Scalar helper utilities

Scalar helper utilities shared across Uni20 core algorithms. More...

Files
file	scalar_precision.hpp
	Runtime selection of configured Uni20 real scalar precisions.

Concepts
concept	uni20::Integer
	Concept for integer scalar types (excluding char and bool).
concept	uni20::Real
	Concept for real scalar types (float, double, etc.).
concept	uni20::Complex
	Concept for complex scalar types.
concept	uni20::Scalar
	Concept for numeric scalar types (integer, real, or complex).
concept	uni20::RealOrComplex
	Concept for types that are either real or complex.
concept	uni20::BlasReal
	Real scalar types supported by the configured raw-pointer BLAS wrappers.
concept	uni20::BlasComplex
	Complex scalar types supported by the configured raw-pointer BLAS wrappers.
concept	uni20::BlasScalar
	Scalar types supported by the configured raw-pointer BLAS wrappers.
concept	uni20::LapackReal
	Real scalar types supported by the configured raw-pointer LAPACK wrappers.
concept	uni20::LapackComplex
	Complex scalar types supported by the configured raw-pointer LAPACK wrappers.
concept	uni20::LapackRealOrComplex
	Concept for real or complex scalar fields with real LAPACK coverage.
concept	uni20::LapackComplexReal
	Concept for real precisions whose Uni20 complex scalar has LAPACK coverage.
concept	uni20::LapackScalar
	Concept for scalar types with a configured dense LAPACK backend.
concept	uni20::ScalarValued
	Concept for scalar types or types whose recursive value_type resolves to a scalar.
concept	uni20::IntegerScalarValued
	Concept for scalar-valued types whose scalar_t<T> is an integer scalar.
concept	uni20::RealScalarValued
	Concept for scalar-valued types whose scalar_t<T> is a real scalar.
concept	uni20::ComplexScalarValued
	Concept for scalar-valued types whose scalar_t<T> is a complex scalar.
concept	uni20::RealOrComplexScalarValued
	Concept for scalar-valued types whose scalar_t<T> is real or complex.

Classes
struct	uni20::is_complex_t< T >
	Trait to detect whether a type is a complex scalar type. More...
struct	uni20::is_integer_t< T >
	Trait to detect whether a type is an integer scalar (excluding bool). More...
struct	uni20::is_real_t< T >
	Trait to detect whether a type is a real-valued scalar. More...
struct	uni20::make_complex< T >
	Metafunction to convert a type to its complexified analog. More...
struct	uni20::make_complex< T >
	Metafunction that produces the complex counterpart of a real-valued scalar. More...
struct	uni20::make_real< T >
	Metafunction to convert a type to its real-valued analog. More...
struct	uni20::numeric_limits< T >
	Project-level numeric limits customization point. More...
struct	uni20::scalar_format_options
	Formatting options for Uni20 real and complex scalars. More...
struct	uni20::scalar_type< T >
	Trait to extract the scalar type from a type T. More...

Typedefs
template<typename Real >
using	uni20::complex = typename detail::complex_type< Real >::type
	Project-level complex scalar spelling.
template<typename T >
using	uni20::make_complex_t = typename make_complex< T >::type
	Alias for the complexified version of T.
template<typename T >
using	uni20::make_real_t = typename make_real< T >::type
	Alias for the underlying real-valued type of T.

Enumerations
enum class	uni20::real_format_notation { uni20::real_format_notation::general , uni20::real_format_notation::fixed , uni20::real_format_notation::scientific }
	Selects how real scalar values are rendered as text. More...

Functions
template<typename T >
uni20::complex< T >	uni20::conj (detail::standard_complex< T > x)
	Returns the complex conjugate for complex-valued scalars.
template<Integer I>
constexpr I	uni20::conj (I const &x)
	Returns the conjugate of an integer scalar.
template<Real R>
constexpr R	uni20::conj (R const &x)
	Returns the conjugate of a real-valued scalar.
template<Complex T>
std::string	uni20::format_complex (T const &value, scalar_format_options const &options={})
	Format a Uni20 complex scalar as real+imagi.
template<Real T>
std::string	uni20::format_real (T value, scalar_format_options const &options={})
	Format a Uni20 real scalar.
template<RealOrComplex T>
std::string	uni20::format_scalar (T const &value, scalar_format_options const &options={})
	Format any Uni20 real or complex scalar.
template<Scalar S>
constexpr auto	uni20::herm (S x)
	Computes the Hermitian adjoint of a scalar value.
template<typename T >
constexpr T &	uni20::imag (detail::standard_complex< T > &z) noexcept
	Provides mutable access to the imaginary component of a uni20::complex value.
template<Complex C>
constexpr bool	uni20::isfinite (C const &z)
	Returns whether both components of a complex scalar are finite.
template<Integer I>
constexpr bool	uni20::isfinite (I const &x) noexcept
	Returns whether an integer scalar is finite.
template<Real R>
constexpr bool	uni20::isfinite (R const &x)
	Returns whether a real scalar is neither NaN nor positive/negative infinity.
template<Real T>
T	uni20::parse_real (std::string_view text)
	Parse a Uni20 real scalar from text.
template<Real T>
std::istream &	uni20::read_real (std::istream &stream, T &value)
	Read a Uni20 real scalar from a stream token.
template<typename T >
constexpr T &	uni20::real (detail::standard_complex< T > &z) noexcept
	Provides mutable access to the real component of a uni20::complex value.

Variables
template<typename T >
constexpr bool	uni20::has_numeric_limits_v
	True when Uni20 has numeric limits for T.
template<typename T >
constexpr bool	uni20::has_trivial_conj = Real<T> || Integer<T>
	Indicates whether the Uni20 conjugation helper is a no-op for the provided scalar type.
template<typename T >
constexpr bool	uni20::is_complex_scalar_valued_v = is_scalar_valued_v<T> && is_complex_v<scalar_t<T>>
	Trait to detect whether T is scalar-valued with a complex scalar.
template<typename T >
constexpr bool	uni20::is_complex_v = is_complex_t<std::remove_cvref_t<T>>::value
	Convenience alias that exposes the value of is_complex_t.
template<typename T >
constexpr bool	uni20::is_integer_scalar_valued_v = is_scalar_valued_v<T> && is_integer_v<scalar_t<T>>
	Trait to detect whether T is scalar-valued with an integer scalar.
template<typename T >
constexpr bool	uni20::is_integer_v = is_integer_t<std::remove_cvref_t<T>>::value
	Convenience alias that exposes the value of is_integer_t.
template<typename T >
constexpr bool	uni20::is_real_or_complex_scalar_valued_v = is_scalar_valued_v<T> && is_real_or_complex_v<scalar_t<T>>
	Trait to detect whether T is scalar-valued with a real or complex scalar.
template<typename T >
constexpr bool	uni20::is_real_or_complex_v = is_real_v<T> || is_complex_v<T>
	Trait to detect whether a type is a real or complex scalar.
template<typename T >
constexpr bool	uni20::is_real_scalar_valued_v = is_scalar_valued_v<T> && is_real_v<scalar_t<T>>
	Trait to detect whether T is scalar-valued with a real scalar.
template<typename T >
constexpr bool	uni20::is_real_v = is_real_t<std::remove_cvref_t<T>>::value
	Convenience alias that exposes the value of is_real_t.
template<typename T >
constexpr bool	uni20::is_scalar_v = is_real_v<T> || is_complex_v<T> || is_integer_v<T>
	Trait to detect whether a type is a numeric scalar (real, complex, or integer).
template<typename T >
constexpr bool	uni20::is_scalar_valued_v = !std::same_as<scalar_t<T>, void>
	Trait to detect whether T is scalar-valued.

Detailed Description

Scalar helper utilities shared across Uni20 core algorithms.

Typedef Documentation

complex

template<typename Real >

using uni20::complex = typedef typename detail::complex_type<Real>::type

Project-level complex scalar spelling.

Native real types retain std::complex identity and ABI. With MPC enabled, mpreal selects the owning MPC scalar. Generic functions should deduce the complex value type directly rather than deducing through this alias.

Template Parameters

Real	Underlying real scalar type.

make_complex_t

template<typename T >

using uni20::make_complex_t = typedef typename make_complex<T>::type

Alias for the complexified version of T.

Template Parameters

T	Type to complexify.

make_real_t

template<typename T >

using uni20::make_real_t = typedef typename make_real<T>::type

Alias for the underlying real-valued type of T.

Template Parameters

T	Type to convert.

Enumeration Type Documentation

real_format_notation

enum class uni20::real_format_notation

strong

Selects how real scalar values are rendered as text.

Enumerator
general
fixed
scientific

Function Documentation

conj() [1/3]

template<typename T >

uni20::complex< T > uni20::conj

(

detail::standard_complex< T >

x

)

Returns the complex conjugate for complex-valued scalars.

This overload forwards to std::conj and therefore returns a uni20::complex<T> copy of the input value. It inherits the constexpr availability of std::conj (currently not constexpr).

Template Parameters

T	Component type of the complex scalar.

Parameters

x	Complex value whose conjugate is requested.

Returns

The complex conjugate of x.

conj() [2/3]

template<Integer I>

constexpr I uni20::conj ( I const &  x )

constexpr

Returns the conjugate of an integer scalar.

Integer values are treated as reals for conjugation and therefore returned unchanged. The overload is constexpr, enabling compile-time evaluation for literal arguments.

Template Parameters

I	Integer scalar type.

Parameters

x	Integer scalar to return.

Returns

x, unchanged.

conj() [3/3]

template<Real R>

constexpr R uni20::conj ( R const &  x )

constexpr

Returns the conjugate of a real-valued scalar.

Real numbers are unchanged by conjugation, so the value is returned verbatim. The overload is constexpr, enabling compile-time evaluation for literal arguments.

Template Parameters

R	Real scalar type.

Parameters

x	Real scalar to return.

Returns

x, unchanged.

format_complex()

template<Complex T>

std::string uni20::format_complex	(	T const &	value,
		scalar_format_options const &	options = {}
	)

Format a Uni20 complex scalar as real+imagi.

Template Parameters

T	Complex scalar type.

Parameters

value	Value to format.
options	Text formatting options.

Returns

Formatted scalar text.

format_real()

template<Real T>

std::string uni20::format_real	(	T	value,
		scalar_format_options const &	options = {}
	)

Format a Uni20 real scalar.

Template Parameters

T	Real scalar type.

Parameters

value	Value to format.
options	Text formatting options.

Returns

Formatted scalar text.

format_scalar()

template<RealOrComplex T>

std::string uni20::format_scalar	(	T const &	value,
		scalar_format_options const &	options = {}
	)

Format any Uni20 real or complex scalar.

Template Parameters

T	Real or complex scalar type.

Parameters

value	Value to format.
options	Text formatting options.

Returns

Formatted scalar text.

herm()

template<Scalar S>

constexpr auto uni20::herm ( S  x )

constexpr

Computes the Hermitian adjoint of a scalar value.

For scalar inputs the Hermitian adjoint is equivalent to the complex conjugate, so this helper simply forwards to conj. When the selected conj overload is constexpr, this helper is as well, preserving compile-time evaluation.

Template Parameters

S	Scalar type satisfying Scalar.

Parameters

x	Scalar value whose Hermitian adjoint is requested.

Returns

The result of calling conj(x).

imag()

template<typename T >

constexpr T & uni20::imag ( detail::standard_complex< T > &  z )

constexprnoexcept

Provides mutable access to the imaginary component of a uni20::complex value.

This helper mirrors the std::imag overload for lvalues while remaining constexpr and noexcept for direct reference access.

Template Parameters

T	Component type of the complex scalar.

Parameters

z	Complex number whose imaginary component will be exposed.

Returns

Reference to the imaginary component of z.

isfinite() [1/3]

template<Complex C>

constexpr bool uni20::isfinite ( C const &  z )

constexpr

Returns whether both components of a complex scalar are finite.

Template Parameters

T	Real component type.

Parameters

z	Complex scalar to inspect.

Returns

true when both the real and imaginary components are finite.

isfinite() [2/3]

template<Integer I>

constexpr bool uni20::isfinite ( I const &  x )

constexprnoexcept

Returns whether an integer scalar is finite.

Integer Uni20 scalars have no NaN or infinity representation, so every value is finite.

Template Parameters

I	Integer scalar type.

Parameters

x	Integer scalar to inspect.

Returns

Always true.

isfinite() [3/3]

template<Real R>

constexpr bool uni20::isfinite ( R const &  x )

constexpr

Returns whether a real scalar is neither NaN nor positive/negative infinity.

This uses uni20::numeric_limits<T> so extension real scalar types can define their own infinity representation without depending on standard-library overload coverage for std::isfinite. Runtime-precision mpreal uses its native classification instead of type-only limits.

Template Parameters

R	Real scalar type.

Parameters

x	Real scalar to inspect.

Returns

true when x is finite.

parse_real()

template<Real T>

T uni20::parse_real

(

std::string_view

text

)

Parse a Uni20 real scalar from text.

Template Parameters

T	Real scalar type.

Parameters

text	Text containing one complete real literal.

Returns

Parsed value.

Exceptions

std::invalid_argument	if the text is not a complete real literal.
std::out_of_range	if the literal overflows or underflows the target type.

read_real()

template<Real T>

std::istream & uni20::read_real	(	std::istream &	stream,
		T &	value
	)

Read a Uni20 real scalar from a stream token.

This helper exists because extension real aliases such as uni20::float128 cannot portably receive ordinary overloaded stream extraction operators. For mpreal, parsing retains the destination's working precision; invalid input leaves its value unchanged.

Template Parameters

T	Real scalar type.

Parameters

stream	Input stream.
value	Destination value.

Returns

The input stream.

real()

template<typename T >

constexpr T & uni20::real ( detail::standard_complex< T > &  z )

constexprnoexcept

Provides mutable access to the real component of a uni20::complex value.

This helper mirrors the std::real overload for lvalues while remaining constexpr and noexcept for direct reference access.

Template Parameters

T	Component type of the complex scalar.

Parameters

z	Complex number whose real component will be exposed.

Returns

Reference to the real component of z.

Variable Documentation

has_numeric_limits_v

template<typename T >

constexpr bool uni20::has_numeric_limits_v

inlineconstexpr

Initial value:

=
    requires { requires numeric_limits<std::remove_cvref_t<T>>::is_specialized; }

True when Uni20 has numeric limits for T.

Runtime-precision specializations require a value or precision for precision-dependent queries; this trait does not promise static limits.

Template Parameters

T	Type to inspect.

has_trivial_conj

template<typename T >

constexpr bool uni20::has_trivial_conj = Real<T> || Integer<T>

inlineconstexpr

Indicates whether the Uni20 conjugation helper is a no-op for the provided scalar type.

Evaluates to true when the scalar is already real-valued or integral, allowing callers to skip complex conjugation work. The variable template is constexpr, so the result may be used in constant-expression contexts.

Template Parameters

T	Scalar type to inspect.

is_complex_scalar_valued_v

template<typename T >

constexpr bool uni20::is_complex_scalar_valued_v = is_scalar_valued_v<T> && is_complex_v<scalar_t<T>>

inlineconstexpr

Trait to detect whether T is scalar-valued with a complex scalar.

Template Parameters

T	Type to inspect.

is_complex_v

template<typename T >

constexpr bool uni20::is_complex_v = is_complex_t<std::remove_cvref_t<T>>::value

inlineconstexpr

Convenience alias that exposes the value of is_complex_t.

Template Parameters

T	Type to inspect.

is_integer_scalar_valued_v

template<typename T >

constexpr bool uni20::is_integer_scalar_valued_v = is_scalar_valued_v<T> && is_integer_v<scalar_t<T>>

inlineconstexpr

Trait to detect whether T is scalar-valued with an integer scalar.

Template Parameters

T	Type to inspect.

is_integer_v

template<typename T >

constexpr bool uni20::is_integer_v = is_integer_t<std::remove_cvref_t<T>>::value

inlineconstexpr

Convenience alias that exposes the value of is_integer_t.

Template Parameters

T	Type to inspect.

is_real_or_complex_scalar_valued_v

template<typename T >

constexpr bool uni20::is_real_or_complex_scalar_valued_v = is_scalar_valued_v<T> && is_real_or_complex_v<scalar_t<T>>

inlineconstexpr

Trait to detect whether T is scalar-valued with a real or complex scalar.

Template Parameters

T	Type to inspect.

is_real_or_complex_v

template<typename T >

constexpr bool uni20::is_real_or_complex_v = is_real_v<T> || is_complex_v<T>

inlineconstexpr

Trait to detect whether a type is a real or complex scalar.

Template Parameters

T	Type to inspect.

is_real_scalar_valued_v

template<typename T >

constexpr bool uni20::is_real_scalar_valued_v = is_scalar_valued_v<T> && is_real_v<scalar_t<T>>

inlineconstexpr

Trait to detect whether T is scalar-valued with a real scalar.

Template Parameters

T	Type to inspect.

is_real_v

template<typename T >

constexpr bool uni20::is_real_v = is_real_t<std::remove_cvref_t<T>>::value

inlineconstexpr

Convenience alias that exposes the value of is_real_t.

Template Parameters

T	Type to inspect.

is_scalar_v

template<typename T >

constexpr bool uni20::is_scalar_v = is_real_v<T> || is_complex_v<T> || is_integer_v<T>

inlineconstexpr

Trait to detect whether a type is a numeric scalar (real, complex, or integer).

Template Parameters

T	Type to inspect.

is_scalar_valued_v

template<typename T >

constexpr bool uni20::is_scalar_valued_v = !std::same_as<scalar_t<T>, void>

inlineconstexpr

Trait to detect whether T is scalar-valued.

A scalar-valued type is either a scalar itself or a type whose recursive value_type chain resolves to a Uni20 scalar. Use is_scalar_v<T> when constraining a type that must be the scalar value itself.

Template Parameters

T	Type to inspect.