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Maths › Combinatorics ›

Arithmetic

Expx2

Computes the exponential of a squared argument.
double expx2 (double x, int sign=1)

Factorial

Calculates the factorial of an integer number.
double factorial (int n)

Falling Factorial

Calculates the falling factorial with arguments \e x and \e n.
double falling_factorial (double x, int n)

Multinomial

Calculates the multinomial coefficient with the given arguments.
int multinomial (int n, int *factors)

Rising Factorial

Calculates the rising factorial with arguments \e x and \e n.
double rising_factorial (double x, int n)

Binomial Coefficient Gamma

Computes the binomial coefficient with the given arguments.
int binomial_coefficient_gamma (int n, int k)

Multinomial Gamma

Calculates the multinomial coefficient with the given arguments.
int multinomial_gamma (int n, int *factors)

Cube Root

Returns the cube root of the argument, which may be negative.
double cubeRoot (double x)

Exp Sub1

Exponentiates a number and subtracts 1.
double exp_sub1 (double x)

Ln Add1

Evaluates the natural logarithm of a number + 1.
double ln_add1 (double x)

Xsub Ln Add1

Evaluation of the function x - ln(1 + x)
double xsub_ln_add1 (double x)

Binomial Coefficient

Returns the binomial coefficient using the factorial function.
double binomial_coefficient (int n, int k)[inline]

Add

Performs the addition of two long positive integers in the given base.
std::string add (std::string a, std::string b, int base = 10)

Subtract

Performs the subtraction of two long positive integers in the given base.
std::string subtract (std::string a, std::string b, int base = 10)

Multiply

Performs the multiplication of two long positive integers in the given base.
std::string multiply (std::string a, std::string b, int base = 10)

Karatsuba

Main Karatsuba recursive algorithm
std::string karatsuba_mul (std::string a, std::string b, int base = 10)
std::string karatsuba (std::string a, std::string b, int base = 10)

Log Factorial

Calculates the logarithm of the factorial with given argument.
double log_factorial (int n)

Log Binomial

Calculates the logarithm of the binomial coefficient with given arguments.
double log_binomial (int n, int k)[inline]

Gcd

Compute the greatest common divisor of two values. Excel: GCD
double gcd (double a, double b)

Nroot

A function that calculates the nth root of an object
template<class T> T nroot (const T& x, const T& n)

Log Inv

Computes the inverse logarithm
double log_inv (unsigned int base, double result)