real_analysis.h File Reference

Real functions. More...

#include "./core_traits.h"
#include "./constants.h"
#include "./error.h"

Go to the source code of this file.

Namespaces
	theoretica
	Main namespace of the library which contains all functions and objects.

Functions
TH_CONSTEXPR real	theoretica::identity (real x)
	Identity.
template<typename Type , typename = std::enable_if<is_real_type<Type>::value>>
TH_CONSTEXPR Type	theoretica::conjugate (Type x)
	Complex conjugate of a real number (identity)
TH_CONSTEXPR real	theoretica::square (real x)
	Compute the square of a real number. More...
TH_CONSTEXPR real	theoretica::cube (real x)
	Compute the cube of a real number. More...
template<typename UnsignedIntType = uint64_t>
UnsignedIntType	theoretica::isqrt (UnsignedIntType n)
	Compute the integer square root of a positive integer. More...
template<typename UnsignedIntType = uint64_t>
UnsignedIntType	theoretica::icbrt (UnsignedIntType n)
	Compute the integer cubic root of a positive integer. More...
real	theoretica::sqrt (real x)
	Compute the square root of a real number. More...
real	theoretica::cbrt (real x)
	Compute the cubic root of x. More...
real	theoretica::abs (real x)
	Compute the absolute value of a real number. More...
int	theoretica::sgn (real x)
	Return the sign of x (1 if positive, -1 if negative, 0 if null) More...
TH_CONSTEXPR int	theoretica::floor (real x)
	Compute the floor of x Computes the maximum integer number that is smaller than x. More...
real	theoretica::fract (real x)
	Compute the fractional part of a real number. More...
real	theoretica::max (real x, real y)
	Return the greatest number between two real numbers. More...
template<typename T >
T	theoretica::max (T x, T y)
	Compare two objects and return the greatest. More...
real	theoretica::min (real x, real y)
	Return the smallest number between two real numbers. More...
template<typename T >
T	theoretica::min (T x, T y)
	Compare two objects and return the greatest. More...
real	theoretica::clamp (real x, real a, real b)
	Clamp x between a and b. More...
template<typename T >
T	theoretica::clamp (T x, T a, T b)
	Clamp a value between two other values. More...
real	theoretica::log2 (real x)
	Compute the binary logarithm of a real number. More...
real	theoretica::log10 (real x)
	Compute the base-10 logarithm of x. More...
real	theoretica::ln (real x)
	Compute the natural logarithm of x. More...
template<typename UnsignedIntType = uint64_t>
UnsignedIntType	theoretica::ilog2 (UnsignedIntType x)
	Find the integer logarithm of x. More...
template<typename UnsignedIntType = uint64_t>
UnsignedIntType	theoretica::pad2 (UnsignedIntType x)
	Get the smallest power of 2 bigger than or equal to x. More...
template<typename T = real>
TH_CONSTEXPR T	theoretica::pow (T x, int n)
	Compute the n-th power of x (where n is natural) More...
template<typename T = real>
TH_CONSTEXPR T	theoretica::ipow (T x, unsigned int n, T neutral_element=T(1))
	Compute the n-th positive power of x (where n is natural) More...
template<typename IntType = uint64_t>
TH_CONSTEXPR IntType	theoretica::fact (unsigned int n)
	Compute the factorial of n.
template<typename T = uint64_t>
TH_CONSTEXPR T	theoretica::falling_fact (T x, unsigned int n)
	Compute the falling factorial of n.
template<typename T = uint64_t>
TH_CONSTEXPR T	theoretica::rising_fact (T x, unsigned int n)
	Compute the rising factorial of n.
template<typename IntType = unsigned long long int>
TH_CONSTEXPR IntType	theoretica::double_fact (unsigned int n)
	Compute the double factorial of n.
real	theoretica::exp (real x)
	Compute the real exponential. More...
real	theoretica::expm1 (real x)
	Compute the exponential of x minus 1 more accurately for really small x. More...
real	theoretica::powf (real x, real a)
	Approximate x elevated to a real exponent. More...
real	theoretica::root (real x, int n)
	Compute the n-th root of x. More...
real	theoretica::sin (real x)
	Compute the sine of a real number. More...
real	theoretica::cos (real x)
	Compute the cosine of a real number. More...
real	theoretica::tan (real x)
	Compute the tangent of x. More...
real	theoretica::cot (real x)
	Compute the cotangent of x. More...
real	theoretica::atan (real x)
	Compute the arctangent. More...
real	theoretica::asin (real x)
	Compute the arcsine. More...
real	theoretica::acos (real x)
	Compute the arccosine. More...
real	theoretica::atan2 (real y, real x)
	Compute the 2 argument arctangent. More...
real	theoretica::sinh (real x)
	Compute the hyperbolic sine. More...
real	theoretica::cosh (real x)
	Compute the hyperbolic cosine. More...
real	theoretica::tanh (real x)
	Compute the hyperbolic tangent. More...
real	theoretica::coth (real x)
	Compute the hyperbolic cotangent. More...
real	theoretica::asinh (real x)
	Compute the inverse hyperbolic sine.
real	theoretica::acosh (real x)
	Compute the inverse hyperbolic cosine.
real	theoretica::atanh (real x)
	Compute the inverse hyperbolic tangent.
real	theoretica::sigmoid (real x)
	Compute the sigmoid function. More...
real	theoretica::sinc (real x)
	Compute the normalized sinc function. More...
real	theoretica::heaviside (real x)
	Compute the heaviside function. More...
template<typename IntType = unsigned long long int>
TH_CONSTEXPR IntType	theoretica::binomial_coeff (unsigned int n, unsigned int m)
	Compute the binomial coefficient. More...
TH_CONSTEXPR real	theoretica::radians (real degrees)
	Convert degrees to radians. More...
TH_CONSTEXPR real	theoretica::degrees (real radians)
	Convert radians to degrees. More...
template<typename T >
TH_CONSTEXPR T	theoretica::kronecker_delta (T i, T j)
	Kronecker delta, equals 1 if i is equal to j, 0 otherwise. More...
template<typename IntType = unsigned long long int>
TH_CONSTEXPR IntType	theoretica::catalan (unsigned int n)
	The n-th Catalan number.

Detailed Description

Real functions.