance
      r.strip();
    } else {
      // r is a BN v5 instance
      r._strip();
    }
  }

  return r;
};

MPrime.prototype.split = function split(input, out) {
  input.iushrn(this.n, 0, out);
};

MPrime.prototype.imulK = function imulK(num) {
  return num.imul(this.k);
};

function K256() {
  MPrime.call(
    this,
    "k256",
    "ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f",
  );
}
inherits(K256, MPrime);

K256.prototype.split = function split(input, output) {
  // 256 = 9 * 26 + 22
  var mask = 0x3fffff;

  var outLen = Math.min(input.length, 9);
  for (var i = 0; i < outLen; i++) {
    output.words[i] = input.words[i];
  }
  output.length = outLen;

  if (input.length <= 9) {
    input.words[0] = 0;
    input.length = 1;
    return;
  }

  // Shift by 9 limbs
  var prev = input.words[9];
  output.words[output.length++] = prev & mask;

  for (i = 10; i < input.length; i++) {
    var next = input.words[i] | 0;
    input.words[i - 10] = ((next & mask) << 4) | (prev >>> 22);
    prev = next;
  }
  prev >>>= 22;
  input.words[i - 10] = prev;
  if (prev === 0 && input.length > 10) {
    input.length -= 10;
  } else {
    input.length -= 9;
  }
};

K256.prototype.imulK = function imulK(num) {
  // K = 0x1000003d1 = [ 0x40, 0x3d1 ]
  num.words[num.length] = 0;
  num.words[num.length + 1] = 0;
  num.length += 2;

  // bounded at: 0x40 * 0x3ffffff + 0x3d0 = 0x100000390
  var lo = 0;
  for (var i = 0; i < num.length; i++) {
    var w = num.words[i] | 0;
    lo += w * 0x3d1;
    num.words[i] = lo & 0x3ffffff;
    lo = w * 0x40 + ((lo / 0x4000000) | 0);
  }

  // Fast length reduction
  if (num.words[num.length - 1] === 0) {
    num.length--;
    if (num.words[num.length - 1] === 0) {
      num.length--;
    }
  }
  return num;
};

function P224() {
  MPrime.call(
    this,
    "p224",
    "ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001",
  );
}
inherits(P224, MPrime);

function P192() {
  MPrime.call(
    this,
    "p192",
    "ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff",
  );
}
inherits(P192, MPrime);

function P25519() {
  // 2 ^ 255 - 19
  MPrime.call(
    this,
    "25519",
    "7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed",
  );
}
inherits(P25519, MPrime);

P25519.prototype.imulK = function imulK(num) {
  // K = 0x13
  var carry = 0;
  for (var i = 0; i < num.length; i++) {
    var hi = (num.words[i] | 0) * 0x13 + carry;
    var lo = hi & 0x3ffffff;
    hi >>>= 26;

    num.words[i] = lo;
    carry = hi;
  }
  if (carry !== 0) {
    num.words[num.length++] = carry;
  }
  return num;
};

// Exported mostly for testing purposes, use plain name instead
BN._prime = function prime(name) {
  // Cached version of prime
  if (primes[name]) return primes[name];

  var prime;
  if (name === "k256") {
    prime = new K256();
  } else if (name === "p224") {
    prime = new P224();
  } else if (name === "p192") {
    prime = new P192();
  } else if (name === "p25519") {
    prime = new P25519();
  } else {
    throw new Error("Unknown prime " + name);
  }
  primes[name] = prime;

  return prime;
};

//
// Base reduction engine
//
function Red(m) {
  if (typeof m === "string") {
    var prime = BN._prime(m);
    this.m = prime.p;
    this.prime = prime;
  } else {
    assert(m.gtn(1), "modulus must be greater than 1");
    this.m = m;
    this.prime = null;
  }
}

Red.prototype._verify1 = function _verify1(a) {
  assert(a.negative === 0, "red works only with positives");
  assert(a.red, "red works only with red numbers");
};

Red.prototype._verify2 = function _verify2(a, b) {
  assert((a.negative | b.negative) === 0, "red works only with positives");
  assert(a.red && a.red === b.red, "red works only with red numbers");
};

Red.prototype.imod = function imod(a) {
  if (this.prime) return this.prime.ireduce(a)._forceRed(this);

  move(a, a.umod(this.m)._forceRed(this));
  return a;
};

Red.prototype.neg = function neg(a) {
  if (a.isZero()) {
    return a.clone();
  }

  return this.m.sub(a)._forceRed(this);
};

Red.prototype.add = function add(a, b) {
  this._verify2(a, b);

  var res = a.add(b);
  if (res.cmp(this.m) >= 0) {
    res.isub(this.m);
  }
  return res._forceRed(this);
};

Red.prototype.iadd = function iadd(a, b) {
  this._verify2(a, b);

  var res = a.iadd(b);
  if (res.cmp(this.m) >= 0) {
    res.isub(this.m);
  }
  return res;
};

Red.prototype.sub = function sub(a, b) {
  this._verify2(a, b);

  var res = a.sub(b);
  if (res.cmpn(0) < 0) {
    res.iadd(this.m);
  }
  return res._forceRed(this);
};

Red.prototype.isub = function isub(a, b) {
  this._verify2(a, b);

  var res = a.isub(b);
  if (res.cmpn(0) < 0) {
    res.iadd(this.m);
  }
  return res;
};

Red.prototype.shl = function shl(a, num) {
  this._verify1(a);
  return this.imod(a.ushln(num));
};

Red.prototype.imul = function imul(a, b) {
  this._verify2(a, b);
  return this.imod(a.imul(b));
};

Red.prototype.mul = function mul(a, b) {
  this._verify2(a, b);
  return this.imod(a.mul(b));
};

Red.prototype.isqr = function isqr(a) {
  return this.imul(a, a.clone());
};

Red.prototype.sqr = function sqr(a) {
  return this.mul(a, a);
};

Red.prototype.sqrt = function sqrt(a) {
  if (a.isZero()) return a.clone();

  var mod3 = this.m.andln(3);
  assert(mod3 % 2 === 1);

  // Fast case
  if (mod3 === 3) {
    var pow = this.m.add(new BN(1)).iushrn(2);
    return this.pow(a, pow);
  }

  // Tonelli-Shanks algorithm (Totally unoptimized and slow)
  //
  // Find Q and S, that Q * 2 ^ S = (P - 1)
  var q = this.m.subn(1);
  var s = 0;
  while (!q.isZero() && q.andln(1) === 0) {
    s++;
    q.iushrn(1);
  }
  assert(!q.isZero());

  var one = new BN(1).toRed(this);
  var nOne = one.redNeg();

  // Find quadratic non-residue
  // NOTE: Max is such because of generalized Riemann hypothesis.
  var lpow = this.m.subn(1).iushrn(1);
  var z = this.m.bitLength();
  z = new BN(2 * z * z).toRed(this);

  while (this.pow(z, lpow).cmp(nOne) !== 0) {
    z.redIAdd(nOne);
  }

  var c = this.pow(z, q);
  var r = this.pow(a, q.addn(1).iushrn(1));
  var t = this.pow(a, q);
  var m = s;
  while (t.cmp(one) !== 0) {
    var tmp = t;
    for (var i = 0; tmp.cmp(one) !== 0; i++) {
      tmp = tmp.redSqr();
    }
    assert(i < m);
    var b = this.pow(c, new BN(1).iushln(m - i - 1));

    r = r.redMul(b);
    c = b.redSqr();
    t = t.redMul(c);
    m = i;
  }

  return r;
};

Red.prototype.invm = function invm(a) {
  var inv = a._invmp(this.m);
  if (inv.negative !== 0) {
    inv.negative = 0;
    return this.imod(inv).redNeg();
  } else {
    return this.imod(inv);
  }
};

Red.prototype.pow = function pow(a, num) {
  if (num.isZero()) return new BN(1).toRed(this);
  if (num.cmpn(1) === 0) return a.clone();

  var windowSize = 4;
  var wnd = new Array(1 << windowSize);
  wnd[0] = new BN(1).toRed(this);
  wnd[1] = a;
  for (var i = 2; i < wnd.length; i++) {
    wnd[i] = this.mul(wnd[i - 1], a);
  }

  var res = wnd[0];
  var current = 0;
  var currentLen = 0;
  var start = num.bitLength() % 26;
  if (start === 0) {
    start = 26;
  }

  for (i = num.length - 1; i >= 0; i--) {
    var word = num.words[i];
    for (var j = start - 1; j >= 0; j--) {
      var bit = (word >> j) & 1;
      if (res !== wnd[0]) {
        res = this.sqr(res);
      }

      if (bit === 0 && current === 0) {
        currentLen = 0;
        continue;
      }

      current <<= 1;
      current |= bit;
      currentLen++;
      if (currentLen !== windowSize && (i !== 0 || j !== 0)) continue;

      res = this.mul(res, wnd[current]);
      currentLen = 0;
      current = 0;
    }
    start = 26;
  }

  return res;
};

Red.prototype.convertTo = function convertTo(num) {
  var r = num.umod(this.m);

  return r === num ? r.clone() : r;
};

Red.prototype.convertFrom = function convertFrom(num) {
  var res = num.clone();
  res.red = null;
  return res;
};

//
// Montgomery method engine
//

BN.mont = function mont(num) {
  return new Mont(num);
};

function Mont(m) {
  Red.call(this, m);

  this.shift = this.m.bitLength();
  if (this.shift % 26 !== 0) {
    this.shift += 26 - (this.shift % 26);
  }

  this.r = new BN(1).iushln(this.shift);
  this.r2 = this.imod(this.r.sqr());
  this.rinv = this.r._invmp(this.m);

  this.minv = this.rinv.mul(this.r).isubn(1).div(this.m);
  this.minv = this.minv.umod(this.r);
  this.minv = this.r.sub(this.minv);
}
inherits(Mont, Red);

Mont.prototype.convertTo = function convertTo(num) {
  return this.imod(num.ushln(this.shift));
};

Mont.prototype.convertFrom = function convertFrom(num) {
  var r = this.imod(num.mul(this.rinv));
  r.red = null;
  return r;
};

Mont.prototype.imul = function imul(a, b) {
  if (a.isZero() || b.isZero()) {
    a.words[0] = 0;
    a.length = 1;
    return a;
  }

  var t = a.imul(b);
  var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
  var u = t.isub(c).iushrn(this.shift);
  var res = u;

  if (u.cmp(this.m) >= 0) {
    res = u.isub(this.m);
  } else if (u.cmpn(0) < 0) {
    res = u.iadd(this.m);
  }

  return res._forceRed(this);
};

Mont.prototype.mul = function mul(a, b) {
  if (a.isZero() || b.isZero()) return new BN(0)._forceRed(this);

  var t = a.mul(b);
  var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
  var u = t.isub(c).iushrn(this.shift);
  var res = u;
  if (u.cmp(this.m) >= 0) {
    res = u.isub(this.m);
  } else if (u.cmpn(0) < 0) {
    res = u.iadd(this.m);
  }

  return res._forceRed(this);
};

Mont.prototype.invm = function invm(a) {
  // (AR)^-1 * R^2 = (A^-1 * R^-1) * R^2 = A^-1 * R
  var res = this.imod(a._invmp(this.m).mul(this.r2));
  return res._forceRed(this);
};