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User manual HP, model OpenVMS 8.4

Manafacture: HP
File size: 43.03 kb
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HP Fortran for OpenVMS
HP EXTENDED MATH LIBRARY (CXML) ALPHA

Use of blocked algorithms that minimize translation
ONLY
buffer misses and unnecessary paging
HP Extended Math Library (CXML) for OpenVMS Alpha
Since CXML routines can be called from all languages
is a set of mathematical subprograms that are optimized
that support the OpenVMS calling standard, the library
for HP architectures. Included subprograms cover the
provides optimized computation for applications written
areas of:
in these languages. Where appropriate, most subpro-
grams are available in both real and complex versions,

Basic Linear Algebra
as well as in both single and double precision. CXML for

Linear System and Eigenproblem Solvers
OpenVMS Alpha supports both IEEE and VAX floating-
point formats.

Sparse Linear System Solvers

Sorting
Basic Linear Algebra Subprograms

Random Number Generation
Linear algebra operations are fundamental to many

Signal Processing
mathematical applications, and several libraries of linear
algebra subprograms exist throughout the computer in-
The Basic Linear Algebra library includes the industry-
dustry. The CXML BLAS library contains the most com-
standard Basic Linear Algebra Subprograms (BLAS)
monly used linear algebra subprograms.
Level 1, Level 2, and Level 3. Also included are sub-
programs for BLAS Level 1 Extensions, Sparse BLAS
The CXML linear algebra library contains five groups of
Level 1, and Array Math Functions (VLIB).
subprograms at three levels:
The Linear System and Eigenproblem Solver library pro-

Basic Linear Algebra Subprograms (BLAS) Level 1
vides the complete LAPACK v2 package developed by

BLAS Level 1 Extensions
a consortium of university and government laboratories.
LAPACK is an industry-standard subprogram package

BLAS Level 1 Sparse Extensions
offering an extensive set of linear system and eigenprob-

BLAS Level 2
lem solvers. LAPACK uses blocked algorithms that are
better suited to most modern architectures, particularly

BLAS Level 3
ones with memory hierarchies. LAPACK will supersede
LINPACK and EISPACK for most users.
BLAS Level 1 (Scalar/Vector and Vector/Vector
The Sparse Linear System library provides both direct
Operations)
and iterative sparse linear system solvers. The direct
solver package supports both symmetric and nonsym-
BLAS Level 1 provides a set of elementary vector func-
metric sparse matrices stored using the skyline storage
tions, operating on one or two vectors. These are typ-
scheme. The iterative solver package contains a basic
ically very small routines, and they make less efficient
set of storage schemes, preconditioners, and iterative
use of the computing resources of modern computer ar-
solvers. The design of this package is modular and
chitectures than the Level 2 and 3 operations.
matrix-free, allowing future expansion and easy modifi-
CXML provides the 15 standard BLAS Level 1 opera-
cation by users.
tions:
The Signal Processing library provides a basic set of sig-

The index of the element of a vector having maximum
nal processing functions. Included are one-, two-, and
absolute value
three-dimensional Fast Fourier Transforms (FFT), group
FFTs, Cosine/Sine Transforms (FCT/FST), Convolution,

The sum of the absolute values of the elements of a
Correlation, and Digital Filters.
vector
Many CXML subprograms are optimized for the sup-

Inner product of two real vectors
ported hardware platforms. Optimization techniques in-

Scalar plus the extended precision inner product of
clude traditional optimizations such as loop unrolling and
two real vectors
loop reordering. CXML subprograms also provide effi-
cient management of the hierarchical memory system,

Conjugated inner product of two complex vectors
using techniques such as the following:

Unconjugated inner product of two complex vectors

Reuse of data within registers to minimize memory

Square root of the sum of squares (norm) of the el-
accesses
ements of a vector

Efficient cache management

Scalar times a vector plus a vector
5


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