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HP Fortran for OpenVMS
HP EXTENDED MATH LIBRARY (CXML) ALPHA
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Use of blocked algorithms that minimize translation
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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,
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Basic Linear Algebra
as well as in both single and double precision. CXML for
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Linear System and Eigenproblem Solvers
OpenVMS Alpha supports both IEEE and VAX floating-
point formats.
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Sparse Linear System Solvers
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Sorting
Basic Linear Algebra Subprograms
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Random Number Generation
Linear algebra operations are fundamental to many
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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-
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Basic Linear Algebra Subprograms (BLAS) Level 1
vides the complete LAPACK v2 package developed by
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BLAS Level 1 Extensions
a consortium of university and government laboratories.
LAPACK is an industry-standard subprogram package
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BLAS Level 1 Sparse Extensions
offering an extensive set of linear system and eigenprob-
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BLAS Level 2
lem solvers. LAPACK uses blocked algorithms that are
better suited to most modern architectures, particularly
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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-
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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,
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The sum of the absolute values of the elements of a
Correlation, and Digital Filters.
vector
Many CXML subprograms are optimized for the sup-
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Inner product of two real vectors
ported hardware platforms. Optimization techniques in-
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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,
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Conjugated inner product of two complex vectors
using techniques such as the following:
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Unconjugated inner product of two complex vectors
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Reuse of data within registers to minimize memory
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Square root of the sum of squares (norm) of the el-
accesses
ements of a vector
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Efficient cache management
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Scalar times a vector plus a vector
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