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

Detailed Description

Real functions.