funclib

Description

funclib is a dynamic mathematical expression parsing and evaluation library designed to facilitate the definition and utilization of math functions at runtime. As a single header library, it is easy to integrate and use. Written in C++ for applications requiring flexible and efficient mathematical computations. It uses the common mathematical notations and semantics to describe the body of the function. funclib currently supports functions from Rⁿ to R¹ domains.

funclib comes pre-equipped with many common and useful mathematical functions. List of predefined functions and operators

Usage

To use funclib, follow these steps:

1. Include the header file funclib.hpp.
2. Create an instance of the FuncVM object.
3. Call the create function with the function signature and function body as parameters.
4. A Function object is returned.
5. Call the Function object with the appropriate arguments.

Important!

• To use the special math functions provided by the C++ STL, you must enable the C++17 standard std=c++17.
• In MSVC, you also have to define /Zc:__cplusplus flag.

Simple Example

#include "funclib.hpp"

int main() {
    // Step 2: Create an instance of FuncVM
    funclib::FuncVM vm;

    // Step 3: Define a function with the signature "f(x)" and body "x * x"
    funclib::Function f = vm.CreateFunction("f(x)", "x * x");
    
    // Step 5: Call the function with an argument
    double result = f(5); // Should return 25
    std::cout << "f(5) = " << result << std::endl;
    
    // Another example with multiple arguments
    funclib::Function g = vm.CreateFunction("g(x, y)", "x + y * y");
    double result2 = g(3, 4); // Should return 19
    std::cout << "g(3, 4) = " << result2 << std::endl;
    
    // Example with calling user defined functions
    funclib::Function fog = vm.CreateFunction("fog(x,y)", "f(g(x,y))");
    double result3 = fog(3, 4); // Should return 19^2 = 361
    std::cout << "fog(3, 4) = " << result3 << std::endl;

    // You can also use a std::vector to call the function
    std::vector<double> args = {3, 4};
    result3 = fog(args);
    std::cout << "fog(3, 4) = " << result3 << std::endl;

    // It is also possible to set the arguments once and call the function multiple times
    fog.SetArgs(3, 4); // Identical to fog.SetArgs(args)
    result3 = fog.Call();
    std::cout << "fog(3, 4) = " << result3 << std::endl;
}

Predefined Functions and Operators

Operators

• Factorial !
• Exponentiation ^
• Multiplication * ( Juxtaposition is supported i.e 2x will be considered as 2*x)
• Division /
• Addition +
• Subtraction -

Common Math Functions

• Arc cosine acos
• Inverse hyperbolic cosine acosh
• Arc sine asin
• Inverse hyperbolic sine asinh
• Arc tangent atan
• Inverse hyperbolic tangent atanh
• Cube root cbrt
• Ceiling ceil
• Cosine cos
• Hyperbolic cosine cosh
• Exponential (e^x) exp
• Exponential (2^x) exp2
• Exponential minus 1 (e^x - 1) expm1
• Absolute value abs
• Floor floor
• Natural logarithm (base e) ln
• Common logarithm (base 10) log
• Logarithm of 1 plus x log1p
• Binary logarithm (base 2) log2
• Rounds to the nearest integer nearbyint
• Rounds to the nearest integer value rint
• Rounds to the nearest integer, halfway cases away from zero round
• Sine sin
• Hyperbolic sine sinh
• Square root sqrt
• Tangent tan
• Hyperbolic tangent tanh
• Truncate trunc
• Arc tangent of y/x atan2
• Floating-point remainder of x/y fmod
• x raised to the power y pow
• Hypotenuse (sqrt(x^2 + y^2)) hypot
• Remainder of x/y rounded to the nearest integer remainder
• Max of x and y max
• Min of x and y min
• Greatest common divisor gcd
• Least common multiple lcm
• nPr npr
• nCr ncr

Probability Distributions Functions

• Exponential distribution exp_dist
• Chi squared distribution chi2_dist
• T distribution t_dist
• Normal distribution normal_dist
• Gamma distribution gamma_dist
• Beta distribution beta_dist
• Logistic distribution logistic_dist
• Cauchy distribution cauchy_dist
• Weibull distribution weibull_dist
• Log normal distribution lognorm_dist
• Pareto distribution pareto_dist

Special Functions

• Error function erf
• Inverse error function erfinv
• Complementary error function erfc
• Gamma function gamma
• Natural logarithm of the gamma function lngamma
• Associated Laguerre polynomials (n, m, x) assoc_laguerre
• Associated Legendre polynomials (n, m, x) assoc_legendre
• Beta function beta
• Complete elliptic integral 1 kind comp_ellint_1
• Complete elliptic integral of the second kind comp_ellint_2
• Complete elliptic integral of the third kind comp_ellint_3
• Regular modified cylindrical Bessel functions (nu, x) cyl_bessel_i
• Cylindrical Bessel functions (of the first kind) (nu, x) cyl_bessel_j
• Irregular modified cylindrical Bessel functions (nu, x) cyl_bessel_k
• Cylindrical Neumann functions (nu, x) cyl_newmann
• Incomplete elliptic integral of the first kind (k, phi) ellint_1
• Incomplete elliptic integral of the second kind (k, phi) ellint_2
• Incomplete elliptic integral of the third kind (k, nu, phi) ellint_3
• Exponential integral expint
• Hermite polynomials (n, x) hermite
• Legendre polynomials (n, x) legendre
• Laguerre polynomials (n, x) laguerre
• Riemann zeta function zeta
• Spherical Bessel functions (of the first kind) (n, x) sph_bessel
• Spherical associated Legendre functions (l, m, theta) sph_legendre
• Spherical Neumann functions (n, x) sph_neumann

Examples and Benchmarks

• You can find the source code for the following test case and the examples in the tests directory

Possible Improvements

• Optimizing the expression.
• Improving the expression evaluation procedure (possibly a bytecode interpreter)
• Support for the complex domain.
• Handling vector valued functions.