Merge pull request #435 from zsfelfoldi/poc-9

Natspec + test

3 files changed, 3633 insertions, 0 deletions

diff --git a/ethutil/natspec/natspec.go b/ethutil/natspec/natspec.go
new file mode 100644
index 000000000..00e6f8720
--- /dev/null
+++ b/ethutil/natspec/natspec.go
@@ -0,0 +1,65 @@
+package natspec
+
+import (
+	"github.com/obscuren/otto"
+	"io/ioutil"
+)
+
+type NatSpec struct {
+	jsvm *otto.Otto
+}
+
+func NewNATSpec(transaction string) (self *NatSpec, err error) {
+
+	self = new(NatSpec)
+	self.jsvm = otto.New()
+	code, err := ioutil.ReadFile("natspec.js")
+	if err != nil {
+		return
+	}
+
+	_, err = self.jsvm.Run(string(code))
+	if err != nil {
+		return
+	}
+	_, err = self.jsvm.Run("var natspec = require('natspec');")
+	if err != nil {
+		return
+	}
+
+	self.jsvm.Run("var transaction = " + transaction + ";")
+
+	return
+}
+
+func (self *NatSpec) SetDescription(desc string) (err error) {
+
+	_, err = self.jsvm.Run("var expression = \"" + desc + "\";")
+	return
+
+}
+
+func (self *NatSpec) SetABI(abi string) (err error) {
+
+	_, err = self.jsvm.Run("var abi = " + abi + ";")
+	return
+
+}
+
+func (self *NatSpec) SetMethod(method string) (err error) {
+
+	_, err = self.jsvm.Run("var method = '" + method + "';")
+	return
+
+}
+
+func (self *NatSpec) Parse() string {
+
+	self.jsvm.Run("var call = {method: method,abi: abi,transaction: transaction};")
+	value, err := self.jsvm.Run("natspec.evaluateExpression(expression, call);")
+	if err != nil {
+		return err.Error()
+	}
+	return value.String()
+
+}
diff --git a/ethutil/natspec/natspec.js b/ethutil/natspec/natspec.js
new file mode 100644
index 000000000..419ccd5c9
--- /dev/null
+++ b/ethutil/natspec/natspec.js
@@ -0,0 +1,3517 @@
+require=(function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
+
+},{}],2:[function(require,module,exports){
+// shim for using process in browser
+
+var process = module.exports = {};
+var queue = [];
+var draining = false;
+
+function drainQueue() {
+    if (draining) {
+        return;
+    }
+    draining = true;
+    var currentQueue;
+    var len = queue.length;
+    while(len) {
+        currentQueue = queue;
+        queue = [];
+        var i = -1;
+        while (++i < len) {
+            currentQueue[i]();
+        }
+        len = queue.length;
+    }
+    draining = false;
+}
+process.nextTick = function (fun) {
+    queue.push(fun);
+    if (!draining) {
+        setTimeout(drainQueue, 0);
+    }
+};
+
+process.title = 'browser';
+process.browser = true;
+process.env = {};
+process.argv = [];
+process.version = ''; // empty string to avoid regexp issues
+
+function noop() {}
+
+process.on = noop;
+process.addListener = noop;
+process.once = noop;
+process.off = noop;
+process.removeListener = noop;
+process.removeAllListeners = noop;
+process.emit = noop;
+
+process.binding = function (name) {
+    throw new Error('process.binding is not supported');
+};
+
+// TODO(shtylman)
+process.cwd = function () { return '/' };
+process.chdir = function (dir) {
+    throw new Error('process.chdir is not supported');
+};
+process.umask = function() { return 0; };
+
+},{}],3:[function(require,module,exports){
+/*
+    This file is part of ethereum.js.
+
+    ethereum.js is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    ethereum.js is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with ethereum.js.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/** @file abi.js
+ * @authors:
+ *   Marek Kotewicz <marek@ethdev.com>
+ *   Gav Wood <g@ethdev.com>
+ * @date 2014
+ */
+
+var utils = require('./utils');
+var types = require('./types');
+var c = require('./const');
+var f = require('./formatters');
+
+var displayTypeError = function (type) {
+    console.error('parser does not support type: ' + type);
+};
+
+/// This method should be called if we want to check if givent type is an array type
+/// @returns true if it is, otherwise false
+var arrayType = function (type) {
+    return type.slice(-2) === '[]';
+};
+
+var dynamicTypeBytes = function (type, value) {
+    // TODO: decide what to do with array of strings
+    if (arrayType(type) || type === 'string')    // only string itself that is dynamic; stringX is static length.
+        return f.formatInputInt(value.length);
+    return "";
+};
+
+var inputTypes = types.inputTypes();
+
+/// Formats input params to bytes
+/// @param abi contract method inputs
+/// @param array of params that will be formatted to bytes
+/// @returns bytes representation of input params
+var formatInput = function (inputs, params) {
+    var bytes = "";
+    var toAppendConstant = "";
+    var toAppendArrayContent = "";
+
+    /// first we iterate in search for dynamic
+    inputs.forEach(function (input, index) {
+        bytes += dynamicTypeBytes(input.type, params[index]);
+    });
+
+    inputs.forEach(function (input, i) {
+        /*jshint maxcomplexity:5 */
+        var typeMatch = false;
+        for (var j = 0; j < inputTypes.length && !typeMatch; j++) {
+            typeMatch = inputTypes[j].type(inputs[i].type, params[i]);
+        }
+        if (!typeMatch) {
+            displayTypeError(inputs[i].type);
+        }
+
+        var formatter = inputTypes[j - 1].format;
+
+        if (arrayType(inputs[i].type))
+            toAppendArrayContent += params[i].reduce(function (acc, curr) {
+                return acc + formatter(curr);
+            }, "");
+        else if (inputs[i].type === 'string')
+            toAppendArrayContent += formatter(params[i]);
+        else
+            toAppendConstant += formatter(params[i]);
+    });
+
+    bytes += toAppendConstant + toAppendArrayContent;
+
+    return bytes;
+};
+
+var dynamicBytesLength = function (type) {
+    if (arrayType(type) || type === 'string')   // only string itself that is dynamic; stringX is static length.
+        return c.ETH_PADDING * 2;
+    return 0;
+};
+
+var outputTypes = types.outputTypes();
+
+/// Formats output bytes back to param list
+/// @param contract abi method outputs
+/// @param bytes representtion of output
+/// @returns array of output params
+var formatOutput = function (outs, output) {
+
+    output = output.slice(2);
+    var result = [];
+    var padding = c.ETH_PADDING * 2;
+
+    var dynamicPartLength = outs.reduce(function (acc, curr) {
+        return acc + dynamicBytesLength(curr.type);
+    }, 0);
+
+    var dynamicPart = output.slice(0, dynamicPartLength);
+    output = output.slice(dynamicPartLength);
+
+    outs.forEach(function (out, i) {
+        /*jshint maxcomplexity:6 */
+        var typeMatch = false;
+        for (var j = 0; j < outputTypes.length && !typeMatch; j++) {
+            typeMatch = outputTypes[j].type(outs[i].type);
+        }
+
+        if (!typeMatch) {
+            displayTypeError(outs[i].type);
+        }
+
+        var formatter = outputTypes[j - 1].format;
+        if (arrayType(outs[i].type)) {
+            var size = f.formatOutputUInt(dynamicPart.slice(0, padding));
+            dynamicPart = dynamicPart.slice(padding);
+            var array = [];
+            for (var k = 0; k < size; k++) {
+                array.push(formatter(output.slice(0, padding)));
+                output = output.slice(padding);
+            }
+            result.push(array);
+        }
+        else if (types.prefixedType('string')(outs[i].type)) {
+            dynamicPart = dynamicPart.slice(padding);
+            result.push(formatter(output.slice(0, padding)));
+            output = output.slice(padding);
+        } else {
+            result.push(formatter(output.slice(0, padding)));
+            output = output.slice(padding);
+        }
+    });
+
+    return result;
+};
+
+/// @param json abi for contract
+/// @returns input parser object for given json abi
+/// TODO: refactor creating the parser, do not double logic from contract
+var inputParser = function (json) {
+    var parser = {};
+    json.forEach(function (method) {
+        var displayName = utils.extractDisplayName(method.name);
+        var typeName = utils.extractTypeName(method.name);
+
+        var impl = function () {
+            var params = Array.prototype.slice.call(arguments);
+            return formatInput(method.inputs, params);
+        };
+
+        if (parser[displayName] === undefined) {
+            parser[displayName] = impl;
+        }
+
+        parser[displayName][typeName] = impl;
+    });
+
+    return parser;
+};
+
+/// @param json abi for contract
+/// @returns output parser for given json abi
+var outputParser = function (json) {
+    var parser = {};
+    json.forEach(function (method) {
+
+        var displayName = utils.extractDisplayName(method.name);
+        var typeName = utils.extractTypeName(method.name);
+
+        var impl = function (output) {
+            return formatOutput(method.outputs, output);
+        };
+
+        if (parser[displayName] === undefined) {
+            parser[displayName] = impl;
+        }
+
+        parser[displayName][typeName] = impl;
+    });
+
+    return parser;
+};
+
+module.exports = {
+    inputParser: inputParser,
+    outputParser: outputParser,
+    formatInput: formatInput,
+    formatOutput: formatOutput
+};
+
+},{"./const":4,"./formatters":5,"./types":6,"./utils":7}],4:[function(require,module,exports){
+(function (process){
+/*
+    This file is part of ethereum.js.
+
+    ethereum.js is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    ethereum.js is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with ethereum.js.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/** @file const.js
+ * @authors:
+ *   Marek Kotewicz <marek@ethdev.com>
+ * @date 2015
+ */
+
+/// required to define ETH_BIGNUMBER_ROUNDING_MODE
+if (process.env.NODE_ENV !== 'build') {
+    var BigNumber = require('bignumber.js'); // jshint ignore:line
+}
+
+var ETH_UNITS = [ 
+    'wei', 
+    'Kwei', 
+    'Mwei', 
+    'Gwei', 
+    'szabo', 
+    'finney', 
+    'ether', 
+    'grand', 
+    'Mether', 
+    'Gether', 
+    'Tether', 
+    'Pether', 
+    'Eether', 
+    'Zether', 
+    'Yether', 
+    'Nether', 
+    'Dether', 
+    'Vether', 
+    'Uether' 
+];
+
+module.exports = {
+    ETH_PADDING: 32,
+    ETH_SIGNATURE_LENGTH: 4,
+    ETH_UNITS: ETH_UNITS,
+    ETH_BIGNUMBER_ROUNDING_MODE: { ROUNDING_MODE: BigNumber.ROUND_DOWN },
+    ETH_POLLING_TIMEOUT: 1000
+};
+
+
+}).call(this,require('_process'))
+},{"_process":2,"bignumber.js":8}],5:[function(require,module,exports){
+(function (process){
+/*
+    This file is part of ethereum.js.
+
+    ethereum.js is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    ethereum.js is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with ethereum.js.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/** @file formatters.js
+ * @authors:
+ *   Marek Kotewicz <marek@ethdev.com>
+ * @date 2015
+ */
+
+if (process.env.NODE_ENV !== 'build') {
+    var BigNumber = require('bignumber.js'); // jshint ignore:line
+}
+
+var utils = require('./utils');
+var c = require('./const');
+
+/// @param string string to be padded
+/// @param number of characters that result string should have
+/// @param sign, by default 0
+/// @returns right aligned string
+var padLeft = function (string, chars, sign) {
+    return new Array(chars - string.length + 1).join(sign ? sign : "0") + string;
+};
+
+/// Formats input value to byte representation of int
+/// If value is negative, return it's two's complement
+/// If the value is floating point, round it down
+/// @returns right-aligned byte representation of int
+var formatInputInt = function (value) {
+    /*jshint maxcomplexity:7 */
+    var padding = c.ETH_PADDING * 2;
+    if (value instanceof BigNumber || typeof value === 'number') {
+        if (typeof value === 'number')
+            value = new BigNumber(value);
+        BigNumber.config(c.ETH_BIGNUMBER_ROUNDING_MODE);
+        value = value.round();
+
+        if (value.lessThan(0)) 
+            value = new BigNumber("ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", 16).plus(value).plus(1);
+        value = value.toString(16);
+    }
+    else if (value.indexOf('0x') === 0)
+        value = value.substr(2);
+    else if (typeof value === 'string')
+        value = formatInputInt(new BigNumber(value));
+    else
+        value = (+value).toString(16);
+    return padLeft(value, padding);
+};
+
+/// Formats input value to byte representation of string
+/// @returns left-algined byte representation of string
+var formatInputString = function (value) {
+    return utils.fromAscii(value, c.ETH_PADDING).substr(2);
+};
+
+/// Formats input value to byte representation of bool
+/// @returns right-aligned byte representation bool
+var formatInputBool = function (value) {
+    return '000000000000000000000000000000000000000000000000000000000000000' + (value ?  '1' : '0');
+};
+
+/// Formats input value to byte representation of real
+/// Values are multiplied by 2^m and encoded as integers
+/// @returns byte representation of real
+var formatInputReal = function (value) {
+    return formatInputInt(new BigNumber(value).times(new BigNumber(2).pow(128))); 
+};
+
+
+/// Check if input value is negative
+/// @param value is hex format
+/// @returns true if it is negative, otherwise false
+var signedIsNegative = function (value) {
+    return (new BigNumber(value.substr(0, 1), 16).toString(2).substr(0, 1)) === '1';
+};
+
+/// Formats input right-aligned input bytes to int
+/// @returns right-aligned input bytes formatted to int
+var formatOutputInt = function (value) {
+    value = value || "0";
+    // check if it's negative number
+    // it it is, return two's complement
+    if (signedIsNegative(value)) {
+        return new BigNumber(value, 16).minus(new BigNumber('ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff', 16)).minus(1);
+    }
+    return new BigNumber(value, 16);
+};
+
+/// Formats big right-aligned input bytes to uint
+/// @returns right-aligned input bytes formatted to uint
+var formatOutputUInt = function (value) {
+    value = value || "0";
+    return new BigNumber(value, 16);
+};
+
+/// @returns input bytes formatted to real
+var formatOutputReal = function (value) {
+    return formatOutputInt(value).dividedBy(new BigNumber(2).pow(128)); 
+};
+
+/// @returns input bytes formatted to ureal
+var formatOutputUReal = function (value) {
+    return formatOutputUInt(value).dividedBy(new BigNumber(2).pow(128)); 
+};
+
+/// @returns right-aligned input bytes formatted to hex
+var formatOutputHash = function (value) {
+    return "0x" + value;
+};
+
+/// @returns right-aligned input bytes formatted to bool
+var formatOutputBool = function (value) {
+    return value === '0000000000000000000000000000000000000000000000000000000000000001' ? true : false;
+};
+
+/// @returns left-aligned input bytes formatted to ascii string
+var formatOutputString = function (value) {
+    return utils.toAscii(value);
+};
+
+/// @returns right-aligned input bytes formatted to address
+var formatOutputAddress = function (value) {
+    return "0x" + value.slice(value.length - 40, value.length);
+};
+
+
+module.exports = {
+    formatInputInt: formatInputInt,
+    formatInputString: formatInputString,
+    formatInputBool: formatInputBool,
+    formatInputReal: formatInputReal,
+    formatOutputInt: formatOutputInt,
+    formatOutputUInt: formatOutputUInt,
+    formatOutputReal: formatOutputReal,
+    formatOutputUReal: formatOutputUReal,
+    formatOutputHash: formatOutputHash,
+    formatOutputBool: formatOutputBool,
+    formatOutputString: formatOutputString,
+    formatOutputAddress: formatOutputAddress
+};
+
+
+}).call(this,require('_process'))
+},{"./const":4,"./utils":7,"_process":2,"bignumber.js":8}],6:[function(require,module,exports){
+/*
+    This file is part of ethereum.js.
+
+    ethereum.js is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    ethereum.js is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with ethereum.js.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/** @file types.js
+ * @authors:
+ *   Marek Kotewicz <marek@ethdev.com>
+ * @date 2015
+ */
+
+var f = require('./formatters');
+
+/// @param expected type prefix (string)
+/// @returns function which checks if type has matching prefix. if yes, returns true, otherwise false
+var prefixedType = function (prefix) {
+    return function (type) {
+        return type.indexOf(prefix) === 0;
+    };
+};
+
+/// @param expected type name (string)
+/// @returns function which checks if type is matching expected one. if yes, returns true, otherwise false
+var namedType = function (name) {
+    return function (type) {
+        return name === type;
+    };
+};
+
+/// Setups input formatters for solidity types
+/// @returns an array of input formatters 
+var inputTypes = function () {
+    
+    return [
+        { type: prefixedType('uint'), format: f.formatInputInt },
+        { type: prefixedType('int'), format: f.formatInputInt },
+        { type: prefixedType('hash'), format: f.formatInputInt },
+        { type: prefixedType('string'), format: f.formatInputString }, 
+        { type: prefixedType('real'), format: f.formatInputReal },
+        { type: prefixedType('ureal'), format: f.formatInputReal },
+        { type: namedType('address'), format: f.formatInputInt },
+        { type: namedType('bool'), format: f.formatInputBool }
+    ];
+};
+
+/// Setups output formaters for solidity types
+/// @returns an array of output formatters
+var outputTypes = function () {
+
+    return [
+        { type: prefixedType('uint'), format: f.formatOutputUInt },
+        { type: prefixedType('int'), format: f.formatOutputInt },
+        { type: prefixedType('hash'), format: f.formatOutputHash },
+        { type: prefixedType('string'), format: f.formatOutputString },
+        { type: prefixedType('real'), format: f.formatOutputReal },
+        { type: prefixedType('ureal'), format: f.formatOutputUReal },
+        { type: namedType('address'), format: f.formatOutputAddress },
+        { type: namedType('bool'), format: f.formatOutputBool }
+    ];
+};
+
+module.exports = {
+    prefixedType: prefixedType,
+    namedType: namedType,
+    inputTypes: inputTypes,
+    outputTypes: outputTypes
+};
+
+
+},{"./formatters":5}],7:[function(require,module,exports){
+/*
+    This file is part of ethereum.js.
+
+    ethereum.js is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    ethereum.js is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with ethereum.js.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/** @file utils.js
+ * @authors:
+ *   Marek Kotewicz <marek@ethdev.com>
+ * @date 2015
+ */
+
+var c = require('./const');
+
+/// Finds first index of array element matching pattern
+/// @param array
+/// @param callback pattern
+/// @returns index of element
+var findIndex = function (array, callback) {
+    var end = false;
+    var i = 0;
+    for (; i < array.length && !end; i++) {
+        end = callback(array[i]);
+    }
+    return end ? i - 1 : -1;
+};
+
+/// @returns ascii string representation of hex value prefixed with 0x
+var toAscii = function(hex) {
+// Find termination
+    var str = "";
+    var i = 0, l = hex.length;
+    if (hex.substring(0, 2) === '0x') {
+        i = 2;
+    }
+    for (; i < l; i+=2) {
+        var code = parseInt(hex.substr(i, 2), 16);
+        if (code === 0) {
+            break;
+        }
+
+        str += String.fromCharCode(code);
+    }
+
+    return str;
+};
+    
+var toHex = function(str) {
+    var hex = "";
+    for(var i = 0; i < str.length; i++) {
+        var n = str.charCodeAt(i).toString(16);
+        hex += n.length < 2 ? '0' + n : n;
+    }
+
+    return hex;
+};
+
+/// @returns hex representation (prefixed by 0x) of ascii string
+var fromAscii = function(str, pad) {
+    pad = pad === undefined ? 0 : pad;
+    var hex = toHex(str);
+    while (hex.length < pad*2)
+        hex += "00";
+    return "0x" + hex;
+};
+
+/// @returns display name for function/event eg. multiply(uint256) -> multiply
+var extractDisplayName = function (name) {
+    var length = name.indexOf('('); 
+    return length !== -1 ? name.substr(0, length) : name;
+};
+
+/// @returns overloaded part of function/event name
+var extractTypeName = function (name) {
+    /// TODO: make it invulnerable
+    var length = name.indexOf('(');
+    return length !== -1 ? name.substr(length + 1, name.length - 1 - (length + 1)).replace(' ', '') : "";
+};
+
+/// Filters all function from input abi
+/// @returns abi array with filtered objects of type 'function'
+var filterFunctions = function (json) {
+    return json.filter(function (current) {
+        return current.type === 'function'; 
+    }); 
+};
+
+/// Filters all events form input abi
+/// @returns abi array with filtered objects of type 'event'
+var filterEvents = function (json) {
+    return json.filter(function (current) {
+        return current.type === 'event';
+    });
+};
+
+/// used to transform value/string to eth string
+/// TODO: use BigNumber.js to parse int
+/// TODO: add tests for it!
+var toEth = function (str) {
+     /*jshint maxcomplexity:7 */
+    var val = typeof str === "string" ? str.indexOf('0x') === 0 ? parseInt(str.substr(2), 16) : parseInt(str) : str;
+    var unit = 0;
+    var units = c.ETH_UNITS;
+    while (val > 3000 && unit < units.length - 1)
+    {
+        val /= 1000;
+        unit++;
+    }
+    var s = val.toString().length < val.toFixed(2).length ? val.toString() : val.toFixed(2);
+    var replaceFunction = function($0, $1, $2) {
+        return $1 + ',' + $2;
+    };
+
+    while (true) {
+        var o = s;
+        s = s.replace(/(\d)(\d\d\d[\.\,])/, replaceFunction);
+        if (o === s)
+            break;
+    }
+    return s + ' ' + units[unit];
+};
+
+module.exports = {
+    findIndex: findIndex,
+    toAscii: toAscii,
+    fromAscii: fromAscii,
+    extractDisplayName: extractDisplayName,
+    extractTypeName: extractTypeName,
+    filterFunctions: filterFunctions,
+    filterEvents: filterEvents,
+    toEth: toEth
+};
+
+
+},{"./const":4}],8:[function(require,module,exports){
+/*! bignumber.js v2.0.3 https://github.com/MikeMcl/bignumber.js/LICENCE */
+
+;(function (global) {
+    'use strict';
+
+    /*
+      bignumber.js v2.0.3
+      A JavaScript library for arbitrary-precision arithmetic.
+      https://github.com/MikeMcl/bignumber.js
+      Copyright (c) 2015 Michael Mclaughlin <M8ch88l@gmail.com>
+      MIT Expat Licence
+    */
+
+
+    var BigNumber, crypto, parseNumeric,
+        isNumeric = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/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 ) );
+
+                    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++;
+
+                    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 ) {
+                                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.
+                                cmp = compare( prod, rem, prodL, remL );
+
+                                // product > remainder.
+                                if ( cmp == 1 ) {
+                                    n--;
+
+                                    // Subtract divisor from product.
+                                    subtract( prod, yL < prodL ? yz : yc, prodL, base );
+                                }
+                            } else {
+
+                                // 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, compare yc and rem again below.
+                                if ( n == 0 ) cmp = n = 1;
+                                prod = yc.slice();
+                            }
+
+                            prodL = prod.length;
+                            if ( prodL < remL ) prod.unshift(0);
+
+                            // Subtract product from remainder.
+                            subtract( rem, prod, remL, base );
+
+                            // If product was < previous remainder.
+                            if ( cmp == -1 ) {
+                                remL = rem.length;
+
+                                // Compare divisor and new remainder.
+                                cmp = compare( yc, rem, yL, remL );
+
+                                // If divisor < new remainder, subtract divisor from remainder.
+                                if ( cmp < 1 ) {
+                                    n++;
+
+                                    // Subtract divisor from remainder.
+                                    subtract( rem, yL < remL ? yz : yc, remL, base );
+                                }
+                            }
+                            remL = rem.length;
+                        } else if ( cmp === 0 ) {
+                            n++;
+                            rem = [0];
+                        }
+                        // if cmp === 1, n will be 0
+
+                        // Add the next digit, n, to the result array.
+                        qc[i++] = n;
+
+                        // Update the remainder.
+                        if ( cmp && 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])(?=\w[\w.]*$)/i,
+            var basePrefix = /^(-?)0([xbo])/i,
+                dotAfter = /^([^.]+)\.$/,
+                dotBefore = /^\.([^.]+)$/,
+                isInfinityOrNaN = /^-?(Infinity|NaN)$/,
+//                whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
+                whitespaceOrPlus = /^\s*\+[\w.]|^\s+|\s+$/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[ 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":1}],"natspec":[function(require,module,exports){
+/*
+    This file is part of natspec.js.
+
+    natspec.js is free software: you can redistribute it and/or modify
+    it under the terms of the GNU Lesser General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    natspec.js is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public License
+    along with natspec.js.  If not, see <http://www.gnu.org/licenses/>.
+*/
+/** @file natspec.js
+ * @authors:
+ *   Marek Kotewicz <marek@ethdev.com>
+ * @date 2015
+ */
+
+var abi = require('./node_modules/ethereum.js/lib/abi.js'); 
+
+/**
+ * This object should be used to evaluate natspec expression
+ * It has one method evaluateExpression which shoul be used
+ */
+var natspec = (function () {
+    /// Helper method
+    /// Should be called to copy values from object to global context
+    var copyToContext = function (obj, context) {
+        Object.keys(obj).forEach(function (key) {
+            context[key] = obj[key];
+        });
+    }
+    
+    /// generate codes, which will be evaluated
+    var generateCode = function (obj) {
+        return Object.keys(obj).reduce(function (acc, key) {
+            return acc + "var " + key + " = context['" + key + "'];\n";
+        }, "");
+    };
+
+    /// Helper method
+    /// Should be called to get method with given name from the abi
+    /// @param contract's abi
+    /// @param name of the method that we are looking for
+    var getMethodWithName = function(abi, name) {
+        return abi.filter(function (method) {
+            return method.name === name;
+        })[0];
+    };
+
+    /// Function called to get all contract method input variables
+    /// @returns hashmap with all contract's method input variables
+    var getMethodInputParams = function (method, transaction) {
+        // do it with output formatter (cause we have to decode)
+        var params = abi.formatOutput(method.inputs, '0x' + transaction.params[0].data.slice(10)); 
+
+        return method.inputs.reduce(function (acc, current, index) {
+            acc[current.name] = params[index];
+            return acc;
+        }, {});
+    };
+    
+    /// Should be called to evaluate expression
+    var mapExpressionsToEvaluate = function (expression, cb) {
+        var evaluatedExpression = "";
+
+        // match everything in `` quotes
+        var pattern = /\`(?:\\.|[^`\\])*\`/gim
+        var match;
+        var lastIndex = 0;
+        while ((match = pattern.exec(expression)) !== null) {
+            var startIndex = pattern.lastIndex - match[0].length;
+            var toEval = match[0].slice(1, match[0].length - 1);
+            evaluatedExpression += expression.slice(lastIndex, startIndex);
+            var evaluatedPart = cb(toEval);
+            evaluatedExpression += evaluatedPart;
+            lastIndex = pattern.lastIndex;
+        }
+        
+        evaluatedExpression += expression.slice(lastIndex);
+    
+        return evaluatedExpression;
+    };
+
+    /// Should be called to evaluate single expression
+    /// Is internally using javascript's 'eval' method
+    /// @param expression which should be evaluated
+    /// @param [call] object containing contract abi, transaction, called method
+    /// TODO: separate evaluation from getting input params, so as not to spoil 'evaluateExpression' function
+    var evaluateExpression = function (expression, call) {
+        //var self = this;
+        var context = {};
+        
+        if (!!call) {
+            try {
+                var method = getMethodWithName(call.abi, call.method);
+                var params = getMethodInputParams(method, call.transaction); 
+                copyToContext(params, context);
+            }
+            catch (err) {
+                return "Natspec evaluation failed, wrong input params";
+            }
+        }
+
+        var code = generateCode(context);
+
+        var evaluatedExpression = mapExpressionsToEvaluate(expression, function (toEval) {
+            try {
+                var fn = new Function("context", code + "return " + toEval + ";");
+                return fn(context).toString();
+            }
+            catch (err) {
+                return 'undefined'; 
+            }
+        });
+
+        return evaluatedExpression;
+    };
+
+    return {
+        evaluateExpression: evaluateExpression
+    };
+
+})();
+
+module.exports = natspec; 
+
+
+},{"./node_modules/ethereum.js/lib/abi.js":3}]},{},[]);
diff --git a/ethutil/natspec/natspec_test.go b/ethutil/natspec/natspec_test.go
new file mode 100644
index 000000000..48a9cb25c
--- /dev/null
+++ b/ethutil/natspec/natspec_test.go
@@ -0,0 +1,51 @@
+package natspec
+
+import (
+	"testing"
+)
+
+func TestNotice(t *testing.T) {
+
+	ns, err := NewNATSpec(`
+	{
+            "jsonrpc": "2.0",
+            "method": "eth_call",
+            "params": [{
+                "to": "0x8521742d3f456bd237e312d6e30724960f72517a",
+                "data": "0xc6888fa1000000000000000000000000000000000000000000000000000000000000007a"
+            }],
+            "id": 6
+        }
+	`)
+
+	if err != nil {
+		t.Errorf("NewNATSpec error %v", err)
+	}
+
+	ns.SetABI(`
+	[{
+            "name": "multiply",
+            "constant": false,
+            "type": "function",
+            "inputs": [{
+                "name": "a",
+                "type": "uint256"
+            }],
+            "outputs": [{
+                "name": "d",
+                "type": "uint256"
+            }]
+        }]
+	`)
+	ns.SetDescription("Will multiply `a` by 7 and return `a * 7`.")
+	ns.SetMethod("multiply")
+
+	notice := ns.Parse()
+
+	expected := "Will multiply 122 by 7 and return 854."
+	if notice != expected {
+		t.Errorf("incorrect notice. expected %v, got %v", expected, notice)
+	} else {
+		t.Logf("returned notice \"%v\"", notice)
+	}
+}