Monthly Archives: May 2016

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!

v.3.0.0 (2016-05-18): Major update: Random numbers, Probability distributions & Random variables, Double precision rounding, ULP rounding, epsilon comparison, New special functions.

.NET: since v.3.0.0 dll - different private key used for signing.

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

Enjoy 🙂

mXparser 3.0.0 is very close to release

Dear All,

I am happy to announce that mXparser 3.0.0 is very close to release. Change will bring a lot of new features 🙂 including:

  • Random numbers
  • Probability distributions
  • Random variables
  • Double precision rounding
  • Intelligent automatic ULP rounding to minimize issues similar to  0.1 + 0.1 + 0.1 = 0.30000000000000004
  • Epsilon comparison from binary relations
  • New special functions (non-elementary)
  • Significant code reorganization

Best regards