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.
+*/
+/** @file abi.js
+ * @authors:
+ * Marek Kotewicz
+ * Gav Wood
+ * @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 .
+*/
+/** @file const.js
+ * @authors:
+ * Marek Kotewicz
+ * @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 .
+*/
+/** @file formatters.js
+ * @authors:
+ * Marek Kotewicz
+ * @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 .
+*/
+/** @file types.js
+ * @authors:
+ * Marek Kotewicz
+ * @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 .
+*/
+/** @file utils.js
+ * @authors:
+ * Marek Kotewicz
+ * @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 + ',' + $2;
+ };
+
+ while (true) {
+ var o = s;
+ s = s.replace(/(\d)(\d\d\d[\.\,])/, replaceFunction);
+ if (o === s)
+ break;
+ }
+ return s + ' ' + units[unit];
+};
+
+module.exports = {
+ findIndex: findIndex,
+ toAscii: toAscii,
+ fromAscii: fromAscii,
+ extractDisplayName: extractDisplayName,
+ extractTypeName: extractTypeName,
+ filterFunctions: filterFunctions,
+ filterEvents: filterEvents,
+ toEth: toEth
+};
+
+
+},{"./const":4}],8:[function(require,module,exports){
+/*! bignumber.js v2.0.3 https://github.com/MikeMcl/bignumber.js/LICENCE */
+
+;(function (global) {
+ 'use strict';
+
+ /*
+ bignumber.js v2.0.3
+ A JavaScript library for arbitrary-precision arithmetic.
+ https://github.com/MikeMcl/bignumber.js
+ Copyright (c) 2015 Michael Mclaughlin
+ MIT Expat Licence
+ */
+
+
+ var BigNumber, crypto, parseNumeric,
+ isNumeric = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/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 .
+*/
+/** @file natspec.js
+ * @authors:
+ * Marek Kotewicz
+ * @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)
+ }
+}