crow

Utility library

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Probability

Crow Library by Ross Smith

#include "crow/probability.hpp"
namespace Crow;

Contents

• Probability
  • Contents
  • Probability class

Probability class

template <std::floating_point T> class Probability;

This represents a probability, stored in a floating point value of type T. The representation is optimised for values close to 0 or 1; values close to 1 will be preserved much more accurately than they would be in a raw T value.

constexpr Probability::Probability() noexcept;

The default constructor sets the value to zero.

constexpr Probability::Probability(T t) noexcept;

The argument is clamped to the range [0,1].

constexpr Probability::Probability(const Probability& p) noexcept;
constexpr Probability::Probability(Probability&& p) noexcept;
constexpr Probability::~Probability() noexcept;
constexpr Probability&
    Probability::operator=(const Probability& p) noexcept;
constexpr Probability&
    Probability::operator=(Probability&& p) noexcept;

Other life cycle operations.

constexpr T Probability::value() const noexcept;
constexpr explicit Probability::operator T() const noexcept;

Return the probability value.

constexpr T Probability::complement() const noexcept;

Returns the complement of the value (1-value). If the actual value is close to 1, this will be more accurate than explicitly calculating 1-value().

static constexpr Probability Probability::complementary(T t) noexcept;

Returns the complementary probability (1-t). If t is close to zero, this will store a more accurate value than explicitly constructing Probability(1-t).

std::string Probability::str(FormatSpec spec = {}) const;
std::ostream& operator<<(std::ostream& out, Probability x);

Format the probability as a string. The format spec follows the same rules as for ordinary floating point arguments, except that the default formatting mode is "pz6".

T Probability::z() const noexcept;
static Probability Probability::from_z(T z) noexcept;

Convert between a probability and the corresponding standard normal variate. Probability values equal to 0 or 1, or z values equal to plus or minus infinity, are handled correctly.

constexpr Probability Probability::operator~() const noexcept;

Returns the complementary probability (1-p).

constexpr Probability& Probability::operator+=(Probability y) noexcept;
constexpr Probability& Probability::operator-=(Probability y) noexcept;
constexpr Probability& Probability::operator*=(T y) noexcept;
constexpr Probability& Probability::operator/=(T y) noexcept;
constexpr Probability operator+(Probability x, Probability y) noexcept;
constexpr Probability operator-(Probability x, Probability y) noexcept;
constexpr Probability operator*(Probability x, T y) noexcept;
constexpr Probability operator*(T y, Probability x) noexcept;
constexpr Probability operator/(Probability x, T y) noexcept;

Arithmetic operators. These all have the natural meaning; the output is always clamped to [0,1]. Where practical, arguments and results close to 1 will be handled more accurately than simple arithmetic on the values. Behaviour is undefined if the second argument to the division operator is zero.

constexpr bool operator==(Probability x, Probability y) noexcept;
constexpr bool operator==(Probability x, T y) noexcept;
constexpr bool operator==(T x, Probability y) noexcept;
constexpr bool operator!=(Probability x, Probability y) noexcept;
constexpr bool operator!=(Probability x, T y) noexcept;
constexpr bool operator!=(T x, Probability y) noexcept;
constexpr bool operator<(Probability x, Probability y) noexcept;
constexpr bool operator<(Probability x, T y) noexcept;
constexpr bool operator<(T x, Probability y) noexcept;
constexpr bool operator>(Probability x, Probability y) noexcept;
constexpr bool operator>(Probability x, T y) noexcept;
constexpr bool operator>(T x, Probability y) noexcept;
constexpr bool operator<=(Probability x, Probability y) noexcept;
constexpr bool operator<=(Probability x, T y) noexcept;
constexpr bool operator<=(T x, Probability y) noexcept;
constexpr bool operator>=(Probability x, Probability y) noexcept;
constexpr bool operator>=(Probability x, T y) noexcept;
constexpr bool operator>=(T x, Probability y) noexcept;
constexpr std::strong_ordering
    operator<=>(Probability x, Probability y) noexcept;
constexpr std::partial_ordering operator<=>(Probability x, T y) noexcept;
constexpr std::partial_ordering operator<=>(T x, Probability y) noexcept;

Comparison operators. These all have the natural meaning.

Probability pow(Probability x, T y) noexcept;
Probability cmp_pow(Probability x, T y) noexcept;

Power functions. The pow() function returns x^y; cmp_pow() returns the complementary power, 1-(1-x)^y. The output is always clamped to [0,1]. Where practical, arguments and results close to 1 will be handled more accurately than simply calling std::pow(x.value(),y). Behaviour is undefined for pow() if x=0 and y<=0, and for cmp_pow() if x=1 and y<=0,