bn.js

(function (module, exports) {

'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) {
  // May be `new BN(bn)` ?
  if (number !== null &&
      typeof number === 'object' &&
      Array.isArray(number.words)) {
    return number;
  }

  this.sign = false;
  this.words = null;
  this.length = 0;

  // Reduction context
  this.red = null;

  if (base === 'le' || base === 'be') {
    endian = base;
    base = 10;
  }

  if (number !== null)
    this._init(number || 0, base || 10, endian || 'be');
}
if (typeof module === 'object')
  module.exports = BN;
else
  exports.BN = BN;

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

BN.prototype._init = function init(number, base, endian) {
  if (typeof number === 'number') {
    if (number < 0) {
      this.sign = true;
      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;
    }
    return;
  } else 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++;

  if (base === 16)
    this._parseHex(number, start);
  else
    this._parseBase(number, base, start);

  if (number[0] === '-')
    this.sign = true;

  this.strip();
};

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 off = 0;
  if (endian === 'be') {
    for (var i = number.length - 1, j = 0; i >= 0; i -= 3) {
      var 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 (var i = 0, j = 0; i < number.length; i += 3) {
      var 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 parseHex(str, start, end) {
  var r = 0;
  var len = Math.min(str.length, end);
  for (var i = start; i < len; i++) {
    var c = str.charCodeAt(i) - 48;

    r <<= 4;

    // 'a' - 'f'
    if (c >= 49 && c <= 54)
      r |= c - 49 + 0xa;

    // 'A' - 'F'
    else if (c >= 17 && c <= 22)
      r |= c - 17 + 0xa;

    // '0' - '9'
    else
      r |= c & 0xf;
  }
  return r;
}

BN.prototype._parseHex = function _parseHex(number, start) {
  // 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;

  // Scan 24-bit chunks and add them to the number
  var off = 0;
  for (var i = number.length - 6, j = 0; i >= start; i -= 6) {
    var w = parseHex(number, i, i + 6);
    this.words[j] |= (w << off) & 0x3ffffff;
    this.words[j + 1] |= w >>> (26 - off) & 0x3fffff;
    off += 24;
    if (off >= 26) {
      off -= 26;
      j++;
    }
  }
  if (i + 6 !== start) {
    var w = parseHex(number, start, i + 6);
    this.words[j] |= (w << off) & 0x3ffffff;
    this.words[j + 1] |= w >>> (26 - off) & 0x3fffff;
  }
  this.strip();
};

function parseBase(str, start, end, mul) {
  var r = 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)
      r += c - 49 + 0xa;

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

    // '0' - '9'
    else
      r += c;
  }
  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;
    var word = parseBase(number, i, number.length, base);

    for (var i = 0; i < mod; i++)
      pow *= base;
    this.imuln(pow);
    if (this.words[0] + word < 0x4000000)
      this.words[0] += word;
    else
      this._iaddn(word);
  }
};

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.sign = this.sign;
  dest.red = this.red;
};

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

// 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.sign = false;
  return this;
};

BN.prototype.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;
  if (base === 16 || base === 'hex') {
    var out = '';
    var off = 0;
    var padding = padding | 0 || 1;
    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;
      if (carry !== 0 || i !== this.length - 1)
        out = zeros[6 - word.length] + word + out;
      else
        out = word + out;
      off += 2;
      if (off >= 26) {
        off -= 26;
        i--;
      }
    }
    if (carry !== 0)
      out = carry.toString(16) + out;
    while (out.length % padding !== 0)
      out = '0' + out;
    if (this.sign)
      out = '-' + out;
    return out;
  } else 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];
    var out = '';
    var c = this.clone();
    c.sign = false;
    while (c.cmpn(0) !== 0) {
      var r = c.modn(groupBase).toString(base);
      c = c.idivn(groupBase);

      if (c.cmpn(0) !== 0)
        out = zeros[groupSize - r.length] + r + out;
      else
        out = r + out;
    }
    if (this.cmpn(0) === 0)
      out = '0' + out;
    if (this.sign)
      out = '-' + out;
    return out;
  } else {
    assert(false, 'Base should be between 2 and 36');
  }
};

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

BN.prototype.toArray = function toArray() {
  this.strip();
  var res = new Array(this.byteLength());
  res[0] = 0;

  var q = this.clone();
  for (var i = 0; q.cmpn(0) !== 0; i++) {
    var b = q.andln(0xff);
    q.ishrn(8);

    // Assume big-endian
    res[res.length - i - 1] = b;
  }

  return res;
};

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 hi = 0;
  var w = this.words[this.length - 1];
  var hi = this._countBits(w);
  return (this.length - 1) * 26 + hi;
};

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

// Return negative clone of `this`
BN.prototype.neg = function neg() {
  if (this.cmpn(0) === 0)
    return this.clone();

  var r = this.clone();
  r.sign = !this.sign;
  return r;
};


// Or `num` with `this` in-place
BN.prototype.ior = function ior(num) {
  this.sign = this.sign || num.sign;

  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();
};


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


// And `num` with `this` in-place
BN.prototype.iand = function iand(num) {
  this.sign = this.sign && num.sign;

  // 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();
};


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


// Xor `num` with `this` in-place
BN.prototype.ixor = function ixor(num) {
  this.sign = this.sign || num.sign;

  // 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();
};


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


// 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;

  while (this.length <= off)
    this.words[this.length++] = 0;

  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) {
  // negative + positive
  if (this.sign && !num.sign) {
    this.sign = false;
    var r = this.isub(num);
    this.sign = !this.sign;
    return this._normSign();

  // positive + negative
  } else if (!this.sign && num.sign) {
    num.sign = false;
    var r = this.isub(num);
    num.sign = true;
    return r._normSign();
  }

  // a.length > b.length
  var a;
  var 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++) {
    var r = a.words[i] + b.words[i] + carry;
    this.words[i] = r & 0x3ffffff;
    carry = r >>> 26;
  }
  for (; carry !== 0 && i < a.length; i++) {
    var r = a.words[i] + 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) {
  if (num.sign && !this.sign) {
    num.sign = false;
    var res = this.sub(num);
    num.sign = true;
    return res;
  } else if (!num.sign && this.sign) {
    this.sign = false;
    var res = num.sub(this);
    this.sign = true;
    return res;
  }

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

// Subtract `num` from `this` in-place
BN.prototype.isub = function isub(num) {
  // this - (-num) = this + num
  if (num.sign) {
    num.sign = false;
    var r = this.iadd(num);
    num.sign = true;
    return r._normSign();

  // -this - num = -(this + num)
  } else if (this.sign) {
    this.sign = false;
    this.iadd(num);
    this.sign = true;
    return this._normSign();
  }

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

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

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

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

  return this.strip();
};

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

/*
// NOTE: This could be potentionally used to generate loop-less multiplications
function _genCombMulTo(alen, blen) {
  var len = alen + blen - 1;
  var src = [
    'var a = this.words, b = num.words, o = out.words, c = 0, w, ' +
        'mask = 0x3ffffff, shift = 0x4000000;',
    'out.length = ' + len + ';'
  ];
  for (var k = 0; k < len; k++) {
    var minJ = Math.max(0, k - alen + 1);
    var maxJ = Math.min(k, blen - 1);

    for (var j = minJ; j <= maxJ; j++) {
      var i = k - j;
      var mul = 'a[' + i + '] * b[' + j + ']';

      if (j === minJ) {
        src.push('w = ' + mul + ' + c;');
        src.push('c = (w / shift) | 0;');
      } else {
        src.push('w += ' + mul + ';');
        src.push('c += (w / shift) | 0;');
      }
      src.push('w &= mask;');
    }
    src.push('o[' + k + '] = w;');
  }
  src.push('if (c !== 0) {',
           '  o[' + k + '] = c;',
           '  out.length++;',
           '}',
           'return out;');

  return src.join('\n');
}
*/

BN.prototype._smallMulTo = function _smallMulTo(num, out) {
  out.sign = num.sign !== this.sign;
  out.length = this.length + num.length;

  var carry = 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 = carry >>> 26;
    var rword = carry & 0x3ffffff;
    var maxJ = Math.min(k, num.length - 1);
    for (var j = Math.max(0, k - this.length + 1); j <= maxJ; j++) {
      var i = k - j;
      var a = this.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;
    }
    out.words[k] = rword;
    carry = ncarry;
  }
  if (carry !== 0) {
    out.words[k] = carry;
  } else {
    out.length--;
  }

  return out.strip();
};

BN.prototype._bigMulTo = function _bigMulTo(num, out) {
  out.sign = num.sign !== this.sign;
  out.length = this.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 - this.length + 1); j <= maxJ; j++) {
      var i = k - j;
      var a = this.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();
};

BN.prototype.mulTo = function mulTo(num, out) {
  var res;
  if (this.length + num.length < 63)
    res = this._smallMulTo(num, out);
  else
    res = this._bigMulTo(num, out);
  return res;
};

// 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);
};

// In-place Multiplication
BN.prototype.imul = function imul(num) {
  if (this.cmpn(0) === 0 || num.cmpn(0) === 0) {
    this.words[0] = 0;
    this.length = 1;
    return this;
  }

  var tlen = this.length;
  var nlen = num.length;

  this.sign = num.sign !== this.sign;
  this.length = this.length + num.length;
  this.words[this.length - 1] = 0;

  for (var k = this.length - 2; k >= 0; k--) {
    // Sum all words with the same `i + j = k` and accumulate `carry`,
    // note that carry could be >= 0x3ffffff
    var carry = 0;
    var rword = 0;
    var maxJ = Math.min(k, nlen - 1);
    for (var j = Math.max(0, k - tlen + 1); j <= maxJ; j++) {
      var i = k - j;
      var a = this.words[i];
      var b = num.words[j];
      var r = a * b;

      var lo = r & 0x3ffffff;
      carry += (r / 0x4000000) | 0;
      lo += rword;
      rword = lo & 0x3ffffff;
      carry += lo >>> 26;
    }
    this.words[k] = rword;
    this.words[k + 1] += carry;
    carry = 0;
  }

  // Propagate overflows
  var carry = 0;
  for (var i = 1; i < this.length; i++) {
    var w = this.words[i] + carry;
    this.words[i] = w & 0x3ffffff;
    carry = w >>> 26;
  }

  return this.strip();
};

BN.prototype.imuln = function imuln(num) {
  assert(typeof num === 'number');

  // Carry
  var carry = 0;
  for (var i = 0; i < this.length; i++) {
    var w = this.words[i] * 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 this;
};

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

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

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

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

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

  return this.strip();
};

// 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.ishrn = function ishrn(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 (var 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 (var i = this.length - 1; i >= 0 && (carry !== 0 || i >= h); i--) {
    var word = this.words[i];
    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;
  }

  this.strip();

  return this;
};

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

// Shift-right
BN.prototype.shrn = function shrn(bits) {
  return this.clone().ishrn(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.sign, 'imaskn works only with positive numbers');

  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');
  if (num < 0)
    return this.isubn(-num);

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

    this.sign = false;
    this.isubn(num);
    this.sign = true;
    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');
  if (num < 0)
    return this.iaddn(-num);

  if (this.sign) {
    this.sign = false;
    this.iaddn(num);
    this.sign = true;
    return this;
  }

  this.words[0] -= num;

  // 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.sign = false;

  return this;
};

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

BN.prototype._ishlnsubmul = function _ishlnsubmul(num, mul, shift) {
  // Bigger storage is needed
  var len = num.length + shift;
  var i;
  if (this.words.length < len) {
    var t = new Array(len);
    for (var i = 0; i < this.length; i++)
      t[i] = this.words[i];
    this.words = t;
  } else {
    i = this.length;
  }

  // Zeroify rest
  this.length = Math.max(this.length, len);
  for (; i < this.length; i++)
    this.words[i] = 0;

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

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

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

  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];
  var bhiBits = this._countBits(bhi);
  shift = 26 - bhiBits;
  if (shift !== 0) {
    b = b.shln(shift);
    a.ishln(shift);
    bhi = b.words[b.length - 1];
  }

  // 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.sign) {
    a = diff;
    if (q)
      q.words[m] = 1;
  }

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

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

    a._ishlnsubmul(b, qj, j);
    while (a.sign) {
      qj--;
      a.sign = false;
      a._ishlnsubmul(b, 1, j);
      if (a.cmpn(0) !== 0)
        a.sign = !a.sign;
    }
    if (q)
      q.words[j] = qj;
  }
  if (q)
    q.strip();
  a.strip();

  // Denormalize
  if (mode !== 'div' && shift !== 0)
    a.ishrn(shift);
  return { div: q ? q : null, mod: a };
};

BN.prototype.divmod = function divmod(num, mode) {
  assert(num.cmpn(0) !== 0);

  if (this.sign && !num.sign) {
    var res = this.neg().divmod(num, mode);
    var div;
    var mod;
    if (mode !== 'mod')
      div = res.div.neg();
    if (mode !== 'div')
      mod = res.mod.cmpn(0) === 0 ? res.mod : num.sub(res.mod);
    return {
      div: div,
      mod: mod
    };
  } else if (!this.sign && num.sign) {
    var res = this.divmod(num.neg(), mode);
    var div;
    if (mode !== 'mod')
      div = res.div.neg();
    return { div: div, mod: res.mod };
  } else if (this.sign && num.sign) {
    return this.neg().divmod(num.neg(), mode);
  }

  // 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 };
    else if (mode === 'mod')
      return { div: null, mod: new BN(this.modn(num.words[0])) };
    return {
      div: this.divn(num.words[0]),
      mod: new BN(this.modn(num.words[0]))
    };
  }

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

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

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

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

  // Fast case - exact division
  if (dm.mod.cmpn(0) === 0)
    return dm.div;

  var mod = dm.div.sign ? dm.mod.isub(num) : dm.mod;

  var half = num.shrn(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.sign ? dm.div.isubn(1) : dm.div.iaddn(1);
};

BN.prototype.modn = function modn(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]) % num;

  return acc;
};

// In-place division by number
BN.prototype.idivn = function idivn(num) {
  assert(num <= 0x3ffffff);

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

  return this.strip();
};

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

BN.prototype.egcd = function egcd(p) {
  assert(!p.sign);
  assert(p.cmpn(0) !== 0);

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

  if (x.sign)
    x = x.mod(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.ishrn(1);
    y.ishrn(1);
    ++g;
  }

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

  while (x.cmpn(0) !== 0) {
    while (x.isEven()) {
      x.ishrn(1);
      if (A.isEven() && B.isEven()) {
        A.ishrn(1);
        B.ishrn(1);
      } else {
        A.iadd(yp).ishrn(1);
        B.isub(xp).ishrn(1);
      }
    }

    while (y.isEven()) {
      y.ishrn(1);
      if (C.isEven() && D.isEven()) {
        C.ishrn(1);
        D.ishrn(1);
      } else {
        C.iadd(yp).ishrn(1);
        D.isub(xp).ishrn(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.ishln(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.sign);
  assert(p.cmpn(0) !== 0);

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

  if (a.sign)
    a = a.mod(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) {
    while (a.isEven()) {
      a.ishrn(1);
      if (x1.isEven())
        x1.ishrn(1);
      else
        x1.iadd(delta).ishrn(1);
    }
    while (b.isEven()) {
      b.ishrn(1);
      if (x2.isEven())
        x2.ishrn(1);
      else
        x2.iadd(delta).ishrn(1);
    }
    if (a.cmp(b) >= 0) {
      a.isub(b);
      x1.isub(x2);
    } else {
      b.isub(a);
      x2.isub(x1);
    }
  }
  if (a.cmpn(1) === 0)
    return x1;
  else
    return x2;
};

BN.prototype.gcd = function gcd(num) {
  if (this.cmpn(0) === 0)
    return num.clone();
  if (num.cmpn(0) === 0)
    return this.clone();

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

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

  do {
    while (a.isEven())
      a.ishrn(1);
    while (b.isEven())
      b.ishrn(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.ishln(shift);
};

// Invert number in the field F(num)
BN.prototype.invm = function invm(num) {
  return this.egcd(num).a.mod(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) {
    for (var i = this.length; i < s + 1; i++)
      this.words[i] = 0;
    this.words[s] |= q;
    this.length = s + 1;
    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];
    w += carry;
    carry = w >>> 26;
    w &= 0x3ffffff;
    this.words[i] = w;
  }
  if (carry !== 0) {
    this.words[i] = carry;
    this.length++;
  }
  return this;
};

BN.prototype.cmpn = function cmpn(num) {
  var sign = num < 0;
  if (sign)
    num = -num;

  if (this.sign && !sign)
    return -1;
  else if (!this.sign && sign)
    return 1;

  num &= 0x3ffffff;
  this.strip();

  var res;
  if (this.length > 1) {
    res = 1;
  } else {
    var w = this.words[0];
    res = w === num ? 0 : w < num ? -1 : 1;
  }
  if (this.sign)
    res = -res;
  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.sign && !num.sign)
    return -1;
  else if (!this.sign && num.sign)
    return 1;

  var res = this.ucmp(num);
  if (this.sign)
    return -res;
  else
    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;
  else if (this.length < num.length)
    return -1;

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

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

//
// 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.sign, '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).ishln(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 {
    r.strip();
  }

  return r;
};

MPrime.prototype.split = function split(input, out) {
  input.ishrn(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 (var i = 10; i < input.length; i++) {
    var next = input.words[i];
    input.words[i - 10] = ((next & mask) << 4) | (prev >>> 22);
    prev = next;
  }
  input.words[i - 10] = prev >>> 22;
  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 hi;
  var lo = 0;
  for (var i = 0; i < num.length; i++) {
    var w = num.words[i];
    hi = w * 0x40;
    lo += w * 0x3d1;
    hi += (lo / 0x4000000) | 0;
    lo &= 0x3ffffff;

    num.words[i] = lo;

    lo = hi;
  }

  // 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] * 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 {
    this.m = m;
    this.prime = null;
  }
}

Red.prototype._verify1 = function _verify1(a) {
  assert(!a.sign, 'red works only with positives');
  assert(a.red, 'red works only with red numbers');
};

Red.prototype._verify2 = function _verify2(a, b) {
  assert(!a.sign && !b.sign, '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);
  return a.mod(this.m)._forceRed(this);
};

Red.prototype.neg = function neg(a) {
  var r = a.clone();
  r.sign = !r.sign;
  return r.iadd(this.m)._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.shln(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);
};

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

Red.prototype.sqrt = function sqrt(a) {
  if (a.cmpn(0) === 0)
    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)).ishrn(2);
    var r = this.pow(a, pow);
    return r;
  }

  // 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.cmpn(0) !== 0 && q.andln(1) === 0) {
    s++;
    q.ishrn(1);
  }
  assert(q.cmpn(0) !== 0);

  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).ishrn(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).ishrn(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).ishln(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.sign) {
    inv.sign = false;
    return this.imod(inv).redNeg();
  } else {
    return this.imod(inv);
  }
};

Red.prototype.pow = function pow(a, num) {
  var w = [];

  if (num.cmpn(0) === 0)
    return new BN(1);

  var q = num.clone();

  while (q.cmpn(0) !== 0) {
    w.push(q.andln(1));
    q.ishrn(1);
  }

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

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

  return res;
};

Red.prototype.convertTo = function convertTo(num) {
  var r = num.mod(this.m);
  if (r === num)
    return r.clone();
  else
    return 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).ishln(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.sign = true;
  this.minv = this.minv.mod(this.r);
}
inherits(Mont, Red);

Mont.prototype.convertTo = function convertTo(num) {
  return this.imod(num.shln(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.cmpn(0) === 0 || b.cmpn(0) === 0) {
    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).ishrn(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.cmpn(0) === 0 || b.cmpn(0) === 0)
    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).ishrn(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);
};

})(typeof module === 'undefined' || module, this);