Ratio

#include <xo/ratio/ratio.hpp>

A ratio represents an exact fraction of two integers.

template<typename Int> class ratio: represent a ratio of two Int values.

Instance Variables

group ratio-instance-variables

Variables

Int num_ = 0: numerator

Int den_ = 1: denominator

Types

group ratio-types

Typedefs

using component_type = Int: representation for (numerator, denominator)

Constructors

group ratio-ctor

Functions

constexpr ratio() = default: construct ratio 0/1

inline constexpr ratio(Int n, Int d)

construct ratio with numerator n and denominator d.

Ratio need not be normalized

Static Methods

group ratio-static-methods

Functions

static inline constexpr ratio reduce(Int n, Int d): ratio in lowest commono terms

static inline constexpr ratio add(const ratio &x, const ratio &y)

add ratios x and y

Post:: result ratio is normalized

static inline constexpr ratio subtract(const ratio &x, const ratio &y)

subtract ratio y from ratio x

Post:: result ratio is normalized

static inline constexpr ratio multiply(const ratio &x, const ratio &y)

multiply ratios x and y

Post:: result ratio is normalized

static inline constexpr ratio divide(const ratio &x, const ratio &y)

divide ratio y into ratio x

Post:: result ratio is normalized

static inline constexpr auto compare(ratio x, ratio y): 3-way compare two ratios

Access Methods

group ratio-access

Functions

inline constexpr Int num() const noexcept: fetch ratio’s numerator

inline constexpr Int den() const noexcept: fetch ratio’s denominator

inline constexpr bool is_zero() const noexcept: true if and only if ratio is equal to zero

inline constexpr bool is_unity() const noexcept: true if and only if ratio is equal to one

inline constexpr bool is_integer() const noexcept

true if and only if ratio represents an integer

(denominator is +/- 1)

General Methods

group ratio-methods

Functions

inline constexpr ratio negate() const: r.negate() is the exact ratio representing -r

inline constexpr ratio reciprocal() const: r.reciprocal() is the eact ratio representing 1/r

inline constexpr Int floor() const: r.floor() is the largest integer x : x <= r

inline constexpr Int ceil() const: r.ceil() is the smallest integer x : r < x.

inline constexpr ratio normalize() const

reduce to lowest terms

Pre:: Int type must be totally ordered

inline constexpr ratio maybe_reduce() const

reduce to lowest terms, if Int representation admits

Otherwise fallback to identity function

inline constexpr ratio frac() const

return fractional part of this ratio

Pre:: Int type must be totally ordered

inline constexpr ratio power(int p) const: compute integer exponent p of this ratio

Note

time complexity is O(log p)

inline constexpr ratio operator-() const: negate operator

Conversion

group ratio-conversion

Functions

template<typename Repr> inline constexpr Repr to() const noexcept

convert to non-ratio representation

For example: to int or double

template<std::size_t N> inline constexpr flatstring<N> to_str() const noexcept

convert to short human-friendly flatstring representation

Example:

ratio(7,1).to_str<5>();   // "7"
ratio(1,7).to_str<5>();   // "(1/7)"
ratio(-1,7).to_str<10>(); // "(-1/7)"
ratio(-1,7).to_str<5>();  // "(-1/"

template<typename Ratio2> inline constexpr operator Ratio2() const noexcept: convert to representation using different integer types