text: 'use strict';
  
  var endsWith = require('../../utils/string').endsWith;
  var clone = require('../../utils/object').clone;
  var constants = require('../../utils/bignumber/constants');
  
  function factory (type, config, load, typed, math) {
    var add       = load(require('../../function/arithmetic/addScalar'));
    var subtract  = load(require('../../function/arithmetic/subtract'));
    var multiply  = load(require('../../function/arithmetic/multiplyScalar'));
    var divide    = load(require('../../function/arithmetic/divideScalar'));
    var pow       = load(require('../../function/arithmetic/pow'));
    var abs       = load(require('../../function/arithmetic/abs'));
    var equal     = load(require('../../function/relational/equal'));
    var isNumeric = load(require('../../function/utils/isNumeric'));
    var format    = load(require('../../function/string/format'));
    var getTypeOf = load(require('../../function/utils/typeof'));
    var toNumber  = load(require('../../type/number'));
    var Complex   = load(require('../../type/complex/Complex'));
  
    /**
     * A unit can be constructed in the following ways:
     *     var a = new Unit(value, name);
     *     var b = new Unit(null, name);
     *     var c = Unit.parse(str);
     *
     * Example usage:
     *     var a = new Unit(5, 'cm');               // 50 mm
     *     var b = Unit.parse('23 kg');             // 23 kg
     *     var c = math.in(a, new Unit(null, 'm');  // 0.05 m
     *     var d = new Unit(9.81, "m/s^2");         // 9.81 m/s^2
     *
     * @class Unit
     * @constructor Unit
     * @param {number | BigNumber | Fraction | Complex | boolean} [value]  A value like 5.2
     * @param {string} [name]   A unit name like "cm" or "inch", or a derived unit of the form: "u1[^ex1] [u2[^ex2] ...] [/ u3[^ex3] [u4[^ex4]]]", such as "kg m^2/s^2", where each unit appearing after the forward slash is taken to be in the denominator. "kg m^2 s^-2" is a synonym and is also acceptable. Any of the units can include a prefix.
     */
    function Unit(value, name) {
      if (!(this instanceof Unit)) {
        throw new Error('Constructor must be called with the new operator');
      }
  
      if (!(value === undefined || isNumeric(value) || value.isComplex)) {
        throw new TypeError('First parameter in Unit constructor must be number, BigNumber, Fraction, Complex, or undefined');
      }
      if (name != undefined && (typeof name !== 'string' || name == '')) {
        throw new TypeError('Second parameter in Unit constructor must be a string');
      }
  
      if (name != undefined) {
        var u = Unit.parse(name);
        this.units = u.units;
        this.dimensions = u.dimensions;
      }
      else {
        this.units = [
          {
            unit: UNIT_NONE,
            prefix: PREFIXES.NONE,  // link to a list with supported prefixes
            power: 0
          }
        ];
        this.dimensions = [0, 0, 0, 0, 0, 0, 0, 0, 0];
      }
  
      this.value = (value != undefined) ? this._normalize(value) : null;
  
      this.fixPrefix = false; // if true, function format will not search for the
                              // best prefix but leave it as initially provided.
                              // fixPrefix is set true by the method Unit.to
  
      // The justification behind this is that if the constructor is explicitly called,
      // the caller wishes the units to be returned exactly as he supplied.
      this.isUnitListSimplified = true;
  
    }
  
    /**
     * Attach type information
     */
    Unit.prototype.type = 'Unit';
    Unit.prototype.isUnit = true;
  
    // private variables and functions for the Unit parser
    var text, index, c;
  
    function skipWhitespace() {
      while (c == ' ' || c == '\t') {
        next();
      }
    }
  
    function isDigitDot(c) {
      return ((c >= '0' && c <= '9') || c == '.');
    }
  
    function isDigit(c) {
      return ((c >= '0' && c <= '9'));
    }
  
    function next() {
      index++;
      c = text.charAt(index);
    }
  
    function revert(oldIndex) {
      index = oldIndex;
      c = text.charAt(index);
    }
  
    function parseNumber() {
      var number = '';
      var oldIndex;
      oldIndex = index;
  
      if (c == '+') {
        next();
      }
      else if (c == '-') {
        number += c;
        next();
      }
  
      if (!isDigitDot(c)) {
        // a + or - must be followed by a digit
        revert(oldIndex);
        return null;
      }
  
      // get number, can have a single dot
      if (c == '.') {
        number += c;
        next();
        if (!isDigit(c)) {
          // this is no legal number, it is just a dot
          revert(oldIndex);
          return null;
        }
      }
      else {
        while (isDigit(c)) {
          number += c;
          next();
        }
        if (c == '.') {
          number += c;
          next();
        }
      }
      while (isDigit(c)) {
        number += c;
        next();
      }
  
      // check for exponential notation like "2.3e-4" or "1.23e50"
      if (c == 'E' || c == 'e') {
        // The grammar branches here. This could either be part of an exponent or the start of a unit that begins with the letter e, such as "4exabytes"
  
        var tentativeNumber = '';
        var tentativeIndex = index;
  
        tentativeNumber += c;
        next();
  
        if (c == '+' || c == '-') {
          tentativeNumber += c;
          next();
        }
  
        // Scientific notation MUST be followed by an exponent (otherwise we assume it is not scientific notation)
        if (!isDigit(c)) {
          // The e or E must belong to something else, so return the number without the e or E.
          revert(tentativeIndex);
          return number;
        }
        
        // We can now safely say that this is scientific notation.
        number = number + tentativeNumber;
        while (isDigit(c)) {
          number += c;
          next();
        }
      }
  
      return number;
    }
  
    function parseUnit() {
      var unitName = '';
  
      // Alphanumeric characters only; matches [a-zA-Z0-9]
      var code = text.charCodeAt(index);
      while ( (code >= 48 && code <= 57) ||
              (code >= 65 && code <= 90) ||
              (code >= 97 && code <= 122)) {
        unitName += c;
        next();
        code = text.charCodeAt(index);
      }
  
      // Must begin with [a-zA-Z]
      code = unitName.charCodeAt(0);
      if ((code >= 65 && code <= 90) ||
          (code >= 97 && code <= 122)) {
          return unitName || null;
      } 
      else {
        return null;
      }
    }
  
    function parseCharacter(toFind) {
      if (c === toFind) {
        next();
        return toFind;
      }
      else {
        return null;
      }
    }
  
    /**
     * Parse a string into a unit. The value of the unit is parsed as number,
     * BigNumber, or Fraction depending on the math.js config setting `number`.
     *
     * Throws an exception if the provided string does not contain a valid unit or
     * cannot be parsed.
     * @memberof Unit
     * @param {string} str        A string like "5.2 inch", "4e2 cm/s^2"
     * @return {Unit} unit
     */
    Unit.parse = function (str) {
      text = str;
      index = -1;
      c = '';
  
      if (typeof text !== 'string') {
        throw new TypeError('Invalid argument in Unit.parse, string expected');
      }
  
      var unit = new Unit();
      unit.units = [];
  
      // A unit should follow this pattern:
      // [number]unit[^number] [unit[^number]]...[/unit[^number] [unit[^number]]]
  
      // Rules:
      // number is any floating point number.
      // unit is any alphanumeric string beginning with an alpha. Units with names like e3 should be avoided because they look like the exponent of a floating point number!
      // The string may optionally begin with a number.
      // Each unit may optionally be followed by ^number.
      // Whitespace or a forward slash is recommended between consecutive units, although the following technically is parseable:
      //   2m^2kg/s^2
      // it is not good form. If a unit starts with e, then it could be confused as a floating point number:
      //   4erg
  
      next();
      skipWhitespace();
      // Optional number at the start of the string
      var valueStr = parseNumber();
      var value = null;
      if(valueStr) {
        if (config.number === 'BigNumber') {
          value = new type.BigNumber(valueStr);
        }
        else if (config.number === 'Fraction') {
          value = new type.Fraction(valueStr);
        }
        else { // number
          value = parseFloat(valueStr);
        }
      }
      skipWhitespace();    // Whitespace is not required here
  
      // Next, we read any number of unit[^number]
      var powerMultiplierCurrent = 1;
      var expectingUnit = false;
  
      // Stack to keep track of powerMultipliers applied to each parentheses group
      var powerMultiplierStack = [];
  
      // Running product of all elements in powerMultiplierStack
      var powerMultiplierStackProduct = 1;
  
      while (true) {
        skipWhitespace();
  
        // Check for and consume opening parentheses, pushing powerMultiplierCurrent to the stack
        // A '(' will always appear directly before a unit.
        while (c === '(') {
          powerMultiplierStack.push(powerMultiplierCurrent);
          powerMultiplierStackProduct *= powerMultiplierCurrent;
          powerMultiplierCurrent = 1;
          next();
          skipWhitespace();
        }
  
        // Is there something here?
        if(c) {
          var oldC = c;
          var uStr = parseUnit();
          if(uStr == null) {
            throw new SyntaxError('Unexpected "' + oldC + '" in "' + text + '" at index ' + index.toString());
          }
        }
        else {
          // End of input.
          break;
        }
  
        // Verify the unit exists and get the prefix (if any)
        var res = _findUnit(uStr);
        if(res == null) {
          // Unit not found.
          throw new SyntaxError('Unit "' + uStr + '" not found.');
        }
  
        var power = powerMultiplierCurrent * powerMultiplierStackProduct;
        // Is there a "^ number"?
        skipWhitespace();
        if (parseCharacter('^')) {
          skipWhitespace();
          var p = parseNumber();
          if(p == null) {
            // No valid number found for the power!
            throw new SyntaxError('In "' + str + '", "^" must be followed by a floating-point number');
          }
          power *= p;
        }
  
        // Add the unit to the list
        unit.units.push( {
          unit: res.unit,
          prefix: res.prefix,
          power: power
        });
        for(var i=0; i<BASE_DIMENSIONS.length; i++) {
          unit.dimensions[i] += res.unit.dimensions[i] * power;
        }
  
        // Check for and consume closing parentheses, popping from the stack.
        // A ')' will always follow a unit.
        skipWhitespace();
        while (c === ')') {
          if(powerMultiplierStack.length === 0) {
            throw new SyntaxError('Unmatched ")" in "' + text + '" at index ' + index.toString());
          }
          powerMultiplierStackProduct /= powerMultiplierStack.pop();
          next();
          skipWhitespace();
        }
  
        // "*" and "/" should mean we are expecting something to come next.
        // Is there a forward slash? If so, negate powerMultiplierCurrent. The next unit or paren group is in the denominator.
        expectingUnit = false;
  
        if (parseCharacter('*')) {
          // explicit multiplication
          powerMultiplierCurrent = 1;
          expectingUnit = true;
        }
        else if (parseCharacter('/')) {
          // division
          powerMultiplierCurrent = -1;
          expectingUnit = true;
        }
        else {
          // implicit multiplication
          powerMultiplierCurrent = 1;
        }
  
        // Replace the unit into the auto unit system
        var baseDim = res.unit.base.key;
        UNIT_SYSTEMS.auto[baseDim] = {
          unit: res.unit,
          prefix: res.prefix
        };
      }
      
      // Has the string been entirely consumed?
      skipWhitespace();
      if(c) {
        throw new SyntaxError('Could not parse: "' + str + '"');
      }
  
      // Is there a trailing slash?
      if(expectingUnit) {
        throw new SyntaxError('Trailing characters: "' + str + '"');
      }
  
      // Is the parentheses stack empty?
      if(powerMultiplierStack.length !== 0) {
        throw new SyntaxError('Unmatched "(" in "' + text + '"');
      }
  
      // Are there any units at all?
      if(unit.units.length == 0) {
        throw new SyntaxError('"' + str + '" contains no units');
      }
  
      unit.value = (value != undefined) ? unit._normalize(value) : null;
      return unit;
    };
  
    /**
     * create a copy of this unit
     * @memberof Unit
     * @return {Unit} Returns a cloned version of the unit
     */
    Unit.prototype.clone = function () {
      var unit = new Unit();
  
      unit.fixPrefix = this.fixPrefix;
      unit.isUnitListSimplified = this.isUnitListSimplified;
  
      unit.value = clone(this.value);
      unit.dimensions = this.dimensions.slice(0);
      unit.units = [];
      for(var i = 0; i < this.units.length; i++) {
        unit.units[i] = { };
        for (var p in this.units[i]) {
          if (this.units[i].hasOwnProperty(p)) {
            unit.units[i][p] = this.units[i][p];
          }
        }
      }
  
      return unit;
    };
  
    /**
     * Return whether the unit is derived (such as m/s, or cm^2, but not N)
     * @memberof Unit
     * @return {boolean} True if the unit is derived
     */
    Unit.prototype._isDerived = function() {
      if(this.units.length === 0) {
        return false;
      }
      return this.units.length > 1 || Math.abs(this.units[0].power - 1.0) > 1e-15;
    };
  
    /**
     * Normalize a value, based on its currently set unit(s)
     * @memberof Unit
     * @param {number | BigNumber | Fraction | boolean} value
     * @return {number | BigNumber | Fraction | boolean} normalized value
     * @private
     */
    Unit.prototype._normalize = function (value) {
      var unitValue, unitOffset, unitPower, unitPrefixValue;
      var convert;
  
      if (value == null || this.units.length === 0) {
        return value;
      }
      else if (this._isDerived()) {
        // This is a derived unit, so do not apply offsets.
        // For example, with J kg^-1 degC^-1 you would NOT want to apply the offset.
        var res = value;
        convert = Unit._getNumberConverter(getTypeOf(value)); // convert to Fraction or BigNumber if needed
  
        for(var i=0; i < this.units.length; i++) {
          unitValue       = convert(this.units[i].unit.value);
          unitPrefixValue = convert(this.units[i].prefix.value);
          unitPower       = convert(this.units[i].power);
          res = multiply(res, pow(multiply(unitValue, unitPrefixValue), unitPower));
        }
  
        return res;
      }
      else {
        // This is a single unit of power 1, like kg or degC
        convert = Unit._getNumberConverter(getTypeOf(value)); // convert to Fraction or BigNumber if needed
  
        unitValue       = convert(this.units[0].unit.value);
        unitOffset      = convert(this.units[0].unit.offset);
        unitPrefixValue = convert(this.units[0].prefix.value);
  
        return multiply(add(value, unitOffset), multiply(unitValue, unitPrefixValue));
      }
    };
  
    /**
     * Denormalize a value, based on its currently set unit(s)
     * @memberof Unit
     * @param {number} value
     * @param {number} [prefixValue]    Optional prefix value to be used (ignored if this is a derived unit)
     * @return {number} denormalized value
     * @private
     */
    Unit.prototype._denormalize = function (value, prefixValue) {
      var unitValue, unitOffset, unitPower, unitPrefixValue;
      var convert;
  
      if (value == null || this.units.length === 0) {
        return value;
      }
      else if (this._isDerived()) {
        // This is a derived unit, so do not apply offsets.
        // For example, with J kg^-1 degC^-1 you would NOT want to apply the offset.
        // Also, prefixValue is ignored--but we will still use the prefix value stored in each unit, since kg is usually preferable to g unless the user decides otherwise.
        var res = value;
        convert = Unit._getNumberConverter(getTypeOf(value)); // convert to Fraction or BigNumber if needed
  
        for (var i = 0; i < this.units.length; i++) {
          unitValue       = convert(this.units[i].unit.value);
          unitPrefixValue = convert(this.units[i].prefix.value);
          unitPower       = convert(this.units[i].power);
          res = divide(res, pow(multiply(unitValue, unitPrefixValue), unitPower));
        }
  
        return res;
      }
      else {
        // This is a single unit of power 1, like kg or degC
        convert = Unit._getNumberConverter(getTypeOf(value)); // convert to Fraction or BigNumber if needed
  
        unitValue       = convert(this.units[0].unit.value);
        unitPrefixValue = convert(this.units[0].prefix.value);
        unitOffset      = convert(this.units[0].unit.offset);
  
        if (prefixValue == undefined) {
          return subtract(divide(divide(value, unitValue), unitPrefixValue), unitOffset);
        }
        else {
          return subtract(divide(divide(value, unitValue), prefixValue), unitOffset);
        }
      }
    };
  
    /**
     * Find a unit from a string
     * @memberof Unit
     * @param {string} str              A string like 'cm' or 'inch'
     * @returns {Object | null} result  When found, an object with fields unit and
     *                                  prefix is returned. Else, null is returned.
     * @private
     */
    function _findUnit(str) {
      for (var name in UNITS) {
        if (UNITS.hasOwnProperty(name)) {
          if (endsWith(str, name)) {
            var unit = UNITS[name];
            var prefixLen = (str.length - name.length);
            var prefixName = str.substring(0, prefixLen);
            var prefix = unit.prefixes[prefixName];
            if (prefix !== undefined) {
              // store unit, prefix, and value
              return {
                unit: unit,
                prefix: prefix
              };
            }
          }
        }
      }
  
      return null;
    }
  
    /**
     * Test if the given expression is a unit.
     * The unit can have a prefix but cannot have a value.
     * @memberof Unit
     * @param {string} name   A string to be tested whether it is a value less unit.
     *                        The unit can have prefix, like "cm"
     * @return {boolean}      true if the given string is a unit
     */
    Unit.isValuelessUnit = function (name) {
      return (_findUnit(name) != null);
    };
  
    /**
     * check if this unit has given base unit
     * If this unit is a derived unit, this will ALWAYS return false, since by definition base units are not derived.
     * @memberof Unit
     * @param {BASE_UNITS | string | undefined} base
     */
    Unit.prototype.hasBase = function (base) {
  
      if(typeof(base) === "string") {
        base = BASE_UNITS[base];
      }
  
      if(!base)
        return false;
  
  
      // All dimensions must be the same
      for(var i=0; i<BASE_DIMENSIONS.length; i++) {
        if (Math.abs(this.dimensions[i] - base.dimensions[i]) > 1e-12) {
          return false;
        }
      }
      return true;
  
    };
  
    /**
     * Check if this unit has a base or bases equal to another base or bases
     * For derived units, the exponent on each base also must match
     * @memberof Unit
     * @param {Unit} other
     * @return {boolean} true if equal base
     */
    Unit.prototype.equalBase = function (other) {
      // All dimensions must be the same
      for(var i=0; i<BASE_DIMENSIONS.length; i++) {
        if (Math.abs(this.dimensions[i] - other.dimensions[i]) > 1e-12) {
          return false;
        }
      }
      return true;
    };
  
    /**
     * Check if this unit equals another unit
     * @memberof Unit
     * @param {Unit} other
     * @return {boolean} true if both units are equal
     */
    Unit.prototype.equals = function (other) {
      return (this.equalBase(other) && equal(this.value, other.value));
    };
  
    /**
     * Multiply this unit with another one
     * @memberof Unit
     * @param {Unit} other
     * @return {Unit} product of this unit and the other unit
     */
    Unit.prototype.multiply = function (other) {
      var res = this.clone();
      
      for(var i = 0; i<BASE_DIMENSIONS.length; i++) {
        res.dimensions[i] = this.dimensions[i] + other.dimensions[i];
      }
  
      // Append other's units list onto res (simplify later in Unit.prototype.format)
      for(var i=0; i<other.units.length; i++) {
        var inverted = JSON.parse(JSON.stringify(other.units[i])); 
        res.units.push(inverted);
      }
  
      // If at least one operand has a value, then the result should also have a value
      if(this.value != null || other.value != null) {
        var valThis = this.value == null ? this._normalize(1) : this.value;
        var valOther = other.value == null ? other._normalize(1) : other.value;
        res.value = multiply(valThis, valOther);
      }
      else {
        res.value = null;
      }
  
      // Trigger simplification of the unit list at some future time
      res.isUnitListSimplified = false;
      return res;
    };
  
    /**
     * Divide this unit by another one
     * @memberof Unit
     * @param {Unit} other
     * @return {Unit} result of dividing this unit by the other unit
     */
    Unit.prototype.divide = function (other) {
      var res = this.clone();
      
      for(var i=0; i<BASE_DIMENSIONS.length; i++) {
        res.dimensions[i] = this.dimensions[i] - other.dimensions[i];
      }
  
      // Invert and append other's units list onto res (simplify later in Unit.prototype.format)
      for(var i=0; i<other.units.length; i++) {
        // Clone other's unit
        var inverted = JSON.parse(JSON.stringify(other.units[i])); 
        inverted.power = -inverted.power;
        res.units.push(inverted);
      }
  
      // If at least one operand has a value, the result should have a value
      if (this.value != null || other.value != null) {
        var valThis = this.value == null ? this._normalize(1) : this.value;
        var valOther = other.value == null ? other._normalize(1) : other.value;
        res.value = divide(valThis, valOther);
      }
      else {
        res.value = null;
      }
  
      // Trigger simplification of the unit list at some future time
      res.isUnitListSimplified = false;
      return res;
    };
  
    /**
     * Calculate the power of a unit
     * @memberof Unit
     * @param {number | Fraction | BigNumber} p
     * @returns {Unit}      The result: this^p
     */
    Unit.prototype.pow = function (p) {
      var res = this.clone();
      
      for(var i=0; i<BASE_DIMENSIONS.length; i++) {
        res.dimensions[i] = this.dimensions[i] * p;
      }
  
      // Adjust the power of each unit in the list
      for(var i=0; i<res.units.length; i++) {
        res.units[i].power *= p;
      }
  
      if(res.value != null) {
        res.value = pow(res.value, p);
  
        // only allow numeric output, we don't want to return a Complex number
        //if (!isNumeric(res.value)) {
        //  res.value = NaN;
        //}
        // Update: Complex supported now
      }
      else {
        res.value = null;
      }
  
      // Trigger lazy evaluation of the unit list
      res.isUnitListSimplified = false;
      return res;
    };
  
    /**
     * Calculate the absolute value of a unit
     * @memberof Unit
     * @param {number | Fraction | BigNumber} x
     * @returns {Unit}      The result: |x|, absolute value of x
     */
    Unit.prototype.abs = function () {
      // This gives correct, but unexpected, results for units with an offset.
      // For example, abs(-283.15 degC) = -263.15 degC !!!
      var ret = this.clone();
      ret.value = abs(ret.value);
  
      for(var i in ret.units) {
        if(ret.units[i].unit.name === 'VA' || ret.units[i].unit.name === 'VAR') {
          ret.units[i].unit = UNITS["W"];
        }
      }
  
      return ret;
    };
  
    /**
     * Convert the unit to a specific unit name.
     * @memberof Unit
     * @param {string | Unit} valuelessUnit   A unit without value. Can have prefix, like "cm"
     * @returns {Unit} Returns a clone of the unit with a fixed prefix and unit.
     */
    Unit.prototype.to = function (valuelessUnit) {
      var other;
      var value = this.value == null ? this._normalize(1) : this.value;
      if (typeof valuelessUnit === 'string') {
        //other = new Unit(null, valuelessUnit);
        other = Unit.parse(valuelessUnit);
        if (!this.equalBase(other)) {
          throw new Error('Units do not match');
        }
        if (other.value !== null) {
          throw new Error('Cannot convert to a unit with a value');
        }
  
        other.value = clone(value);
        other.fixPrefix = true;
        other.isUnitListSimplified = true;
        return other;
      }
      else if (valuelessUnit && valuelessUnit.isUnit) {
        if (!this.equalBase(valuelessUnit)) {
          throw new Error('Units do not match');
        }
        if (valuelessUnit.value !== null) {
          throw new Error('Cannot convert to a unit with a value');
        }
        other = valuelessUnit.clone();
        other.value = clone(value);
        other.fixPrefix = true;
        other.isUnitListSimplified = true;
        return other;
      }
      else {
        throw new Error('String or Unit expected as parameter');
      }
    };
  
    /**
     * Return the value of the unit when represented with given valueless unit
     * @memberof Unit
     * @param {string | Unit} valuelessUnit    For example 'cm' or 'inch'
     * @return {number} Returns the unit value as number.
     */
    // TODO: deprecate Unit.toNumber? It's always better to use toNumeric
    Unit.prototype.toNumber = function (valuelessUnit) {
      return toNumber(this.toNumeric(valuelessUnit));
    };
  
    /**
     * Return the value of the unit in the original numeric type
     * @memberof Unit
     * @param {string | Unit} valuelessUnit    For example 'cm' or 'inch'
     * @return {number | BigNumber | Fraction} Returns the unit value
     */
    Unit.prototype.toNumeric = function (valuelessUnit) {
      var other = this.to(valuelessUnit);
      if(other._isDerived()) {
        return other._denormalize(other.value);
      }
      else {
        return other._denormalize(other.value, other.units[0].prefix.value);
      }
    };
  
    /**
     * Get a string representation of the unit.
     * @memberof Unit
     * @return {string}
     */
    Unit.prototype.toString = function () {
      return this.format();
    };
  
    /**
     * Get a JSON representation of the unit
     * @memberof Unit
     * @returns {Object} Returns a JSON object structured as:
     *                   `{"mathjs": "Unit", "value": 2, "unit": "cm", "fixPrefix": false}`
     */
    Unit.prototype.toJSON = function () {
      return {
        mathjs: 'Unit',
        value: this._denormalize(this.value),
        unit: this.formatUnits(),
        fixPrefix: this.fixPrefix
      };
    };
  
    /**
     * Instantiate a Unit from a JSON object
     * @memberof Unit
     * @param {Object} json  A JSON object structured as:
     *                       `{"mathjs": "Unit", "value": 2, "unit": "cm", "fixPrefix": false}`
     * @return {Unit}
     */
    Unit.fromJSON = function (json) {
      var unit = new Unit(json.value, json.unit);
      unit.fixPrefix = json.fixPrefix || false;
      return unit;
    };
  
    /**
     * Returns the string representation of the unit.
     * @memberof Unit
     * @return {string}
     */
    Unit.prototype.valueOf = Unit.prototype.toString;
  
    /**
     * Attempt to simplify the list of units for this unit according to the dimensions array and the current unit system. After the call, this Unit will contain a list of the "best" units for formatting.
     * Intended to be evaluated lazily. You must set isUnitListSimplified = false before the call! After the call, isUnitListSimplified will be set to true.
     */
    Unit.prototype.simplifyUnitListLazy = function() {
  
      if (this.isUnitListSimplified || this.value == null) {
        return;
      }
  
      var proposedUnitList = [];
  
      // Search for a matching base
      var matchingBase;
      for(var key in currentUnitSystem) {
        if(this.hasBase(BASE_UNITS[key])) {
          matchingBase = key;
          break;
        }
      }
  
      if(matchingBase === 'NONE')
      {
        this.units = [];
      }
      else {
        var matchingUnit;
        if(matchingBase) {
          // Does the unit system have a matching unit?
          if(currentUnitSystem.hasOwnProperty(matchingBase)) {
            matchingUnit = currentUnitSystem[matchingBase]
          }
        }
  
        var value;
        var str;
        if(matchingUnit) {
          this.units = [{
            unit: matchingUnit.unit,
            prefix: matchingUnit.prefix,
            power: 1.0
          }];
        }
        else {
          // Multiple units or units with powers are formatted like this:
          // 5 (kg m^2) / (s^3 mol)
          // Build an representation from the base units of the current unit system
          for(var i=0; i<BASE_DIMENSIONS.length; i++) {
            var baseDim = BASE_DIMENSIONS[i];
            if(Math.abs(this.dimensions[i]) > 1e-12) {
              proposedUnitList.push({
                unit: currentUnitSystem[baseDim].unit,
                prefix: currentUnitSystem[baseDim].prefix,
                power: this.dimensions[i]
              });
            }
          }
  
          // Is the proposed unit list "simpler" than the existing one?
          if(proposedUnitList.length < this.units.length) {
            // Replace this unit list with the proposed list
            this.units = proposedUnitList;
          }
        }
      }
  
      this.isUnitListSimplified = true;
    };
  
    /**
     * Get a string representation of the units of this Unit, without the value.
     * @memberof Unit
     * @return {string}
     */
    Unit.prototype.formatUnits = function () {
  
      // Lazy evaluation of the unit list
      this.simplifyUnitListLazy();
  
      var strNum = "";
      var strDen = "";
      var nNum = 0;
      var nDen = 0;
  
      for(var i=0; i<this.units.length; i++) {
        if(this.units[i].power > 0) {
          nNum++;
          strNum += " " + this.units[i].prefix.name + this.units[i].unit.name;
          if(Math.abs(this.units[i].power - 1.0) > 1e-15) {
            strNum += "^" + this.units[i].power;
          }
        }
        else if(this.units[i].power < 0) {
          nDen++;
        }
      }
  
      if(nDen > 0) {
        for(var i=0; i<this.units.length; i++) {
          if(this.units[i].power < 0) {
            if(nNum > 0) {
              strDen += " " + this.units[i].prefix.name + this.units[i].unit.name;
              if(Math.abs(this.units[i].power + 1.0) > 1e-15) {
                strDen += "^" + (-this.units[i].power);
              }
            }
            else {
              strDen += " " + this.units[i].prefix.name + this.units[i].unit.name;
              strDen += "^" + (this.units[i].power);
            }
          }
        }
      }
      // Remove leading " "
      strNum = strNum.substr(1);
      strDen = strDen.substr(1);
  
      // Add parans for better copy/paste back into the eval, for example, or for better pretty print formatting
      if(nNum > 1 && nDen > 0) {
        strNum = "(" + strNum + ")";
      }
      if(nDen > 1 && nNum > 0) {
        strDen = "(" + strDen + ")";
      }
  
      var str = strNum;
      if(nNum > 0 && nDen > 0) {
        str += " / ";
      }
      str += strDen;
  
      return str;
    };
  
    /**
     * Get a string representation of the Unit, with optional formatting options.
     * @memberof Unit
     * @param {Object | number | Function} [options]  Formatting options. See
     *                                                lib/utils/number:format for a
     *                                                description of the available
     *                                                options.
     * @return {string}
     */
    Unit.prototype.format = function (options) {
  
      // Simplfy the unit list, if necessary
      this.simplifyUnitListLazy();
  
      // Apply some custom logic for handling VA and VAR. The goal is to express the value of the unit as a real value, if possible. Otherwise, use a real-valued unit instead of a complex-valued one.
      var isImaginary = false;
      var isReal = true;
      if(typeof(this.value) !== 'undefined' && this.value !== null && this.value.isComplex) {
        // TODO: Make this better, for example, use relative magnitude of re and im rather than absolute
        isImaginary = Math.abs(this.value.re) < 1e-14;
        isReal = Math.abs(this.value.im) < 1e-14;
      }
      
      for(var i in this.units) {
        if(this.units[i].unit) {
          if(this.units[i].unit.name === 'VA' && isImaginary) {
            this.units[i].unit = UNITS["VAR"];
          }
          else if(this.units[i].unit.name === 'VAR' && !isImaginary) {
            this.units[i].unit = UNITS["VA"];
          }
        }
      }
  
  
      // Now apply the best prefix
      // Units must have only one unit and not have the fixPrefix flag set
      if (this.units.length === 1 && !this.fixPrefix) {
        // Units must have integer powers, otherwise the prefix will change the
        // outputted value by not-an-integer-power-of-ten
        if (Math.abs(this.units[0].power - Math.round(this.units[0].power)) < 1e-14) {
          // Apply the best prefix
          this.units[0].prefix = this._bestPrefix();
        }
      }
  
      var value = this._denormalize(this.value);
      var str = (this.value !== null) ? format(value, options || {}) : '';
      var unitStr = this.formatUnits();
      if(this.value && this.value.isComplex) {
        str = "(" + str + ")";    // Surround complex values with ( ) to enable better parsing 
      }
      if(unitStr.length > 0 && str.length > 0) {
        str += " ";
      }
      str += unitStr;
  
      return str;
    };
  
    /**
     * Calculate the best prefix using current value.
     * @memberof Unit
     * @returns {Object} prefix
     * @private
     */
    Unit.prototype._bestPrefix = function () {
      if (this.units.length !== 1) {
        throw new Error("Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!");
      }
      if (Math.abs(this.units[0].power - Math.round(this.units[0].power)) >= 1e-14) {
        throw new Error("Can only compute the best prefix for single units with integer powers, like kg, s^2, N^-1, and so forth!");
      }
  
      // find the best prefix value (resulting in the value of which
      // the absolute value of the log10 is closest to zero,
      // though with a little offset of 1.2 for nicer values: you get a
      // sequence 1mm 100mm 500mm 0.6m 1m 10m 100m 500m 0.6km 1km ...
  
      // Note: the units value can be any numeric type, but to find the best
      // prefix it's enough to work with limited precision of a regular number
      // Update: using mathjs abs since we also allow complex numbers
      var absValue = abs(this.value);
      var absUnitValue = abs(this.units[0].unit.value);
      var bestPrefix = this.units[0].prefix;
      if (absValue === 0) {
        return bestPrefix;
      }
      var power = this.units[0].power;
      var bestDiff = Math.abs(
          Math.log(absValue / Math.pow(bestPrefix.value * absUnitValue, power)) / Math.LN10 - 1.2);
  
      var prefixes = this.units[0].unit.prefixes;
      for (var p in prefixes) {
        if (prefixes.hasOwnProperty(p)) {
          var prefix = prefixes[p];
          if (prefix.scientific) {
  
            var diff = Math.abs(
                Math.log(absValue / Math.pow(prefix.value * absUnitValue, power)) / Math.LN10 - 1.2);
  
            if (diff < bestDiff
                || (diff === bestDiff && prefix.name.length < bestPrefix.name.length)) {
                  // choose the prefix with the smallest diff, or if equal, choose the one
                  // with the shortest name (can happen with SHORTLONG for example)
                  bestPrefix = prefix;
                  bestDiff = diff;
            }
          }
        }
      }
  
      return bestPrefix;
    };
  
    var PREFIXES = {
      NONE: {
        '': {name: '', value: 1, scientific: true}
      },
      SHORT: {
        '': {name: '', value: 1, scientific: true},
  
        'da': {name: 'da', value: 1e1, scientific: false},
        'h': {name: 'h', value: 1e2, scientific: false},
        'k': {name: 'k', value: 1e3, scientific: true},
        'M': {name: 'M', value: 1e6, scientific: true},
        'G': {name: 'G', value: 1e9, scientific: true},
        'T': {name: 'T', value: 1e12, scientific: true},
        'P': {name: 'P', value: 1e15, scientific: true},
        'E': {name: 'E', value: 1e18, scientific: true},
        'Z': {name: 'Z', value: 1e21, scientific: true},
        'Y': {name: 'Y', value: 1e24, scientific: true},
  
        'd': {name: 'd', value: 1e-1, scientific: false},
        'c': {name: 'c', value: 1e-2, scientific: false},
        'm': {name: 'm', value: 1e-3, scientific: true},
        'u': {name: 'u', value: 1e-6, scientific: true},
        'n': {name: 'n', value: 1e-9, scientific: true},
        'p': {name: 'p', value: 1e-12, scientific: true},
        'f': {name: 'f', value: 1e-15, scientific: true},
        'a': {name: 'a', value: 1e-18, scientific: true},
        'z': {name: 'z', value: 1e-21, scientific: true},
        'y': {name: 'y', value: 1e-24, scientific: true}
      },
      LONG: {
        '': {name: '', value: 1, scientific: true},
  
        'deca': {name: 'deca', value: 1e1, scientific: false},
        'hecto': {name: 'hecto', value: 1e2, scientific: false},
        'kilo': {name: 'kilo', value: 1e3, scientific: true},
        'mega': {name: 'mega', value: 1e6, scientific: true},
        'giga': {name: 'giga', value: 1e9, scientific: true},
        'tera': {name: 'tera', value: 1e12, scientific: true},
        'peta': {name: 'peta', value: 1e15, scientific: true},
        'exa': {name: 'exa', value: 1e18, scientific: true},
        'zetta': {name: 'zetta', value: 1e21, scientific: true},
        'yotta': {name: 'yotta', value: 1e24, scientific: true},
  
        'deci': {name: 'deci', value: 1e-1, scientific: false},
        'centi': {name: 'centi', value: 1e-2, scientific: false},
        'milli': {name: 'milli', value: 1e-3, scientific: true},
        'micro': {name: 'micro', value: 1e-6, scientific: true},
        'nano': {name: 'nano', value: 1e-9, scientific: true},
        'pico': {name: 'pico', value: 1e-12, scientific: true},
        'femto': {name: 'femto', value: 1e-15, scientific: true},
        'atto': {name: 'atto', value: 1e-18, scientific: true},
        'zepto': {name: 'zepto', value: 1e-21, scientific: true},
        'yocto': {name: 'yocto', value: 1e-24, scientific: true}
      },
      SQUARED: {
        '': {name: '', value: 1, scientific: true},
  
        'da': {name: 'da', value: 1e2, scientific: false},
        'h': {name: 'h', value: 1e4, scientific: false},
        'k': {name: 'k', value: 1e6, scientific: true},
        'M': {name: 'M', value: 1e12, scientific: true},
        'G': {name: 'G', value: 1e18, scientific: true},
        'T': {name: 'T', value: 1e24, scientific: true},
        'P': {name: 'P', value: 1e30, scientific: true},
        'E': {name: 'E', value: 1e36, scientific: true},
        'Z': {name: 'Z', value: 1e42, scientific: true},
        'Y': {name: 'Y', value: 1e48, scientific: true},
  
        'd': {name: 'd', value: 1e-2, scientific: false},
        'c': {name: 'c', value: 1e-4, scientific: false},
        'm': {name: 'm', value: 1e-6, scientific: true},
        'u': {name: 'u', value: 1e-12, scientific: true},
        'n': {name: 'n', value: 1e-18, scientific: true},
        'p': {name: 'p', value: 1e-24, scientific: true},
        'f': {name: 'f', value: 1e-30, scientific: true},
        'a': {name: 'a', value: 1e-36, scientific: true},
        'z': {name: 'z', value: 1e-42, scientific: true},
        'y': {name: 'y', value: 1e-48, scientific: true}
      },
      CUBIC: {
        '': {name: '', value: 1, scientific: true},
  
        'da': {name: 'da', value: 1e3, scientific: false},
        'h': {name: 'h', value: 1e6, scientific: false},
        'k': {name: 'k', value: 1e9, scientific: true},
        'M': {name: 'M', value: 1e18, scientific: true},
        'G': {name: 'G', value: 1e27, scientific: true},
        'T': {name: 'T', value: 1e36, scientific: true},
        'P': {name: 'P', value: 1e45, scientific: true},
        'E': {name: 'E', value: 1e54, scientific: true},
        'Z': {name: 'Z', value: 1e63, scientific: true},
        'Y': {name: 'Y', value: 1e72, scientific: true},
  
        'd': {name: 'd', value: 1e-3, scientific: false},
        'c': {name: 'c', value: 1e-6, scientific: false},
        'm': {name: 'm', value: 1e-9, scientific: true},
        'u': {name: 'u', value: 1e-18, scientific: true},
        'n': {name: 'n', value: 1e-27, scientific: true},
        'p': {name: 'p', value: 1e-36, scientific: true},
        'f': {name: 'f', value: 1e-45, scientific: true},
        'a': {name: 'a', value: 1e-54, scientific: true},
        'z': {name: 'z', value: 1e-63, scientific: true},
        'y': {name: 'y', value: 1e-72, scientific: true}
      },
      BINARY_SHORT: {
        '': {name: '', value: 1, scientific: true},
        'k': {name: 'k', value: 1e3, scientific: true},
        'M': {name: 'M', value: 1e6, scientific: true},
        'G': {name: 'G', value: 1e9, scientific: true},
        'T': {name: 'T', value: 1e12, scientific: true},
        'P': {name: 'P', value: 1e15, scientific: true},
        'E': {name: 'E', value: 1e18, scientific: true},
        'Z': {name: 'Z', value: 1e21, scientific: true},
        'Y': {name: 'Y', value: 1e24, scientific: true},
  
        'Ki': {name: 'Ki', value: 1024, scientific: true},
        'Mi': {name: 'Mi', value: Math.pow(1024, 2), scientific: true},
        'Gi': {name: 'Gi', value: Math.pow(1024, 3), scientific: true},
        'Ti': {name: 'Ti', value: Math.pow(1024, 4), scientific: true},
        'Pi': {name: 'Pi', value: Math.pow(1024, 5), scientific: true},
        'Ei': {name: 'Ei', value: Math.pow(1024, 6), scientific: true},
        'Zi': {name: 'Zi', value: Math.pow(1024, 7), scientific: true},
        'Yi': {name: 'Yi', value: Math.pow(1024, 8), scientific: true}
      },
      BINARY_LONG: {
        '': {name: '', value: 1, scientific: true},
        'kilo': {name: 'kilo', value: 1e3, scientific: true},
        'mega': {name: 'mega', value: 1e6, scientific: true},
        'giga': {name: 'giga', value: 1e9, scientific: true},
        'tera': {name: 'tera', value: 1e12, scientific: true},
        'peta': {name: 'peta', value: 1e15, scientific: true},
        'exa': {name: 'exa', value: 1e18, scientific: true},
        'zetta': {name: 'zetta', value: 1e21, scientific: true},
        'yotta': {name: 'yotta', value: 1e24, scientific: true},
  
        'kibi': {name: 'kibi', value: 1024, scientific: true},
        'mebi': {name: 'mebi', value: Math.pow(1024, 2), scientific: true},
        'gibi': {name: 'gibi', value: Math.pow(1024, 3), scientific: true},
        'tebi': {name: 'tebi', value: Math.pow(1024, 4), scientific: true},
        'pebi': {name: 'pebi', value: Math.pow(1024, 5), scientific: true},
        'exi': {name: 'exi', value: Math.pow(1024, 6), scientific: true},
        'zebi': {name: 'zebi', value: Math.pow(1024, 7), scientific: true},
        'yobi': {name: 'yobi', value: Math.pow(1024, 8), scientific: true}
      },
      BTU: {
        '':   {name: '',   value: 1,   scientific: true},
        'MM': {name: 'MM', value: 1e6, scientific: true}
      }
    };
  
    // Add a prefix list for both short and long prefixes (for ohm in particular, since Mohm and megaohm are both acceptable):
    PREFIXES.SHORTLONG = {};
    for (var key in PREFIXES.SHORT) {
      if(PREFIXES.SHORT.hasOwnProperty(key)) {
        PREFIXES.SHORTLONG[key] = PREFIXES.SHORT[key];
      }
    }
    for (var key in PREFIXES.LONG) {
      if(PREFIXES.LONG.hasOwnProperty(key)) {
        PREFIXES.SHORTLONG[key] = PREFIXES.LONG[key];
      }
    }
  
    /* Internally, each unit is represented by a value and a dimension array. The elements of the dimensions array have the following meaning:
     * Index  Dimension
     * -----  ---------
     *   0    Length
     *   1    Mass
     *   2    Time
     *   3    Current
     *   4    Temperature
     *   5    Luminous intensity
     *   6    Amount of substance
     *   7    Angle
     *   8    Bit (digital)
     * For example, the unit "298.15 K" is a pure temperature and would have a value of 298.15 and a dimension array of [0, 0, 0, 0, 1, 0, 0, 0, 0]. The unit "1 cal / (gm °C)" can be written in terms of the 9 fundamental dimensions as [length^2] / ([time^2] * [temperature]), and would a value of (after conversion to SI) 4184.0 and a dimensions array of [2, 0, -2, 0, -1, 0, 0, 0, 0].
     *
     */
  
    var BASE_DIMENSIONS = ["MASS", "LENGTH", "TIME", "CURRENT", "TEMPERATURE", "LUMINOUS_INTENSITY", "AMOUNT_OF_SUBSTANCE", "ANGLE", "BIT"];
  
    var BASE_UNITS = {
      NONE: {
        dimensions: [0, 0, 0, 0, 0, 0, 0, 0, 0]
      },
      MASS: {
        dimensions: [1, 0, 0, 0, 0, 0, 0, 0, 0]
      },
      LENGTH: {
        dimensions: [0, 1, 0, 0, 0, 0, 0, 0, 0]
      },
      TIME: {
        dimensions: [0, 0, 1, 0, 0, 0, 0, 0, 0]
      },
      CURRENT: {
        dimensions: [0, 0, 0, 1, 0, 0, 0, 0, 0]
      },
      TEMPERATURE: {
        dimensions: [0, 0, 0, 0, 1, 0, 0, 0, 0]
      },
      LUMINOUS_INTENSITY: {
        dimensions: [0, 0, 0, 0, 0, 1, 0, 0, 0]
      },
      AMOUNT_OF_SUBSTANCE: {
        dimensions: [0, 0, 0, 0, 0, 0, 1, 0, 0]
      },
  
      FORCE: {
        dimensions: [1, 1, -2, 0, 0, 0, 0, 0, 0]
      },
      SURFACE: {
        dimensions: [0, 2, 0, 0, 0, 0, 0, 0, 0]
      },
      VOLUME: {
        dimensions: [0, 3, 0, 0, 0, 0, 0, 0, 0]
      },
      ENERGY: {
        dimensions: [1, 2, -2, 0, 0, 0, 0, 0, 0]
      },
      POWER: {
        dimensions: [1, 2, -3, 0, 0, 0, 0, 0, 0]
      },
      PRESSURE: {
        dimensions: [1, -1, -2, 0, 0, 0, 0, 0, 0]
      },
  
      ELECTRIC_CHARGE: {
        dimensions: [0, 0, 1, 1, 0, 0, 0, 0, 0]
      },
      ELECTRIC_CAPACITANCE: {
        dimensions: [-1, -2, 4, 2, 0, 0, 0, 0, 0]
      },
      ELECTRIC_POTENTIAL: {
        dimensions: [1, 2, -3, -1, 0, 0, 0, 0, 0]
      },
      ELECTRIC_RESISTANCE: {
        dimensions: [1, 2, -3, -2, 0, 0, 0, 0, 0]
      },
      ELECTRIC_INDUCTANCE: {
        dimensions: [1, 2, -2, -2, 0, 0, 0, 0, 0]
      },
      ELECTRIC_CONDUCTANCE: {
        dimensions: [-1, -2, 3, 2, 0, 0, 0, 0, 0]
      },
      MAGNETIC_FLUX: {
        dimensions: [1, 2, -2, -1, 0, 0, 0, 0, 0]
      },
      MAGNETIC_FLUX_DENSITY: {
        dimensions: [1, 0, -2, -1, 0, 0, 0, 0, 0]
      },
  
      FREQUENCY: {
        dimensions: [0, 0, -1, 0, 0, 0, 0, 0, 0]
      },
      ANGLE: {
        dimensions: [0, 0, 0, 0, 0, 0, 0, 1, 0]
      },
      BIT: {
        dimensions: [0, 0, 0, 0, 0, 0, 0, 0, 1]
      }
    };
  
    for(var key in BASE_UNITS) {
      BASE_UNITS[key].key = key;
    }
  
    var BASE_UNIT_NONE = {};
  
    var UNIT_NONE = {name: '', base: BASE_UNIT_NONE, value: 1, offset: 0, dimensions: [0,0,0,0,0,0,0,0,0]};
  
    var UNITS = {
      // length
      meter: {
        name: 'meter',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      inch: {
        name: 'inch',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 0.0254,
        offset: 0
      },
      foot: {
        name: 'foot',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 0.3048,
        offset: 0
      },
      yard: {
        name: 'yard',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 0.9144,
        offset: 0
      },
      mile: {
        name: 'mile',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 1609.344,
        offset: 0
      },
      link: {
        name: 'link',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 0.201168,
        offset: 0
      },
      rod: {
        name: 'rod',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 5.029210,
        offset: 0
      },
      chain: {
        name: 'chain',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 20.1168,
        offset: 0
      },
      angstrom: {
        name: 'angstrom',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 1e-10,
        offset: 0
      },
  
      m: {
        name: 'm',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      'in': {
        name: 'in',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 0.0254,
        offset: 0
      },
      ft: {
        name: 'ft',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 0.3048,
        offset: 0
      },
      yd: {
        name: 'yd',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 0.9144,
        offset: 0
      },
      mi: {
        name: 'mi',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 1609.344,
        offset: 0
      },
      li: {
        name: 'li',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 0.201168,
        offset: 0
      },
      rd: {
        name: 'rd',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 5.029210,
        offset: 0
      },
      ch: {
        name: 'ch',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 20.1168,
        offset: 0
      },
      mil: {
        name: 'mil',
        base: BASE_UNITS.LENGTH,
        prefixes: PREFIXES.NONE,
        value: 0.0000254,
        offset: 0
      }, // 1/1000 inch
  
      // Surface
      m2: {
        name: 'm2',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.SQUARED,
        value: 1,
        offset: 0
      },
      sqin: {
        name: 'sqin',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.NONE,
        value: 0.00064516,
        offset: 0
      }, // 645.16 mm2
      sqft: {
        name: 'sqft',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.NONE,
        value: 0.09290304,
        offset: 0
      }, // 0.09290304 m2
      sqyd: {
        name: 'sqyd',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.NONE,
        value: 0.83612736,
        offset: 0
      }, // 0.83612736 m2
      sqmi: {
        name: 'sqmi',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.NONE,
        value: 2589988.110336,
        offset: 0
      }, // 2.589988110336 km2
      sqrd: {
        name: 'sqrd',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.NONE,
        value: 25.29295,
        offset: 0
      }, // 25.29295 m2
      sqch: {
        name: 'sqch',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.NONE,
        value: 404.6873,
        offset: 0
      }, // 404.6873 m2
      sqmil: {
        name: 'sqmil',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.NONE,
        value: 6.4516e-10,
        offset: 0
      }, // 6.4516 * 10^-10 m2
      acre: {
        name: 'acre',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.NONE,
        value: 4046.86,
        offset: 0
      }, // 4046.86 m2
      hectare: {
        name: 'hectare',
        base: BASE_UNITS.SURFACE,
        prefixes: PREFIXES.NONE,
        value: 10000,
        offset: 0
      }, // 10000 m2
  
      // Volume
      m3: {
        name: 'm3',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.CUBIC,
        value: 1,
        offset: 0
      },
      L: {
        name: 'L',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.SHORT,
        value: 0.001,
        offset: 0
      }, // litre
      l: {
        name: 'l',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.SHORT,
        value: 0.001,
        offset: 0
      }, // litre
      litre: {
        name: 'litre',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.LONG,
        value: 0.001,
        offset: 0
      },
      cuin: {
        name: 'cuin',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 1.6387064e-5,
        offset: 0
      }, // 1.6387064e-5 m3
      cuft: {
        name: 'cuft',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.028316846592,
        offset: 0
      }, // 28.316 846 592 L
      cuyd: {
        name: 'cuyd',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.764554857984,
        offset: 0
      }, // 764.554 857 984 L
      teaspoon: {
        name: 'teaspoon',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.000005,
        offset: 0
      }, // 5 mL
      tablespoon: {
        name: 'tablespoon',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.000015,
        offset: 0
      }, // 15 mL
      //{name: 'cup', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.000240, offset: 0}, // 240 mL  // not possible, we have already another cup
      drop: {
        name: 'drop',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 5e-8,
        offset: 0
      },  // 0.05 mL = 5e-8 m3
      gtt: {
        name: 'gtt',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 5e-8,
        offset: 0
      },  // 0.05 mL = 5e-8 m3
  
      // Liquid volume
      minim: {
        name: 'minim',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.00000006161152,
        offset: 0
      }, // 0.06161152 mL
      fluiddram: {
        name: 'fluiddram',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0000036966911,
        offset: 0
      },  // 3.696691 mL
      fluidounce: {
        name: 'fluidounce',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.00002957353,
        offset: 0
      }, // 29.57353 mL
      gill: {
        name: 'gill',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0001182941,
        offset: 0
      }, // 118.2941 mL
      cc: {
        name: 'cc',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 1e-6,
        offset: 0
      }, // 1e-6 L
      cup: {
        name: 'cup',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0002365882,
        offset: 0
      }, // 236.5882 mL
      pint: {
        name: 'pint',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0004731765,
        offset: 0
      }, // 473.1765 mL
      quart: {
        name: 'quart',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0009463529,
        offset: 0
      }, // 946.3529 mL
      gallon: {
        name: 'gallon',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.003785412,
        offset: 0
      }, // 3.785412 L
      beerbarrel: {
        name: 'beerbarrel',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.1173478,
        offset: 0
      }, // 117.3478 L
      oilbarrel: {
        name: 'oilbarrel',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.1589873,
        offset: 0
      }, // 158.9873 L
      hogshead: {
        name: 'hogshead',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.2384810,
        offset: 0
      }, // 238.4810 L
  
      //{name: 'min', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.00000006161152, offset: 0}, // 0.06161152 mL // min is already in use as minute
      fldr: {
        name: 'fldr',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0000036966911,
        offset: 0
      },  // 3.696691 mL
      floz: {
        name: 'floz',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.00002957353,
        offset: 0
      }, // 29.57353 mL
      gi: {
        name: 'gi',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0001182941,
        offset: 0
      }, // 118.2941 mL
      cp: {
        name: 'cp',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0002365882,
        offset: 0
      }, // 236.5882 mL
      pt: {
        name: 'pt',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0004731765,
        offset: 0
      }, // 473.1765 mL
      qt: {
        name: 'qt',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.0009463529,
        offset: 0
      }, // 946.3529 mL
      gal: {
        name: 'gal',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.003785412,
        offset: 0
      }, // 3.785412 L
      bbl: {
        name: 'bbl',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.1173478,
        offset: 0
      }, // 117.3478 L
      obl: {
        name: 'obl',
        base: BASE_UNITS.VOLUME,
        prefixes: PREFIXES.NONE,
        value: 0.1589873,
        offset: 0
      }, // 158.9873 L
      //{name: 'hogshead', base: BASE_UNITS.VOLUME, prefixes: PREFIXES.NONE, value: 0.2384810, offset: 0}, // 238.4810 L // TODO: hh?
  
      // Mass
      g: {
        name: 'g',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.SHORT,
        value: 0.001,
        offset: 0
      },
      gram: {
        name: 'gram',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.LONG,
        value: 0.001,
        offset: 0
      },
  
      ton: {
        name: 'ton',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.SHORT,
        value: 907.18474,
        offset: 0
      },
      tonne: {
        name: 'tonne',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.SHORT,
        value: 1000,
        offset: 0
      },
  
      grain: {
        name: 'grain',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 64.79891e-6,
        offset: 0
      },
      dram: {
        name: 'dram',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 1.7718451953125e-3,
        offset: 0
      },
      ounce: {
        name: 'ounce',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 28.349523125e-3,
        offset: 0
      },
      poundmass: {
        name: 'poundmass',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 453.59237e-3,
        offset: 0
      },
      hundredweight: {
        name: 'hundredweight',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 45.359237,
        offset: 0
      },
      stick: {
        name: 'stick',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 115e-3,
        offset: 0
      },
      stone: {
        name: 'stone',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 6.35029318,
        offset: 0
      },
  
      gr: {
        name: 'gr',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 64.79891e-6,
        offset: 0
      },
      dr: {
        name: 'dr',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 1.7718451953125e-3,
        offset: 0
      },
      oz: {
        name: 'oz',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 28.349523125e-3,
        offset: 0
      },
      lbm: {
        name: 'lbm',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 453.59237e-3,
        offset: 0
      },
      cwt: {
        name: 'cwt',
        base: BASE_UNITS.MASS,
        prefixes: PREFIXES.NONE,
        value: 45.359237,
        offset: 0
      },
  
      // Time
      s: {
        name: 's',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      min: {
        name: 'min',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 60,
        offset: 0
      },
      h: {
        name: 'h',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 3600,
        offset: 0
      },
      second: {
        name: 'second',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      sec: {
        name: 'sec',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      minute: {
        name: 'minute',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 60,
        offset: 0
      },
      hour: {
        name: 'hour',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 3600,
        offset: 0
      },
      day: {
        name: 'day',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 86400,
        offset: 0
      },
      week: {
        name: 'week',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 7*86400,
        offset: 0
      },
      month: {
        name: 'month',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 2629800, //1/12th of Julian year
        offset: 0
      },
      year: {
        name: 'year',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 31557600, //Julian year
        offset: 0
      },
      decade: {
        name: 'year',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 315576000, //Julian decade
        offset: 0
      },
      century: {
        name: 'century',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 3155760000, //Julian century
        offset: 0
      },
      millennium: {
        name: 'millennium',
        base: BASE_UNITS.TIME,
        prefixes: PREFIXES.NONE,
        value: 31557600000, //Julian millennium
        offset: 0
      },
  
      // Frequency
      hertz: {
        name: 'Hertz',
        base: BASE_UNITS.FREQUENCY,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0,
        reciprocal: true
      },
      Hz: {
        name: 'Hz',
        base: BASE_UNITS.FREQUENCY,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0,
        reciprocal: true
      },
  
      // Angle
      rad: {
        name: 'rad',
        base: BASE_UNITS.ANGLE,
        prefixes: PREFIXES.NONE,
        value: 1,
        offset: 0
      },
      // deg = rad / (2*pi) * 360 = rad / 0.017453292519943295769236907684888
      deg: {
        name: 'deg',
        base: BASE_UNITS.ANGLE,
        prefixes: PREFIXES.NONE,
        value: null, // will be filled in by calculateAngleValues()
        offset: 0
      },
      // grad = rad / (2*pi) * 400  = rad / 0.015707963267948966192313216916399
      grad: {
        name: 'grad',
        base: BASE_UNITS.ANGLE,
        prefixes: PREFIXES.NONE,
        value: null, // will be filled in by calculateAngleValues()
        offset: 0
      },
      // cycle = rad / (2*pi) = rad / 6.2831853071795864769252867665793
      cycle: {
        name: 'cycle',
        base: BASE_UNITS.ANGLE,
        prefixes: PREFIXES.NONE,
        value: null, // will be filled in by calculateAngleValues()
        offset: 0
      },
      // arcsec = rad / (3600 * (360 / 2 * pi)) = rad / 0.0000048481368110953599358991410235795
      arcsec: {
        name: 'arcsec',
        base: BASE_UNITS.ANGLE,
        prefixes: PREFIXES.NONE,
        value: null, // will be filled in by calculateAngleValues()
        offset: 0
      },
      // arcmin = rad / (60 * (360 / 2 * pi)) = rad / 0.00029088820866572159615394846141477
      arcmin: {
        name: 'arcmin',
        base: BASE_UNITS.ANGLE,
        prefixes: PREFIXES.NONE,
        value: null, // will be filled in by calculateAngleValues()
        offset: 0
      },
      
      // Electric current
      A: {
        name: 'A',
        base: BASE_UNITS.CURRENT,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      ampere: {
        name: 'ampere',
        base: BASE_UNITS.CURRENT,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
  
      // Temperature
      // K(C) = °C + 273.15
      // K(F) = (°F + 459.67) / 1.8
      // K(R) = °R / 1.8
      K: {
        name: 'K',
        base: BASE_UNITS.TEMPERATURE,
        prefixes: PREFIXES.NONE,
        value: 1,
        offset: 0
      },
      degC: {
        name: 'degC',
        base: BASE_UNITS.TEMPERATURE,
        prefixes: PREFIXES.NONE,
        value: 1,
        offset: 273.15
      },
      degF: {
        name: 'degF',
        base: BASE_UNITS.TEMPERATURE,
        prefixes: PREFIXES.NONE,
        value: 1 / 1.8,
        offset: 459.67
      },
      degR: {
        name: 'degR',
        base: BASE_UNITS.TEMPERATURE,
        prefixes: PREFIXES.NONE,
        value: 1 / 1.8,
        offset: 0
      },
      kelvin: {
        name: 'kelvin',
        base: BASE_UNITS.TEMPERATURE,
        prefixes: PREFIXES.NONE,
        value: 1,
        offset: 0
      },
      celsius: {
        name: 'celsius',
        base: BASE_UNITS.TEMPERATURE,
        prefixes: PREFIXES.NONE,
        value: 1,
        offset: 273.15
      },
      fahrenheit: {
        name: 'fahrenheit',
        base: BASE_UNITS.TEMPERATURE,
        prefixes: PREFIXES.NONE,
        value: 1 / 1.8,
        offset: 459.67
      },
      rankine: {
        name: 'rankine',
        base: BASE_UNITS.TEMPERATURE,
        prefixes: PREFIXES.NONE,
        value: 1 / 1.8,
        offset: 0
      },
  
      // amount of substance
      mol: {
        name: 'mol',
        base: BASE_UNITS.AMOUNT_OF_SUBSTANCE,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      mole: {
        name: 'mole',
        base: BASE_UNITS.AMOUNT_OF_SUBSTANCE,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
  
      // luminous intensity
      cd: {
        name: 'cd',
        base: BASE_UNITS.LUMINOUS_INTENSITY,
        prefixes: PREFIXES.NONE,
        value: 1,
        offset: 0
      },
      candela: {
        name: 'candela',
        base: BASE_UNITS.LUMINOUS_INTENSITY,
        prefixes: PREFIXES.NONE,
        value: 1,
        offset: 0
      },
      // TODO: units STERADIAN
      //{name: 'sr', base: BASE_UNITS.STERADIAN, prefixes: PREFIXES.NONE, value: 1, offset: 0},
      //{name: 'steradian', base: BASE_UNITS.STERADIAN, prefixes: PREFIXES.NONE, value: 1, offset: 0},
  
      // Force
      N: {
        name: 'N',
        base: BASE_UNITS.FORCE,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      newton: {
        name: 'newton',
        base: BASE_UNITS.FORCE,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      dyn: {
        name: 'dyn',
        base: BASE_UNITS.FORCE,
        prefixes: PREFIXES.SHORT,
        value: 0.00001,
        offset: 0
      },
      dyne: {
        name: 'dyne',
        base: BASE_UNITS.FORCE,
        prefixes: PREFIXES.LONG,
        value: 0.00001,
        offset: 0
      },
      lbf: {
        name: 'lbf',
        base: BASE_UNITS.FORCE,
        prefixes: PREFIXES.NONE,
        value: 4.4482216152605,
        offset: 0
      },
      poundforce: {
        name: 'poundforce',
        base: BASE_UNITS.FORCE,
        prefixes: PREFIXES.NONE,
        value: 4.4482216152605,
        offset: 0
      },
      kip: {
        name: 'kip',
        base: BASE_UNITS.FORCE,
        prefixes: PREFIXES.LONG,
        value: 4448.2216,
        offset: 0
      },
  	
      // Energy
      J: {
        name: 'J',
        base: BASE_UNITS.ENERGY,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      joule: {
        name: 'joule',
        base: BASE_UNITS.ENERGY,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      erg: {
        name: 'erg',
        base: BASE_UNITS.ENERGY,
        prefixes: PREFIXES.NONE,
        value: 1e-5,
        offset: 0
      },
      Wh: {
        name: 'Wh',
        base: BASE_UNITS.ENERGY,
        prefixes: PREFIXES.SHORT,
        value: 3600,
        offset: 0
      },
      BTU: {
        name: 'BTU',
        base: BASE_UNITS.ENERGY,
        prefixes: PREFIXES.BTU,
        value: 1055.05585262,
        offset: 0
      },
      eV: {
        name: 'eV',
        base: BASE_UNITS.ENERGY,
        prefixes: PREFIXES.SHORT,
        value: 1.602176565e-19,
        offset: 0
      },
      electronvolt: {
        name: 'electronvolt',
        base: BASE_UNITS.ENERGY,
        prefixes: PREFIXES.LONG,
        value: 1.602176565e-19,
        offset: 0
      },
  
  
      // Power
      W: {
        name: 'W',
        base: BASE_UNITS.POWER,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      watt: {
        name: 'W',
        base: BASE_UNITS.POWER,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      hp: {
        name: 'hp',
        base: BASE_UNITS.POWER,
        prefixes: PREFIXES.NONE,
        value: 745.6998715386,
        offset: 0
      },
  
      // Electrical power units
      VAR: {
        name: 'VAR',
        base: BASE_UNITS.POWER,
        prefixes: PREFIXES.SHORT,
        value: Complex.I,
        offset: 0
      },
      
      VA: {
        name: 'VA',
        base: BASE_UNITS.POWER,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
  
      // Pressure
      Pa: {
        name: 'Pa',
        base: BASE_UNITS.PRESSURE,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      psi: {
        name: 'psi',
        base: BASE_UNITS.PRESSURE,
        prefixes: PREFIXES.NONE,
        value: 6894.75729276459,
        offset: 0
      },
      atm: {
        name: 'atm',
        base: BASE_UNITS.PRESSURE,
        prefixes: PREFIXES.NONE,
        value: 101325,
        offset: 0
      },
      bar: {
        name: 'bar',
        base: BASE_UNITS.PRESSURE,
        prefixes: PREFIXES.NONE,
        value: 100000,
        offset: 0
      },
      torr: {
        name: 'torr',
        base: BASE_UNITS.PRESSURE,
        prefixes: PREFIXES.NONE,
        value: 133.322,
        offset: 0
      },
      mmHg: {
        name: 'mmHg',
        base: BASE_UNITS.PRESSURE,
        prefixes: PREFIXES.NONE,
        value: 133.322,
        offset: 0
      },
      mmH2O: {
        name: 'mmH2O',
        base: BASE_UNITS.PRESSURE,
        prefixes: PREFIXES.NONE,
        value: 9.80665,
        offset: 0
      },
      cmH2O: {
        name: 'cmH2O',
        base: BASE_UNITS.PRESSURE,
        prefixes: PREFIXES.NONE,
        value: 98.0665,
        offset: 0
      },
  
      // Electric charge
      coulomb: {
        name: 'coulomb',
        base: BASE_UNITS.ELECTRIC_CHARGE,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      C: {
        name: 'C',
        base: BASE_UNITS.ELECTRIC_CHARGE,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      // Electric capacitance
      farad: {
        name: 'farad',
        base: BASE_UNITS.ELECTRIC_CAPACITANCE,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      F: {
        name: 'F',
        base: BASE_UNITS.ELECTRIC_CAPACITANCE,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      // Electric potential
      volt: {
        name: 'volt',
        base: BASE_UNITS.ELECTRIC_POTENTIAL,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      V: {
        name: 'V',
        base: BASE_UNITS.ELECTRIC_POTENTIAL,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      // Electric resistance
      ohm: {
        name: 'ohm',
        base: BASE_UNITS.ELECTRIC_RESISTANCE,
        prefixes: PREFIXES.SHORTLONG,    // Both Mohm and megaohm are acceptable
        value: 1,
        offset: 0
      },
      /*
       * Unicode breaks in browsers if charset is not specified
      Ω: {
        name: 'Ω',
        base: BASE_UNITS.ELECTRIC_RESISTANCE,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      */
      // Electric inductance
      henry: {
        name: 'henry',
        base: BASE_UNITS.ELECTRIC_INDUCTANCE,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      H: {
        name: 'H',
        base: BASE_UNITS.ELECTRIC_INDUCTANCE,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      // Electric conductance
      siemens: {
        name: 'siemens',
        base: BASE_UNITS.ELECTRIC_CONDUCTANCE,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      S: {
        name: 'S',
        base: BASE_UNITS.ELECTRIC_CONDUCTANCE,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      // Magnetic flux
      weber: {
        name: 'weber',
        base: BASE_UNITS.MAGNETIC_FLUX,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      Wb: {
        name: 'Wb',
        base: BASE_UNITS.MAGNETIC_FLUX,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
      // Magnetic flux density
      tesla: {
        name: 'tesla',
        base: BASE_UNITS.MAGNETIC_FLUX_DENSITY,
        prefixes: PREFIXES.LONG,
        value: 1,
        offset: 0
      },
      T: {
        name: 'T',
        base: BASE_UNITS.MAGNETIC_FLUX_DENSITY,
        prefixes: PREFIXES.SHORT,
        value: 1,
        offset: 0
      },
  
      // Binary
      b: {
        name: 'b',
        base: BASE_UNITS.BIT,
        prefixes: PREFIXES.BINARY_SHORT,
        value: 1,
        offset: 0
      },
      bits: {
        name: 'bits',
        base: BASE_UNITS.BIT,
        prefixes: PREFIXES.BINARY_LONG,
        value: 1,
        offset: 0
      },
      B: {
        name: 'B',
        base: BASE_UNITS.BIT,
        prefixes: PREFIXES.BINARY_SHORT,
        value: 8,
        offset: 0
      },
      bytes: {
        name: 'bytes',
        base: BASE_UNITS.BIT,
        prefixes: PREFIXES.BINARY_LONG,
        value: 8,
        offset: 0
      }
    };
  
    // aliases (formerly plurals)
    var ALIASES = {
      meters: 'meter',
      inches: 'inch',
      feet: 'foot',
      yards: 'yard',
      miles: 'mile',
      links: 'link',
      rods: 'rod',
      chains: 'chain',
      angstroms: 'angstrom',
  
      lt: 'l',
      litres: 'litre',
      liter: 'litre',
      liters: 'litre',
      teaspoons: 'teaspoon',
      tablespoons: 'tablespoon',
      minims: 'minim',
      fluiddrams: 'fluiddram',
      fluidounces: 'fluidounce',
      gills: 'gill',
      cups: 'cup',
      pints: 'pint',
      quarts: 'quart',
      gallons: 'gallon',
      beerbarrels: 'beerbarrel',
      oilbarrels: 'oilbarrel',
      hogsheads: 'hogshead',
      gtts: 'gtt',
  
      grams: 'gram',
      tons: 'ton',
      tonnes: 'tonne',
      grains: 'grain',
      drams: 'dram',
      ounces: 'ounce',
      poundmasses: 'poundmass',
      hundredweights: 'hundredweight',
      sticks: 'stick',
      lb: 'lbm',
      lbs: 'lbm',
  	
      kips: 'kip',
  
      acres: 'acre',
      hectares: 'hectare',
      sqfeet: 'sqft',
      sqyard: 'sqyd',
      sqmile: 'sqmi',
      sqmiles: 'sqmi',
  
      mmhg: 'mmHg',
      mmh2o: 'mmH2O',
      cmh2o: 'cmH2O',
  
      seconds: 'second',
      secs: 'second',
      minutes: 'minute',
      mins: 'minute',
      hours: 'hour',
      hr: 'hour',
      hrs: 'hour',
      days: 'day',
      weeks: 'week',
      months: 'month',
      years: 'year',
  
      hertz: 'hertz',
  
      radians: 'rad',
      degree: 'deg',
      degrees: 'deg',
      gradian: 'grad',
      gradians: 'grad',
      cycles: 'cycle',
      arcsecond: 'arcsec',
      arcseconds: 'arcsec',
      arcminute: 'arcmin',
      arcminutes: 'arcmin',
  
      BTUs: 'BTU',
      watts: 'watt',
      joules: 'joule',
  
      amperes: 'ampere',
      coulombs: 'coulomb',
      volts: 'volt',
      ohms: 'ohm',
      farads: 'farad',
      webers: 'weber',
      teslas: 'tesla',
      electronvolts: 'electronvolt',
      moles: 'mole'
  
    };
  
    /**
     * Calculate the values for the angle units.
     * Value is calculated as number or BigNumber depending on the configuration
     * @param {{number: 'number' | 'BigNumber'}} config
     */
    function calculateAngleValues (config) {
      if (config.number === 'BigNumber') {
        var pi = constants.pi(type.BigNumber);
        UNITS.rad.value = new type.BigNumber(1);
        UNITS.deg.value = pi.div(180);        // 2 * pi / 360;
        UNITS.grad.value = pi.div(200);       // 2 * pi / 400;
        UNITS.cycle.value = pi.times(2);      // 2 * pi
        UNITS.arcsec.value = pi.div(648000);  // 2 * pi / 360 / 3600
        UNITS.arcmin.value = pi.div(10800);   // 2 * pi / 360 / 60
      }
      else { // number
        UNITS.rad.value = 1;
        UNITS.deg.value = Math.PI / 180;        // 2 * pi / 360;
        UNITS.grad.value = Math.PI / 200;       // 2 * pi / 400;
        UNITS.cycle.value = Math.PI * 2;        // 2 * pi
        UNITS.arcsec.value = Math.PI / 648000;  // 2 * pi / 360 / 3600;
        UNITS.arcmin.value = Math.PI / 10800;   // 2 * pi / 360 / 60;
      }
    }
  
    // apply the angle values now
    calculateAngleValues(config);
  
    // recalculate the values on change of configuration
    math.on('config', function (curr, prev) {
      if (curr.number !== prev.number) {
        calculateAngleValues(curr);
      }
    });
  
    /**
     * A unit system is a set of dimensionally independent base units plus a set of derived units, formed by multiplication and division of the base units, that are by convention used with the unit system.
     * A user perhaps could issue a command to select a preferred unit system, or use the default (see below).
     * Auto unit system: The default unit system is updated on the fly anytime a unit is parsed. The corresponding unit in the default unit system is updated, so that answers are given in the same units the user supplies.
     */
    var UNIT_SYSTEMS = {
      si: {
        // Base units
        NONE:                  {unit: UNIT_NONE, prefix: PREFIXES.NONE['']},
        LENGTH:                {unit: UNITS.m,   prefix: PREFIXES.SHORT['']},
        MASS:                  {unit: UNITS.g,   prefix: PREFIXES.SHORT['k']}, 
        TIME:                  {unit: UNITS.s,   prefix: PREFIXES.SHORT['']}, 
        CURRENT:               {unit: UNITS.A,   prefix: PREFIXES.SHORT['']}, 
        TEMPERATURE:           {unit: UNITS.K,   prefix: PREFIXES.SHORT['']}, 
        LUMINOUS_INTENSITY:    {unit: UNITS.cd,  prefix: PREFIXES.SHORT['']}, 
        AMOUNT_OF_SUBSTANCE:   {unit: UNITS.mol, prefix: PREFIXES.SHORT['']}, 
        ANGLE:                 {unit: UNITS.rad, prefix: PREFIXES.SHORT['']}, 
        BIT:                   {unit: UNITS.bit, prefix: PREFIXES.SHORT['']}, 
  
        // Derived units
        FORCE:                 {unit: UNITS.N,   prefix: PREFIXES.SHORT['']}, 
        ENERGY:                {unit: UNITS.J,   prefix: PREFIXES.SHORT['']},
        POWER:                 {unit: UNITS.W,   prefix: PREFIXES.SHORT['']},
        PRESSURE:              {unit: UNITS.Pa,  prefix: PREFIXES.SHORT['']},
        ELECTRIC_CHARGE:       {unit: UNITS.C,   prefix: PREFIXES.SHORT['']},
        ELECTRIC_CAPACITANCE:  {unit: UNITS.F,   prefix: PREFIXES.SHORT['']},
        ELECTRIC_POTENTIAL:    {unit: UNITS.V,   prefix: PREFIXES.SHORT['']},
        ELECTRIC_RESISTANCE:   {unit: UNITS.ohm, prefix: PREFIXES.SHORT['']},
        ELECTRIC_INDUCTANCE:   {unit: UNITS.H,   prefix: PREFIXES.SHORT['']},
        ELECTRIC_CONDUCTANCE:  {unit: UNITS.S,   prefix: PREFIXES.SHORT['']},
        MAGNETIC_FLUX:         {unit: UNITS.Wb,  prefix: PREFIXES.SHORT['']},
        MAGNETIC_FLUX_DENSITY: {unit: UNITS.T,   prefix: PREFIXES.SHORT['']},
        FREQUENCY:             {unit: UNITS.Hz,  prefix: PREFIXES.SHORT['']}
      }
    };
  
    // Clone to create the other unit systems
    UNIT_SYSTEMS.cgs = JSON.parse(JSON.stringify(UNIT_SYSTEMS.si));
    UNIT_SYSTEMS.cgs.LENGTH = {unit: UNITS.m,   prefix: PREFIXES.SHORT['c']};
    UNIT_SYSTEMS.cgs.MASS =   {unit: UNITS.g,   prefix: PREFIXES.SHORT['']};
    UNIT_SYSTEMS.cgs.FORCE =  {unit: UNITS.dyn, prefix: PREFIXES.SHORT['']};
    UNIT_SYSTEMS.cgs.ENERGY = {unit: UNITS.erg, prefix: PREFIXES.NONE['']};
    // there are wholly 4 unique cgs systems for electricity and magnetism,
    // so let's not worry about it unless somebody complains
    
    UNIT_SYSTEMS.us = JSON.parse(JSON.stringify(UNIT_SYSTEMS.si));
    UNIT_SYSTEMS.us.LENGTH =      {unit: UNITS.ft,   prefix: PREFIXES.NONE['']};
    UNIT_SYSTEMS.us.MASS =        {unit: UNITS.lbm,  prefix: PREFIXES.NONE['']};
    UNIT_SYSTEMS.us.TEMPERATURE = {unit: UNITS.degF, prefix: PREFIXES.NONE['']};
    UNIT_SYSTEMS.us.FORCE =       {unit: UNITS.lbf,  prefix: PREFIXES.NONE['']};
    UNIT_SYSTEMS.us.ENERGY =      {unit: UNITS.BTU,  prefix: PREFIXES.BTU['']};
    UNIT_SYSTEMS.us.POWER =       {unit: UNITS.hp,   prefix: PREFIXES.NONE['']};
    UNIT_SYSTEMS.us.PRESSURE =    {unit: UNITS.psi,  prefix: PREFIXES.NONE['']};
  
    // Add additional unit systems here.
  
  
  
    // Choose a unit system to seed the auto unit system.
    UNIT_SYSTEMS.auto = JSON.parse(JSON.stringify(UNIT_SYSTEMS.si));
  
    // Set the current unit system
    var currentUnitSystem = UNIT_SYSTEMS.auto;
  
    /**
     * Set a unit system for formatting derived units.
     * @param {string} [name] The name of the unit system.
     */
    Unit.setUnitSystem = function(name) {
      if(UNIT_SYSTEMS.hasOwnProperty(name)) {
        currentUnitSystem = UNIT_SYSTEMS[name];
      }
      else {
        throw new Error('Unit system ' + name + ' does not exist. Choices are: ' + Object.keys(UNIT_SYSTEMS).join(', '));
      }
    };
  
    /**
     * Return the current unit system.
     * @return {string} The current unit system.
     */
    Unit.getUnitSystem = function() {
      for(var key in UNIT_SYSTEMS) {
        if(UNIT_SYSTEMS[key] === currentUnitSystem) {
          return key;
        }
      }
    };
  
    /**
     * Converters to convert from number to an other numeric type like BigNumber
     * or Fraction
     */
    Unit.typeConverters = {
      BigNumber: function (x) {
        return new type.BigNumber(x + ''); // stringify to prevent constructor error
      },
  
      Fraction: function (x) {
        return new type.Fraction(x);
      },
  
      Complex: function (x) {
        return x;
      },
  
      number: function (x) {
        return x;
      }
    };
  
    /**
     * Retrieve the right convertor function corresponding with the type
     * of provided exampleValue.
     *
     * @param {string} type   A string 'number', 'BigNumber', or 'Fraction'
     *                        In case of an unknown type,
     * @return {Function}
     */
    Unit._getNumberConverter = function (type) {
      if (!Unit.typeConverters[type]) {
        throw new TypeError('Unsupported type "' + type + '"');
      }
  
      return Unit.typeConverters[type];
    };
  
    // Add dimensions to each built-in unit
    for (var key in UNITS) {
      var unit = UNITS[key];
      unit.dimensions = unit.base.dimensions;
    }    
  
    // Create aliases
    for (var name in ALIASES) {
      /* istanbul ignore next (we cannot really test next statement) */
      if (ALIASES.hasOwnProperty(name)) {
        var unit = UNITS[ALIASES[name]];
        var alias = Object.create(unit);
        alias.name = name;
        UNITS[name] = alias;
      }
    }
  
    Unit.PREFIXES = PREFIXES;
    Unit.BASE_UNITS = BASE_UNITS;
    Unit.UNITS = UNITS;
    Unit.UNIT_SYSTEMS = UNIT_SYSTEMS;
  
    return Unit;
  }
  
  exports.name = 'Unit';
  exports.path = 'type';
  exports.factory = factory;
  exports.math = true; // request access to the math namespace
  