# NASA Core Flight System uses MathParser.org-mXparser

NASA Core Flight System (CFS) Command and Data Dictionary (CCDD) utility uses mXparser! Dear NASA - thank you for your t(h)rust 🙂 Best regards, Thank you!

# Why this formula gives approximation of e?

mXparser code:

Function s = new Function("s(n, x) = if( x >= 1, n, s(n+1, x + rUni(0,1) ) )");
Expression e = new Expression("avg( i, 1, 10000, s(0,0) )", s);


Result:

[mXparser-v.4.1.1] 2.7194


Best regards, • 1 year period:  c.a. 23 downloads daily
• Last 6 weeks: c.a. 44 downloads daily !!

Best regards,

# Port to various .NET frameworks

MathParser.org-mXparser is now available for various .NET frameworks

• .NET Framework: 2.0, 3.0, 3.5, 4.0, 4.5, 4.5.1, 4.5.2, 4.6, 4.6.1, 4.6.2
• .NET Core: 1.0, 1.1
• .NET Standard: 1.0, 1.6
• .NET PCL: portable45-net45+win8+wpa81
• Xamarin.Andoird: 1.0, 6.0
• Xamarin.iOS: 1.0

Enjoy 🙂

Best regards,

# mXparser - v.4.0.0 - released! Major update!

### v.4.0.0 (2017-03-27): Major update: Bitwise Operators, Numbers in scientific notation, Units, Physical & Astronomical Constants, Equations solving via finding function root, Better tokens handling, Function Extensions - possibility of using your own implementation, Bugs fixed!

#### Bitwise Operators

• @~ - Bitwise unary complement
• @& - Bitwise AND
• @^ - Bitwise exclusive OR
• @| - Bitwise inclusive OR
• @<< - Signed left shift
• @>> - Signed right shift

• 1.2e10
• 1.2e-10
• 1.2e+10
• 1.2E10
• 1.2E-10
• 1.2E+10
• ...

#### Units

• [%] - <Ratio, Fraction> Percentage = 0.01
• [%%] - <Ratio, Fraction> Promil, Per mille = 0.001
• [Y] - Septillion / Yotta = 10^24
• [sept] - Septillion / Yotta = 10^24
• [Z] - Sextillion / Zetta = 10^21
• [sext] - Sextillion / Zetta = 10^21
• [E] - Quintillion / Exa = 10^18
• [quint] - Quintillion / Exa = 10^18
• [P] - Quadrillion / Peta = 10^15
• [quad] - Quadrillion / Peta = 10^15
• [T] - Trillion / Tera = 10^12
• [tril] - Trillion / Tera = 10^12
• [G] - Billion / Giga = 10^9
• [bil] - Billion / Giga = 10^9
• [M] - Million / Mega = 10^6
• [mil] - Million / Mega = 10^6
• [k] - Thousand / Kilo = 10^3
• [th] - Thousand / Kilo = 10^3
• [hecto] - Hundred / Hecto = 10^2
• [hund] - Hundred / Hecto = 10^2
• [deca] - Ten / Deca = 10
• [ten] - Ten / Deca = 10
• [deci] - Tenth / Deci = 0.1
• [centi] - Hundredth / Centi = 0.01
• [milli] - Thousandth / Milli = 0.001
• [mic] - Millionth / Micro = 10^-6
• [n] - Billionth / Nano = 10^-9
• [p] - Trillionth / Pico = 10^-12
• [f] - Quadrillionth / Femto = 10^-15
• [a] - Quintillionth / Atoo = 10^-18
• [z] - Sextillionth / Zepto = 10^-21
• [y] - Septillionth / Yocto = 10^-24
• [m] - Metre / Meter (m=1)
• [km] - Kilometre / Kilometer (m=1)
• [cm] - Centimetre / Centimeter (m=1)
• [mm] - Millimetre / Millimeter (m=1)
• [inch] - Inch (m=1)
• [yd] - Yard (m=1)
• [ft] - Feet (m=1)
• [mile] - Mile (m=1)
• [nmi] - Nautical mile (m=1)
• [m2] - Square metre / Square meter (m=
• [cm2] - Square centimetre / Square cent
• [mm2] - Square millimetre / Square mill
• [are] - Are (m=1)
• [ha] - Hectare (m=1)
• [acre] - Acre (m=1)
• [km2] - Square kilometre / Square kilom
• [mm3] - Cubic millimetre / Cubic mill
• [cm3] - Cubic centimetre / Cubic cent
• [m3] - Cubic metre / Cubic meter (m=
• [km3] - Cubic kilometre / Cubic kilom
• [ml] - Millilitre / Milliliter (m=1)
• [l] - Litre / Liter (m=1)
• [gall] - Gallon (m=1)
• [pint] - Pint (m=1)
• [s] - Second (s=1)
• [ms] - Millisecond (s=1)
• [min] - Minute (s=1)
• [h] - Hour (s=1)
• [day] - Day (s=1)
• [week] - Week (s=1)
• [yearj] - Julian year = 365.25 days (s=1)
• [kg] - Kilogram (kg=1)
• [gr] - Gram (kg=1)
• [mg] - Milligram (kg=1)
• [dag] - Decagram (kg=1)
• [t] - Tonne (kg=1)
• [oz] - Ounce (kg=1)
• [lb] - Pound (kg=1)
• [b] - Bit (bit=1)
• [kb] - Kilobit (bit=1)
• [Mb] - Megabit (bit=1)
• [Gb] - Gigabit (bit=1)
• [Tb] - Terabit (bit=1)
• [Pb] - Petabit (bit=1)
• [Eb] - Exabit (bit=1)
• [Zb] - Zettabit (bit=1)
• [Yb] - Yottabit (bit=1)
• [B] - Byte (bit=1)
• [kB] - Kilobyte (bit=1)
• [MB] - Megabyte (bit=1)
• [GB] - Gigabyte (bit=1)
• [TB] - Terabyte (bit=1)
• [PB] - Petabyte (bit=1)
• [EB] - Exabyte (bit=1)
• [ZB] - Zettabyte (bit=1)
• [YB] - Yottabyte (bit=1)
• [J] - Joule (m=1, kg=1, s=1)
• [eV] - Electronovolt (m=1, kg=1, s=1
• [keV] - Kiloelectronovolt (m=1, kg=1,
• [MeV] - Megaelectronovolt (m=1, kg=1,
• [GeV] - Gigaelectronovolt (m=1, kg=1,
• [TeV] - Teraelectronovolt (m=1, kg=1,
• [m/s] - Metre / Meter per second (m=1,
• [km/h] - Kilometre / Kilometer per hour
• [mi/h] - Mile per hour (m=1, s=1)
• [knot] - Knot (m=1, s=1)
• [m/s2] - Metre / Meter per squar
• [km/h2] - Kilometre / Kilometer p
• [mi/h2] - Mile per square hour (m
• [deg] - Degree of arc (rad=1)
• ['] - Minute of arc (rad=1)
• [''] - Second of arc (rad=1)

#### Physical Constants

• - Light speed in vacuum [m/s] (m=1, s=1)
• [G.] - Gravitational constant (m=1, kg=1, s=1)]
• [g] - Gravitational acceleration on Earth [m/s^2] (m=1, s=1)
• [hP] - Planck constant (m=1, kg=1, s=1)
• [h-] - Reduced Planck constant / Dirac constant (m=1, kg=1, s=1)]
• [lP] - Planck length [m] (m=1)
• [mP] - Planck mass [kg] (kg=1)
• [tP] - Planck time [s] (s=1)

#### Astronomical Constants

• [ly] - Light year [m] (m=1)
• [au] - Astronomical unit [m] (m=1)
• [pc] - Parsec [m] (m=1)
• [kpc] - Kiloparsec [m] (m=1)
• [Earth-R-eq - ]Earth equatorial radius [m] (m=1)
• [Earth-R-po] - Earth polar radius [m] (m=1)
• [Earth-R] - Earth mean radius (m=1)
• [Earth-M] - Earth mass [kg] (kg=1)
• [Earth-D] - Earth-Sun distance - semi major axis [m] (m=1)
• [Moon-R] - Moon mean radius [m] (m=1)
• [Moon-M] - Moon mass [kg] (kg=1)
• [Moon-D] - Moon-Earth distance - semi major axis [m] (m=1)
• [Solar-R] - Solar mean radius [m] (m=1)
• [Solar-M] - Solar mass [kg] (kg=1)
• [Mercury-R] - Mercury mean radius [m] (m=1)
• [Mercury-M] - - Mercury mass [kg] (kg=1)
• [Mercury-D]Mercury-Sun distance - semi major axis [m] (m=1)
• [Venus-R] - Venus mean radius [m] (m=1)
• [Venus-M] - Venus mass [kg] (kg=1)
• [Venus-D] - Venus-Sun distance - semi major axis [m] (m=1)
• [Mars-R] - Mars mean radius [m] (m=1)
• [Mars-M] - Mars mass [kg] (kg=1)
• [Mars-D] - Mars-Sun distance - semi major axis [m] (m=1)
• [Jupiter-R] - Jupiter mean radius [m] (m=1)
• [Jupiter-M] - Jupiter mass [kg] (kg=1)
• [Jupiter-D] - Jupiter-Sun distance - semi major axis [m] (m=1)
• [Saturn-R] - Saturn mean radius [m] (m=1)
• [Saturn-M] - Saturn mass [kg] (kg=1)
• [Saturn-D] - Saturn-Sun distance - semi major axis [m] (m=1)
• [Uranus-R] - Uranus mean radius [m] (m=1)
• [Uranus-M] - Uranus mass [kg] (kg=1)
• [Uranus-D] - Uranus-Sun distance - semi major axis [m] (m=1)
• [Neptune-R] - Neptune mean radius [m] (m=1)
• [Neptune-M] - Neptune mass [kg] (kg=1)
• [Neptune-D] - Neptune-Sun distance - semi major axis [m] (m=1)

#### Equations solving via finding function root

• solve( f(x), x, a, b ) - solving f(x) = 0

#### Better tokens handling

• Better handling of invalid / not known tokens
• Looks like functionality

#### Function Extensions - possibility of using your own implementation

• FunctionExtension interface + new constructor in Function class

#### Bugs fixed

• Exception thrown by getCopyOfInitialTokens() #21
• System.format.exception - system.IO.EndOfStreamException #20
• Expression relating factorial "!" cause the application to hang #17
• Negative sign missing when is right of operators #16
• Negative in if statement #12
• Speed when debugging #11
• User defined arguments ending in e #10

#### New regression tests - current tests coverage:

• 622 expression related tests
• 114 syntax related tests
• 30 api related tests
• 20 performance tests

# mathMC - Math function plotter in Minecraft - powered by mXparser

mathMC "is a 3d function plotter in Minecraft. You can easily plot math functions in your MC world. Minecraft is a 3-dimensional world, so it's perfect for 3d functions."

I am happy that mathMC is powered by mXparser 🙂   Best regards,

# Estimating Pi by Monte Carlo using mXparser

Using built-in random variable [Uni] from uniform continuous distribution over [0; 1] interval we sample two numbers (x,y) then check if point is inside the circle. Operation is repeated n-times, then proportion falling into circle is being measured. This is only 1/4 of the circle (positive x and positive y) with radius 1, so 4 times proportion should give estimation of pi.

Argument n = new Argument("n = 100000");
Expression e = new Expression("4 * sum(i, 1, n, if( [Uni]^2 + [Uni]^2 <= 1; 1; 0) ) / n", n);
mXparser.consolePrintln("Res. : " + e.getExpressionString() + " = " + e.calculate());

[mXparser-v.3.0.0] Res. : 4 * sum(i, 1, n, if( [Uni]^2 + [Uni]^2 <= 1; 1; 0) ) / n = 3.14748


Best regards

# mXparser - v.3.0.0 - released!

## Random numbers - new functions

• rUni(a, b) - Random number from uniform continuous distribution U(a,b)
• rUnid(a, b) - Random number from uniform discrete distribution U{a,b}
• rNor(m, s) - Random number from normal distribution N(m,s)
• rList(a1, a2, ..., an) - Random number from given list of numbers

## Probability distributions - new functions

• pUni(x, a, b) - Probability distribution function - Uniform continuous distribution U(a,b)
• cUni(x, a, b) - Cumulative distribution function - Uniform continuous distribution U(a,b)
• qUni(q, a, b) - Quantile function (inverse cumulative distribution function) - Uniform continuous distribution U(a,b)
• pNor(x, a, b) - Probability distribution function - Normal distribution N(m,s)
• cNor(x, a, b) - Cumulative distribution function - Normal distribution N(m,s)
• qNor(q, m, s) - Quantile function (inverse cumulative distribution function) - Normal distribution N(m,s)

## Random variables (predefined) - acting as random constant (no parameters)

• [Int] - Random variable - random integer
• [Int1] - Random variable - random integer - Uniform discrete distribution U{-10^1, 10^1}
• [Int2] - Random variable - random integer - Uniform discrete distribution U{-10^2, 10^2}
• [Int3] - Random variable - random integer - Uniform discrete distribution U{-10^3, 10^3}
• [Int4] - Random variable - random integer - Uniform discrete distribution U{-10^4, 10^4}
• [Int5] - Random variable - random integer - Uniform discrete distribution U{-10^5, 10^5}
• [Int6] - Random variable - random integer - Uniform discrete distribution U{-10^6, 10^6}
• [Int7] - Random variable - random integer - Uniform discrete distribution U{-10^7, 10^7}
• [Int8] - Random variable - random integer - Uniform discrete distribution U{-10^8, 10^8}
• [Int9] - Random variable - random integer - Uniform discrete distribution U{-10^9, 10^9}
• [nat] - Random variable - random natural number including 0
• [nat1] - Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^1}
• [nat2] - Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^2}
• [nat3] - Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^3}
• [nat4] - Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^4}
• [nat5] - Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^5}
• [nat6] - Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^6}
• [nat7] - Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^7}
• [nat8] - Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^8}
• [nat9] - Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^9}
• [Nat] - Random variable - random natural number
• [Nat1] - Random variable - random natural number - Uniform discrete distribution U{1, 10^1}
• [Nat2] - Random variable - random natural number - Uniform discrete distribution U{1, 10^2}
• [Nat3] - Random variable - random natural number - Uniform discrete distribution U{1, 10^3}
• [Nat4] - Random variable - random natural number - Uniform discrete distribution U{1, 10^4}
• [Nat5] - Random variable - random natural number - Uniform discrete distribution U{1, 10^5}
• [Nat6] - Random variable - random natural number - Uniform discrete distribution U{1, 10^6}
• [Nat7] - Random variable - random natural number - Uniform discrete distribution U{1, 10^7}
• [Nat8] - Random variable - random natural number - Uniform discrete distribution U{1, 10^8}
• [Nat9] - Random variable - random natural number - Uniform discrete distribution U{1, 10^9}
• [Nor] - Random variable - Normal distribution N(0,1)

## Double precision rounding

• round(value, places) - decimal rounding (half-up)

## New special functions

• erf(x) - Gauss error function
• erfc(x) - Gauss complementary error function
• erfInv(x) - Inverse Gauss error function
• erfcInv(x) - Inverse Gauss complementary error function

## Other functions

• ulp(x) - Unit in The Last Place

## Binary relations - epsilon+ulp comparison - enabled as default

If a rel b then applied epsilon is maximum from epsilon and ulp(b) : i.e. a eq b if a \in [b-eps; b+eps] inclusive

• mXparser.setExactComparison()
• mXparser.setEpsilonComparison()
• mXparser.setEpsilon(double epsilon)
• mXparser.setDefaultEpsilon()
• mXparser.getEpsilon()
• mXparser.checkIfEpsilonMode()
• mXparser.checkIfExactMode()

## Intelligent automatic double ULP rounding - enabled as default

** Try 0.1 + 0.1 + 0.1 - it will give exact 0.3 🙂 **

• mXparser.enableUlpRounding()
• mXparser.disableUlpRounding()
• mXparser.checkIfUlpRounding()

## Parser tokens definition now public in API

• mxparser.parsertokens

## Expression after tokenization now public in API

• Expression.getCopyOfInitialTokens()
• mxparser.parsertokens
• mXparser.consolePrintTokens()

## Significant reorganization of code

• Mainly mathcollection & parser tokens

## Backwards compatibility

• is preserved for String API, Expression, Function, Argument, Constnat, ...
• other public API was reorganized (mainly mxparser.mathcollection)

## Bugs fixed

• bugs related to iterated operators

## Other changes

• Many new regression tests