algebra_util.hpp File Reference

#include <array>
#include <cmath>
#include <limits>
#include <optional>
#include "akreon/linalg/constants.hpp"
#include "vector_concepts.hpp"

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Namespaces
namespace	linalg

Macros
#define	MAX_STEP_EVAL   256
	Maximum Newton/refinement iterations used by constexpr utilities.
#define	LINALG_HAS_CXX26_CONSTEXPR_CMATH   0
	Whether the active standard library supports P1383R2 <cmath>.
#define	LINALG_HAS_CXX26_CONSTEXPR_COMPLEX_MATH   0
	Whether the active standard library supports P1383R2 <complex>.

Functions
template<typename T , std::size_t N>
constexpr auto	linalg::array_to_tuple (const std::array< T, N > &x)
	Copy a fixed-size array into a tuple of the same length.
template<Field T>
constexpr bool	linalg::is_real (const std::complex< T > &z, real_type_t< T > tol=1e-10)
	Check whether a complex value's imaginary component is below a bound.
template<Real T>
constexpr std::optional< T >	linalg::constexpr_div (T num, T den)
	Divide two real scalars with an explicit zero-denominator result.
template<Real T>
constexpr T	linalg::constexpr_div_safe (T num, T den, T fallback=T(0))
	Divide two real scalars, returning a fallback for a zero denominator.
template<Real T>
constexpr T	linalg::constexpr_pow (T x, std::size_t power)
	Raise a real scalar to a nonnegative integral power.
template<Real T>
constexpr std::optional< T >	linalg::constexpr_sqrt (T x, T g=1e-10, T tol=1e-10)
	Approximate a nonnegative square root with Newton iteration.
template<Real T>
constexpr T	linalg::constexpr_sqrt_safe (T x, T floor=T(0), T g=1e-10, T tol=1e-10)
	Return a scalar square root with a sanitized fallback radicand.
template<Real T>
constexpr T	linalg::constexpr_abs (T x)
	Compute real absolute value or complex magnitude.
template<Complex T>
constexpr auto	linalg::constexpr_abs (const T &x)
template<Real T>
constexpr std::optional< T >	linalg::constexpr_nrt (T x, std::size_t root, T g=1e-10, T tol=1e-10)
	Approximate a real nth root with Newton iteration.
template<Real T>
constexpr T	linalg::constexpr_nrt_safe (T x, std::size_t root, T floor=T(0), T g=1e-10, T tol=1e-10)
	Return a scalar nth root with a sanitized fallback radicand.
template<Real T>
constexpr auto	linalg::constexpr_sin (T x, int terms=16)
	Approximate sine with a truncated Taylor recurrence.
template<Real T>
constexpr auto	linalg::constexpr_cos (T x, int terms=16)
	Approximate cosine with a truncated Taylor recurrence.
template<Real T>
constexpr std::optional< T >	linalg::constexpr_atanh (T x, int terms=16)
	atanh (inverse hyperbolic tangent function)
template<Real T>
constexpr T	linalg::constexpr_atanh_safe (T x, T fallback=T(0), int terms=16)
	constexpr-safe atanh with fallback
template<Real T>
constexpr auto	linalg::constexpr_expi (T theta, int terms=16)
	Approximate exp(i * theta) on the complex unit circle.
template<Real T>
constexpr auto	linalg::constexpr_exp (T x, int terms=16)
	Approximate the real exponential with a truncated power series.
template<Complex T>
constexpr auto	linalg::constexpr_exp_lambda (const T &lambda, int terms=16)
	Approximate the exponential of a complex scalar.
template<Real T>
constexpr std::optional< T >	linalg::constexpr_ln (T x_in, int terms=16)
	natural log
template<Real T>
constexpr T	linalg::constexpr_ln_safe (T x, T floor=std::numeric_limits< T >::min(), int terms=16)
	natural log with domain sanitization and fallback
template<std::size_t Start, std::size_t End, typename Func > requires (End - Start >= 0)
constexpr void	linalg::constexpr_for (Func &&f)
	constexpr for loop which recursively unrolls a dynamic for loop into compile time recursive loop
template<Complex T>
constexpr bool	linalg::is_same (const T &a, const T &b, real_type_t< T > tol=1e-10)
	Compare complex scalars by magnitude of their difference.
template<VectorContainer Vec> requires (Real<vector_element_t<Vec>>)
constexpr auto	linalg::argsort_desc (const Vec &x)
	Return coordinate indices sorted by descending real value.

Macro Definition Documentation

LINALG_HAS_CXX26_CONSTEXPR_CMATH

#define LINALG_HAS_CXX26_CONSTEXPR_CMATH   0

Whether the active standard library supports P1383R2 <cmath>.

Definition at line 28 of file algebra_util.hpp.

LINALG_HAS_CXX26_CONSTEXPR_COMPLEX_MATH

#define LINALG_HAS_CXX26_CONSTEXPR_COMPLEX_MATH   0

Whether the active standard library supports P1383R2 <complex>.

Definition at line 36 of file algebra_util.hpp.

MAX_STEP_EVAL

#define MAX_STEP_EVAL   256

Maximum Newton/refinement iterations used by constexpr utilities.

The cap keeps compile-time evaluation bounded on compilers with finite constexpr step budgets.

Definition at line 22 of file algebra_util.hpp.