diff options
Diffstat (limited to 'node_modules/bn.js/lib')
| -rw-r--r-- | node_modules/bn.js/lib/bn.js | 3540 |
1 files changed, 3540 insertions, 0 deletions
diff --git a/node_modules/bn.js/lib/bn.js b/node_modules/bn.js/lib/bn.js new file mode 100644 index 0000000..982f638 --- /dev/null +++ b/node_modules/bn.js/lib/bn.js @@ -0,0 +1,3540 @@ +(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 { + 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++; + } + + if (base === 16) { + this._parseHex(number, start); + } else { + this._parseBase(number, base, start); + } + + if (number[0] === '-') { + this.negative = 1; + } + + this._strip(); + + if (endian !== 'le') return; + + 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 parseHex (str, start, end) { + var r = 0; + var len = Math.min(str.length, end); + var z = 0; + for (var i = start; i < len; i++) { + var c = str.charCodeAt(i) - 48; + + r <<= 4; + + var b; + + // 'a' - 'f' + if (c >= 49 && c <= 54) { + b = c - 49 + 0xa; + + // 'A' - 'F' + } else if (c >= 17 && c <= 22) { + b = c - 17 + 0xa; + + // '0' - '9' + } else { + b = c; + } + + r |= b; + z |= b; + } + + assert(!(z & 0xf0), 'Invalid character in ' + str); + return r; + } + + BN.prototype._parseHex = function _parseHex (number, start) { + // Create possibly bigger array to ensure that it fits the number + this.length = Math.ceil((number.length - start) / 6); + this.words = new Array(this.length); + for (var i = 0; i < this.length; i++) { + this.words[i] = 0; + } + + var j, w; + // Scan 24-bit chunks and add them to the number + var off = 0; + for (i = number.length - 6, j = 0; i >= start; i -= 6) { + w = parseHex(number, i, i + 6); + this.words[j] |= (w << off) & 0x3ffffff; + // NOTE: `0x3fffff` is intentional here, 26bits max shift + 24bit hex limb + this.words[j + 1] |= w >>> (26 - off) & 0x3fffff; + off += 24; + if (off >= 26) { + off -= 26; + j++; + } + } + if (i + 6 !== start) { + w = parseHex(number, start, i + 6); + this.words[j] |= (w << off) & 0x3ffffff; + this.words[j + 1] |= w >>> (26 - off) & 0x3fffff; + } + this._strip(); + }; + + function parseBase (str, start, end, mul) { + var r = 0; + var 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); + } + } + }; + + 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; + if (carry !== 0 || i !== this.length - 1) { + out = zeros[6 - word.length] + word + out; + } else { + out = word + out; + } + off += 2; + if (off >= 26) { + off -= 26; + i--; + } + } + if (carry !== 0) { + out = carry.toString(16) + out; + } + while (out.length % padding !== 0) { + out = '0' + out; + } + if (this.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); |