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formula.js
// Copyright (c) 2012 Sutoiku, Inc.
// 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.
// Some algorithms have been ported from Apache OpenOffice:
/**************************************************************
*
* Licensed to the Apache Software Foundation (ASF) under one
* or more contributor license agreements. See the NOTICE file
* distributed with this work for additional information
* regarding copyright ownership. The ASF licenses this file
* to you under the Apache License, Version 2.0 (the
* "License"); you may not use this file except in compliance
* with the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing,
* software distributed under the License is distributed on an
* "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
* KIND, either express or implied. See the License for the
* specific language governing permissions and limitations
* under the License.
*
*************************************************************/
/*jslint evil: true*/
/*jshint -W079 */
/*global define */
(function () {
var root = this;
var Formula = root.Formula = {};
var _ = root._;
var numeric = root.numeric;
var numeral = root.numeral;
var jStat = root.jStat;
var moment = root.moment;
var lodash = root.lodash;
var md5 = root.md5;
if (typeof exports !== "undefined") {
Formula = exports;
_ = lodash = require('lodash');
numeral = require('numeral');
numeric = require('numeric');
jStat = require('jStat').jStat;
moment = require('moment');
md5 = require('blueimp-md5').md5;
_.str = require('underscore.string');
}
else if (typeof define === "function" && define.amd) {
define(
'formula',
['numeric', 'numeral', 'jStat', 'moment', 'lodash', 'underscore.string', 'md5'],
function () {
return Formula;
}
);
}
var _s = _.str;
var MEMOIZED_FACT = [];
var SQRT2PI = 2.5066282746310002;
var WEEK_STARTS = [
undefined,
0,
1,
undefined,
undefined,
undefined,
undefined,
undefined,
undefined,
undefined,
undefined,
undefined,
1,
2,
3,
4,
5,
6,
0
];
var WEEK_TYPES = [
[],
[1, 2, 3, 4, 5, 6, 7],
[7, 1, 2, 3, 4, 5, 6],
[6, 0, 1, 2, 3, 4, 5],
[],
[],
[],
[],
[],
[],
[],
[7, 1, 2, 3, 4, 5, 6],
[6, 7, 1, 2, 3, 4, 5],
[5, 6, 7, 1, 2, 3, 4],
[4, 5, 6, 7, 1, 2, 3],
[3, 4, 5, 6, 7, 1, 2],
[2, 3, 4, 5, 6, 7, 1],
[1, 2, 3, 4, 5, 6, 7]
];
var WEEKEND_TYPES = [
[],
[6, 0],
[0, 1],
[1, 2],
[2, 3],
[3, 4],
[4, 5],
[5, 6],
undefined,
undefined,
undefined,
[0],
[1],
[2],
[3],
[4],
[5],
[6]
];
// Override some functions
Formula.UNIQUE = function () {
return lodash.unique(arguments);
};
Formula.FLATTEN = function () {
return lodash.flatten(arguments);
};
// Generate a callback function
Formula.FUNCTION = function () {
var args = Array.prototype.slice.call(arguments);
var expression = args[args.length - 1];
var regexp = /(\w+)\(/g;
var newExpression = expression.replace(regexp, function () {
return "Formulae." + arguments[0];
});
args[args.length - 1] = "return " + newExpression + ";";
if (newExpression !== expression) {
args.unshift('Formulae');
}
return Function.apply(null, args);
};
// Moment functions
Formula.MOMENT = function (timestamp, format) {
return moment(timestamp).format(format);
};
Formula.MOMENTADD = function (start_date, period, number) {
return moment(start_date).add(period, number);
};
Formula.MOMENTDIFF = function (start_date, end_date, period) {
return moment(end_date).diff(moment.utc(start_date), period);
};
Formula.MOMENTSUB = function (start_date, period, number) {
return moment(start_date).subtract(period, number);
};
Formula.MOMENTUTC = function (timestamp, format) {
return moment.utc(timestamp).format(format);
};
Formula.MOMENTUTCADD = function (start_date, period, number) {
return moment.utc(start_date).add(period, number);
};
Formula.MOMENTUTCDIFF = function (start_date, end_date, period) {
return moment.utc(end_date).diff(moment.utc(start_date), period);
};
Formula.MOMENTUTCSUB = function (start_date, period, number) {
return moment.utc(start_date).subtract(period, number);
};
Formula.MOMENTUNIX = function (unixTime) {
return moment.unix(unixTime).toDate();
};
Formula.MOMENTFORMAT = function (date, format) {
return moment(date).format(format);
};
Formula.MOMENTISLEAPYEAR = function (date, format) {
return moment(date, format).isLeapYear();
};
Formula.MOMENTISDST = function (date, format) {
return moment(date, format).isDST();
};
Formula.MOMENTSTARTOF = function (date, units, format) {
return moment(date, format).startOf(units).toDate();
};
Formula.MOMENTENDOF = function (date, units, format) {
return moment(date, format).endOf(units).toDate();
};
Formula.MOMENTISAFTER = function (date1, date2, format) {
return moment(date1, format).isAfter(moment(date2, format));
};
Formula.MOMENTISBEFORE = function (date1, date2, format) {
return moment(date1, format).isBefore(moment(date2, format));
};
// Custom Functions
Formula.ARGSCONCAT = function (args) {
var result = [];
for (var i = 0; i < args.length; i++) {
result = result.concat(args[i]);
}
return result;
};
Formula.ARGSTOARRAY = function (args) {
return Array.prototype.slice.call(args, 0);
};
Formula.CLEANFLOAT = function (number) {
var power = Math.pow(10, 14);
return Math.round(number * power) / power;
};
Formula.COUNTIN = function (range, value) {
var result = 0;
for (var i = 0; i < range.length; i++) {
if (range[i] === value) {
result++;
}
}
return result;
};
Formula.GETJSON = function (file) {
var request = new XMLHttpRequest();
request.open('GET', file, false);
request.send(null);
if (request.status === 200) {
return JSON.parse(request.responseText);
}
};
// Date functions
Formula.DATE = function (year, month, day) {
return new Date(year, month - 1, day);
};
Formula.DATEVALUE = function (date_text) {
return Math.ceil((moment(date_text) - moment('1900-1-1')) / 86400000) + 2;
};
Formula.DAY = function (date) {
return moment(new Date(date)).date();
};
Formula.DAYS = function (end_date, start_date) {
return moment(new Date(end_date)).diff(moment(new Date(start_date)), 'days');
};
Formula.DAYS360 = function (start_date, end_date, method) {
var start = moment(new Date(start_date));
var end = moment(new Date(end_date));
var smd = 31;
var emd = 31;
var sd = start.date();
var ed = end.date();
if (method) {
sd = (sd === 31) ? 30 : sd;
ed = (ed === 31) ? 30 : ed;
}
else {
if (start.month() === 1) {
smd = start.daysInMonth();
}
if (end.month() === 1) {
emd = end.daysInMonth();
}
sd = (sd === smd) ? 30 : sd;
if (sd === 30 || sd === smd) {
ed = (ed === emd) ? 30 : ed;
}
}
return 360 * (end.year() - start.year()) + 30 * (end.month() - start.month()) + (ed - sd);
};
Formula.EDATE = function (start_date, months) {
return moment(new Date(start_date)).add('months', months).toDate();
};
Formula.EOMONTH = function (start_date, months) {
var edate = moment(new Date(start_date)).add('months', months);
return new Date(edate.year(), edate.month(), edate.daysInMonth());
};
Formula.HOUR = function (timestamp) {
return (timestamp <= 1) ? Math.floor(24 * timestamp) : moment(new Date(timestamp)).hours();
};
Formula.MINUTE = function (timestamp) {
return (timestamp <= 1) ? Math.floor(24 * 60 * timestamp) - 60 * Math.floor(24 * timestamp) : moment(new Date(timestamp)).minutes();
};
Formula.ISOWEEKNUM = function (date) {
return moment(new Date(date)).format('w');
};
Formula.MONTH = function (timestamp) {
return moment(new Date(timestamp)).month() + 1;
};
Formula.NETWORKDAYS = function (start_date, end_date, holidays) {
return Formula.NETWORKDAYSINTL(start_date, end_date, 1, holidays);
};
Formula.NETWORKDAYSINTL = function (start_date, end_date, weekend, holidays) {
var weekend_type = (typeof weekend === 'undefined') ? 1 : weekend;
var weekend_days = WEEKEND_TYPES[weekend_type];
var sd = moment(start_date);
var ed = moment(end_date);
var net_days = ed.diff(sd, 'days') + 1;
var net_work_days = net_days;
var day_of_week = '';
var cd = sd;
var holiday_dates = [];
if (typeof holidays !== 'undefined') {
for (var i = 0; i < holidays.length; i++) {
holiday_dates[i] = moment(new Date(holidays[i])).format('MM-DD-YYYY');
}
}
var j = 0;
while (j < net_days) {
day_of_week = cd.format('d');
if (weekend_days.indexOf(parseInt(day_of_week, 10)) >= 0) {
net_work_days--;
} else if (holiday_dates.indexOf(cd.format('MM-DD-YYYY')) >= 0) {
net_work_days--;
}
cd = cd.add('days', 1);
j++;
}
return net_work_days;
};
Formula.NOW = function () {
return new Date();
};
Formula.SECOND = function (timestamp) {
return moment(new Date(timestamp)).seconds();
};
Formula.TIME = function (hour, minute, second) {
return (3600 * hour + 60 * minute + second) / 86400;
};
Formula.TIMEVALUE = function (time_text) {
var timestamp = moment(new Date(time_text));
return (3600 * timestamp.hours() + 60 * timestamp.minutes() + timestamp.seconds()) / 86400;
};
Formula.TODAY = function () {
return new Date();
};
Formula.WEEKDAY = function (date, type) {
var week_day = moment(new Date(date)).format('d');
var week_type = (typeof type === 'undefined') ? 1 : type;
return WEEK_TYPES[week_type][week_day];
};
Formula.WEEKNUM = function (date, type) {
var current_date = moment(new Date(date));
var january_first = moment(new Date(current_date.year(), 0, 1));
var week_type = (typeof type === 'undefined') ? 1 : type;
var week_start = WEEK_STARTS[week_type];
var first_day = january_first.format('d');
var offset = (first_day < week_start) ? week_start - first_day + 1 : first_day - week_start;
if (week_type === 21) {
return Formula.ISOWEEKNUM(date);
} else {
return Math.floor(current_date.diff(january_first.subtract('days', offset), 'days') / 7) + 1;
}
};
Formula.WORKDAY = function (start_date, days, holidays) {
return Formula.WORKDAYINTL(start_date, days, 1, holidays);
};
Formula.WORKDAYINTL = function (start_date, days, weekend, holidays) {
var weekend_type = (typeof weekend === 'undefined') ? 1 : weekend;
var weekend_days = WEEKEND_TYPES[weekend_type];
var sd = moment(new Date(start_date));
var cd = sd;
var day_of_week = '';
var holiday_dates = [];
if (typeof holidays !== 'undefined') {
for (var i = 0; i < holidays.length; i++) {
holiday_dates[i] = moment(new Date(holidays[i])).format('MM-DD-YYYY');
}
}
var j = 0;
while (j < days) {
cd = cd.add('days', 1);
day_of_week = cd.format('d');
if (weekend_days.indexOf(parseInt(day_of_week, 10)) < 0 && holiday_dates.indexOf(cd.format('MM-DD-YYYY')) < 0) {
j++;
}
}
return cd.toDate();
};
Formula.YEAR = function (date) {
return moment(new Date(date)).year();
};
Formula.YEARFRAC = function (start_date, end_date, basis) {
// Credits: David A. Wheeler [http://www.dwheeler.com/]
// Initialize parameters
basis = (typeof basis === 'undefined') ? 0 : basis;
var sdate = moment(new Date(start_date));
var edate = moment(new Date(end_date));
// Return error if either date is invalid
if (!sdate.isValid() || !edate.isValid()) {
return '#VALUE!';
}
// Return error if basis is neither 0, 1, 2, 3, or 4
if ([0, 1, 2, 3, 4].indexOf(basis) === -1) {
return '#NUM!';
}
// Return zero if start_date and end_date are the same
if (sdate === edate) {
return 0;
}
// Swap dates if start_date is later than end_date
if (sdate.diff(edate) > 0) {
edate = moment(new Date(start_date));
sdate = moment(new Date(end_date));
}
// Lookup years, months, and days
var syear = sdate.year();
var smonth = sdate.month();
var sday = sdate.date();
var eyear = edate.year();
var emonth = edate.month();
var eday = edate.date();
switch (basis) {
case 0:
// US (NASD) 30/360
// Note: if eday == 31, it stays 31 if sday < 30
if (sday === 31 && eday === 31) {
sday = 30;
eday = 30;
} else if (sday === 31) {
sday = 30;
} else if (sday === 30 && eday === 31) {
eday = 30;
} else if (smonth === 1 && emonth === 1 && sdate.daysInMonth() === sday && edate.daysInMonth() === eday) {
sday = 30;
eday = 30;
} else if (smonth === 1 && sdate.daysInMonth() === sday) {
sday = 30;
}
return ((eday + emonth * 30 + eyear * 360) - (sday + smonth * 30 + syear * 360)) / 360;
case 1:
// Actual/actual
var feb29Between = function (date1, date2) {
// Requires year2 == (year1 + 1) or year2 == year1
// Returns TRUE if February 29 is between the two dates (date1 may be February 29), with two possibilities:
// year1 is a leap year and date1 <= Februay 29 of year1
// year2 is a leap year and date2 > Februay 29 of year2
var mar1year1 = moment(new Date(date1.year(), 2, 1));
if (moment([date1.year()]).isLeapYear() && date1.diff(mar1year1) < 0 && date2.diff(mar1year1) >= 0) {
return true;
}
var mar1year2 = moment(new Date(date2.year(), 2, 1));
if (moment([date2.year()]).isLeapYear() && date2.diff(mar1year2) >= 0 && date1.diff(mar1year2) < 0) {
return true;
}
return false;
};
var ylength = 365;
if (syear === eyear || ((syear + 1) === eyear) && ((smonth > emonth) || ((smonth === emonth) && (sday >= eday)))) {
if (syear === eyear && moment([syear]).isLeapYear()) {
ylength = 366;
} else if (feb29Between(sdate, edate) || (emonth === 1 && eday === 29)) {
ylength = 366;
}
return edate.diff(sdate, 'days') / ylength;
} else {
var years = (eyear - syear) + 1;
var days = moment(new Date(eyear + 1, 0, 1)).diff(moment(new Date(syear, 0, 1)), 'days');
var average = days / years;
return edate.diff(sdate, 'days') / average;
}
break;
case 2:
// Actual/360
return edate.diff(sdate, 'days') / 360;
case 3:
// Actual/365
return edate.diff(sdate, 'days') / 365;
case 4:
// European 30/360
if (sday === 31) {
sday = 30;
}
if (eday === 31) {
eday = 30;
}
// Remarkably, do NOT change February 28 or February 29 at ALL
return ((eday + emonth * 30 + eyear * 360) - (sday + smonth * 30 + syear * 360)) / 360;
}
};
// Engineering functions
Formula.BESSELI = function () {
return;
};
Formula.BESSELJ = function () {
return;
};
Formula.BESSELK = function () {
return;
};
Formula.BESSELY = function () {
return;
};
Formula.VALIDBIN = function (number) {
return (/^[01]{1,10}$/).test(number);
};
Formula.BIN2DEC = function (number) {
// Return error if number is not binary or contains more than 10 characters (10 digits)
if (!Formula.VALIDBIN(number)) {
return '#NUM!';
}
// Convert binary number to decimal
var result = parseInt(number, 2);
// Handle negative numbers
var stringified = number.toString();
if (stringified.length === 10 && stringified.substring(0, 1) === '1') {
return parseInt(stringified.substring(1), 2) - 512;
} else {
return result;
}
};
Formula.BIN2HEX = function (number, places) {
// Return error if number is not binary or contains more than 10 characters (10 digits)
if (!Formula.VALIDBIN(number)) {
return '#NUM!';
}
// Ignore places and return a 10-character hexadecimal number if number is negative
var stringified = number.toString();
if (stringified.length === 10 && stringified.substring(0, 1) === '1') {
return (1099511627264 + parseInt(stringified.substring(1), 2)).toString(16);
}
// Convert binary number to hexadecimal
var result = parseInt(number, 2).toString(16);
// Return hexadecimal number using the minimum number of characters necessary if places is undefined
if (typeof places === 'undefined') {
return result;
} else {
// Return error if places is nonnumeric
if (isNaN(places)) {
return '#VALUE!';
}
// Return error if places is negative
if (places < 0) {
return '#NUM!';
}
// Truncate places in case it is not an integer
places = Math.floor(places);
// Pad return value with leading 0s (zeros) if necessary (using Underscore.string)
return (places >= result.length) ? _s.repeat('0', places - result.length) + result : '#NUM!';
}
};
Formula.BIN2OCT = function (number, places) {
// Return error if number is not binary or contains more than 10 characters (10 digits)
if (!Formula.VALIDBIN(number)) {
return '#NUM!';
}
// Ignore places and return a 10-character octal number if number is negative
var stringified = number.toString();
if (stringified.length === 10 && stringified.substring(0, 1) === '1') {
return (1073741312 + parseInt(stringified.substring(1), 2)).toString(8);
}
// Convert binary number to octal
var result = parseInt(number, 2).toString(8);
// Return octal number using the minimum number of characters necessary if places is undefined
if (typeof places === 'undefined') {
return result;
} else {
// Return error if places is nonnumeric
if (isNaN(places)) {
return '#VALUE!';
}
// Return error if places is negative
if (places < 0) {
return '#NUM!';
}
// Truncate places in case it is not an integer
places = Math.floor(places);
// Pad return value with leading 0s (zeros) if necessary (using Underscore.string)
return (places >= result.length) ? _s.repeat('0', places - result.length) + result : '#NUM!';
}
};
Formula.BITAND = function (number1, number2) {
// Return error if either number is a non-numeric value
if (isNaN(number1) || isNaN(number2)) {
return '#VALUE!';
}
// Return error if either number is less than 0
if (number1 < 0 || number2 < 0) {
return '#NUM!';
}
// Return error if either number is a non-integer
if (Math.floor(number1) !== number1 || Math.floor(number2) !== number2) {
return '#NUM!';
}
// Return error if either number is greater than (2^48)-1
if (number1 > 281474976710655 || number2 > 281474976710655) {
return '#NUM!';
}
// Return bitwise AND of two numbers
return number1 & number2;
};
Formula.BITLSHIFT = function (number, shift) {
// Return error if either number is a non-numeric value
if (isNaN(number) || isNaN(shift)) {
return '#VALUE!';
}
// Return error if number is less than 0
if (number < 0) {
return '#NUM!';
}
// Return error if number is a non-integer
if (Math.floor(number) !== number) {
return '#NUM!';
}
// Return error if number is greater than (2^48)-1
if (number > 281474976710655) {
return '#NUM!';
}
// Return error if the absolute value of shift is greater than 53
if (Math.abs(shift) > 53) {
return '#NUM!';
}
// Return number shifted by shift bits to the left or to the right if shift is negative
return (shift >= 0 ) ? number << shift : number >> -shift;
};
Formula.BITOR = function (number1, number2) {
// Return error if either number is a non-numeric value
if (isNaN(number1) || isNaN(number2)) {
return '#VALUE!';
}
// Return error if either number is less than 0
if (number1 < 0 || number2 < 0) {
return '#NUM!';
}
// Return error if either number is a non-integer
if (Math.floor(number1) !== number1 || Math.floor(number2) !== number2) {
return '#NUM!';
}
// Return error if either number is greater than (2^48)-1
if (number1 > 281474976710655 || number2 > 281474976710655) {
return '#NUM!';
}
// Return bitwise OR of two numbers
return number1 | number2;
};
Formula.BITRSHIFT = function (number, shift) {
// Return error if either number is a non-numeric value
if (isNaN(number) || isNaN(shift)) {
return '#VALUE!';
}
// Return error if number is less than 0
if (number < 0) {
return '#NUM!';
}
// Return error if number is a non-integer
if (Math.floor(number) !== number) {
return '#NUM!';
}
// Return error if number is greater than (2^48)-1
if (number > 281474976710655) {
return '#NUM!';
}
// Return error if the absolute value of shift is greater than 53
if (Math.abs(shift) > 53) {
return '#NUM!';
}
// Return number shifted by shift bits to the right or to the left if shift is negative
return (shift >= 0 ) ? number >> shift : number << -shift;
};
Formula.BITXOR = function (number1, number2) {
// Return error if either number is a non-numeric value
if (isNaN(number1) || isNaN(number2)) {
return '#VALUE!';
}
// Return error if either number is less than 0
if (number1 < 0 || number2 < 0) {
return '#NUM!';
}
// Return error if either number is a non-integer
if (Math.floor(number1) !== number1 || Math.floor(number2) !== number2) {
return '#NUM!';
}
// Return error if either number is greater than (2^48)-1
if (number1 > 281474976710655 || number2 > 281474976710655) {
return '#NUM!';
}
// Return bitwise XOR of two numbers
return number1 ^ number2;
};
Formula.COMPLEX = function (real, imaginary, suffix) {
// Return error if either number is a non-numeric value
if (isNaN(real) || isNaN(imaginary)) {
return '#VALUE!';
}
// Set suffix
suffix = (typeof suffix === 'undefined') ? 'i' : suffix;
// Return error if suffix is neither "i" nor "j"
if (suffix !== 'i' && suffix !== 'j') {
return '#VALUE!';
}
// Return complex number
if (real === 0 && imaginary === 0) {
return 0;
} else if (real === 0) {
return (imaginary === 1) ? suffix : imaginary.toString() + suffix;
} else if (imaginary === 0) {
return real.toString();
} else {
var sign = (imaginary > 0) ? '+' : '';
return real.toString() + sign + ((imaginary === 1) ? suffix : imaginary.toString() + suffix);
}
};
Formula.CONVERT = function (number, from_unit, to_unit) {
// Return error if number is a non-numeric value
if (isNaN(number)) {
return '#VALUE!';
}
// List of units supported by CONVERT and units defined by the International System of Units
// [Name, Symbol, Alternate symbols, Quantity, ISU, CONVERT, Conversion ratio]
var units = [
["a.u. of action", "?", null, "action", false, false, 1.05457168181818e-34],
["a.u. of charge", "e", null, "electric_charge", false, false, 1.60217653141414e-19],
["a.u. of energy", "Eh", null, "energy", false, false, 4.35974417757576e-18],
["a.u. of length", "a?", null, "length", false, false, 5.29177210818182e-11],
["a.u. of mass", "m?", null, "mass", false, false, 9.10938261616162e-31],
["a.u. of time", "?/Eh", null, "time", false, false, 2.41888432650516e-17],
["admiralty knot", "admkn", null, "speed", false, true, 0.514773333],
["ampere", "A", null, "electric_current", true, false, 1],
["ampere per meter", "A/m", null, "magnetic_field_intensity", true, false, 1],
["ångström", "Å", ["ang"], "length", false, true, 1e-10],
["are", "ar", null, "area", false, true, 100],
["astronomical unit", "ua", null, "length", false, false, 1.49597870691667e-11],
["bar", "bar", null, "pressure", false, false, 100000],
["barn", "b", null, "area", false, false, 1e-28],
["becquerel", "Bq", null, "radioactivity", true, false, 1],
["bit", "bit", ["b"], "information", false, true, 1],
["btu", "BTU", ["btu"], "energy", false, true, 1055.05585262],
["byte", "byte", null, "information", false, true, 8],
["candela", "cd", null, "luminous_intensity", true, false, 1],
["candela per square metre", "cd/m?", null, "luminance", true, false, 1],
["coulomb", "C", null, "electric_charge", true, false, 1],
["cubic ångström", "ang3", ["ang^3"], "volume", false, true, 1e-30],
["cubic foot", "ft3", ["ft^3"], "volume", false, true, 0.028316846592],
["cubic inch", "in3", ["in^3"], "volume", false, true, 0.000016387064],
["cubic light-year", "ly3", ["ly^3"], "volume", false, true, 8.46786664623715e-47],
["cubic metre", "m?", null, "volume", true, true, 1],
["cubic mile", "mi3", ["mi^3"], "volume", false, true, 4168181825.44058],
["cubic nautical mile", "Nmi3", ["Nmi^3"], "volume", false, true, 6352182208],
["cubic Pica", "Pica3", ["Picapt3", "Pica^3", "Picapt^3"], "volume", false, true, 7.58660370370369e-8],
["cubic yard", "yd3", ["yd^3"], "volume", false, true, 0.764554857984],
["cup", "cup", null, "volume", false, true, 0.0002365882365],
["dalton", "Da", ["u"], "mass", false, false, 1.66053886282828e-27],
["day", "d", ["day"], "time", false, true, 86400],
["degree", "°", null, "angle", false, false, 0.0174532925199433],
["degrees Rankine", "Rank", null, "temperature", false, true, 0.555555555555556],
["dyne", "dyn", ["dy"], "force", false, true, 0.00001],
["electronvolt", "eV", ["ev"], "energy", false, true, 1.60217656514141],
["ell", "ell", null, "length", false, true, 1.143],
["erg", "erg", ["e"], "energy", false, true, 1e-7],
["farad", "F", null, "electric_capacitance", true, false, 1],
["fluid ounce", "oz", null, "volume", false, true, 0.0000295735295625],
["foot", "ft", null, "length", false, true, 0.3048],
["foot-pound", "flb", null, "energy", false, true, 1.3558179483314],
["gal", "Gal", null, "acceleration", false, false, 0.01],
["gallon", "gal", null, "volume", false, true, 0.003785411784],
["gauss", "G", ["ga"], "magnetic_flux_density", false, true, 1],
["grain", "grain", null, "mass", false, true, 0.0000647989],
["gram", "g", null, "mass", false, true, 0.001],
["gray", "Gy", null, "absorbed_dose", true, false, 1],
["gross registered ton", "GRT", ["regton"], "volume", false, true, 2.8316846592],
["hectare", "ha", null, "area", false, true, 10000],
["henry", "H", null, "inductance", true, false, 1],
["hertz", "Hz", null, "frequency", true, false, 1],
["horsepower", "HP", ["h"], "power", false, true, 745.69987158227],
["horsepower-hour", "HPh", ["hh", "hph"], "energy", false, true, 2684519.538],
["hour", "h", ["hr"], "time", false, true, 3600],
["imperial gallon (U.K.)", "uk_gal", null, "volume", false, true, 0.00454609],
["imperial hundredweight", "lcwt", ["uk_cwt", "hweight"], "mass", false, true, 50.802345],
["imperial quart (U.K)", "uk_qt", null, "volume", false, true, 0.0011365225],
["imperial ton", "brton", ["uk_ton", "LTON"], "mass", false, true, 1016.046909],
["inch", "in", null, "length", false, true, 0.0254],
["international acre", "uk_acre", null, "area", false, true, 4046.8564224],
["IT calorie", "cal", null, "energy", false, true, 4.1868],
["joule", "J", null, "energy", true, true, 1],
["katal", "kat", null, "catalytic_activity", true, false, 1],
["kelvin", "K", ["kel"], "temperature", true, true, 1],
["kilogram", "kg", null, "mass", true, true, 1],
["knot", "kn", null, "speed", false, true, 0.514444444444444],
["light-year", "ly", null, "length", false, true, 9460730472580800],
["litre", "L", ["l", "lt"], "volume", false, true, 0.001],
["lumen", "lm", null, "luminous_flux", true, false, 1],
["lux", "lx", null, "illuminance", true, false, 1],
["maxwell", "Mx", null, "magnetic_flux", false, false, 1e-18],
["measurement ton", "MTON", null, "volume", false, true, 1.13267386368],
["meter per hour", "m/h", ["m/hr"], "speed", false, true, 0.00027777777777778],
["meter per second", "m/s", ["m/sec"], "speed", true, true, 1],
["meter per second squared", "m?s??", null, "acceleration", true, false, 1],
["parsec", "pc", ["parsec"], "length", false, true, 30856775814671900],
["meter squared per second", "m?/s", null, "kinematic_viscosity", true, false, 1],
["metre", "m", null, "length", true, true, 1],
["miles per hour", "mph", null, "speed", false, true, 0.44704],
["millimetre of mercury", "mmHg", null, "pressure", false, false, 133.322],
["minute", "?", null, "angle", false, false, 0.000290888208665722],
["minute", "min", ["mn"], "time", false, true, 60],
["modern teaspoon", "tspm", null, "volume", false, true, 0.000005],
["mole", "mol", null, "amount_of_substance", true, false, 1],
["morgen", "Morgen", null, "area", false, true, 2500],
["n.u. of action", "?", null, "action", false, false, 1.05457168181818e-34],
["n.u. of mass", "m?", null, "mass", false, false, 9.10938261616162e-31],
["n.u. of speed", "c?", null, "speed", false, false, 299792458],
["n.u. of time", "?/(me?c??)", null, "time", false, false, 1.28808866778687e-21],
["nautical mile", "M", ["Nmi"], "length", false, true, 1852],
["newton", "N", null, "force", true, true, 1],
["œrsted", "Oe ", null, "magnetic_field_intensity", false, false, 79.5774715459477],
["ohm", "Ω", null, "electric_resistance", true, false, 1],
["ounce mass", "ozm", null, "mass", false, true, 0.028349523125],
["pascal", "Pa", null, "pressure", true, false, 1],
["pascal second", "Pa?s", null, "dynamic_viscosity", true, false, 1],
["pferdestärke", "PS", null, "power", false, true, 735.49875],
["phot", "ph", null, "illuminance", false, false, 0.0001],
["pica (1/6 inch)", "pica", null, "length", false, true, 0.00035277777777778],
["pica (1/72 inch)", "Pica", ["Picapt"], "length", false, true, 0.00423333333333333],
["poise", "P", null, "dynamic_viscosity", false, false, 0.1],
["pond", "pond", null, "force", false, true, 0.00980665],
["pound force", "lbf", null, "force", false, true, 4.4482216152605],
["pound mass", "lbm", null, "mass", false, true, 0.45359237],
["quart", "qt", null, "volume", false, true, 0.000946352946],
["radian", "rad", null, "angle", true, false, 1],
["second", "?", null, "angle", false, false, 0.00000484813681109536],
["second", "s", ["sec"], "time", true, true, 1],
["short hundredweight", "cwt", ["shweight"], "mass", false, true, 45.359237],
["siemens", "S", null, "electrical_conductance", true, false, 1],
["sievert", "Sv", null, "equivalent_dose", true, false, 1],
["slug", "sg", null, "mass", false, true, 14.59390294],
["square ångström", "ang2", ["ang^2"], "area", false, true, 1e-20],
["square foot", "ft2", ["ft^2"], "area", false, true, 0.09290304],
["square inch", "in2", ["in^2"], "area", false, true, 0.00064516],
["square light-year", "ly2", ["ly^2"], "area", false, true, 8.95054210748189e+31],
["square meter", "m?", null, "area", true, true, 1],
["square mile", "mi2", ["mi^2"], "area", false, true, 2589988.110336],
["square nautical mile", "Nmi2", ["Nmi^2"], "area", false, true, 3429904],
["square Pica", "Pica2", ["Picapt2", "Pica^2", "Picapt^2"], "area", false, true, 0.00001792111111111],
["square yard", "yd2", ["yd^2"], "area", false, true, 0.83612736],
["statute mile", "mi", null, "length", false, true, 1609.344],
["steradian", "sr", null, "solid_angle", true, false, 1],
["stilb", "sb", null, "luminance", false, false, 0.0001],
["stokes", "St", null, "kinematic_viscosity", false, false, 0.0001],
["stone", "stone", null, "mass", false, true, 6.35029318],
["tablespoon", "tbs", null, "volume", false, true, 0.0000147868],
["teaspoon", "tsp", null, "volume", false, true, 0.00000492892],
["tesla", "T", null, "magnetic_flux_density", true, true, 1],
["thermodynamic calorie", "c", null, "energy", false, true, 4.184],
["ton", "ton", null, "mass", false, true, 907.18474],
["tonne", "t", null, "mass", false, false, 1000],
["U.K. pint", "uk_pt", null, "volume", false, true, 0.00056826125],
["U.S. bushel", "bushel", null, "volume", false, true, 0.03523907],
["U.S. oil barrel", "barrel", null, "volume", false, true, 0.158987295],
["U.S. pint", "pt", ["us_pt"], "volume", false, true, 0.000473176473],
["U.S. survey mile", "survey_mi", null, "length", false, true, 1609.347219],
["U.S. survey/statute acre", "us_acre", null, "area", false, true, 4046.87261],
["volt", "V", null, "voltage", true, false, 1],
["watt", "W", null, "power", true, true, 1],
["watt-hour", "Wh", ["wh"], "energy", false, true, 3600],
["weber", "Wb", null, "magnetic_flux", true, false, 1],
["yard", "yd", null, "length", false, true, 0.9144],
["year", "yr", null, "time", false, true, 31557600]
];
// Binary prefixes
// [Name, Prefix power of 2 value, Previx value, Abbreviation, Derived from]
var binary_prefixes = {
Yi: ["yobi", 80, 1208925819614629174706176, "Yi", "yotta"],
Zi: ["zebi", 70, 1180591620717411303424, "Zi", "zetta"],
Ei: ["exbi", 60, 1152921504606846976, "Ei", "exa"],
Pi: ["pebi", 50, 1125899906842624, "Pi", "peta"],
Ti: ["tebi", 40, 1099511627776, "Ti", "tera"],
Gi: ["gibi", 30, 1073741824, "Gi", "giga"],
Mi: ["mebi", 20, 1048576, "Mi", "mega"],
ki: ["kibi", 10, 1024, "ki", "kilo"]
};
// Unit prefixes
// [Name, Multiplier, Abbreviation]
var unit_prefixes = {
Y: ["yotta", 1e+24, "Y"],
Z: ["zetta", 1e+21, "Z"],
E: ["exa", 1e+18, "E"],
P: ["peta", 1e+15, "P"],
T: ["tera", 1e+12, "T"],
G: ["giga", 1e+09, "G"],
M: ["mega", 1e+06, "M"],
k: ["kilo", 1e+03, "k"],
h: ["hecto", 1e+02, "h"],
e: ["dekao", 1e+01, "e"],
d: ["deci", 1e-01, "d"],
c: ["centi", 1e-02, "c"],
m: ["milli", 1e-03, "m"],
u: ["micro", 1e-06, "u"],
n: ["nano", 1e-09, "n"],
p: ["pico", 1e-12, "p"],
f: ["femto", 1e-15, "f"],
a: ["atto", 1e-18, "a"],
z: ["zepto", 1e-21, "z"],
y: ["yocto", 1e-24, "y"]
};
// Initialize units and multipliers
var from = null;
var to = null;
var base_from_unit = from_unit;
var base_to_unit = to_unit;
var from_multiplier = 1;
var to_multiplier = 1;
var alt;
// Lookup from and to units
for (var i = 0; i < units.length; i++) {
alt = (units[i][2] === null) ? [] : units[i][2];
if (units[i][1] === base_from_unit || alt.indexOf(base_from_unit) >= 0) {
from = units[i];
}
if (units[i][1] === base_to_unit || alt.indexOf(base_to_unit) >= 0) {
to = units[i];
}
}
// Lookup from prefix
if (from === null) {
var from_binary_prefix = binary_prefixes[from_unit.substring(0, 2)];
var from_unit_prefix = unit_prefixes[from_unit.substring(0, 1)];
// Handle dekao unit prefix (only unit prefix with two characters)
if (from_unit.substring(0, 2) === 'da') {
from_unit_prefix = ["dekao", 1e+01, "da"];
}
// Handle binary prefixes first (so that 'Yi' is processed before 'Y')
if (from_binary_prefix) {
from_multiplier = from_binary_prefix[2];
base_from_unit = from_unit.substring(2);
} else if (from_unit_prefix) {
from_multiplier = from_unit_prefix[1];
base_from_unit = from_unit.substring(from_unit_prefix[2].length);
}
// Lookup from unit
for (var j = 0; j < units.length; j++) {
alt = (units[j][2] === null) ? [] : units[j][2];
if (units[j][1] === base_from_unit || alt.indexOf(base_from_unit) >= 0) {
from = units[j];
}
}
}
// Lookup to prefix
if (to === null) {
var to_binary_prefix = binary_prefixes[to_unit.substring(0, 2)];
var to_unit_prefix = unit_prefixes[to_unit.substring(0, 1)];
// Handle dekao unit prefix (only unit prefix with two characters)
if (to_unit.substring(0, 2) === 'da') {
to_unit_prefix = ["dekao", 1e+01, "da"];
}
// Handle binary prefixes first (so that 'Yi' is processed before 'Y')
if (to_binary_prefix) {
to_multiplier = to_binary_prefix[2];
base_to_unit = to_unit.substring(2);
} else if (to_unit_prefix) {
to_multiplier = to_unit_prefix[1];
base_to_unit = to_unit.substring(to_unit_prefix[2].length);
}
// Lookup to unit
for (var k = 0; k < units.length; k++) {
alt = (units[k][2] === null) ? [] : units[k][2];
if (units[k][1] === base_to_unit || alt.indexOf(base_to_unit) >= 0) {
to = units[k];
}
}
}
// Return error if a unit does not exist
if (from === null || to === null) {
return '#N/A';
}
// Return error if units represent different quantities
if (from[3] !== to[3]) {
return '#N/A';
}
// Return converted number
return number * from[6] * from_multiplier / (to[6] * to_multiplier);
};
Formula.DEC2BIN = function (number, places) {
// Return error if number is not a number
if (isNaN(number)) {
return '#VALUE!';
}
// Return error if number is not decimal, is lower than -512, or is greater than 511
if (!/^-?[0-9]{1,3}$/.test(number) || number < -512 || number > 511) {
return '#NUM!';
}
// Ignore places and return a 10-character binary number if number is negative
if (number < 0) {
return '1' + _s.repeat('0', 9 - (512 + number).toString(2).length) + (512 + number).toString(2);
}
// Convert decimal number to binary
var result = parseInt(number, 10).toString(2);
// Return binary number using the minimum number of characters necessary if places is undefined
if (typeof places === 'undefined') {
return result;
} else {
// Return error if places is nonnumeric
if (isNaN(places)) {
return '#VALUE!';
}
// Return error if places is negative
if (places < 0) {
return '#NUM!';
}
// Truncate places in case it is not an integer
places = Math.floor(places);
// Pad return value with leading 0s (zeros) if necessary (using Underscore.string)
return (places >= result.length) ? _s.repeat('0', places - result.length) + result : '#NUM!';
}
};
Formula.DEC2HEX = function (number, places) {
// Return error if number is not a number
if (isNaN(number)) {
return '#VALUE!';
}
// Return error if number is not decimal, is lower than -549755813888, or is greater than 549755813887
if (!/^-?[0-9]{1,12}$/.test(number) || number < -549755813888 || number > 549755813887) {
return '#NUM!';
}
// Ignore places and return a 10-character hexadecimal number if number is negative
if (number < 0) {
return (1099511627776 + number).toString(16);
}
// Convert decimal number to hexadecimal
var result = parseInt(number, 10).toString(16);
// Return hexadecimal number using the minimum number of characters necessary if places is undefined
if (typeof places === 'undefined') {
return result;
} else {
// Return error if places is nonnumeric
if (isNaN(places)) {
return '#VALUE!';
}
// Return error if places is negative
if (places < 0) {
return '#NUM!';
}
// Truncate places in case it is not an integer
places = Math.floor(places);
// Pad return value with leading 0s (zeros) if necessary (using Underscore.string)
return (places >= result.length) ? _s.repeat('0', places - result.length) + result : '#NUM!';
}
};
Formula.DEC2OCT = function (number, places) {
// Return error if number is not a number
if (isNaN(number)) {
return '#VALUE!';
}
// Return error if number is not decimal, is lower than -549755813888, or is greater than 549755813887
if (!/^-?[0-9]{1,9}$/.test(number) || number < -536870912 || number > 536870911) {
return '#NUM!';
}
// Ignore places and return a 10-character octal number if number is negative
if (number < 0) {
return (1073741824 + number).toString(8);
}
// Convert decimal number to octal
var result = parseInt(number, 10).toString(8);
// Return octal number using the minimum number of characters necessary if places is undefined
if (typeof places === 'undefined') {
return result;
} else {
// Return error if places is nonnumeric
if (isNaN(places)) {
return '#VALUE!';
}
// Return error if places is negative
if (places < 0) {
return '#NUM!';
}
// Truncate places in case it is not an integer
places = Math.floor(places);
// Pad return value with leading 0s (zeros) if necessary (using Underscore.string)
return (places >= result.length) ? _s.repeat('0', places - result.length) + result : '#NUM!';
}
};
Formula.DELTA = function (number1, number2) {
// Set number2 to zero if undefined
number2 = (typeof number2 === 'undefined') ? 0 : number2;
// Return error if either number is not a number
if (isNaN(number1) || isNaN(number2)) {
return '#VALUE!';
}
// Return delta
return (number1 === number2) ? 1 : 0;
};
Formula.ERF = function (lower_bound, upper_bound) {
// Set number2 to zero if undefined
upper_bound = (typeof upper_bound === 'undefined') ? 0 : upper_bound;
// Return error if either number is not a number
if (isNaN(lower_bound) || isNaN(upper_bound)) {
return '#VALUE!';
}
// Return ERFC using jStat [http://www.jstat.org/]
return jStat.erf(lower_bound);
};
Formula.ERFC = function (x) {
// Return error if x is not a number
if (isNaN(x)) {
return '#VALUE!';
}
// Return ERFC using jStat [http://www.jstat.org/]
return jStat.erfc(x);
};
Formula.ERFCPRECISE = function () {
return;
};
Formula.ERFPRECISE = function () {
return;
};
Formula.GESTEP = function (number, step) {
// Set step to zero if undefined
step = (typeof step === 'undefined') ? 0 : step;
// Return error if either number is not a number
if (isNaN(number) || isNaN(step)) {
return '#VALUE!';
}
// Return delta
return (number >= step) ? 1 : 0;
};
Formula.HEX2BIN = function (number, places) {
// Return error if number is not hexadecimal or contains more than ten characters (10 digits)
if (!/^[0-9A-Fa-f]{1,10}$/.test(number)) {
return '#NUM!';
}
// Check if number is negative
var negative = (number.length === 10 && number.substring(0, 1).toLowerCase() === 'f') ? true : false;
// Convert hexadecimal number to decimal
var decimal = (negative) ? parseInt(number, 16) - 1099511627776 : parseInt(number, 16);
// Return error if number is lower than -512 or greater than 511
if (decimal < -512 || decimal > 511) {
return '#NUM!';
}
// Ignore places and return a 10-character binary number if number is negative
if (negative) {
return '1' + _s.repeat('0', 9 - (512 + decimal).toString(2).length) + (512 + decimal).toString(2);
}
// Convert decimal number to binary
var result = decimal.toString(2);
// Return binary number using the minimum number of characters necessary if places is undefined
if (typeof places === 'undefined') {
return result;
} else {
// Return error if places is nonnumeric
if (isNaN(places)) {
return '#VALUE!';
}
// Return error if places is negative
if (places < 0) {
return '#NUM!';
}
// Truncate places in case it is not an integer
places = Math.floor(places);
// Pad return value with leading 0s (zeros) if necessary (using Underscore.string)
return (places >= result.length) ? _s.repeat('0', places - result.length) + result : '#NUM!';
}
};
Formula.HEX2DEC = function (number) {
// Return error if number is not hexadecimal or contains more than ten characters (10 digits)
if (!/^[0-9A-Fa-f]{1,10}$/.test(number)) {
return '#NUM!';
}
// Convert hexadecimal number to decimal
var decimal = parseInt(number, 16);
// Return decimal number
return (decimal >= 549755813888) ? decimal - 1099511627776 : decimal;
};
Formula.HEX2OCT = function (number, places) {
// Return error if number is not hexadecimal or contains more than ten characters (10 digits)
if (!/^[0-9A-Fa-f]{1,10}$/.test(number)) {
return '#NUM!';
}
// Convert hexadecimal number to decimal
var decimal = parseInt(number, 16);
// Return error if number is positive and greater than 0x1fffffff (536870911)
if (decimal > 536870911 && decimal < 1098974756864) {
return '#NUM!';
}
// Ignore places and return a 10-character octal number if number is negative
if (decimal >= 1098974756864) {
return (decimal - 1098437885952).toString(8);
}
// Convert decimal number to octal
var result = decimal.toString(8);
// Return octal number using the minimum number of characters necessary if places is undefined
if (typeof places === 'undefined') {
return result;
} else {
// Return error if places is nonnumeric
if (isNaN(places)) {
return '#VALUE!';
}
// Return error if places is negative
if (places < 0) {
return '#NUM!';
}
// Truncate places in case it is not an integer
places = Math.floor(places);
// Pad return value with leading 0s (zeros) if necessary (using Underscore.string)
return (places >= result.length) ? _s.repeat('0', places - result.length) + result : '#NUM!';
}
};
Formula.IMABS = function (inumber) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return absolute value of complex number
return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));
};
Formula.IMAGINARY = function (inumber) {
// Return 0 if inumber is equal to 0
if (inumber === 0 || inumber === '0') {
return 0;
}
// Handle special cases
if (['i', 'j'].indexOf(inumber) >= 0) {
return 1;
}
// Normalize imaginary coefficient
inumber = inumber.replace('+i', '+1i').replace('-i', '-1i').replace('+j', '+1j').replace('-j', '-1j');
// Lookup sign
var plus = inumber.indexOf('+');
var minus = inumber.indexOf('-');
if (plus === 0) {
plus = inumber.indexOf('+', 1);
}
if (minus === 0) {
minus = inumber.indexOf('-', 1);
}
// Lookup imaginary unit
var last = inumber.substring(inumber.length - 1, inumber.length);
var unit = (last === 'i' || last === 'j');
if (plus >= 0 || minus >= 0) {
// Return error if imaginary unit is neither i nor j
if (!unit) {
return '#NUM!';
}
// Return imaginary coefficient of complex number
if (plus >= 0) {
return (isNaN(inumber.substring(0, plus)) || isNaN(inumber.substring(plus + 1, inumber.length - 1))) ?
'#NUM!' :
Number(inumber.substring(plus + 1, inumber.length - 1));
} else {
return (isNaN(inumber.substring(0, minus)) || isNaN(inumber.substring(minus + 1, inumber.length - 1))) ?
'#NUM!' :
-Number(inumber.substring(minus + 1, inumber.length - 1));
}
} else {
if (unit) {
return (isNaN(inumber.substring(0, inumber.length - 1))) ? '#NUM!' : inumber.substring(0, inumber.length - 1);
} else {
return (isNaN(inumber)) ? '#NUM!' : 0;
}
}
};
Formula.IMARGUMENT = function (inumber) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return error if inumber is equal to zero
if (x === 0 && y === 0) {
return '#DIV/0!';
}
// Return PI/2 if x is equal to zero and y is positive
if (x === 0 && y > 0) {
return Math.PI / 2;
}
// Return -PI/2 if x is equal to zero and y is negative
if (x === 0 && y < 0) {
return -Math.PI / 2;
}
// Return zero if x is negative and y is equal to zero
if (y === 0 && x > 0) {
return 0;
}
// Return zero if x is negative and y is equal to zero
if (y === 0 && x < 0) {
return -Math.PI;
}
// Return argument of complex number
if (x > 0) {
return Math.atan(y / x);
} else if (x < 0 && y >= 0) {
return Math.atan(y / x) + Math.PI;
} else {
return Math.atan(y / x) - Math.PI;
}
};
Formula.IMCONJUGATE = function (inumber) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return conjugate of complex number
return (y !== 0) ? Formula.COMPLEX(x, -y, unit) : inumber;
};
Formula.IMCOS = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return cosine of complex number
return Formula.COMPLEX(Math.cos(x) * (Math.exp(y) + Math.exp(-y)) / 2, -Math.sin(x) * (Math.exp(y) - Math.exp(-y)) / 2, unit);
};
Formula.IMCOSH = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return hyperbolic cosine of complex number
return Formula.COMPLEX(Math.cos(y) * (Math.exp(x) + Math.exp(-x)) / 2, Math.sin(y) * (Math.exp(x) - Math.exp(-x)) / 2, unit);
};
Formula.IMCOT = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return cotangent of complex number
return Formula.IMDIV(Formula.IMCOS(inumber), Formula.IMSIN(inumber));
};
Formula.IMCSC = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return cosecant of complex number
return Formula.IMDIV('1', Formula.IMSIN(inumber));
};
Formula.IMCSCH = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return hyperbolic cosecant of complex number
return Formula.IMDIV('1', Formula.IMSINH(inumber));
};
Formula.IMDIV = function (inumber1, inumber2) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var a = Formula.IMREAL(inumber1);
var b = Formula.IMAGINARY(inumber1);
var c = Formula.IMREAL(inumber2);
var d = Formula.IMAGINARY(inumber2);
// Lookup imaginary unit
var unit1 = inumber1.substring(inumber1.length - 1);
var unit2 = inumber1.substring(inumber1.length - 1);
var unit = 'i';
if (unit1 === 'j') {
unit = 'j';
} else if (unit2 === 'j') {
unit = 'j';
}
// Return error if either coefficient is not a number
if (a === '#NUM!' || b === '#NUM!' || c === '#NUM!' || d === '#NUM!') {
return '#NUM!';
}
// Return error if inumber2 is null
if (c === 0 && d === 0) {
return '#NUM!';
}
// Return exponential of complex number
var den = c * c + d * d;
return Formula.COMPLEX((a * c + b * d) / den, (b * c - a * d) / den, unit);
};
Formula.IMEXP = function (inumber) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return exponential of complex number
var e = Math.exp(x);
return Formula.COMPLEX(e * Math.cos(y), e * Math.sin(y), unit);
};
Formula.IMLN = function (inumber) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return exponential of complex number
return Formula.COMPLEX(Math.log(Math.sqrt(x * x + y * y)), Math.atan(y / x), unit);
};
Formula.IMLOG10 = function (inumber) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return exponential of complex number
return Formula.COMPLEX(Math.log(Math.sqrt(x * x + y * y)) / Math.log(10), Math.atan(y / x) / Math.log(10), unit);
};
Formula.IMLOG2 = function (inumber) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return exponential of complex number
return Formula.COMPLEX(Math.log(Math.sqrt(x * x + y * y)) / Math.log(2), Math.atan(y / x) / Math.log(2), unit);
};
Formula.IMPOWER = function (inumber, number) {
// Return error if number is nonnumeric
if (isNaN(number)) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Calculate power of modulus
var p = Math.pow(Formula.IMABS(inumber), number);
// Calculate argument
var t = Formula.IMARGUMENT(inumber);
// Return exponential of complex number
return Formula.COMPLEX(p * Math.cos(number * t), p * Math.sin(number * t), unit);
};
Formula.IMPRODUCT = function () {
// Initialize result
var result = arguments[0];
// Loop on all numbers
for (var i = 1; i < arguments.length; i++) {
// Lookup coefficients of two complex numbers
var a = Formula.IMREAL(result);
var b = Formula.IMAGINARY(result);
var c = Formula.IMREAL(arguments[i]);
var d = Formula.IMAGINARY(arguments[i]);
// Return error if either coefficient is not a number
if (a === '#NUM!' || b === '#NUM!' || c === '#NUM!' || d === '#NUM!') {
return '#NUM!';
}
// Complute product of two complex numbers
result = Formula.COMPLEX(a * c - b * d, a * d + b * c);
}
// Return product of complex numbers
return result;
};
Formula.IMREAL = function (inumber) {
// Return 0 if inumber is equal to 0
if (inumber === 0 || inumber === '0') {
return 0;
}
// Handle special cases
if (['i', '+i', '1i', '+1i', '-i', '-1i', 'j', '+j', '1j', '+1j', '-j', '-1j'].indexOf(inumber) >= 0) {
return 0;
}
// Lookup sign
var plus = inumber.indexOf('+');
var minus = inumber.indexOf('-');
if (plus === 0) {
plus = inumber.indexOf('+', 1);
}
if (minus === 0) {
minus = inumber.indexOf('-', 1);
}
// Lookup imaginary unit
var last = inumber.substring(inumber.length - 1, inumber.length);
var unit = (last === 'i' || last === 'j');
if (plus >= 0 || minus >= 0) {
// Return error if imaginary unit is neither i nor j
if (!unit) {
return '#NUM!';
}
// Return real coefficient of complex number
if (plus >= 0) {
return (isNaN(inumber.substring(0, plus)) || isNaN(inumber.substring(plus + 1, inumber.length - 1))) ?
'#NUM!' :
Number(inumber.substring(0, plus));
} else {
return (isNaN(inumber.substring(0, minus)) || isNaN(inumber.substring(minus + 1, inumber.length - 1))) ?
'#NUM!' :
Number(inumber.substring(0, minus));
}
} else {
if (unit) {
return (isNaN(inumber.substring(0, inumber.length - 1))) ? '#NUM!' : 0;
} else {
return (isNaN(inumber)) ? '#NUM!' : inumber;
}
}
};
Formula.IMSEC = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return secant of complex number
return Formula.IMDIV('1', Formula.IMCOS(inumber));
};
Formula.IMSECH = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return hyperbolic secant of complex number
return Formula.IMDIV('1', Formula.IMCOSH(inumber));
};
Formula.IMSIN = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return sine of complex number
return Formula.COMPLEX(Math.sin(x) * (Math.exp(y) + Math.exp(-y)) / 2, Math.cos(x) * (Math.exp(y) - Math.exp(-y)) / 2, unit);
};
Formula.IMSINH = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return hyperbolic sine of complex number
return Formula.COMPLEX(Math.cos(y) * (Math.exp(x) - Math.exp(-x)) / 2, Math.sin(y) * (Math.exp(x) + Math.exp(-x)) / 2, unit);
};
Formula.IMSQRT = function (inumber) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Lookup imaginary unit
var unit = inumber.substring(inumber.length - 1);
unit = (unit === 'i' || unit === 'j') ? unit : 'i';
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Calculate power of modulus
var s = Math.sqrt(Formula.IMABS(inumber));
// Calculate argument
var t = Formula.IMARGUMENT(inumber);
// Return exponential of complex number
return Formula.COMPLEX(s * Math.cos(t / 2), s * Math.sin(t / 2), unit);
};
Formula.IMSUB = function (inumber1, inumber2) {
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var a = Formula.IMREAL(inumber1);
var b = Formula.IMAGINARY(inumber1);
var c = Formula.IMREAL(inumber2);
var d = Formula.IMAGINARY(inumber2);
// Lookup imaginary unit
var unit1 = inumber1.substring(inumber1.length - 1);
var unit2 = inumber1.substring(inumber1.length - 1);
var unit = 'i';
if (unit1 === 'j') {
unit = 'j';
} else if (unit2 === 'j') {
unit = 'j';
}
// Return error if either coefficient is not a number
if (a === '#NUM!' || b === '#NUM!' || c === '#NUM!' || d === '#NUM!') {
return '#NUM!';
}
// Return _ of two complex numbers
return Formula.COMPLEX(a - c, b - d, unit);
};
Formula.IMSUM = function () {
// Initialize result
var result = arguments[0];
// Loop on all numbers
for (var i = 1; i < arguments.length; i++) {
// Lookup coefficients of two complex numbers
var a = Formula.IMREAL(result);
var b = Formula.IMAGINARY(result);
var c = Formula.IMREAL(arguments[i]);
var d = Formula.IMAGINARY(arguments[i]);
// Return error if either coefficient is not a number
if (a === '#NUM!' || b === '#NUM!' || c === '#NUM!' || d === '#NUM!') {
return '#NUM!';
}
// Complute product of two complex numbers
result = Formula.COMPLEX(a + c, b + d);
}
// Return sum of complex numbers
return result;
};
Formula.IMTAN = function (inumber) {
// Return error if inumber is a logical value
if (inumber === true || inumber === false) {
return '#VALUE!';
}
// Lookup real and imaginary coefficients using Formula.js [http://formulajs.org]
var x = Formula.IMREAL(inumber);
var y = Formula.IMAGINARY(inumber);
// Return error if either coefficient is not a number
if (x === '#NUM!' || y === '#NUM!') {
return '#NUM!';
}
// Return tangent of complex number
return Formula.IMDIV(Formula.IMSIN(inumber), Formula.IMCOS(inumber));
};
Formula.OCT2BIN = function (number, places) {
// Return error if number is not hexadecimal or contains more than ten characters (10 digits)
if (!/^[0-7]{1,10}$/.test(number)) {
return '#NUM!';
}
// Check if number is negative
var negative = (number.length === 10 && number.substring(0, 1) === '7') ? true : false;
// Convert octal number to decimal
var decimal = (negative) ? parseInt(number, 8) - 1073741824 : parseInt(number, 8);
// Return error if number is lower than -512 or greater than 511
if (decimal < -512 || decimal > 511) {
return '#NUM!';
}
// Ignore places and return a 10-character binary number if number is negative
if (negative) {
return '1' + _s.repeat('0', 9 - (512 + decimal).toString(2).length) + (512 + decimal).toString(2);
}
// Convert decimal number to binary
var result = decimal.toString(2);
// Return binary number using the minimum number of characters necessary if places is undefined
if (typeof places === 'undefined') {
return result;
} else {
// Return error if places is nonnumeric
if (isNaN(places)) {
return '#VALUE!';
}
// Return error if places is negative
if (places < 0) {
return '#NUM!';
}
// Truncate places in case it is not an integer
places = Math.floor(places);
// Pad return value with leading 0s (zeros) if necessary (using Underscore.string)
return (places >= result.length) ? _s.repeat('0', places - result.length) + result : '#NUM!';
}
};
Formula.OCT2DEC = function (number) {
// Return error if number is not octal or contains more than ten characters (10 digits)
if (!/^[0-7]{1,10}$/.test(number)) {
return '#NUM!';
}
// Convert octal number to decimal
var decimal = parseInt(number, 8);
// Return decimal number
return (decimal >= 536870912) ? decimal - 1073741824 : decimal;
};
Formula.OCT2HEX = function (number, places) {
// Return error if number is not octal or contains more than ten characters (10 digits)
if (!/^[0-7]{1,10}$/.test(number)) {
return '#NUM!';
}
// Convert octal number to decimal
var decimal = parseInt(number, 8);
// Ignore places and return a 10-character octal number if number is negative
if (decimal >= 536870912) {
return 'ff' + (decimal + 3221225472).toString(16);
}
// Convert decimal number to hexadecimal
var result = decimal.toString(16);
// Return hexadecimal number using the minimum number of characters necessary if places is undefined
if (typeof places === 'undefined') {
return result;
} else {
// Return error if places is nonnumeric
if (isNaN(places)) {
return '#VALUE!';
}
// Return error if places is negative
if (places < 0) {
return '#NUM!';
}
// Truncate places in case it is not an integer
places = Math.floor(places);
// Pad return value with leading 0s (zeros) if necessary (using Underscore.string)
return (places >= result.length) ? _s.repeat('0', places - result.length) + result : '#NUM!';
}
};
// Financial functions
Formula.ACCRINT = function (issue, first, settlement, rate, par, frequency, basis, method) {
// Return error if either date is invalid
if (!moment(issue).isValid() || !moment(first).isValid() || !moment(settlement).isValid()) {
return '#VALUE!';
}
// Return error if either rate or par are lower than or equal to zero
if (rate <= 0 || par <= 0) {
return '#NUM!';
}
// Return error if frequency is neither 1, 2, or 4
if ([1, 2, 4].indexOf(frequency) === -1) {
return '#NUM!';
}
// Return error if basis is neither 0, 1, 2, 3, or 4
if ([0, 1, 2, 3, 4].indexOf(basis) === -1) {
return '#NUM!';
}
// Return error if issue greater than or equal to settlement
if (moment(issue).diff(moment(settlement)) >= 0) {
return '#NUM!';
}
// Set default values
par = (typeof par === 'undefined') ? 0 : par;
basis = (typeof basis === 'undefined') ? 0 : basis;
method = (typeof method === 'undefined') ? true : method;
// Compute accrued interest
var factor = 0;
var id = moment(new Date(issue));
var fd = moment(new Date(first));
var sd = moment(new Date(settlement));
var days = (moment([id.year()]).isLeapYear()) ? 366 : 365;
switch (basis) {
case 0:
// US (NASD) 30/360
factor = Formula.YEARFRAC(issue, settlement, basis);
break;
case 1:
// Actual/actual
factor = Formula.YEARFRAC(issue, settlement, basis);
break;
case 2:
// Actual/360
factor = Formula.YEARFRAC(issue, settlement, basis);
break;
case 3:
// Actual/365
factor = Formula.YEARFRAC(issue, settlement, basis);
break;
case 4:
// European 30/360
factor = Formula.YEARFRAC(issue, settlement, basis);
break;
}
return par * rate * factor;
};
Formula.ACCRINTM = function () {
return;
};
Formula.AMORDEGRC = function () {
return;
};
Formula.AMORLINC = function () {
return;
};
Formula.COUPDAYBS = function () {
return;
};
Formula.COUPDAYS = function () {
return;
};
Formula.COUPDAYSNC = function () {
return;
};
Formula.COUPNCD = function () {
return;
};
Formula.COUPNUM = function () {
return;
};
Formula.COUPPCD = function () {
return;
};
Formula.CUMIPMT = function (rate, periods, value, start, end, type) {
// Credits: algorithm inspired by Apache OpenOffice
// Credits: Hannes Stiebitzhofer for the translations of function and variable names
// Requires Formula.FV() and Formula.PMT() from Formula.js [http://stoic.com/formula/]
// Evaluate rate and periods (TODO: replace with secure expression evaluator)
rate = eval(rate);
periods = eval(periods);
// Return error if either rate, periods, or value are lower than or equal to zero
if (rate <= 0 || periods <= 0 || value <= 0) {
return '#NUM!';
}
// Return error if start < 1, end < 1, or start > end
if (start < 1 || end < 1 || start > end) {
return '#NUM!';
}
// Return error if type is neither 0 nor 1
if (type !== 0 && type !== 1) {
return '#NUM!';
}
// Compute cumulative interest
var payment = Formula.PMT(rate, periods, value, 0, type);
var interest = 0;
if (start === 1) {
if (type === 0) {
interest = -value;
start++;
}
}
for (var i = start; i <= end; i++) {
if (type === 1) {
interest += Formula.FV(rate, i - 2, payment, value, 1) - payment;
} else {
interest += Formula.FV(rate, i - 1, payment, value, 0);
}
}
interest *= rate;
// Return cumulative interest
return interest;
};
Formula.CUMPRINC = function (rate, periods, value, start, end, type) {
// Credits: algorithm inspired by Apache OpenOffice
// Credits: Hannes Stiebitzhofer for the translations of function and variable names
// Requires Formula.FV() and Formula.PMT() from Formula.js [http://stoic.com/formula/]
// Evaluate rate and periods (TODO: replace with secure expression evaluator)
rate = eval(rate);
periods = eval(periods);
// Return error if either rate, periods, or value are lower than or equal to zero
if (rate <= 0 || periods <= 0 || value <= 0) {
return '#NUM!';
}
// Return error if start < 1, end < 1, or start > end
if (start < 1 || end < 1 || start > end) {
return '#NUM!';
}
// Return error if type is neither 0 nor 1
if (type !== 0 && type !== 1) {
return '#NUM!';
}
// Compute cumulative principal
var payment = Formula.PMT(rate, periods, value, 0, type);
var principal = 0;
if (start === 1) {
if (type === 0) {
principal = payment + value * rate;
} else {
principal = payment;
}
start++;
}
for (var i = start; i <= end; i++) {
if (type > 0) {
principal += payment - (Formula.FV(rate, i - 2, payment, value, 1) - payment) * rate;
} else {
principal += payment - Formula.FV(rate, i - 1, payment, value, 0) * rate;
}
}
// Return cumulative principal
return principal;
};
Formula.DB = function (cost, salvage, life, period, month) {
// Initialize month
month = (typeof month === 'undefined') ? 12 : month;
// Return error if any of the parameters is not a number
if (isNaN(cost) || isNaN(salvage) || isNaN(life) || isNaN(period) || isNaN(month)) {
return '#VALUE!';
}
// Return error if any of the parameters is negative [
if (cost < 0 || salvage < 0 || life < 0 || period < 0) {
return '#NUM!';
}
// Return error if month is not an integer between 1 and 12
if ([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12].indexOf(month) === -1) {
return '#NUM!';
}
// Return error if period is greater than life
if (period > life) {
return '#NUM!';
}
// Return 0 (zero) if salvage is greater than or equal to cost
if (salvage >= cost) {
return 0;
}
// Rate is rounded to three decimals places
var rate = (1 - Math.pow(salvage / cost, 1 / life)).toFixed(3);
// Compute initial depreciation
var initial = cost * rate * month / 12;
// Compute total depreciation
var total = initial;
var current = 0;
var ceiling = (period === life) ? life - 1 : period;
for (var i = 2; i <= ceiling; i++) {
current = (cost - total) * rate;
total += current;
}
// Depreciation for the first and last periods are special cases
if (period === 1) {
// First period
return initial;
} else if (period === life) {
// Last period
return (cost - total) * rate;
} else {
return current;
}
};
Formula.DDB = function (cost, salvage, life, period, factor) {
// Initialize factor
factor = (typeof factor === 'undefined') ? 2 : factor;
// Return error if any of the parameters is not a number
if (isNaN(cost) || isNaN(salvage) || isNaN(life) || isNaN(period) || isNaN(factor)) {
return '#VALUE!';
}
// Return error if any of the parameters is negative or if factor is null
if (cost < 0 || salvage < 0 || life < 0 || period < 0 || factor <= 0) {
return '#NUM!';
}
// Return error if period is greater than life
if (period > life) {
return '#NUM!';
}
// Return 0 (zero) if salvage is greater than or equal to cost
if (salvage >= cost) {
return 0;
}
// Compute depreciation
var total = 0;
var current = 0;
for (var i = 1; i <= period; i++) {
current = Math.min((cost - total) * (factor / life), (cost - salvage - total));
total += current;
}
// Return depreciation
return current;
};
Formula.DISC = function () {
return;
};
Formula.DOLLARDE = function (dollar, fraction) {
// Credits: algorithm inspired by Apache OpenOffice
// Return error if any of the parameters is not a number
if (isNaN(dollar) || isNaN(fraction)) {
return '#VALUE!';
}
// Return error if fraction is negative
if (fraction < 0) {
return '#NUM!';
}
// Return error if fraction is greater than or equal to 0 and less than 1
if (fraction >= 0 && fraction < 1) {
return '#DIV/0!';
}
// Truncate fraction if it is not an integer
fraction = parseInt(fraction, 10);
// Compute integer part
var result = parseInt(dollar, 10);
// Add decimal part
result += (dollar % 1) * Math.pow(10, Math.ceil(Math.log(fraction) / Math.LN10)) / fraction;
// Round result
var power = Math.pow(10, Math.ceil(Math.log(fraction) / Math.LN2) + 1);
result = Math.round(result * power) / power;
// Return converted dollar price
return result;
};
Formula.DOLLARFR = function (dollar, fraction) {
// Credits: algorithm inspired by Apache OpenOffice
// Return error if any of the parameters is not a number
if (isNaN(dollar) || isNaN(fraction)) {
return '#VALUE!';
}
// Return error if fraction is negative
if (fraction < 0) {
return '#NUM!';
}
// Return error if fraction is greater than or equal to 0 and less than 1
if (fraction >= 0 && fraction < 1) {
return '#DIV/0!';
}
// Truncate fraction if it is not an integer
fraction = parseInt(fraction, 10);
// Compute integer part
var result = parseInt(dollar, 10);
// Add decimal part
result += (dollar % 1) * Math.pow(10, -Math.ceil(Math.log(fraction) / Math.LN10)) * fraction;
// Return converted dollar price
return result;
};
Formula.DURATION = function () {
return;
};
Formula.EFFECT = function (rate, periods) {
// Return error if any of the parameters is not a number
if (isNaN(rate) || isNaN(periods)) {
return '#VALUE!';
}
// Return error if rate <=0 or periods < 1
if (rate <= 0 || periods < 1) {
return '#NUM!';
}
// Truncate periods if it is not an integer
periods = parseInt(periods, 10);
// Return effective annual interest rate
return Math.pow(1 + rate / periods, periods) - 1;
};
Formula.FV = function (rate, periods, payment, value, type) {
// Credits: algorithm inspired by Apache OpenOffice
// Initialize type
type = (typeof type === 'undefined') ? 0 : type;
// Evaluate rate (TODO: replace with secure expression evaluator)
rate = eval(rate);
// Return future value
var result;
if (rate === 0) {
result = value + payment * periods;
} else {
var term = Math.pow(1 + rate, periods);
if (type === 1) {
result = value * term + payment * (1 + rate) * (term - 1.0) / rate;
} else {
result = value * term + payment * (term - 1) / rate;
}
}
return -result;
};
Formula.FVSCHEDULE = function (principal, schedule) {
// Initialize future value
var future = principal;
// Apply all interests in schedule
for (var i = 0; i < schedule.length; i++) {
// Return error if schedule value is not a number
if (isNaN(schedule[i])) {
return '#VALUE!';
}
// Apply scheduled interest
future *= 1 + schedule[i];
}
// Return future value
return future;
};
Formula.INTRATE = function () {
return;
};
Formula.IPMT = function (rate, period, periods, present, future, type) {
// Credits: algorithm inspired by Apache OpenOffice
// Initialize type
type = (typeof type === 'undefined') ? 0 : type;
// Evaluate rate and periods (TODO: replace with secure expression evaluator)
rate = eval(rate);
periods = eval(periods);
// Compute payment
var payment = Formula.PMT(rate, periods, present, future, type);
// Compute interest
var interest;
if (period === 1) {
if (type === 1) {
interest = 0;
} else {
interest = -present;
}
} else {
if (type === 1) {
interest = Formula.FV(rate, period - 2, payment, present, 1) - payment;
} else {
interest = Formula.FV(rate, period - 1, payment, present, 0);
}
}
// Return interest
return interest * rate;
};
Formula.IRR = function (values, guess) {
// Credits: algorithm inspired by Apache OpenOffice
// Calculates the resulting amount
var irrResult = function (values, dates, rate) {
var r = rate + 1;
var result = values[0];
for (var i = 1; i < values.length; i++) {
result += values[i] / Math.pow(r, (dates[i] - dates[0]) / 365);
}
return result;
};
// Calculates the first derivation
var irrResultDeriv = function (values, dates, rate) {
var r = rate + 1;
var result = 0;
for (var i = 1; i < values.length; i++) {
var frac = (dates[i] - dates[0]) / 365;
result -= frac * values[i] / Math.pow(r, frac + 1);
}
return result;
};
// Initialize dates and check that values contains at least one positive value and one negative value
var dates = [];
var positive = false;
var negative = false;
for (var i = 0; i < values.length; i++) {
dates[i] = (i === 0) ? 0 : dates[i - 1] + 365;
if (values[i] > 0) {
positive = true;
}
if (values[i] < 0) {
negative = true;
}
}
// Return error if values does not contain at least one positive value and one negative value
if (!positive || !negative) {
return '#NUM!';
}
// Initialize guess and resultRate
guess = (typeof guess === 'undefined') ? 0.1 : guess;
var resultRate = guess;
// Set maximum epsilon for end of iteration
var epsMax = 1e-10;
// Set maximum number of iterations
var iterMax = 50;
// Implement Newton's method
var newRate, epsRate, resultValue;
var iteration = 0;
var contLoop = true;
do {
resultValue = irrResult(values, dates, resultRate);
newRate = resultRate - resultValue / irrResultDeriv(values, dates, resultRate);
epsRate = Math.abs(newRate - resultRate);
resultRate = newRate;
contLoop = (epsRate > epsMax) && (Math.abs(resultValue) > epsMax);
} while (contLoop && (++iteration < iterMax));
if (contLoop) {
return '#NUM!';
}
// Return internal rate of return
return resultRate;
};
Formula.ISPMT = function (rate, period, periods, value) {
// Evaluate rate and periods (TODO: replace with secure expression evaluator)
rate = eval(rate);
periods = eval(periods);
// Return interest
return value * rate * (period / periods - 1);
};
Formula.MDURATION = function () {
return;
};
Formula.MIRR = function (values, finance_rate, reinvest_rate) {
// Initialize number of values
var n = values.length;
// Lookup payments (negative values) and incomes (positive values)
var payments = [];
var incomes = [];
for (var i = 0; i < n; i++) {
if (values[i] < 0) {
payments.push(values[i]);
} else {
incomes.push(values[i]);
}
}
// Return modified internal rate of return
var num = -Formula.NPV(reinvest_rate, incomes) * Math.pow(1 + reinvest_rate, n - 1);
var den = Formula.NPV(finance_rate, payments) * (1 + finance_rate);
return Math.pow(num / den, 1 / (n - 1)) - 1;
};
Formula.NOMINAL = function (rate, periods) {
// Return error if any of the parameters is not a number
if (isNaN(rate) || isNaN(periods)) {
return '#VALUE!';
}
// Return error if rate <=0 or periods < 1
if (rate <= 0 || periods < 1) {
return '#NUM!';
}
// Truncate periods if it is not an integer
periods = parseInt(periods, 10);
// Return nominal annual interest rate
return (Math.pow(rate + 1, 1 / periods) - 1) * periods;
};
Formula.NPER = function (rate, payment, present, future, type) {
// Initialize type
type = (typeof type === 'undefined') ? 0 : type;
// Initialize future value
future = (typeof future === 'undefined') ? 0 : future;
// Evaluate rate and periods (TODO: replace with secure expression evaluator)
rate = eval(rate);
// Return number of periods
var num = payment * (1 + rate * type) - future * rate;
var den = (present * rate + payment * (1 + rate * type));
return Math.log(num / den) / Math.log(1 + rate);
};
Formula.NPV = function () {
// Cast arguments to array
var args = [];
for (var i = 0; i < arguments.length; i++) {
args = args.concat(arguments[i]);
}
// Lookup rate
var rate = args[0];
// Initialize net present value
var value = 0;
// Loop on all values
for (var j = 1; j < args.length; j++) {
value += args[j] / Math.pow(1 + rate, j);
}
// Return net present value
return value;
};
Formula.ODDFPRICE = function () {
return;
};
Formula.ODDFYIELD = function () {
return;
};
Formula.ODDLPRICE = function () {
return;
};
Formula.ODDLYIELD = function () {
return;
};
Formula.PDURATION = function (rate, present, future) {
// Return error if any of the parameters is not a number
if (isNaN(rate) || isNaN(present) || isNaN(future)) {
return '#VALUE!';
}
// Return error if rate <=0
if (rate <= 0) {
return '#NUM!';
}
// Return number of periods
return (Math.log(future) - Math.log(present)) / Math.log(1 + rate);
};
Formula.PMT = function (rate, periods, present, future, type) {
// Credits: algorithm inspired by Apache OpenOffice
// Initialize type
type = (typeof type === 'undefined') ? 0 : type;
// Evaluate rate and periods (TODO: replace with secure expression evaluator)
rate = eval(rate);
periods = eval(periods);
// Return payment
var result;
if (rate === 0) {
result = (present + future) / periods;
} else {
var term = Math.pow(1 + rate, periods);
if (type === 1) {
result = (future * rate / (term - 1) + present * rate / (1 - 1 / term)) / (1 + rate);
} else {
result = future * rate / (term - 1) + present * rate / (1 - 1 / term);
}
}
return -result;
};
Formula.PPMT = function (rate, period, periods, present, future, type) {
return Formula.PMT(rate, periods, present, future, type) - Formula.IPMT(rate, period, periods, present, future, type);
};
Formula.PRICE = function () {
return;
};
Formula.PRICEDISC = function () {
return;
};
Formula.PRICEMAT = function () {
return;
};
Formula.PV = function (rate, periods, payment, future, type) {
// Initialize type
type = (typeof type === 'undefined') ? 0 : type;
// Evaluate rate and periods (TODO: replace with secure expression evaluator)
rate = eval(rate);
periods = eval(periods);
// Return present value
if (rate === 0) {
return -payment * periods - future;
} else {
return (((1 - Math.pow(1 + rate, periods)) / rate) * payment * (1 + rate * type) - future) / Math.pow(1 + rate, periods);
}
};
Formula.RATE = function (periods, payment, present, future, type, guess) {
// Credits: rabugento
// Initialize guess
guess = (typeof guess === 'undefined') ? 0.01 : guess;
// Initialize future
future = (typeof future === 'undefined') ? 0 : future;
// Initialize type
type = (typeof type === 'undefined') ? 0 : type;
// Evaluate periods (TODO: replace with secure expression evaluator)
periods = eval(periods);
// Set maximum epsilon for end of iteration
var epsMax = 1e-10;
// Set maximum number of iterations
var iterMax = 50;
// Implement Newton's method
var y, y0, y1, x0, x1 = 0, f = 0, i = 0;
var rate = guess;
if (Math.abs(rate) < epsMax) {
y = present * (1 + periods * rate) + payment * (1 + rate * type) * periods + future;
} else {
f = Math.exp(periods * Math.log(1 + rate));
y = present * f + payment * (1 / rate + type) * (f - 1) + future;
}
y0 = present + payment * periods + future;
y1 = present * f + payment * (1 / rate + type) * (f - 1) + future;
i = x0 = 0;
x1 = rate;
while ((Math.abs(y0 - y1) > epsMax) && (i < iterMax)) {
rate = (y1 * x0 - y0 * x1) / (y1 - y0);
x0 = x1;
x1 = rate;
if (Math.abs(rate) < epsMax) {
y = present * (1 + periods * rate) + payment * (1 + rate * type) * periods + future;
} else {
f = Math.exp(periods * Math.log(1 + rate));
y = present * f + payment * (1 / rate + type) * (f - 1) + future;
}
y0 = y1;
y1 = y;
++i;
}
return rate;
};
Formula.RECEIVED = function () {
return;
};
Formula.RRI = function (periods, present, future) {
// Return error if any of the parameters is not a number
if (isNaN(periods) || isNaN(present) || isNaN(future)) {
return '#VALUE!';
}
// Return error if periods or present is equal to 0 (zero)
if (periods === 0 || present === 0) {
return '#NUM!';
}
// Return equivalent interest rate
return Math.pow(future / present, 1 / periods) - 1;
};
Formula.SLN = function (cost, salvage, life) {
// Return error if any of the parameters is not a number
if (isNaN(cost) || isNaN(salvage) || isNaN(life)) {
return '#VALUE!';
}
// Return error if life equal to 0 (zero)
if (life === 0) {
return '#NUM!';
}
// Return straight-line depreciation
return (cost - salvage) / life;
};
Formula.SYD = function (cost, salvage, life, period) {
// Return error if any of the parameters is not a number
if (isNaN(cost) || isNaN(salvage) || isNaN(life) || isNaN(period)) {
return '#VALUE!';
}
// Return error if life equal to 0 (zero)
if (life === 0) {
return '#NUM!';
}
// Return error if period is lower than 1 or greater than life
if (period < 1 || period > life) {
return '#NUM!';
}
// Truncate period if it is not an integer
period = parseInt(period, 10);
// Return straight-line depreciation
return (cost - salvage) * (life - period + 1) * 2 / (life * (life + 1));
};
Formula.TBILLEQ = function (settlement, maturity, discount) {
// Return error if either date is invalid
if (!moment(settlement).isValid() || !moment(maturity).isValid()) {
return '#VALUE!';
}
// Return error if discount is lower than or equal to zero
if (discount <= 0) {
return '#NUM!';
}
// Return error if settlement is greater than maturity
if (moment(settlement).diff(moment(maturity)) > 0) {
return '#NUM!';
}
// Return error if maturity is more than one year after settlement
if (moment(maturity).diff(moment(settlement), 'years') > 1) {
return '#NUM!';
}
// Return bond-equivalent yield
return (365 * discount) / (360 - discount * Formula.DAYS360(settlement, maturity));
};
Formula.TBILLPRICE = function (settlement, maturity, discount) {
// Return error if either date is invalid
if (!moment(settlement).isValid() || !moment(maturity).isValid()) {
return '#VALUE!';
}
// Return error if discount is lower than or equal to zero
if (discount <= 0) {
return '#NUM!';
}
// Return error if settlement is greater than maturity
if (moment(settlement).diff(moment(maturity)) > 0) {
return '#NUM!';
}
// Return error if maturity is more than one year after settlement
if (moment(maturity).diff(moment(settlement), 'years') > 1) {
return '#NUM!';
}
// Return bond-equivalent yield
return 100 * (1 - discount * Formula.DAYS360(settlement, maturity) / 360);
};
Formula.TBILLYIELD = function (settlement, maturity, price) {
// Return error if either date is invalid
if (!moment(settlement).isValid() || !moment(maturity).isValid()) {
return '#VALUE!';
}
// Return error if price is lower than or equal to zero
if (price <= 0) {
return '#NUM!';
}
// Return error if settlement is greater than maturity
if (moment(settlement).diff(moment(maturity)) > 0) {
return '#NUM!';
}
// Return error if maturity is more than one year after settlement
if (moment(maturity).diff(moment(settlement), 'years') > 1) {
return '#NUM!';
}
// Return bond-equivalent yield
return (100 - price) * 360 / (price * Formula.DAYS360(settlement, maturity));
};
Formula.VDB = function () {
return;
};
Formula.XIRR = function (values, dates, guess) {
// Credits: algorithm inspired by Apache OpenOffice
// Calculates the resulting amount
var irrResult = function (values, dates, rate) {
var r = rate + 1;
var result = values[0];
for (var i = 1; i < values.length; i++) {
result += values[i] / Math.pow(r, moment(dates[i]).diff(moment(dates[0]), 'days') / 365);
}
return result;
};
// Calculates the first derivation
var irrResultDeriv = function (values, dates, rate) {
var r = rate + 1;
var result = 0;
for (var i = 1; i < values.length; i++) {
var frac = moment(dates[i]).diff(moment(dates[0]), 'days') / 365;
result -= frac * values[i] / Math.pow(r, frac + 1);
}
return result;
};
// Check that values contains at least one positive value and one negative value
var positive = false;
var negative = false;
for (var i = 0; i < values.length; i++) {
if (values[i] > 0) {
positive = true;
}
if (values[i] < 0) {
negative = true;
}
}
// Return error if values does not contain at least one positive value and one negative value
if (!positive || !negative) {
return '#NUM!';
}
// Initialize guess and resultRate
guess = guess || 0.1;
var resultRate = guess;
// Set maximum epsilon for end of iteration
var epsMax = 1e-10;
// Set maximum number of iterations
var iterMax = 50;
// Implement Newton's method
var newRate, epsRate, resultValue;
var iteration = 0;
var contLoop = true;
do {
resultValue = irrResult(values, dates, resultRate);
newRate = resultRate - resultValue / irrResultDeriv(values, dates, resultRate);
epsRate = Math.abs(newRate - resultRate);
resultRate = newRate;
contLoop = (epsRate > epsMax) && (Math.abs(resultValue) > epsMax);
} while (contLoop && (++iteration < iterMax));
if (contLoop) {
return '#NUM!';
}
// Return internal rate of return
return resultRate;
};
Formula.XNPV = function (rate, values, dates) {
var result = 0;
for (var i = 0; i < values.length; i++) {
result += values[i] / Math.pow(1 + rate, moment(dates[i]).diff(moment(dates[0]), 'days') / 365);
}
return result;
};
Formula.YIELD = function () {
return;
};
Formula.YIELDDISC = function () {
return;
};
Formula.YIELDMAT = function () {
};
// Information functions
Formula.ISNUMBER = function (number) {
return (!isNaN(parseFloat(number)) && isFinite(number)) ? true : false;
};
// Logical functions
Formula.AND = function () {
var result = true;
for (var i = 0; i < arguments.length; i++) {
if (!arguments[i]) {
result = false;
}
}
return result;
};
Formula.FALSE = function () {
return false;
};
Formula.SWITCH = function() {
var result;
if (arguments.length > 0) {
var targetValue = arguments[0];
var argc = arguments.length - 1;
var switchCount = Math.floor(argc / 2);
var switchSatisfied = false;
var defaultClause = argc % 2 === 0 ? null : arguments[arguments.length - 1];
if (switchCount) {
for (var index = 0; index < switchCount; index++) {
if (targetValue === arguments[index * 2 + 1]) {
result = arguments[index * 2 + 2];
switchSatisfied = true;
break;
}
}
}
if (!switchSatisfied && defaultClause) {
result = defaultClause;
}
}
return result;
};
Formula.IF = function (test, then_value, otherwise_value) {
if (test) {
return (typeof then_value === 'undefined') ? true : then_value;
} else {
return (typeof otherwise_value === 'undefined') ? true : otherwise_value;
}
};
Formula.IFERROR = function (value, value_if_error) {
return (['#DIV/0!', '#N/A', '#NAME?', '#NUM!', '#NULL!', '#REF!', '#VALUE!'].indexOf(value) >= 0 ) ? value_if_error : value;
};
Formula.IFNA = function (value, value_if_na) {
return (value === '#N/A') ? value_if_na : value;
};
Formula.NOT = function (logical) {
return !logical;
};
Formula.OR = function () {
var result = false;
for (var i = 0; i < arguments.length; i++) {
if (arguments[i]) {
result = true;
}
}
return result;
};
Formula.TRUE = function () {
return true;
};
Formula.XOR = function () {
var result = 0;
for (var i = 0; i < arguments.length; i++) {
if (arguments[i]) {
result++;
}
}
return (Math.floor(Math.abs(result)) & 1) ? true : false;
};
// Lookup and reference functions
Formula.REFERENCE = function (context, reference) {
try {
var path = reference.split('.'),
result = context;
_(path).forEach(function (step) {
if (step[step.length - 1] === ']') {
var opening = step.indexOf('[');
var index = step.substring(opening + 1, step.length - 1);
result = result[step.substring(0, opening)][index];
} else {
result = result[step];
}
});
return result;
} catch (error) {
return;
}
};
// Math functions
Formula.ABS = function (number) {
return Math.abs(number);
};
Formula.ACOS = function (number) {
return Math.acos(number);
};
Formula.ACOSH = function (number) {
return Math.log(number + Math.sqrt(number * number - 1));
};
Formula.ACOT = function (number) {
return Math.atan(1 / number);
};
Formula.ACOTH = function (number) {
return 0.5 * Math.log((number + 1) / (number - 1));
};
Formula.AGGREGATE = function (function_code, options) {
var result = [];
for (var i = 2; i < arguments.length; i++) {
switch (function_code) {
case 1:
result[i - 2] = Formula.AVERAGE(arguments[i]);
break;
case 2:
result[i - 2] = Formula.COUNT(arguments[i]);
break;
case 3:
result[i - 2] = Formula.COUNTA(arguments[i]);
break;
case 4:
result[i - 2] = Formula.MAX(arguments[i]);
break;
case 5:
result[i - 2] = Formula.MIN(arguments[i]);
break;
case 6:
result[i - 2] = Formula.PRODUCT(arguments[i]);
break;
case 7:
result[i - 2] = Formula.STDEVS(arguments[i]);
break;
case 8:
result[i - 2] = Formula.STDEVP(arguments[i]);
break;
case 9:
result[i - 2] = Formula.SUM(arguments[i]);
break;
case 10:
result[i - 2] = Formula.VARS(arguments[i]);
break;
case 11:
result[i - 2] = Formula.VARP(arguments[i]);
break;
case 12:
result[i - 2] = Formula.MEDIAN(arguments[i]);
break;
case 13:
result[i - 2] = Formula.MODESNGL(arguments[i]);
break;
case 14:
result[i - 2] = Formula.LARGE(arguments[i]);
break;
case 15:
result[i - 2] = Formula.SMALL(arguments[i]);
break;
case 16:
result[i - 2] = Formula.PERCENTILEINC(arguments[i]);
break;
case 17:
result[i - 2] = Formula.QUARTILEINC(arguments[i]);
break;
case 18:
result[i - 2] = Formula.PERCENTILEEXC(arguments[i]);
break;
case 19:
result[i - 2] = Formula.QUARTILEEXC(arguments[i]);
break;
}
}
return result;
};
Formula.ARABIC = function (text) {
// Credits: Rafa? Kukawski
if (!/^M*(?:D?C{0,3}|C[MD])(?:L?X{0,3}|X[CL])(?:V?I{0,3}|I[XV])$/.test(text)) {
throw new Error('Incorrect roman number');
}
var r = 0;
text.replace(/[MDLV]|C[MD]?|X[CL]?|I[XV]?/g, function (i) {
r += {M: 1000, CM: 900, D: 500, CD: 400, C: 100, XC: 90, L: 50, XL: 40, X: 10, IX: 9, V: 5, IV: 4, I: 1}[i];
});
return r;
};
Formula.ASIN = function (number) {
return Math.asin(number);
};
Formula.ASINH = function (number) {
return Math.log(number + Math.sqrt(number * number + 1));
};
Formula.ATAN = function (number) {
return Math.atan(number);
};
Formula.ATAN2 = function (number_x, number_y) {
return Math.atan2(number_x, number_y);
};
Formula.ATANH = function (number) {
return Math.log((1 + number) / (1 - number)) / 2;
};
Formula.BASE = function (number, radix, min_length) {
min_length = (typeof min_length === 'undefined') ? 0 : min_length;
var result = number.toString(radix);
return new Array(Math.max(min_length + 1 - result.length, 0)).join('0') + result;
};
Formula.CEILING = function (number, significance, mode) {
if (significance === 0) {
return 0;
}
significance = (typeof significance === 'undefined') ? 1 : Math.abs(significance);
mode = (typeof mode === 'undefined') ? 0 : mode;
var precision = -Math.floor(Math.log(significance) / Math.log(10));
if (number >= 0) {
return Formula.ROUND(Math.ceil(number / significance) * significance, precision);
} else {
if (mode === 0) {
return -Formula.ROUND(Math.floor(Math.abs(number) / significance) * significance, precision);
} else {
return -Formula.ROUND(Math.ceil(Math.abs(number) / significance) * significance, precision);
}
}
};
Formula.CEILINGMATH = Formula.CEILING;
Formula.CEILINGPRECISE = Formula.CEILING;
Formula.COMBIN = function (number, number_chosen) {
return Formula.FACT(number) / (Formula.FACT(number_chosen) * Formula.FACT(number - number_chosen));
};
Formula.COMBINA = function (number, number_chosen) {
return (number === 0 && number_chosen === 0) ? 1 : Formula.COMBIN(number + number_chosen - 1, number - 1);
};
Formula.COS = function (number) {
return Math.cos(number);
};
Formula.COSH = function (number) {
return (Math.exp(number) + Math.exp(-number)) / 2;
};
Formula.COT = function (number) {
return 1 / Math.tan(number);
};
Formula.COTH = function (number) {
var e2 = Math.exp(2 * number);
return (e2 + 1) / (e2 - 1);
};
Formula.CSC = function (number) {
return 1 / Math.sin(number);
};
Formula.CSCH = function (number) {
return 2 / (Math.exp(number) - Math.exp(-number));
};
Formula.DECIMAL = function (number, radix) {
return parseInt(number, radix);
};
Formula.DEGREES = function (number) {
return number * 180 / Math.PI;
};
Formula.EVEN = function (number) {
return Formula.CEILING(number, -2, -1);
};
Formula.EXP = function (number) {
return Math.exp(number);
};
Formula.FACT = function (number) {
var n = Math.floor(number);
if (n === 0 || n === 1) {
return 1;
} else if (MEMOIZED_FACT[n] > 0) {
return MEMOIZED_FACT[n];
} else {
MEMOIZED_FACT[n] = Formula.FACT(n - 1) * n;
return MEMOIZED_FACT[n];
}
};
Formula.FACTDOUBLE = function (number) {
var n = Math.floor(number);
if (n <= 0) {
return 1;
} else {
return n * Formula.FACTDOUBLE(n - 2);
}
};
Formula.FLOOR = function (number, significance, mode) {
if (significance === 0) {
return 0;
}
significance = (typeof significance === 'undefined') ? 1 : Math.abs(significance);
mode = (typeof mode === 'undefined') ? 0 : mode;
var precision = -Math.floor(Math.log(significance) / Math.log(10));
if (number >= 0) {
return Formula.ROUND(Math.floor(number / significance) * significance, precision);
} else {
if (mode === 0) {
return -Formula.ROUND(Math.ceil(Math.abs(number) / significance) * significance, precision);
} else {
return -Formula.ROUND(Math.floor(Math.abs(number) / significance) * significance, precision);
}
}
};
Formula.FLOORMATH = Formula.FLOOR;
Formula.FLOORPRECISE = Formula.FLOOR;
Formula.GCD = function () {
// Credits: Andrew Pociu
for (var r, a, i = arguments.length - 1, result = arguments[i]; i;) {
for (a = arguments[--i]; (r = a % result); a = result, result = r) {
//empty
}
}
return result;
};
Formula.INT = function (number) {
return Math.floor(number);
};
Formula.ISEVEN = function (number) {
return (Math.floor(Math.abs(number)) & 1) ? false : true;
};
Formula.ISOCEILING = Formula.CEILING;
Formula.ISODD = function (number) {
return (Math.floor(Math.abs(number)) & 1) ? true : false;
};
Formula.LCM = function () {
// Credits: Jonas Raoni Soares Silva
var o = Formula.ARGSTOARRAY(arguments);
for (var i, j, n, d, r = 1; (n = o.pop()) !== undefined;) {
while (n > 1) {
if (n % 2) {
for (i = 3, j = Math.floor(Math.sqrt(n)); i <= j && n % i; i += 2) {
//empty
}
d = (i <= j) ? i : n;
} else {
d = 2;
}
for (n /= d, r *= d, i = o.length; i; (o[--i] % d) === 0 && (o[i] /= d) === 1 && o.splice(i, 1)) {
//empty
}
}
}
return r;
};
Formula.LN = function (number) {
return Math.log(number);
};
Formula.LOG = function (number, base) {
base = (typeof base === 'undefined') ? 10 : base;
return Math.log(number) / Math.log(base);
};
Formula.LOG10 = function (number) {
return Math.log(number) / Math.log(10);
};
Formula.MDETERM = numeric.det;
Formula.MINVERSE = numeric.inv;
Formula.MMULT = numeric.dot;
Formula.MOD = function (dividend, divisor) {
var modulus = Math.abs(dividend % divisor);
return (divisor > 0) ? modulus : -modulus;
};
Formula.MROUND = function (number, multiple) {
if (number * multiple < 0) {
throw new Error('Number and multiple must have the same sign.');
}
return Math.round(number / multiple) * multiple;
};
Formula.MULTINOMIAL = function () {
var sum = 0;
var divisor = 1;
for (var i = 0; i < arguments.length; i++) {
sum += arguments[i];
divisor *= Formula.FACT(arguments[i]);
}
return Formula.FACT(sum) / divisor;
};
Formula.MUNIT = numeric.identity;
Formula.ODD = function (number) {
var temp = Math.ceil(Math.abs(number));
temp = (temp & 1) ? temp : temp + 1;
return (number > 0) ? temp : -temp;
};
Formula.PI = function () {
return Math.PI;
};
Formula.POWER = function (number, power) {
return Math.pow(number, power);
};
Formula.PRODUCT = function () {
var result = 1;
for (var i = 0; i < arguments.length; i++) {
result *= arguments[i];
}
return result;
};
Formula.QUOTIENT = function (numerator, denominator) {
return (numerator / denominator).toFixed(0);
};
Formula.RADIANS = function (number) {
return number * Math.PI / 180;
};
Formula.RAND = function () {
return Math.random();
};
Formula.RANDBETWEEN = function (bottom, top) {
// Creative Commons Attribution 3.0 License
// Copyright (c) 2012 eqcode
return bottom + Math.ceil((top - bottom + 1) * Math.random()) - 1;
};
Formula.ROUND = function (number, digits) {
return Math.round(number * Math.pow(10, digits)) / Math.pow(10, digits);
};
Formula.ROUNDDOWN = function (number, digits) {
var sign = (number > 0) ? 1 : -1;
return sign * (Math.floor(Math.abs(number) * Math.pow(10, digits))) / Math.pow(10, digits);
};
Formula.ROUNDUP = function (number, digits) {
var sign = (number > 0) ? 1 : -1;
return sign * (Math.ceil(Math.abs(number) * Math.pow(10, digits))) / Math.pow(10, digits);
};
Formula.SERIESSUM = function (x, n, m, coefficients) {
var result = coefficients[0] * Math.pow(x, n);
for (var i = 1; i < coefficients.length; i++) {
result += coefficients[i] * Math.pow(x, n + i * m);
}
return result;
};
Formula.SEC = function (number) {
return 1 / Math.cos(number);
};
Formula.SECH = function (number) {
return 2 / (Math.exp(number) + Math.exp(-number));
};
Formula.SIGN = function (number) {
if (number < 0) {
return -1;
} else if (number === 0) {
return 0;
} else {
return 1;
}
};
Formula.SIN = function (number) {
return Math.sin(number);
};
Formula.SINH = function (number) {
return (Math.exp(number) - Math.exp(-number)) / 2;
};
Formula.SQRT = function (number) {
return Math.sqrt(number);
};
Formula.SQRTPI = function (number) {
return Math.sqrt(number * Math.PI);
};
Formula.SUBTOTAL = function (function_code) {
var result = [];
for (var i = 1; i < arguments.length; i++) {
switch (function_code) {
case 1:
result[i - 1] = Formula.AVERAGE(arguments[i]);
break;
case 2:
result[i - 1] = Formula.COUNT(arguments[i]);
break;
case 3:
result[i - 1] = Formula.COUNTA(arguments[i]);
break;
case 4:
result[i - 1] = Formula.MAX(arguments[i]);
break;
case 5:
result[i - 1] = Formula.MIN(arguments[i]);
break;
case 6:
result[i - 1] = Formula.PRODUCT(arguments[i]);
break;
case 7:
result[i - 1] = Formula.STDEV(arguments[i]);
break;
case 8:
result[i - 1] = Formula.STDEVP(arguments[i]);
break;
case 9:
result[i - 1] = Formula.SUM(arguments[i]);
break;
case 10:
result[i - 1] = Formula.VAR(arguments[i]);
break;
case 11:
result[i - 1] = Formula.VARP(arguments[i]);
break;
}
}
return result;
};
Formula.SUM = function () {
var numbers = Formula.ARGSTOARRAY(arguments);
var result = 0;
for (var i = 0; i < numbers.length; i++) {
if (numbers[i] instanceof Array) {
for (var j = 0; j < numbers[i].length; j++) {
result += (Formula.ISNUMBER(numbers[i][j])) ? numbers[i][j] : 0;
}
} else {
result += (Formula.ISNUMBER(numbers[i])) ? numbers[i] : 0;
}
}
return result;
};
Formula.SUMIF = function (range, criteria) {
var result = 0;
for (var i = 0; i < range.length; i++) {
result += (eval(range[i] + criteria)) ? range[i] : 0;
}
return result;
};
Formula.SUMIFS = function () {
var criteria = (arguments.length - 1) / 2;
var range = arguments[0];
var result = 0;
for (var i = 0; i < range.length; i++) {
var fit = true;
for (var j = 0; j < criteria; j++) {
if (!eval(arguments[2 * j + 1][i] + arguments[2 * j + 2])) {
fit = false;
}
}
result += (fit) ? range[i] : 0;
}
return result;
};
Formula.SUMPRODUCT = function () {
var arrays = arguments.length + 1;
var result = 0;
for (var i = 0; i < arguments[0].length; i++) {
for (var j = 0; j < arguments[0][i].length; j++) {
var product = 1;
for (var k = 1; k < arrays; k++) {
product *= arguments[k - 1][i][j];
}
result += product;
}
}
return result;
};
Formula.SUMSQ = function () {
var numbers = Formula.ARGSTOARRAY(arguments);
var result = 0;
for (var i = 0; i < numbers.length; i++) {
result += (Formula.ISNUMBER(numbers[i])) ? numbers[i] * numbers[i] : 0;
}
return result;
};
Formula.SUMX2MY2 = function (array_x, array_y) {
var result = 0;
for (var i = 0; i < array_x.length; i++) {
result += array_x[i] * array_x[i] - array_y[i] * array_y[i];
}
return result;
};
Formula.SUMX2PY2 = function (array_x, array_y) {
var result = 0;
for (var i = 0; i < array_x.length; i++) {
result += array_x[i] * array_x[i] + array_y[i] * array_y[i];
}
return result;
};
Formula.SUMXMY2 = function (array_x, array_y) {
var result = 0;
for (var i = 0; i < array_x.length; i++) {
result += Math.pow(array_x[i] - array_y[i], 2);
}
return result;
};
Formula.TAN = function (number) {
return Math.tan(number);
};
Formula.TANH = function (number) {
var e2 = Math.exp(2 * number);
return (e2 - 1) / (e2 + 1);
};
Formula.TRUNC = function (number, digits) {
digits = (typeof digits === 'undefined') ? 0 : digits;
var sign = (number > 0) ? 1 : -1;
return sign * (Math.floor(Math.abs(number) * Math.pow(10, digits))) / Math.pow(10, digits);
};
// Statistical functions
Formula.AVEDEV = function () {
var range = Formula.ARGSCONCAT(arguments);
return jStat.sum(jStat(range).subtract(jStat.mean(range)).abs()[0]) / range.length;
};
Formula.AVERAGE = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var count = 0;
var sigma = 0;
for (var i = 0; i < n; i++) {
if (range[i] !== true && range[i] !== false) {
sigma += range[i];
count++;
}
}
return sigma / count;
};
Formula.AVERAGEA = function () {
return jStat.mean(Formula.ARGSCONCAT(arguments));
};
Formula.AVERAGEIF = function (range, criteria, average_range) {
average_range = (typeof average_range === 'undefined') ? range : average_range;
var average_count = 0;
var result = 0;
for (var i = 0; i < range.length; i++) {
if (eval(range[i] + criteria)) {
result += average_range[i];
average_count++;
}
}
return result / average_count;
};
Formula.AVERAGEIFS = function () {
var criteria = (arguments.length - 1) / 2;
var range = arguments[0];
var count = 0;
var result = 0;
for (var i = 0; i < range.length; i++) {
var fit = true;
for (var j = 0; j < criteria; j++) {
if (!eval(arguments[2 * j + 1][i] + arguments[2 * j + 2])) {
fit = false;
}
}
if (fit) {
result += range[i];
count++;
}
}
return result / count;
};
Formula.BETADIST = function (x, alpha, beta, cumulative, A, B) {
A = (typeof A === 'undefined') ? 0 : A;
B = (typeof B === 'undefined') ? 1 : B;
x = (x - A) / (B - A);
return (cumulative) ? jStat.beta.cdf(x, alpha, beta) : jStat.beta.pdf(x, alpha, beta);
};
Formula.BETAINV = function (probability, alpha, beta, A, B) {
A = (typeof A === 'undefined') ? 0 : A;
B = (typeof B === 'undefined') ? 1 : B;
return jStat.beta.inv(probability, alpha, beta) * (B - A) + A;
};
Formula.BINOMDIST = function (successes, trials, probability, cumulative) {
return (cumulative) ? jStat.binomial.cdf(successes, trials, probability) : jStat.binomial.pdf(successes, trials, probability);
};
Formula.BINOMDISTRANGE = function (trials, probability, successes, successes2) {
successes2 = (typeof successes2 === 'undefined') ? successes : successes2;
var result = 0;
for (var i = successes; i <= successes2; i++) {
result += Formula.COMBIN(trials, i) * Math.pow(probability, i) * Math.pow(1 - probability, trials - i);
}
return result;
};
Formula.BINOMINV = function (trials, probability, alpha) {
var x = 0;
while (x <= trials) {
if (jStat.binomial.cdf(x, trials, probability) >= alpha) {
return x;
}
x++;
}
};
Formula.CHISQDIST = function (x, k, cumulative) {
return (cumulative) ? jStat.chisquare.cdf(x, k) : jStat.chisquare.pdf(x, k);
};
Formula.CHISQDISTRT = function (x, k) {
return;
};
Formula.CHISQINV = function (probability, k) {
return jStat.chisquare.inv(probability, k);
};
Formula.CHISQINVRT = function () {
return;
};
Formula.CHISQTEST = function () {
return;
};
Formula.CONFIDENCENORM = function (alpha, sd, n) {
return jStat.normalci(1, alpha, sd, n)[1] - 1;
};
Formula.CONFIDENCET = function (alpha, sd, n) {
return jStat.tci(1, alpha, sd, n)[1] - 1;
};
Formula.CORREL = function () {
return jStat.corrcoeff.apply(this, arguments);
};
Formula.COUNT = function () {
return Formula.ARGSCONCAT(arguments).length;
};
Formula.COUNTA = function () {
var range = Formula.ARGSCONCAT(arguments);
return range.length - Formula.COUNTBLANK(range);
};
Formula.COUNTBLANK = function () {
var range = Formula.ARGSCONCAT(arguments);
var blanks = 0;
for (var i = 0; i < range.length; i++) {
if (range[i] === null || range[i] === '') {
blanks++;
}
}
return blanks;
};
Formula.COUNTIF = function (range, criteria) {
var matches = 0;
for (var i = 0; i < range.length; i++) {
if (range[i].match(new RegExp(criteria))) {
matches++;
}
}
return matches;
};
Formula.COUNTIFS = function () {
var criteria = (arguments.length - 1) / 2;
var range = arguments[0];
var result = 0;
for (var i = 0; i < range.length; i++) {
var fit = true;
for (var j = 0; j < criteria; j++) {
if (!eval(arguments[2 * j + 1][i] + arguments[2 * j + 2])) {
fit = false;
}
}
result += (fit) ? 1 : 0;
}
return result;
};
Formula.COUNTUNIQUE = function () {
return _.uniq(Formula.ARGSCONCAT(arguments)).length;
};
Formula.COVARIANCEP = function (array1, array2) {
var mean1 = jStat.mean(array1);
var mean2 = jStat.mean(array2);
var result = 0;
var n = array1.length;
for (var i = 0; i < n; i++) {
result += (array1[i] - mean1) * (array2[i] - mean2);
}
return result / n;
};
Formula.COVARIANCES = function () {
return jStat.covariance.apply(this, arguments);
};
Formula.DEVSQ = function () {
var range = Formula.ARGSCONCAT(arguments);
var mean = jStat.mean(range);
var result = 0;
for (var i = 0; i < range.length; i++) {
result += Math.pow((range[i] - mean), 2);
}
return result;
};
Formula.EXPONDIST = function (x, lambda, cumulative) {
return (cumulative) ? jStat.exponential.cdf(x, lambda) : jStat.exponential.pdf(x, lambda);
};
Formula.FDIST = function (x, d1, d2, cumulative) {
return (cumulative) ? jStat.centralF.cdf(x, d1, d2) : jStat.centralF.pdf(x, d1, d2);
};
Formula.FDISTRT = function () {
return;
};
Formula.FINV = function (probability, d1, d2) {
return jStat.centralF.inv(probability, d1, d2);
};
Formula.FINVRT = function () {
return;
};
Formula.FTEST = function () {
return;
};
Formula.FISHER = function (x) {
return Math.log((1 + x) / (1 - x)) / 2;
};
Formula.FISHERINV = function (y) {
var e2y = Math.exp(2 * y);
return (e2y - 1) / (e2y + 1);
};
Formula.FORECAST = function (x, data_y, data_x) {
var xmean = jStat.mean(data_x);
var ymean = jStat.mean(data_y);
var n = data_x.length;
var num = 0;
var den = 0;
for (var i = 0; i < n; i++) {
num += (data_x[i] - xmean) * (data_y[i] - ymean);
den += Math.pow(data_x[i] - xmean, 2);
}
var b = num / den;
var a = ymean - b * xmean;
return a + b * x;
};
Formula.FREQUENCY = function (data, bins) {
var n = data.length;
var b = bins.length;
var r = [];
for (var i = 0; i <= b; i++) {
r[i] = 0;
for (var j = 0; j < n; j++) {
if (i === 0) {
if (data[j] <= bins[0]) {
r[0] += 1;
}
} else if (i < b) {
if (data[j] > bins[i - 1] && data[j] <= bins[i]) {
r[i] += 1;
}
} else if (i === b) {
if (data[j] > bins[b - 1]) {
r[b] += 1;
}
}
}
}
return r;
};
Formula.GAMMA = function () {
return jStat.gammafn.apply(this, arguments);
};
Formula.GAMMADIST = function (x, alpha, beta, cumulative) {
/*
var shape = alpha;
var scale = 1 / beta;
return (cumulative) ? jStat.gamma.cdf(x, shape, scale) : jStat.gamma.pdf(x, shape, scale);
*/
return;
};
Formula.GAMMAINV = function (probability, alpha, beta) {
/*
var shape = alpha;
var scale = 1 / beta;
return jStat.gamma.inv(probability, shape, scale);
*/
return;
};
Formula.GAMMALN = function () {
return jStat.gammaln.apply(this, arguments);
};
Formula.GAMMALNPRECISE = function () {
return;
};
Formula.GAUSS = function (z) {
return jStat.normal.cdf(z, 0, 1) - 0.5;
};
Formula.GEOMEAN = function () {
return jStat.geomean(Formula.ARGSCONCAT(arguments));
};
Formula.GROWTH = function (known_y, known_x, new_x, use_const) {
// Credits: Ilmari Karonen
// Default values for optional parameters:
var i;
if (typeof(known_x) === 'undefined') {
known_x = [];
for (i = 1; i <= known_y.length; i++) {
known_x.push(i);
}
}
if (typeof(new_x) === 'undefined') {
new_x = [];
for (i = 1; i <= known_y.length; i++) {
new_x.push(i);
}
}
if (typeof(use_const) === 'undefined') {
use_const = true;
}
// Calculate sums over the data:
var n = known_y.length;
var avg_x = 0;
var avg_y = 0;
var avg_xy = 0;
var avg_xx = 0;
for (i = 0; i < n; i++) {
var x = known_x[i];
var y = Math.log(known_y[i]);
avg_x += x;
avg_y += y;
avg_xy += x * y;
avg_xx += x * x;
}
avg_x /= n;
avg_y /= n;
avg_xy /= n;
avg_xx /= n;
// Compute linear regression coefficients:
var beta;
var alpha;
if (use_const) {
beta = (avg_xy - avg_x * avg_y) / (avg_xx - avg_x * avg_x);
alpha = avg_y - beta * avg_x;
} else {
beta = avg_xy / avg_xx;
alpha = 0;
}
// Compute and return result array:
var new_y = [];
for (i = 0; i < new_x.length; i++) {
new_y.push(Math.exp(alpha + beta * new_x[i]));
}
return new_y;
};
Formula.HARMEAN = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var den = 0;
for (var i = 0; i < n; i++) {
den += 1 / range[i];
}
return n / den;
};
Formula.HYPGEOMDIST = function (x, n, M, N, cumulative) {
function pdf(x, n, M, N) {
return Formula.COMBIN(M, x) * Formula.COMBIN(N - M, n - x) / Formula.COMBIN(N, n);
}
function cdf(x, n, M, N) {
var result = 0;
for (var i = 0; i <= x; i++) {
result += pdf(i, n, M, N);
}
return result;
}
return (cumulative) ? cdf(x, n, M, N) : pdf(x, n, M, N);
};
Formula.INTERCEPT = function (data_y, data_x) {
return Formula.FORECAST(0, data_y, data_x);
};
Formula.KURT = function () {
var range = Formula.ARGSCONCAT(arguments);
var mean = jStat.mean(range);
var n = range.length;
var sigma = 0;
for (var i = 0; i < n; i++) {
sigma += Math.pow(range[i] - mean, 4);
}
sigma = sigma / Math.pow(jStat.stdev(range, true), 4);
return ((n * (n + 1)) / ((n - 1) * (n - 2) * (n - 3))) * sigma - 3 * (n - 1) * (n - 1) / ((n - 2) * (n - 3));
};
Formula.LARGE = function (array, k) {
return array.sort(function (a, b) {
return b - a;
})[k - 1];
};
Formula.LINEST = function (data_y, data_x) {
var xmean = jStat.mean(data_x);
var ymean = jStat.mean(data_y);
var n = data_x.length;
var num = 0;
var den = 0;
for (var i = 0; i < n; i++) {
num += (data_x[i] - xmean) * (data_y[i] - ymean);
den += Math.pow(data_x[i] - xmean, 2);
}
var m = num / den;
var b = ymean - m * xmean;
return [m, b];
};
Formula.LOGEST = function () {
return;
};
Formula.LOGNORMDIST = function (x, mean, sd, cumulative) {
return (cumulative) ? jStat.lognormal.cdf(x, mean, sd) : jStat.lognormal.pdf(x, mean, sd);
};
Formula.LOGNORMINV = function (probability, mean, sd) {
return jStat.lognormal.inv(probability, mean, sd);
};
Formula.MAX = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var max = (n > 0) ? range[0] : 0;
for (var i = 0; i < n; i++) {
max = (range[i] > max && (range[i] !== true) && (range[i] !== false)) ? range[i] : max;
}
return max;
};
Formula.MAXA = function () {
var range = Formula.ARGSCONCAT(arguments);
return (range.length > 0) ? Math.max.apply(Math, range) : 0;
};
Formula.MEDIAN = function () {
return jStat.median(Formula.ARGSCONCAT(arguments));
};
Formula.MIN = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var min = (n > 0) ? range[0] : 0;
for (var i = 0; i < n; i++) {
min = (range[i] < min && (range[i] !== true) && (range[i] !== false)) ? range[i] : min;
}
return min;
};
Formula.MINA = function () {
var range = Formula.ARGSCONCAT(arguments);
return (range.length > 0) ? Math.min.apply(Math, range) : 0;
};
Formula.MODEMULT = function () {
// Credits: Roönaän
var range = Formula.ARGSCONCAT(arguments),
n = range.length,
count = {},
maxItems = [],
max = 0,
currentItem;
for (var i = 0; i < n; i++) {
currentItem = range[i];
count[currentItem] = count[currentItem] ? count[currentItem] + 1 : 1;
if (count[currentItem] > max) {
max = count[currentItem];
maxItems = [];
}
if (count[currentItem] === max) {
maxItems[maxItems.length] = currentItem;
}
}
return maxItems;
};
Formula.MODESNGL = function () {
return Formula.MODEMULT(Formula.ARGSCONCAT(arguments)).sort(function (a, b) {
return a - b;
})[0];
};
Formula.NEGBINOMDIST = function (k, r, p, cumulative) {
return (cumulative) ? jStat.negbin.cdf(k, r, p) : jStat.negbin.pdf(k, r, p);
};
Formula.NORMDIST = function (x, mean, sd, cumulative) {
// Check parameters
if (isNaN(x) || isNaN(mean) || isNaN(sd)) {
return '#VALUE!';
}
if (sd <= 0) {
return '#NUM!';
}
// Return normal distribution computed by jStat [http://jstat.org]
return (cumulative) ? jStat.normal.cdf(x, mean, sd) : jStat.normal.pdf(x, mean, sd);
};
Formula.NORMINV = function (probability, mean, sd) {
return jStat.normal.inv(probability, mean, sd);
};
Formula.NORMSDIST = function (z, cumulative) {
return (cumulative) ? jStat.normal.cdf(z, 0, 1) : jStat.normal.pdf(z, 0, 1);
};
Formula.NORMSINV = function (probability) {
return jStat.normal.inv(probability, 0, 1);
};
Formula.PEARSON = function (data_x, data_y) {
var xmean = jStat.mean(data_x);
var ymean = jStat.mean(data_y);
var n = data_x.length;
var num = 0;
var den1 = 0;
var den2 = 0;
for (var i = 0; i < n; i++) {
num += (data_x[i] - xmean) * (data_y[i] - ymean);
den1 += Math.pow(data_x[i] - xmean, 2);
den2 += Math.pow(data_y[i] - ymean, 2);
}
return num / Math.sqrt(den1 * den2);
};
Formula.PERCENTILEEXC = function (array, k) {
array = array.sort(function (a, b) {
{
return a - b;
}
});
var n = array.length;
if (k < 1 / (n + 1) || k > 1 - 1 / (n + 1)) {
return '#NUM!';
}
var l = k * (n + 1) - 1;
var fl = Math.floor(l);
return Formula.CLEANFLOAT((l === fl) ? array[l] : array[fl] + (l - fl) * (array[fl + 1] - array[fl]));
};
Formula.PERCENTILEINC = function (array, k) {
array = array.sort(function (a, b) {
return a - b;
});
var n = array.length;
var l = k * (n - 1);
var fl = Math.floor(l);
return Formula.CLEANFLOAT((l === fl) ? array[l] : array[fl] + (l - fl) * (array[fl + 1] - array[fl]));
};
Formula.PERCENTRANKEXC = function (array, x, significance) {
array = array.sort(function (a, b) {
return a - b;
});
var uniques = _.uniq(array);
var n = array.length;
var m = uniques.length;
significance = (typeof significance === 'undefined') ? 3 : significance;
var power = Math.pow(10, significance);
var result = 0;
var match = false;
var i = 0;
while (!match && i < m) {
if (x === uniques[i]) {
result = (array.indexOf(uniques[i]) + 1) / (n + 1);
match = true;
} else if (x >= uniques[i] && (x < uniques[i + 1] || i === m - 1)) {
result = (array.indexOf(uniques[i]) + 1 + (x - uniques[i]) / (uniques[i + 1] - uniques[i])) / (n + 1);
match = true;
}
i++;
}
return Math.floor(result * power) / power;
};
Formula.PERCENTRANKINC = function (array, x, significance) {
array = array.sort(function (a, b) {
return a - b;
});
var uniques = _.uniq(array);
var n = array.length;
var m = uniques.length;
significance = (typeof significance === 'undefined') ? 3 : significance;
var power = Math.pow(10, significance);
var result = 0;
var match = false;
var i = 0;
while (!match && i < m) {
if (x === uniques[i]) {
result = array.indexOf(uniques[i]) / (n - 1);
match = true;
} else if (x >= uniques[i] && (x < uniques[i + 1] || i === m - 1)) {
result = (array.indexOf(uniques[i]) + (x - uniques[i]) / (uniques[i + 1] - uniques[i])) / (n - 1);
match = true;
}
i++;
}
return Math.floor(result * power) / power;
};
Formula.PERMUT = function (number, number_chosen) {
return Formula.FACT(number) / Formula.FACT(number - number_chosen);
};
Formula.PERMUTATIONA = function (number, number_chosen) {
return Math.pow(number, number_chosen);
};
Formula.PHI = function (x) {
return Math.exp(-0.5 * x * x) / SQRT2PI;
};
Formula.POISSONDIST = function (x, mean, cumulative) {
return (cumulative) ? jStat.poisson.cdf(x, mean) : jStat.poisson.pdf(x, mean);
};
Formula.PROB = function (range, probability, lower, upper) {
if (typeof lower === 'undefined') {
return 0;
}
upper = (typeof upper === 'undefined') ? lower : upper;
if (lower === upper) {
return (range.indexOf(lower) >= 0) ? probability[range.indexOf(lower)] : 0;
}
var sorted = range.sort(function (a, b) {
return a - b;
});
var n = sorted.length;
var result = 0;
for (var i = 0; i < n; i++) {
if (sorted[i] >= lower && sorted[i] <= upper) {
result += probability[range.indexOf(sorted[i])];
}
}
return result;
};
Formula.QUARTILEEXC = function (range, quart) {
switch (quart) {
case 1:
return Formula.PERCENTILEEXC(range, 0.25);
case 2:
return Formula.PERCENTILEEXC(range, 0.5);
case 3:
return Formula.PERCENTILEEXC(range, 0.75);
default:
return '#NUM!';
}
};
Formula.QUARTILEINC = function (range, quart) {
switch (quart) {
case 1:
return Formula.PERCENTILEINC(range, 0.25);
case 2:
return Formula.PERCENTILEINC(range, 0.5);
case 3:
return Formula.PERCENTILEINC(range, 0.75);
default:
return '#NUM!';
}
};
Formula.RANKAVG = function (number, range, order) {
order = (typeof order === 'undefined') ? false : order;
var sort = (order) ? function (a, b) {
return a - b;
} : function (a, b) {
return b - a;
};
range = range.sort(sort);
var count = Formula.COUNTIN(range, number);
return (count > 1) ? (2 * range.indexOf(number) + count + 1) / 2 : range.indexOf(number) + 1;
};
Formula.RANKEQ = function (number, range, order) {
order = (typeof order === 'undefined') ? false : order;
var sort = (order) ? function (a, b) {
return a - b;
} : function (a, b) {
return b - a;
};
range = range.sort(sort);
return range.indexOf(number) + 1;
};
Formula.RSQ = function (data_x, data_y) {
return Math.pow(Formula.PEARSON(data_x, data_y), 2);
};
Formula.SKEW = function () {
var range = Formula.ARGSCONCAT(arguments);
var mean = jStat.mean(range);
var n = range.length;
var sigma = 0;
for (var i = 0; i < n; i++) {
sigma += Math.pow(range[i] - mean, 3);
}
return n * sigma / ((n - 1) * (n - 2) * Math.pow(jStat.stdev(range, true), 3));
};
Formula.SKEWP = function () {
var range = Formula.ARGSCONCAT(arguments);
var mean = jStat.mean(range);
var n = range.length;
var m2 = 0;
var m3 = 0;
for (var i = 0; i < n; i++) {
m3 += Math.pow(range[i] - mean, 3);
m2 += Math.pow(range[i] - mean, 2);
}
m3 = m3 / n;
m2 = m2 / n;
return m3 / Math.pow(m2, 3 / 2);
};
Formula.SLOPE = function (data_y, data_x) {
var xmean = jStat.mean(data_x);
var ymean = jStat.mean(data_y);
var n = data_x.length;
var num = 0;
var den = 0;
for (var i = 0; i < n; i++) {
num += (data_x[i] - xmean) * (data_y[i] - ymean);
den += Math.pow(data_x[i] - xmean, 2);
}
return num / den;
};
Formula.SMALL = function (array, k) {
return array.sort(function (a, b) {
return a - b;
})[k - 1];
};
Formula.STANDARDIZE = function (x, mean, sd) {
return (x - mean) / sd;
};
Formula.STDEVA = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var sigma = 0;
var mean = jStat.mean(range);
for (var i = 0; i < n; i++) {
sigma += Math.pow(range[i] - mean, 2);
}
return Math.sqrt(sigma / (n - 1));
};
Formula.STDEVP = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var sigma = 0;
var count = 0;
var mean = Formula.AVERAGE(range);
for (var i = 0; i < n; i++) {
if (range[i] !== true && range[i] !== false) {
sigma += Math.pow(range[i] - mean, 2);
count++;
}
}
return Math.sqrt(sigma / count);
};
Formula.STDEVPA = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var sigma = 0;
var mean = jStat.mean(range);
for (var i = 0; i < n; i++) {
sigma += Math.pow(range[i] - mean, 2);
}
return Math.sqrt(sigma / n);
};
Formula.STDEVS = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var sigma = 0;
var count = 0;
var mean = Formula.AVERAGE(range);
for (var i = 0; i < n; i++) {
if (range[i] !== true && range[i] !== false) {
sigma += Math.pow(range[i] - mean, 2);
count++;
}
}
return Math.sqrt(sigma / (count - 1));
};
Formula.STEYX = function (data_y, data_x) {
var xmean = jStat.mean(data_x);
var ymean = jStat.mean(data_y);
var n = data_x.length;
var lft = 0;
var num = 0;
var den = 0;
for (var i = 0; i < n; i++) {
lft += Math.pow(data_y[i] - ymean, 2);
num += (data_x[i] - xmean) * (data_y[i] - ymean);
den += Math.pow(data_x[i] - xmean, 2);
}
return Math.sqrt((lft - num * num / den) / (n - 2));
};
Formula.TDIST = function (x, df, cumulative) {
return (cumulative) ? jStat.studentt.cdf(x, df) : jStat.studentt.pdf(x, df);
};
Formula.TDIST2T = function () {
return;
};
Formula.TDISTRT = function () {
return;
};
Formula.TINV = function (probability, df) {
return jStat.studentt.inv(probability, df);
};
Formula.TINV2T = function () {
return;
};
Formula.TTEST = function () {
return;
};
Formula.TREND = function () {
return;
};
Formula.TRIMMEAN = function (range, percent) {
var n = range.length;
var trim = Formula.FLOOR(range.length * percent, 2) / 2;
return jStat.mean(_.initial(_.rest(range.sort(function (a, b) {
return a - b;
}), trim), trim));
};
Formula.VARA = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var sigma = 0;
var mean = jStat.mean(range);
for (var i = 0; i < n; i++) {
sigma += Math.pow(range[i] - mean, 2);
}
return sigma / (n - 1);
};
Formula.VARP = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var sigma = 0;
var count = 0;
var mean = Formula.AVERAGE(range);
for (var i = 0; i < n; i++) {
if (range[i] !== true && range[i] !== false) {
sigma += Math.pow(range[i] - mean, 2);
count++;
}
}
return sigma / count;
};
Formula.VARPA = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var sigma = 0;
var mean = jStat.mean(range);
for (var i = 0; i < n; i++) {
sigma += Math.pow(range[i] - mean, 2);
}
return sigma / n;
};
Formula.VARS = function () {
var range = Formula.ARGSCONCAT(arguments);
var n = range.length;
var sigma = 0;
var count = 0;
var mean = Formula.AVERAGE(range);
for (var i = 0; i < n; i++) {
if (range[i] !== true && range[i] !== false) {
sigma += Math.pow(range[i] - mean, 2);
count++;
}
}
return sigma / (count - 1);
};
Formula.WEIBULLDIST = function (x, alpha, beta, cumulative) {
return (cumulative) ? 1 - Math.exp(-Math.pow(x / beta, alpha)) : Math.pow(x, alpha - 1) * Math.exp(-Math.pow(x / beta, alpha)) * alpha / Math.pow(beta, alpha);
};
Formula.ZTEST = function (range, x, sigma) {
var n = range.length;
var sd = (typeof sigma === 'undefined') ? Formula.STDEVS(range) : sigma;
return 1 - Formula.NORMSDIST((Formula.AVERAGE(range) - x) / (sd / Math.sqrt(n)), Formula.TRUE);
};
// Text functions
Formula.CHAR = function (number) {
return String.fromCharCode(number);
};
Formula.CLEAN = function (text) {
var re = /[\0-\x1F]/g;
return text.replace(re, "");
};
Formula.CODE = function (text) {
return text.charCodeAt(0);
};
Formula.CONCATENATE = function () {
var string = '';
for (var i = 0; i < arguments.length; i++) {
if (arguments[i] !== null && arguments[i] !== undefined) {
string += arguments[i];
}
}
return string;
};
Formula.DOLLAR = function (number, decimals) {
decimals = (typeof decimals === 'undefined') ? 2 : decimals;
var format = '';
if (decimals <= 0) {
number = Math.round(number * Math.pow(10, decimals)) / Math.pow(10, decimals);
format = '($0,0)';
} else if (decimals > 0) {
format = '($0,0.' + new Array(decimals + 1).join('0') + ')';
}
return numeral(number).format(format);
};
Formula.EXACT = function (text1, text2) {
return text1 === text2;
};
Formula.FIND = function (find_text, within_text, position) {
position = (typeof position === 'undefined') ? 0 : position;
return within_text.indexOf(find_text, position - 1) + 1;
};
Formula.FIXED = function (number, decimals, no_commas) {
decimals = (typeof decimals === 'undefined') ? 2 : decimals;
no_commas = (typeof no_commas === 'undefined') ? false : no_commas;
var format = no_commas ? '0' : '0,0';
if (decimals <= 0) {
number = Math.round(number * Math.pow(10, decimals)) / Math.pow(10, decimals);
} else if (decimals > 0) {
format += '.' + new Array(decimals + 1).join('0');
}
return numeral(number).format(format);
};
Formula.JOIN = function (separator, array) {
return array.join(separator);
};
Formula.LEFT = function (text, number) {
number = (typeof number === 'undefined') ? 1 : number;
return text.substring(0, number);
};
Formula.LEN = function (text) {
return text.length;
};
Formula.LOWER = function (text) {
return text ? text.toLowerCase() : text;
};
Formula.MID = function (text, start, number) {
return text.substring(start - 1, number);
};
Formula.NUMBERVALUE = function (text, decimal_separator, group_separator) {
decimal_separator = (typeof decimal_separator === 'undefined') ? '.' : decimal_separator;
group_separator = (typeof group_separator === 'undefined') ? ',' : group_separator;
return Number(text.replace(decimal_separator, '.').replace(group_separator, ''));
};
Formula.PROPER = function (text) {
return text.replace(/\w\S*/g, function (txt) {
return txt.charAt(0).toUpperCase() + txt.substr(1).toLowerCase();
});
};
Formula.REGEXEXTRACT = function (text, regular_expression) {
var match = text.match(new RegExp(regular_expression));
return match ? match[0] : null;
};
Formula.REGEXMATCH = function (text, regular_expression) {
return text.match(new RegExp(regular_expression)) ? true : false;
};
Formula.REGEXREPLACE = function (text, regular_expression, replacement) {
return text.replace(new RegExp(regular_expression), replacement);
};
Formula.REPLACE = function (text, position, length, new_text) {
return text.substr(0, position - 1) + new_text + text.substr(position - 1 + length);
};
Formula.REPT = function (text, number) {
return new Array(number + 1).join(text);
};
Formula.RIGHT = function (text, number) {
number = (typeof number === 'undefined') ? 1 : number;
return text.substring(text.length - number);
};
Formula.ROMAN = function (number) {
// The MIT License
// Copyright (c) 2008 Steven Levithan
var digits = String(number).split('');
var key = ['', 'C', 'CC', 'CCC', 'CD', 'D', 'DC', 'DCC', 'DCCC', 'CM', '', 'X', 'XX', 'XXX', 'XL', 'L', 'LX', 'LXX', 'LXXX', 'XC', '', 'I', 'II', 'III', 'IV', 'V', 'VI', 'VII', 'VIII', 'IX'];
var roman = '';
var i = 3;
while (i--) {
roman = (key[+digits.pop() + (i * 10)] || '') + roman;
}
return new Array(+digits.join('') + 1).join('M') + roman;
};
Formula.SEARCH = function (find_text, within_text, position) {
position = (typeof position === 'undefined') ? 0 : position;
return within_text.toLowerCase().indexOf(find_text.toLowerCase(), position - 1) + 1;
};
Formula.SPLIT = function (text, separator) {
return _s.words(text, separator);
};
Formula.SUBSTITUTE = function (text, old_text, new_text, occurrence) {
if (!text || !old_text || !new_text) {
return text;
} else if (typeof occurrence === 'undefined') {
return text.replace(new RegExp(old_text, 'g'), new_text);
} else {
var index = 0;
var i = 0;
while (text.indexOf(old_text, index) > 0) {
index = text.indexOf(old_text, index + 1);
i++;
if (i === occurrence) {
return text.substring(0, index) + new_text + text.substring(index + old_text.length);
}
}
}
};
Formula.T = function (value) {
return (typeof value === "string") ? value : null;
};
Formula.HTML2TEXT = function (value) {
var result = '';
if (value) {
if (value instanceof Array) {
value.forEach(function(line) {
if (result !== '') {
result += '\n';
}
result += (line.replace(/<(?:.|\n)*?>/gm, ''));
});
} else {
result = value.replace(/<(?:.|\n)*?>/gm, '');
}
}
return result;
};
Formula.HUMANIZE = function(value) {
if (value instanceof Date) {
var dvalue = moment(value);
if (dvalue.hours() || dvalue.minutes() || dvalue.seconds()) {
return dvalue.format("dddd, MMMM Do YYYY, h:mm:ss");
} else {
return dvalue.format("dddd, MMMM Do YYYY");
}
}
return value;
};
Formula.TEXT = function (value, format) {
var text = '';
if (value) {
if (value instanceof Object) {
try {
text = JSON.stringify(value);
} catch (err) {
// ignore
}
} else if (typeof value === 'string') {
if (format) {
text = (format.indexOf('0') >= 0) ? numeral(value).format(format) : moment(new Date(value)).format(format);
} else {
text = value;
}
} else if (value.toString && typeof value.toString === 'function') {
text = value.toString();
}
}
return text;
};
Formula.TRIM = function (text) {
return _s.clean(text);
};
Formula.UNICHAR = Formula.CHAR;
Formula.UNICODE = Formula.CODE;
Formula.UPPER = function (text) {
return text.toUpperCase();
};
Formula.VALUE = function (text) {
return numeral().unformat(text);
};
// Hashing function
Formula.MD5 = function (data, key, raw) {
return md5(data, key, raw);
};
Formula.NUMERAL = function(number, format) {
return numeral(number).format(format);
};
}).call(this);
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