num::kernel::raw Namespace Reference

Functions
template<std::floating_point T>
NUM_K_AINLINE void	scale (T *NUM_K_RESTRICT x, T alpha, idx n) noexcept
	x[i] *= alpha
template<std::floating_point T>
NUM_K_AINLINE void	axpy (T *NUM_K_RESTRICT y, const T *NUM_K_RESTRICT x, T alpha, idx n) noexcept
	y[i] += alpha * x[i]
template<std::floating_point T>
NUM_K_AINLINE void	axpby (T *NUM_K_RESTRICT y, const T *NUM_K_RESTRICT x, T a, T b, idx n) noexcept
	y[i] = a*x[i] + b*y[i].
template<std::floating_point T>
NUM_K_AINLINE void	axpbyz (T *NUM_K_RESTRICT z, const T *NUM_K_RESTRICT x, const T *NUM_K_RESTRICT y, T a, T b, idx n) noexcept
	z[i] = a*x[i] + b*y[i].
template<std::floating_point T>
NUM_K_AINLINE T	dot (const T *NUM_K_RESTRICT x, const T *NUM_K_RESTRICT y, idx n) noexcept
	dot product: return sum x[i] * y[i]
template<std::floating_point T>
NUM_K_AINLINE T	norm_sq (const T *NUM_K_RESTRICT x, idx n) noexcept
	sum x[i]^2 (no sqrt; use for convergence checks to avoid sqrt cost)
template<std::floating_point T>
NUM_K_AINLINE T	norm (const T *NUM_K_RESTRICT x, idx n) noexcept
	Euclidean norm: sqrt(sum x[i]^2)
template<std::floating_point T>
NUM_K_AINLINE T	l1_norm (const T *NUM_K_RESTRICT x, idx n) noexcept
	L1 norm: sum |x[i]|.
template<std::floating_point T>
NUM_K_AINLINE T	linf_norm (const T *NUM_K_RESTRICT x, idx n) noexcept
	L-infinity norm: max |x[i]|.
template<std::floating_point T>
NUM_K_AINLINE T	sum (const T *NUM_K_RESTRICT x, idx n) noexcept
	Scalar sum: return sum x[i].
template<std::floating_point T>
NUM_K_AINLINE void	matvec (T *NUM_K_RESTRICT y, const T *NUM_K_RESTRICT A, const T *NUM_K_RESTRICT x, idx m, idx n) noexcept
	y[i] = sum_j A[i*n + j] * x[j] (m x n row-major matrix)
template<std::floating_point T>
NUM_K_AINLINE void	ger (T *NUM_K_RESTRICT A, const T *NUM_K_RESTRICT x, const T *NUM_K_RESTRICT y, T alpha, idx m, idx n) noexcept
	Rank-1 update: A[i*n + j] += alpha * x[i] * y[j] (m x n row-major)
template<std::floating_point T>
NUM_K_AINLINE void	trsv_lower (T *NUM_K_RESTRICT x, const T *NUM_K_RESTRICT L, const T *NUM_K_RESTRICT b, idx n) noexcept
	Forward substitution: solve Lx = b, L lower triangular (n x n, row-major).
template<std::floating_point T>
NUM_K_AINLINE void	trsv_upper (T *NUM_K_RESTRICT x, const T *NUM_K_RESTRICT U, const T *NUM_K_RESTRICT b, idx n) noexcept
	Back substitution: solve Ux = b, U upper triangular (n x n, row-major).

Function Documentation

axpby()

template<std::floating_point T>

NUM_K_AINLINE void num::kernel::raw::axpby ( T *NUM_K_RESTRICT  y, const T *NUM_K_RESTRICT  x, T  a, T  b, idx  n  )

noexcept

y[i] = a*x[i] + b*y[i].

Definition at line 46 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by num::kernel::array::axpby().

axpbyz()

template<std::floating_point T>

NUM_K_AINLINE void num::kernel::raw::axpbyz ( T *NUM_K_RESTRICT  z, const T *NUM_K_RESTRICT  x, const T *NUM_K_RESTRICT  y, T  a, T  b, idx  n  )

noexcept

z[i] = a*x[i] + b*y[i].

Definition at line 59 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by num::kernel::array::axpbyz(), and num::backends::seq::matadd().

axpy()

template<std::floating_point T>

NUM_K_AINLINE void num::kernel::raw::axpy ( T *NUM_K_RESTRICT  y, const T *NUM_K_RESTRICT  x, T  alpha, idx  n  )

noexcept

y[i] += alpha * x[i]

Definition at line 34 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by num::backends::seq::axpy().

dot()

template<std::floating_point T>

NUM_K_AINLINE T num::kernel::raw::dot ( const T *NUM_K_RESTRICT  x, const T *NUM_K_RESTRICT  y, idx  n  )

noexcept

dot product: return sum x[i] * y[i]

Definition at line 73 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by num::backends::seq::dot().

ger()

template<std::floating_point T>

NUM_K_AINLINE void num::kernel::raw::ger ( T *NUM_K_RESTRICT  A, const T *NUM_K_RESTRICT  x, const T *NUM_K_RESTRICT  y, T  alpha, idx  m, idx  n  )

noexcept

Rank-1 update: A[i*n + j] += alpha * x[i] * y[j] (m x n row-major)

Inner loop over j is independent and vectorizable.

Definition at line 160 of file raw.hpp.

References NUM_K_IVDEP, and NUM_K_RESTRICT.

Referenced by num::kernel::dense::ger().

l1_norm()

template<std::floating_point T>

NUM_K_AINLINE T num::kernel::raw::l1_norm ( const T *NUM_K_RESTRICT  x, idx  n  )

noexcept

L1 norm: sum |x[i]|.

Definition at line 103 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by num::kernel::reduce::l1_norm().

linf_norm()

template<std::floating_point T>

NUM_K_AINLINE T num::kernel::raw::linf_norm ( const T *NUM_K_RESTRICT  x, idx  n  )

noexcept

L-infinity norm: max |x[i]|.

Definition at line 114 of file raw.hpp.

Referenced by num::kernel::reduce::linf_norm().

matvec()

template<std::floating_point T>

NUM_K_AINLINE void num::kernel::raw::matvec ( T *NUM_K_RESTRICT  y, const T *NUM_K_RESTRICT  A, const T *NUM_K_RESTRICT  x, idx  m, idx  n  )

noexcept

y[i] = sum_j A[i*n + j] * x[j] (m x n row-major matrix)

y must be pre-allocated with size m. y and x must not alias A.

Definition at line 140 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by num::backends::seq::matvec().

norm()

template<std::floating_point T>

NUM_K_AINLINE T num::kernel::raw::norm ( const T *NUM_K_RESTRICT  x, idx  n  )

noexcept

Euclidean norm: sqrt(sum x[i]^2)

Definition at line 97 of file raw.hpp.

References norm_sq().

Referenced by num::backends::seq::norm().

norm_sq()

template<std::floating_point T>

NUM_K_AINLINE T num::kernel::raw::norm_sq ( const T *NUM_K_RESTRICT  x, idx  n  )

noexcept

sum x[i]^2 (no sqrt; use for convergence checks to avoid sqrt cost)

Definition at line 86 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by norm().

scale()

template<std::floating_point T>

NUM_K_AINLINE void num::kernel::raw::scale ( T *NUM_K_RESTRICT  x, T  alpha, idx  n  )

noexcept

x[i] *= alpha

Definition at line 25 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by num::backends::seq::scale().

sum()

template<std::floating_point T>

NUM_K_AINLINE T num::kernel::raw::sum ( const T *NUM_K_RESTRICT  x, idx  n  )

noexcept

Scalar sum: return sum x[i].

Definition at line 127 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by num::kernel::reduce::sum().

trsv_lower()

template<std::floating_point T>

NUM_K_AINLINE void num::kernel::raw::trsv_lower ( T *NUM_K_RESTRICT  x, const T *NUM_K_RESTRICT  L, const T *NUM_K_RESTRICT  b, idx  n  )

noexcept

Forward substitution: solve Lx = b, L lower triangular (n x n, row-major).

x must be pre-allocated with size n. b and x must not alias each other.

Definition at line 181 of file raw.hpp.

Referenced by num::kernel::dense::trsv_lower().

trsv_upper()

template<std::floating_point T>

NUM_K_AINLINE void num::kernel::raw::trsv_upper ( T *NUM_K_RESTRICT  x, const T *NUM_K_RESTRICT  U, const T *NUM_K_RESTRICT  b, idx  n  )

noexcept

Back substitution: solve Ux = b, U upper triangular (n x n, row-major).

x must be pre-allocated with size n. b and x must not alias each other.

Definition at line 200 of file raw.hpp.

Referenced by num::kernel::dense::trsv_upper().