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wallet-core/node_modules/bn.js/lib/bn.js
Florian Dold de98e0b232
node_modules
2017-05-03 15:35:00 +02:00

3428 lines
85 KiB
JavaScript
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(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('buf' + 'fer').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);
for (var i = start; i < len; i++) {
var c = str.charCodeAt(i) - 48;
r <<= 4;
// 'a' - 'f'
if (c >= 49 && c <= 54) {
r |= c - 49 + 0xa;
// 'A' - 'F'
} else if (c >= 17 && c <= 22) {
r |= c - 17 + 0xa;
// '0' - '9'
} else {
r |= c & 0xf;
}
}
return r;
}
BN.prototype._parseHex = function _parseHex (number, start) {
// Create possibly bigger array to ensure that it fits the number
this.length = Math.ceil((number.length - start) / 6);
this.words = new Array(this.length);
for (var i = 0; i < this.length; i++) {
this.words[i] = 0;
}
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 len = Math.min(str.length, end);
for (var i = start; i < len; i++) {
var c = str.charCodeAt(i) - 48;
r *= mul;
// 'a'
if (c >= 49) {
r += c - 49 + 0xa;
// 'A'
} else if (c >= 17) {
r += c - 17 + 0xa;
// '0' - '9'
} else {
r += c;
}
}
return r;
}
BN.prototype._parseBase = function _parseBase (number, base, start) {
// Initialize as zero
this.words = [ 0 ];
this.length = 1;
// Find length of limb in base
for (var limbLen = 0, limbPow = 1; limbPow <= 0x3ffffff; limbPow *= base) {
limbLen++;
}
limbLen--;
limbPow = (limbPow / base) | 0;
var total = number.length - start;
var mod = total % limbLen;
var end = Math.min(total, total - mod) + start;
var word = 0;
for (var i = start; i < end; i += limbLen) {
word = parseBase(number, i, i + limbLen, base);
this.imuln(limbPow);
if (this.words[0] + word < 0x4000000) {
this.words[0] += word;
} else {
this._iaddn(word);
}
}
if (mod !== 0) {
var pow = 1;
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;
};
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;
};
BN.prototype.inspect = function inspect () {
return (this.red ? '<BN-R: ' : '<BN: ') + this.toString(16) + '>';
};
/*
var zeros = [];
var groupSizes = [];
var groupBases = [];
var s = '';
var i = -1;
while (++i < BN.wordSize) {
zeros[i] = s;
s += '0';
}
groupSizes[0] = 0;
groupSizes[1] = 0;
groupBases[0] = 0;
groupBases[1] = 0;
var base = 2 - 1;
while (++base < 36 + 1) {
var groupSize = 0;
var groupBase = 1;
while (groupBase < (1 << BN.wordSize) / base) {
groupBase *= base;
groupSize += 1;
}
groupSizes[base] = groupSize;
groupBases[base] = groupBase;
}
*/
var zeros = [
'',
'0',
'00',
'000',
'0000',
'00000',
'000000',
'0000000',
'00000000',
'000000000',
'0000000000',
'00000000000',
'000000000000',
'0000000000000',
'00000000000000',
'000000000000000',
'0000000000000000',
'00000000000000000',
'000000000000000000',
'0000000000000000000',
'00000000000000000000',
'000000000000000000000',
'0000000000000000000000',
'00000000000000000000000',
'000000000000000000000000',
'0000000000000000000000000'
];
var groupSizes = [
0, 0,
25, 16, 12, 11, 10, 9, 8,
8, 7, 7, 7, 7, 6, 6,
6, 6, 6, 6, 6, 5, 5,
5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5
];
var groupBases = [
0, 0,
33554432, 43046721, 16777216, 48828125, 60466176, 40353607, 16777216,
43046721, 10000000, 19487171, 35831808, 62748517, 7529536, 11390625,
16777216, 24137569, 34012224, 47045881, 64000000, 4084101, 5153632,
6436343, 7962624, 9765625, 11881376, 14348907, 17210368, 20511149,
24300000, 28629151, 33554432, 39135393, 45435424, 52521875, 60466176
];
BN.prototype.toString = function toString (base, padding) {
base = base || 10;
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.modn(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);
};
BN.prototype.toBuffer = function toBuffer (endian, length) {
assert(typeof Buffer !== 'undefined');
return this.toArrayLike(Buffer, endian, length);
};
BN.prototype.toArray = function toArray (endian, length) {
return this.toArrayLike(Array, endian, length);
};
BN.prototype.toArrayLike = function toArrayLike (ArrayType, endian, length) {
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');
this.strip();
var littleEndian = endian === 'le';
var res = new ArrayType(reqLength);
var b, i;
var q = this.clone();
if (!littleEndian) {
// Assume big-endian
for (i = 0; i < reqLength - byteLength; i++) {
res[i] = 0;
}
for (i = 0; !q.isZero(); i++) {
b = q.andln(0xff);
q.iushrn(8);
res[reqLength - i - 1] = b;
}
} else {
for (i = 0; !q.isZero(); i++) {
b = q.andln(0xff);
q.iushrn(8);
res[i] = b;
}
for (; i < reqLength; i++) {
res[i] = 0;
}
}
return res;
};
if (Math.clz32) {
BN.prototype._countBits = function _countBits (w) {
return 32 - Math.clz32(w);
};
} else {
BN.prototype._countBits = function _countBits (w) {
var t = w;
var r = 0;
if (t >= 0x1000) {
r += 13;
t >>>= 13;
}
if (t >= 0x40) {
r += 7;
t >>>= 7;
}
if (t >= 0x8) {
r += 4;
t >>>= 4;
}
if (t >= 0x02) {
r += 2;
t >>>= 2;
}
return r + t;
};
}
BN.prototype._zeroBits = function _zeroBits (w) {
// Short-cut
if (w === 0) return 26;
var t = w;
var r = 0;
if ((t & 0x1fff) === 0) {
r += 13;
t >>>= 13;
}
if ((t & 0x7f) === 0) {
r += 7;
t >>>= 7;
}
if ((t & 0xf) === 0) {
r += 4;
t >>>= 4;
}
if ((t & 0x3) === 0) {
r += 2;
t >>>= 2;
}
if ((t & 0x1) === 0) {
r++;
}
return r;
};
// Return number of used bits in a BN
BN.prototype.bitLength = function bitLength () {
var 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] & (1 << wbit)) >>> wbit;
}
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) {
var fftm = new FFTM();
return fftm.mulp(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) {
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 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.modn(num.words[0]))
};
}
return {
div: this.divn(num.words[0]),
mod: new BN(this.modn(num.words[0]))
};
}
return this._wordDiv(num, mode);
};
// Find `this` / `num`
BN.prototype.div = function div (num) {
return this.divmod(num, 'div', 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.modn = function modn (num) {
assert(num <= 0x3ffffff);
var p = (1 << 26) % num;
var acc = 0;
for (var i = this.length - 1; i >= 0; i--) {
acc = (p * acc + (this.words[i] | 0)) % num;
}
return acc;
};
// In-place division by number
BN.prototype.idivn = function idivn (num) {
assert(num <= 0x3ffffff);
var carry = 0;
for (var i = this.length - 1; i >= 0; i--) {
var w = (this.words[i] | 0) + carry * 0x4000000;
this.words[i] = (w / num) | 0;
carry = w % num;
}
return this.strip();
};
BN.prototype.divn = function divn (num) {
return this.clone().idivn(num);
};
BN.prototype.egcd = function egcd (p) {
assert(p.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 {
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);
return a.umod(this.m)._forceRed(this);
};
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);
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);
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