Functions
NUM_K_AINLINE void	scale (real *NUM_K_RESTRICT x, real alpha, idx n) noexcept
	x[i] *= alpha

NUM_K_AINLINE void	axpy (real NUM_K_RESTRICT y, const real NUM_K_RESTRICT x, real alpha, idx n) noexcept
	y[i] += alpha * x[i]

NUM_K_AINLINE void	axpby (real NUM_K_RESTRICT y, const real NUM_K_RESTRICT x, real a, real b, idx n) noexcept
	y[i] = ax[i] + by[i] (fused scale-and-add, one memory pass)

NUM_K_AINLINE void	axpbyz (real NUM_K_RESTRICT z, const real NUM_K_RESTRICT x, const real *NUM_K_RESTRICT y, real a, real b, idx n) noexcept
	z[i] = ax[i] + by[i] (fused, three-array, one pass each)

NUM_K_AINLINE real	dot (const real NUM_K_RESTRICT x, const real NUM_K_RESTRICT y, idx n) noexcept
	dot product: return sum x[i] * y[i]

NUM_K_AINLINE real	norm_sq (const real *NUM_K_RESTRICT x, idx n) noexcept
	sum x[i]^2 (no sqrt; use for convergence checks to avoid sqrt cost)

NUM_K_AINLINE real	norm (const real *NUM_K_RESTRICT x, idx n) noexcept
	Euclidean norm: sqrt(sum x[i]^2)

NUM_K_AINLINE real	l1_norm (const real *NUM_K_RESTRICT x, idx n) noexcept
	L1 norm: sum \|x[i]\|.

NUM_K_AINLINE real	linf_norm (const real *NUM_K_RESTRICT x, idx n) noexcept
	L-infinity norm: max \|x[i]\|.

NUM_K_AINLINE real	sum (const real *NUM_K_RESTRICT x, idx n) noexcept
	Scalar sum: return sum x[i].

NUM_K_AINLINE void	matvec (real NUM_K_RESTRICT y, const real NUM_K_RESTRICT A, const real *NUM_K_RESTRICT x, idx m, idx n) noexcept
	y[i] = sum_j A[in + j] x[j] (m x n row-major matrix)

NUM_K_AINLINE void	ger (real NUM_K_RESTRICT A, const real NUM_K_RESTRICT x, const real *NUM_K_RESTRICT y, real alpha, idx m, idx n) noexcept
	Rank-1 update: A[in + j] += alpha x[i] * y[j] (m x n row-major)

NUM_K_AINLINE void	trsv_lower (real NUM_K_RESTRICT x, const real NUM_K_RESTRICT L, const real *NUM_K_RESTRICT b, idx n) noexcept
	Forward substitution: solve Lx = b, L lower triangular (n x n, row-major).

NUM_K_AINLINE void	trsv_upper (real NUM_K_RESTRICT x, const real NUM_K_RESTRICT U, const real *NUM_K_RESTRICT b, idx n) noexcept
	Back substitution: solve Ux = b, U upper triangular (n x n, row-major).

Function Documentation

◆ axpby()

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

noexcept

y[i] = a*x[i] + b*y[i] (fused scale-and-add, one memory pass)

No direct BLAS equivalent. Avoids a separate scale pass then axpy pass: compared to scale(y,b); axpy(a,x,y), this reads y only once.

Definition at line 113 of file raw.hpp.

References NUM_K_IVDEP.

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

◆ axpbyz()

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

noexcept

z[i] = a*x[i] + b*y[i] (fused, three-array, one pass each)

No direct BLAS equivalent. z may alias x or y; otherwise fully independent.

Definition at line 125 of file raw.hpp.

References NUM_K_IVDEP.

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

◆ axpy()

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

noexcept

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

Definition at line 96 of file raw.hpp.

References NUM_K_IVDEP.

◆ dot()

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

noexcept

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

Definition at line 137 of file raw.hpp.

References NUM_K_IVDEP.

◆ ger()

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

noexcept

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

BLAS dger equivalent. Inner loop over j is independent and vectorizable.

Definition at line 254 of file raw.hpp.

References NUM_K_IVDEP, and NUM_K_RESTRICT.

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

◆ l1_norm()

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

noexcept

L1 norm: sum |x[i]|.

Definition at line 174 of file raw.hpp.

References NUM_K_IVDEP.

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

◆ linf_norm()

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

noexcept

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

Definition at line 189 of file raw.hpp.

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

◆ matvec()

NUM_K_AINLINE void num::kernel::raw::matvec	(	real *NUM_K_RESTRICT	y,
		const real *NUM_K_RESTRICT	A,
		const real *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 227 of file raw.hpp.

References NUM_K_IVDEP.

◆ norm()

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

noexcept

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

Definition at line 164 of file raw.hpp.

References norm_sq().

◆ norm_sq()

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

noexcept

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

Definition at line 153 of file raw.hpp.

References NUM_K_IVDEP.

Referenced by norm().

◆ scale()

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

noexcept

x[i] *= alpha

Definition at line 83 of file raw.hpp.

References NUM_K_IVDEP.

◆ sum()

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

noexcept

Scalar sum: return sum x[i].

No BLAS equivalent (cblas_dasum sums absolute values; this does not).

Definition at line 210 of file raw.hpp.

References NUM_K_IVDEP.

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

◆ trsv_lower()

NUM_K_AINLINE void num::kernel::raw::trsv_lower	(	real *NUM_K_RESTRICT	x,
		const real *NUM_K_RESTRICT	L,
		const real *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. Uses BLAS dtrsv when available (copies b -> x first, then solves in-place).

Definition at line 280 of file raw.hpp.

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

◆ trsv_upper()

NUM_K_AINLINE void num::kernel::raw::trsv_upper	(	real *NUM_K_RESTRICT	x,
		const real *NUM_K_RESTRICT	U,
		const real *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. Uses BLAS dtrsv when available (copies b -> x first, then solves in-place).

Definition at line 305 of file raw.hpp.

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

Functions

Function Documentation

◆ axpby()

◆ axpbyz()

◆ axpy()

◆ dot()

◆ ger()

◆ l1_norm()

◆ linf_norm()

◆ matvec()

◆ norm()

◆ norm_sq()

◆ scale()

◆ sum()

◆ trsv_lower()

◆ trsv_upper()