Fixed-point numeric type with configurable storage and fractional precision. More...

Classes
class	RawConstructorTag
	Internal tag for constructing from raw storage. More...

Public Member Functions
constexpr	fixed () noexcept=default
	Default constructor.
template<integral T>
constexpr	fixed (const T &value) noexcept
	Constructs from an integral value.
template<floating_point T>
constexpr	fixed (const T &value) noexcept
	Constructs from a floating-point value.
template<typename OtherBase, typename OtherIntermediate, unsigned OtherFraction, bool OtherRounding>
constexpr	fixed (const fixed< OtherBase, OtherIntermediate, OtherFraction, OtherRounding > &value) noexcept
	Constructs by converting from another toy::math::fixed type.
template<integral T>
constexpr	operator T () const noexcept
	Converts to an integral type.
template<floating_point T>
constexpr	operator T () const noexcept
	Converts to a floating-point type.
constexpr Base	rawValue () const noexcept
	Returns raw fixed-point storage value.
template<bool OtherRounding>
constexpr fixed &	operator= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
	Assigns from another toy::math::fixed with the same Base, Intermediate, and Fraction.
template<integral T>
constexpr fixed &	operator= (const T &other) noexcept
	Assigns from an integral value.
template<bool OtherRounding>
constexpr fixed &	operator+= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
	Adds another toy::math::fixed value in place.
template<integral T>
constexpr fixed &	operator+= (const T &other) noexcept
	Adds an integral value in place.
template<bool OtherRounding>
constexpr fixed &	operator-= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
	Subtracts another toy::math::fixed value in place.
template<integral T>
constexpr fixed &	operator-= (const T &other) noexcept
	Subtracts an integral value in place.
template<bool OtherRounding>
constexpr fixed &	operator*= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
	Multiplies by another toy::math::fixed value in place.
template<integral T>
constexpr fixed &	operator*= (const T &other) noexcept
	Multiplies by an integral value in place.
template<bool OtherRounding>
constexpr fixed &	operator/= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
	Divides by another toy::math::fixed value in place.
template<integral T>
constexpr fixed &	operator/= (const T &other) noexcept
	Divides by an integral value in place.
template<unsigned NumFractionBits, integral T>
constexpr fixed< Base, Intermediate, Fraction, Rounding >	fromFixedPoint (const T &value) noexcept
template<bool OtherRounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
template<integral T>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator= (const T &other) noexcept
template<bool OtherRounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator+= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
template<integral T>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator+= (const T &other) noexcept
template<bool OtherRounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator-= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
template<integral T>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator-= (const T &other) noexcept
template<bool OtherRounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator*= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
template<integral T>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator*= (const T &other) noexcept
template<bool OtherRounding>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator/= (const fixed< Base, Intermediate, Fraction, OtherRounding > &other) noexcept
template<integral T>
constexpr fixed< Base, Intermediate, Fraction, Rounding > &	operator/= (const T &other) noexcept

Static Public Member Functions
static constexpr fixed	fromRawValue (const Base &value) noexcept
	Creates a fixed-point value from raw storage bits.
template<unsigned NumFractionBits, integral T>
static constexpr fixed	fromFixedPoint (const T &value) noexcept
	Builds a toy::math::fixed from a raw value with a different number of fraction bits.
template<unsigned NumFractionBits, integral T>
static constexpr fixed	fromFixedPoint (const T &value) noexcept
	Builds a toy::math::fixed from a raw value with fewer or equal fraction bits.

Private Member Functions
constexpr	fixed (const Base &val, RawConstructorTag) noexcept
	Constructs directly from raw storage value.

Static Private Member Functions
static consteval Intermediate	_fractionMult () noexcept
	Compile-time scaling factor 2^Fraction.

Private Attributes
Base	_value
	Raw fixed-point storage value (scaled by 2^Fraction).

Detailed Description

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>
requires ValidFixedPointTypes<Base, Intermediate, Fraction>
class toy::math::fixed< Base, Intermediate, Fraction, Rounding >

Fixed-point numeric type with configurable storage and fractional precision.

Stores values as scaled integers using Fraction fractional bits. Conversions from integral and floating-point types are explicit.

Template Parameters

Base	Storage type for raw fixed-point value.
Intermediate	Wider type used for intermediate calculations.
Fraction	Number of fractional bits.
Rounding	If `true`, floating-point construction rounds to nearest value.

Key Features

Constexpr: All operations and constructors are constexpr; usable at compile time.
Configurable precision: Base and Fraction choose storage size and fractional bits.
No exceptions: All operations are noexcept; no dynamic allocation.
Type safety: toy::math::ValidFixedPointTypes concept constrains template parameters.
Rounding policy: Optional rounding when converting from floating-point or scaling down fraction bits.

Usage Example

#include "math.hpp"
 
using fixed_type = toy::math::fixed<int32_t, int64_t, 8>;
constexpr fixed_type a(2);
constexpr fixed_type b(3);
constexpr auto sum = a + b;
constexpr auto raw = fixed_type::fromRawValue(256);

Performance Characteristics

Construction, conversion, arithmetic: O(1). All operations are integer-based.
Memory: sizeof(Base); no heap allocation.

Safety Guarantees

Contracts: Division by zero is checked in debug builds via assert_message; undefined behavior if divisor is zero in release.
Exception safety: All operations are noexcept; no exceptions thrown.
Type safety: Explicit conversions only; no implicit narrowing.

Compatibility

C++ standard: C++20 (concepts, constexpr, consteval).
Embedded: No heap allocation; suitable for constrained environments.

See also: toy::math::ValidFixedPointTypes

Constructor & Destructor Documentation

◆ fixed() [1/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

toy::math::fixed< Base, Intermediate, Fraction, Rounding >::fixed ( )

constexprdefaultnoexcept

Default constructor.

Leaves storage uninitialized. Use explicit construction or assignment before use.

◆ fixed() [2/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>

template<floating_point T>

toy::math::fixed< Base, Intermediate, Fraction, Rounding >::fixed ( const T & value )

explicitconstexprnoexcept

Constructs from an integral value.

Parameters

value Source integral value.

◆ fixed() [3/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<floating_point T>

toy::math::fixed< Base, Intermediate, Fraction, Rounding >::fixed ( const T & value )

explicitconstexprnoexcept

Constructs from a floating-point value.

Parameters

value Source floating-point value.

◆ fixed() [4/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>

template<typename OtherBase, typename OtherIntermediate, unsigned OtherFraction, bool OtherRounding>

toy::math::fixed< Base, Intermediate, Fraction, Rounding >::fixed ( const fixed< OtherBase, OtherIntermediate, OtherFraction, OtherRounding > & value )

explicitconstexprnoexcept

Constructs by converting from another toy::math::fixed type.

The source may have different Base, Intermediate, fraction bits, or rounding policy. The value is converted to this instance's Fraction using fromFixedPoint; when the source has more fraction bits, rounding is applied if Rounding is true.

Template Parameters

OtherBase	Storage type of the source fixed.
OtherIntermediate	Intermediate type of the source fixed.
OtherFraction	Number of fraction bits of the source fixed.
OtherRounding	Rounding policy of the source fixed.

Parameters

value Source fixed-point value.

◆ fixed() [5/5]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>

toy::math::fixed< Base, Intermediate, Fraction, Rounding >::fixed	(	const Base &	val,
		RawConstructorTag	)

constexprprivatenoexcept

Constructs directly from raw storage value.

Parameters

val	Raw fixed-point storage value.

Member Function Documentation

◆ _fractionMult()

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>

Intermediate toy::math::fixed< Base, Intermediate, Fraction, Rounding >::_fractionMult ( )

staticconstevalprivatenoexcept

Compile-time scaling factor 2^Fraction.

◆ fromFixedPoint() [1/3]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<unsigned NumFractionBits, integral T>

constexpr fixed toy::math::fixed< Base, Intermediate, Fraction, Rounding >::fromFixedPoint ( const T & value )

staticnodiscardconstexprnoexcept

Builds a toy::math::fixed from a raw value with fewer or equal fraction bits.

When NumFractionBits is less than Fraction, the value is scaled up (left-shifted); no rounding is needed. When NumFractionBits equals Fraction, the raw value is used as-is.

Template Parameters

NumFractionBits	Number of fraction bits of the source raw value.
T	Integral type of the source raw value.

Parameters

value Raw fixed-point value in NumFractionBits fractional bits.

Returns: Fixed-point value with this instance's Fraction and Rounding.

◆ fromFixedPoint() [2/3]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<unsigned NumFractionBits, integral T>

constexpr fixed toy::math::fixed< Base, Intermediate, Fraction, Rounding >::fromFixedPoint ( const T & value )

staticnodiscardconstexprnoexcept

Builds a toy::math::fixed from a raw value with a different number of fraction bits.

When NumFractionBits is greater than Fraction, the value is scaled down (right-shifted). If Rounding is true, the result is rounded to the nearest representable value, otherwise the result is truncated.

Template Parameters

NumFractionBits	Number of fraction bits of the source raw value.
T	Integral type of the source raw value.

Parameters

value Raw fixed-point value in NumFractionBits fractional bits.

Returns: Fixed-point value with this instance's Fraction and Rounding.

◆ fromFixedPoint() [3/3]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>

template<unsigned NumFractionBits, integral T>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::fixed< Base, Intermediate, Fraction, Rounding >::fromFixedPoint ( const T & value )

constexprnoexcept

◆ fromRawValue()

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>

fixed< Base, Intermediate, Fraction, Rounding > toy::math::fixed< Base, Intermediate, Fraction, Rounding >::fromRawValue ( const Base & value )

staticnodiscardconstexprnoexcept

Creates a fixed-point value from raw storage bits.

Parameters

value Raw fixed-point value.

Returns: Fixed-point value with raw storage set to value.

◆ operator T() [1/2]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<floating_point T>

toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator T ( ) const

explicitconstexprnoexcept

Converts to a floating-point type.

Returns: Value converted to T.

◆ operator T() [2/2]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>

template<floating_point T>

toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator T ( ) const

explicitconstexprnoexcept

Converts to an integral type.

Returns: Value converted to T.

◆ operator*=() [1/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator*= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

Multiplies by another toy::math::fixed value in place.

Accepts any toy::math::fixed with the same Base, Intermediate, and Fraction, regardless of Rounding. Uses raw storage; when Rounding is true, the result is rounded to the nearest representable value.

Template Parameters

OtherRounding Rounding of the right-hand side type (may differ from this instance).

Parameters

other Value to multiply by.

Returns: Reference to *this.

◆ operator*=() [2/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator*= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

◆ operator*=() [3/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator*= ( const T & other )

constexprnoexcept

Multiplies by an integral value in place.

other scales the fixed-point value (whole units). Raw storage is multiplied by other directly.

Template Parameters

T	Integral type.

Parameters

other Multiplier (fixed-point whole units).

Returns: Reference to *this.

◆ operator*=() [4/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator*= ( const T & other )

constexprnoexcept

◆ operator+=() [1/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator+= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

Adds another toy::math::fixed value in place.

Accepts any toy::math::fixed with the same Base, Intermediate, and Fraction, regardless of Rounding. The operation uses raw storage; rounding policy of other does not affect the result.

Template Parameters

OtherRounding Rounding of the right-hand side type (may differ from this instance).

Parameters

other Value to add.

Returns: Reference to *this.

◆ operator+=() [2/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator+= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

◆ operator+=() [3/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator+= ( const T & other )

constexprnoexcept

Adds an integral value in place.

other is scaled by 2^Fraction and added to the raw storage.

Template Parameters

T	Integral type.

Parameters

other Value to add (interpreted as fixed-point whole units).

Returns: Reference to *this.

◆ operator+=() [4/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator+= ( const T & other )

constexprnoexcept

◆ operator-=() [1/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator-= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

Subtracts another toy::math::fixed value in place.

Accepts any toy::math::fixed with the same Base, Intermediate, and Fraction, regardless of Rounding. The operation uses raw storage; rounding policy of other does not affect the result.

Template Parameters

OtherRounding Rounding of the right-hand side type (may differ from this instance).

Parameters

other Value to subtract.

Returns: Reference to *this.

◆ operator-=() [2/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator-= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

◆ operator-=() [3/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator-= ( const T & other )

constexprnoexcept

Subtracts an integral value in place.

other is scaled by 2^Fraction and subtracted from the raw storage.

Template Parameters

T	Integral type.

Parameters

other Value to subtract (interpreted as fixed-point whole units).

Returns: Reference to *this.

◆ operator-=() [4/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator-= ( const T & other )

constexprnoexcept

◆ operator/=() [1/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator/= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

Divides by another toy::math::fixed value in place.

Accepts any toy::math::fixed with the same Base, Intermediate, and Fraction, regardless of Rounding. Uses raw storage; rounding policy of other does not affect the result. Behavior is undefined if other is zero.

Template Parameters

OtherRounding Rounding of the right-hand side type (may differ from this instance).

Parameters

other Divisor (must not be zero).

Returns: Reference to *this.

◆ operator/=() [2/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator/= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

◆ operator/=() [3/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator/= ( const T & other )

constexprnoexcept

Divides by an integral value in place.

other is the divisor (fixed-point whole units). Behavior is undefined if other is zero.

Template Parameters

T	Integral type.

Parameters

other Divisor (must not be zero).

Returns: Reference to *this.

◆ operator/=() [4/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator/= ( const T & other )

constexprnoexcept

◆ operator=() [1/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

Assigns from another toy::math::fixed with the same Base, Intermediate, and Fraction.

Copies raw storage from other; Rounding of other does not affect the result. Accepts any fixed with the same representation (including different OtherRounding).

Template Parameters

OtherRounding Rounding policy of the source (may differ from this instance).

Parameters

other Source value.

Returns: Reference to *this.

◆ operator=() [2/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<bool OtherRounding>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator= ( const fixed< Base, Intermediate, Fraction, OtherRounding > & other )

constexprnoexcept

◆ operator=() [3/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator= ( const T & other )

constexprnoexcept

Assigns from an integral value.

other is scaled by 2^Fraction and stored as raw value (same as constructing from other).

Template Parameters

T	Integral type; must satisfy `integral`.

Parameters

other Integral value in whole units.

Returns: Reference to *this.

◆ operator=() [4/4]

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

template<integral T>

fixed< Base, Intermediate, Fraction, Rounding > & toy::math::fixed< Base, Intermediate, Fraction, Rounding >::operator= ( const T & other )

constexprnoexcept

◆ rawValue()

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding>

Base toy::math::fixed< Base, Intermediate, Fraction, Rounding >::rawValue ( ) const

nodiscardconstexprnoexcept

Returns raw fixed-point storage value.

Returns: Raw scaled integer (storage value).

Member Data Documentation

◆ _value

template<typename Base, typename Intermediate, unsigned Fraction, bool Rounding = true>

Base toy::math::fixed< Base, Intermediate, Fraction, Rounding >::_value

private

Raw fixed-point storage value (scaled by 2^Fraction).

The documentation for this class was generated from the following files:

include/math/fixed.hpp
include/math/fixed.inl

Classes

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Detailed Description

Key Features

Usage Example

Performance Characteristics

Safety Guarantees

Compatibility

Constructor & Destructor Documentation

◆ fixed() [1/5]

◆ fixed() [2/5]

◆ fixed() [3/5]

◆ fixed() [4/5]

◆ fixed() [5/5]

Member Function Documentation

◆ _fractionMult()

◆ fromFixedPoint() [1/3]

◆ fromFixedPoint() [2/3]

◆ fromFixedPoint() [3/3]

◆ fromRawValue()

◆ operator T() [1/2]

◆ operator T() [2/2]

◆ operator*=() [1/4]

◆ operator*=() [2/4]

◆ operator*=() [3/4]

◆ operator*=() [4/4]

◆ operator+=() [1/4]

◆ operator+=() [2/4]

◆ operator+=() [3/4]

◆ operator+=() [4/4]

◆ operator-=() [1/4]

◆ operator-=() [2/4]

◆ operator-=() [3/4]

◆ operator-=() [4/4]

◆ operator/=() [1/4]

◆ operator/=() [2/4]

◆ operator/=() [3/4]

◆ operator/=() [4/4]

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ rawValue()

Member Data Documentation

◆ _value