/*!
Copyright © 2006-2007 Kevin C. Olbrich
Copyright © 2010-2013 LIM SAS (http://lim.eu) - Julien Sanchez

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
/*jshint eqeqeq:true, immed:true, undef:true */
/*global module:false, define:false */
(function (root, factory) {
    if (typeof exports === 'object') {
        // Node. Does not work with strict CommonJS, but
        // only CommonJS-like enviroments that support module.exports,
        // like Node.
        module.exports = factory();
    } else if (typeof define === 'function' && define.amd) {
        // AMD. Register as an anonymous module.
        define(factory);
    } else {
        // Browser globals
        root.Qty = factory();
    }
}(this, function() {
  var UNITS = {
    /* prefixes */
    "<googol>" : [["googol"], 1e100, "prefix"],
    "<kibi>"  :  [["Ki","Kibi","kibi"], Math.pow(2,10), "prefix"],
    "<mebi>"  :  [["Mi","Mebi","mebi"], Math.pow(2,20), "prefix"],
    "<gibi>"  :  [["Gi","Gibi","gibi"], Math.pow(2,30), "prefix"],
    "<tebi>"  :  [["Ti","Tebi","tebi"], Math.pow(2,40), "prefix"],
    "<pebi>"  :  [["Pi","Pebi","pebi"], Math.pow(2,50), "prefix"],
    "<exi>"   :  [["Ei","Exi","exi"], Math.pow(2,60), "prefix"],
    "<zebi>"  :  [["Zi","Zebi","zebi"], Math.pow(2,70), "prefix"],
    "<yebi>"  :  [["Yi","Yebi","yebi"], Math.pow(2,80), "prefix"],
    "<yotta>" :  [["Y","Yotta","yotta"], 1e24, "prefix"],
    "<zetta>" :  [["Z","Zetta","zetta"], 1e21, "prefix"],
    "<exa>"   :  [["E","Exa","exa"], 1e18, "prefix"],
    "<peta>"  :  [["P","Peta","peta"], 1e15, "prefix"],
    "<tera>"  :  [["T","Tera","tera"], 1e12, "prefix"],
    "<giga>"  :  [["G","Giga","giga"], 1e9, "prefix"],
    "<mega>"  :  [["M","Mega","mega"], 1e6, "prefix"],
    "<kilo>"  :  [["k","kilo"], 1e3, "prefix"],
    "<hecto>" :  [["h","Hecto","hecto"], 1e2, "prefix"],
    "<deca>"  :  [["da","Deca","deca","deka"], 1e1, "prefix"],
    "<deci>"  :  [["d","Deci","deci"], 1e-1, "prefix"],
    "<centi>"  : [["c","Centi","centi"], 1e-2, "prefix"],
    "<milli>" :  [["m","Milli","milli"], 1e-3, "prefix"],
    "<micro>"  : [["u","Micro","micro"], 1e-6, "prefix"],
    "<nano>"  :  [["n","Nano","nano"], 1e-9, "prefix"],
    "<pico>"  :  [["p","Pico","pico"], 1e-12, "prefix"],
    "<femto>" :  [["f","Femto","femto"], 1e-15, "prefix"],
    "<atto>"  :  [["a","Atto","atto"], 1e-18, "prefix"],
    "<zepto>" :  [["z","Zepto","zepto"], 1e-21, "prefix"],
    "<yocto>" :  [["y","Yocto","yocto"], 1e-24, "prefix"],

    "<1>"     :  [["1", "<1>"], 1, ""],
    /* length units */
    "<meter>" :  [["m","meter","meters","metre","metres"], 1.0, "length", ["<meter>"] ],
    "<inch>"  :  [["in","inch","inches","\""], 0.0254, "length", ["<meter>"]],
    "<foot>"  :  [["ft","foot","feet","'"], 0.3048, "length", ["<meter>"]],
    "<yard>"  :  [["yd","yard","yards"], 0.9144, "length", ["<meter>"]],
    "<mile>"  :  [["mi","mile","miles"], 1609.344, "length", ["<meter>"]],
    "<naut-mile>" : [["nmi"], 1852, "length", ["<meter>"]],
    "<league>":  [["league","leagues"], 4828, "length", ["<meter>"]],
    "<furlong>": [["furlong","furlongs"], 201.2, "length", ["<meter>"]],
    "<rod>"   :  [["rd","rod","rods"], 5.029, "length", ["<meter>"]],
    "<mil>"   :  [["mil","mils"], 0.0000254, "length", ["<meter>"]],
    "<angstrom>"  :[["ang","angstrom","angstroms"], 1e-10, "length", ["<meter>"]],
    "<fathom>" : [["fathom","fathoms"], 1.829, "length", ["<meter>"]],
    "<pica>"  : [["pica","picas"], 0.004217, "length", ["<meter>"]],
    "<point>" : [["pt","point","points"], 0.0003514, "length", ["<meter>"]],
    "<redshift>" : [["z","red-shift"], 1.302773e26, "length", ["<meter>"]],
    "<AU>"    : [["AU","astronomical-unit"], 149597900000, "length", ["<meter>"]],
    "<light-second>":[["ls","light-second"], 299792500, "length", ["<meter>"]],
    "<light-minute>":[["lmin","light-minute"], 17987550000, "length", ["<meter>"]],
    "<light-year>" : [["ly","light-year"], 9460528000000000, "length", ["<meter>"]],
    "<parsec>"  : [["pc","parsec","parsecs"], 30856780000000000, "length", ["<meter>"]],

    /* mass */
    "<kilogram>" : [["kg","kilogram","kilograms"], 1.0, "mass", ["<kilogram>"]],
    "<AMU>" : [["u","AMU","amu"], 6.0221415e26, "mass", ["<kilogram>"]],
    "<dalton>" : [["Da","Dalton","Daltons","dalton","daltons"], 6.0221415e26, "mass", ["<kilogram>"]],
    "<slug>" : [["slug","slugs"], 14.5939029, "mass", ["<kilogram>"]],
    "<short-ton>" : [["tn","ton"], 907.18474, "mass", ["<kilogram>"]],
    "<metric-ton>":[["tonne"], 1000, "mass", ["<kilogram>"]],
    "<carat>" : [["ct","carat","carats"], 0.0002, "mass", ["<kilogram>"]],
    "<pound>" : [["lbs","lb","pound","pounds","#"], 0.45359237, "mass", ["<kilogram>"]],
    "<ounce>" : [["oz","ounce","ounces"], 0.0283495231, "mass", ["<kilogram>"]],
    "<gram>"    :  [["g","gram","grams","gramme","grammes"], 1e-3, "mass", ["<kilogram>"]],
    "<grain>" : [["grain","grains","gr"], 6.479891e-5, "mass", ["<kilogram>"]],
    "<dram>"  : [["dram","drams","dr"], 0.0017718452, "mass",["<kilogram>"]],
    "<stone>" : [["stone","stones","st"],6.35029318, "mass",["<kilogram>"]],

    /* area */
    "<hectare>":[["hectare"], 10000, "area", ["<meter>","<meter>"]],
    "<acre>":[["acre","acres"], 4046.85642, "area", ["<meter>","<meter>"]],
    "<sqft>":[["sqft"], 1, "area", ["<feet>","<feet>"]],

    /* volume */
    "<liter>" : [["l","L","liter","liters","litre","litres"], 0.001, "volume", ["<meter>","<meter>","<meter>"]],
    "<gallon>":  [["gal","gallon","gallons"], 0.0037854118, "volume", ["<meter>","<meter>","<meter>"]],
    "<quart>":  [["qt","quart","quarts"], 0.00094635295, "volume", ["<meter>","<meter>","<meter>"]],
    "<pint>":  [["pt","pint","pints"], 0.000473176475, "volume", ["<meter>","<meter>","<meter>"]],
    "<cup>":  [["cu","cup","cups"], 0.000236588238, "volume", ["<meter>","<meter>","<meter>"]],
    "<fluid-ounce>":  [["floz","fluid-ounce"], 2.95735297e-5, "volume", ["<meter>","<meter>","<meter>"]],
    "<tablespoon>":  [["tbs","tablespoon","tablespoons"], 1.47867648e-5, "volume", ["<meter>","<meter>","<meter>"]],
    "<teaspoon>":  [["tsp","teaspoon","teaspoons"], 4.92892161e-6, "volume", ["<meter>","<meter>","<meter>"]],

    /* speed */
    "<kph>" : [["kph"], 0.277777778, "speed", ["<meter>"], ["<second>"]],
    "<mph>" : [["mph"], 0.44704, "speed", ["<meter>"], ["<second>"]],
    "<knot>" : [["kt","kn","kts","knot","knots"], 0.514444444, "speed", ["<meter>"], ["<second>"]],
    "<fps>"  : [["fps"], 0.3048, "speed", ["<meter>"], ["<second>"]],

    /* acceleration */
    "<gee>" : [["gee"], 9.80665, "acceleration", ["<meter>"], ["<second>","<second>"]],

    /* temperature_difference */
    "<kelvin>" : [["degK","kelvin"], 1.0, "temperature", ["<kelvin>"]],
    "<celsius>" : [["degC","celsius","celsius","centigrade"], 1.0, "temperature", ["<kelvin>"]],
    "<fahrenheit>" : [["degF","fahrenheit"], 5/9, "temperature", ["<kelvin>"]],
    "<rankine>" : [["degR","rankine"], 5/9, "temperature", ["<kelvin>"]],
    "<temp-K>"  : [["tempK"], 1.0, "temperature", ["<temp-K>"]],
    "<temp-C>"  : [["tempC"], 1.0, "temperature", ["<temp-K>"]],
    "<temp-F>"  : [["tempF"], 5/9, "temperature", ["<temp-K>"]],
    "<temp-R>"  : [["tempR"], 5/9, "temperature", ["<temp-K>"]],

    /* time */
    "<second>":  [["s","sec","second","seconds"], 1.0, "time", ["<second>"]],
    "<minute>":  [["min","minute","minutes"], 60.0, "time", ["<second>"]],
    "<hour>":  [["h","hr","hrs","hour","hours"], 3600.0, "time", ["<second>"]],
    "<day>":  [["d","day","days"], 3600*24, "time", ["<second>"]],
    "<week>":  [["wk","week","weeks"], 7*3600*24, "time", ["<second>"]],
    "<fortnight>": [["fortnight","fortnights"], 1209600, "time", ["<second>"]],
    "<year>":  [["y","yr","year","years","annum"], 31556926, "time", ["<second>"]],
    "<decade>":[["decade","decades"], 315569260, "time", ["<second>"]],
    "<century>":[["century","centuries"], 3155692600, "time", ["<second>"]],

    /* pressure */
    "<pascal>" : [["Pa","pascal","Pascal"], 1.0, "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
    "<bar>" : [["bar","bars"], 100000, "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
    "<mmHg>" : [["mmHg"], 133.322368, "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
    "<inHg>" : [["inHg"], 3386.3881472, "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
    "<torr>" : [["torr"], 133.322368, "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
    "<atm>" : [["atm","ATM","atmosphere","atmospheres"], 101325, "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
    "<psi>" : [["psi"], 6894.76, "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
    "<cmh2o>" : [["cmH2O"], 98.0638, "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
    "<inh2o>" : [["inH2O"], 249.082052, "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],

    /* viscosity */
    "<poise>"  : [["P","poise"], 0.1, "viscosity", ["<kilogram>"],["<meter>","<second>"] ],
    "<stokes>" : [["St","stokes"], 1e-4, "viscosity", ["<meter>","<meter>"], ["<second>"]],

    /* substance */
    "<mole>"  :  [["mol","mole"], 1.0, "substance", ["<mole>"]],

    /* concentration */
    "<molar>" : [["M","molar"], 1000, "concentration", ["<mole>"], ["<meter>","<meter>","<meter>"]],
    "<wtpercent>"  : [["wt%","wtpercent"], 10, "concentration", ["<kilogram>"], ["<meter>","<meter>","<meter>"]],

    /* activity */
    "<katal>" :  [["kat","katal","Katal"], 1.0, "activity", ["<mole>"], ["<second>"]],
    "<unit>"  :  [["U","enzUnit"], 16.667e-16, "activity", ["<mole>"], ["<second>"]],

    /* capacitance */
    "<farad>" :  [["F","farad","Farad"], 1.0, "capacitance", ["<farad>"]],

    /* charge */
    "<coulomb>" :  [["C","coulomb","Coulomb"], 1.0, "charge", ["<ampere>","<second>"]],

    /* current */
    "<ampere>"  :  [["A","Ampere","ampere","amp","amps"], 1.0, "current", ["<ampere>"]],

    /* conductance */
    "<siemens>" : [["S","Siemens","siemens"], 1.0, "conductance", ["<second>","<second>","<second>","<ampere>","<ampere>"], ["<kilogram>","<meter>","<meter>"]],

    /* inductance */
    "<henry>" :  [["H","Henry","henry"], 1.0, "inductance", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>","<ampere>","<ampere>"]],

    /* potential */
    "<volt>"  :  [["V","Volt","volt","volts"], 1.0, "potential", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>","<second>","<ampere>"]],

    /* resistance */
    "<ohm>" :  [["Ohm","ohm"], 1.0, "resistance", ["<meter>","<meter>","<kilogram>"],["<second>","<second>","<second>","<ampere>","<ampere>"]],

    /* magnetism */
    "<weber>" : [["Wb","weber","webers"], 1.0, "magnetism", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>","<ampere>"]],
    "<tesla>"  : [["T","tesla","teslas"], 1.0, "magnetism", ["<kilogram>"], ["<second>","<second>","<ampere>"]],
    "<gauss>" : [["G","gauss"], 1e-4, "magnetism",  ["<kilogram>"], ["<second>","<second>","<ampere>"]],
    "<maxwell>" : [["Mx","maxwell","maxwells"], 1e-8, "magnetism", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>","<ampere>"]],
    "<oersted>"  : [["Oe","oersted","oersteds"], 250.0/Math.PI, "magnetism", ["<ampere>"], ["<meter>"]],

    /* energy */
    "<joule>" :  [["J","joule","Joule","joules"], 1.0, "energy", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],
    "<erg>"   :  [["erg","ergs"], 1e-7, "energy", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],
    "<btu>"   :  [["BTU","btu","BTUs"], 1055.056, "energy", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],
    "<calorie>" :  [["cal","calorie","calories"], 4.18400, "energy",["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],
    "<Calorie>" :  [["Cal","Calorie","Calories"], 4184.00, "energy",["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],
    "<therm-US>" : [["th","therm","therms","Therm"], 105480400, "energy",["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],

    /* force */
    "<newton>"  : [["N","Newton","newton"], 1.0, "force", ["<kilogram>","<meter>"], ["<second>","<second>"]],
    "<dyne>"  : [["dyn","dyne"], 1e-5, "force", ["<kilogram>","<meter>"], ["<second>","<second>"]],
    "<pound-force>"  : [["lbf","pound-force"], 4.448222, "force", ["<kilogram>","<meter>"], ["<second>","<second>"]],

    /* frequency */
    "<hertz>" : [["Hz","hertz","Hertz"], 1.0, "frequency", ["<1>"], ["<second>"]],

    /* angle */
    "<radian>" :[["rad","radian","radian"], 1.0, "angle", ["<radian>"]],
    "<degree>" :[["deg","degree","degrees"], Math.PI / 180.0, "angle", ["<radian>"]],
    "<grad>"   :[["grad","gradian","grads"], Math.PI / 200.0, "angle", ["<radian>"]],
    "<steradian>"  : [["sr","steradian","steradians"], 1.0, "solid_angle", ["<steradian>"]],

    /* rotation */
    "<rotation>" : [["rotation"], 2.0*Math.PI, "angle", ["<radian>"]],
    "<rpm>"   :[["rpm"], 2.0*Math.PI / 60.0, "angular_velocity", ["<radian>"], ["<second>"]],

    /* memory */
    "<byte>"  :[["B","byte"], 1.0, "memory", ["<byte>"]],
    "<bit>"  :[["b","bit"], 0.125, "memory", ["<byte>"]],

    /* currency */
    "<dollar>":[["USD","dollar"], 1.0, "currency", ["<dollar>"]],
    "<cents>" :[["cents"], 0.01, "currency", ["<dollar>"]],

    /* luminosity */
    "<candela>" : [["cd","candela"], 1.0, "luminosity", ["<candela>"]],
    "<lumen>" : [["lm","lumen"], 1.0, "luminous_power", ["<candela>","<steradian>"]],
    "<lux>" :[["lux"], 1.0, "illuminance", ["<candela>","<steradian>"], ["<meter>","<meter>"]],

    /* power */
    "<watt>"  : [["W","watt","watts"], 1.0, "power", ["<kilogram>","<meter>","<meter>"], ["<second>","<second>","<second>"]],
    "<horsepower>"  :  [["hp","horsepower"], 745.699872, "power", ["<kilogram>","<meter>","<meter>"], ["<second>","<second>","<second>"]],

    /* radiation */
    "<gray>" : [["Gy","gray","grays"], 1.0, "radiation", ["<meter>","<meter>"], ["<second>","<second>"]],
    "<roentgen>" : [["R","roentgen"], 0.009330, "radiation", ["<meter>","<meter>"], ["<second>","<second>"]],
    "<sievert>" : [["Sv","sievert","sieverts"], 1.0, "radiation", ["<meter>","<meter>"], ["<second>","<second>"]],
    "<becquerel>" : [["Bq","bequerel","bequerels"], 1.0, "radiation", ["<1>"],["<second>"]],
    "<curie>" : [["Ci","curie","curies"], 3.7e10, "radiation", ["<1>"],["<second>"]],

    /* rate */
    "<cpm>" : [["cpm"], 1.0/60.0, "rate", ["<count>"],["<second>"]],
    "<dpm>" : [["dpm"], 1.0/60.0, "rate", ["<count>"],["<second>"]],
    "<bpm>" : [["bpm"], 1.0/60.0, "rate", ["<count>"],["<second>"]],

    /* resolution / typography */
    "<dot>" : [["dot","dots"], 1, "resolution", ["<each>"]],
    "<pixel>" : [["pixel","px"], 1, "resolution", ["<each>"]],
    "<ppi>" : [["ppi"], 1, "resolution", ["<pixel>"], ["<inch>"]],
    "<dpi>" : [["dpi"], 1, "typography", ["<dot>"], ["<inch>"]],

    /* other */
    "<cell>" : [["cells","cell"], 1, "counting", ["<each>"]],
    "<each>" : [["each"], 1.0, "counting", ["<each>"]],
    "<count>" : [["count"], 1.0, "counting", ["<each>"]],
    "<base-pair>"  : [["bp"], 1.0, "counting", ["<each>"]],
    "<nucleotide>" : [["nt"], 1.0, "counting", ["<each>"]],
    "<molecule>" : [["molecule","molecules"], 1.0, "counting", ["<1>"]],
    "<dozen>" :  [["doz","dz","dozen"],12.0,"prefix_only", ["<each>"]],
    "<percent>": [["%","percent"], 0.01, "prefix_only", ["<1>"]],
    "<ppm>" :  [["ppm"],1e-6, "prefix_only", ["<1>"]],
    "<ppt>" :  [["ppt"],1e-9, "prefix_only", ["<1>"]],
    "<gross>" :  [["gr","gross"],144.0, "prefix_only", ["<dozen>","<dozen>"]],
    "<decibel>"  : [["dB","decibel","decibels"], 1.0, "logarithmic", ["<decibel>"]]
  };


  var BASE_UNITS = ['<meter>','<kilogram>','<second>','<mole>', '<farad>', '<ampere>','<radian>','<kelvin>','<temp-K>','<byte>','<dollar>','<candela>','<each>','<steradian>','<decibel>'];
  var UNITY = '<1>';
  var UNITY_ARRAY= [UNITY];
  var SCI_NUMBER = "([+-]?\\d*(?:\\.\\d+)?(?:[Ee][+-]?\\d+)?)";
  var SCI_NUMBER_REGEX = new RegExp(SCI_NUMBER);
  var QTY_STRING = SCI_NUMBER + "\\s*([^/]*)(?:\/(.+))?";
  var QTY_STRING_REGEX = new RegExp("^" + QTY_STRING + "$");
  var POWER_OP = "\\^|\\*{2}";
  var TOP_REGEX = new RegExp ("([^ \\*]+?)(?:" + POWER_OP + ")?(-?\\d+)");
  var BOTTOM_REGEX = new RegExp("([^ \\*]+?)(?:" + POWER_OP + ")?(\\d+)");

  var SIGNATURE_VECTOR = ["length", "time", "temperature", "mass", "current", "substance", "luminosity", "currency", "memory", "angle", "capacitance"];
  var KINDS = {
    "-312058": "resistance",
    "-312038": "inductance",
    "-152040": "magnetism",
    "-152038": "magnetism",
    "-152058": "potential",
    "-39": "acceleration",
    "-38": "radiation",
    "-20": "frequency",
    "-19": "speed",
    "-18": "viscosity",
    "0": "unitless",
    "1": "length",
    "2": "area",
    "3": "volume",
    "20": "time",
    "400": "temperature",
    "7942": "power",
    "7959": "pressure",
    "7962": "energy",
    "7979": "viscosity",
    "7981": "force",
    "7997": "mass_concentration",
    "8000": "mass",
    "159999": "magnetism",
    "160000": "current",
    "160020": "charge",
    "312058": "conductance",
    "3199980": "activity",
    "3199997": "molar_concentration",
    "3200000": "substance",
    "63999998": "illuminance",
    "64000000": "luminous_power",
    "1280000000": "currency",
    "25600000000": "memory",
    "511999999980": "angular_velocity",
    "512000000000": "angle",
    "10240000000000": "capacitance"
  };

  var baseUnitCache = {};

  function Qty(init_value) {
    this.scalar = null;
    this.base_scalar = null;
    this.signature = null;
    this.output = {};
    this.numerator = UNITY_ARRAY;
    this.denominator = UNITY_ARRAY;

    if(init_value.constructor === String) {
      init_value = init_value.trim();
      parse.call(this, init_value);
    }
    else {
      this.scalar = init_value.scalar;
      this.numerator = (init_value.numerator && init_value.numerator.length !== 0)? init_value.numerator : UNITY_ARRAY;
      this.denominator = (init_value.denominator && init_value.denominator.length !== 0)? init_value.denominator : UNITY_ARRAY;
    }

    // math with temperatures is very limited
    if(this.denominator.join('*').indexOf('temp') >= 0) {
      throw "Cannot divide with temperatures";
    }
    if(this.numerator.join('*').indexOf('temp') >= 0) {
      if(this.numerator.length > 1) {
        throw "Cannot multiply by temperatures";
      }
      if(!compareArray(this.denominator, UNITY_ARRAY)) {
        throw "Cannot divide with temperatures";
      }
    }

    this.init_value = init_value;
    updateBaseScalar.call(this);

    if(this.isTemperature() && this.base_scalar < 0) {
      throw "Temperatures must not be less than absolute zero";
    }
  }

  /**
   * Parses a string as a quantity
   * @param {string} value - quantity as text
   * @throws if value is not a string
   * @returns {Qty|null} Parsed quantity or null if unrecognized
   */
  Qty.parse = function parse(value) {
    if(typeof value !== 'string' && !(value instanceof String)) {
      throw "Argument should be a string";
    }

    try {
      return new Qty(value);
    }
    catch(e) {
      return null;
    }
  };

  /**
   * Configures and returns a fast function to convert
   * Number values from units to others.
   * Useful to efficiently convert large array of values
   * with same units into others with iterative methods.
   * Does not take care of rounding issues.
   *
   * @param {string} srcUnits Units of values to convert
   * @param {string} dstUnits Units to convert to
   *
   * @returns {Function} Converting function accepting Number value
   *   and returning converted value
   *
   * @throws "Incompatible units" if units are incompatible
   *
   * @example
   * // Converting large array of numbers with the same units
   * // into other units
   * var converter = Qty.swiftConverter("m/h", "ft/s");
   * var convertedSerie = largeSerie.map(converter);
   *
   */
  Qty.swiftConverter = function swiftConverter(srcUnits, dstUnits) {
    var srcQty = new Qty(srcUnits);
    var dstQty = new Qty(dstUnits);

    if(srcQty.eq(dstQty)) {
      return identity;
    }

    if(!srcQty.isTemperature()) {
      return function(value) {
        return value * srcQty.base_scalar / dstQty.base_scalar;
      };
    }
    else {
      return function(value) {
        // TODO Not optimized
        return srcQty.mul(value).to(dstQty).scalar;
      };
    }
  };

  function updateBaseScalar() {
    if(this.base_scalar) {
      return this.base_scalar;
    }
    if(this.isBase()) {
      this.base_scalar = this.scalar;
      this.signature = unitSignature.call(this);
    }
    else {
      var base = this.toBase();
      this.base_scalar = base.scalar;
      this.signature = base.signature;
    }
  }

  /*
  calculates the unit signature id for use in comparing compatible units and simplification
  the signature is based on a simple classification of units and is based on the following publication

  Novak, G.S., Jr. "Conversion of units of measurement", IEEE Transactions on Software Engineering,
  21(8), Aug 1995, pp.651-661
  doi://10.1109/32.403789
  http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel1/32/9079/00403789.pdf?isnumber=9079&prod=JNL&arnumber=403789&arSt=651&ared=661&arAuthor=Novak%2C+G.S.%2C+Jr.
  */
  function unitSignature() {
    if(this.signature) {
      return this.signature;
    }
    var vector = unitSignatureVector.call(this);
    for(var i = 0; i < vector.length; i++) {
      vector[i] *= Math.pow(20, i);
    }

    return vector.reduce(function(previous, current, index, array) {return previous + current;}, 0);
  }

  // calculates the unit signature vector used by unit_signature
  function unitSignatureVector() {
    if(!this.isBase()) {
      return unitSignatureVector.call(this.toBase());
    }

    var vector = new Array(SIGNATURE_VECTOR.length);
    for(var i = 0; i < vector.length; i++) {
      vector[i] = 0;
    }
    var r, n;
    for(var j = 0; j < this.numerator.length; j++) {
      if((r = UNITS[this.numerator[j]])) {
        n = SIGNATURE_VECTOR.indexOf(r[2]);
        if(n >= 0) {
          vector[n] = vector[n] + 1;
        }
      }
    }

    for(var k = 0; k < this.denominator.length; k++) {
      if((r = UNITS[this.denominator[k]])) {
        n = SIGNATURE_VECTOR.indexOf(r[2]);
        if(n >= 0) {
          vector[n] = vector[n] - 1;
        }
      }
    }
    return vector;
  }

  /* parse a string into a unit object.
   * Typical formats like :
   * "5.6 kg*m/s^2"
   * "5.6 kg*m*s^-2"
   * "5.6 kilogram*meter*second^-2"
   * "2.2 kPa"
   * "37 degC"
   * "1"  -- creates a unitless constant with value 1
   * "GPa"  -- creates a unit with scalar 1 with units 'GPa'
   * 6'4"  -- recognized as 6 feet + 4 inches
   * 8 lbs 8 oz -- recognized as 8 lbs + 8 ounces
   */
  function parse(val) {
    var result = QTY_STRING_REGEX.exec(val);
    if(!result) {
      throw val + ": Quantity not recognized";
    }

    if(val.trim() === '') {
      throw "Unit not recognized";
    }

    this.scalar = result[1] ? parseFloat(result[1]) : 1.0;
    var top = result[2];
    var bottom = result[3];

    var n, x, nx;
    // TODO DRY me
    while((result = TOP_REGEX.exec(top))) {
      n = parseFloat(result[2]);
      if(isNaN(n)) {
        // Prevents infinite loops
        throw "Unit exponent is not a number";
      }
      // Disallow unrecognized unit even if exponent is 0
      if(n === 0 && !UNIT_TEST_REGEX.test(result[1])) {
        throw "Unit not recognized";
      }
      x = result[1] + " ";
      nx = "";
      for(var i = 0; i < Math.abs(n) ; i++) {
        nx += x;
      }
      if(n >= 0) {
        top = top.replace(result[0], nx);
      }
      else {
        bottom = bottom ? bottom + nx : nx;
        top = top.replace(result[0], "");
      }
    }

    while((result = BOTTOM_REGEX.exec(bottom))) {
      n = parseFloat(result[2]);
      if(isNaN(n)) {
        // Prevents infinite loops
        throw "Unit exponent is not a number";
      }
      // Disallow unrecognized unit even if exponent is 0
      if(n === 0 && !UNIT_TEST_REGEX.test(result[1])) {
        throw "Unit not recognized";
      }
      x = result[1] + " ";
      nx = "";
      for(var j = 0; j < n ; j++) {
        nx += x;
      }

      bottom = bottom.replace(result[0], nx, "g");
    }

    if(top) {
      this.numerator = parseUnits(top.trim());
    }
    if(bottom) {
      this.denominator = parseUnits(bottom.trim());
    }

  }

  /*
   * Throws incompatible units error
   *
   * @throws "Incompatible units" error
   */
  function throwIncompatibleUnits() {
    throw "Incompatible units";
  }

  Qty.prototype = {

    // Properly set up constructor
    constructor: Qty,

    // Converts the unit back to a float if it is unitless.  Otherwise raises an exception
    toFloat: function() {
      if(this.isUnitless()) {
        return this.scalar;
      }
      throw "Can't convert to Float unless unitless.  Use Unit#scalar";
    },

    // returns true if no associated units
    // false, even if the units are "unitless" like 'radians, each, etc'
    isUnitless: function() {
      return compareArray(this.numerator, UNITY_ARRAY) && compareArray(this.denominator, UNITY_ARRAY);
    },

    /*
    check to see if units are compatible, but not the scalar part
    this check is done by comparing signatures for performance reasons
    if passed a string, it will create a unit object with the string and then do the comparison
    this permits a syntax like:
    unit =~ "mm"
    if you want to do a regexp on the unit string do this ...
    unit.units =~ /regexp/
    */
    isCompatible: function(other) {
      if(other && other.constructor === String) {
        return this.isCompatible(new Qty(other));
      }

      if(!(other instanceof Qty)) {
        return false;
      }

      if(other.signature !== undefined) {
        return this.signature === other.signature;
      }
      else {
        return false;
      }
    },

    /*
    check to see if units are inverse of each other, but not the scalar part
    this check is done by comparing signatures for performance reasons
    if passed a string, it will create a unit object with the string and then do the comparison
    this permits a syntax like:
    unit =~ "mm"
    if you want to do a regexp on the unit string do this ...
    unit.units =~ /regexp/
    */
    isInverse: function(other) {
      return this.inverse().isCompatible(other);
    },

    kind: function() {
      return KINDS[this.signature.toString()];
    },

    // Returns 'true' if the Unit is represented in base units
    isBase: function() {
      if(this.is_base !== undefined) {
        return this.is_base;
      }
      if(this.isDegrees() && this.numerator[0].match(/<(kelvin|temp-K)>/)) {
        this.is_base = true;
        return this.is_base;
      }

      this.numerator.concat(this.denominator).forEach(function(item) {
        if(item !== UNITY && BASE_UNITS.indexOf(item) === -1 ) {
          this.is_base = false;
        }
      }, this);
      if(this.is_base === false) {
        return this.is_base;
      }
      this.is_base = true;
      return this.is_base;
    },

    // convert to base SI units
    // results of the conversion are cached so subsequent calls to this will be fast
    toBase: function() {
      if(this.isBase()) {
        return this;
      }

      if(this.isTemperature()) {
        return toTempK(this);
      }

      var cached = baseUnitCache[this.units()];
      if(!cached) {
        cached = toBaseUnits(this.numerator,this.denominator);
        baseUnitCache[this.units()] = cached;
      }
      return cached.mul(this.scalar);
    },

    // returns the 'unit' part of the Unit object without the scalar
    units: function() {
      if(this._units !== undefined) {
        return this._units;
      }

      var numIsUnity = compareArray(this.numerator, UNITY_ARRAY),
          denIsUnity = compareArray(this.denominator, UNITY_ARRAY);
      if(numIsUnity && denIsUnity) {
        this._units = "";
        return this._units;
      }

      var numUnits = stringifyUnits(this.numerator),
          denUnits = stringifyUnits(this.denominator);
      this._units = numUnits + (denIsUnity ? '':('/' + denUnits));
      return this._units;
    },

    eq: function(other) {
      return this.compareTo(other) === 0;
    },
    lt: function(other) {
      return this.compareTo(other) === -1;
    },
    lte: function(other) {
      return this.eq(other) || this.lt(other);
    },
    gt: function(other) {
      return this.compareTo(other) === 1;
    },
    gte: function(other) {
      return this.eq(other) || this.gt(other);
    },

    // return a new quantity with same units rounded
    // at the nearest value according to quantity passed
    // as precision
    toPrec: function(prec_quantity) {
      if(prec_quantity && prec_quantity.constructor === String) {
        prec_quantity = new Qty(prec_quantity);
      }
      if(typeof prec_quantity === "number") {
        prec_quantity = new Qty(prec_quantity+' '+this.units());
      }

      if(!this.isUnitless()) {
        prec_quantity = prec_quantity.to(this.units());
      }
      else if(!prec_quantity.isUnitless()) {
        throwIncompatibleUnits();
      }

      if(prec_quantity.scalar === 0)
        throw "Divide by zero";
      var prec_rounded_result = Math.round(this.scalar/prec_quantity.scalar)*prec_quantity.scalar;

      // Remove potential floating error based on prec_quantity exponent
      var prec_exponent = exponent_of(prec_quantity.scalar);
      prec_rounded_result = round(prec_rounded_result, -prec_exponent);

      return new Qty(prec_rounded_result + this.units());
    },

    // Generate human readable output.
    // If the name of a unit is passed, the unit will first be converted to the target unit before output.
    // output is cached so subsequent calls for the same format will be fast
    toString: function(target_units_or_max_decimals_or_prec, max_decimals) {
      var target_units;
      if(typeof target_units_or_max_decimals_or_prec === "number") {
        max_decimals = target_units_or_max_decimals_or_prec;
      }
      else if(typeof target_units_or_max_decimals_or_prec === "string") {
        target_units = target_units_or_max_decimals_or_prec;
      }
      else if(target_units_or_max_decimals_or_prec instanceof Qty) {
        return this.toPrec(target_units_or_max_decimals_or_prec).toString(max_decimals);
      }

      var out;
      if(!max_decimals && this.output[target_units]) {
        out = this.output[target_units];
      }
      else if(target_units) {
        out = this.to(target_units);
        // Caching simple unit conversion
        this.output[target_units] = out;
      }
      else {
        out = this;
      }
      var out_scalar = max_decimals !== undefined ? round(out.scalar, max_decimals) : out.scalar;
      out = (out_scalar + " " + out.units()).trim();
      return out;
    },

    // Compare two Qty objects. Throws an exception if they are not of compatible types.
    // Comparisons are done based on the value of the quantity in base SI units.
    //
    // NOTE: We cannot compare inverses as that breaks the general compareTo contract:
    //   if a.compareTo(b) < 0 then b.compareTo(a) > 0
    //   if a.compareTo(b) == 0 then b.compareTo(a) == 0
    //
    //   Since "10S" == ".1ohm" (10 > .1) and "10ohm" == ".1S" (10 > .1)
    //     new Qty("10S").inverse().compareTo("10ohm") == -1
    //     new Qty("10ohm").inverse().compareTo("10S") == -1
    //
    //   If including inverses in the sort is needed, I suggest writing: Qty.sort(qtyArray,units)
    compareTo: function(other) {
      if(other && other.constructor === String) {
        return this.compareTo(new Qty(other));
      }
      if(!this.isCompatible(other)) {
        throwIncompatibleUnits();
      }
      if(this.base_scalar < other.base_scalar) {
        return -1;
      }
      else if(this.base_scalar === other.base_scalar) {
        return 0;
      }
      else if(this.base_scalar > other.base_scalar) {
        return 1;
      }
    },

    // Return true if quantities and units match
    // Unit("100 cm").same(Unit("100 cm"))  # => true
    // Unit("100 cm").same(Unit("1 m"))     # => false
    same: function(other) {
      return (this.scalar === other.scalar) && (this.units() === other.units());
    },

    // Returns a Qty that is the inverse of this Qty,
    inverse: function() {
      if(this.isTemperature()) {
        throw "Cannot divide with temperatures";
      }
      if(this.scalar === 0) {
        throw "Divide by zero";
      }
      return new Qty({"scalar": 1/this.scalar, "numerator": this.denominator, "denominator": this.numerator});
    },

    isDegrees: function() {
      // signature may not have been calculated yet
      return (this.signature === null || this.signature === 400) &&
        this.numerator.length === 1 &&
        compareArray(this.denominator, UNITY_ARRAY) &&
        (this.numerator[0].match(/<temp-[CFRK]>/) || this.numerator[0].match(/<(kelvin|celsius|rankine|fahrenheit)>/));
    },

    isTemperature: function() {
      return this.isDegrees() && this.numerator[0].match(/<temp-[CFRK]>/);
    },

    // convert to a specified unit string or to the same units as another Qty
    // qty.to("kg")  will convert to kilograms
    // qty1.to(qty2) converts to same units as qty2 object (ignoring scalar of qty2)
    //
    // Throws an exception if the requested target units are incompatible with current Unit or its inverse.
    to: function(other) {
      if(other && other.constructor !== String) {
        return this.to(other.units());
      }

      // Instantiating target to normalize units
      var target = new Qty(other);

      if(target.units() === this.units()) {
        return this;
      }

      if(!this.isCompatible(target)) {
        if(this.isInverse(target)) {
          return this.inverse().to(other);
        }
        throwIncompatibleUnits();
      }

      if(target.isTemperature()) {
        return toTemp(this,target);
      }
      else if(target.isDegrees()) {
        return toDegrees(this,target);
      }

      var q = div_safe(this.base_scalar, target.base_scalar);
      return new Qty({"scalar": q, "numerator": target.numerator, "denominator": target.denominator});
    },

    // Quantity operators
    // Returns new instance with this units
    add: function(other) {
      if(other && other.constructor === String) {
        other = new Qty(other);
      }

      if(!this.isCompatible(other)) {
        throwIncompatibleUnits();
      }

      if(this.isTemperature() && other.isTemperature()) {
        throw "Cannot add two temperatures";
      }
      else if(this.isTemperature()) {
        return addTempDegrees(this,other);
      }
      else if(other.isTemperature()) {
        return addTempDegrees(other,this);
      }

      return new Qty({"scalar": this.scalar + other.to(this).scalar, "numerator": this.numerator, "denominator": this.denominator});
    },

    sub: function(other) {
      if(other && other.constructor === String) {
        other = new Qty(other);
      }

      if(!this.isCompatible(other)) {
        throwIncompatibleUnits();
      }

      if(this.isTemperature() && other.isTemperature()) {
        return subtractTemperatures(this,other);
      }
      else if(this.isTemperature()) {
        return subtractTempDegrees(this,other);
      }
      else if(other.isTemperature()) {
        throw "Cannot subtract a temperature from a differential degree unit";
      }

      return new Qty({"scalar": this.scalar - other.to(this).scalar, "numerator": this.numerator, "denominator": this.denominator});
    },

    mul: function(other) {
      if(typeof other === "number") {
        return new Qty({"scalar": mul_safe(this.scalar, other), "numerator": this.numerator, "denominator": this.denominator});
      }
      else if(other && other.constructor === String) {
        other = new Qty(other);
      }

      if((this.isTemperature()||other.isTemperature()) && !(this.isUnitless()||other.isUnitless())) {
        throw "Cannot multiply by temperatures";
      }

      // Quantities should be multiplied with same units if compatible, with base units else
      var op1 = this;
      var op2 = other;

      // so as not to confuse results, multiplication and division between temperature degrees will maintain original unit info in num/den
      // multiplication and division between deg[CFRK] can never factor each other out, only themselves: "degK*degC/degC^2" == "degK/degC"
      if(op1.isCompatible(op2) && op1.signature !== 400) {
        op2 = op2.to(op1);
      }
      var numden = cleanTerms(op1.numerator.concat(op2.numerator), op1.denominator.concat(op2.denominator));

      return new Qty({"scalar": mul_safe(op1.scalar, op2.scalar) , "numerator": numden[0], "denominator": numden[1]});
    },

    div: function(other) {
      if(typeof other === "number") {
        if(other === 0) {
          throw "Divide by zero";
        }
        return new Qty({"scalar": this.scalar / other, "numerator": this.numerator, "denominator": this.denominator});
      }
      else if(other && other.constructor === String) {
        other = new Qty(other);
      }

      if(other.scalar === 0) {
        throw "Divide by zero";
      }

      if(other.isTemperature()) {
        throw "Cannot divide with temperatures";
      }
      else if(this.isTemperature() && !other.isUnitless()) {
        throw "Cannot divide with temperatures";
      }

      // Quantities should be multiplied with same units if compatible, with base units else
      var op1 = this;
      var op2 = other;

      // so as not to confuse results, multiplication and division between temperature degrees will maintain original unit info in num/den
      // multiplication and division between deg[CFRK] can never factor each other out, only themselves: "degK*degC/degC^2" == "degK/degC"
      if(op1.isCompatible(op2) && op1.signature !== 400) {
        op2 = op2.to(op1);
      }
      var numden = cleanTerms(op1.numerator.concat(op2.denominator), op1.denominator.concat(op2.numerator));

      return new Qty({"scalar": op1.scalar / op2.scalar, "numerator": numden[0], "denominator": numden[1]});
    }

  };

  function toBaseUnits (numerator,denominator) {
    var num = [];
    var den = [];
    var q = 1;
    var unit;
    for(var i = 0; i < numerator.length; i++) {
      unit = numerator[i];
      if(PREFIX_VALUES[unit]) {
        // workaround to fix
        // 0.1 * 0.1 => 0.010000000000000002
        q = mul_safe(q, PREFIX_VALUES[unit]);
      }
      else {
        if(UNIT_VALUES[unit]) {
          q *= UNIT_VALUES[unit].scalar;

          if(UNIT_VALUES[unit].numerator) {
            num.push(UNIT_VALUES[unit].numerator);
          }
          if(UNIT_VALUES[unit].denominator) {
            den.push(UNIT_VALUES[unit].denominator);
          }
        }
      }
    }
    for(var j = 0; j < denominator.length; j++) {
      unit = denominator[j];
      if(PREFIX_VALUES[unit]) {
        q /= PREFIX_VALUES[unit];
      }
      else {
        if(UNIT_VALUES[unit]) {
          q /= UNIT_VALUES[unit].scalar;

          if(UNIT_VALUES[unit].numerator) {
            den.push(UNIT_VALUES[unit].numerator);
          }
          if(UNIT_VALUES[unit].denominator) {
            num.push(UNIT_VALUES[unit].denominator);
          }
        }
      }
    }

    // Flatten
    num = num.reduce(function(a,b) {
      return a.concat(b);
    }, []);
    den = den.reduce(function(a,b) {
      return a.concat(b);
    }, []);

    return new Qty({"scalar": q, "numerator": num, "denominator": den});
  }

  var parsedUnitsCache = {};
  /**
   * Parses and converts units string to normalized unit array.
   * Result is cached to speed up next calls.
   *
   * @param {string} units Units string
   * @returns {string[]} Array of normalized units
   *
   * @example
   * // Returns ["<second>", "<meter>", "<second>"]
   * parseUnits("s m s");
   *
   */
  function parseUnits(units) {
    var cached = parsedUnitsCache[units];
    if(cached) {
      return cached;
    }

    var unit_match, normalizedUnits = [];
    // Scan
    if(!UNIT_TEST_REGEX.test(units)) {
      throw "Unit not recognized";
    }

    while((unit_match = UNIT_MATCH_REGEX.exec(units))) {
      normalizedUnits.push(unit_match.slice(1));
    }

    normalizedUnits = normalizedUnits.map(function(item) {
      return PREFIX_MAP[item[0]] ? [PREFIX_MAP[item[0]], UNIT_MAP[item[1]]] : [UNIT_MAP[item[1]]];
    });

    // Flatten and remove null elements
    normalizedUnits = normalizedUnits.reduce(function(a,b) {
      return a.concat(b);
    }, []);
    normalizedUnits = normalizedUnits.filter(function(item) {
      return item;
    });

    parsedUnitsCache[units] = normalizedUnits;

    return normalizedUnits;
  }

  function NestedMap() {}

  NestedMap.prototype.get = function(keys) {

    // Allows to pass key1, key2, ... instead of [key1, key2, ...]
    if(arguments.length > 1) {
      // Slower with Firefox but faster with Chrome than
      // Array.prototype.slice.call(arguments)
      // See http://jsperf.com/array-apply-versus-array-prototype-slice-call
      keys = Array.apply(null, arguments);
    }

    return keys.reduce(function(map, key, index) {
      if (map) {

        var childMap = map[key];

        if (index === keys.length - 1) {
          return childMap ? childMap.data : undefined;
        }
        else {
          return childMap;
        }
      }
    },
    this);
  };

  NestedMap.prototype.set = function(keys, value) {

      if(arguments.length > 2) {
        keys = Array.prototype.slice.call(arguments, 0, -1);
        value = arguments[arguments.length - 1];
      }

      return keys.reduce(function(map, key, index) {

        var childMap = map[key];
        if (childMap === undefined) {
          childMap = map[key] = {};
        }

        if (index === keys.length - 1) {
          childMap.data = value;
          return value;
        }
        else {
          return childMap;
        }
      },
      this);
  };

  var stringifiedUnitsCache = new NestedMap();
  /**
   * Returns a string representing a normalized unit array
   *
   * @param {string[]} units Normalized unit array
   * @returns {string} String representing passed normalized unit array and
   *   suitable for output
   *
   */
  function stringifyUnits(units) {

    var stringified = stringifiedUnitsCache.get(units);
    if(stringified) {
      return stringified;
    }

    var isUnity = compareArray(units, UNITY_ARRAY);
    if(isUnity) {
      stringified = "1";
    }
    else {
      stringified = simplify(getOutputNames(units)).join("*");
    }

    // Cache result
    stringifiedUnitsCache.set(units, stringified);

    return stringified;
  }

  function getOutputNames(units) {
    var unitNames = [], token, token_next;
    for(var i = 0; i < units.length; i++) {
      token = units[i];
      token_next = units[i+1];
      if(PREFIX_VALUES[token]) {
        unitNames.push(OUTPUT_MAP[token] + OUTPUT_MAP[token_next]);
        i++;
      }
      else {
        unitNames.push(OUTPUT_MAP[token]);
      }
    }
    return unitNames;
  }

  function simplify (units) {
    // this turns ['s','m','s'] into ['s2','m']

    var unitCounts = units.reduce(function(acc, unit) {
      var unitCounter = acc[unit];
      if(!unitCounter) {
        acc.push(unitCounter = acc[unit] = [unit, 0]);
      }

      unitCounter[1]++;

      return acc;
    }, []);

    return unitCounts.map(function(unitCount) {
      return unitCount[0] + (unitCount[1] > 1 ? unitCount[1] : "");
    });
  }

  function compareArray(array1, array2) {
    if (array2.length !== array1.length) {
      return false;
    }
    for (var i = 0; i < array1.length; i++) {
      if (array2[i].compareArray) {
        if (!array2[i].compareArray(array1[i])) {
          return false;
        }
      }
      if (array2[i] !== array1[i]) {
        return false;
      }
    }
    return true;
  }

  function round(val, decimals) {
    return Math.round(val*Math.pow(10, decimals))/Math.pow(10, decimals);
  }

  // significand x 10 ^ exponent
  function exponent_of(val) {
    return Math.floor(Math.log(Math.abs(val)) / Math.LN10);
  }

  var num_regex = /^-?(\d+)(?:\.(\d+))?$/;
  var exp_regex = /^-?(\d+)e-?(\d+)$/;

  function subtractTemperatures(lhs,rhs) {
    var lhsUnits = lhs.units();
    var rhsConverted = rhs.to(lhsUnits);
    var dstDegrees = new Qty(getDegreeUnits(lhsUnits));
    return new Qty({"scalar": lhs.scalar - rhsConverted.scalar, "numerator": dstDegrees.numerator, "denominator": dstDegrees.denominator});
  }

  function subtractTempDegrees(temp,deg) {
    var tempDegrees = deg.to(getDegreeUnits(temp.units()));
    return new Qty({"scalar": temp.scalar - tempDegrees.scalar, "numerator": temp.numerator, "denominator": temp.denominator});
  }

  function addTempDegrees(temp,deg) {
    var tempDegrees = deg.to(getDegreeUnits(temp.units()));
    return new Qty({"scalar": temp.scalar + tempDegrees.scalar, "numerator": temp.numerator, "denominator": temp.denominator});
  }

  function getDegreeUnits(units) {
    if(units === 'tempK') {
      return 'degK';
    }
    else if(units === 'tempC') {
      return 'degC';
    }
    else if(units === 'tempF') {
      return 'degF';
    }
    else if(units === 'tempR') {
      return 'degR';
    }
    else {
      throw "Unknown type for temp conversion from: " + units;
    }
  }

  function toDegrees(src,dst) {
    var srcDegK = toDegK(src);
    var dstUnits = dst.units();
    var dstScalar;

    if(dstUnits === 'degK') {
      dstScalar = srcDegK.scalar;
    }
    else if(dstUnits === 'degC') {
      dstScalar = srcDegK.scalar ;
    }
    else if(dstUnits === 'degF') {
      dstScalar = srcDegK.scalar * 9/5;
    }
    else if(dstUnits === 'degR') {
      dstScalar = srcDegK.scalar * 9/5;
    }
    else {
      throw "Unknown type for degree conversion to: " + dstUnits;
    }

    return new Qty({"scalar": dstScalar, "numerator": dst.numerator, "denominator": dst.denominator});
  }

  function toDegK(qty) {
    var units = qty.units();
    var q;
    if(units.match(/(deg)[CFRK]/)) {
      q = qty.base_scalar;
    }
    else if(units === 'tempK') {
      q = qty.scalar;
    }
    else if(units === 'tempC') {
      q = qty.scalar;
    }
    else if(units === 'tempF') {
      q = qty.scalar * 5/9;
    }
    else if(units === 'tempR') {
      q = qty.scalar * 5/9;
    }
    else {
      throw "Unknown type for temp conversion from: " + units;
    }

    return new Qty({"scalar": q, "numerator": ["<kelvin>"], "denominator": UNITY_ARRAY});
  }

  function toTemp(src,dst) {
    var dstUnits = dst.units();
    var dstScalar;

    if(dstUnits === 'tempK') {
      dstScalar = src.base_scalar;
    }
    else if(dstUnits === 'tempC') {
      dstScalar = src.base_scalar - 273.15;
    }
    else if(dstUnits === 'tempF') {
      dstScalar = (src.base_scalar * 9/5) - 459.67;
    }
    else if(dstUnits === 'tempR') {
      dstScalar = src.base_scalar * 9/5;
    }
    else {
      throw "Unknown type for temp conversion to: " + dstUnits;
    }

    return new Qty({"scalar": dstScalar, "numerator": dst.numerator, "denominator": dst.denominator});
  }

  function toTempK(qty) {
    var units = qty.units();
    var q;
    if(units.match(/(deg)[CFRK]/)) {
      q = qty.base_scalar;
    }
    else if(units === 'tempK') {
      q = qty.scalar;
    }
    else if(units === 'tempC') {
      q = qty.scalar + 273.15;
    }
    else if(units === 'tempF') {
      q = (qty.scalar + 459.67) * 5/9;
    }
    else if(units === 'tempR') {
      q = qty.scalar * 5/9;
    }
    else {
      throw "Unknown type for temp conversion from: " + units;
    }

    return new Qty({"scalar": q, "numerator": ["<temp-K>"], "denominator": UNITY_ARRAY});
  }

  // Multiply numbers avoiding floating errors
  // workaround to fix
  // 0.1 * 0.1 => 0.010000000000000002
  // mul_safe(0.1, 0.1) => 0.01
  function mul_safe() {
    var result = 1, decimals = 0;
    for(var i = 0; i < arguments.length; i++) {
      var arg = arguments[i];
      decimals = decimals + getFractional(arg);
      result *= arg;
    }

    return decimals !== 0 ? round(result, decimals) : result;
  }

  function div_safe(num, den) {
    if(den === 0)
      throw "Divide by zero";
    return mul_safe(num, 1/den);
  }

  function getFractional(num) {
    var fractional, match;
    if((match = num_regex.exec(num)) && match[2]) {
      fractional = match[2].length;
    }
    else if((match = exp_regex.exec(num))) {
      fractional = parseInt(match[2], 10);
    }
    // arg could be Infinities
    return fractional || 0;
  }

  Qty.mul_safe = mul_safe;
  Qty.div_safe = div_safe;

  function cleanTerms(num, den) {
    num = num.filter(function(val) {return val !== UNITY;});
    den = den.filter(function(val) {return val !== UNITY;});

    var combined = {};

    var k;
    for(var i = 0; i < num.length; i++) {
      if(PREFIX_VALUES[num[i]]) {
        k = [num[i], num[i+1]];
        i++;
      }
      else {
        k = num[i];
      }
      if(k && k !== UNITY) {
        if(combined[k]) {
          combined[k][0]++;
        }
        else {
          combined[k] = [1, k];
        }
      }
    }

    for(var j = 0; j < den.length; j++) {
      if(PREFIX_VALUES[den[j]]) {
        k = [den[j], den[j+1]];
        j++;
      }
      else {
        k = den[j];
      }
      if(k && k !== UNITY) {
        if(combined[k]) {
          combined[k][0]--;
        }
        else {
          combined[k] = [-1, k];
        }
      }
    }

    num = [];
    den = [];

    for(var prop in combined) {
      if(combined.hasOwnProperty(prop)) {
        var item = combined[prop];
        var n;
        if(item[0] > 0) {
          for(n = 0; n < item[0]; n++) {
            num.push(item[1]);
          }
        }
        else if(item[0] < 0) {
          for(n = 0; n < -item[0]; n++) {
            den.push(item[1]);
          }
        }
      }
    }

    if(num.length === 0) {
      num = UNITY_ARRAY;
    }
    if(den.length === 0) {
      den = UNITY_ARRAY;
    }

    // Flatten
    num = num.reduce(function(a,b) {
      return a.concat(b);
    }, []);
    den = den.reduce(function(a,b) {
      return a.concat(b);
    }, []);

    return [num, den];
  }

  /*
   * Identity function
   */
  function identity(value) {
    return value;
  }

  // Setup
  var PREFIX_VALUES = {};
  var PREFIX_MAP = {};
  var UNIT_VALUES = {};
  var UNIT_MAP = {};
  var OUTPUT_MAP = {};
  for(var unit_def in UNITS) {
    if(UNITS.hasOwnProperty(unit_def)) {
      var definition = UNITS[unit_def];
      if(definition[2] === "prefix") {
        PREFIX_VALUES[unit_def] = definition[1];
        for(var i = 0; i < definition[0].length; i++) {
          PREFIX_MAP[definition[0][i]] = unit_def;
        }
      }
      else {
        UNIT_VALUES[unit_def] = {
          scalar: definition[1],
          numerator: definition[3],
          denominator: definition[4]
        };
        for(var j = 0; j < definition[0].length; j++) {
          UNIT_MAP[definition[0][j]] = unit_def;
        }
      }
      OUTPUT_MAP[unit_def] = definition[0][0];
    }
  }
  var PREFIX_REGEX = Object.keys(PREFIX_MAP).sort(function(a, b) {
    return b.length - a.length;
  }).join('|');
  var UNIT_REGEX = Object.keys(UNIT_MAP).sort(function(a, b) {
    return b.length - a.length;
  }).join('|');
  var UNIT_MATCH = "(" + PREFIX_REGEX + ")*?(" + UNIT_REGEX + ")\\b";
  var UNIT_MATCH_REGEX = new RegExp(UNIT_MATCH, "g"); // g flag for multiple occurences
  var UNIT_TEST_REGEX = new RegExp("^\\s*(" + UNIT_MATCH + "\\s*\\*?\\s*)+$");

  return Qty;
}));