Secp256k1.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) {
        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');
        }
    }
    if (typeof module === 'object') {
        module.exports = BN;
    } else {
        exports.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);
    };
})(typeof module === 'undefined' || module, this);
(function () {
    if (typeof module !== 'undefined') {
        BN = module.require('bn.js')
        randomBytes = module.require('crypto').randomBytes
    } else {
        // bn.js must have been included by the main html file
        randomBytes = length => window.crypto.getRandomValues(new Uint8Array(length))
        window.Secp256k1 = exports = {}
    }

    function uint256(x, base) {
        return new BN(x, base)
    }

    function rnd(P) {
        return uint256(randomBytes(32)).umod(P)//TODO red
    }

    const A  = uint256(0)
    const B  = uint256(7)
    const GX = uint256("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", 16)
    const GY = uint256("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", 16)
    const P  = uint256("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", 16)
    const N  = uint256("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16)
    //const RED = BN.red(P)
    const _0 = uint256(0)
    const _1 = uint256(1)

    // function for elliptic curve multiplication in jacobian coordinates using Double-and-add method
    function ecmul(_p, _d) {
        let R = [_0,_0,_0]

        //return (0,0) if d=0 or (x1,y1)=(0,0)
        if (_d == 0 || ((_p[0] == 0) && (_p[1] == 0)) ) {
            return R
        }
        let T = [
            _p[0], //x-coordinate temp
            _p[1], //y-coordinate temp
            _p[2], //z-coordinate temp
        ]

        const d = _d.clone()
        while (d != 0) {
            if (d.testn(0)) {  //if last bit is 1 add T to result
                R = ecadd(T,R)
            }
            T = ecdouble(T);    //double temporary coordinates
            d.iushrn(1);      //"cut off" last bit
        }

        return R
    }

    function mulmod(a, b, P) {
        return a.mul(b).umod(P)//TODO red
    }

    function addmod(a, b, P) {
        return a.add(b).umod(P)//TODO red
    }

    function invmod(a, P) {
        return a.invm(P)//TODO redq
    }

    function mulG(k) {
        const GinJ = AtoJ(GX, GY)
        const PUBinJ = ecmul(GinJ, k)
        return JtoA(PUBinJ)
    }

    function assert(cond, msg) {
        if (!cond) {
            throw Error("assertion failed: " + msg)
        }
    }

    function ecsign(d, z) {
        assert(d != 0, "d must not be 0")
        assert(z != 0, "z must not be 0")
        while (true) {
            const k = rnd(P)
            const R = mulG(k)
            if (R[0] == 0) continue
            const s = mulmod(invmod(k, N), addmod(z, mulmod(R[0], d, N), N), N)
            if (s == 0) continue
            //FIXME: why do I need this
            if (s.testn(255)) continue
            return {r: toHex(R[0]), s: toHex(s), v: R[1].testn(0) ? 1 : 0}
        }
    }

    function JtoA(p) {
        const zInv = invmod(p[2], P)
        const zInv2 = mulmod(zInv, zInv, P)
        return [mulmod(p[0], zInv2, P), mulmod(p[1], mulmod(zInv, zInv2, P), P)]
    }

    //point doubling for elliptic curve in jacobian coordinates
    //formula from https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
    function ecdouble(_p) {
        if (_p[1] == 0) {
            //return point at infinity
            return [_1, _1, _0]
        }

        const z2 = mulmod(_p[2], _p[2], P)
        const m = addmod(mulmod(A, mulmod(z2, z2, P), P), mulmod(uint256(3), mulmod(_p[0], _p[0], P), P), P)
        const y2 = mulmod(_p[1], _p[1], P)
        const s = mulmod(uint256(4), mulmod(_p[0], y2, P), P)

        const x = addmod(mulmod(m, m, P), negmod(mulmod(s, uint256(2), P), P), P)
        return [
            x,
            addmod(mulmod(m, addmod(s, negmod(x, P), P), P), negmod(mulmod(uint256(8), mulmod(y2, y2, P), P), P), P),
            mulmod(uint256(2), mulmod(_p[1], _p[2], P), P)
        ]
    }

    function negmod(a, P) {
        return P.sub(a)
    }

    // point addition for elliptic curve in jacobian coordinates
    // formula from https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
    function ecadd(_p, _q) {
        if (_q[0] == 0 && _q[1] == 0 && _q[2] == 0) {
            return _p
        }

        let z2 = mulmod(_q[2], _q[2], P)
        const u1 = mulmod(_p[0], z2, P)
        const s1 = mulmod(_p[1], mulmod(z2, _q[2], P), P)
        z2 = mulmod(_p[2], _p[2], P)
        let u2 = mulmod(_q[0], z2, P)
        let s2 = mulmod(_q[1], mulmod(z2, _p[2], P), P)

        if (u1.eq(u2)) {
            if (!s1.eq(s2)) {
                //return point at infinity
                return [_1, _1, _0]
            }
            else {
                return ecdouble(_p)
            }
        }

        u2 = addmod(u2, negmod(u1, P), P)
        z2 = mulmod(u2, u2, P)
        const t2 = mulmod(u1, z2, P)
        z2 = mulmod(u2, z2, P)
        s2 = addmod(s2, negmod(s1, P), P)
        const x = addmod(addmod(mulmod(s2, s2, P), negmod(z2, P), P), negmod(mulmod(uint256(2), t2, P), P), P)
        return [
            x,
            addmod(mulmod(s2, addmod(t2, negmod(x, P), P), P), negmod(mulmod(s1, z2, P), P), P),
            mulmod(u2, mulmod(_p[2], _q[2], P), P)
        ]
    }

    function AtoJ(x, y) {
        return [
            uint256(x),
            uint256(y),
            _1
        ]
    }

    function isValidPoint(x, y) {
        const yy = addmod(mulmod(mulmod(x, x, P), x, P), B, P)
        return yy.eq(mulmod(y, y, P))
    }

    function toHex(bn) {
        return ('00000000000000000000000000000000000000000000000000000000000000000000000000000000' + bn.toString(16)).slice(-64)
    }

    function decompressKey(x, yBit) {
        let redP = BN.red('k256');
        x = x.toRed(redP)
        const y = x.redMul(x).redMul(x).redAdd(B.toRed(redP)).redSqrt()
        const sign = y.testn(0)
        return (sign != yBit ? y.redNeg() : y).fromRed()
    }

    function generatePublicKeyFromPrivateKeyData(pk) {
        const p = mulG(pk)
        return {x: toHex(p[0]), y: toHex(p[1])}
    }

    function ecrecover(recId, sigr, sigs, message) {
        assert(recId >= 0 && recId <= 3, "recId must be 0..3")
        assert(sigr != 0, "sigr must not be 0")
        assert(sigs != 0, "sigs must not be 0")
        // 1.0 For j from 0 to h   (h == recId here and the loop is outside this function)
        //   1.1 Let x = r + jn
        const x = addmod(uint256(sigr), P.muln(recId >> 1), P)
        //   1.2. Convert the integer x to an octet string X of length mlen using the conversion routine
        //        specified in Section 2.3.7, where mlen = ⌈(log2 p)/8⌉ or mlen = ⌈m/8⌉.
        //   1.3. Convert the octet string (16 set binary digits)||X to an elliptic curve point R using the
        //        conversion routine specified in Section 2.3.4. If this conversion routine outputs “invalid”, then
        //        do another iteration of Step 1.
        //
        // More concisely, what these points mean is to use X as a compressed public key.
        if (x.gte(P)) {
            // Cannot have point co-ordinates larger than this as everything takes place modulo Q.
            return null
        }
        // Compressed keys require you to know an extra bit of data about the y-coord as there are two possibilities.
        // So it's encoded in the recId.
        const y = decompressKey(x, (recId & 1) == 1)
        //   1.4. If nR != point at infinity, then do another iteration of Step 1 (callers responsibility).
        // if (!R.mul(N).isInfinity())
        //     return null
        //   1.5. Compute e from M using Steps 2 and 3 of ECDSA signature verification.
        const e = uint256(message)
        //   1.6. For k from 1 to 2 do the following.   (loop is outside this function via iterating recId)
        //   1.6.1. Compute a candidate public key as:
        //               Q = mi(r) * (sR - eG)
        //
        // Where mi(x) is the modular multiplicative inverse. We transform this into the following:
        //               Q = (mi(r) * s ** R) + (mi(r) * -e ** G)
        // Where -e is the modular additive inverse of e, that is z such that z + e = 0 (mod n). In the above equation
        // ** is point multiplication and + is point addition (the EC group operator).
        //
        // We can find the additive inverse by subtracting e from zero then taking the mod. For example the additive
        // inverse of 3 modulo 11 is 8 because 3 + 8 mod 11 = 0, and -3 mod 11 = 8.
        const eNeg = negmod(e, N)
        const rInv = invmod(sigr, N)
        const srInv = mulmod(rInv, sigs, N)
        const eNegrInv = mulmod(rInv, eNeg, N)
        const R = AtoJ(x, y)
        const G = AtoJ(GX, GY)
        const qinJ = ecadd(ecmul(G, eNegrInv), ecmul(R, srInv))
        const p = JtoA(qinJ)
        return {x: toHex(p[0]), y: toHex(p[1])}
    }

    function ecverify (Qx, Qy, sigr, sigs, z) {
        if (sigs == 0 || sigr == 0) {
            return false
        }
        const w = invmod(sigs, N)
        const u1 = mulmod(z, w, N)
        const u2 = mulmod(sigr, w, N)
        const Q = AtoJ(Qx, Qy)
        const G = AtoJ(GX, GY)
        const RinJ = ecadd(ecmul(G, u1), ecmul(Q, u2))
        const r = JtoA(RinJ)
        return sigr.eq(r[0])
    }

    exports.uint256 = uint256
    exports.ecsign = ecsign
    exports.ecrecover = ecrecover
    exports.generatePublicKeyFromPrivateKeyData = generatePublicKeyFromPrivateKeyData
    exports.decompressKey = decompressKey
    exports.isValidPoint = isValidPoint
    exports.ecverify = ecverify
})();