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quantities.js
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Numbas.addExtension('quantities',['math','jme','jme-display','js-quantities', 'decimal'],function(quantities) {
var jme = Numbas.jme;
var superscripts = '⁰¹²³⁴⁵⁶⁷⁸⁹';
function superscript(n) {
return (n+'').replace(/\d/g,function(d){ d=parseInt(d); return superscripts[d]; });
}
var TQuantity = function(quantity) {
this.value = quantity;
};
jme.registerType(
TQuantity,
'quantity',
{
'string': function(q) {
return new jme.types.TString(quantity_string(q.value));
}
}
);
jme.display.texOps['quantity'] = function(thing,texArgs) {
if(thing.args[1].tok.type=='string') {
var units = Qty(thing.args[1].tok.value).format(function(s,units) { return tex_units(units) });
return texArgs[0] + ' \\, ' + units;
} else {
return '\\operatorname{quantity} \\left ( '+texArgs.join(' , ')+' \\right )';
}
};
var unit_names = {
'tempC': '°C',
'degC': '°C',
'tempF': '°F',
'degF': '°F',
'tempK': 'K',
'degK': 'K'
}
function fix_unit_name(name) {
return unit_names[name] || name;
}
/** Fix the rendering of a units string, for display in plain text.
* js-quantities writes 'kg^2' as 'kg2', and doesn't expose the output names of units, so we can't write our own formatter
* so instead, assume that digits never appear in the names of units, and apply this regex
*/
function fix_units(units) {
var m = /([^\/]+)?(?:\/(.*))?/.exec(units);
function fix_prod(units) {
var bits = units.split('*').map(function(b) {
return b.replace(/(\D+)(-?\d+)?/g,function(m,name,exponent) {
return fix_unit_name(name)+(exponent ? superscript(exponent) : '');
});
});
return bits.join('⋅');
}
var out = fix_prod(m[1] || '');
if(m[2]) {
out += '/'+fix_prod(m[2]);
}
return out;
}
function plain_units(units) {
return units.replace(/(\D)(-?\d+)/g,function(m,name,exponent) { return fix_unit_name(name)+'^'+exponent; });
}
function tex_units(units) {
units = units.replace(/([a-zA-Z%]+)(\d+)?/g, function(s,name,exponent) {
return '\\text{'+fix_unit_name(name)+(exponent ? superscript(exponent) : '')+'}';
});
units = units.replace(/\*/g,' \\cdot ');
return units;
}
function quantity_string(q,style) {
return q.format(function(scalar,units) {
var scalar_display = Numbas.math.niceDecimal(scalar.toDecimal(),{style:style});
var units_display = fix_units(units);
return scalar_display+(units_display ? ' '+units_display : '');
});
}
function plain_quantity_string(q,style) {
return q.format(function(scalar,units) {
return Numbas.math.niceDecimal(scalar.toDecimal(),{style:style})+' '+plain_units(units);
});
}
jme.display.registerType(TQuantity,{
tex: function(thing,tok,texArgs) {
var texifier = this;
return tok.value.format(function(scalar,units) {
return texifier.number(scalar)+' \\, '+tex_units(units);
});
},
jme: function(tree,tok,bits) {
var scalar = tok.value.format(function(scalar){return scalar.toString();});
var units = tok.value.format(function(scalar,units) { return units.replace(/(\D+?)(\d+)/g,'$1^$2'); });
return 'quantity('+scalar+', "'+jme.escape(units)+'")';
},
displayString: function(tok) {
return quantity_string(tok.value);
}
});
Numbas.util.equalityTests['quantity'] = function(a,b) {
return a.value.isCompatible(b.value) && a.value.eq(b.value);
};
Numbas.jme.tokenComparisons['quantity'] = function(a,b) {
if(!a.value.isCompatible(b.value)) {
return 0;
}
return a.value.gt(b.value) ? 1 : a.value.lt(b.value) ? -1 : 0;
}
var funcObj = jme.funcObj;
var TString = jme.types.TString;
var TNum = jme.types.TNum;
var TDecimal = jme.types.TDecimal;
var TInt = jme.types.TInt;
var TList = jme.types.TList;
var TBool = jme.types.TBool;
function addFunction(name,deps,outtype,fn,options) {
return quantities.scope.addFunction(new funcObj(name,deps,outtype,fn,options));
};
quantities.scope.setVariable('quantity_kinds',jme.wrapValue(Qty.getKinds()));
function unit_quantity(units) {
if(units.match(/^\s*(\d|-)/) && !units.match(/^\s*1\s*\//)) {
throw(new Error("Invalid description of units: "+units));
}
return Qty(1,units);
}
jme.funcSynonyms['qty'] = 'quantity';
addFunction('quantity',[TString],TQuantity,function(q) { return unit_quantity(q); });
addFunction('quantity',[TDecimal,TString],TQuantity,function(n,q) { return unit_quantity(q).mul(n.re); });
addFunction('units_of_kind',[TString],TList,function(kind) {
if(kind=='unitless') {
return [''];
}
var units = Qty.getUnits(kind);
var extras = {
'yank': 'kg*m/s3',
'momentum': 'kg*m',
'angular_momentum': 'kg*m2/s',
'density': 'kg/m3',
'area_density': 'kg/m2',
'radiation_exposure': 'A*s/kg',
'molar_concentration': 'mol/m3',
'elastance': 'kg*m2/A2*s4',
'specific_volume': 'm3/kg',
'snap': 'm/s4',
'jolt': 'm/s3',
'volumetric_flow': 'm3/s',
'wavenumber': '1/m'
}
if(extras[kind]) {
if(!units.contains(extras[kind])) {
units.push(extras[kind]);
}
}
if(units.length) {
var si = Qty(units[0]).toBase().units();
if(!units.contains(si)) {
units.push(si);
}
}
return units.map(function(u){return new TString(u)});
});
addFunction('aliases',[TString],TList,function(unit) { return Qty.getAliases(unit).map(function(u){return new TString(u)}); });
addFunction('compatible',[TQuantity,TQuantity],TBool,function(a,b) { return a.isCompatible(b); });
addFunction('kind',[TQuantity],TString,function(q) { return q.kind() || ''; });
addFunction('unitless',[TQuantity],TBool,function(q) { return q.isUnitless(); });
addFunction('isbase',[TQuantity],TBool,function(q) { return q.isBase(); });
addFunction('tobase',[TQuantity],TQuantity,function(q) { return q.toBase(); });
addFunction('in',[TQuantity,TString],TQuantity,function(q,unit) { return q.to(unit); });
addFunction('in',[TQuantity,TQuantity],TQuantity,function(q,unit) { return q.to(unit); });
addFunction('inverse',[TQuantity],TQuantity,function(q) { return q.inverse(); });
addFunction('same',[TQuantity,TQuantity],TBool,function(a,b) { return a.same(b); });
addFunction('<',[TQuantity,TQuantity],TBool,function(a,b) { return a.lt(b); });
addFunction('<=',[TQuantity,TQuantity],TBool,function(a,b) { return a.lte(b); });
addFunction('>',[TQuantity,TQuantity],TBool,function(a,b) { return a.gt(b); });
addFunction('>=',[TQuantity,TQuantity],TBool,function(a,b) { return a.gte(b); });
addFunction('+',[TQuantity,TQuantity],TQuantity,function(a,b) { return a.add(b); });
addFunction('-',[TQuantity,TQuantity],TQuantity,function(a,b) { return a.sub(b); });
addFunction('+u',[TQuantity],TQuantity,function(q){ return q; });
addFunction('-u',[TQuantity],TQuantity,function(q){ return Qty({scalar:-q.scalar, numerator:q.numerator, denominator: q.denominator}); });
addFunction('*',[TQuantity,TQuantity],TQuantity,function(a,b) { return a.mul(b); });
addFunction('*',[TDecimal,TQuantity],TQuantity,function(n,u) { return u.mul(n.re); });
addFunction('*',[TQuantity,TDecimal],TQuantity,function(u,n) { return u.mul(n.re); });
addFunction('/',[TQuantity,TQuantity],TQuantity,function(a,b) { return a.div(b); });
addFunction('/',[TQuantity,TDecimal],TQuantity,function(u,n) { return u.div(n.re); });
addFunction('/',[TDecimal,TQuantity],TQuantity,function(n,u) { return u.inverse().mul(n.re); });
addFunction('round',[TQuantity,TString],TQuantity,function(q,precision) { return q.toPrec(precision); });
addFunction('round',[TQuantity,TQuantity],TQuantity,function(q,precision) { return q.toPrec(precision.toString()); });
addFunction('round',[TQuantity],TQuantity,function(q){ return q.toPrec(1); });
addFunction('abs',[TQuantity],TQuantity,function(q){ return Qty({scalar:Math.abs(q.scalar), numerator: q.numerator, denominator: q.denominator}); });
addFunction('sign',[TQuantity],TNum,function(q) { return Decimal.sign(q.scalar.toDecimal()); });
addFunction('scalar',[TQuantity],TDecimal,function(q){ return q.scalar.toDecimal(); });
/** Round this quantity's scalar to the given number of decimal places.
* @param {Quantity} q
* @param {Number} dp
* @returns {Quantity}
*/
quantities.precround = function(q,dp) {
var v = q.scalar;
return Qty({scalar: v.toDecimalPlaces(dp), numerator: q.numerator, denominator: q.denominator});
}
/** Round this quantity's scalar to the given number of significant figures.
* @param {Quantity} q
* @param {Number} dp
* @returns {Quantity}
*/
quantities.siground = function(q,dp) {
var v = q.scalar;
return Qty({scalar: v.toSignificantDigits(dp), numerator: q.numerator, denominator: q.denominator});
}
addFunction('precround',[TQuantity,TNum], TQuantity, quantities.precround);
addFunction('siground',[TQuantity,TNum], TQuantity, quantities.siground);
addFunction('string',[TQuantity],TString,function(q){
return quantity_string(q);
});
addFunction('string',[TQuantity,TString],TString,function(q,style){
// string(quantity, number notation style)
return quantity_string(q,style);
});
addFunction('plain_string',[TQuantity],TString,function(q){
return plain_quantity_string(q);
});
addFunction('plain_string',[TQuantity,TString],TString,function(q,style){
// string(quantity, number notation style)
return plain_quantity_string(q,style);
});
function clean_units(units) {
return units.map(function(u){return new TString(u.replace(/^<(.*)>$/,'$1'))});
}
addFunction('units_numerator',[TQuantity],TList,function(q) { return clean_units(q.numerator); });
addFunction('units_denominator',[TQuantity],TList,function(q) { return clean_units(q.denominator); });
addFunction('units',[TQuantity],TQuantity,function(q) { return Qty(q.units()); });
addFunction('units_string',[TQuantity],TString,function(q) { return fix_units(q.units()); });
addFunction('plain_units_string',[TQuantity],TString,function(q) { return plain_units(q.units()); });
var SIGNATURE_VECTOR = Qty.SIGNATURE_VECTOR;
var SIGNATURE_POWER = Qty.SIGNATURE_POWER;
quantities.decode_signature = function(n) {
if(n<0) {
var s = quantities.decode_signature(-n);
for(var x in s) {
s[x] = -s[x];
}
return s;
}
var l = [];
while(n) {
var m = n%SIGNATURE_POWER;
l.push(m);
n = (n-m)/SIGNATURE_POWER;
}
for(var i=0;i<l.length;i++) {
if(l[i]>10) {
l[i] -= SIGNATURE_POWER;
if(i>=l.length-1) {
l.push(0);
}
l[i+1] += 1;
}
}
var d = {};
l.forEach(function(p,i) {
d[SIGNATURE_VECTOR[i]] = p;
});
return d;
}
var si_units = quantities.si_units = {
"unitless": "",
"length": "m",
"area": "m2",
"volume": "m3",
"time": "s",
"temperature": "kelvin",
"yank": "N/s",
"power": "W",
"pressure": "Pa",
"force": "N",
"energy": "J",
"viscosity": "poise",
"momentum": "kg*m",
"angular_momentum": "kg*m2/s",
"density": "kg/m3",
"area_density": "kg/m2",
"mass": "kg",
"radiation_exposure": "C/kg",
"magnetism": "Wb",
"current": "A",
"charge": "C",
"conductance": "S",
"capacitance": "F",
"activity": "katal",
"molar_concentration": "mol/m3",
"substance": "mole",
"illuminance": "lux",
"luminous_power": "lumen",
"currency": "dollar",
"elastance": "1/farad",
"resistance": "ohm",
"inductance": "henry",
"potential": "V",
"specific_volume": "m3/kg",
"snap": "m/s4",
"jolt": "m/s3",
"acceleration": "m/s2",
"radiation": "sievert",
"frequency": "Hz",
"speed": "m/s",
"volumetric_flow": "m^3/s",
"wavenumber": "1/s",
"information_rate": "byte/s",
"information": "byte",
"angular_velocity": "radian/s",
"angle": "radian"
}
addFunction('as_si',[TQuantity],TQuantity,function(q) {
var kind = q.kind();
if(kind) {
var unit = si_units[kind];
return q.to(si_units[kind]);
} else {
var kinds = quantities.decode_signature(q.signature);
var numerator = [];
var denominator = [];
for(var x in kinds) {
var unit = si_units[x];
if(kinds[x]>0) {
numerator.push(unit+'^'+kinds[x]);
} else if(kinds[x]<0) {
denominator.push(unit+'^'+(-kinds[x]));
}
}
if(!numerator.length) {
numerator.push('1');
}
var units = numerator.join('*')+(denominator.length ? '/'+denominator.join('*') : '');
return q.to(units);
}
});
});
Numbas.queueScript('js-quantities',['decimal'],function(module) {
var exports = module.exports;
/** start of quantities.js **/
/*
The MIT License (MIT)
Copyright © 2006-2007 Kevin C. Olbrich
Copyright © 2010-2016 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.
*/
(function (global, factory) {
typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
typeof define === 'function' && define.amd ? define(factory) :
(global = typeof globalThis !== 'undefined' ? globalThis : global || self, global.Qty = factory());
})(this, (function () { 'use strict';
/**
* Tests if a value is a string
*
* @param {*} value - Value to test
*
* @returns {boolean} true if value is a string, false otherwise
*/
function isString(value) {
return typeof value === "string" || value instanceof String;
}
/*
* Prefer stricter Number.isFinite if currently supported.
* To be dropped when ES6 is finalized. Obsolete browsers will
* have to use ES6 polyfills.
*/
const isFiniteImpl = Number.isFinite || window.isFinite;
/**
* Tests if a value is a number
*
* @param {*} value - Value to test
*
* @returns {boolean} true if value is a number, false otherwise
*/
function isNumber(value) {
// Number.isFinite allows not to consider NaN or '1' as numbers
return isFiniteImpl(value);
}
/*
* Identity function
*/
function identity(value) {
return value;
}
/**
* Returns unique strings from list
*
* @param {string[]} strings - array of strings
*
*
* @returns {string[]} a new array of strings without duplicates
*/
function uniq(strings) {
var seen = {};
return strings.filter(function(item) {
return seen.hasOwnProperty(item) ? false : (seen[item] = true);
});
}
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 assign(target, properties) {
Object.keys(properties).forEach(function(key) {
target[key] = properties[key];
});
}
/**
* Safely multiplies numbers while avoiding floating errors
* like 0.1 * 0.1 => 0.010000000000000002
*
* @param {...number} numbers - numbers to multiply
*
* @returns {number} result
*/
function mulSafe() {
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;
}
/**
* Safely divides two numbers while avoiding floating errors
* like 0.3 / 0.05 => 5.999999999999999
*
* @returns {number} result
* @param {number} num Numerator
* @param {number} den Denominator
*/
function divSafe(num, den) {
if (den === 0) {
throw new Error("Divide by zero");
}
var factor = Math.pow(10, getFractional(den));
var invDen = factor / (factor * den);
return mulSafe(num, invDen);
}
/**
* Rounds value at the specified number of decimals
*
* @param {number} val - value to round
* @param {number} decimals - number of decimals
*
* @returns {number} rounded number
*/
function round(val, decimals) {
return Math.round(val * Math.pow(10, decimals)) / Math.pow(10, decimals);
}
function getFractional(num) {
// Check for NaNs or Infinities
if (!isFinite(num)) {
return 0;
}
// Faster than parsing strings
// http://jsperf.com/count-decimals/2
var count = 0;
while (num % 1 !== 0) {
num *= 10;
count++;
}
return count;
}
const fields = {};
const NumberField = fields.NumberField = {
isMember: (n) => isNumber(n),
fromString: (s) => parseFloat(s),
fromNumber: (n) => n,
toNumber: (n) => n,
one: () => 1,
zero: () => 0,
add: (a,b) => a + b,
sub: (a,b) => a - b,
mul: (a,b) => a * b,
mulSafe: function() {
return mulSafe.apply(this,arguments);
},
div: (a,b) => a / b,
divSafe: divSafe,
inverse: (n) => 1 / n,
isExactlyZero: (n) => n === 0,
round: Math.round,
roundTo: round,
lt: (a,b) => a < b,
gt: (a,b) => a > b,
eq: (a,b) => a === b,
pow: Math.pow,
PI: Math.PI,
abs: Math.abs
};
let Field = NumberField;
try {
const Decimal = window.Decimal;
class DecimalFraction {
constructor(n,d) {
if (!Decimal.isDecimal(n)) {
n = new Decimal(n);
}
if (!Decimal.isDecimal(d)) {
d = new Decimal(d);
}
this.n = n;
this.d = d;
}
toString() {
return this.toDecimal().toString();
}
toDecimal() {
if (this.d.eq(1)) {
return this.n;
}
else {
return this.n.div(this.d);
}
}
plus(b) {
return new DecimalFraction(this.n.mul(b.d).add(b.n.mul(this.d)),this.d.mul(b.d));
}
minus(b) {
return new DecimalFraction(this.n.mul(b.d).sub(b.n.mul(this.d)),this.d.mul(b.d));
}
times(b) {
return new DecimalFraction(this.n.mul(b.n), this.d.mul(b.d));
}
dividedBy(b) {
return new DecimalFraction(this.n.mul(b.d), this.d.mul(b.n));
}
inverse() {
return new DecimalFraction(this.d,this.n);
}
isZero() {
return this.n.isZero();
}
round() {
return new DecimalFraction(this.toDecimal().round(), new Decimal(1));
}
toDecimalPlaces(decimals) {
return new DecimalFraction(this.toDecimal().toDecimalPlaces(decimals), new Decimal(1));
}
toSignificantDigits(digits) {
return new DecimalFraction(this.toDecimal().toSignificantDigits(digits), new Decimal(1));
}
lessThan(b) {
return this.toDecimal().lessThan(b.toDecimal());
}
greaterThan(b) {
return this.toDecimal().greaterThan(b.toDecimal());
}
equals(b) {
return this.toDecimal().equals(b.toDecimal());
}
toPower(b) {
return new DecimalFraction(this.n.toPower(b.toDecimal()), this.d.toPower(b.toDecimal()));
}
abs() {
return new DecimalFraction(this.n.absoluteValue(), this.d.absoluteValue());
}
}
function fr(n) {
if (!(n instanceof DecimalFraction)) {
return new DecimalFraction(n,1);
}
return n;
}
const DecimalOne = new DecimalFraction(1,1);
const DecimalZero = new DecimalFraction(0,1);
const DecimalField = fields.DecimalField = {
isMember: (n) => {
return n instanceof DecimalFraction || n instanceof Decimal;
},
fromString: (s) => {
return new DecimalFraction(new Decimal(s), 1);
},
fromNumber: (n) => {
return (new DecimalFraction(n,1)).toDecimalPlaces(12);
},
toNumber: (n) => {
return n.toDecimal().toNumber();
},
one: () => {
return DecimalOne;
},
zero: () => {
return DecimalZero;
},
add: (a,b) => {
return fr(a).plus(fr(b));
},
sub: (a,b) => {
return fr(a).minus(fr(b));
},
mul: function() {
let result = DecimalOne;
for (var i = 0; i < arguments.length; i++) {
result = result.times(fr(arguments[i]));
}
return result;
},
div: (a,b) => {
return fr(a).dividedBy(fr(b));
},
inverse: (n) => {
return fr(n).inverse();
},
isExactlyZero: (n) => {
return fr(n).isZero();
},
round: (n) => {
return fr(n).round();
},
roundTo: (n,decimals) => {
return fr(n).toDecimalPlaces(decimals);
},
lt: (a,b) => {
return fr(a).lessThan(fr(b));
},
gt: (a,b) => {
return fr(a).greaterThan(fr(b));
},
eq: (a,b) => {
return fr(a).equals(fr(b));
},
pow: (a,b) => {
return fr(a).toPower(fr(b));
},
abs: (n) => {
return fr(n).abs();
},
PI: new DecimalFraction(Decimal.acos(-1),1),
};
DecimalField.divSafe = DecimalField.div;
DecimalField.mulSafe = DecimalField.mul;
Field = DecimalField;
}
catch (e) {
}
/**
* Custom error type definition
* @constructor
*/
function QtyError() {
var err;
if (!this) { // Allows to instantiate QtyError without new()
err = Object.create(QtyError.prototype);
QtyError.apply(err, arguments);
return err;
}
err = Error.apply(this, arguments);
this.name = "QtyError";
this.message = err.message;
this.stack = err.stack;
}
QtyError.prototype = Object.create(Error.prototype, {constructor: { value: QtyError }});
/*
* Throws incompatible units error
* @param {string} left - units
* @param {string} right - units incompatible with first argument
* @throws "Incompatible units" error
*/
function throwIncompatibleUnits(left, right) {
throw new QtyError("Incompatible units: " + left + " and " + right);
}
const n = Field.fromNumber;
const { PI, pow, mul, div } = Field;
var UNITS = {
/* prefixes */
"<googol>" : [["googol"], pow(n(10),n(100)), "prefix"],
"<kibi>" : [["Ki","Kibi","kibi"], pow(n(2),n(10)), "prefix"],
"<mebi>" : [["Mi","Mebi","mebi"], pow(n(2),n(20)), "prefix"],
"<gibi>" : [["Gi","Gibi","gibi"], pow(n(2),n(30)), "prefix"],
"<tebi>" : [["Ti","Tebi","tebi"], pow(n(2),n(40)), "prefix"],
"<pebi>" : [["Pi","Pebi","pebi"], pow(n(2),n(50)), "prefix"],
"<exi>" : [["Ei","Exi","exi"], pow(n(2),n(60)), "prefix"],
"<zebi>" : [["Zi","Zebi","zebi"], pow(n(2),n(70)), "prefix"],
"<yebi>" : [["Yi","Yebi","yebi"], pow(n(2),n(80)), "prefix"],
"<yotta>" : [["Y","Yotta","yotta"], n(1e24), "prefix"],
"<zetta>" : [["Z","Zetta","zetta"], n(1e21), "prefix"],
"<exa>" : [["E","Exa","exa"], n(1e18), "prefix"],
"<peta>" : [["P","Peta","peta"], n(1e15), "prefix"],
"<tera>" : [["T","Tera","tera"], n(1e12), "prefix"],
"<giga>" : [["G","Giga","giga"], n(1e9), "prefix"],
"<mega>" : [["M","Mega","mega"], n(1e6), "prefix"],
"<kilo>" : [["k","kilo"], n(1e3), "prefix"],
"<hecto>" : [["h","Hecto","hecto"], n(1e2), "prefix"],
"<deca>" : [["da","Deca","deca","deka"], n(1e1), "prefix"],
"<deci>" : [["d","Deci","deci"], n(1e-1), "prefix"],
"<centi>" : [["c","Centi","centi"], n(1e-2), "prefix"],
"<milli>" : [["m","Milli","milli"], n(1e-3), "prefix"],
"<micro>" : [
["u","\u03BC"/*µ as greek letter*/,"\u00B5"/*µ as micro sign*/,"Micro","mc","micro"],
n(1e-6),
"prefix"
],
"<nano>" : [["n","Nano","nano"], n(1e-9), "prefix"],
"<pico>" : [["p","Pico","pico"], n(1e-12), "prefix"],
"<femto>" : [["f","Femto","femto"], n(1e-15), "prefix"],
"<atto>" : [["a","Atto","atto"], n(1e-18), "prefix"],
"<zepto>" : [["z","Zepto","zepto"], n(1e-21), "prefix"],
"<yocto>" : [["y","Yocto","yocto"], n(1e-24), "prefix"],
"<1>" : [["1", "<1>"], n(1), ""],
/* length units */
"<meter>" : [["m","meter","meters","metre","metres"], n(1.0), "length", ["<meter>"] ],
"<inch>" : [["in","inch","inches","\""], n(0.0254), "length", ["<meter>"]],
"<foot>" : [["ft","foot","feet","'"], n(0.3048), "length", ["<meter>"]],
"<yard>" : [["yd","yard","yards"], n(0.9144), "length", ["<meter>"]],
"<mile>" : [["mi","mile","miles"], n(1609.344), "length", ["<meter>"]],
"<naut-mile>" : [["nmi","naut-mile"], n(1852), "length", ["<meter>"]],
"<league>": [["league","leagues"], n(4828), "length", ["<meter>"]],
"<furlong>": [["furlong","furlongs"], n(201.2), "length", ["<meter>"]],
"<rod>" : [["rd","rod","rods"], n(5.029), "length", ["<meter>"]],
"<mil>" : [["mil","mils"], n(0.0000254), "length", ["<meter>"]],
"<angstrom>" :[["ang","angstrom","angstroms"], n(1e-10), "length", ["<meter>"]],
"<fathom>" : [["fathom","fathoms"], n(1.829), "length", ["<meter>"]],
"<pica>" : [["pica","picas"], n(0.00423333333), "length", ["<meter>"]],
"<point>" : [["pt","point","points"], n(0.000352777778), "length", ["<meter>"]],
"<redshift>" : [["z","red-shift", "redshift"], n(1.302773e26), "length", ["<meter>"]],
"<AU>" : [["AU","astronomical-unit"], n(149597900000), "length", ["<meter>"]],
"<light-second>":[["ls","light-second"], n(299792500), "length", ["<meter>"]],
"<light-minute>":[["lmin","light-minute"], n(17987550000), "length", ["<meter>"]],
"<light-year>" : [["ly","light-year"], n(9460528000000000), "length", ["<meter>"]],
"<parsec>" : [["pc","parsec","parsecs"], n(30856780000000000), "length", ["<meter>"]],
"<datamile>" : [["DM","datamile"], n(1828.8), "length", ["<meter>"]],
/* mass */
"<kilogram>" : [["kg","kilogram","kilograms"], n(1.0), "mass", ["<kilogram>"]],
"<AMU>" : [["u","AMU","amu"], n(1.660538921e-27), "mass", ["<kilogram>"]],
"<dalton>" : [["Da","Dalton","Daltons","dalton","daltons"], n(1.660538921e-27), "mass", ["<kilogram>"]],
"<slug>" : [["slug","slugs"], n(14.5939029), "mass", ["<kilogram>"]],
"<short-ton>" : [["tn","ton","short-ton"], n(907.18474), "mass", ["<kilogram>"]],
"<metric-ton>":[["t","tonne","metric-ton"], n(1000), "mass", ["<kilogram>"]],
"<carat>" : [["ct","carat","carats"], n(0.0002), "mass", ["<kilogram>"]],
"<pound>" : [["lbs","lb","pound","pounds","#"], n(0.45359237), "mass", ["<kilogram>"]],
"<ounce>" : [["oz","ounce","ounces"], n(0.0283495231), "mass", ["<kilogram>"]],
"<gram>" : [["g","gram","grams","gramme","grammes"], n(1e-3), "mass", ["<kilogram>"]],
"<grain>" : [["grain","grains","gr"], n(6.479891e-5), "mass", ["<kilogram>"]],
"<dram>" : [["dram","drams","dr"], n(0.0017718452), "mass",["<kilogram>"]],
"<stone>" : [["stone","stones","st"],n(6.35029318), "mass",["<kilogram>"]],
/* area */
"<hectare>":[["hectare"], n(10000), "area", ["<meter>","<meter>"]],
"<acre>":[["acre","acres"], n(4046.85642), "area", ["<meter>","<meter>"]],
"<sqft>":[["sqft"], n(0.09290304), "area", ["<foot>","<foot>"]],
/* volume */
"<liter>" : [["l","L","liter","liters","litre","litres"], n(0.001), "volume", ["<meter>","<meter>","<meter>"]],
"<gallon>": [["gal","gallon","gallons"], n(0.0037854118), "volume", ["<meter>","<meter>","<meter>"]],
"<gallon-imp>": [["galimp","gallon-imp","gallons-imp"], n(0.0045460900), "volume", ["<meter>","<meter>","<meter>"]],
"<quart>": [["qt","quart","quarts"], n(0.00094635295), "volume", ["<meter>","<meter>","<meter>"]],
"<pint>": [["pt","pint","pints"], n(0.000473176475), "volume", ["<meter>","<meter>","<meter>"]],
"<pint-imp>": [["ptimp","pint-imp","pints-imp"], n(5.6826125e-4), "volume", ["<meter>","<meter>","<meter>"]],
"<cup>": [["cu","cup","cups"], n(0.000236588238), "volume", ["<meter>","<meter>","<meter>"]],
"<fluid-ounce>": [["floz","fluid-ounce","fluid-ounces"], n(2.95735297e-5), "volume", ["<meter>","<meter>","<meter>"]],
"<fluid-ounce-imp>": [["flozimp", "floz-imp","fluid-ounce-imp","fluid-ounces-imp"], n(2.84130625e-5), "volume", ["<meter>","<meter>","<meter>"]],
"<tablespoon>": [["tb","tbsp","tbs","tablespoon","tablespoons"], n(1.47867648e-5), "volume", ["<meter>","<meter>","<meter>"]],
"<teaspoon>": [["tsp","teaspoon","teaspoons"], n(4.92892161e-6), "volume", ["<meter>","<meter>","<meter>"]],
"<bushel>": [["bu","bsh","bushel","bushels"], n(0.035239072), "volume", ["<meter>","<meter>","<meter>"]],
"<oilbarrel>": [["bbl","oilbarrel", "oilbarrels", "oil-barrel","oil-barrels"], n(0.158987294928), "volume", ["<meter>","<meter>","<meter>"]],
"<beerbarrel>": [["bl","bl-us","beerbarrel", "beerbarrels", "beer-barrel","beer-barrels"], n(0.1173477658), "volume", ["<meter>","<meter>","<meter>"]],
"<beerbarrel-imp>": [["blimp","bl-imp","beerbarrel-imp", "beerbarrels-imp", "beer-barrel-imp","beer-barrels-imp"], n(0.16365924), "volume", ["<meter>","<meter>","<meter>"]],
/* speed */
"<kph>" : [["kph"], n(0.277777778), "speed", ["<meter>"], ["<second>"]],
"<mph>" : [["mph"], n(0.44704), "speed", ["<meter>"], ["<second>"]],
"<knot>" : [["kt","kn","kts","knot","knots"], n(0.514444444), "speed", ["<meter>"], ["<second>"]],
"<fps>" : [["fps"], n(0.3048), "speed", ["<meter>"], ["<second>"]],
/* acceleration */
"<gee>" : [["gee"], n(9.80665), "acceleration", ["<meter>"], ["<second>","<second>"]],
"<Gal>" : [["Gal"], n(1e-2), "acceleration", ["<meter>"], ["<second>","<second>"]],
/* temperature_difference */
"<kelvin>" : [["degK","kelvin"], n(1.0), "temperature", ["<kelvin>"]],
"<celsius>" : [["degC","celsius","celsius","centigrade"], n(1.0), "temperature", ["<kelvin>"]],
"<fahrenheit>" : [["degF","fahrenheit"], div(n(5), n(9)), "temperature", ["<kelvin>"]],
"<rankine>" : [["degR","rankine"], div(n(5), n(9)), "temperature", ["<kelvin>"]],
"<temp-K>" : [["tempK","temp-K"], n(1.0), "temperature", ["<temp-K>"]],
"<temp-C>" : [["tempC","temp-C"], n(1.0), "temperature", ["<temp-K>"]],
"<temp-F>" : [["tempF","temp-F"], div(n(5), n(9)), "temperature", ["<temp-K>"]],
"<temp-R>" : [["tempR","temp-R"], div(n(5), n(9)), "temperature", ["<temp-K>"]],
/* time */
"<second>": [["s","sec","secs","second","seconds"], n(1.0), "time", ["<second>"]],
"<minute>": [["min","mins","minute","minutes"], n(60.0), "time", ["<second>"]],
"<hour>": [["h","hr","hrs","hour","hours"], n(3600.0), "time", ["<second>"]],
"<day>": [["d","day","days"], mul(n(3600), n(24)), "time", ["<second>"]],
"<week>": [["wk","week","weeks"], mul(n(7), mul(n(3600), n(24))), "time", ["<second>"]],
"<fortnight>": [["fortnight","fortnights"], n(1209600), "time", ["<second>"]],
"<year>": [["y","yr","year","years","annum"], n(31556926), "time", ["<second>"]],
"<decade>":[["decade","decades"], n(315569260), "time", ["<second>"]],
"<century>":[["century","centuries"], n(3155692600), "time", ["<second>"]],
/* pressure */
"<pascal>" : [["Pa","pascal","Pascal"], n(1.0), "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
"<bar>" : [["bar","bars"], n(100000), "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
"<mmHg>" : [["mmHg"], n(133.322368), "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
"<inHg>" : [["inHg"], n(3386.3881472), "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
"<torr>" : [["torr"], n(133.322368), "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
"<atm>" : [["atm","ATM","atmosphere","atmospheres"], n(101325), "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
"<psi>" : [["psi"], n(6894.76), "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
"<cmh2o>" : [["cmH2O","cmh2o"], n(98.0638), "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
"<inh2o>" : [["inH2O","inh2o"], n(249.082052), "pressure", ["<kilogram>"],["<meter>","<second>","<second>"]],
/* viscosity */
"<poise>" : [["P","poise"], n(0.1), "viscosity", ["<kilogram>"],["<meter>","<second>"] ],
"<stokes>" : [["St","stokes"], n(1e-4), "viscosity", ["<meter>","<meter>"], ["<second>"]],
/* substance */
"<mole>" : [["mol","mole"], n(1.0), "substance", ["<mole>"]],
/* concentration */
"<molar>" : [["M","molar"], n(1000), "molar_concentration", ["<mole>"], ["<meter>","<meter>","<meter>"]],
"<wtpercent>" : [["wt%","wtpercent"], n(10), "molar_concentration", ["<kilogram>"], ["<meter>","<meter>","<meter>"]],
/* activity */
"<katal>" : [["kat","katal","Katal"], n(1.0), "activity", ["<mole>"], ["<second>"]],
"<unit>" : [["U","enzUnit","unit"], n(16.667e-16), "activity", ["<mole>"], ["<second>"]],
/* capacitance */
"<farad>" : [["F","farad","Farad"], n(1.0), "capacitance", ["<second>","<second>","<second>","<second>","<ampere>","<ampere>"], ["<meter>", "<meter>", "<kilogram>"]],
/* charge */
"<coulomb>" : [["C","coulomb","Coulomb"], n(1.0), "charge", ["<ampere>","<second>"]],
"<Ah>" : [["Ah"], n(3600), "charge", ["<ampere>","<second>"]],
"<elementary-charge>" : [["e"], n(1.602176634e-19), "charge", ["<ampere>","<second>"]],
/* current */
"<ampere>" : [["A","Ampere","ampere","amp","amps"], n(1.0), "current", ["<ampere>"]],
/* conductance */
"<siemens>" : [["S","Siemens","siemens"], n(1.0), "conductance", ["<second>","<second>","<second>","<ampere>","<ampere>"], ["<kilogram>","<meter>","<meter>"]],
/* inductance */
"<henry>" : [["H","Henry","henry"], n(1.0), "inductance", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>","<ampere>","<ampere>"]],
/* potential */
"<volt>" : [["V","Volt","volt","volts"], n(1.0), "potential", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>","<second>","<ampere>"]],
/* resistance */
"<ohm>" : [
["Ohm","ohm","Ohms","ohms","\u03A9"/*Ω as greek letter*/,"\u2126"/*Ω as ohm sign*/],
n(1.0),
"resistance",
["<meter>","<meter>","<kilogram>"],["<second>","<second>","<second>","<ampere>","<ampere>"]
],
/* magnetism */
"<weber>" : [["Wb","weber","webers"], n(1.0), "magnetism", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>","<ampere>"]],
"<tesla>" : [["T","tesla","teslas"], n(1.0), "magnetism", ["<kilogram>"], ["<second>","<second>","<ampere>"]],
"<gauss>" : [["G","gauss"], n(1e-4), "magnetism", ["<kilogram>"], ["<second>","<second>","<ampere>"]],
"<maxwell>" : [["Mx","maxwell","maxwells"], n(1e-8), "magnetism", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>","<ampere>"]],
"<oersted>" : [["Oe","oersted","oersteds"], div(n(250.0), PI), "magnetism", ["<ampere>"], ["<meter>"]],
/* energy */
"<joule>" : [["J","joule","Joule","joules","Joules"], n(1.0), "energy", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],
"<erg>" : [["erg","ergs"], n(1e-7), "energy", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],
"<btu>" : [["BTU","btu","BTUs"], n(1055.056), "energy", ["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],
"<calorie>" : [["cal","calorie","calories"], n(4.18400), "energy",["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],
"<Calorie>" : [["Cal","Calorie","Calories"], n(4184.00), "energy",["<meter>","<meter>","<kilogram>"], ["<second>","<second>"]],