diff --git a/js/build/embark.bundle.js b/js/build/embark.bundle.js
index f33568a1..403c6785 100644
--- a/js/build/embark.bundle.js
+++ b/js/build/embark.bundle.js
@@ -372,6 +372,8 @@ var EmbarkJS =
 	        web3.version.getWhisper(function(err, res) {
 	            if (err) {
 	                console.log("whisper not available");
+	            } else if (web3.version.whisper >= 5) {
+	                console.log("this version of whisper is not supported yet; try a version of geth bellow 1.6.1");
 	            } else {
 	                self.currentMessages.identity = web3.shh.newIdentity();
 	            }
diff --git a/js/embark.js b/js/embark.js
index b44548fb..3acaab72 100644
--- a/js/embark.js
+++ b/js/embark.js
@@ -325,6 +325,8 @@ EmbarkJS.Messages.setProvider = function(provider, options) {
         web3.version.getWhisper(function(err, res) {
             if (err) {
                 console.log("whisper not available");
+            } else if (web3.version.whisper >= 5) {
+                console.log("this version of whisper is not supported yet; try a version of geth bellow 1.6.1");
             } else {
                 self.currentMessages.identity = web3.shh.newIdentity();
             }
diff --git a/js/web3.js b/js/web3.js
index b576349a..416e7971 100644
--- a/js/web3.js
+++ b/js/web3.js
@@ -1842,7 +1842,7 @@ module.exports = function (value, options) {
 };
 
 
-},{"crypto-js":59,"crypto-js/sha3":80}],20:[function(require,module,exports){
+},{"crypto-js":58,"crypto-js/sha3":79}],20:[function(require,module,exports){
 /*
     This file is part of web3.js.
 
@@ -1884,7 +1884,7 @@ var sha3 = require('./sha3.js');
 var utf8 = require('utf8');
 
 var unitMap = {
-    'noether':      '0',    
+    'noether':      '0',
     'wei':          '1',
     'kwei':         '1000',
     'Kwei':         '1000',
@@ -2104,7 +2104,7 @@ var toHex = function (val) {
     if (isBigNumber(val))
         return fromDecimal(val);
 
-    if (isObject(val))
+    if (typeof val === 'object')
         return fromUtf8(JSON.stringify(val));
 
     // if its a negative number, pass it through fromDecimal
@@ -2258,8 +2258,6 @@ var isAddress = function (address) {
     }
 };
 
-
-
 /**
  * Checks if the given string is a checksummed address
  *
@@ -2267,18 +2265,18 @@ var isAddress = function (address) {
  * @param {String} address the given HEX adress
  * @return {Boolean}
 */
-var isChecksumAddress = function (address) {    
+var isChecksumAddress = function (address) {
     // Check each case
     address = address.replace('0x','');
     var addressHash = sha3(address.toLowerCase());
 
-    for (var i = 0; i < 40; i++ ) { 
+    for (var i = 0; i < 40; i++ ) {
         // the nth letter should be uppercase if the nth digit of casemap is 1
         if ((parseInt(addressHash[i], 16) > 7 && address[i].toUpperCase() !== address[i]) || (parseInt(addressHash[i], 16) <= 7 && address[i].toLowerCase() !== address[i])) {
             return false;
         }
     }
-    return true;    
+    return true;
 };
 
 
@@ -2290,15 +2288,15 @@ var isChecksumAddress = function (address) {
  * @param {String} address the given HEX adress
  * @return {String}
 */
-var toChecksumAddress = function (address) { 
+var toChecksumAddress = function (address) {
     if (typeof address === 'undefined') return '';
 
     address = address.toLowerCase().replace('0x','');
     var addressHash = sha3(address);
     var checksumAddress = '0x';
 
-    for (var i = 0; i < address.length; i++ ) { 
-        // If ith character is 9 to f then make it uppercase 
+    for (var i = 0; i < address.length; i++ ) {
+        // If ith character is 9 to f then make it uppercase
         if (parseInt(addressHash[i], 16) > 7) {
           checksumAddress += address[i].toUpperCase();
         } else {
@@ -2370,7 +2368,7 @@ var isFunction = function (object) {
  * @return {Boolean}
  */
 var isObject = function (object) {
-    return typeof object === 'object';
+    return object !== null && !(object instanceof Array) && typeof object === 'object';
 };
 
 /**
@@ -2410,6 +2408,38 @@ var isJson = function (str) {
     }
 };
 
+/**
+ * Returns true if given string is a valid Ethereum block header bloom.
+ *
+ * @method isBloom
+ * @param {String} hex encoded bloom filter
+ * @return {Boolean}
+ */
+var isBloom = function (bloom) {
+    if (!/^(0x)?[0-9a-f]{512}$/i.test(bloom)) {
+        return false;
+    } else if (/^(0x)?[0-9a-f]{512}$/.test(bloom) || /^(0x)?[0-9A-F]{512}$/.test(bloom)) {
+        return true;
+    }
+    return false;
+};
+
+/**
+ * Returns true if given string is a valid log topic.
+ *
+ * @method isTopic
+ * @param {String} hex encoded topic
+ * @return {Boolean}
+ */
+var isTopic = function (topic) {
+    if (!/^(0x)?[0-9a-f]{64}$/i.test(topic)) {
+        return false;
+    } else if (/^(0x)?[0-9a-f]{64}$/.test(topic) || /^(0x)?[0-9A-F]{64}$/.test(topic)) {
+        return true;
+    }
+    return false;
+};
+
 module.exports = {
     padLeft: padLeft,
     padRight: padRight,
@@ -2438,12 +2468,14 @@ module.exports = {
     isObject: isObject,
     isBoolean: isBoolean,
     isArray: isArray,
-    isJson: isJson
+    isJson: isJson,
+    isBloom: isBloom,
+    isTopic: isTopic,
 };
 
-},{"./sha3.js":19,"bignumber.js":"bignumber.js","utf8":85}],21:[function(require,module,exports){
+},{"./sha3.js":19,"bignumber.js":"bignumber.js","utf8":84}],21:[function(require,module,exports){
 module.exports={
-    "version": "0.18.2"
+    "version": "0.19.0"
 }
 
 },{}],22:[function(require,module,exports){
@@ -2549,6 +2581,8 @@ Web3.prototype.isAddress = utils.isAddress;
 Web3.prototype.isChecksumAddress = utils.isChecksumAddress;
 Web3.prototype.toChecksumAddress = utils.toChecksumAddress;
 Web3.prototype.isIBAN = utils.isIBAN;
+Web3.prototype.padLeft = utils.padLeft;
+Web3.prototype.padRight = utils.padRight;
 
 
 Web3.prototype.sha3 = function(string, options) {
@@ -2957,7 +2991,7 @@ var ContractFactory = function (eth, abi) {
         if (options.value > 0) {
             var constructorAbi = abi.filter(function (json) {
                 return json.type === 'constructor' && json.inputs.length === args.length;
-            })[0] || {};
+            })[0] || {};
 
             if (!constructorAbi.payable) {
                 throw new Error('Cannot send value to non-payable constructor');
@@ -3092,8 +3126,11 @@ module.exports = ContractFactory;
  */
 
 module.exports = {
-    InvalidNumberOfParams: function () {
-        return new Error('Invalid number of input parameters');
+    InvalidNumberOfSolidityArgs: function () {
+        return new Error('Invalid number of arguments to Solidity function');
+    },
+    InvalidNumberOfRPCParams: function () {
+        return new Error('Invalid number of input parameters to RPC method');
     },
     InvalidConnection: function (host){
         return new Error('CONNECTION ERROR: Couldn\'t connect to node '+ host +'.');
@@ -3523,7 +3560,9 @@ var Filter = function (requestManager, options, methods, formatter, callback, fi
             self.callbacks.forEach(function(cb){
                 cb(error);
             });
-            filterCreationErrorCallback(error);
+            if (typeof filterCreationErrorCallback === 'function') {
+              filterCreationErrorCallback(error);
+            }
         } else {
             self.filterId = id;
 
@@ -3937,6 +3976,7 @@ module.exports = {
 
 var coder = require('../solidity/coder');
 var utils = require('../utils/utils');
+var errors = require('./errors');
 var formatters = require('./formatters');
 var sha3 = require('../utils/sha3');
 
@@ -3969,6 +4009,23 @@ SolidityFunction.prototype.extractDefaultBlock = function (args) {
     }
 };
 
+/**
+ * Should be called to check if the number of arguments is correct
+ *
+ * @method validateArgs
+ * @param {Array} arguments
+ * @throws {Error} if it is not
+ */
+SolidityFunction.prototype.validateArgs = function (args) {
+    var inputArgs = args.filter(function (a) {
+      // filter the options object but not arguments that are arrays
+      return !(utils.isObject(a) === true && utils.isArray(a) === false);
+    });
+    if (inputArgs.length !== this._inputTypes.length) {
+        throw errors.InvalidNumberOfSolidityArgs();
+    }
+};
+
 /**
  * Should be used to create payload from arguments
  *
@@ -3981,6 +4038,7 @@ SolidityFunction.prototype.toPayload = function (args) {
     if (args.length > this._inputTypes.length && utils.isObject(args[args.length -1])) {
         options = args[args.length - 1];
     }
+    this.validateArgs(args);
     options.to = this._address;
     options.data = '0x' + this.signature() + coder.encodeParams(this._inputTypes, args);
     return options;
@@ -4175,8 +4233,7 @@ SolidityFunction.prototype.attachToContract = function (contract) {
 
 module.exports = SolidityFunction;
 
-
-},{"../solidity/coder":7,"../utils/sha3":19,"../utils/utils":20,"./formatters":30}],32:[function(require,module,exports){
+},{"../solidity/coder":7,"../utils/sha3":19,"../utils/utils":20,"./errors":26,"./formatters":30}],32:[function(require,module,exports){
 /*
     This file is part of web3.js.
 
@@ -4331,7 +4388,7 @@ HttpProvider.prototype.isConnected = function() {
 
 module.exports = HttpProvider;
 
-},{"./errors":26,"xhr2":86,"xmlhttprequest":17}],33:[function(require,module,exports){
+},{"./errors":26,"xhr2":85,"xmlhttprequest":17}],33:[function(require,module,exports){
 /*
     This file is part of web3.js.
 
@@ -4928,7 +4985,7 @@ Method.prototype.extractCallback = function (args) {
  */
 Method.prototype.validateArgs = function (args) {
     if (args.length !== this.params) {
-        throw errors.InvalidNumberOfParams();
+        throw errors.InvalidNumberOfRPCParams();
     }
 };
 
@@ -5022,7 +5079,6 @@ Method.prototype.request = function () {
 
 module.exports = Method;
 
-
 },{"../utils/utils":20,"./errors":26}],37:[function(require,module,exports){
 /*
     This file is part of web3.js.
@@ -5155,12 +5211,12 @@ function Eth(web3) {
 
     var self = this;
 
-    methods().forEach(function(method) { 
+    methods().forEach(function(method) {
         method.attachToObject(self);
         method.setRequestManager(self._requestManager);
     });
 
-    properties().forEach(function(p) { 
+    properties().forEach(function(p) {
         p.attachToObject(self);
         p.setRequestManager(self._requestManager);
     });
@@ -5296,6 +5352,13 @@ var methods = function () {
         inputFormatter: [formatters.inputTransactionFormatter]
     });
 
+    var signTransaction = new Method({
+        name: 'signTransaction',
+        call: 'eth_signTransaction',
+        params: 1,
+        inputFormatter: [formatters.inputTransactionFormatter]
+    });
+
     var sign = new Method({
         name: 'sign',
         call: 'eth_sign',
@@ -5364,6 +5427,7 @@ var methods = function () {
         call,
         estimateGas,
         sendRawTransaction,
+        signTransaction,
         sendTransaction,
         sign,
         compileSolidity,
@@ -5421,8 +5485,8 @@ Eth.prototype.contract = function (abi) {
     return factory;
 };
 
-Eth.prototype.filter = function (fil, callback) {
-    return new Filter(this._requestManager, fil, watches.eth(), formatters.outputLogFormatter, callback);
+Eth.prototype.filter = function (fil, callback, filterCreationErrorCallback) {
+    return new Filter(this._requestManager, fil, watches.eth(), formatters.outputLogFormatter, callback, filterCreationErrorCallback);
 };
 
 Eth.prototype.namereg = function () {
@@ -5439,7 +5503,6 @@ Eth.prototype.isSyncing = function (callback) {
 
 module.exports = Eth;
 
-
 },{"../../utils/config":18,"../../utils/utils":20,"../contract":25,"../filter":29,"../formatters":30,"../iban":33,"../method":36,"../namereg":44,"../property":45,"../syncing":48,"../transfer":49,"./watches":43}],39:[function(require,module,exports){
 /*
     This file is part of web3.js.
@@ -5548,6 +5611,25 @@ var methods = function () {
         inputFormatter: [null]
     });
 
+    var importRawKey = new Method({
+        name: 'importRawKey',
+		call: 'personal_importRawKey',
+		params: 2
+    });
+
+    var sign = new Method({
+        name: 'sign',
+		call: 'personal_sign',
+		params: 3,
+		inputFormatter: [null, formatters.inputAddressFormatter, null]
+    });
+
+    var ecRecover = new Method({
+        name: 'ecRecover',
+		call: 'personal_ecRecover',
+		params: 2
+    });
+
     var unlockAccount = new Method({
         name: 'unlockAccount',
         call: 'personal_unlockAccount',
@@ -5571,7 +5653,10 @@ var methods = function () {
 
     return [
         newAccount,
+        importRawKey,
         unlockAccount,
+        ecRecover,
+        sign,
         sendTransaction,
         lockAccount
     ];
@@ -6595,8 +6680,6 @@ module.exports = transfer;
 
 
 },{"../contracts/SmartExchange.json":3,"./iban":33}],50:[function(require,module,exports){
-
-},{}],51:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -6829,7 +6912,7 @@ module.exports = transfer;
 	return CryptoJS.AES;
 
 }));
-},{"./cipher-core":52,"./core":53,"./enc-base64":54,"./evpkdf":56,"./md5":61}],52:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52,"./enc-base64":53,"./evpkdf":55,"./md5":60}],51:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -7705,7 +7788,7 @@ module.exports = transfer;
 
 
 }));
-},{"./core":53}],53:[function(require,module,exports){
+},{"./core":52}],52:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -8466,7 +8549,7 @@ module.exports = transfer;
 	return CryptoJS;
 
 }));
-},{}],54:[function(require,module,exports){
+},{}],53:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -8602,7 +8685,7 @@ module.exports = transfer;
 	return CryptoJS.enc.Base64;
 
 }));
-},{"./core":53}],55:[function(require,module,exports){
+},{"./core":52}],54:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -8752,7 +8835,7 @@ module.exports = transfer;
 	return CryptoJS.enc.Utf16;
 
 }));
-},{"./core":53}],56:[function(require,module,exports){
+},{"./core":52}],55:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -8885,7 +8968,7 @@ module.exports = transfer;
 	return CryptoJS.EvpKDF;
 
 }));
-},{"./core":53,"./hmac":58,"./sha1":77}],57:[function(require,module,exports){
+},{"./core":52,"./hmac":57,"./sha1":76}],56:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -8952,7 +9035,7 @@ module.exports = transfer;
 	return CryptoJS.format.Hex;
 
 }));
-},{"./cipher-core":52,"./core":53}],58:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],57:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9096,7 +9179,7 @@ module.exports = transfer;
 
 
 }));
-},{"./core":53}],59:[function(require,module,exports){
+},{"./core":52}],58:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9115,7 +9198,7 @@ module.exports = transfer;
 	return CryptoJS;
 
 }));
-},{"./aes":51,"./cipher-core":52,"./core":53,"./enc-base64":54,"./enc-utf16":55,"./evpkdf":56,"./format-hex":57,"./hmac":58,"./lib-typedarrays":60,"./md5":61,"./mode-cfb":62,"./mode-ctr":64,"./mode-ctr-gladman":63,"./mode-ecb":65,"./mode-ofb":66,"./pad-ansix923":67,"./pad-iso10126":68,"./pad-iso97971":69,"./pad-nopadding":70,"./pad-zeropadding":71,"./pbkdf2":72,"./rabbit":74,"./rabbit-legacy":73,"./rc4":75,"./ripemd160":76,"./sha1":77,"./sha224":78,"./sha256":79,"./sha3":80,"./sha384":81,"./sha512":82,"./tripledes":83,"./x64-core":84}],60:[function(require,module,exports){
+},{"./aes":50,"./cipher-core":51,"./core":52,"./enc-base64":53,"./enc-utf16":54,"./evpkdf":55,"./format-hex":56,"./hmac":57,"./lib-typedarrays":59,"./md5":60,"./mode-cfb":61,"./mode-ctr":63,"./mode-ctr-gladman":62,"./mode-ecb":64,"./mode-ofb":65,"./pad-ansix923":66,"./pad-iso10126":67,"./pad-iso97971":68,"./pad-nopadding":69,"./pad-zeropadding":70,"./pbkdf2":71,"./rabbit":73,"./rabbit-legacy":72,"./rc4":74,"./ripemd160":75,"./sha1":76,"./sha224":77,"./sha256":78,"./sha3":79,"./sha384":80,"./sha512":81,"./tripledes":82,"./x64-core":83}],59:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9192,7 +9275,7 @@ module.exports = transfer;
 	return CryptoJS.lib.WordArray;
 
 }));
-},{"./core":53}],61:[function(require,module,exports){
+},{"./core":52}],60:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9461,7 +9544,7 @@ module.exports = transfer;
 	return CryptoJS.MD5;
 
 }));
-},{"./core":53}],62:[function(require,module,exports){
+},{"./core":52}],61:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9540,7 +9623,7 @@ module.exports = transfer;
 	return CryptoJS.mode.CFB;
 
 }));
-},{"./cipher-core":52,"./core":53}],63:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],62:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9657,7 +9740,7 @@ module.exports = transfer;
 	return CryptoJS.mode.CTRGladman;
 
 }));
-},{"./cipher-core":52,"./core":53}],64:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],63:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9716,7 +9799,7 @@ module.exports = transfer;
 	return CryptoJS.mode.CTR;
 
 }));
-},{"./cipher-core":52,"./core":53}],65:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],64:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9757,7 +9840,7 @@ module.exports = transfer;
 	return CryptoJS.mode.ECB;
 
 }));
-},{"./cipher-core":52,"./core":53}],66:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],65:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9812,7 +9895,7 @@ module.exports = transfer;
 	return CryptoJS.mode.OFB;
 
 }));
-},{"./cipher-core":52,"./core":53}],67:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],66:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9862,7 +9945,7 @@ module.exports = transfer;
 	return CryptoJS.pad.Ansix923;
 
 }));
-},{"./cipher-core":52,"./core":53}],68:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],67:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9907,7 +9990,7 @@ module.exports = transfer;
 	return CryptoJS.pad.Iso10126;
 
 }));
-},{"./cipher-core":52,"./core":53}],69:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],68:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9948,7 +10031,7 @@ module.exports = transfer;
 	return CryptoJS.pad.Iso97971;
 
 }));
-},{"./cipher-core":52,"./core":53}],70:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],69:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -9979,7 +10062,7 @@ module.exports = transfer;
 	return CryptoJS.pad.NoPadding;
 
 }));
-},{"./cipher-core":52,"./core":53}],71:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],70:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -10025,7 +10108,7 @@ module.exports = transfer;
 	return CryptoJS.pad.ZeroPadding;
 
 }));
-},{"./cipher-core":52,"./core":53}],72:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52}],71:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -10171,7 +10254,7 @@ module.exports = transfer;
 	return CryptoJS.PBKDF2;
 
 }));
-},{"./core":53,"./hmac":58,"./sha1":77}],73:[function(require,module,exports){
+},{"./core":52,"./hmac":57,"./sha1":76}],72:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -10362,7 +10445,7 @@ module.exports = transfer;
 	return CryptoJS.RabbitLegacy;
 
 }));
-},{"./cipher-core":52,"./core":53,"./enc-base64":54,"./evpkdf":56,"./md5":61}],74:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52,"./enc-base64":53,"./evpkdf":55,"./md5":60}],73:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -10555,7 +10638,7 @@ module.exports = transfer;
 	return CryptoJS.Rabbit;
 
 }));
-},{"./cipher-core":52,"./core":53,"./enc-base64":54,"./evpkdf":56,"./md5":61}],75:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52,"./enc-base64":53,"./evpkdf":55,"./md5":60}],74:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -10695,7 +10778,7 @@ module.exports = transfer;
 	return CryptoJS.RC4;
 
 }));
-},{"./cipher-core":52,"./core":53,"./enc-base64":54,"./evpkdf":56,"./md5":61}],76:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52,"./enc-base64":53,"./evpkdf":55,"./md5":60}],75:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -10963,7 +11046,7 @@ module.exports = transfer;
 	return CryptoJS.RIPEMD160;
 
 }));
-},{"./core":53}],77:[function(require,module,exports){
+},{"./core":52}],76:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -11114,7 +11197,7 @@ module.exports = transfer;
 	return CryptoJS.SHA1;
 
 }));
-},{"./core":53}],78:[function(require,module,exports){
+},{"./core":52}],77:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -11195,7 +11278,7 @@ module.exports = transfer;
 	return CryptoJS.SHA224;
 
 }));
-},{"./core":53,"./sha256":79}],79:[function(require,module,exports){
+},{"./core":52,"./sha256":78}],78:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -11395,7 +11478,7 @@ module.exports = transfer;
 	return CryptoJS.SHA256;
 
 }));
-},{"./core":53}],80:[function(require,module,exports){
+},{"./core":52}],79:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -11719,7 +11802,7 @@ module.exports = transfer;
 	return CryptoJS.SHA3;
 
 }));
-},{"./core":53,"./x64-core":84}],81:[function(require,module,exports){
+},{"./core":52,"./x64-core":83}],80:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -11803,7 +11886,7 @@ module.exports = transfer;
 	return CryptoJS.SHA384;
 
 }));
-},{"./core":53,"./sha512":82,"./x64-core":84}],82:[function(require,module,exports){
+},{"./core":52,"./sha512":81,"./x64-core":83}],81:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -12127,7 +12210,7 @@ module.exports = transfer;
 	return CryptoJS.SHA512;
 
 }));
-},{"./core":53,"./x64-core":84}],83:[function(require,module,exports){
+},{"./core":52,"./x64-core":83}],82:[function(require,module,exports){
 ;(function (root, factory, undef) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -12898,7 +12981,7 @@ module.exports = transfer;
 	return CryptoJS.TripleDES;
 
 }));
-},{"./cipher-core":52,"./core":53,"./enc-base64":54,"./evpkdf":56,"./md5":61}],84:[function(require,module,exports){
+},{"./cipher-core":51,"./core":52,"./enc-base64":53,"./evpkdf":55,"./md5":60}],83:[function(require,module,exports){
 ;(function (root, factory) {
 	if (typeof exports === "object") {
 		// CommonJS
@@ -13203,7 +13286,7 @@ module.exports = transfer;
 	return CryptoJS;
 
 }));
-},{"./core":53}],85:[function(require,module,exports){
+},{"./core":52}],84:[function(require,module,exports){
 /*! https://mths.be/utf8js v2.1.2 by @mathias */
 ;(function(root) {
 
@@ -13449,2695 +13532,2746 @@ module.exports = transfer;
 
 }(this));
 
-},{}],86:[function(require,module,exports){
+},{}],85:[function(require,module,exports){
 module.exports = XMLHttpRequest;
 
 },{}],"bignumber.js":[function(require,module,exports){
-/*! bignumber.js v2.0.7 https://github.com/MikeMcl/bignumber.js/LICENCE */
-
-;(function (global) {
-    'use strict';
-
-    /*
-      bignumber.js v2.0.7
-      A JavaScript library for arbitrary-precision arithmetic.
-      https://github.com/MikeMcl/bignumber.js
-      Copyright (c) 2015 Michael Mclaughlin <M8ch88l@gmail.com>
-      MIT Expat Licence
-    */
-
-
-    var BigNumber, crypto, parseNumeric,
-        isNumeric = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
-        mathceil = Math.ceil,
-        mathfloor = Math.floor,
-        notBool = ' not a boolean or binary digit',
-        roundingMode = 'rounding mode',
-        tooManyDigits = 'number type has more than 15 significant digits',
-        ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_',
-        BASE = 1e14,
-        LOG_BASE = 14,
-        MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
-        // MAX_INT32 = 0x7fffffff,                   // 2^31 - 1
-        POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
-        SQRT_BASE = 1e7,
-
-        /*
-         * The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
-         * the arguments to toExponential, toFixed, toFormat, and toPrecision, beyond which an
-         * exception is thrown (if ERRORS is true).
-         */
-        MAX = 1E9;                                   // 0 to MAX_INT32
-
-
-    /*
-     * Create and return a BigNumber constructor.
-     */
-    function another(configObj) {
-        var div,
-
-            // id tracks the caller function, so its name can be included in error messages.
-            id = 0,
-            P = BigNumber.prototype,
-            ONE = new BigNumber(1),
-
-
-            /********************************* EDITABLE DEFAULTS **********************************/
-
-
-            /*
-             * The default values below must be integers within the inclusive ranges stated.
-             * The values can also be changed at run-time using BigNumber.config.
-             */
-
-            // The maximum number of decimal places for operations involving division.
-            DECIMAL_PLACES = 20,                     // 0 to MAX
-
-            /*
-             * The rounding mode used when rounding to the above decimal places, and when using
-             * toExponential, toFixed, toFormat and toPrecision, and round (default value).
-             * UP         0 Away from zero.
-             * DOWN       1 Towards zero.
-             * CEIL       2 Towards +Infinity.
-             * FLOOR      3 Towards -Infinity.
-             * HALF_UP    4 Towards nearest neighbour. If equidistant, up.
-             * HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
-             * HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
-             * HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
-             * HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
-             */
-            ROUNDING_MODE = 4,                       // 0 to 8
-
-            // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
-
-            // The exponent value at and beneath which toString returns exponential notation.
-            // Number type: -7
-            TO_EXP_NEG = -7,                         // 0 to -MAX
-
-            // The exponent value at and above which toString returns exponential notation.
-            // Number type: 21
-            TO_EXP_POS = 21,                         // 0 to MAX
-
-            // RANGE : [MIN_EXP, MAX_EXP]
-
-            // The minimum exponent value, beneath which underflow to zero occurs.
-            // Number type: -324  (5e-324)
-            MIN_EXP = -1e7,                          // -1 to -MAX
-
-            // The maximum exponent value, above which overflow to Infinity occurs.
-            // Number type:  308  (1.7976931348623157e+308)
-            // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
-            MAX_EXP = 1e7,                           // 1 to MAX
-
-            // Whether BigNumber Errors are ever thrown.
-            ERRORS = true,                           // true or false
-
-            // Change to intValidatorNoErrors if ERRORS is false.
-            isValidInt = intValidatorWithErrors,     // intValidatorWithErrors/intValidatorNoErrors
-
-            // Whether to use cryptographically-secure random number generation, if available.
-            CRYPTO = false,                          // true or false
-
-            /*
-             * The modulo mode used when calculating the modulus: a mod n.
-             * The quotient (q = a / n) is calculated according to the corresponding rounding mode.
-             * The remainder (r) is calculated as: r = a - n * q.
-             *
-             * UP        0 The remainder is positive if the dividend is negative, else is negative.
-             * DOWN      1 The remainder has the same sign as the dividend.
-             *             This modulo mode is commonly known as 'truncated division' and is
-             *             equivalent to (a % n) in JavaScript.
-             * FLOOR     3 The remainder has the same sign as the divisor (Python %).
-             * HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
-             * EUCLID    9 Euclidian division. q = sign(n) * floor(a / abs(n)).
-             *             The remainder is always positive.
-             *
-             * The truncated division, floored division, Euclidian division and IEEE 754 remainder
-             * modes are commonly used for the modulus operation.
-             * Although the other rounding modes can also be used, they may not give useful results.
-             */
-            MODULO_MODE = 1,                         // 0 to 9
-
-            // The maximum number of significant digits of the result of the toPower operation.
-            // If POW_PRECISION is 0, there will be unlimited significant digits.
-            POW_PRECISION = 100,                     // 0 to MAX
-
-            // The format specification used by the BigNumber.prototype.toFormat method.
-            FORMAT = {
-                decimalSeparator: '.',
-                groupSeparator: ',',
-                groupSize: 3,
-                secondaryGroupSize: 0,
-                fractionGroupSeparator: '\xA0',      // non-breaking space
-                fractionGroupSize: 0
-            };
-
-
-        /******************************************************************************************/
-
-
-        // CONSTRUCTOR
-
-
-        /*
-         * The BigNumber constructor and exported function.
-         * Create and return a new instance of a BigNumber object.
-         *
-         * n {number|string|BigNumber} A numeric value.
-         * [b] {number} The base of n. Integer, 2 to 64 inclusive.
-         */
-        function BigNumber( n, b ) {
-            var c, e, i, num, len, str,
-                x = this;
-
-            // Enable constructor usage without new.
-            if ( !( x instanceof BigNumber ) ) {
-
-                // 'BigNumber() constructor call without new: {n}'
-                if (ERRORS) raise( 26, 'constructor call without new', n );
-                return new BigNumber( n, b );
-            }
-
-            // 'new BigNumber() base not an integer: {b}'
-            // 'new BigNumber() base out of range: {b}'
-            if ( b == null || !isValidInt( b, 2, 64, id, 'base' ) ) {
-
-                // Duplicate.
-                if ( n instanceof BigNumber ) {
-                    x.s = n.s;
-                    x.e = n.e;
-                    x.c = ( n = n.c ) ? n.slice() : n;
-                    id = 0;
-                    return;
-                }
-
-                if ( ( num = typeof n == 'number' ) && n * 0 == 0 ) {
-                    x.s = 1 / n < 0 ? ( n = -n, -1 ) : 1;
-
-                    // Fast path for integers.
-                    if ( n === ~~n ) {
-                        for ( e = 0, i = n; i >= 10; i /= 10, e++ );
-                        x.e = e;
-                        x.c = [n];
-                        id = 0;
-                        return;
-                    }
-
-                    str = n + '';
-                } else {
-                    if ( !isNumeric.test( str = n + '' ) ) return parseNumeric( x, str, num );
-                    x.s = str.charCodeAt(0) === 45 ? ( str = str.slice(1), -1 ) : 1;
-                }
-            } else {
-                b = b | 0;
-                str = n + '';
-
-                // Ensure return value is rounded to DECIMAL_PLACES as with other bases.
-                // Allow exponential notation to be used with base 10 argument.
-                if ( b == 10 ) {
-                    x = new BigNumber( n instanceof BigNumber ? n : str );
-                    return round( x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE );
-                }
-
-                // Avoid potential interpretation of Infinity and NaN as base 44+ values.
-                // Any number in exponential form will fail due to the [Ee][+-].
-                if ( ( num = typeof n == 'number' ) && n * 0 != 0 ||
-                  !( new RegExp( '^-?' + ( c = '[' + ALPHABET.slice( 0, b ) + ']+' ) +
-                    '(?:\\.' + c + ')?$',b < 37 ? 'i' : '' ) ).test(str) ) {
-                    return parseNumeric( x, str, num, b );
-                }
-
-                if (num) {
-                    x.s = 1 / n < 0 ? ( str = str.slice(1), -1 ) : 1;
-
-                    if ( ERRORS && str.replace( /^0\.0*|\./, '' ).length > 15 ) {
-
-                        // 'new BigNumber() number type has more than 15 significant digits: {n}'
-                        raise( id, tooManyDigits, n );
-                    }
-
-                    // Prevent later check for length on converted number.
-                    num = false;
-                } else {
-                    x.s = str.charCodeAt(0) === 45 ? ( str = str.slice(1), -1 ) : 1;
-                }
-
-                str = convertBase( str, 10, b, x.s );
-            }
-
-            // Decimal point?
-            if ( ( e = str.indexOf('.') ) > -1 ) str = str.replace( '.', '' );
-
-            // Exponential form?
-            if ( ( i = str.search( /e/i ) ) > 0 ) {
-
-                // Determine exponent.
-                if ( e < 0 ) e = i;
-                e += +str.slice( i + 1 );
-                str = str.substring( 0, i );
-            } else if ( e < 0 ) {
-
-                // Integer.
-                e = str.length;
-            }
-
-            // Determine leading zeros.
-            for ( i = 0; str.charCodeAt(i) === 48; i++ );
-
-            // Determine trailing zeros.
-            for ( len = str.length; str.charCodeAt(--len) === 48; );
-            str = str.slice( i, len + 1 );
-
-            if (str) {
-                len = str.length;
-
-                // Disallow numbers with over 15 significant digits if number type.
-                // 'new BigNumber() number type has more than 15 significant digits: {n}'
-                if ( num && ERRORS && len > 15 ) raise( id, tooManyDigits, x.s * n );
-
-                e = e - i - 1;
-
-                 // Overflow?
-                if ( e > MAX_EXP ) {
-
-                    // Infinity.
-                    x.c = x.e = null;
-
-                // Underflow?
-                } else if ( e < MIN_EXP ) {
-
-                    // Zero.
-                    x.c = [ x.e = 0 ];
-                } else {
-                    x.e = e;
-                    x.c = [];
-
-                    // Transform base
-
-                    // e is the base 10 exponent.
-                    // i is where to slice str to get the first element of the coefficient array.
-                    i = ( e + 1 ) % LOG_BASE;
-                    if ( e < 0 ) i += LOG_BASE;
-
-                    if ( i < len ) {
-                        if (i) x.c.push( +str.slice( 0, i ) );
-
-                        for ( len -= LOG_BASE; i < len; ) {
-                            x.c.push( +str.slice( i, i += LOG_BASE ) );
-                        }
-
-                        str = str.slice(i);
-                        i = LOG_BASE - str.length;
-                    } else {
-                        i -= len;
-                    }
-
-                    for ( ; i--; str += '0' );
-                    x.c.push( +str );
-                }
-            } else {
-
-                // Zero.
-                x.c = [ x.e = 0 ];
-            }
-
-            id = 0;
-        }
-
-
-        // CONSTRUCTOR PROPERTIES
-
-
-        BigNumber.another = another;
-
-        BigNumber.ROUND_UP = 0;
-        BigNumber.ROUND_DOWN = 1;
-        BigNumber.ROUND_CEIL = 2;
-        BigNumber.ROUND_FLOOR = 3;
-        BigNumber.ROUND_HALF_UP = 4;
-        BigNumber.ROUND_HALF_DOWN = 5;
-        BigNumber.ROUND_HALF_EVEN = 6;
-        BigNumber.ROUND_HALF_CEIL = 7;
-        BigNumber.ROUND_HALF_FLOOR = 8;
-        BigNumber.EUCLID = 9;
-
-
-        /*
-         * Configure infrequently-changing library-wide settings.
-         *
-         * Accept an object or an argument list, with one or many of the following properties or
-         * parameters respectively:
-         *
-         *   DECIMAL_PLACES  {number}  Integer, 0 to MAX inclusive
-         *   ROUNDING_MODE   {number}  Integer, 0 to 8 inclusive
-         *   EXPONENTIAL_AT  {number|number[]}  Integer, -MAX to MAX inclusive or
-         *                                      [integer -MAX to 0 incl., 0 to MAX incl.]
-         *   RANGE           {number|number[]}  Non-zero integer, -MAX to MAX inclusive or
-         *                                      [integer -MAX to -1 incl., integer 1 to MAX incl.]
-         *   ERRORS          {boolean|number}   true, false, 1 or 0
-         *   CRYPTO          {boolean|number}   true, false, 1 or 0
-         *   MODULO_MODE     {number}           0 to 9 inclusive
-         *   POW_PRECISION   {number}           0 to MAX inclusive
-         *   FORMAT          {object}           See BigNumber.prototype.toFormat
-         *      decimalSeparator       {string}
-         *      groupSeparator         {string}
-         *      groupSize              {number}
-         *      secondaryGroupSize     {number}
-         *      fractionGroupSeparator {string}
-         *      fractionGroupSize      {number}
-         *
-         * (The values assigned to the above FORMAT object properties are not checked for validity.)
-         *
-         * E.g.
-         * BigNumber.config(20, 4) is equivalent to
-         * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
-         *
-         * Ignore properties/parameters set to null or undefined.
-         * Return an object with the properties current values.
-         */
-        BigNumber.config = function () {
-            var v, p,
-                i = 0,
-                r = {},
-                a = arguments,
-                o = a[0],
-                has = o && typeof o == 'object'
-                  ? function () { if ( o.hasOwnProperty(p) ) return ( v = o[p] ) != null; }
-                  : function () { if ( a.length > i ) return ( v = a[i++] ) != null; };
-
-            // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
-            // 'config() DECIMAL_PLACES not an integer: {v}'
-            // 'config() DECIMAL_PLACES out of range: {v}'
-            if ( has( p = 'DECIMAL_PLACES' ) && isValidInt( v, 0, MAX, 2, p ) ) {
-                DECIMAL_PLACES = v | 0;
-            }
-            r[p] = DECIMAL_PLACES;
-
-            // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
-            // 'config() ROUNDING_MODE not an integer: {v}'
-            // 'config() ROUNDING_MODE out of range: {v}'
-            if ( has( p = 'ROUNDING_MODE' ) && isValidInt( v, 0, 8, 2, p ) ) {
-                ROUNDING_MODE = v | 0;
-            }
-            r[p] = ROUNDING_MODE;
-
-            // EXPONENTIAL_AT {number|number[]}
-            // Integer, -MAX to MAX inclusive or [integer -MAX to 0 inclusive, 0 to MAX inclusive].
-            // 'config() EXPONENTIAL_AT not an integer: {v}'
-            // 'config() EXPONENTIAL_AT out of range: {v}'
-            if ( has( p = 'EXPONENTIAL_AT' ) ) {
-
-                if ( isArray(v) ) {
-                    if ( isValidInt( v[0], -MAX, 0, 2, p ) && isValidInt( v[1], 0, MAX, 2, p ) ) {
-                        TO_EXP_NEG = v[0] | 0;
-                        TO_EXP_POS = v[1] | 0;
-                    }
-                } else if ( isValidInt( v, -MAX, MAX, 2, p ) ) {
-                    TO_EXP_NEG = -( TO_EXP_POS = ( v < 0 ? -v : v ) | 0 );
-                }
-            }
-            r[p] = [ TO_EXP_NEG, TO_EXP_POS ];
-
-            // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
-            // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
-            // 'config() RANGE not an integer: {v}'
-            // 'config() RANGE cannot be zero: {v}'
-            // 'config() RANGE out of range: {v}'
-            if ( has( p = 'RANGE' ) ) {
-
-                if ( isArray(v) ) {
-                    if ( isValidInt( v[0], -MAX, -1, 2, p ) && isValidInt( v[1], 1, MAX, 2, p ) ) {
-                        MIN_EXP = v[0] | 0;
-                        MAX_EXP = v[1] | 0;
-                    }
-                } else if ( isValidInt( v, -MAX, MAX, 2, p ) ) {
-                    if ( v | 0 ) MIN_EXP = -( MAX_EXP = ( v < 0 ? -v : v ) | 0 );
-                    else if (ERRORS) raise( 2, p + ' cannot be zero', v );
-                }
-            }
-            r[p] = [ MIN_EXP, MAX_EXP ];
-
-            // ERRORS {boolean|number} true, false, 1 or 0.
-            // 'config() ERRORS not a boolean or binary digit: {v}'
-            if ( has( p = 'ERRORS' ) ) {
-
-                if ( v === !!v || v === 1 || v === 0 ) {
-                    id = 0;
-                    isValidInt = ( ERRORS = !!v ) ? intValidatorWithErrors : intValidatorNoErrors;
-                } else if (ERRORS) {
-                    raise( 2, p + notBool, v );
-                }
-            }
-            r[p] = ERRORS;
-
-            // CRYPTO {boolean|number} true, false, 1 or 0.
-            // 'config() CRYPTO not a boolean or binary digit: {v}'
-            // 'config() crypto unavailable: {crypto}'
-            if ( has( p = 'CRYPTO' ) ) {
-
-                if ( v === !!v || v === 1 || v === 0 ) {
-                    CRYPTO = !!( v && crypto && typeof crypto == 'object' );
-                    if ( v && !CRYPTO && ERRORS ) raise( 2, 'crypto unavailable', crypto );
-                } else if (ERRORS) {
-                    raise( 2, p + notBool, v );
-                }
-            }
-            r[p] = CRYPTO;
-
-            // MODULO_MODE {number} Integer, 0 to 9 inclusive.
-            // 'config() MODULO_MODE not an integer: {v}'
-            // 'config() MODULO_MODE out of range: {v}'
-            if ( has( p = 'MODULO_MODE' ) && isValidInt( v, 0, 9, 2, p ) ) {
-                MODULO_MODE = v | 0;
-            }
-            r[p] = MODULO_MODE;
-
-            // POW_PRECISION {number} Integer, 0 to MAX inclusive.
-            // 'config() POW_PRECISION not an integer: {v}'
-            // 'config() POW_PRECISION out of range: {v}'
-            if ( has( p = 'POW_PRECISION' ) && isValidInt( v, 0, MAX, 2, p ) ) {
-                POW_PRECISION = v | 0;
-            }
-            r[p] = POW_PRECISION;
-
-            // FORMAT {object}
-            // 'config() FORMAT not an object: {v}'
-            if ( has( p = 'FORMAT' ) ) {
-
-                if ( typeof v == 'object' ) {
-                    FORMAT = v;
-                } else if (ERRORS) {
-                    raise( 2, p + ' not an object', v );
-                }
-            }
-            r[p] = FORMAT;
-
-            return r;
-        };
-
-
-        /*
-         * Return a new BigNumber whose value is the maximum of the arguments.
-         *
-         * arguments {number|string|BigNumber}
-         */
-        BigNumber.max = function () { return maxOrMin( arguments, P.lt ); };
-
-
-        /*
-         * Return a new BigNumber whose value is the minimum of the arguments.
-         *
-         * arguments {number|string|BigNumber}
-         */
-        BigNumber.min = function () { return maxOrMin( arguments, P.gt ); };
-
-
-        /*
-         * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
-         * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
-         * zeros are produced).
-         *
-         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
-         *
-         * 'random() decimal places not an integer: {dp}'
-         * 'random() decimal places out of range: {dp}'
-         * 'random() crypto unavailable: {crypto}'
-         */
-        BigNumber.random = (function () {
-            var pow2_53 = 0x20000000000000;
-
-            // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
-            // Check if Math.random() produces more than 32 bits of randomness.
-            // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
-            // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
-            var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
-              ? function () { return mathfloor( Math.random() * pow2_53 ); }
-              : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
-                  (Math.random() * 0x800000 | 0); };
-
-            return function (dp) {
-                var a, b, e, k, v,
-                    i = 0,
-                    c = [],
-                    rand = new BigNumber(ONE);
-
-                dp = dp == null || !isValidInt( dp, 0, MAX, 14 ) ? DECIMAL_PLACES : dp | 0;
-                k = mathceil( dp / LOG_BASE );
-
-                if (CRYPTO) {
-
-                    // Browsers supporting crypto.getRandomValues.
-                    if ( crypto && crypto.getRandomValues ) {
-
-                        a = crypto.getRandomValues( new Uint32Array( k *= 2 ) );
-
-                        for ( ; i < k; ) {
-
-                            // 53 bits:
-                            // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
-                            // 11111 11111111 11111111 11111111 11100000 00000000 00000000
-                            // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
-                            //                                     11111 11111111 11111111
-                            // 0x20000 is 2^21.
-                            v = a[i] * 0x20000 + (a[i + 1] >>> 11);
-
-                            // Rejection sampling:
-                            // 0 <= v < 9007199254740992
-                            // Probability that v >= 9e15, is
-                            // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
-                            if ( v >= 9e15 ) {
-                                b = crypto.getRandomValues( new Uint32Array(2) );
-                                a[i] = b[0];
-                                a[i + 1] = b[1];
-                            } else {
-
-                                // 0 <= v <= 8999999999999999
-                                // 0 <= (v % 1e14) <= 99999999999999
-                                c.push( v % 1e14 );
-                                i += 2;
-                            }
-                        }
-                        i = k / 2;
-
-                    // Node.js supporting crypto.randomBytes.
-                    } else if ( crypto && crypto.randomBytes ) {
-
-                        // buffer
-                        a = crypto.randomBytes( k *= 7 );
-
-                        for ( ; i < k; ) {
-
-                            // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
-                            // 0x100000000 is 2^32, 0x1000000 is 2^24
-                            // 11111 11111111 11111111 11111111 11111111 11111111 11111111
-                            // 0 <= v < 9007199254740992
-                            v = ( ( a[i] & 31 ) * 0x1000000000000 ) + ( a[i + 1] * 0x10000000000 ) +
-                                  ( a[i + 2] * 0x100000000 ) + ( a[i + 3] * 0x1000000 ) +
-                                  ( a[i + 4] << 16 ) + ( a[i + 5] << 8 ) + a[i + 6];
-
-                            if ( v >= 9e15 ) {
-                                crypto.randomBytes(7).copy( a, i );
-                            } else {
-
-                                // 0 <= (v % 1e14) <= 99999999999999
-                                c.push( v % 1e14 );
-                                i += 7;
-                            }
-                        }
-                        i = k / 7;
-                    } else if (ERRORS) {
-                        raise( 14, 'crypto unavailable', crypto );
-                    }
-                }
-
-                // Use Math.random: CRYPTO is false or crypto is unavailable and ERRORS is false.
-                if (!i) {
-
-                    for ( ; i < k; ) {
-                        v = random53bitInt();
-                        if ( v < 9e15 ) c[i++] = v % 1e14;
-                    }
-                }
-
-                k = c[--i];
-                dp %= LOG_BASE;
-
-                // Convert trailing digits to zeros according to dp.
-                if ( k && dp ) {
-                    v = POWS_TEN[LOG_BASE - dp];
-                    c[i] = mathfloor( k / v ) * v;
-                }
-
-                // Remove trailing elements which are zero.
-                for ( ; c[i] === 0; c.pop(), i-- );
-
-                // Zero?
-                if ( i < 0 ) {
-                    c = [ e = 0 ];
-                } else {
-
-                    // Remove leading elements which are zero and adjust exponent accordingly.
-                    for ( e = -1 ; c[0] === 0; c.shift(), e -= LOG_BASE);
-
-                    // Count the digits of the first element of c to determine leading zeros, and...
-                    for ( i = 1, v = c[0]; v >= 10; v /= 10, i++);
-
-                    // adjust the exponent accordingly.
-                    if ( i < LOG_BASE ) e -= LOG_BASE - i;
-                }
-
-                rand.e = e;
-                rand.c = c;
-                return rand;
-            };
-        })();
-
-
-        // PRIVATE FUNCTIONS
-
-
-        // Convert a numeric string of baseIn to a numeric string of baseOut.
-        function convertBase( str, baseOut, baseIn, sign ) {
-            var d, e, k, r, x, xc, y,
-                i = str.indexOf( '.' ),
-                dp = DECIMAL_PLACES,
-                rm = ROUNDING_MODE;
-
-            if ( baseIn < 37 ) str = str.toLowerCase();
-
-            // Non-integer.
-            if ( i >= 0 ) {
-                k = POW_PRECISION;
-
-                // Unlimited precision.
-                POW_PRECISION = 0;
-                str = str.replace( '.', '' );
-                y = new BigNumber(baseIn);
-                x = y.pow( str.length - i );
-                POW_PRECISION = k;
-
-                // Convert str as if an integer, then restore the fraction part by dividing the
-                // result by its base raised to a power.
-                y.c = toBaseOut( toFixedPoint( coeffToString( x.c ), x.e ), 10, baseOut );
-                y.e = y.c.length;
-            }
-
-            // Convert the number as integer.
-            xc = toBaseOut( str, baseIn, baseOut );
-            e = k = xc.length;
-
-            // Remove trailing zeros.
-            for ( ; xc[--k] == 0; xc.pop() );
-            if ( !xc[0] ) return '0';
-
-            if ( i < 0 ) {
-                --e;
-            } else {
-                x.c = xc;
-                x.e = e;
-
-                // sign is needed for correct rounding.
-                x.s = sign;
-                x = div( x, y, dp, rm, baseOut );
-                xc = x.c;
-                r = x.r;
-                e = x.e;
-            }
-
-            d = e + dp + 1;
-
-            // The rounding digit, i.e. the digit to the right of the digit that may be rounded up.
-            i = xc[d];
-            k = baseOut / 2;
-            r = r || d < 0 || xc[d + 1] != null;
-
-            r = rm < 4 ? ( i != null || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
-                       : i > k || i == k &&( rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
-                         rm == ( x.s < 0 ? 8 : 7 ) );
-
-            if ( d < 1 || !xc[0] ) {
-
-                // 1^-dp or 0.
-                str = r ? toFixedPoint( '1', -dp ) : '0';
-            } else {
-                xc.length = d;
-
-                if (r) {
-
-                    // Rounding up may mean the previous digit has to be rounded up and so on.
-                    for ( --baseOut; ++xc[--d] > baseOut; ) {
-                        xc[d] = 0;
-
-                        if ( !d ) {
-                            ++e;
-                            xc.unshift(1);
-                        }
-                    }
-                }
-
-                // Determine trailing zeros.
-                for ( k = xc.length; !xc[--k]; );
-
-                // E.g. [4, 11, 15] becomes 4bf.
-                for ( i = 0, str = ''; i <= k; str += ALPHABET.charAt( xc[i++] ) );
-                str = toFixedPoint( str, e );
-            }
-
-            // The caller will add the sign.
-            return str;
-        }
-
-
-        // Perform division in the specified base. Called by div and convertBase.
-        div = (function () {
-
-            // Assume non-zero x and k.
-            function multiply( x, k, base ) {
-                var m, temp, xlo, xhi,
-                    carry = 0,
-                    i = x.length,
-                    klo = k % SQRT_BASE,
-                    khi = k / SQRT_BASE | 0;
-
-                for ( x = x.slice(); i--; ) {
-                    xlo = x[i] % SQRT_BASE;
-                    xhi = x[i] / SQRT_BASE | 0;
-                    m = khi * xlo + xhi * klo;
-                    temp = klo * xlo + ( ( m % SQRT_BASE ) * SQRT_BASE ) + carry;
-                    carry = ( temp / base | 0 ) + ( m / SQRT_BASE | 0 ) + khi * xhi;
-                    x[i] = temp % base;
-                }
-
-                if (carry) x.unshift(carry);
-
-                return x;
-            }
-
-            function compare( a, b, aL, bL ) {
-                var i, cmp;
-
-                if ( aL != bL ) {
-                    cmp = aL > bL ? 1 : -1;
-                } else {
-
-                    for ( i = cmp = 0; i < aL; i++ ) {
-
-                        if ( a[i] != b[i] ) {
-                            cmp = a[i] > b[i] ? 1 : -1;
-                            break;
-                        }
-                    }
-                }
-                return cmp;
-            }
-
-            function subtract( a, b, aL, base ) {
-                var i = 0;
-
-                // Subtract b from a.
-                for ( ; aL--; ) {
-                    a[aL] -= i;
-                    i = a[aL] < b[aL] ? 1 : 0;
-                    a[aL] = i * base + a[aL] - b[aL];
-                }
-
-                // Remove leading zeros.
-                for ( ; !a[0] && a.length > 1; a.shift() );
-            }
-
-            // x: dividend, y: divisor.
-            return function ( x, y, dp, rm, base ) {
-                var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
-                    yL, yz,
-                    s = x.s == y.s ? 1 : -1,
-                    xc = x.c,
-                    yc = y.c;
-
-                // Either NaN, Infinity or 0?
-                if ( !xc || !xc[0] || !yc || !yc[0] ) {
-
-                    return new BigNumber(
-
-                      // Return NaN if either NaN, or both Infinity or 0.
-                      !x.s || !y.s || ( xc ? yc && xc[0] == yc[0] : !yc ) ? NaN :
-
-                        // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
-                        xc && xc[0] == 0 || !yc ? s * 0 : s / 0
-                    );
-                }
-
-                q = new BigNumber(s);
-                qc = q.c = [];
-                e = x.e - y.e;
-                s = dp + e + 1;
-
-                if ( !base ) {
-                    base = BASE;
-                    e = bitFloor( x.e / LOG_BASE ) - bitFloor( y.e / LOG_BASE );
-                    s = s / LOG_BASE | 0;
-                }
-
-                // Result exponent may be one less then the current value of e.
-                // The coefficients of the BigNumbers from convertBase may have trailing zeros.
-                for ( i = 0; yc[i] == ( xc[i] || 0 ); i++ );
-                if ( yc[i] > ( xc[i] || 0 ) ) e--;
-
-                if ( s < 0 ) {
-                    qc.push(1);
-                    more = true;
-                } else {
-                    xL = xc.length;
-                    yL = yc.length;
-                    i = 0;
-                    s += 2;
-
-                    // Normalise xc and yc so highest order digit of yc is >= base / 2.
-
-                    n = mathfloor( base / ( yc[0] + 1 ) );
-
-                    // Not necessary, but to handle odd bases where yc[0] == ( base / 2 ) - 1.
-                    // if ( n > 1 || n++ == 1 && yc[0] < base / 2 ) {
-                    if ( n > 1 ) {
-                        yc = multiply( yc, n, base );
-                        xc = multiply( xc, n, base );
-                        yL = yc.length;
-                        xL = xc.length;
-                    }
-
-                    xi = yL;
-                    rem = xc.slice( 0, yL );
-                    remL = rem.length;
-
-                    // Add zeros to make remainder as long as divisor.
-                    for ( ; remL < yL; rem[remL++] = 0 );
-                    yz = yc.slice();
-                    yz.unshift(0);
-                    yc0 = yc[0];
-                    if ( yc[1] >= base / 2 ) yc0++;
-                    // Not necessary, but to prevent trial digit n > base, when using base 3.
-                    // else if ( base == 3 && yc0 == 1 ) yc0 = 1 + 1e-15;
-
-                    do {
-                        n = 0;
-
-                        // Compare divisor and remainder.
-                        cmp = compare( yc, rem, yL, remL );
-
-                        // If divisor < remainder.
-                        if ( cmp < 0 ) {
-
-                            // Calculate trial digit, n.
-
-                            rem0 = rem[0];
-                            if ( yL != remL ) rem0 = rem0 * base + ( rem[1] || 0 );
-
-                            // n is how many times the divisor goes into the current remainder.
-                            n = mathfloor( rem0 / yc0 );
-
-                            //  Algorithm:
-                            //  1. product = divisor * trial digit (n)
-                            //  2. if product > remainder: product -= divisor, n--
-                            //  3. remainder -= product
-                            //  4. if product was < remainder at 2:
-                            //    5. compare new remainder and divisor
-                            //    6. If remainder > divisor: remainder -= divisor, n++
-
-                            if ( n > 1 ) {
-
-                                // n may be > base only when base is 3.
-                                if (n >= base) n = base - 1;
-
-                                // product = divisor * trial digit.
-                                prod = multiply( yc, n, base );
-                                prodL = prod.length;
-                                remL = rem.length;
-
-                                // Compare product and remainder.
-                                // If product > remainder.
-                                // Trial digit n too high.
-                                // n is 1 too high about 5% of the time, and is not known to have
-                                // ever been more than 1 too high.
-                                while ( compare( prod, rem, prodL, remL ) == 1 ) {
-                                    n--;
-
-                                    // Subtract divisor from product.
-                                    subtract( prod, yL < prodL ? yz : yc, prodL, base );
-                                    prodL = prod.length;
-                                    cmp = 1;
-                                }
-                            } else {
-
-                                // n is 0 or 1, cmp is -1.
-                                // If n is 0, there is no need to compare yc and rem again below,
-                                // so change cmp to 1 to avoid it.
-                                // If n is 1, leave cmp as -1, so yc and rem are compared again.
-                                if ( n == 0 ) {
-
-                                    // divisor < remainder, so n must be at least 1.
-                                    cmp = n = 1;
-                                }
-
-                                // product = divisor
-                                prod = yc.slice();
-                                prodL = prod.length;
-                            }
-
-                            if ( prodL < remL ) prod.unshift(0);
-
-                            // Subtract product from remainder.
-                            subtract( rem, prod, remL, base );
-                            remL = rem.length;
-
-                             // If product was < remainder.
-                            if ( cmp == -1 ) {
-
-                                // Compare divisor and new remainder.
-                                // If divisor < new remainder, subtract divisor from remainder.
-                                // Trial digit n too low.
-                                // n is 1 too low about 5% of the time, and very rarely 2 too low.
-                                while ( compare( yc, rem, yL, remL ) < 1 ) {
-                                    n++;
-
-                                    // Subtract divisor from remainder.
-                                    subtract( rem, yL < remL ? yz : yc, remL, base );
-                                    remL = rem.length;
-                                }
-                            }
-                        } else if ( cmp === 0 ) {
-                            n++;
-                            rem = [0];
-                        } // else cmp === 1 and n will be 0
-
-                        // Add the next digit, n, to the result array.
-                        qc[i++] = n;
-
-                        // Update the remainder.
-                        if ( rem[0] ) {
-                            rem[remL++] = xc[xi] || 0;
-                        } else {
-                            rem = [ xc[xi] ];
-                            remL = 1;
-                        }
-                    } while ( ( xi++ < xL || rem[0] != null ) && s-- );
-
-                    more = rem[0] != null;
-
-                    // Leading zero?
-                    if ( !qc[0] ) qc.shift();
-                }
-
-                if ( base == BASE ) {
-
-                    // To calculate q.e, first get the number of digits of qc[0].
-                    for ( i = 1, s = qc[0]; s >= 10; s /= 10, i++ );
-                    round( q, dp + ( q.e = i + e * LOG_BASE - 1 ) + 1, rm, more );
-
-                // Caller is convertBase.
-                } else {
-                    q.e = e;
-                    q.r = +more;
-                }
-
-                return q;
-            };
-        })();
-
-
-        /*
-         * Return a string representing the value of BigNumber n in fixed-point or exponential
-         * notation rounded to the specified decimal places or significant digits.
-         *
-         * n is a BigNumber.
-         * i is the index of the last digit required (i.e. the digit that may be rounded up).
-         * rm is the rounding mode.
-         * caller is caller id: toExponential 19, toFixed 20, toFormat 21, toPrecision 24.
-         */
-        function format( n, i, rm, caller ) {
-            var c0, e, ne, len, str;
-
-            rm = rm != null && isValidInt( rm, 0, 8, caller, roundingMode )
-              ? rm | 0 : ROUNDING_MODE;
-
-            if ( !n.c ) return n.toString();
-            c0 = n.c[0];
-            ne = n.e;
-
-            if ( i == null ) {
-                str = coeffToString( n.c );
-                str = caller == 19 || caller == 24 && ne <= TO_EXP_NEG
-                  ? toExponential( str, ne )
-                  : toFixedPoint( str, ne );
-            } else {
-                n = round( new BigNumber(n), i, rm );
-
-                // n.e may have changed if the value was rounded up.
-                e = n.e;
-
-                str = coeffToString( n.c );
-                len = str.length;
-
-                // toPrecision returns exponential notation if the number of significant digits
-                // specified is less than the number of digits necessary to represent the integer
-                // part of the value in fixed-point notation.
-
-                // Exponential notation.
-                if ( caller == 19 || caller == 24 && ( i <= e || e <= TO_EXP_NEG ) ) {
-
-                    // Append zeros?
-                    for ( ; len < i; str += '0', len++ );
-                    str = toExponential( str, e );
-
-                // Fixed-point notation.
-                } else {
-                    i -= ne;
-                    str = toFixedPoint( str, e );
-
-                    // Append zeros?
-                    if ( e + 1 > len ) {
-                        if ( --i > 0 ) for ( str += '.'; i--; str += '0' );
-                    } else {
-                        i += e - len;
-                        if ( i > 0 ) {
-                            if ( e + 1 == len ) str += '.';
-                            for ( ; i--; str += '0' );
-                        }
-                    }
-                }
-            }
-
-            return n.s < 0 && c0 ? '-' + str : str;
-        }
-
-
-        // Handle BigNumber.max and BigNumber.min.
-        function maxOrMin( args, method ) {
-            var m, n,
-                i = 0;
-
-            if ( isArray( args[0] ) ) args = args[0];
-            m = new BigNumber( args[0] );
-
-            for ( ; ++i < args.length; ) {
-                n = new BigNumber( args[i] );
-
-                // If any number is NaN, return NaN.
-                if ( !n.s ) {
-                    m = n;
-                    break;
-                } else if ( method.call( m, n ) ) {
-                    m = n;
-                }
-            }
-
-            return m;
-        }
-
-
-        /*
-         * Return true if n is an integer in range, otherwise throw.
-         * Use for argument validation when ERRORS is true.
-         */
-        function intValidatorWithErrors( n, min, max, caller, name ) {
-            if ( n < min || n > max || n != truncate(n) ) {
-                raise( caller, ( name || 'decimal places' ) +
-                  ( n < min || n > max ? ' out of range' : ' not an integer' ), n );
-            }
-
-            return true;
-        }
-
-
-        /*
-         * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
-         * Called by minus, plus and times.
-         */
-        function normalise( n, c, e ) {
-            var i = 1,
-                j = c.length;
-
-             // Remove trailing zeros.
-            for ( ; !c[--j]; c.pop() );
-
-            // Calculate the base 10 exponent. First get the number of digits of c[0].
-            for ( j = c[0]; j >= 10; j /= 10, i++ );
-
-            // Overflow?
-            if ( ( e = i + e * LOG_BASE - 1 ) > MAX_EXP ) {
-
-                // Infinity.
-                n.c = n.e = null;
-
-            // Underflow?
-            } else if ( e < MIN_EXP ) {
-
-                // Zero.
-                n.c = [ n.e = 0 ];
-            } else {
-                n.e = e;
-                n.c = c;
-            }
-
-            return n;
-        }
-
-
-        // Handle values that fail the validity test in BigNumber.
-        parseNumeric = (function () {
-            var basePrefix = /^(-?)0([xbo])/i,
-                dotAfter = /^([^.]+)\.$/,
-                dotBefore = /^\.([^.]+)$/,
-                isInfinityOrNaN = /^-?(Infinity|NaN)$/,
-                whitespaceOrPlus = /^\s*\+|^\s+|\s+$/g;
-
-            return function ( x, str, num, b ) {
-                var base,
-                    s = num ? str : str.replace( whitespaceOrPlus, '' );
-
-                // No exception on ±Infinity or NaN.
-                if ( isInfinityOrNaN.test(s) ) {
-                    x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
-                } else {
-                    if ( !num ) {
-
-                        // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
-                        s = s.replace( basePrefix, function ( m, p1, p2 ) {
-                            base = ( p2 = p2.toLowerCase() ) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
-                            return !b || b == base ? p1 : m;
-                        });
-
-                        if (b) {
-                            base = b;
-
-                            // E.g. '1.' to '1', '.1' to '0.1'
-                            s = s.replace( dotAfter, '$1' ).replace( dotBefore, '0.$1' );
-                        }
-
-                        if ( str != s ) return new BigNumber( s, base );
-                    }
-
-                    // 'new BigNumber() not a number: {n}'
-                    // 'new BigNumber() not a base {b} number: {n}'
-                    if (ERRORS) raise( id, 'not a' + ( b ? ' base ' + b : '' ) + ' number', str );
-                    x.s = null;
-                }
-
-                x.c = x.e = null;
-                id = 0;
-            }
-        })();
-
-
-        // Throw a BigNumber Error.
-        function raise( caller, msg, val ) {
-            var error = new Error( [
-                'new BigNumber',     // 0
-                'cmp',               // 1
-                'config',            // 2
-                'div',               // 3
-                'divToInt',          // 4
-                'eq',                // 5
-                'gt',                // 6
-                'gte',               // 7
-                'lt',                // 8
-                'lte',               // 9
-                'minus',             // 10
-                'mod',               // 11
-                'plus',              // 12
-                'precision',         // 13
-                'random',            // 14
-                'round',             // 15
-                'shift',             // 16
-                'times',             // 17
-                'toDigits',          // 18
-                'toExponential',     // 19
-                'toFixed',           // 20
-                'toFormat',          // 21
-                'toFraction',        // 22
-                'pow',               // 23
-                'toPrecision',       // 24
-                'toString',          // 25
-                'BigNumber'          // 26
-            ][caller] + '() ' + msg + ': ' + val );
-
-            error.name = 'BigNumber Error';
-            id = 0;
-            throw error;
-        }
-
-
-        /*
-         * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
-         * If r is truthy, it is known that there are more digits after the rounding digit.
-         */
-        function round( x, sd, rm, r ) {
-            var d, i, j, k, n, ni, rd,
-                xc = x.c,
-                pows10 = POWS_TEN;
-
-            // if x is not Infinity or NaN...
-            if (xc) {
-
-                // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
-                // n is a base 1e14 number, the value of the element of array x.c containing rd.
-                // ni is the index of n within x.c.
-                // d is the number of digits of n.
-                // i is the index of rd within n including leading zeros.
-                // j is the actual index of rd within n (if < 0, rd is a leading zero).
-                out: {
-
-                    // Get the number of digits of the first element of xc.
-                    for ( d = 1, k = xc[0]; k >= 10; k /= 10, d++ );
-                    i = sd - d;
-
-                    // If the rounding digit is in the first element of xc...
-                    if ( i < 0 ) {
-                        i += LOG_BASE;
-                        j = sd;
-                        n = xc[ ni = 0 ];
-
-                        // Get the rounding digit at index j of n.
-                        rd = n / pows10[ d - j - 1 ] % 10 | 0;
-                    } else {
-                        ni = mathceil( ( i + 1 ) / LOG_BASE );
-
-                        if ( ni >= xc.length ) {
-
-                            if (r) {
-
-                                // Needed by sqrt.
-                                for ( ; xc.length <= ni; xc.push(0) );
-                                n = rd = 0;
-                                d = 1;
-                                i %= LOG_BASE;
-                                j = i - LOG_BASE + 1;
-                            } else {
-                                break out;
-                            }
-                        } else {
-                            n = k = xc[ni];
-
-                            // Get the number of digits of n.
-                            for ( d = 1; k >= 10; k /= 10, d++ );
-
-                            // Get the index of rd within n.
-                            i %= LOG_BASE;
-
-                            // Get the index of rd within n, adjusted for leading zeros.
-                            // The number of leading zeros of n is given by LOG_BASE - d.
-                            j = i - LOG_BASE + d;
-
-                            // Get the rounding digit at index j of n.
-                            rd = j < 0 ? 0 : n / pows10[ d - j - 1 ] % 10 | 0;
-                        }
-                    }
-
-                    r = r || sd < 0 ||
-
-                    // Are there any non-zero digits after the rounding digit?
-                    // The expression  n % pows10[ d - j - 1 ]  returns all digits of n to the right
-                    // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
-                      xc[ni + 1] != null || ( j < 0 ? n : n % pows10[ d - j - 1 ] );
-
-                    r = rm < 4
-                      ? ( rd || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
-                      : rd > 5 || rd == 5 && ( rm == 4 || r || rm == 6 &&
-
-                        // Check whether the digit to the left of the rounding digit is odd.
-                        ( ( i > 0 ? j > 0 ? n / pows10[ d - j ] : 0 : xc[ni - 1] ) % 10 ) & 1 ||
-                          rm == ( x.s < 0 ? 8 : 7 ) );
-
-                    if ( sd < 1 || !xc[0] ) {
-                        xc.length = 0;
-
-                        if (r) {
-
-                            // Convert sd to decimal places.
-                            sd -= x.e + 1;
-
-                            // 1, 0.1, 0.01, 0.001, 0.0001 etc.
-                            xc[0] = pows10[ sd % LOG_BASE ];
-                            x.e = -sd || 0;
-                        } else {
-
-                            // Zero.
-                            xc[0] = x.e = 0;
-                        }
-
-                        return x;
-                    }
-
-                    // Remove excess digits.
-                    if ( i == 0 ) {
-                        xc.length = ni;
-                        k = 1;
-                        ni--;
-                    } else {
-                        xc.length = ni + 1;
-                        k = pows10[ LOG_BASE - i ];
-
-                        // E.g. 56700 becomes 56000 if 7 is the rounding digit.
-                        // j > 0 means i > number of leading zeros of n.
-                        xc[ni] = j > 0 ? mathfloor( n / pows10[ d - j ] % pows10[j] ) * k : 0;
-                    }
-
-                    // Round up?
-                    if (r) {
-
-                        for ( ; ; ) {
-
-                            // If the digit to be rounded up is in the first element of xc...
-                            if ( ni == 0 ) {
-
-                                // i will be the length of xc[0] before k is added.
-                                for ( i = 1, j = xc[0]; j >= 10; j /= 10, i++ );
-                                j = xc[0] += k;
-                                for ( k = 1; j >= 10; j /= 10, k++ );
-
-                                // if i != k the length has increased.
-                                if ( i != k ) {
-                                    x.e++;
-                                    if ( xc[0] == BASE ) xc[0] = 1;
-                                }
-
-                                break;
-                            } else {
-                                xc[ni] += k;
-                                if ( xc[ni] != BASE ) break;
-                                xc[ni--] = 0;
-                                k = 1;
-                            }
-                        }
-                    }
-
-                    // Remove trailing zeros.
-                    for ( i = xc.length; xc[--i] === 0; xc.pop() );
-                }
-
-                // Overflow? Infinity.
-                if ( x.e > MAX_EXP ) {
-                    x.c = x.e = null;
-
-                // Underflow? Zero.
-                } else if ( x.e < MIN_EXP ) {
-                    x.c = [ x.e = 0 ];
-                }
-            }
-
-            return x;
-        }
-
-
-        // PROTOTYPE/INSTANCE METHODS
-
-
-        /*
-         * Return a new BigNumber whose value is the absolute value of this BigNumber.
-         */
-        P.absoluteValue = P.abs = function () {
-            var x = new BigNumber(this);
-            if ( x.s < 0 ) x.s = 1;
-            return x;
-        };
-
-
-        /*
-         * Return a new BigNumber whose value is the value of this BigNumber rounded to a whole
-         * number in the direction of Infinity.
-         */
-        P.ceil = function () {
-            return round( new BigNumber(this), this.e + 1, 2 );
-        };
-
-
-        /*
-         * Return
-         * 1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
-         * -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
-         * 0 if they have the same value,
-         * or null if the value of either is NaN.
-         */
-        P.comparedTo = P.cmp = function ( y, b ) {
-            id = 1;
-            return compare( this, new BigNumber( y, b ) );
-        };
-
-
-        /*
-         * Return the number of decimal places of the value of this BigNumber, or null if the value
-         * of this BigNumber is ±Infinity or NaN.
-         */
-        P.decimalPlaces = P.dp = function () {
-            var n, v,
-                c = this.c;
-
-            if ( !c ) return null;
-            n = ( ( v = c.length - 1 ) - bitFloor( this.e / LOG_BASE ) ) * LOG_BASE;
-
-            // Subtract the number of trailing zeros of the last number.
-            if ( v = c[v] ) for ( ; v % 10 == 0; v /= 10, n-- );
-            if ( n < 0 ) n = 0;
-
-            return n;
-        };
-
-
-        /*
-         *  n / 0 = I
-         *  n / N = N
-         *  n / I = 0
-         *  0 / n = 0
-         *  0 / 0 = N
-         *  0 / N = N
-         *  0 / I = 0
-         *  N / n = N
-         *  N / 0 = N
-         *  N / N = N
-         *  N / I = N
-         *  I / n = I
-         *  I / 0 = I
-         *  I / N = N
-         *  I / I = N
-         *
-         * Return a new BigNumber whose value is the value of this BigNumber divided by the value of
-         * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
-         */
-        P.dividedBy = P.div = function ( y, b ) {
-            id = 3;
-            return div( this, new BigNumber( y, b ), DECIMAL_PLACES, ROUNDING_MODE );
-        };
-
-
-        /*
-         * Return a new BigNumber whose value is the integer part of dividing the value of this
-         * BigNumber by the value of BigNumber(y, b).
-         */
-        P.dividedToIntegerBy = P.divToInt = function ( y, b ) {
-            id = 4;
-            return div( this, new BigNumber( y, b ), 0, 1 );
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
-         * otherwise returns false.
-         */
-        P.equals = P.eq = function ( y, b ) {
-            id = 5;
-            return compare( this, new BigNumber( y, b ) ) === 0;
-        };
-
-
-        /*
-         * Return a new BigNumber whose value is the value of this BigNumber rounded to a whole
-         * number in the direction of -Infinity.
-         */
-        P.floor = function () {
-            return round( new BigNumber(this), this.e + 1, 3 );
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
-         * otherwise returns false.
-         */
-        P.greaterThan = P.gt = function ( y, b ) {
-            id = 6;
-            return compare( this, new BigNumber( y, b ) ) > 0;
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is greater than or equal to the value of
-         * BigNumber(y, b), otherwise returns false.
-         */
-        P.greaterThanOrEqualTo = P.gte = function ( y, b ) {
-            id = 7;
-            return ( b = compare( this, new BigNumber( y, b ) ) ) === 1 || b === 0;
-
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is a finite number, otherwise returns false.
-         */
-        P.isFinite = function () {
-            return !!this.c;
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is an integer, otherwise return false.
-         */
-        P.isInteger = P.isInt = function () {
-            return !!this.c && bitFloor( this.e / LOG_BASE ) > this.c.length - 2;
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is NaN, otherwise returns false.
-         */
-        P.isNaN = function () {
-            return !this.s;
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is negative, otherwise returns false.
-         */
-        P.isNegative = P.isNeg = function () {
-            return this.s < 0;
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is 0 or -0, otherwise returns false.
-         */
-        P.isZero = function () {
-            return !!this.c && this.c[0] == 0;
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
-         * otherwise returns false.
-         */
-        P.lessThan = P.lt = function ( y, b ) {
-            id = 8;
-            return compare( this, new BigNumber( y, b ) ) < 0;
-        };
-
-
-        /*
-         * Return true if the value of this BigNumber is less than or equal to the value of
-         * BigNumber(y, b), otherwise returns false.
-         */
-        P.lessThanOrEqualTo = P.lte = function ( y, b ) {
-            id = 9;
-            return ( b = compare( this, new BigNumber( y, b ) ) ) === -1 || b === 0;
-        };
-
-
-        /*
-         *  n - 0 = n
-         *  n - N = N
-         *  n - I = -I
-         *  0 - n = -n
-         *  0 - 0 = 0
-         *  0 - N = N
-         *  0 - I = -I
-         *  N - n = N
-         *  N - 0 = N
-         *  N - N = N
-         *  N - I = N
-         *  I - n = I
-         *  I - 0 = I
-         *  I - N = N
-         *  I - I = N
-         *
-         * Return a new BigNumber whose value is the value of this BigNumber minus the value of
-         * BigNumber(y, b).
-         */
-        P.minus = P.sub = function ( y, b ) {
-            var i, j, t, xLTy,
-                x = this,
-                a = x.s;
-
-            id = 10;
-            y = new BigNumber( y, b );
-            b = y.s;
-
-            // Either NaN?
-            if ( !a || !b ) return new BigNumber(NaN);
-
-            // Signs differ?
-            if ( a != b ) {
-                y.s = -b;
-                return x.plus(y);
-            }
-
-            var xe = x.e / LOG_BASE,
-                ye = y.e / LOG_BASE,
-                xc = x.c,
-                yc = y.c;
-
-            if ( !xe || !ye ) {
-
-                // Either Infinity?
-                if ( !xc || !yc ) return xc ? ( y.s = -b, y ) : new BigNumber( yc ? x : NaN );
-
-                // Either zero?
-                if ( !xc[0] || !yc[0] ) {
-
-                    // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
-                    return yc[0] ? ( y.s = -b, y ) : new BigNumber( xc[0] ? x :
-
-                      // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
-                      ROUNDING_MODE == 3 ? -0 : 0 );
-                }
-            }
-
-            xe = bitFloor(xe);
-            ye = bitFloor(ye);
-            xc = xc.slice();
-
-            // Determine which is the bigger number.
-            if ( a = xe - ye ) {
-
-                if ( xLTy = a < 0 ) {
-                    a = -a;
-                    t = xc;
-                } else {
-                    ye = xe;
-                    t = yc;
-                }
-
-                t.reverse();
-
-                // Prepend zeros to equalise exponents.
-                for ( b = a; b--; t.push(0) );
-                t.reverse();
-            } else {
-
-                // Exponents equal. Check digit by digit.
-                j = ( xLTy = ( a = xc.length ) < ( b = yc.length ) ) ? a : b;
-
-                for ( a = b = 0; b < j; b++ ) {
-
-                    if ( xc[b] != yc[b] ) {
-                        xLTy = xc[b] < yc[b];
-                        break;
-                    }
-                }
-            }
-
-            // x < y? Point xc to the array of the bigger number.
-            if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
-
-            b = ( j = yc.length ) - ( i = xc.length );
-
-            // Append zeros to xc if shorter.
-            // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
-            if ( b > 0 ) for ( ; b--; xc[i++] = 0 );
-            b = BASE - 1;
-
-            // Subtract yc from xc.
-            for ( ; j > a; ) {
-
-                if ( xc[--j] < yc[j] ) {
-                    for ( i = j; i && !xc[--i]; xc[i] = b );
-                    --xc[i];
-                    xc[j] += BASE;
-                }
-
-                xc[j] -= yc[j];
-            }
-
-            // Remove leading zeros and adjust exponent accordingly.
-            for ( ; xc[0] == 0; xc.shift(), --ye );
-
-            // Zero?
-            if ( !xc[0] ) {
-
-                // Following IEEE 754 (2008) 6.3,
-                // n - n = +0  but  n - n = -0  when rounding towards -Infinity.
-                y.s = ROUNDING_MODE == 3 ? -1 : 1;
-                y.c = [ y.e = 0 ];
-                return y;
-            }
-
-            // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
-            // for finite x and y.
-            return normalise( y, xc, ye );
-        };
-
-
-        /*
-         *   n % 0 =  N
-         *   n % N =  N
-         *   n % I =  n
-         *   0 % n =  0
-         *  -0 % n = -0
-         *   0 % 0 =  N
-         *   0 % N =  N
-         *   0 % I =  0
-         *   N % n =  N
-         *   N % 0 =  N
-         *   N % N =  N
-         *   N % I =  N
-         *   I % n =  N
-         *   I % 0 =  N
-         *   I % N =  N
-         *   I % I =  N
-         *
-         * Return a new BigNumber whose value is the value of this BigNumber modulo the value of
-         * BigNumber(y, b). The result depends on the value of MODULO_MODE.
-         */
-        P.modulo = P.mod = function ( y, b ) {
-            var q, s,
-                x = this;
-
-            id = 11;
-            y = new BigNumber( y, b );
-
-            // Return NaN if x is Infinity or NaN, or y is NaN or zero.
-            if ( !x.c || !y.s || y.c && !y.c[0] ) {
-                return new BigNumber(NaN);
-
-            // Return x if y is Infinity or x is zero.
-            } else if ( !y.c || x.c && !x.c[0] ) {
-                return new BigNumber(x);
-            }
-
-            if ( MODULO_MODE == 9 ) {
-
-                // Euclidian division: q = sign(y) * floor(x / abs(y))
-                // r = x - qy    where  0 <= r < abs(y)
-                s = y.s;
-                y.s = 1;
-                q = div( x, y, 0, 3 );
-                y.s = s;
-                q.s *= s;
-            } else {
-                q = div( x, y, 0, MODULO_MODE );
-            }
-
-            return x.minus( q.times(y) );
-        };
-
-
-        /*
-         * Return a new BigNumber whose value is the value of this BigNumber negated,
-         * i.e. multiplied by -1.
-         */
-        P.negated = P.neg = function () {
-            var x = new BigNumber(this);
-            x.s = -x.s || null;
-            return x;
-        };
-
-
-        /*
-         *  n + 0 = n
-         *  n + N = N
-         *  n + I = I
-         *  0 + n = n
-         *  0 + 0 = 0
-         *  0 + N = N
-         *  0 + I = I
-         *  N + n = N
-         *  N + 0 = N
-         *  N + N = N
-         *  N + I = N
-         *  I + n = I
-         *  I + 0 = I
-         *  I + N = N
-         *  I + I = I
-         *
-         * Return a new BigNumber whose value is the value of this BigNumber plus the value of
-         * BigNumber(y, b).
-         */
-        P.plus = P.add = function ( y, b ) {
-            var t,
-                x = this,
-                a = x.s;
-
-            id = 12;
-            y = new BigNumber( y, b );
-            b = y.s;
-
-            // Either NaN?
-            if ( !a || !b ) return new BigNumber(NaN);
-
-            // Signs differ?
-             if ( a != b ) {
-                y.s = -b;
-                return x.minus(y);
-            }
-
-            var xe = x.e / LOG_BASE,
-                ye = y.e / LOG_BASE,
-                xc = x.c,
-                yc = y.c;
-
-            if ( !xe || !ye ) {
-
-                // Return ±Infinity if either ±Infinity.
-                if ( !xc || !yc ) return new BigNumber( a / 0 );
-
-                // Either zero?
-                // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
-                if ( !xc[0] || !yc[0] ) return yc[0] ? y : new BigNumber( xc[0] ? x : a * 0 );
-            }
-
-            xe = bitFloor(xe);
-            ye = bitFloor(ye);
-            xc = xc.slice();
-
-            // Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
-            if ( a = xe - ye ) {
-                if ( a > 0 ) {
-                    ye = xe;
-                    t = yc;
-                } else {
-                    a = -a;
-                    t = xc;
-                }
-
-                t.reverse();
-                for ( ; a--; t.push(0) );
-                t.reverse();
-            }
-
-            a = xc.length;
-            b = yc.length;
-
-            // Point xc to the longer array, and b to the shorter length.
-            if ( a - b < 0 ) t = yc, yc = xc, xc = t, b = a;
-
-            // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
-            for ( a = 0; b; ) {
-                a = ( xc[--b] = xc[b] + yc[b] + a ) / BASE | 0;
-                xc[b] %= BASE;
-            }
-
-            if (a) {
-                xc.unshift(a);
-                ++ye;
-            }
-
-            // No need to check for zero, as +x + +y != 0 && -x + -y != 0
-            // ye = MAX_EXP + 1 possible
-            return normalise( y, xc, ye );
-        };
-
-
-        /*
-         * Return the number of significant digits of the value of this BigNumber.
-         *
-         * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
-         */
-        P.precision = P.sd = function (z) {
-            var n, v,
-                x = this,
-                c = x.c;
-
-            // 'precision() argument not a boolean or binary digit: {z}'
-            if ( z != null && z !== !!z && z !== 1 && z !== 0 ) {
-                if (ERRORS) raise( 13, 'argument' + notBool, z );
-                if ( z != !!z ) z = null;
-            }
-
-            if ( !c ) return null;
-            v = c.length - 1;
-            n = v * LOG_BASE + 1;
-
-            if ( v = c[v] ) {
-
-                // Subtract the number of trailing zeros of the last element.
-                for ( ; v % 10 == 0; v /= 10, n-- );
-
-                // Add the number of digits of the first element.
-                for ( v = c[0]; v >= 10; v /= 10, n++ );
-            }
-
-            if ( z && x.e + 1 > n ) n = x.e + 1;
-
-            return n;
-        };
-
-
-        /*
-         * Return a new BigNumber whose value is the value of this BigNumber rounded to a maximum of
-         * dp decimal places using rounding mode rm, or to 0 and ROUNDING_MODE respectively if
-         * omitted.
-         *
-         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
-         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-         *
-         * 'round() decimal places out of range: {dp}'
-         * 'round() decimal places not an integer: {dp}'
-         * 'round() rounding mode not an integer: {rm}'
-         * 'round() rounding mode out of range: {rm}'
-         */
-        P.round = function ( dp, rm ) {
-            var n = new BigNumber(this);
-
-            if ( dp == null || isValidInt( dp, 0, MAX, 15 ) ) {
-                round( n, ~~dp + this.e + 1, rm == null ||
-                  !isValidInt( rm, 0, 8, 15, roundingMode ) ? ROUNDING_MODE : rm | 0 );
-            }
-
-            return n;
-        };
-
-
-        /*
-         * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
-         * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
-         *
-         * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
-         *
-         * If k is out of range and ERRORS is false, the result will be ±0 if k < 0, or ±Infinity
-         * otherwise.
-         *
-         * 'shift() argument not an integer: {k}'
-         * 'shift() argument out of range: {k}'
-         */
-        P.shift = function (k) {
-            var n = this;
-            return isValidInt( k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER, 16, 'argument' )
-
-              // k < 1e+21, or truncate(k) will produce exponential notation.
-              ? n.times( '1e' + truncate(k) )
-              : new BigNumber( n.c && n.c[0] && ( k < -MAX_SAFE_INTEGER || k > MAX_SAFE_INTEGER )
-                ? n.s * ( k < 0 ? 0 : 1 / 0 )
-                : n );
-        };
-
-
-        /*
-         *  sqrt(-n) =  N
-         *  sqrt( N) =  N
-         *  sqrt(-I) =  N
-         *  sqrt( I) =  I
-         *  sqrt( 0) =  0
-         *  sqrt(-0) = -0
-         *
-         * Return a new BigNumber whose value is the square root of the value of this BigNumber,
-         * rounded according to DECIMAL_PLACES and ROUNDING_MODE.
-         */
-        P.squareRoot = P.sqrt = function () {
-            var m, n, r, rep, t,
-                x = this,
-                c = x.c,
-                s = x.s,
-                e = x.e,
-                dp = DECIMAL_PLACES + 4,
-                half = new BigNumber('0.5');
-
-            // Negative/NaN/Infinity/zero?
-            if ( s !== 1 || !c || !c[0] ) {
-                return new BigNumber( !s || s < 0 && ( !c || c[0] ) ? NaN : c ? x : 1 / 0 );
-            }
-
-            // Initial estimate.
-            s = Math.sqrt( +x );
-
-            // Math.sqrt underflow/overflow?
-            // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
-            if ( s == 0 || s == 1 / 0 ) {
-                n = coeffToString(c);
-                if ( ( n.length + e ) % 2 == 0 ) n += '0';
-                s = Math.sqrt(n);
-                e = bitFloor( ( e + 1 ) / 2 ) - ( e < 0 || e % 2 );
-
-                if ( s == 1 / 0 ) {
-                    n = '1e' + e;
-                } else {
-                    n = s.toExponential();
-                    n = n.slice( 0, n.indexOf('e') + 1 ) + e;
-                }
-
-                r = new BigNumber(n);
-            } else {
-                r = new BigNumber( s + '' );
-            }
-
-            // Check for zero.
-            // r could be zero if MIN_EXP is changed after the this value was created.
-            // This would cause a division by zero (x/t) and hence Infinity below, which would cause
-            // coeffToString to throw.
-            if ( r.c[0] ) {
-                e = r.e;
-                s = e + dp;
-                if ( s < 3 ) s = 0;
-
-                // Newton-Raphson iteration.
-                for ( ; ; ) {
-                    t = r;
-                    r = half.times( t.plus( div( x, t, dp, 1 ) ) );
-
-                    if ( coeffToString( t.c   ).slice( 0, s ) === ( n =
-                         coeffToString( r.c ) ).slice( 0, s ) ) {
-
-                        // The exponent of r may here be one less than the final result exponent,
-                        // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
-                        // are indexed correctly.
-                        if ( r.e < e ) --s;
-                        n = n.slice( s - 3, s + 1 );
-
-                        // The 4th rounding digit may be in error by -1 so if the 4 rounding digits
-                        // are 9999 or 4999 (i.e. approaching a rounding boundary) continue the
-                        // iteration.
-                        if ( n == '9999' || !rep && n == '4999' ) {
-
-                            // On the first iteration only, check to see if rounding up gives the
-                            // exact result as the nines may infinitely repeat.
-                            if ( !rep ) {
-                                round( t, t.e + DECIMAL_PLACES + 2, 0 );
-
-                                if ( t.times(t).eq(x) ) {
-                                    r = t;
-                                    break;
-                                }
-                            }
-
-                            dp += 4;
-                            s += 4;
-                            rep = 1;
-                        } else {
-
-                            // If rounding digits are null, 0{0,4} or 50{0,3}, check for exact
-                            // result. If not, then there are further digits and m will be truthy.
-                            if ( !+n || !+n.slice(1) && n.charAt(0) == '5' ) {
-
-                                // Truncate to the first rounding digit.
-                                round( r, r.e + DECIMAL_PLACES + 2, 1 );
-                                m = !r.times(r).eq(x);
-                            }
-
-                            break;
-                        }
-                    }
-                }
-            }
-
-            return round( r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m );
-        };
-
-
-        /*
-         *  n * 0 = 0
-         *  n * N = N
-         *  n * I = I
-         *  0 * n = 0
-         *  0 * 0 = 0
-         *  0 * N = N
-         *  0 * I = N
-         *  N * n = N
-         *  N * 0 = N
-         *  N * N = N
-         *  N * I = N
-         *  I * n = I
-         *  I * 0 = N
-         *  I * N = N
-         *  I * I = I
-         *
-         * Return a new BigNumber whose value is the value of this BigNumber times the value of
-         * BigNumber(y, b).
-         */
-        P.times = P.mul = function ( y, b ) {
-            var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
-                base, sqrtBase,
-                x = this,
-                xc = x.c,
-                yc = ( id = 17, y = new BigNumber( y, b ) ).c;
-
-            // Either NaN, ±Infinity or ±0?
-            if ( !xc || !yc || !xc[0] || !yc[0] ) {
-
-                // Return NaN if either is NaN, or one is 0 and the other is Infinity.
-                if ( !x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc ) {
-                    y.c = y.e = y.s = null;
-                } else {
-                    y.s *= x.s;
-
-                    // Return ±Infinity if either is ±Infinity.
-                    if ( !xc || !yc ) {
-                        y.c = y.e = null;
-
-                    // Return ±0 if either is ±0.
-                    } else {
-                        y.c = [0];
-                        y.e = 0;
-                    }
-                }
-
-                return y;
-            }
-
-            e = bitFloor( x.e / LOG_BASE ) + bitFloor( y.e / LOG_BASE );
-            y.s *= x.s;
-            xcL = xc.length;
-            ycL = yc.length;
-
-            // Ensure xc points to longer array and xcL to its length.
-            if ( xcL < ycL ) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
-
-            // Initialise the result array with zeros.
-            for ( i = xcL + ycL, zc = []; i--; zc.push(0) );
-
-            base = BASE;
-            sqrtBase = SQRT_BASE;
-
-            for ( i = ycL; --i >= 0; ) {
-                c = 0;
-                ylo = yc[i] % sqrtBase;
-                yhi = yc[i] / sqrtBase | 0;
-
-                for ( k = xcL, j = i + k; j > i; ) {
-                    xlo = xc[--k] % sqrtBase;
-                    xhi = xc[k] / sqrtBase | 0;
-                    m = yhi * xlo + xhi * ylo;
-                    xlo = ylo * xlo + ( ( m % sqrtBase ) * sqrtBase ) + zc[j] + c;
-                    c = ( xlo / base | 0 ) + ( m / sqrtBase | 0 ) + yhi * xhi;
-                    zc[j--] = xlo % base;
-                }
-
-                zc[j] = c;
-            }
-
-            if (c) {
-                ++e;
-            } else {
-                zc.shift();
-            }
-
-            return normalise( y, zc, e );
-        };
-
-
-        /*
-         * Return a new BigNumber whose value is the value of this BigNumber rounded to a maximum of
-         * sd significant digits using rounding mode rm, or ROUNDING_MODE if rm is omitted.
-         *
-         * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
-         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-         *
-         * 'toDigits() precision out of range: {sd}'
-         * 'toDigits() precision not an integer: {sd}'
-         * 'toDigits() rounding mode not an integer: {rm}'
-         * 'toDigits() rounding mode out of range: {rm}'
-         */
-        P.toDigits = function ( sd, rm ) {
-            var n = new BigNumber(this);
-            sd = sd == null || !isValidInt( sd, 1, MAX, 18, 'precision' ) ? null : sd | 0;
-            rm = rm == null || !isValidInt( rm, 0, 8, 18, roundingMode ) ? ROUNDING_MODE : rm | 0;
-            return sd ? round( n, sd, rm ) : n;
-        };
-
-
-        /*
-         * Return a string representing the value of this BigNumber in exponential notation and
-         * rounded using ROUNDING_MODE to dp fixed decimal places.
-         *
-         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
-         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-         *
-         * 'toExponential() decimal places not an integer: {dp}'
-         * 'toExponential() decimal places out of range: {dp}'
-         * 'toExponential() rounding mode not an integer: {rm}'
-         * 'toExponential() rounding mode out of range: {rm}'
-         */
-        P.toExponential = function ( dp, rm ) {
-            return format( this,
-              dp != null && isValidInt( dp, 0, MAX, 19 ) ? ~~dp + 1 : null, rm, 19 );
-        };
-
-
-        /*
-         * Return a string representing the value of this BigNumber in fixed-point notation rounding
-         * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
-         *
-         * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
-         * but e.g. (-0.00001).toFixed(0) is '-0'.
-         *
-         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
-         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-         *
-         * 'toFixed() decimal places not an integer: {dp}'
-         * 'toFixed() decimal places out of range: {dp}'
-         * 'toFixed() rounding mode not an integer: {rm}'
-         * 'toFixed() rounding mode out of range: {rm}'
-         */
-        P.toFixed = function ( dp, rm ) {
-            return format( this, dp != null && isValidInt( dp, 0, MAX, 20 )
-              ? ~~dp + this.e + 1 : null, rm, 20 );
-        };
-
-
-        /*
-         * Return a string representing the value of this BigNumber in fixed-point notation rounded
-         * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
-         * of the FORMAT object (see BigNumber.config).
-         *
-         * FORMAT = {
-         *      decimalSeparator : '.',
-         *      groupSeparator : ',',
-         *      groupSize : 3,
-         *      secondaryGroupSize : 0,
-         *      fractionGroupSeparator : '\xA0',    // non-breaking space
-         *      fractionGroupSize : 0
-         * };
-         *
-         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
-         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-         *
-         * 'toFormat() decimal places not an integer: {dp}'
-         * 'toFormat() decimal places out of range: {dp}'
-         * 'toFormat() rounding mode not an integer: {rm}'
-         * 'toFormat() rounding mode out of range: {rm}'
-         */
-        P.toFormat = function ( dp, rm ) {
-            var str = format( this, dp != null && isValidInt( dp, 0, MAX, 21 )
-              ? ~~dp + this.e + 1 : null, rm, 21 );
-
-            if ( this.c ) {
-                var i,
-                    arr = str.split('.'),
-                    g1 = +FORMAT.groupSize,
-                    g2 = +FORMAT.secondaryGroupSize,
-                    groupSeparator = FORMAT.groupSeparator,
-                    intPart = arr[0],
-                    fractionPart = arr[1],
-                    isNeg = this.s < 0,
-                    intDigits = isNeg ? intPart.slice(1) : intPart,
-                    len = intDigits.length;
-
-                if (g2) i = g1, g1 = g2, g2 = i, len -= i;
-
-                if ( g1 > 0 && len > 0 ) {
-                    i = len % g1 || g1;
-                    intPart = intDigits.substr( 0, i );
-
-                    for ( ; i < len; i += g1 ) {
-                        intPart += groupSeparator + intDigits.substr( i, g1 );
-                    }
-
-                    if ( g2 > 0 ) intPart += groupSeparator + intDigits.slice(i);
-                    if (isNeg) intPart = '-' + intPart;
-                }
-
-                str = fractionPart
-                  ? intPart + FORMAT.decimalSeparator + ( ( g2 = +FORMAT.fractionGroupSize )
-                    ? fractionPart.replace( new RegExp( '\\d{' + g2 + '}\\B', 'g' ),
-                      '$&' + FORMAT.fractionGroupSeparator )
-                    : fractionPart )
-                  : intPart;
-            }
-
-            return str;
-        };
-
-
-        /*
-         * Return a string array representing the value of this BigNumber as a simple fraction with
-         * an integer numerator and an integer denominator. The denominator will be a positive
-         * non-zero value less than or equal to the specified maximum denominator. If a maximum
-         * denominator is not specified, the denominator will be the lowest value necessary to
-         * represent the number exactly.
-         *
-         * [md] {number|string|BigNumber} Integer >= 1 and < Infinity. The maximum denominator.
-         *
-         * 'toFraction() max denominator not an integer: {md}'
-         * 'toFraction() max denominator out of range: {md}'
-         */
-        P.toFraction = function (md) {
-            var arr, d0, d2, e, exp, n, n0, q, s,
-                k = ERRORS,
-                x = this,
-                xc = x.c,
-                d = new BigNumber(ONE),
-                n1 = d0 = new BigNumber(ONE),
-                d1 = n0 = new BigNumber(ONE);
-
-            if ( md != null ) {
-                ERRORS = false;
-                n = new BigNumber(md);
-                ERRORS = k;
-
-                if ( !( k = n.isInt() ) || n.lt(ONE) ) {
-
-                    if (ERRORS) {
-                        raise( 22,
-                          'max denominator ' + ( k ? 'out of range' : 'not an integer' ), md );
-                    }
-
-                    // ERRORS is false:
-                    // If md is a finite non-integer >= 1, round it to an integer and use it.
-                    md = !k && n.c && round( n, n.e + 1, 1 ).gte(ONE) ? n : null;
-                }
-            }
-
-            if ( !xc ) return x.toString();
-            s = coeffToString(xc);
-
-            // Determine initial denominator.
-            // d is a power of 10 and the minimum max denominator that specifies the value exactly.
-            e = d.e = s.length - x.e - 1;
-            d.c[0] = POWS_TEN[ ( exp = e % LOG_BASE ) < 0 ? LOG_BASE + exp : exp ];
-            md = !md || n.cmp(d) > 0 ? ( e > 0 ? d : n1 ) : n;
-
-            exp = MAX_EXP;
-            MAX_EXP = 1 / 0;
-            n = new BigNumber(s);
-
-            // n0 = d1 = 0
-            n0.c[0] = 0;
-
-            for ( ; ; )  {
-                q = div( n, d, 0, 1 );
-                d2 = d0.plus( q.times(d1) );
-                if ( d2.cmp(md) == 1 ) break;
-                d0 = d1;
-                d1 = d2;
-                n1 = n0.plus( q.times( d2 = n1 ) );
-                n0 = d2;
-                d = n.minus( q.times( d2 = d ) );
-                n = d2;
-            }
-
-            d2 = div( md.minus(d0), d1, 0, 1 );
-            n0 = n0.plus( d2.times(n1) );
-            d0 = d0.plus( d2.times(d1) );
-            n0.s = n1.s = x.s;
-            e *= 2;
-
-            // Determine which fraction is closer to x, n0/d0 or n1/d1
-            arr = div( n1, d1, e, ROUNDING_MODE ).minus(x).abs().cmp(
-                  div( n0, d0, e, ROUNDING_MODE ).minus(x).abs() ) < 1
-                    ? [ n1.toString(), d1.toString() ]
-                    : [ n0.toString(), d0.toString() ];
-
-            MAX_EXP = exp;
-            return arr;
-        };
-
-
-        /*
-         * Return the value of this BigNumber converted to a number primitive.
-         */
-        P.toNumber = function () {
-            var x = this;
-
-            // Ensure zero has correct sign.
-            return +x || ( x.s ? x.s * 0 : NaN );
-        };
-
-
-        /*
-         * Return a BigNumber whose value is the value of this BigNumber raised to the power n.
-         * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
-         * If POW_PRECISION is not 0, round to POW_PRECISION using ROUNDING_MODE.
-         *
-         * n {number} Integer, -9007199254740992 to 9007199254740992 inclusive.
-         * (Performs 54 loop iterations for n of 9007199254740992.)
-         *
-         * 'pow() exponent not an integer: {n}'
-         * 'pow() exponent out of range: {n}'
-         */
-        P.toPower = P.pow = function (n) {
-            var k, y,
-                i = mathfloor( n < 0 ? -n : +n ),
-                x = this;
-
-            // Pass ±Infinity to Math.pow if exponent is out of range.
-            if ( !isValidInt( n, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER, 23, 'exponent' ) &&
-              ( !isFinite(n) || i > MAX_SAFE_INTEGER && ( n /= 0 ) ||
-                parseFloat(n) != n && !( n = NaN ) ) ) {
-                return new BigNumber( Math.pow( +x, n ) );
-            }
-
-            // Truncating each coefficient array to a length of k after each multiplication equates
-            // to truncating significant digits to POW_PRECISION + [28, 41], i.e. there will be a
-            // minimum of 28 guard digits retained. (Using + 1.5 would give [9, 21] guard digits.)
-            k = POW_PRECISION ? mathceil( POW_PRECISION / LOG_BASE + 2 ) : 0;
-            y = new BigNumber(ONE);
-
-            for ( ; ; ) {
-
-                if ( i % 2 ) {
-                    y = y.times(x);
-                    if ( !y.c ) break;
-                    if ( k && y.c.length > k ) y.c.length = k;
-                }
-
-                i = mathfloor( i / 2 );
-                if ( !i ) break;
-
-                x = x.times(x);
-                if ( k && x.c && x.c.length > k ) x.c.length = k;
-            }
-
-            if ( n < 0 ) y = ONE.div(y);
-            return k ? round( y, POW_PRECISION, ROUNDING_MODE ) : y;
-        };
-
-
-        /*
-         * Return a string representing the value of this BigNumber rounded to sd significant digits
-         * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
-         * necessary to represent the integer part of the value in fixed-point notation, then use
-         * exponential notation.
-         *
-         * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
-         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
-         *
-         * 'toPrecision() precision not an integer: {sd}'
-         * 'toPrecision() precision out of range: {sd}'
-         * 'toPrecision() rounding mode not an integer: {rm}'
-         * 'toPrecision() rounding mode out of range: {rm}'
-         */
-        P.toPrecision = function ( sd, rm ) {
-            return format( this, sd != null && isValidInt( sd, 1, MAX, 24, 'precision' )
-              ? sd | 0 : null, rm, 24 );
-        };
-
-
-        /*
-         * Return a string representing the value of this BigNumber in base b, or base 10 if b is
-         * omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
-         * ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
-         * that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
-         * TO_EXP_NEG, return exponential notation.
-         *
-         * [b] {number} Integer, 2 to 64 inclusive.
-         *
-         * 'toString() base not an integer: {b}'
-         * 'toString() base out of range: {b}'
-         */
-        P.toString = function (b) {
-            var str,
-                n = this,
-                s = n.s,
-                e = n.e;
-
-            // Infinity or NaN?
-            if ( e === null ) {
-
-                if (s) {
-                    str = 'Infinity';
-                    if ( s < 0 ) str = '-' + str;
-                } else {
-                    str = 'NaN';
-                }
-            } else {
-                str = coeffToString( n.c );
-
-                if ( b == null || !isValidInt( b, 2, 64, 25, 'base' ) ) {
-                    str = e <= TO_EXP_NEG || e >= TO_EXP_POS
-                      ? toExponential( str, e )
-                      : toFixedPoint( str, e );
-                } else {
-                    str = convertBase( toFixedPoint( str, e ), b | 0, 10, s );
-                }
-
-                if ( s < 0 && n.c[0] ) str = '-' + str;
-            }
-
-            return str;
-        };
-
-
-        /*
-         * Return a new BigNumber whose value is the value of this BigNumber truncated to a whole
-         * number.
-         */
-        P.truncated = P.trunc = function () {
-            return round( new BigNumber(this), this.e + 1, 1 );
-        };
-
-
-
-        /*
-         * Return as toString, but do not accept a base argument.
-         */
-        P.valueOf = P.toJSON = function () {
-            return this.toString();
-        };
-
-
-        // Aliases for BigDecimal methods.
-        //P.add = P.plus;         // P.add included above
-        //P.subtract = P.minus;   // P.sub included above
-        //P.multiply = P.times;   // P.mul included above
-        //P.divide = P.div;
-        //P.remainder = P.mod;
-        //P.compareTo = P.cmp;
-        //P.negate = P.neg;
-
-
-        if ( configObj != null ) BigNumber.config(configObj);
-
-        return BigNumber;
-    }
-
-
-    // PRIVATE HELPER FUNCTIONS
-
-
-    function bitFloor(n) {
-        var i = n | 0;
-        return n > 0 || n === i ? i : i - 1;
-    }
-
-
-    // Return a coefficient array as a string of base 10 digits.
-    function coeffToString(a) {
-        var s, z,
-            i = 1,
-            j = a.length,
-            r = a[0] + '';
-
-        for ( ; i < j; ) {
-            s = a[i++] + '';
-            z = LOG_BASE - s.length;
-            for ( ; z--; s = '0' + s );
-            r += s;
-        }
-
-        // Determine trailing zeros.
-        for ( j = r.length; r.charCodeAt(--j) === 48; );
-        return r.slice( 0, j + 1 || 1 );
-    }
-
-
-    // Compare the value of BigNumbers x and y.
-    function compare( x, y ) {
-        var a, b,
-            xc = x.c,
-            yc = y.c,
-            i = x.s,
-            j = y.s,
-            k = x.e,
-            l = y.e;
-
-        // Either NaN?
-        if ( !i || !j ) return null;
-
-        a = xc && !xc[0];
-        b = yc && !yc[0];
-
-        // Either zero?
-        if ( a || b ) return a ? b ? 0 : -j : i;
-
-        // Signs differ?
-        if ( i != j ) return i;
-
-        a = i < 0;
-        b = k == l;
-
-        // Either Infinity?
-        if ( !xc || !yc ) return b ? 0 : !xc ^ a ? 1 : -1;
-
-        // Compare exponents.
-        if ( !b ) return k > l ^ a ? 1 : -1;
-
-        j = ( k = xc.length ) < ( l = yc.length ) ? k : l;
-
-        // Compare digit by digit.
-        for ( i = 0; i < j; i++ ) if ( xc[i] != yc[i] ) return xc[i] > yc[i] ^ a ? 1 : -1;
-
-        // Compare lengths.
-        return k == l ? 0 : k > l ^ a ? 1 : -1;
-    }
-
-
-    /*
-     * Return true if n is a valid number in range, otherwise false.
-     * Use for argument validation when ERRORS is false.
-     * Note: parseInt('1e+1') == 1 but parseFloat('1e+1') == 10.
-     */
-    function intValidatorNoErrors( n, min, max ) {
-        return ( n = truncate(n) ) >= min && n <= max;
-    }
-
-
-    function isArray(obj) {
-        return Object.prototype.toString.call(obj) == '[object Array]';
-    }
-
-
-    /*
-     * Convert string of baseIn to an array of numbers of baseOut.
-     * Eg. convertBase('255', 10, 16) returns [15, 15].
-     * Eg. convertBase('ff', 16, 10) returns [2, 5, 5].
-     */
-    function toBaseOut( str, baseIn, baseOut ) {
-        var j,
-            arr = [0],
-            arrL,
-            i = 0,
-            len = str.length;
-
-        for ( ; i < len; ) {
-            for ( arrL = arr.length; arrL--; arr[arrL] *= baseIn );
-            arr[ j = 0 ] += ALPHABET.indexOf( str.charAt( i++ ) );
-
-            for ( ; j < arr.length; j++ ) {
-
-                if ( arr[j] > baseOut - 1 ) {
-                    if ( arr[j + 1] == null ) arr[j + 1] = 0;
-                    arr[j + 1] += arr[j] / baseOut | 0;
-                    arr[j] %= baseOut;
-                }
-            }
-        }
-
-        return arr.reverse();
-    }
-
-
-    function toExponential( str, e ) {
-        return ( str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str ) +
-          ( e < 0 ? 'e' : 'e+' ) + e;
-    }
-
-
-    function toFixedPoint( str, e ) {
-        var len, z;
-
-        // Negative exponent?
-        if ( e < 0 ) {
-
-            // Prepend zeros.
-            for ( z = '0.'; ++e; z += '0' );
-            str = z + str;
-
-        // Positive exponent
-        } else {
-            len = str.length;
-
-            // Append zeros.
-            if ( ++e > len ) {
-                for ( z = '0', e -= len; --e; z += '0' );
-                str += z;
-            } else if ( e < len ) {
-                str = str.slice( 0, e ) + '.' + str.slice(e);
-            }
-        }
-
-        return str;
-    }
-
-
-    function truncate(n) {
-        n = parseFloat(n);
-        return n < 0 ? mathceil(n) : mathfloor(n);
-    }
-
-
-    // EXPORT
-
-
-    BigNumber = another();
-
-    // AMD.
-    if ( typeof define == 'function' && define.amd ) {
-        define( function () { return BigNumber; } );
-
-    // Node and other environments that support module.exports.
-    } else if ( typeof module != 'undefined' && module.exports ) {
-        module.exports = BigNumber;
-        if ( !crypto ) try { crypto = require('crypto'); } catch (e) {}
-
-    // Browser.
-    } else {
-        global.BigNumber = BigNumber;
-    }
-})(this);
-
-},{"crypto":50}],"web3":[function(require,module,exports){
+/*! bignumber.js v4.0.2 https://github.com/MikeMcl/bignumber.js/LICENCE */
+
+;(function (globalObj) {
+    'use strict';
+
+    /*
+      bignumber.js v4.0.2
+      A JavaScript library for arbitrary-precision arithmetic.
+      https://github.com/MikeMcl/bignumber.js
+      Copyright (c) 2017 Michael Mclaughlin <M8ch88l@gmail.com>
+      MIT Expat Licence
+    */
+
+
+    var BigNumber,
+        isNumeric = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
+        mathceil = Math.ceil,
+        mathfloor = Math.floor,
+        notBool = ' not a boolean or binary digit',
+        roundingMode = 'rounding mode',
+        tooManyDigits = 'number type has more than 15 significant digits',
+        ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_',
+        BASE = 1e14,
+        LOG_BASE = 14,
+        MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
+        // MAX_INT32 = 0x7fffffff,                   // 2^31 - 1
+        POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
+        SQRT_BASE = 1e7,
+
+        /*
+         * The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
+         * the arguments to toExponential, toFixed, toFormat, and toPrecision, beyond which an
+         * exception is thrown (if ERRORS is true).
+         */
+        MAX = 1E9;                                   // 0 to MAX_INT32
+
+
+    /*
+     * Create and return a BigNumber constructor.
+     */
+    function constructorFactory(config) {
+        var div, parseNumeric,
+
+            // id tracks the caller function, so its name can be included in error messages.
+            id = 0,
+            P = BigNumber.prototype,
+            ONE = new BigNumber(1),
+
+
+            /********************************* EDITABLE DEFAULTS **********************************/
+
+
+            /*
+             * The default values below must be integers within the inclusive ranges stated.
+             * The values can also be changed at run-time using BigNumber.config.
+             */
+
+            // The maximum number of decimal places for operations involving division.
+            DECIMAL_PLACES = 20,                     // 0 to MAX
+
+            /*
+             * The rounding mode used when rounding to the above decimal places, and when using
+             * toExponential, toFixed, toFormat and toPrecision, and round (default value).
+             * UP         0 Away from zero.
+             * DOWN       1 Towards zero.
+             * CEIL       2 Towards +Infinity.
+             * FLOOR      3 Towards -Infinity.
+             * HALF_UP    4 Towards nearest neighbour. If equidistant, up.
+             * HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
+             * HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
+             * HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
+             * HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
+             */
+            ROUNDING_MODE = 4,                       // 0 to 8
+
+            // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
+
+            // The exponent value at and beneath which toString returns exponential notation.
+            // Number type: -7
+            TO_EXP_NEG = -7,                         // 0 to -MAX
+
+            // The exponent value at and above which toString returns exponential notation.
+            // Number type: 21
+            TO_EXP_POS = 21,                         // 0 to MAX
+
+            // RANGE : [MIN_EXP, MAX_EXP]
+
+            // The minimum exponent value, beneath which underflow to zero occurs.
+            // Number type: -324  (5e-324)
+            MIN_EXP = -1e7,                          // -1 to -MAX
+
+            // The maximum exponent value, above which overflow to Infinity occurs.
+            // Number type:  308  (1.7976931348623157e+308)
+            // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
+            MAX_EXP = 1e7,                           // 1 to MAX
+
+            // Whether BigNumber Errors are ever thrown.
+            ERRORS = true,                           // true or false
+
+            // Change to intValidatorNoErrors if ERRORS is false.
+            isValidInt = intValidatorWithErrors,     // intValidatorWithErrors/intValidatorNoErrors
+
+            // Whether to use cryptographically-secure random number generation, if available.
+            CRYPTO = false,                          // true or false
+
+            /*
+             * The modulo mode used when calculating the modulus: a mod n.
+             * The quotient (q = a / n) is calculated according to the corresponding rounding mode.
+             * The remainder (r) is calculated as: r = a - n * q.
+             *
+             * UP        0 The remainder is positive if the dividend is negative, else is negative.
+             * DOWN      1 The remainder has the same sign as the dividend.
+             *             This modulo mode is commonly known as 'truncated division' and is
+             *             equivalent to (a % n) in JavaScript.
+             * FLOOR     3 The remainder has the same sign as the divisor (Python %).
+             * HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
+             * EUCLID    9 Euclidian division. q = sign(n) * floor(a / abs(n)).
+             *             The remainder is always positive.
+             *
+             * The truncated division, floored division, Euclidian division and IEEE 754 remainder
+             * modes are commonly used for the modulus operation.
+             * Although the other rounding modes can also be used, they may not give useful results.
+             */
+            MODULO_MODE = 1,                         // 0 to 9
+
+            // The maximum number of significant digits of the result of the toPower operation.
+            // If POW_PRECISION is 0, there will be unlimited significant digits.
+            POW_PRECISION = 0,                       // 0 to MAX
+
+            // The format specification used by the BigNumber.prototype.toFormat method.
+            FORMAT = {
+                decimalSeparator: '.',
+                groupSeparator: ',',
+                groupSize: 3,
+                secondaryGroupSize: 0,
+                fractionGroupSeparator: '\xA0',      // non-breaking space
+                fractionGroupSize: 0
+            };
+
+
+        /******************************************************************************************/
+
+
+        // CONSTRUCTOR
+
+
+        /*
+         * The BigNumber constructor and exported function.
+         * Create and return a new instance of a BigNumber object.
+         *
+         * n {number|string|BigNumber} A numeric value.
+         * [b] {number} The base of n. Integer, 2 to 64 inclusive.
+         */
+        function BigNumber( n, b ) {
+            var c, e, i, num, len, str,
+                x = this;
+
+            // Enable constructor usage without new.
+            if ( !( x instanceof BigNumber ) ) {
+
+                // 'BigNumber() constructor call without new: {n}'
+                if (ERRORS) raise( 26, 'constructor call without new', n );
+                return new BigNumber( n, b );
+            }
+
+            // 'new BigNumber() base not an integer: {b}'
+            // 'new BigNumber() base out of range: {b}'
+            if ( b == null || !isValidInt( b, 2, 64, id, 'base' ) ) {
+
+                // Duplicate.
+                if ( n instanceof BigNumber ) {
+                    x.s = n.s;
+                    x.e = n.e;
+                    x.c = ( n = n.c ) ? n.slice() : n;
+                    id = 0;
+                    return;
+                }
+
+                if ( ( num = typeof n == 'number' ) && n * 0 == 0 ) {
+                    x.s = 1 / n < 0 ? ( n = -n, -1 ) : 1;
+
+                    // Fast path for integers.
+                    if ( n === ~~n ) {
+                        for ( e = 0, i = n; i >= 10; i /= 10, e++ );
+                        x.e = e;
+                        x.c = [n];
+                        id = 0;
+                        return;
+                    }
+
+                    str = n + '';
+                } else {
+                    if ( !isNumeric.test( str = n + '' ) ) return parseNumeric( x, str, num );
+                    x.s = str.charCodeAt(0) === 45 ? ( str = str.slice(1), -1 ) : 1;
+                }
+            } else {
+                b = b | 0;
+                str = n + '';
+
+                // Ensure return value is rounded to DECIMAL_PLACES as with other bases.
+                // Allow exponential notation to be used with base 10 argument.
+                if ( b == 10 ) {
+                    x = new BigNumber( n instanceof BigNumber ? n : str );
+                    return round( x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE );
+                }
+
+                // Avoid potential interpretation of Infinity and NaN as base 44+ values.
+                // Any number in exponential form will fail due to the [Ee][+-].
+                if ( ( num = typeof n == 'number' ) && n * 0 != 0 ||
+                  !( new RegExp( '^-?' + ( c = '[' + ALPHABET.slice( 0, b ) + ']+' ) +
+                    '(?:\\.' + c + ')?$',b < 37 ? 'i' : '' ) ).test(str) ) {
+                    return parseNumeric( x, str, num, b );
+                }
+
+                if (num) {
+                    x.s = 1 / n < 0 ? ( str = str.slice(1), -1 ) : 1;
+
+                    if ( ERRORS && str.replace( /^0\.0*|\./, '' ).length > 15 ) {
+
+                        // 'new BigNumber() number type has more than 15 significant digits: {n}'
+                        raise( id, tooManyDigits, n );
+                    }
+
+                    // Prevent later check for length on converted number.
+                    num = false;
+                } else {
+                    x.s = str.charCodeAt(0) === 45 ? ( str = str.slice(1), -1 ) : 1;
+                }
+
+                str = convertBase( str, 10, b, x.s );
+            }
+
+            // Decimal point?
+            if ( ( e = str.indexOf('.') ) > -1 ) str = str.replace( '.', '' );
+
+            // Exponential form?
+            if ( ( i = str.search( /e/i ) ) > 0 ) {
+
+                // Determine exponent.
+                if ( e < 0 ) e = i;
+                e += +str.slice( i + 1 );
+                str = str.substring( 0, i );
+            } else if ( e < 0 ) {
+
+                // Integer.
+                e = str.length;
+            }
+
+            // Determine leading zeros.
+            for ( i = 0; str.charCodeAt(i) === 48; i++ );
+
+            // Determine trailing zeros.
+            for ( len = str.length; str.charCodeAt(--len) === 48; );
+            str = str.slice( i, len + 1 );
+
+            if (str) {
+                len = str.length;
+
+                // Disallow numbers with over 15 significant digits if number type.
+                // 'new BigNumber() number type has more than 15 significant digits: {n}'
+                if ( num && ERRORS && len > 15 && ( n > MAX_SAFE_INTEGER || n !== mathfloor(n) ) ) {
+                    raise( id, tooManyDigits, x.s * n );
+                }
+
+                e = e - i - 1;
+
+                 // Overflow?
+                if ( e > MAX_EXP ) {
+
+                    // Infinity.
+                    x.c = x.e = null;
+
+                // Underflow?
+                } else if ( e < MIN_EXP ) {
+
+                    // Zero.
+                    x.c = [ x.e = 0 ];
+                } else {
+                    x.e = e;
+                    x.c = [];
+
+                    // Transform base
+
+                    // e is the base 10 exponent.
+                    // i is where to slice str to get the first element of the coefficient array.
+                    i = ( e + 1 ) % LOG_BASE;
+                    if ( e < 0 ) i += LOG_BASE;
+
+                    if ( i < len ) {
+                        if (i) x.c.push( +str.slice( 0, i ) );
+
+                        for ( len -= LOG_BASE; i < len; ) {
+                            x.c.push( +str.slice( i, i += LOG_BASE ) );
+                        }
+
+                        str = str.slice(i);
+                        i = LOG_BASE - str.length;
+                    } else {
+                        i -= len;
+                    }
+
+                    for ( ; i--; str += '0' );
+                    x.c.push( +str );
+                }
+            } else {
+
+                // Zero.
+                x.c = [ x.e = 0 ];
+            }
+
+            id = 0;
+        }
+
+
+        // CONSTRUCTOR PROPERTIES
+
+
+        BigNumber.another = constructorFactory;
+
+        BigNumber.ROUND_UP = 0;
+        BigNumber.ROUND_DOWN = 1;
+        BigNumber.ROUND_CEIL = 2;
+        BigNumber.ROUND_FLOOR = 3;
+        BigNumber.ROUND_HALF_UP = 4;
+        BigNumber.ROUND_HALF_DOWN = 5;
+        BigNumber.ROUND_HALF_EVEN = 6;
+        BigNumber.ROUND_HALF_CEIL = 7;
+        BigNumber.ROUND_HALF_FLOOR = 8;
+        BigNumber.EUCLID = 9;
+
+
+        /*
+         * Configure infrequently-changing library-wide settings.
+         *
+         * Accept an object or an argument list, with one or many of the following properties or
+         * parameters respectively:
+         *
+         *   DECIMAL_PLACES  {number}  Integer, 0 to MAX inclusive
+         *   ROUNDING_MODE   {number}  Integer, 0 to 8 inclusive
+         *   EXPONENTIAL_AT  {number|number[]}  Integer, -MAX to MAX inclusive or
+         *                                      [integer -MAX to 0 incl., 0 to MAX incl.]
+         *   RANGE           {number|number[]}  Non-zero integer, -MAX to MAX inclusive or
+         *                                      [integer -MAX to -1 incl., integer 1 to MAX incl.]
+         *   ERRORS          {boolean|number}   true, false, 1 or 0
+         *   CRYPTO          {boolean|number}   true, false, 1 or 0
+         *   MODULO_MODE     {number}           0 to 9 inclusive
+         *   POW_PRECISION   {number}           0 to MAX inclusive
+         *   FORMAT          {object}           See BigNumber.prototype.toFormat
+         *      decimalSeparator       {string}
+         *      groupSeparator         {string}
+         *      groupSize              {number}
+         *      secondaryGroupSize     {number}
+         *      fractionGroupSeparator {string}
+         *      fractionGroupSize      {number}
+         *
+         * (The values assigned to the above FORMAT object properties are not checked for validity.)
+         *
+         * E.g.
+         * BigNumber.config(20, 4) is equivalent to
+         * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
+         *
+         * Ignore properties/parameters set to null or undefined.
+         * Return an object with the properties current values.
+         */
+        BigNumber.config = BigNumber.set = function () {
+            var v, p,
+                i = 0,
+                r = {},
+                a = arguments,
+                o = a[0],
+                has = o && typeof o == 'object'
+                  ? function () { if ( o.hasOwnProperty(p) ) return ( v = o[p] ) != null; }
+                  : function () { if ( a.length > i ) return ( v = a[i++] ) != null; };
+
+            // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
+            // 'config() DECIMAL_PLACES not an integer: {v}'
+            // 'config() DECIMAL_PLACES out of range: {v}'
+            if ( has( p = 'DECIMAL_PLACES' ) && isValidInt( v, 0, MAX, 2, p ) ) {
+                DECIMAL_PLACES = v | 0;
+            }
+            r[p] = DECIMAL_PLACES;
+
+            // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
+            // 'config() ROUNDING_MODE not an integer: {v}'
+            // 'config() ROUNDING_MODE out of range: {v}'
+            if ( has( p = 'ROUNDING_MODE' ) && isValidInt( v, 0, 8, 2, p ) ) {
+                ROUNDING_MODE = v | 0;
+            }
+            r[p] = ROUNDING_MODE;
+
+            // EXPONENTIAL_AT {number|number[]}
+            // Integer, -MAX to MAX inclusive or [integer -MAX to 0 inclusive, 0 to MAX inclusive].
+            // 'config() EXPONENTIAL_AT not an integer: {v}'
+            // 'config() EXPONENTIAL_AT out of range: {v}'
+            if ( has( p = 'EXPONENTIAL_AT' ) ) {
+
+                if ( isArray(v) ) {
+                    if ( isValidInt( v[0], -MAX, 0, 2, p ) && isValidInt( v[1], 0, MAX, 2, p ) ) {
+                        TO_EXP_NEG = v[0] | 0;
+                        TO_EXP_POS = v[1] | 0;
+                    }
+                } else if ( isValidInt( v, -MAX, MAX, 2, p ) ) {
+                    TO_EXP_NEG = -( TO_EXP_POS = ( v < 0 ? -v : v ) | 0 );
+                }
+            }
+            r[p] = [ TO_EXP_NEG, TO_EXP_POS ];
+
+            // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
+            // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
+            // 'config() RANGE not an integer: {v}'
+            // 'config() RANGE cannot be zero: {v}'
+            // 'config() RANGE out of range: {v}'
+            if ( has( p = 'RANGE' ) ) {
+
+                if ( isArray(v) ) {
+                    if ( isValidInt( v[0], -MAX, -1, 2, p ) && isValidInt( v[1], 1, MAX, 2, p ) ) {
+                        MIN_EXP = v[0] | 0;
+                        MAX_EXP = v[1] | 0;
+                    }
+                } else if ( isValidInt( v, -MAX, MAX, 2, p ) ) {
+                    if ( v | 0 ) MIN_EXP = -( MAX_EXP = ( v < 0 ? -v : v ) | 0 );
+                    else if (ERRORS) raise( 2, p + ' cannot be zero', v );
+                }
+            }
+            r[p] = [ MIN_EXP, MAX_EXP ];
+
+            // ERRORS {boolean|number} true, false, 1 or 0.
+            // 'config() ERRORS not a boolean or binary digit: {v}'
+            if ( has( p = 'ERRORS' ) ) {
+
+                if ( v === !!v || v === 1 || v === 0 ) {
+                    id = 0;
+                    isValidInt = ( ERRORS = !!v ) ? intValidatorWithErrors : intValidatorNoErrors;
+                } else if (ERRORS) {
+                    raise( 2, p + notBool, v );
+                }
+            }
+            r[p] = ERRORS;
+
+            // CRYPTO {boolean|number} true, false, 1 or 0.
+            // 'config() CRYPTO not a boolean or binary digit: {v}'
+            // 'config() crypto unavailable: {crypto}'
+            if ( has( p = 'CRYPTO' ) ) {
+
+                if ( v === true || v === false || v === 1 || v === 0 ) {
+                    if (v) {
+                        v = typeof crypto == 'undefined';
+                        if ( !v && crypto && (crypto.getRandomValues || crypto.randomBytes)) {
+                            CRYPTO = true;
+                        } else if (ERRORS) {
+                            raise( 2, 'crypto unavailable', v ? void 0 : crypto );
+                        } else {
+                            CRYPTO = false;
+                        }
+                    } else {
+                        CRYPTO = false;
+                    }
+                } else if (ERRORS) {
+                    raise( 2, p + notBool, v );
+                }
+            }
+            r[p] = CRYPTO;
+
+            // MODULO_MODE {number} Integer, 0 to 9 inclusive.
+            // 'config() MODULO_MODE not an integer: {v}'
+            // 'config() MODULO_MODE out of range: {v}'
+            if ( has( p = 'MODULO_MODE' ) && isValidInt( v, 0, 9, 2, p ) ) {
+                MODULO_MODE = v | 0;
+            }
+            r[p] = MODULO_MODE;
+
+            // POW_PRECISION {number} Integer, 0 to MAX inclusive.
+            // 'config() POW_PRECISION not an integer: {v}'
+            // 'config() POW_PRECISION out of range: {v}'
+            if ( has( p = 'POW_PRECISION' ) && isValidInt( v, 0, MAX, 2, p ) ) {
+                POW_PRECISION = v | 0;
+            }
+            r[p] = POW_PRECISION;
+
+            // FORMAT {object}
+            // 'config() FORMAT not an object: {v}'
+            if ( has( p = 'FORMAT' ) ) {
+
+                if ( typeof v == 'object' ) {
+                    FORMAT = v;
+                } else if (ERRORS) {
+                    raise( 2, p + ' not an object', v );
+                }
+            }
+            r[p] = FORMAT;
+
+            return r;
+        };
+
+
+        /*
+         * Return a new BigNumber whose value is the maximum of the arguments.
+         *
+         * arguments {number|string|BigNumber}
+         */
+        BigNumber.max = function () { return maxOrMin( arguments, P.lt ); };
+
+
+        /*
+         * Return a new BigNumber whose value is the minimum of the arguments.
+         *
+         * arguments {number|string|BigNumber}
+         */
+        BigNumber.min = function () { return maxOrMin( arguments, P.gt ); };
+
+
+        /*
+         * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
+         * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
+         * zeros are produced).
+         *
+         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+         *
+         * 'random() decimal places not an integer: {dp}'
+         * 'random() decimal places out of range: {dp}'
+         * 'random() crypto unavailable: {crypto}'
+         */
+        BigNumber.random = (function () {
+            var pow2_53 = 0x20000000000000;
+
+            // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
+            // Check if Math.random() produces more than 32 bits of randomness.
+            // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
+            // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
+            var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
+              ? function () { return mathfloor( Math.random() * pow2_53 ); }
+              : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
+                  (Math.random() * 0x800000 | 0); };
+
+            return function (dp) {
+                var a, b, e, k, v,
+                    i = 0,
+                    c = [],
+                    rand = new BigNumber(ONE);
+
+                dp = dp == null || !isValidInt( dp, 0, MAX, 14 ) ? DECIMAL_PLACES : dp | 0;
+                k = mathceil( dp / LOG_BASE );
+
+                if (CRYPTO) {
+
+                    // Browsers supporting crypto.getRandomValues.
+                    if (crypto.getRandomValues) {
+
+                        a = crypto.getRandomValues( new Uint32Array( k *= 2 ) );
+
+                        for ( ; i < k; ) {
+
+                            // 53 bits:
+                            // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
+                            // 11111 11111111 11111111 11111111 11100000 00000000 00000000
+                            // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
+                            //                                     11111 11111111 11111111
+                            // 0x20000 is 2^21.
+                            v = a[i] * 0x20000 + (a[i + 1] >>> 11);
+
+                            // Rejection sampling:
+                            // 0 <= v < 9007199254740992
+                            // Probability that v >= 9e15, is
+                            // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
+                            if ( v >= 9e15 ) {
+                                b = crypto.getRandomValues( new Uint32Array(2) );
+                                a[i] = b[0];
+                                a[i + 1] = b[1];
+                            } else {
+
+                                // 0 <= v <= 8999999999999999
+                                // 0 <= (v % 1e14) <= 99999999999999
+                                c.push( v % 1e14 );
+                                i += 2;
+                            }
+                        }
+                        i = k / 2;
+
+                    // Node.js supporting crypto.randomBytes.
+                    } else if (crypto.randomBytes) {
+
+                        // buffer
+                        a = crypto.randomBytes( k *= 7 );
+
+                        for ( ; i < k; ) {
+
+                            // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
+                            // 0x100000000 is 2^32, 0x1000000 is 2^24
+                            // 11111 11111111 11111111 11111111 11111111 11111111 11111111
+                            // 0 <= v < 9007199254740992
+                            v = ( ( a[i] & 31 ) * 0x1000000000000 ) + ( a[i + 1] * 0x10000000000 ) +
+                                  ( a[i + 2] * 0x100000000 ) + ( a[i + 3] * 0x1000000 ) +
+                                  ( a[i + 4] << 16 ) + ( a[i + 5] << 8 ) + a[i + 6];
+
+                            if ( v >= 9e15 ) {
+                                crypto.randomBytes(7).copy( a, i );
+                            } else {
+
+                                // 0 <= (v % 1e14) <= 99999999999999
+                                c.push( v % 1e14 );
+                                i += 7;
+                            }
+                        }
+                        i = k / 7;
+                    } else {
+                        CRYPTO = false;
+                        if (ERRORS) raise( 14, 'crypto unavailable', crypto );
+                    }
+                }
+
+                // Use Math.random.
+                if (!CRYPTO) {
+
+                    for ( ; i < k; ) {
+                        v = random53bitInt();
+                        if ( v < 9e15 ) c[i++] = v % 1e14;
+                    }
+                }
+
+                k = c[--i];
+                dp %= LOG_BASE;
+
+                // Convert trailing digits to zeros according to dp.
+                if ( k && dp ) {
+                    v = POWS_TEN[LOG_BASE - dp];
+                    c[i] = mathfloor( k / v ) * v;
+                }
+
+                // Remove trailing elements which are zero.
+                for ( ; c[i] === 0; c.pop(), i-- );
+
+                // Zero?
+                if ( i < 0 ) {
+                    c = [ e = 0 ];
+                } else {
+
+                    // Remove leading elements which are zero and adjust exponent accordingly.
+                    for ( e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
+
+                    // Count the digits of the first element of c to determine leading zeros, and...
+                    for ( i = 1, v = c[0]; v >= 10; v /= 10, i++);
+
+                    // adjust the exponent accordingly.
+                    if ( i < LOG_BASE ) e -= LOG_BASE - i;
+                }
+
+                rand.e = e;
+                rand.c = c;
+                return rand;
+            };
+        })();
+
+
+        // PRIVATE FUNCTIONS
+
+
+        // Convert a numeric string of baseIn to a numeric string of baseOut.
+        function convertBase( str, baseOut, baseIn, sign ) {
+            var d, e, k, r, x, xc, y,
+                i = str.indexOf( '.' ),
+                dp = DECIMAL_PLACES,
+                rm = ROUNDING_MODE;
+
+            if ( baseIn < 37 ) str = str.toLowerCase();
+
+            // Non-integer.
+            if ( i >= 0 ) {
+                k = POW_PRECISION;
+
+                // Unlimited precision.
+                POW_PRECISION = 0;
+                str = str.replace( '.', '' );
+                y = new BigNumber(baseIn);
+                x = y.pow( str.length - i );
+                POW_PRECISION = k;
+
+                // Convert str as if an integer, then restore the fraction part by dividing the
+                // result by its base raised to a power.
+                y.c = toBaseOut( toFixedPoint( coeffToString( x.c ), x.e ), 10, baseOut );
+                y.e = y.c.length;
+            }
+
+            // Convert the number as integer.
+            xc = toBaseOut( str, baseIn, baseOut );
+            e = k = xc.length;
+
+            // Remove trailing zeros.
+            for ( ; xc[--k] == 0; xc.pop() );
+            if ( !xc[0] ) return '0';
+
+            if ( i < 0 ) {
+                --e;
+            } else {
+                x.c = xc;
+                x.e = e;
+
+                // sign is needed for correct rounding.
+                x.s = sign;
+                x = div( x, y, dp, rm, baseOut );
+                xc = x.c;
+                r = x.r;
+                e = x.e;
+            }
+
+            d = e + dp + 1;
+
+            // The rounding digit, i.e. the digit to the right of the digit that may be rounded up.
+            i = xc[d];
+            k = baseOut / 2;
+            r = r || d < 0 || xc[d + 1] != null;
+
+            r = rm < 4 ? ( i != null || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
+                       : i > k || i == k &&( rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
+                         rm == ( x.s < 0 ? 8 : 7 ) );
+
+            if ( d < 1 || !xc[0] ) {
+
+                // 1^-dp or 0.
+                str = r ? toFixedPoint( '1', -dp ) : '0';
+            } else {
+                xc.length = d;
+
+                if (r) {
+
+                    // Rounding up may mean the previous digit has to be rounded up and so on.
+                    for ( --baseOut; ++xc[--d] > baseOut; ) {
+                        xc[d] = 0;
+
+                        if ( !d ) {
+                            ++e;
+                            xc = [1].concat(xc);
+                        }
+                    }
+                }
+
+                // Determine trailing zeros.
+                for ( k = xc.length; !xc[--k]; );
+
+                // E.g. [4, 11, 15] becomes 4bf.
+                for ( i = 0, str = ''; i <= k; str += ALPHABET.charAt( xc[i++] ) );
+                str = toFixedPoint( str, e );
+            }
+
+            // The caller will add the sign.
+            return str;
+        }
+
+
+        // Perform division in the specified base. Called by div and convertBase.
+        div = (function () {
+
+            // Assume non-zero x and k.
+            function multiply( x, k, base ) {
+                var m, temp, xlo, xhi,
+                    carry = 0,
+                    i = x.length,
+                    klo = k % SQRT_BASE,
+                    khi = k / SQRT_BASE | 0;
+
+                for ( x = x.slice(); i--; ) {
+                    xlo = x[i] % SQRT_BASE;
+                    xhi = x[i] / SQRT_BASE | 0;
+                    m = khi * xlo + xhi * klo;
+                    temp = klo * xlo + ( ( m % SQRT_BASE ) * SQRT_BASE ) + carry;
+                    carry = ( temp / base | 0 ) + ( m / SQRT_BASE | 0 ) + khi * xhi;
+                    x[i] = temp % base;
+                }
+
+                if (carry) x = [carry].concat(x);
+
+                return x;
+            }
+
+            function compare( a, b, aL, bL ) {
+                var i, cmp;
+
+                if ( aL != bL ) {
+                    cmp = aL > bL ? 1 : -1;
+                } else {
+
+                    for ( i = cmp = 0; i < aL; i++ ) {
+
+                        if ( a[i] != b[i] ) {
+                            cmp = a[i] > b[i] ? 1 : -1;
+                            break;
+                        }
+                    }
+                }
+                return cmp;
+            }
+
+            function subtract( a, b, aL, base ) {
+                var i = 0;
+
+                // Subtract b from a.
+                for ( ; aL--; ) {
+                    a[aL] -= i;
+                    i = a[aL] < b[aL] ? 1 : 0;
+                    a[aL] = i * base + a[aL] - b[aL];
+                }
+
+                // Remove leading zeros.
+                for ( ; !a[0] && a.length > 1; a.splice(0, 1) );
+            }
+
+            // x: dividend, y: divisor.
+            return function ( x, y, dp, rm, base ) {
+                var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
+                    yL, yz,
+                    s = x.s == y.s ? 1 : -1,
+                    xc = x.c,
+                    yc = y.c;
+
+                // Either NaN, Infinity or 0?
+                if ( !xc || !xc[0] || !yc || !yc[0] ) {
+
+                    return new BigNumber(
+
+                      // Return NaN if either NaN, or both Infinity or 0.
+                      !x.s || !y.s || ( xc ? yc && xc[0] == yc[0] : !yc ) ? NaN :
+
+                        // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
+                        xc && xc[0] == 0 || !yc ? s * 0 : s / 0
+                    );
+                }
+
+                q = new BigNumber(s);
+                qc = q.c = [];
+                e = x.e - y.e;
+                s = dp + e + 1;
+
+                if ( !base ) {
+                    base = BASE;
+                    e = bitFloor( x.e / LOG_BASE ) - bitFloor( y.e / LOG_BASE );
+                    s = s / LOG_BASE | 0;
+                }
+
+                // Result exponent may be one less then the current value of e.
+                // The coefficients of the BigNumbers from convertBase may have trailing zeros.
+                for ( i = 0; yc[i] == ( xc[i] || 0 ); i++ );
+                if ( yc[i] > ( xc[i] || 0 ) ) e--;
+
+                if ( s < 0 ) {
+                    qc.push(1);
+                    more = true;
+                } else {
+                    xL = xc.length;
+                    yL = yc.length;
+                    i = 0;
+                    s += 2;
+
+                    // Normalise xc and yc so highest order digit of yc is >= base / 2.
+
+                    n = mathfloor( base / ( yc[0] + 1 ) );
+
+                    // Not necessary, but to handle odd bases where yc[0] == ( base / 2 ) - 1.
+                    // if ( n > 1 || n++ == 1 && yc[0] < base / 2 ) {
+                    if ( n > 1 ) {
+                        yc = multiply( yc, n, base );
+                        xc = multiply( xc, n, base );
+                        yL = yc.length;
+                        xL = xc.length;
+                    }
+
+                    xi = yL;
+                    rem = xc.slice( 0, yL );
+                    remL = rem.length;
+
+                    // Add zeros to make remainder as long as divisor.
+                    for ( ; remL < yL; rem[remL++] = 0 );
+                    yz = yc.slice();
+                    yz = [0].concat(yz);
+                    yc0 = yc[0];
+                    if ( yc[1] >= base / 2 ) yc0++;
+                    // Not necessary, but to prevent trial digit n > base, when using base 3.
+                    // else if ( base == 3 && yc0 == 1 ) yc0 = 1 + 1e-15;
+
+                    do {
+                        n = 0;
+
+                        // Compare divisor and remainder.
+                        cmp = compare( yc, rem, yL, remL );
+
+                        // If divisor < remainder.
+                        if ( cmp < 0 ) {
+
+                            // Calculate trial digit, n.
+
+                            rem0 = rem[0];
+                            if ( yL != remL ) rem0 = rem0 * base + ( rem[1] || 0 );
+
+                            // n is how many times the divisor goes into the current remainder.
+                            n = mathfloor( rem0 / yc0 );
+
+                            //  Algorithm:
+                            //  1. product = divisor * trial digit (n)
+                            //  2. if product > remainder: product -= divisor, n--
+                            //  3. remainder -= product
+                            //  4. if product was < remainder at 2:
+                            //    5. compare new remainder and divisor
+                            //    6. If remainder > divisor: remainder -= divisor, n++
+
+                            if ( n > 1 ) {
+
+                                // n may be > base only when base is 3.
+                                if (n >= base) n = base - 1;
+
+                                // product = divisor * trial digit.
+                                prod = multiply( yc, n, base );
+                                prodL = prod.length;
+                                remL = rem.length;
+
+                                // Compare product and remainder.
+                                // If product > remainder.
+                                // Trial digit n too high.
+                                // n is 1 too high about 5% of the time, and is not known to have
+                                // ever been more than 1 too high.
+                                while ( compare( prod, rem, prodL, remL ) == 1 ) {
+                                    n--;
+
+                                    // Subtract divisor from product.
+                                    subtract( prod, yL < prodL ? yz : yc, prodL, base );
+                                    prodL = prod.length;
+                                    cmp = 1;
+                                }
+                            } else {
+
+                                // n is 0 or 1, cmp is -1.
+                                // If n is 0, there is no need to compare yc and rem again below,
+                                // so change cmp to 1 to avoid it.
+                                // If n is 1, leave cmp as -1, so yc and rem are compared again.
+                                if ( n == 0 ) {
+
+                                    // divisor < remainder, so n must be at least 1.
+                                    cmp = n = 1;
+                                }
+
+                                // product = divisor
+                                prod = yc.slice();
+                                prodL = prod.length;
+                            }
+
+                            if ( prodL < remL ) prod = [0].concat(prod);
+
+                            // Subtract product from remainder.
+                            subtract( rem, prod, remL, base );
+                            remL = rem.length;
+
+                             // If product was < remainder.
+                            if ( cmp == -1 ) {
+
+                                // Compare divisor and new remainder.
+                                // If divisor < new remainder, subtract divisor from remainder.
+                                // Trial digit n too low.
+                                // n is 1 too low about 5% of the time, and very rarely 2 too low.
+                                while ( compare( yc, rem, yL, remL ) < 1 ) {
+                                    n++;
+
+                                    // Subtract divisor from remainder.
+                                    subtract( rem, yL < remL ? yz : yc, remL, base );
+                                    remL = rem.length;
+                                }
+                            }
+                        } else if ( cmp === 0 ) {
+                            n++;
+                            rem = [0];
+                        } // else cmp === 1 and n will be 0
+
+                        // Add the next digit, n, to the result array.
+                        qc[i++] = n;
+
+                        // Update the remainder.
+                        if ( rem[0] ) {
+                            rem[remL++] = xc[xi] || 0;
+                        } else {
+                            rem = [ xc[xi] ];
+                            remL = 1;
+                        }
+                    } while ( ( xi++ < xL || rem[0] != null ) && s-- );
+
+                    more = rem[0] != null;
+
+                    // Leading zero?
+                    if ( !qc[0] ) qc.splice(0, 1);
+                }
+
+                if ( base == BASE ) {
+
+                    // To calculate q.e, first get the number of digits of qc[0].
+                    for ( i = 1, s = qc[0]; s >= 10; s /= 10, i++ );
+                    round( q, dp + ( q.e = i + e * LOG_BASE - 1 ) + 1, rm, more );
+
+                // Caller is convertBase.
+                } else {
+                    q.e = e;
+                    q.r = +more;
+                }
+
+                return q;
+            };
+        })();
+
+
+        /*
+         * Return a string representing the value of BigNumber n in fixed-point or exponential
+         * notation rounded to the specified decimal places or significant digits.
+         *
+         * n is a BigNumber.
+         * i is the index of the last digit required (i.e. the digit that may be rounded up).
+         * rm is the rounding mode.
+         * caller is caller id: toExponential 19, toFixed 20, toFormat 21, toPrecision 24.
+         */
+        function format( n, i, rm, caller ) {
+            var c0, e, ne, len, str;
+
+            rm = rm != null && isValidInt( rm, 0, 8, caller, roundingMode )
+              ? rm | 0 : ROUNDING_MODE;
+
+            if ( !n.c ) return n.toString();
+            c0 = n.c[0];
+            ne = n.e;
+
+            if ( i == null ) {
+                str = coeffToString( n.c );
+                str = caller == 19 || caller == 24 && ne <= TO_EXP_NEG
+                  ? toExponential( str, ne )
+                  : toFixedPoint( str, ne );
+            } else {
+                n = round( new BigNumber(n), i, rm );
+
+                // n.e may have changed if the value was rounded up.
+                e = n.e;
+
+                str = coeffToString( n.c );
+                len = str.length;
+
+                // toPrecision returns exponential notation if the number of significant digits
+                // specified is less than the number of digits necessary to represent the integer
+                // part of the value in fixed-point notation.
+
+                // Exponential notation.
+                if ( caller == 19 || caller == 24 && ( i <= e || e <= TO_EXP_NEG ) ) {
+
+                    // Append zeros?
+                    for ( ; len < i; str += '0', len++ );
+                    str = toExponential( str, e );
+
+                // Fixed-point notation.
+                } else {
+                    i -= ne;
+                    str = toFixedPoint( str, e );
+
+                    // Append zeros?
+                    if ( e + 1 > len ) {
+                        if ( --i > 0 ) for ( str += '.'; i--; str += '0' );
+                    } else {
+                        i += e - len;
+                        if ( i > 0 ) {
+                            if ( e + 1 == len ) str += '.';
+                            for ( ; i--; str += '0' );
+                        }
+                    }
+                }
+            }
+
+            return n.s < 0 && c0 ? '-' + str : str;
+        }
+
+
+        // Handle BigNumber.max and BigNumber.min.
+        function maxOrMin( args, method ) {
+            var m, n,
+                i = 0;
+
+            if ( isArray( args[0] ) ) args = args[0];
+            m = new BigNumber( args[0] );
+
+            for ( ; ++i < args.length; ) {
+                n = new BigNumber( args[i] );
+
+                // If any number is NaN, return NaN.
+                if ( !n.s ) {
+                    m = n;
+                    break;
+                } else if ( method.call( m, n ) ) {
+                    m = n;
+                }
+            }
+
+            return m;
+        }
+
+
+        /*
+         * Return true if n is an integer in range, otherwise throw.
+         * Use for argument validation when ERRORS is true.
+         */
+        function intValidatorWithErrors( n, min, max, caller, name ) {
+            if ( n < min || n > max || n != truncate(n) ) {
+                raise( caller, ( name || 'decimal places' ) +
+                  ( n < min || n > max ? ' out of range' : ' not an integer' ), n );
+            }
+
+            return true;
+        }
+
+
+        /*
+         * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
+         * Called by minus, plus and times.
+         */
+        function normalise( n, c, e ) {
+            var i = 1,
+                j = c.length;
+
+             // Remove trailing zeros.
+            for ( ; !c[--j]; c.pop() );
+
+            // Calculate the base 10 exponent. First get the number of digits of c[0].
+            for ( j = c[0]; j >= 10; j /= 10, i++ );
+
+            // Overflow?
+            if ( ( e = i + e * LOG_BASE - 1 ) > MAX_EXP ) {
+
+                // Infinity.
+                n.c = n.e = null;
+
+            // Underflow?
+            } else if ( e < MIN_EXP ) {
+
+                // Zero.
+                n.c = [ n.e = 0 ];
+            } else {
+                n.e = e;
+                n.c = c;
+            }
+
+            return n;
+        }
+
+
+        // Handle values that fail the validity test in BigNumber.
+        parseNumeric = (function () {
+            var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
+                dotAfter = /^([^.]+)\.$/,
+                dotBefore = /^\.([^.]+)$/,
+                isInfinityOrNaN = /^-?(Infinity|NaN)$/,
+                whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
+
+            return function ( x, str, num, b ) {
+                var base,
+                    s = num ? str : str.replace( whitespaceOrPlus, '' );
+
+                // No exception on ±Infinity or NaN.
+                if ( isInfinityOrNaN.test(s) ) {
+                    x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
+                } else {
+                    if ( !num ) {
+
+                        // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
+                        s = s.replace( basePrefix, function ( m, p1, p2 ) {
+                            base = ( p2 = p2.toLowerCase() ) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
+                            return !b || b == base ? p1 : m;
+                        });
+
+                        if (b) {
+                            base = b;
+
+                            // E.g. '1.' to '1', '.1' to '0.1'
+                            s = s.replace( dotAfter, '$1' ).replace( dotBefore, '0.$1' );
+                        }
+
+                        if ( str != s ) return new BigNumber( s, base );
+                    }
+
+                    // 'new BigNumber() not a number: {n}'
+                    // 'new BigNumber() not a base {b} number: {n}'
+                    if (ERRORS) raise( id, 'not a' + ( b ? ' base ' + b : '' ) + ' number', str );
+                    x.s = null;
+                }
+
+                x.c = x.e = null;
+                id = 0;
+            }
+        })();
+
+
+        // Throw a BigNumber Error.
+        function raise( caller, msg, val ) {
+            var error = new Error( [
+                'new BigNumber',     // 0
+                'cmp',               // 1
+                'config',            // 2
+                'div',               // 3
+                'divToInt',          // 4
+                'eq',                // 5
+                'gt',                // 6
+                'gte',               // 7
+                'lt',                // 8
+                'lte',               // 9
+                'minus',             // 10
+                'mod',               // 11
+                'plus',              // 12
+                'precision',         // 13
+                'random',            // 14
+                'round',             // 15
+                'shift',             // 16
+                'times',             // 17
+                'toDigits',          // 18
+                'toExponential',     // 19
+                'toFixed',           // 20
+                'toFormat',          // 21
+                'toFraction',        // 22
+                'pow',               // 23
+                'toPrecision',       // 24
+                'toString',          // 25
+                'BigNumber'          // 26
+            ][caller] + '() ' + msg + ': ' + val );
+
+            error.name = 'BigNumber Error';
+            id = 0;
+            throw error;
+        }
+
+
+        /*
+         * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
+         * If r is truthy, it is known that there are more digits after the rounding digit.
+         */
+        function round( x, sd, rm, r ) {
+            var d, i, j, k, n, ni, rd,
+                xc = x.c,
+                pows10 = POWS_TEN;
+
+            // if x is not Infinity or NaN...
+            if (xc) {
+
+                // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
+                // n is a base 1e14 number, the value of the element of array x.c containing rd.
+                // ni is the index of n within x.c.
+                // d is the number of digits of n.
+                // i is the index of rd within n including leading zeros.
+                // j is the actual index of rd within n (if < 0, rd is a leading zero).
+                out: {
+
+                    // Get the number of digits of the first element of xc.
+                    for ( d = 1, k = xc[0]; k >= 10; k /= 10, d++ );
+                    i = sd - d;
+
+                    // If the rounding digit is in the first element of xc...
+                    if ( i < 0 ) {
+                        i += LOG_BASE;
+                        j = sd;
+                        n = xc[ ni = 0 ];
+
+                        // Get the rounding digit at index j of n.
+                        rd = n / pows10[ d - j - 1 ] % 10 | 0;
+                    } else {
+                        ni = mathceil( ( i + 1 ) / LOG_BASE );
+
+                        if ( ni >= xc.length ) {
+
+                            if (r) {
+
+                                // Needed by sqrt.
+                                for ( ; xc.length <= ni; xc.push(0) );
+                                n = rd = 0;
+                                d = 1;
+                                i %= LOG_BASE;
+                                j = i - LOG_BASE + 1;
+                            } else {
+                                break out;
+                            }
+                        } else {
+                            n = k = xc[ni];
+
+                            // Get the number of digits of n.
+                            for ( d = 1; k >= 10; k /= 10, d++ );
+
+                            // Get the index of rd within n.
+                            i %= LOG_BASE;
+
+                            // Get the index of rd within n, adjusted for leading zeros.
+                            // The number of leading zeros of n is given by LOG_BASE - d.
+                            j = i - LOG_BASE + d;
+
+                            // Get the rounding digit at index j of n.
+                            rd = j < 0 ? 0 : n / pows10[ d - j - 1 ] % 10 | 0;
+                        }
+                    }
+
+                    r = r || sd < 0 ||
+
+                    // Are there any non-zero digits after the rounding digit?
+                    // The expression  n % pows10[ d - j - 1 ]  returns all digits of n to the right
+                    // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
+                      xc[ni + 1] != null || ( j < 0 ? n : n % pows10[ d - j - 1 ] );
+
+                    r = rm < 4
+                      ? ( rd || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
+                      : rd > 5 || rd == 5 && ( rm == 4 || r || rm == 6 &&
+
+                        // Check whether the digit to the left of the rounding digit is odd.
+                        ( ( i > 0 ? j > 0 ? n / pows10[ d - j ] : 0 : xc[ni - 1] ) % 10 ) & 1 ||
+                          rm == ( x.s < 0 ? 8 : 7 ) );
+
+                    if ( sd < 1 || !xc[0] ) {
+                        xc.length = 0;
+
+                        if (r) {
+
+                            // Convert sd to decimal places.
+                            sd -= x.e + 1;
+
+                            // 1, 0.1, 0.01, 0.001, 0.0001 etc.
+                            xc[0] = pows10[ ( LOG_BASE - sd % LOG_BASE ) % LOG_BASE ];
+                            x.e = -sd || 0;
+                        } else {
+
+                            // Zero.
+                            xc[0] = x.e = 0;
+                        }
+
+                        return x;
+                    }
+
+                    // Remove excess digits.
+                    if ( i == 0 ) {
+                        xc.length = ni;
+                        k = 1;
+                        ni--;
+                    } else {
+                        xc.length = ni + 1;
+                        k = pows10[ LOG_BASE - i ];
+
+                        // E.g. 56700 becomes 56000 if 7 is the rounding digit.
+                        // j > 0 means i > number of leading zeros of n.
+                        xc[ni] = j > 0 ? mathfloor( n / pows10[ d - j ] % pows10[j] ) * k : 0;
+                    }
+
+                    // Round up?
+                    if (r) {
+
+                        for ( ; ; ) {
+
+                            // If the digit to be rounded up is in the first element of xc...
+                            if ( ni == 0 ) {
+
+                                // i will be the length of xc[0] before k is added.
+                                for ( i = 1, j = xc[0]; j >= 10; j /= 10, i++ );
+                                j = xc[0] += k;
+                                for ( k = 1; j >= 10; j /= 10, k++ );
+
+                                // if i != k the length has increased.
+                                if ( i != k ) {
+                                    x.e++;
+                                    if ( xc[0] == BASE ) xc[0] = 1;
+                                }
+
+                                break;
+                            } else {
+                                xc[ni] += k;
+                                if ( xc[ni] != BASE ) break;
+                                xc[ni--] = 0;
+                                k = 1;
+                            }
+                        }
+                    }
+
+                    // Remove trailing zeros.
+                    for ( i = xc.length; xc[--i] === 0; xc.pop() );
+                }
+
+                // Overflow? Infinity.
+                if ( x.e > MAX_EXP ) {
+                    x.c = x.e = null;
+
+                // Underflow? Zero.
+                } else if ( x.e < MIN_EXP ) {
+                    x.c = [ x.e = 0 ];
+                }
+            }
+
+            return x;
+        }
+
+
+        // PROTOTYPE/INSTANCE METHODS
+
+
+        /*
+         * Return a new BigNumber whose value is the absolute value of this BigNumber.
+         */
+        P.absoluteValue = P.abs = function () {
+            var x = new BigNumber(this);
+            if ( x.s < 0 ) x.s = 1;
+            return x;
+        };
+
+
+        /*
+         * Return a new BigNumber whose value is the value of this BigNumber rounded to a whole
+         * number in the direction of Infinity.
+         */
+        P.ceil = function () {
+            return round( new BigNumber(this), this.e + 1, 2 );
+        };
+
+
+        /*
+         * Return
+         * 1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
+         * -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
+         * 0 if they have the same value,
+         * or null if the value of either is NaN.
+         */
+        P.comparedTo = P.cmp = function ( y, b ) {
+            id = 1;
+            return compare( this, new BigNumber( y, b ) );
+        };
+
+
+        /*
+         * Return the number of decimal places of the value of this BigNumber, or null if the value
+         * of this BigNumber is ±Infinity or NaN.
+         */
+        P.decimalPlaces = P.dp = function () {
+            var n, v,
+                c = this.c;
+
+            if ( !c ) return null;
+            n = ( ( v = c.length - 1 ) - bitFloor( this.e / LOG_BASE ) ) * LOG_BASE;
+
+            // Subtract the number of trailing zeros of the last number.
+            if ( v = c[v] ) for ( ; v % 10 == 0; v /= 10, n-- );
+            if ( n < 0 ) n = 0;
+
+            return n;
+        };
+
+
+        /*
+         *  n / 0 = I
+         *  n / N = N
+         *  n / I = 0
+         *  0 / n = 0
+         *  0 / 0 = N
+         *  0 / N = N
+         *  0 / I = 0
+         *  N / n = N
+         *  N / 0 = N
+         *  N / N = N
+         *  N / I = N
+         *  I / n = I
+         *  I / 0 = I
+         *  I / N = N
+         *  I / I = N
+         *
+         * Return a new BigNumber whose value is the value of this BigNumber divided by the value of
+         * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+         */
+        P.dividedBy = P.div = function ( y, b ) {
+            id = 3;
+            return div( this, new BigNumber( y, b ), DECIMAL_PLACES, ROUNDING_MODE );
+        };
+
+
+        /*
+         * Return a new BigNumber whose value is the integer part of dividing the value of this
+         * BigNumber by the value of BigNumber(y, b).
+         */
+        P.dividedToIntegerBy = P.divToInt = function ( y, b ) {
+            id = 4;
+            return div( this, new BigNumber( y, b ), 0, 1 );
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
+         * otherwise returns false.
+         */
+        P.equals = P.eq = function ( y, b ) {
+            id = 5;
+            return compare( this, new BigNumber( y, b ) ) === 0;
+        };
+
+
+        /*
+         * Return a new BigNumber whose value is the value of this BigNumber rounded to a whole
+         * number in the direction of -Infinity.
+         */
+        P.floor = function () {
+            return round( new BigNumber(this), this.e + 1, 3 );
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
+         * otherwise returns false.
+         */
+        P.greaterThan = P.gt = function ( y, b ) {
+            id = 6;
+            return compare( this, new BigNumber( y, b ) ) > 0;
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is greater than or equal to the value of
+         * BigNumber(y, b), otherwise returns false.
+         */
+        P.greaterThanOrEqualTo = P.gte = function ( y, b ) {
+            id = 7;
+            return ( b = compare( this, new BigNumber( y, b ) ) ) === 1 || b === 0;
+
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is a finite number, otherwise returns false.
+         */
+        P.isFinite = function () {
+            return !!this.c;
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is an integer, otherwise return false.
+         */
+        P.isInteger = P.isInt = function () {
+            return !!this.c && bitFloor( this.e / LOG_BASE ) > this.c.length - 2;
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is NaN, otherwise returns false.
+         */
+        P.isNaN = function () {
+            return !this.s;
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is negative, otherwise returns false.
+         */
+        P.isNegative = P.isNeg = function () {
+            return this.s < 0;
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is 0 or -0, otherwise returns false.
+         */
+        P.isZero = function () {
+            return !!this.c && this.c[0] == 0;
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
+         * otherwise returns false.
+         */
+        P.lessThan = P.lt = function ( y, b ) {
+            id = 8;
+            return compare( this, new BigNumber( y, b ) ) < 0;
+        };
+
+
+        /*
+         * Return true if the value of this BigNumber is less than or equal to the value of
+         * BigNumber(y, b), otherwise returns false.
+         */
+        P.lessThanOrEqualTo = P.lte = function ( y, b ) {
+            id = 9;
+            return ( b = compare( this, new BigNumber( y, b ) ) ) === -1 || b === 0;
+        };
+
+
+        /*
+         *  n - 0 = n
+         *  n - N = N
+         *  n - I = -I
+         *  0 - n = -n
+         *  0 - 0 = 0
+         *  0 - N = N
+         *  0 - I = -I
+         *  N - n = N
+         *  N - 0 = N
+         *  N - N = N
+         *  N - I = N
+         *  I - n = I
+         *  I - 0 = I
+         *  I - N = N
+         *  I - I = N
+         *
+         * Return a new BigNumber whose value is the value of this BigNumber minus the value of
+         * BigNumber(y, b).
+         */
+        P.minus = P.sub = function ( y, b ) {
+            var i, j, t, xLTy,
+                x = this,
+                a = x.s;
+
+            id = 10;
+            y = new BigNumber( y, b );
+            b = y.s;
+
+            // Either NaN?
+            if ( !a || !b ) return new BigNumber(NaN);
+
+            // Signs differ?
+            if ( a != b ) {
+                y.s = -b;
+                return x.plus(y);
+            }
+
+            var xe = x.e / LOG_BASE,
+                ye = y.e / LOG_BASE,
+                xc = x.c,
+                yc = y.c;
+
+            if ( !xe || !ye ) {
+
+                // Either Infinity?
+                if ( !xc || !yc ) return xc ? ( y.s = -b, y ) : new BigNumber( yc ? x : NaN );
+
+                // Either zero?
+                if ( !xc[0] || !yc[0] ) {
+
+                    // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+                    return yc[0] ? ( y.s = -b, y ) : new BigNumber( xc[0] ? x :
+
+                      // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
+                      ROUNDING_MODE == 3 ? -0 : 0 );
+                }
+            }
+
+            xe = bitFloor(xe);
+            ye = bitFloor(ye);
+            xc = xc.slice();
+
+            // Determine which is the bigger number.
+            if ( a = xe - ye ) {
+
+                if ( xLTy = a < 0 ) {
+                    a = -a;
+                    t = xc;
+                } else {
+                    ye = xe;
+                    t = yc;
+                }
+
+                t.reverse();
+
+                // Prepend zeros to equalise exponents.
+                for ( b = a; b--; t.push(0) );
+                t.reverse();
+            } else {
+
+                // Exponents equal. Check digit by digit.
+                j = ( xLTy = ( a = xc.length ) < ( b = yc.length ) ) ? a : b;
+
+                for ( a = b = 0; b < j; b++ ) {
+
+                    if ( xc[b] != yc[b] ) {
+                        xLTy = xc[b] < yc[b];
+                        break;
+                    }
+                }
+            }
+
+            // x < y? Point xc to the array of the bigger number.
+            if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
+
+            b = ( j = yc.length ) - ( i = xc.length );
+
+            // Append zeros to xc if shorter.
+            // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
+            if ( b > 0 ) for ( ; b--; xc[i++] = 0 );
+            b = BASE - 1;
+
+            // Subtract yc from xc.
+            for ( ; j > a; ) {
+
+                if ( xc[--j] < yc[j] ) {
+                    for ( i = j; i && !xc[--i]; xc[i] = b );
+                    --xc[i];
+                    xc[j] += BASE;
+                }
+
+                xc[j] -= yc[j];
+            }
+
+            // Remove leading zeros and adjust exponent accordingly.
+            for ( ; xc[0] == 0; xc.splice(0, 1), --ye );
+
+            // Zero?
+            if ( !xc[0] ) {
+
+                // Following IEEE 754 (2008) 6.3,
+                // n - n = +0  but  n - n = -0  when rounding towards -Infinity.
+                y.s = ROUNDING_MODE == 3 ? -1 : 1;
+                y.c = [ y.e = 0 ];
+                return y;
+            }
+
+            // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
+            // for finite x and y.
+            return normalise( y, xc, ye );
+        };
+
+
+        /*
+         *   n % 0 =  N
+         *   n % N =  N
+         *   n % I =  n
+         *   0 % n =  0
+         *  -0 % n = -0
+         *   0 % 0 =  N
+         *   0 % N =  N
+         *   0 % I =  0
+         *   N % n =  N
+         *   N % 0 =  N
+         *   N % N =  N
+         *   N % I =  N
+         *   I % n =  N
+         *   I % 0 =  N
+         *   I % N =  N
+         *   I % I =  N
+         *
+         * Return a new BigNumber whose value is the value of this BigNumber modulo the value of
+         * BigNumber(y, b). The result depends on the value of MODULO_MODE.
+         */
+        P.modulo = P.mod = function ( y, b ) {
+            var q, s,
+                x = this;
+
+            id = 11;
+            y = new BigNumber( y, b );
+
+            // Return NaN if x is Infinity or NaN, or y is NaN or zero.
+            if ( !x.c || !y.s || y.c && !y.c[0] ) {
+                return new BigNumber(NaN);
+
+            // Return x if y is Infinity or x is zero.
+            } else if ( !y.c || x.c && !x.c[0] ) {
+                return new BigNumber(x);
+            }
+
+            if ( MODULO_MODE == 9 ) {
+
+                // Euclidian division: q = sign(y) * floor(x / abs(y))
+                // r = x - qy    where  0 <= r < abs(y)
+                s = y.s;
+                y.s = 1;
+                q = div( x, y, 0, 3 );
+                y.s = s;
+                q.s *= s;
+            } else {
+                q = div( x, y, 0, MODULO_MODE );
+            }
+
+            return x.minus( q.times(y) );
+        };
+
+
+        /*
+         * Return a new BigNumber whose value is the value of this BigNumber negated,
+         * i.e. multiplied by -1.
+         */
+        P.negated = P.neg = function () {
+            var x = new BigNumber(this);
+            x.s = -x.s || null;
+            return x;
+        };
+
+
+        /*
+         *  n + 0 = n
+         *  n + N = N
+         *  n + I = I
+         *  0 + n = n
+         *  0 + 0 = 0
+         *  0 + N = N
+         *  0 + I = I
+         *  N + n = N
+         *  N + 0 = N
+         *  N + N = N
+         *  N + I = N
+         *  I + n = I
+         *  I + 0 = I
+         *  I + N = N
+         *  I + I = I
+         *
+         * Return a new BigNumber whose value is the value of this BigNumber plus the value of
+         * BigNumber(y, b).
+         */
+        P.plus = P.add = function ( y, b ) {
+            var t,
+                x = this,
+                a = x.s;
+
+            id = 12;
+            y = new BigNumber( y, b );
+            b = y.s;
+
+            // Either NaN?
+            if ( !a || !b ) return new BigNumber(NaN);
+
+            // Signs differ?
+             if ( a != b ) {
+                y.s = -b;
+                return x.minus(y);
+            }
+
+            var xe = x.e / LOG_BASE,
+                ye = y.e / LOG_BASE,
+                xc = x.c,
+                yc = y.c;
+
+            if ( !xe || !ye ) {
+
+                // Return ±Infinity if either ±Infinity.
+                if ( !xc || !yc ) return new BigNumber( a / 0 );
+
+                // Either zero?
+                // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+                if ( !xc[0] || !yc[0] ) return yc[0] ? y : new BigNumber( xc[0] ? x : a * 0 );
+            }
+
+            xe = bitFloor(xe);
+            ye = bitFloor(ye);
+            xc = xc.slice();
+
+            // Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
+            if ( a = xe - ye ) {
+                if ( a > 0 ) {
+                    ye = xe;
+                    t = yc;
+                } else {
+                    a = -a;
+                    t = xc;
+                }
+
+                t.reverse();
+                for ( ; a--; t.push(0) );
+                t.reverse();
+            }
+
+            a = xc.length;
+            b = yc.length;
+
+            // Point xc to the longer array, and b to the shorter length.
+            if ( a - b < 0 ) t = yc, yc = xc, xc = t, b = a;
+
+            // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
+            for ( a = 0; b; ) {
+                a = ( xc[--b] = xc[b] + yc[b] + a ) / BASE | 0;
+                xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
+            }
+
+            if (a) {
+                xc = [a].concat(xc);
+                ++ye;
+            }
+
+            // No need to check for zero, as +x + +y != 0 && -x + -y != 0
+            // ye = MAX_EXP + 1 possible
+            return normalise( y, xc, ye );
+        };
+
+
+        /*
+         * Return the number of significant digits of the value of this BigNumber.
+         *
+         * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0.
+         */
+        P.precision = P.sd = function (z) {
+            var n, v,
+                x = this,
+                c = x.c;
+
+            // 'precision() argument not a boolean or binary digit: {z}'
+            if ( z != null && z !== !!z && z !== 1 && z !== 0 ) {
+                if (ERRORS) raise( 13, 'argument' + notBool, z );
+                if ( z != !!z ) z = null;
+            }
+
+            if ( !c ) return null;
+            v = c.length - 1;
+            n = v * LOG_BASE + 1;
+
+            if ( v = c[v] ) {
+
+                // Subtract the number of trailing zeros of the last element.
+                for ( ; v % 10 == 0; v /= 10, n-- );
+
+                // Add the number of digits of the first element.
+                for ( v = c[0]; v >= 10; v /= 10, n++ );
+            }
+
+            if ( z && x.e + 1 > n ) n = x.e + 1;
+
+            return n;
+        };
+
+
+        /*
+         * Return a new BigNumber whose value is the value of this BigNumber rounded to a maximum of
+         * dp decimal places using rounding mode rm, or to 0 and ROUNDING_MODE respectively if
+         * omitted.
+         *
+         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+         *
+         * 'round() decimal places out of range: {dp}'
+         * 'round() decimal places not an integer: {dp}'
+         * 'round() rounding mode not an integer: {rm}'
+         * 'round() rounding mode out of range: {rm}'
+         */
+        P.round = function ( dp, rm ) {
+            var n = new BigNumber(this);
+
+            if ( dp == null || isValidInt( dp, 0, MAX, 15 ) ) {
+                round( n, ~~dp + this.e + 1, rm == null ||
+                  !isValidInt( rm, 0, 8, 15, roundingMode ) ? ROUNDING_MODE : rm | 0 );
+            }
+
+            return n;
+        };
+
+
+        /*
+         * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
+         * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
+         *
+         * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
+         *
+         * If k is out of range and ERRORS is false, the result will be ±0 if k < 0, or ±Infinity
+         * otherwise.
+         *
+         * 'shift() argument not an integer: {k}'
+         * 'shift() argument out of range: {k}'
+         */
+        P.shift = function (k) {
+            var n = this;
+            return isValidInt( k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER, 16, 'argument' )
+
+              // k < 1e+21, or truncate(k) will produce exponential notation.
+              ? n.times( '1e' + truncate(k) )
+              : new BigNumber( n.c && n.c[0] && ( k < -MAX_SAFE_INTEGER || k > MAX_SAFE_INTEGER )
+                ? n.s * ( k < 0 ? 0 : 1 / 0 )
+                : n );
+        };
+
+
+        /*
+         *  sqrt(-n) =  N
+         *  sqrt( N) =  N
+         *  sqrt(-I) =  N
+         *  sqrt( I) =  I
+         *  sqrt( 0) =  0
+         *  sqrt(-0) = -0
+         *
+         * Return a new BigNumber whose value is the square root of the value of this BigNumber,
+         * rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+         */
+        P.squareRoot = P.sqrt = function () {
+            var m, n, r, rep, t,
+                x = this,
+                c = x.c,
+                s = x.s,
+                e = x.e,
+                dp = DECIMAL_PLACES + 4,
+                half = new BigNumber('0.5');
+
+            // Negative/NaN/Infinity/zero?
+            if ( s !== 1 || !c || !c[0] ) {
+                return new BigNumber( !s || s < 0 && ( !c || c[0] ) ? NaN : c ? x : 1 / 0 );
+            }
+
+            // Initial estimate.
+            s = Math.sqrt( +x );
+
+            // Math.sqrt underflow/overflow?
+            // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
+            if ( s == 0 || s == 1 / 0 ) {
+                n = coeffToString(c);
+                if ( ( n.length + e ) % 2 == 0 ) n += '0';
+                s = Math.sqrt(n);
+                e = bitFloor( ( e + 1 ) / 2 ) - ( e < 0 || e % 2 );
+
+                if ( s == 1 / 0 ) {
+                    n = '1e' + e;
+                } else {
+                    n = s.toExponential();
+                    n = n.slice( 0, n.indexOf('e') + 1 ) + e;
+                }
+
+                r = new BigNumber(n);
+            } else {
+                r = new BigNumber( s + '' );
+            }
+
+            // Check for zero.
+            // r could be zero if MIN_EXP is changed after the this value was created.
+            // This would cause a division by zero (x/t) and hence Infinity below, which would cause
+            // coeffToString to throw.
+            if ( r.c[0] ) {
+                e = r.e;
+                s = e + dp;
+                if ( s < 3 ) s = 0;
+
+                // Newton-Raphson iteration.
+                for ( ; ; ) {
+                    t = r;
+                    r = half.times( t.plus( div( x, t, dp, 1 ) ) );
+
+                    if ( coeffToString( t.c   ).slice( 0, s ) === ( n =
+                         coeffToString( r.c ) ).slice( 0, s ) ) {
+
+                        // The exponent of r may here be one less than the final result exponent,
+                        // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
+                        // are indexed correctly.
+                        if ( r.e < e ) --s;
+                        n = n.slice( s - 3, s + 1 );
+
+                        // The 4th rounding digit may be in error by -1 so if the 4 rounding digits
+                        // are 9999 or 4999 (i.e. approaching a rounding boundary) continue the
+                        // iteration.
+                        if ( n == '9999' || !rep && n == '4999' ) {
+
+                            // On the first iteration only, check to see if rounding up gives the
+                            // exact result as the nines may infinitely repeat.
+                            if ( !rep ) {
+                                round( t, t.e + DECIMAL_PLACES + 2, 0 );
+
+                                if ( t.times(t).eq(x) ) {
+                                    r = t;
+                                    break;
+                                }
+                            }
+
+                            dp += 4;
+                            s += 4;
+                            rep = 1;
+                        } else {
+
+                            // If rounding digits are null, 0{0,4} or 50{0,3}, check for exact
+                            // result. If not, then there are further digits and m will be truthy.
+                            if ( !+n || !+n.slice(1) && n.charAt(0) == '5' ) {
+
+                                // Truncate to the first rounding digit.
+                                round( r, r.e + DECIMAL_PLACES + 2, 1 );
+                                m = !r.times(r).eq(x);
+                            }
+
+                            break;
+                        }
+                    }
+                }
+            }
+
+            return round( r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m );
+        };
+
+
+        /*
+         *  n * 0 = 0
+         *  n * N = N
+         *  n * I = I
+         *  0 * n = 0
+         *  0 * 0 = 0
+         *  0 * N = N
+         *  0 * I = N
+         *  N * n = N
+         *  N * 0 = N
+         *  N * N = N
+         *  N * I = N
+         *  I * n = I
+         *  I * 0 = N
+         *  I * N = N
+         *  I * I = I
+         *
+         * Return a new BigNumber whose value is the value of this BigNumber times the value of
+         * BigNumber(y, b).
+         */
+        P.times = P.mul = function ( y, b ) {
+            var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
+                base, sqrtBase,
+                x = this,
+                xc = x.c,
+                yc = ( id = 17, y = new BigNumber( y, b ) ).c;
+
+            // Either NaN, ±Infinity or ±0?
+            if ( !xc || !yc || !xc[0] || !yc[0] ) {
+
+                // Return NaN if either is NaN, or one is 0 and the other is Infinity.
+                if ( !x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc ) {
+                    y.c = y.e = y.s = null;
+                } else {
+                    y.s *= x.s;
+
+                    // Return ±Infinity if either is ±Infinity.
+                    if ( !xc || !yc ) {
+                        y.c = y.e = null;
+
+                    // Return ±0 if either is ±0.
+                    } else {
+                        y.c = [0];
+                        y.e = 0;
+                    }
+                }
+
+                return y;
+            }
+
+            e = bitFloor( x.e / LOG_BASE ) + bitFloor( y.e / LOG_BASE );
+            y.s *= x.s;
+            xcL = xc.length;
+            ycL = yc.length;
+
+            // Ensure xc points to longer array and xcL to its length.
+            if ( xcL < ycL ) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
+
+            // Initialise the result array with zeros.
+            for ( i = xcL + ycL, zc = []; i--; zc.push(0) );
+
+            base = BASE;
+            sqrtBase = SQRT_BASE;
+
+            for ( i = ycL; --i >= 0; ) {
+                c = 0;
+                ylo = yc[i] % sqrtBase;
+                yhi = yc[i] / sqrtBase | 0;
+
+                for ( k = xcL, j = i + k; j > i; ) {
+                    xlo = xc[--k] % sqrtBase;
+                    xhi = xc[k] / sqrtBase | 0;
+                    m = yhi * xlo + xhi * ylo;
+                    xlo = ylo * xlo + ( ( m % sqrtBase ) * sqrtBase ) + zc[j] + c;
+                    c = ( xlo / base | 0 ) + ( m / sqrtBase | 0 ) + yhi * xhi;
+                    zc[j--] = xlo % base;
+                }
+
+                zc[j] = c;
+            }
+
+            if (c) {
+                ++e;
+            } else {
+                zc.splice(0, 1);
+            }
+
+            return normalise( y, zc, e );
+        };
+
+
+        /*
+         * Return a new BigNumber whose value is the value of this BigNumber rounded to a maximum of
+         * sd significant digits using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+         *
+         * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
+         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+         *
+         * 'toDigits() precision out of range: {sd}'
+         * 'toDigits() precision not an integer: {sd}'
+         * 'toDigits() rounding mode not an integer: {rm}'
+         * 'toDigits() rounding mode out of range: {rm}'
+         */
+        P.toDigits = function ( sd, rm ) {
+            var n = new BigNumber(this);
+            sd = sd == null || !isValidInt( sd, 1, MAX, 18, 'precision' ) ? null : sd | 0;
+            rm = rm == null || !isValidInt( rm, 0, 8, 18, roundingMode ) ? ROUNDING_MODE : rm | 0;
+            return sd ? round( n, sd, rm ) : n;
+        };
+
+
+        /*
+         * Return a string representing the value of this BigNumber in exponential notation and
+         * rounded using ROUNDING_MODE to dp fixed decimal places.
+         *
+         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+         *
+         * 'toExponential() decimal places not an integer: {dp}'
+         * 'toExponential() decimal places out of range: {dp}'
+         * 'toExponential() rounding mode not an integer: {rm}'
+         * 'toExponential() rounding mode out of range: {rm}'
+         */
+        P.toExponential = function ( dp, rm ) {
+            return format( this,
+              dp != null && isValidInt( dp, 0, MAX, 19 ) ? ~~dp + 1 : null, rm, 19 );
+        };
+
+
+        /*
+         * Return a string representing the value of this BigNumber in fixed-point notation rounding
+         * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+         *
+         * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
+         * but e.g. (-0.00001).toFixed(0) is '-0'.
+         *
+         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+         *
+         * 'toFixed() decimal places not an integer: {dp}'
+         * 'toFixed() decimal places out of range: {dp}'
+         * 'toFixed() rounding mode not an integer: {rm}'
+         * 'toFixed() rounding mode out of range: {rm}'
+         */
+        P.toFixed = function ( dp, rm ) {
+            return format( this, dp != null && isValidInt( dp, 0, MAX, 20 )
+              ? ~~dp + this.e + 1 : null, rm, 20 );
+        };
+
+
+        /*
+         * Return a string representing the value of this BigNumber in fixed-point notation rounded
+         * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
+         * of the FORMAT object (see BigNumber.config).
+         *
+         * FORMAT = {
+         *      decimalSeparator : '.',
+         *      groupSeparator : ',',
+         *      groupSize : 3,
+         *      secondaryGroupSize : 0,
+         *      fractionGroupSeparator : '\xA0',    // non-breaking space
+         *      fractionGroupSize : 0
+         * };
+         *
+         * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+         *
+         * 'toFormat() decimal places not an integer: {dp}'
+         * 'toFormat() decimal places out of range: {dp}'
+         * 'toFormat() rounding mode not an integer: {rm}'
+         * 'toFormat() rounding mode out of range: {rm}'
+         */
+        P.toFormat = function ( dp, rm ) {
+            var str = format( this, dp != null && isValidInt( dp, 0, MAX, 21 )
+              ? ~~dp + this.e + 1 : null, rm, 21 );
+
+            if ( this.c ) {
+                var i,
+                    arr = str.split('.'),
+                    g1 = +FORMAT.groupSize,
+                    g2 = +FORMAT.secondaryGroupSize,
+                    groupSeparator = FORMAT.groupSeparator,
+                    intPart = arr[0],
+                    fractionPart = arr[1],
+                    isNeg = this.s < 0,
+                    intDigits = isNeg ? intPart.slice(1) : intPart,
+                    len = intDigits.length;
+
+                if (g2) i = g1, g1 = g2, g2 = i, len -= i;
+
+                if ( g1 > 0 && len > 0 ) {
+                    i = len % g1 || g1;
+                    intPart = intDigits.substr( 0, i );
+
+                    for ( ; i < len; i += g1 ) {
+                        intPart += groupSeparator + intDigits.substr( i, g1 );
+                    }
+
+                    if ( g2 > 0 ) intPart += groupSeparator + intDigits.slice(i);
+                    if (isNeg) intPart = '-' + intPart;
+                }
+
+                str = fractionPart
+                  ? intPart + FORMAT.decimalSeparator + ( ( g2 = +FORMAT.fractionGroupSize )
+                    ? fractionPart.replace( new RegExp( '\\d{' + g2 + '}\\B', 'g' ),
+                      '$&' + FORMAT.fractionGroupSeparator )
+                    : fractionPart )
+                  : intPart;
+            }
+
+            return str;
+        };
+
+
+        /*
+         * Return a string array representing the value of this BigNumber as a simple fraction with
+         * an integer numerator and an integer denominator. The denominator will be a positive
+         * non-zero value less than or equal to the specified maximum denominator. If a maximum
+         * denominator is not specified, the denominator will be the lowest value necessary to
+         * represent the number exactly.
+         *
+         * [md] {number|string|BigNumber} Integer >= 1 and < Infinity. The maximum denominator.
+         *
+         * 'toFraction() max denominator not an integer: {md}'
+         * 'toFraction() max denominator out of range: {md}'
+         */
+        P.toFraction = function (md) {
+            var arr, d0, d2, e, exp, n, n0, q, s,
+                k = ERRORS,
+                x = this,
+                xc = x.c,
+                d = new BigNumber(ONE),
+                n1 = d0 = new BigNumber(ONE),
+                d1 = n0 = new BigNumber(ONE);
+
+            if ( md != null ) {
+                ERRORS = false;
+                n = new BigNumber(md);
+                ERRORS = k;
+
+                if ( !( k = n.isInt() ) || n.lt(ONE) ) {
+
+                    if (ERRORS) {
+                        raise( 22,
+                          'max denominator ' + ( k ? 'out of range' : 'not an integer' ), md );
+                    }
+
+                    // ERRORS is false:
+                    // If md is a finite non-integer >= 1, round it to an integer and use it.
+                    md = !k && n.c && round( n, n.e + 1, 1 ).gte(ONE) ? n : null;
+                }
+            }
+
+            if ( !xc ) return x.toString();
+            s = coeffToString(xc);
+
+            // Determine initial denominator.
+            // d is a power of 10 and the minimum max denominator that specifies the value exactly.
+            e = d.e = s.length - x.e - 1;
+            d.c[0] = POWS_TEN[ ( exp = e % LOG_BASE ) < 0 ? LOG_BASE + exp : exp ];
+            md = !md || n.cmp(d) > 0 ? ( e > 0 ? d : n1 ) : n;
+
+            exp = MAX_EXP;
+            MAX_EXP = 1 / 0;
+            n = new BigNumber(s);
+
+            // n0 = d1 = 0
+            n0.c[0] = 0;
+
+            for ( ; ; )  {
+                q = div( n, d, 0, 1 );
+                d2 = d0.plus( q.times(d1) );
+                if ( d2.cmp(md) == 1 ) break;
+                d0 = d1;
+                d1 = d2;
+                n1 = n0.plus( q.times( d2 = n1 ) );
+                n0 = d2;
+                d = n.minus( q.times( d2 = d ) );
+                n = d2;
+            }
+
+            d2 = div( md.minus(d0), d1, 0, 1 );
+            n0 = n0.plus( d2.times(n1) );
+            d0 = d0.plus( d2.times(d1) );
+            n0.s = n1.s = x.s;
+            e *= 2;
+
+            // Determine which fraction is closer to x, n0/d0 or n1/d1
+            arr = div( n1, d1, e, ROUNDING_MODE ).minus(x).abs().cmp(
+                  div( n0, d0, e, ROUNDING_MODE ).minus(x).abs() ) < 1
+                    ? [ n1.toString(), d1.toString() ]
+                    : [ n0.toString(), d0.toString() ];
+
+            MAX_EXP = exp;
+            return arr;
+        };
+
+
+        /*
+         * Return the value of this BigNumber converted to a number primitive.
+         */
+        P.toNumber = function () {
+            return +this;
+        };
+
+
+        /*
+         * Return a BigNumber whose value is the value of this BigNumber raised to the power n.
+         * If m is present, return the result modulo m.
+         * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
+         * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using
+         * ROUNDING_MODE.
+         *
+         * The modular power operation works efficiently when x, n, and m are positive integers,
+         * otherwise it is equivalent to calculating x.toPower(n).modulo(m) (with POW_PRECISION 0).
+         *
+         * n {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
+         * [m] {number|string|BigNumber} The modulus.
+         *
+         * 'pow() exponent not an integer: {n}'
+         * 'pow() exponent out of range: {n}'
+         *
+         * Performs 54 loop iterations for n of 9007199254740991.
+         */
+        P.toPower = P.pow = function ( n, m ) {
+            var k, y, z,
+                i = mathfloor( n < 0 ? -n : +n ),
+                x = this;
+
+            if ( m != null ) {
+                id = 23;
+                m = new BigNumber(m);
+            }
+
+            // Pass ±Infinity to Math.pow if exponent is out of range.
+            if ( !isValidInt( n, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER, 23, 'exponent' ) &&
+              ( !isFinite(n) || i > MAX_SAFE_INTEGER && ( n /= 0 ) ||
+                parseFloat(n) != n && !( n = NaN ) ) || n == 0 ) {
+                k = Math.pow( +x, n );
+                return new BigNumber( m ? k % m : k );
+            }
+
+            if (m) {
+                if ( n > 1 && x.gt(ONE) && x.isInt() && m.gt(ONE) && m.isInt() ) {
+                    x = x.mod(m);
+                } else {
+                    z = m;
+
+                    // Nullify m so only a single mod operation is performed at the end.
+                    m = null;
+                }
+            } else if (POW_PRECISION) {
+
+                // Truncating each coefficient array to a length of k after each multiplication
+                // equates to truncating significant digits to POW_PRECISION + [28, 41],
+                // i.e. there will be a minimum of 28 guard digits retained.
+                // (Using + 1.5 would give [9, 21] guard digits.)
+                k = mathceil( POW_PRECISION / LOG_BASE + 2 );
+            }
+
+            y = new BigNumber(ONE);
+
+            for ( ; ; ) {
+                if ( i % 2 ) {
+                    y = y.times(x);
+                    if ( !y.c ) break;
+                    if (k) {
+                        if ( y.c.length > k ) y.c.length = k;
+                    } else if (m) {
+                        y = y.mod(m);
+                    }
+                }
+
+                i = mathfloor( i / 2 );
+                if ( !i ) break;
+                x = x.times(x);
+                if (k) {
+                    if ( x.c && x.c.length > k ) x.c.length = k;
+                } else if (m) {
+                    x = x.mod(m);
+                }
+            }
+
+            if (m) return y;
+            if ( n < 0 ) y = ONE.div(y);
+
+            return z ? y.mod(z) : k ? round( y, POW_PRECISION, ROUNDING_MODE ) : y;
+        };
+
+
+        /*
+         * Return a string representing the value of this BigNumber rounded to sd significant digits
+         * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
+         * necessary to represent the integer part of the value in fixed-point notation, then use
+         * exponential notation.
+         *
+         * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
+         * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+         *
+         * 'toPrecision() precision not an integer: {sd}'
+         * 'toPrecision() precision out of range: {sd}'
+         * 'toPrecision() rounding mode not an integer: {rm}'
+         * 'toPrecision() rounding mode out of range: {rm}'
+         */
+        P.toPrecision = function ( sd, rm ) {
+            return format( this, sd != null && isValidInt( sd, 1, MAX, 24, 'precision' )
+              ? sd | 0 : null, rm, 24 );
+        };
+
+
+        /*
+         * Return a string representing the value of this BigNumber in base b, or base 10 if b is
+         * omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
+         * ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
+         * that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
+         * TO_EXP_NEG, return exponential notation.
+         *
+         * [b] {number} Integer, 2 to 64 inclusive.
+         *
+         * 'toString() base not an integer: {b}'
+         * 'toString() base out of range: {b}'
+         */
+        P.toString = function (b) {
+            var str,
+                n = this,
+                s = n.s,
+                e = n.e;
+
+            // Infinity or NaN?
+            if ( e === null ) {
+
+                if (s) {
+                    str = 'Infinity';
+                    if ( s < 0 ) str = '-' + str;
+                } else {
+                    str = 'NaN';
+                }
+            } else {
+                str = coeffToString( n.c );
+
+                if ( b == null || !isValidInt( b, 2, 64, 25, 'base' ) ) {
+                    str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+                      ? toExponential( str, e )
+                      : toFixedPoint( str, e );
+                } else {
+                    str = convertBase( toFixedPoint( str, e ), b | 0, 10, s );
+                }
+
+                if ( s < 0 && n.c[0] ) str = '-' + str;
+            }
+
+            return str;
+        };
+
+
+        /*
+         * Return a new BigNumber whose value is the value of this BigNumber truncated to a whole
+         * number.
+         */
+        P.truncated = P.trunc = function () {
+            return round( new BigNumber(this), this.e + 1, 1 );
+        };
+
+
+        /*
+         * Return as toString, but do not accept a base argument, and include the minus sign for
+         * negative zero.
+         */
+        P.valueOf = P.toJSON = function () {
+            var str,
+                n = this,
+                e = n.e;
+
+            if ( e === null ) return n.toString();
+
+            str = coeffToString( n.c );
+
+            str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+                ? toExponential( str, e )
+                : toFixedPoint( str, e );
+
+            return n.s < 0 ? '-' + str : str;
+        };
+
+
+        P.isBigNumber = true;
+
+        if ( config != null ) BigNumber.config(config);
+
+        return BigNumber;
+    }
+
+
+    // PRIVATE HELPER FUNCTIONS
+
+
+    function bitFloor(n) {
+        var i = n | 0;
+        return n > 0 || n === i ? i : i - 1;
+    }
+
+
+    // Return a coefficient array as a string of base 10 digits.
+    function coeffToString(a) {
+        var s, z,
+            i = 1,
+            j = a.length,
+            r = a[0] + '';
+
+        for ( ; i < j; ) {
+            s = a[i++] + '';
+            z = LOG_BASE - s.length;
+            for ( ; z--; s = '0' + s );
+            r += s;
+        }
+
+        // Determine trailing zeros.
+        for ( j = r.length; r.charCodeAt(--j) === 48; );
+        return r.slice( 0, j + 1 || 1 );
+    }
+
+
+    // Compare the value of BigNumbers x and y.
+    function compare( x, y ) {
+        var a, b,
+            xc = x.c,
+            yc = y.c,
+            i = x.s,
+            j = y.s,
+            k = x.e,
+            l = y.e;
+
+        // Either NaN?
+        if ( !i || !j ) return null;
+
+        a = xc && !xc[0];
+        b = yc && !yc[0];
+
+        // Either zero?
+        if ( a || b ) return a ? b ? 0 : -j : i;
+
+        // Signs differ?
+        if ( i != j ) return i;
+
+        a = i < 0;
+        b = k == l;
+
+        // Either Infinity?
+        if ( !xc || !yc ) return b ? 0 : !xc ^ a ? 1 : -1;
+
+        // Compare exponents.
+        if ( !b ) return k > l ^ a ? 1 : -1;
+
+        j = ( k = xc.length ) < ( l = yc.length ) ? k : l;
+
+        // Compare digit by digit.
+        for ( i = 0; i < j; i++ ) if ( xc[i] != yc[i] ) return xc[i] > yc[i] ^ a ? 1 : -1;
+
+        // Compare lengths.
+        return k == l ? 0 : k > l ^ a ? 1 : -1;
+    }
+
+
+    /*
+     * Return true if n is a valid number in range, otherwise false.
+     * Use for argument validation when ERRORS is false.
+     * Note: parseInt('1e+1') == 1 but parseFloat('1e+1') == 10.
+     */
+    function intValidatorNoErrors( n, min, max ) {
+        return ( n = truncate(n) ) >= min && n <= max;
+    }
+
+
+    function isArray(obj) {
+        return Object.prototype.toString.call(obj) == '[object Array]';
+    }
+
+
+    /*
+     * Convert string of baseIn to an array of numbers of baseOut.
+     * Eg. convertBase('255', 10, 16) returns [15, 15].
+     * Eg. convertBase('ff', 16, 10) returns [2, 5, 5].
+     */
+    function toBaseOut( str, baseIn, baseOut ) {
+        var j,
+            arr = [0],
+            arrL,
+            i = 0,
+            len = str.length;
+
+        for ( ; i < len; ) {
+            for ( arrL = arr.length; arrL--; arr[arrL] *= baseIn );
+            arr[ j = 0 ] += ALPHABET.indexOf( str.charAt( i++ ) );
+
+            for ( ; j < arr.length; j++ ) {
+
+                if ( arr[j] > baseOut - 1 ) {
+                    if ( arr[j + 1] == null ) arr[j + 1] = 0;
+                    arr[j + 1] += arr[j] / baseOut | 0;
+                    arr[j] %= baseOut;
+                }
+            }
+        }
+
+        return arr.reverse();
+    }
+
+
+    function toExponential( str, e ) {
+        return ( str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str ) +
+          ( e < 0 ? 'e' : 'e+' ) + e;
+    }
+
+
+    function toFixedPoint( str, e ) {
+        var len, z;
+
+        // Negative exponent?
+        if ( e < 0 ) {
+
+            // Prepend zeros.
+            for ( z = '0.'; ++e; z += '0' );
+            str = z + str;
+
+        // Positive exponent
+        } else {
+            len = str.length;
+
+            // Append zeros.
+            if ( ++e > len ) {
+                for ( z = '0', e -= len; --e; z += '0' );
+                str += z;
+            } else if ( e < len ) {
+                str = str.slice( 0, e ) + '.' + str.slice(e);
+            }
+        }
+
+        return str;
+    }
+
+
+    function truncate(n) {
+        n = parseFloat(n);
+        return n < 0 ? mathceil(n) : mathfloor(n);
+    }
+
+
+    // EXPORT
+
+
+    BigNumber = constructorFactory();
+    BigNumber['default'] = BigNumber.BigNumber = BigNumber;
+
+
+    // AMD.
+    if ( typeof define == 'function' && define.amd ) {
+        define( function () { return BigNumber; } );
+
+    // Node.js and other environments that support module.exports.
+    } else if ( typeof module != 'undefined' && module.exports ) {
+        module.exports = BigNumber;
+
+    // Browser.
+    } else {
+        if ( !globalObj ) globalObj = typeof self != 'undefined' ? self : Function('return this')();
+        globalObj.BigNumber = BigNumber;
+    }
+})(this);
+
+},{}],"web3":[function(require,module,exports){
 var Web3 = require('./lib/web3');
 
 // dont override global variable
diff --git a/lib/contracts/abi.js b/lib/contracts/abi.js
index 682b086e..55f184c2 100644
--- a/lib/contracts/abi.js
+++ b/lib/contracts/abi.js
@@ -19,8 +19,8 @@ class ABIGenerator {
     }
 
     result += "\nvar whenEnvIsLoaded = function(cb) {";
-    result += "\n  if (typeof window !== 'undefined' && window !== null) {";
-    result += "\n      window.addEventListener('load', cb);";
+    result += "\n  if (typeof document !== 'undefined' && document !== null) {";
+    result += "\n      document.addEventListener('DOMContentLoaded', cb);";
     result += "\n  } else {";
     result += "\n    cb();";
     result += "\n  }";
@@ -73,11 +73,13 @@ class ABIGenerator {
         let gasEstimates = JSON.stringify(contract.gasEstimates);
 
         // TODO: refactor this
-        result += "\nvar whenEnvIsLoaded = function(cb) {";
-        result += "\n  if (typeof window !== 'undefined' && window !== null) {";
-        result += "\n      window.addEventListener('load', cb);";
-        result += "\n  } else {";
-        result += "\n    cb();";
+        result += "\nif (whenEnvIsLoaded === undefined) {";
+        result += "\n  var whenEnvIsLoaded = function(cb) {";
+        result += "\n    if (typeof document !== 'undefined' && document !== null) {";
+        result += "\n        document.addEventListener('DOMContentLoaded', cb);";
+        result += "\n    } else {";
+        result += "\n      cb();";
+        result += "\n    }";
         result += "\n  }";
         result += "\n}";