mathjs
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Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser and offers an integrated solution to work with numbers, big numbers, complex numbers, units, and matrices.
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JavaScript
'use strict';
var format = require('../../utils/number').format;
var endsWith = require('../../utils/string').endsWith;
function factory (type, config, load, typed) {
/**
* @constructor Unit
*
* 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
*
* @param {number} [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 && typeof value !== 'number') {
throw new TypeError('First parameter in Unit constructor must be a number');
}
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: PREFIX_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. Throws an exception if the provided string does not
* contain a valid unit or cannot be parsed.
* @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) {
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
* @return {Unit} clone
*/
Unit.prototype.clone = function () {
var clone = new Unit();
for (var p in this) {
if (this.hasOwnProperty(p)) {
clone[p] = this[p];
}
}
clone.dimensions = this.dimensions.slice(0);
clone.units = [];
for(var i=0; i<this.units.length; i++) {
clone.units[i] = { };
for (var p in this.units[i]) {
if (this.units[i].hasOwnProperty(p)) {
clone.units[i][p] = this.units[i][p];
}
}
}
return clone;
};
/**
* Return whether the unit is derived (such as m/s, or cm^2, but not N)
* @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)
* @param {number} value
* @return {number} normalized value
* @private
*/
Unit.prototype._normalize = function (value) {
if (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;
for(var i=0; i < this.units.length; i++) {
res = res * Math.pow(this.units[i].unit.value * this.units[i].prefix.value, this.units[i].power);
}
return res;
}
else {
// This is a single unit of power 1, like kg or degC
return (value + this.units[0].unit.offset) * this.units[0].unit.value * this.units[0].prefix.value;
}
};
/**
* Denormalize a value, based on its currently set unit(s)
* @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) {
if (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 preferrable to g unless the user decides otherwise.
var res = value;
for(var i=0; i<this.units.length; i++) {
res = res / Math.pow(this.units[i].unit.value * this.units[i].prefix.value, this.units[i].power);
}
return res;
}
else {
// This is a single unit of power 1, like kg or degC
if (prefixValue == undefined) {
return value / this.units[0].unit.value / this.units[0].prefix.value - this.units[0].unit.offset;
}
else {
return value / this.units[0].unit.value / prefixValue - this.units[0].unit.offset;
}
}
};
/**
* Find a unit from a string
* @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.
* @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.
* @param {BASE_UNITS | undefined} base
*/
Unit.prototype.hasBase = function (base) {
// 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
* @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
* @param {Unit} other
* @return {boolean} true if both units are equal
*/
Unit.prototype.equals = function (other) {
return (this.equalBase(other) && this.value == other.value);
};
/**
* Multiply this unit with another one
* @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 = 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
* @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 = 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
* @param {number} p Any real number
* @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 = Math.pow(res.value, p);
}
else {
res.value = null;
}
// Trigger lazy evaluation of the unit list
res.isUnitListSimplified = false;
return res;
};
/**
* Create a clone of this unit with a representation
* @param {string | Unit} valuelessUnit A unit without value. Can have prefix, like "cm"
* @returns {Unit} unit having fixed, specified 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 = 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 = 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
* @param {string | Unit} valuelessUnit For example 'cm' or 'inch'
* @return {number} value
*/
Unit.prototype.toNumber = 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.
* @return {string}
*/
Unit.prototype.toString = function () {
return this.format();
};
/**
* Get a JSON representation of the 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
* @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.
* @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;
return;
}
/**
* Get a string representation of the units of this Unit, without the value.
* @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.
* @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();
// 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 prefix
var bestPrefix = this._bestPrefix();
this.units[0].prefix = bestPrefix;
}
}
var value = this._denormalize(this.value);
var str = (this.value !== null) ? (format(value, options)) : '';
var unitStr = this.formatUnits();
if(unitStr.length > 0 && str.length > 0) {
str += " ";
}
str += unitStr;
return str;
/*
var value,
str;
if (this._isDerived()) {
value = this._denormalize(this.value);
str = (this.value !== null) ? (format(value, options)) : '';
var unitStr = this.formatUnits();
if(unitStr.length > 0 && str.length > 0) {
str += " ";
}
str += unitStr;
}
else if (this.units.length === 1) {
if (this.value !== null && !this.fixPrefix) {
var bestPrefix = this._bestPrefix();
value = this._denormalize(this.value, bestPrefix.value);
str = format(value, options) + ' ';
str += bestPrefix.name + this.units[0].unit.name;
}
else {
value = this._denormalize(this.value);
str = (this.value !== null) ? (format(value, options) + ' ') : '';
str += this.units[0].prefix.name + this.units[0].unit.name;
}
}
else if (this.units.length === 0) {
str = format(this.value, options);
}
return str;
*/
};
/**
* Calculate the best prefix using current value.
* @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 ...
var absValue = Math.abs(this.value); // / 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 * this.units[0].unit.value, 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 * this.units[0].unit.value, 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];
}
}
var PREFIX_NONE = {name: '', value: 1, scientific: true};
/* 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]
},
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
// 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, o