Contents

# OpenMP* Threaded Functions and Problems

The following
Intel® oneAPI Math Kernel Library
function domains are threaded
with the OpenMP* technology
:
• Direct sparse solver.
• LAPACK.
For a list of threaded routines, see LAPACK Routines.
• Level1 and Level2 BLAS.
For a list of threaded routines, see BLAS Level1 and Level2 Routines.
• All Level 3 BLAS and all Sparse BLAS routines except Level 2 Sparse Triangular solvers.
• All Vector Mathematics functions (except service functions).
• FFT.
For a list of FFT transforms that can be threaded, see Threaded FFT Problems.
Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.
Notice revision #20201201

## LAPACK Routines

In this section,
?
stands for a precision prefix of
each
flavor of the respective routine and may have the value of
s, d, c
, or
z
.
The following LAPACK routines are threaded
with OpenMP*
:
• Linear equations, computational routines:
• Factorization:
?getrf, ?getrfnpi, ?gbtrf, ?potrf, ?pptrf, ?sytrf, ?hetrf, ?sptrf, ?hptrf
• Solving:
?dttrsb, ?gbtrs, ?gttrs, ?pptrs, ?pbtrs, ?pttrs, ?sytrs, ?sptrs, ?hptrs, ?tptrs, ?tbtrs
• Orthogonal factorization, computational routines:
?geqrf, ?ormqr, ?unmqr, ?ormlq, ?unmlq, ?ormql, ?unmql, ?ormrq, ?unmrq
• Singular Value Decomposition, computational routines:
?gebrd, ?bdsqr
• Symmetric Eigenvalue Problems, computational routines:
?sytrd, ?hetrd, ?sptrd, ?hptrd, ?steqr, ?stedc
.
• Generalized Nonsymmetric Eigenvalue Problems, computational routines:
chgeqz/zhgeqz
.
A number of other LAPACK routines, which are based on threaded LAPACK or BLAS routines, make effective use of
OpenMP*
parallelism:
?gesv, ?posv, ?gels, ?gesvd, ?syev, ?heev, cgegs/zgegs, cgegv/zgegv, cgges/zgges, cggesx/zggesx, cggev/zggev, cggevx/zggevx,
and so on.

## Threaded BLAS Level1 and Level2 Routines

In the following list,
?
stands for a precision prefix of
each
flavor of the respective routine and may have the value of
s, d, c
, or
z
.
The following routines are threaded
with OpenMP*
:
• Level1 BLAS:
?axpy, ?copy, ?swap, ddot/sdot, cdotc, drot/srot
• Level2 BLAS:
?gemv, ?trsv, ?trmv, dsyr/ssyr, dsyr2/ssyr2, dsymv/ssymv

## Threaded FFT Problems

The following characteristics of a specific problem determine whether your FFT computation may be threaded
with OpenMP*
:
• rank
• domain
• size/length
• precision (single or double)
• placement (in-place or out-of-place)
• strides
• number of transforms
• layout (for example, interleaved or split layout of complex data)
Most FFT problems are threaded. In particular, computation of multiple transforms in one call (number of transforms > 1) is threaded. Details of which transforms are threaded follow.
One-dimensional (1D) transforms
1D transforms are threaded in many cases.
1D complex-to-complex (c2c) transforms of size
N
using interleaved complex data layout are threaded under the following conditions depending on the architecture:
Architecture
Conditions
Intel® 64
N
is a power of 2,
log
2
(
N
) > 9, the transform is double-precision out-of-place, and input/output strides equal 1.
Any
N
is composite,
log
2
(
N
) > 16, and input/output strides equal 1.
1D complex-to-complex transforms using split-complex layout are not threaded.
Multidimensional transforms
All multidimensional transforms on large-volume data are threaded.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.