Software
          Product
          Description

          ___________________________________________________________________

          PRODUCT NAME:  HP Fortran for OpenVMS
                                                                 SPD 56.18.18
          Software
          Product
          Description

          ___________________________________________________________________

          PRODUCT NAME:  HP Fortran for OpenVMS
          <right_line(SPD 56.18.18)

          DESCRIPTION

          This is the Software Product Description (SPD) for HP Fortran (for-
          merly Compaq Fortran) Version 8.2 for OpenVMS[TM] Alpha Systems, and
          HP Fortran Version 8.2 for OpenVMS Integrity Servers (I64). Both HP
          Fortran on OpenVMS Alpha and Integrity contain the HP Fortran 95/90
          Version 8.2 software; only HP Fortran for OpenVMS[TM] Alpha Systems
          contains the HP Fortran 77 Version 8.2 software as well as the HP Ex-
          tended Math Library (CXML). In the following description, HP Fortran
          refers to HP Fortran 95/90 unless a specific reference to the 95/90
          or 77 product is needed to distinguish between the two software prod-
          ucts.

          HP Fortran is an implementation of the Fortran programming language
          that supports the FORTRAN 66, FORTRAN 77, Fortran 90, and Fortran 95
          standards. HP Fortran 95/90 and HP Fortran 77 fully support the fol-
          lowing standards:

          o  ANSI X3.9-1966 (FORTRAN 66)

          o  ANSI X3.9-1978 (FORTRAN 77)

          o  ISO 1539-1980(E) (FORTRAN 77)

          o  MIL-STD-1753

                                                                 October 2007

 



          HP Fortran for OpenVMS


          o  FIPS-69-1 (HP Fortran meets the requirements of this standard by
             conforming to the ANSI Standard and by including a flagger. The flag-
             ger optionally produces diagnostic messages for compile-time el-
             ements that do not conform to the Full-Level ANSI Fortran Standard.)

          HP Fortran 95/90 supports all of the standards that HP Fortran 77 sup-
          ports plus the following new standards:

          o  ANSI X3.198-1992 (Fortran 90)

          o  ISO/IEC 1539-1:1997(E) (Fortran 95)

          HP FORTRAN

          HP Fortran supports extensions to the ISO and ANSI standards, includ-
          ing a number of extensions defined by HP Fortran for the various HP
          Fortran platforms (operating system/architecture pairs). In addition
          to HP OpenVMS Alpha and I64 systems, HP Fortran platforms include:

          o  HP Fortran and HP Fortran 77 on HP Tru64[TM] UNIX[R] Alpha systems

          o  HP Fortran 77 for OpenVMS VAX[TM] systems

          Major additions to the FORTRAN 77 standard introduced by the Fortran
          90 standard include:

          o  Array operations

          o  Improved facilities for numeric computation

          o  Parameterized intrinsic data types

          o  User-defined data types

          o  Facilities for modular data and procedure definitions

          o  Pointers

          o  The concept of language evolution

          o  Support for DATE_AND_TIME intrinsic for obtaining dates using a four-
             digit year format

                                           2

 



          HP Fortran for OpenVMS


          HP Fortran contains full support for the Fortran 95 standard, includ-
          ing the following features:

          o  FORALL statement and construct

          o  Automatic deallocation of ALLOCATABLE arrays

          o  DIM argument to MAXLOC and MINLOC

          o  PURE user-defined subprograms

          o  ELEMENTAL user-defined subprograms (a restricted form of a pure pro-
             cedure)

          o  Pointer initialization (initial value)

          o  The NULL intrinsic to nullify a pointer

          o  Derived-type structure initialization

          o  CPU_TIME intrinsic subroutine

          o  KIND argument to CEILING and FLOOR intrinsics

          o  Nested WHERE constructs, masked ELSEWHERE statement, and named WHERE
             constructs

          o  Comments allowed in namelist input

          o  Generic identifier in END INTERFACE statements

          o  Minimal width field editing using a numeric edit descriptor with
             0 width

          o  Detection of Obsolescent and/or Deleted features listed in the For-
             tran 95 standard. HP Fortran flags these obsolescent and deleted
             features, but fully supports them.

          HP Fortran includes the following features and enhancements:

          o  CDD (Common Data Dictionary) support and DML (Data Manipulation Lan-
             guage) support, formerly only available in the old Fortran 77 (/old_
             f77) compiler, are now available in the Fortran 90/95 compiler

          o  Full support for 64-bit address space, including 64-bit static space

                                           3

 



          HP Fortran for OpenVMS


          o  Support for providing cross-reference information to the DEC Source
             Code Analyzer component of DECset for OpenVMS

          o  Support for linking against static and shared libraries

          o  Support for creating shareable code to be put into a shared library

          o  Support for stack-based storage

          o  Support for dynamic memory allocation

          o  Support for reading and writing binary data files in nonnative for-
             mats, including IEEE[R] (little-endian and big-endian), VAX, IBM[R]
             System\360, and CRAY[R] integer and floating point formats

          o  User control over IEEE floating point exception handling, report-
             ing, and resulting values

          o  Control for memory boundary alignment of items in COMMON and fields
             in structures and warnings for unaligned data

          o  Directives to control listing page titles and subtitles, object file
             identification field, COMMON and record field alignment, and some
             attributes of COMMON blocks

          o  Ability to CALL an external function subprogram

          o  7200 Character Statement Length

          o  Free form unlimited line length

          o  Mixing Subroutines/Functions in Generic Interfaces

          o  Composite data declarations using STRUCTURE, END STRUCTURE, and RECORD
             statements, and access to record components through field refer-
             ences

          o  Explicit specification of storage allocation units for data types
             such as:

                INTEGER*4
                LOGICAL*4
                REAL*4
                REAL*8
                COMPLEX*8

                                           4

 



          HP Fortran for OpenVMS


          o  Support for 64-bit signed integers using INTEGER*8 and LOGICAL*8

          o  Support for 128-bit floating-point real numbers (reals) using REAL*16
             and COMPLEX*32

          o  A set of data types:

             -  BYTE

             -  LOGICAL*1, LOGICAL*2, LOGICAL*4, LOGICAL*8

             -  INTEGER*1, INTEGER*2, INTEGER*4, INTEGER*8

             -  REAL*4, REAL*8, REAL*16

             -  COMPLEX*8, COMPLEX*16, DOUBLE COMPLEX, COMPLEX*32

             -  POINTER (CRAY style)

          o  Data statement style initialization in type declaration statements

          o  AUTOMATIC and STATIC statements

          o  Bit constants to initialize LOGICAL, REAL, and INTEGER values and
             participate in arithmetic and logical expressions

          o  Built-in functions %LOC, %REF, %VAL, and %DESCR

          o  VOLATILE statement

          o  Bit manipulation functions

          o  Binary, hexadecimal, and octal constants and Z and O format edit
             descriptors applicable to all data types

          o  I/O unit numbers that can be any nonnegative INTEGER*4 value

          o  Variable amounts of data can be read from and written to “STREAM”
             files, which contain no record delimiters

          o  ENCODE and DECODE statements

          o  ACCEPT, TYPE, and REWRITE input/output statements

          o  DEFINE FILE, UNLOCK, and DELETE statements

          o  USEROPEN subroutine invocation at file OPEN time

                                           5

 



          HP Fortran for OpenVMS


          o  Support for reading nondelimited character strings as input for char-
             acter NAMELIST items

          o  Debug statements in source

          o  Generation of a source listing file with optional machine code rep-
             resentation of the executable source

          o  Variable format expressions in a FORMAT statement

          o  Optional run-time bounds checking of array subscripts and charac-
             ter substrings

          o  31-character identifiers that can include dollar sign ($) and un-
             derscore (_)

          o  Support for executing in-line assembler code using the ASM intrin-
             sics (Alpha only)

          o  Support for the supercomputer intrinsics POPCNT, POPPAR, LEADZ, TRAILZ,
             and MULT_HIGH

          o  Language elements that support the various extended range and ex-
             tended precision floating point architectural features:

             -  32-bit VAX F_floating data type, with an 8-bit exponent and 24-
                bit mantissa, which provides a range of 0.293873588E-38 to 1.7014117E38
                and a precision of typically 7 decimal digits. Calculations with
                F_floating data on I64 are performed using the S_floating data
                type..

             -  64-bit VAX D_floating data type, with an 8-bit exponent and 56-
                bit mantissa, which provides a range of 0.2938735877055719D-38
                to 1.70141183460469229D38 and a precision of typically 16 dec-
                imal digits. Calculations with D_floating data on Alpha systems
                use G_floating precision (53-bit instead of 56-bit mantissa).
                Calculations with D_floating data on I64 are performed using the
                T_floating data type.



                                           6

 



          HP Fortran for OpenVMS


             -  64-bit VAX G_floating data type, with an 11-bit exponent and 53-
                bit mantissa, which provides a range of 0.5562684646268004D-308
                to 0.89884656743115785407D308 and a precision of typically 15
                decimal digits. Calculations with G_floating data on I64 are per-
                formed using the T_floating data type.

             -  32-bit IEEE S_floating data type, with an 8-bit exponent and 24-
                bit mantissa, which provides a range of 1.17549435E-38 (normal-
                ized) to 3.40282347E38 (the IEEE denormalized limit is 1.40129846E-
                45) and a precision of typically 7 decimal digits

             -  64-bit IEEE T_floating data type, with an 11-bit exponent and
                53-bit mantissa, which provides a range of 2.2250738585072013D-
                308 (normalized) to 1.7976931348623158D308 (the IEEE denormal-
                ized limit is 4.94065645841246544D-324) and a precision of typ-
                ically 15 decimal digits

             -  128-bit IEEE extended Alpha X_floating data type, with a 15-bit
                exponent and a 113-bit mantissa, which provides a range of ap-
                proximately 6.48Q-4966 to 1.18Q4932 and a precision of typically
                33 decimal digits

             -  The following combinations of floating types may be specified:

                -  F, G and X (the default on Alpha)

                -  F, D and X (VAX)

                -  S, T and X (IEEE) (the default on I64)

          o  Command line control for:

             -  The size of default INTEGER, REAL, and DOUBLE PRECISION data items

             -  The levels and types of optimization to be applied to the pro-
                gram

             -  The directories to search for INCLUDE files

             -  Inclusion or suppression of various compile-time warnings

             -  Inclusion or suppression of run-time checking for various I/O
                and computational errors

                                           7

 



          HP Fortran for OpenVMS


             -  Control over whether compilation terminates after a specific num-
                ber of errors has been found

             -  Choosing whether executing code will be thread-reentrant

          o  Internal procedures can be passed as actual arguments to procedures

          o  Kind types for all of the hardware-supported data types:

             -  For 1-, 2-, 4-, and 8-byte LOGICAL data:

                   LOGICAL (KIND=1)
                   LOGICAL (KIND=2)
                   LOGICAL (KIND=4)
                   LOGICAL (KIND=8)

             -  For 1-, 2-, 4-, and 8-byte INTEGER data:

                   INTEGER (KIND=1)
                   INTEGER (KIND=2)
                   INTEGER (KIND=4)
                   INTEGER (KIND=8)

             -  For 4-, 8-, and 16-byte REAL data:

                   REAL (KIND=4)
                   REAL (KIND=8)
                   REAL (KIND=16)

             -  For single precision, double precision, and quad-precision COM-
                PLEX data:

                   COMPLEX (KIND=4)
                   COMPLEX (KIND=8)
                   COMPLEX (KIND=16)

          HP Fortran takes advantage of OpenVMS facilities to include the fol-
          lowing features and enhancements in both HP Fortran 95/90 and HP For-
          tran 77:

          o  Language elements for keyed and sequential access to OpenVMS RMS
             indexed organization files

                                           8

 



          HP Fortran for OpenVMS


          o  The ability to specify an OpenVMS text library module in an INCLUDE
             statement

          o  Support for calls to OpenVMS system service and Run-Time Library
             procedures

          o  Generation of symbol tables for the OpenVMS Symbolic Debugger

          o  LIB$ESTABLISH and LIB$REVERT are provided as intrinsic functions
             for compatibility with HP Fortran exception handling

          o  Support for providing error diagnostics to the DEC Language-Sensitive
             Editor component of DECset for OpenVMS

          o  FDML (Fortran Data Manipulation Language) support (I64 only)

          HP Fortran 77 contains the following extensions to the FORTRAN 77 stan-
          dard: (Alpha only)

          o  Support for recursive subprograms

          o  IMPLICIT NONE statements

          o  INCLUDE statement

          o  NAMELIST-directed I/O

          o  DO WHILE and ENDDO statements

          o  Use of exclamation point (!) for end of line comments

          o  Generation of Cross Reference Listings

          o  Support for NTT Technical Requirement TR550001, Multivendor Inte-
             gration Architecture (MIA) Version 1.1, Division 2, Part 3-2, Pro-
             gramming Language FORTRAN

          o  Support for automatic arrays

          o  Support for the SELECT CASE - CASE - CASE DEFAULT - END SELECT state-
             ments

          o  Support for the EXIT and CYCLE statements and for construct names
             on DO - END DO statements

          o  Reporting of unused and uninitialized variables

                                           9

 



          HP Fortran for OpenVMS


          o  Support for DATE_AND_TIME intrinsic for obtaining dates using a four-
             digit year format

          HP Fortran 77 takes advantage of OpenVMS facilities to include the fol-
          lowing features and enhancements:

          o  Support for translation of CDD/Repository records into Fortran records
             for Fortran F77 on OpenVMS Alpha and Fortran F90 on OpenVMS I64

          o  Support for the extraction of program design information in com-
             ments using the DEC Source Code Analyzer component of DECset for
             OpenVMS

          HP Fortran provides a multiphase optimizer that is capable of perform-
          ing optimizations across entire programs. Specific optimizations per-
          formed by both HP Fortran 95/90 and Compaq Fortran 77 include:

          o  Constant folding

          o  Optimizations of arithmetic IF, logical IF, and block IF-THEN-ELSE

          o  Global common subexpression elimination

          o  Removal of invariant expressions from loops

          o  Global allocation of general registers across program units

          o  In-line expansion of statement functions and routines

          o  Optimization of array addressing in loops

          o  Value propagation

          o  Deletion of redundant and unreachable code

          o  Loop unrolling

          o  Thorough dependence analysis

          o  Software pipelining to rearrange instructions between different un-
             rolled loop iterations

          o  Optimized interface to intrinsic functions

                                           10

 



          HP Fortran for OpenVMS


          o  Loop transformation optimizations that apply to array references
             within loops, including:

             -  Loop blocking

             -  Loop distribution

             -  Loop fusion

             -  Loop interchange

             -  Loop scalar replacement

             -  Outer loop unrolling

          Specific optimizations performed by HP Fortran 95/90 include:

          o  Array temporary elimination

          Both HP Fortran 95/90 and HP Fortran 77 are shareable, re-entrant com-
          pilers that operate under the OpenVMS operating system. They globally
          optimize source programs while taking advantage of the native instruc-
          tion set and the OpenVMS virtual memory system.

          HP EXTENDED MATH LIBRARY (CXML) ALPHA ONLY

          HP Extended Math Library (CXML) for OpenVMS Alpha is a set of math-
          ematical subprograms that are optimized for HP architectures. Included
          subprograms cover the areas of:

          o  Basic Linear Algebra

          o  Linear System and Eigenproblem Solvers

          o  Sparse Linear System Solvers

          o  Sorting

          o  Random Number Generation

          o  Signal Processing

                                           11

 



          HP Fortran for OpenVMS


          The Basic Linear Algebra library includes the industry-standard Ba-
          sic Linear Algebra Subprograms (BLAS) Level 1, Level 2, and Level 3.
          Also included are subprograms for BLAS Level 1 Extensions, Sparse BLAS
          Level 1, and Array Math Functions (VLIB).

          The Linear System and Eigenproblem Solver library provides the com-
          plete LAPACK v2 package developed by a consortium of university and
          government laboratories. LAPACK is an industry-standard subprogram pack-
          age offering an extensive set of linear system and eigenproblem solvers.
          LAPACK uses blocked algorithms that are better suited to most modern
          architectures, particularly ones with memory hierarchies. LAPACK will
          supersede LINPACK and EISPACK for most users.

          The Sparse Linear System library provides both direct and iterative
          sparse linear system solvers. The direct solver package supports both
          symmetric and nonsymmetric sparse matrices stored using the skyline
          storage scheme. The iterative solver package contains a basic set of
          storage schemes, preconditioners, and iterative solvers. The design
          of this package is modular and matrix-free, allowing future expansion
          and easy modification by users.

          The Signal Processing library provides a basic set of signal process-
          ing functions. Included are one-, two-, and three-dimensional Fast Fourier
          Transforms (FFT), group FFTs, Cosine/Sine Transforms (FCT/FST), Con-
          volution, Correlation, and Digital Filters.

          Many CXML subprograms are optimized for the supported hardware plat-
          forms. Optimization techniques include traditional optimizations such
          as loop unrolling and loop reordering. CXML subprograms also provide
          efficient management of the hierarchical memory system, using tech-
          niques such as the following:

          o  Reuse of data within registers to minimize memory accesses

          o  Efficient cache management

          o  Use of blocked algorithms that minimize translation buffer misses
             and unnecessary paging



                                           12

 



          HP Fortran for OpenVMS


          Since CXML routines can be called from all languages that support the
          OpenVMS calling standard, the library provides optimized computation
          for applications written in these languages. Where appropriate, most
          subprograms are available in both real and complex versions, as well
          as in both single and double precision. CXML for OpenVMS Alpha sup-
          ports both IEEE and VAX floating-point formats.


          Basic Linear Algebra Subprograms

          Linear algebra operations are fundamental to many mathematical appli-
          cations, and several libraries of linear algebra subprograms exist through-
          out the computer industry. The CXML BLAS library contains the most com-
          monly used linear algebra subprograms.

          The CXML linear algebra library contains five groups of subprograms
          at three levels:

          o  Basic Linear Algebra Subprograms (BLAS) Level 1

          o  BLAS Level 1 Extensions

          o  BLAS Level 1 Sparse Extensions

          o  BLAS Level 2

          o  BLAS Level 3

          BLAS Level 1 (Scalar/Vector and Vector/Vector Operations)

          BLAS Level 1 provides a set of elementary vector functions, operat-
          ing on one or two vectors. These are typically very small routines,
          and they make less efficient use of the computing resources of mod-
          ern computer architectures than the Level 2 and 3 operations.

          CXML provides the 15 standard BLAS Level 1 operations:

          o  The index of the element of a vector having maximum absolute value

          o  The sum of the absolute values of the elements of a vector

          o  Inner product of two real vectors

                                           13

 



          HP Fortran for OpenVMS


          o  Scalar plus the extended precision inner product of two real vec-
             tors

          o  Conjugated inner product of two complex vectors

          o  Unconjugated inner product of two complex vectors

          o  Square root of the sum of squares (norm) of the elements of a vec-
             tor

          o  Scalar times a vector plus a vector

          o  Copy one vector to another

          o  Apply a Givens rotation

          o  Apply a modified Givens plane rotation

          o  Generate elements for a Givens plane rotation

          o  Generate elements for a modified Givens plane rotation

          o  Product of a vector times a scalar

          o  Swap the elements of two vectors

          BLAS Level 1 Extensions (Vector/Vector Operations)

          When developing mathematical algorithms using the BLAS Level 1, sci-
          entists and engineers found that several additional constructs were
          used on a regular basis. These constructs are well known throughout
          the computer industry as BLAS Level 1 Extensions.

          CXML contains 13 BLAS Level 1 Extension operations:

          o  Index of element having the minimum absolute value

          o  Index of element having the maximum value

          o  Index of element having the minimum value

          o  Largest value of the elements of a vector

          o  Smallest value of the elements of a vector

          o  Largest absolute value of the elements of a vector

                                           14

 



          HP Fortran for OpenVMS


          o  Smallest absolute value of the elements of a vector

          o  Sum of the values of the elements of a vector

          o  Set all elements of a vector equal to a scalar

          o  Constant times a vector set to another
             vector (y = a x)

          o  Euclidean norm with no intermediate scaling

          o  Sum of the squares of the elements of a vector

          o  Constant times a vector plus a vector set to another vector (z =
             a x + y)

          BLAS Level 1 Sparse Extensions (Vector/Vector Operations)

          This group of operations is similar to the BLAS Level 1 routines, but
          is designed to work on sparse vectors (vectors in which most of the
          elements are zero). Six of the routines are from industry standard Sparse
          BLAS 1, and the remaining three are enhancements.

          The nine sparse BLAS Level 1 operations are:

          o  Scalar times a sparse vector plus a vector

          o  Sum of a sparse vector and a full vector

          o  Inner product of a sparse vector and a full vector

          o  Gather a sparse vector from a full vector

          o  Gather a sparse vector from the scaled elements of a full vector

          o  Gather a sparse vector from a full vector and zero corresponding
             elements of full vector

          o  Apply Givens rotation to a sparse vector and a full vector

          o  Scatter a sparse vector into a full vector

          o  Scale and scatter a sparse vector into a full vector

                                           15

 



          HP Fortran for OpenVMS


          BLAS Level 2 (Matrix/Vector Operations)

          The BLAS Level 2 codes make more effective use of the data in the reg-
          isters, reducing the number of register loads and stores required. In
          addition, loop unrolling techniques are used to minimize cache misses
          and page faults. The BLAS Level 2 subprograms use the following types
          of operations:

          o  Matrix/vector products

          o  Rank-1 and rank-2 matrix updates

          o  Solutions of triangular systems of equations

          Six types of matrices are supported by these BLAS Level 2 routines:

          o  General

          o  General band

          o  Symmetric/Hermitian

          o  Symmetric/Hermitian band

          o  Triangular

          o  Triangular band

          BLAS Level 3 (Matrix/Matrix Operations)

          The BLAS Level 3 routines operate at a level that makes the most ef-
          ficient use of machine resources. CXML optimizes these routines by par-
          titioning matrices into blocks and computing matrix/matrix operations
          on each block. This approach avoids excessive memory accesses by pro-
          viding full reuse of data while each block is in the cache or the reg-
          isters. BLAS Level 3 routines provide this kind of blocking for three
          basic types of operations:

          o  Matrix/matrix products

          o  Rank-k and rank-2k updates of a symmetric matrix

                                           16

 



          HP Fortran for OpenVMS


          o  Solving triangular systems of equations with multiple right-hand
             sides

          Three types of matrices are supported by these BLAS Level 3 routines:

          o  General

          o  Symmetric/Hermitian

          o  Triangular

          A set of additional matrix-matrix routines is provided:

          o  Add two matrices

          o  Subtract one matrix from another

          o  Transpose a matrix, in-place or out-of-place

          Array Math Functions

          The Array Math Functions provide a set of basic math functions that
          operate on arrays of numbers rather than on scalars. On vector and su-
          perscalar architectures, such functions have a performance advantage
          over a loop of scalar operations. The library includes the following
          array functions for double precision numbers:

          o  Sine of array

          o  Cosine of array

          o  Cosine and sine of array

          o  Exponent of array

          o  Logarithm of array

          o  Square root of array

          o  Reciprocal of array

                                           17

 



          HP Fortran for OpenVMS


          LAPACK Library Contents

          LAPACK is a library of linear algebra subprograms intended to solve
          a wide range of problems in linear algebra. LAPACK can be used to solve
          dense systems of linear equations, linear least squares problems, eigen-
          value problems, and singular value problems. It is also useful in do-
          ing other computations such as matrix factorizations and estimations
          of condition numbers.

          The CXML LAPACK library provides the complete LAPACK v2 package. CXML’s
          version of LAPACK is provided as a packaged library, compiled, tested,
          and ready to use. Combined with the optimized BLAS Level 3 routines,
          the CXML LAPACK will provide optimal performance on all supported plat-
          forms. LAPACK should be used in place of LINPACK and EISPACK, because
          it is more efficient, accurate, and robust.

          LAPACK supports both real and complex, single and double precision data.
          It operates on the following types of matrices:

          o  Bidiagonal

          o  General band

          o  General unsymmetric

          o  General tridiagonal

          o  Hermitian

          o  Hermitian, packed storage

          o  Upper Hessenberg, generalized problem

          o  Upper Hessenberg

          o  Orthogonal

          o  Orthogonal, packed storage

          o  Symmetric/Hermitian positive definite band

          o  Symmetric/Hermitian positive definite

          o  Symmetric/Hermitian positive definite, packed storage

          o  Symmetric/Hermitian positive definite tridiagonal

                                           18

 



          HP Fortran for OpenVMS


          o  Symmetric band

          o  Symmetric, packed storage

          o  Symmetric tridiagonal

          o  Symmetric

          o  Triangular band

          o  Triangular, generalized problem

          o  Triangular, packed storage

          o  Triangular

          o  Trapezoidal

          o  Unitary

          o  Unitary, packed storage

          LAPACK provides the following operations:

          o  Triangular factorization

          o  Unblocked triangular factorization

          o  Solve a system of linear equations (based on triangular factoriza-
             tion)

          o  Compute the inverse (based on triangular factorization)

          o  Compute a split Cholesky factorization of a symmetric/Hermitian pos-
             itive definite band matrix

          o  Unblocked computation of inverse

          o  Estimate condition number

          o  Refine initial solution returned by solver

          o  Perform QR factorization without pivoting

          o  Unblocked QR factorization

          o  Solve linear least squares problem (based on QR factorization)

          o  Solve the linear equality constrained least squares (LSE) problem

                                           19

 



          HP Fortran for OpenVMS


          o  Solve the Gauss-Markov linear model problem

          o  Perform LQ factorization without pivoting

          o  Unblocked LQ factorization

          o  Solve underdetermined linear system (based on LQ factorization)

          o  Generate a real orthogonal or complex unitary matrix as a product
             of Householder matrices

          o  Unblocked generation of real orthogonal or unitary matrix

          o  Multiply a matrix by a real orthogonal or complex unitary matrix
             by applying a product of Householder matrices

          o  Unblocked version of multiplication of a matrix by a real orthog-
             onal or complex unitary matrix by applying a product of Householder
             matrices

          o  Reduce a square matrix to upper Hessenberg form

          o  Unblocked version of square matrix reduction

          o  Reduce a symmetric matrix to real symmetric tridiagonal form

          o  Reduce a band matrix to bidiagonal form

          o  Unblocked version of symmetric matrix reduction

          o  Reduce a rectangular matrix to bidiagonal form

          o  Reduce a band symmetric/Hermitian matrix to tridiagonal form

          o  Reduce a symmetric/Hermitian-definite banded generalized eigenprob-
             lem to standard form

          o  Compute various norms of a complex Hermitian tridiagonal matrix

          o  Compute eigenvalues and optional Schur factorization or eigenvec-
             tors using QR algorithm

          o  Compute selected eigenvectors by inverse iteration

          o  Compute eigenvectors from Schur factorization

          o  Compute eigenvectors using the Pal-Walker-Kahan variant of the QL
             or QR algorithm

                                           20

 



          HP Fortran for OpenVMS


          o  For a pair of N-by-N real nonsymmetric matrices, compute the gen-
             eralized eigenvalues, the real Schur form, and the left and/or right
             Schur vectors

          o  For a pair of N-by-N real nonsymmetric matrices, compute the gen-
             eralized eigenvalues, and the left and/or right generalized eigen-
             vectors

          o  Solve the generalized nonsymmetric eigenproblem Ax = lambda Bx

          o  Solve the generalized definite banded eigenproblem Ax = lambda Bx

          o  Solve the generalized symmetric/Hermitian-definite banded eigen-
             problem

          o  Solve the symmetric eigenproblem using divide-and-conquer algorithm

          o  Compute singular values and, optionally, singular vectors using the
             QR algorithm

          o  Compute the generalized (quotient) singular value decomposition

          o  Compute the generalized singular value decomposition (GSVD) on the
             M-by-N matrix A and P-by-N matrix B

          o  Solve a generalized linear regression model problem

          Sparse System Solver Subprograms

          The CXML Sparse System Solver library contains a set of subprograms
          that can be used to solve sparse linear systems of equations. Two pack-
          ages providing direct and iterative methods are supported.

          Direct Method Sparse Solver Package:

          The direct solver package includes skyline (profile) solvers for sym-
          metric and nonsymmetric matrices. Separate factorization and solver
          routines are provided to allow repeated use of the solver for multi-
          ple right hand sides, without repeating the factorization. To make the
          subprograms easier to use, both simple and expert driver routines are
          provided. Functions provided include:

          o  LDU factorization

                                           21

 



          HP Fortran for OpenVMS


          o  Solve

          o  Norm evaluation

          o  Condition number estimation

          o  Iterative refinement

          o  Simple and expert drivers

          These storage schemes are supported for symmetric and nonsymmetric ma-
          trices:

          o  Profile-in storage

          o  Structurally symmetric, profile-in storage (for nonsymmetric only)

          o  Diagonal-out storage

          Iterative Method Sparse Solver Package:

          For the iterative method, the library provides a modular set of stor-
          age schemes, preconditioners, and solvers. These solvers and precon-
          ditioners are easily accessed through an integrated driver routine.

          Six iterative sparse solvers for real, double precision data are sup-
          plied:

          o  Preconditioned conjugate gradient method

          o  Preconditioned least squares conjugate gradient method

          o  Preconditioned biconjugate method

          o  Preconditioned conjugate gradient squared method

          o  Preconditioned generalized minimum residual method

          o  Preconditioned transpose free QMR method

          Routines for three storage schemes are provided, or the user can de-
          velop routines to employ a custom storage scheme. The supplied stor-
          age schemes include:

          o  Symmetric diagonal

                                           22

 



          HP Fortran for OpenVMS


          o  Unsymmetric diagonal

          o  General storage by rows

          Three preconditioners are supplied, which can be selectively applied
          to the data. Users can also supply custom preconditioners. The pre-
          conditioners supplied include:

          o  Diagonal

          o  Polynomial (Neumann)

          o  Incomplete LU with zero diagonals added

          Sorting Subprograms

          Two sort subprograms using the Quicksort algorithm and two general pur-
          pose radix sort subprograms are provided, as follows:

          o  Sort elements of a vector using the Quicksort algorithm

          o  Sort an indexed vector of data using the Quicksort algorithm

          o  Sort data using a radix sort algorithm

          o  Sort an indexed vector of data using a radix sort algorithm

          All of the above sorts operate on data stored in memory.

          Random Number Subprograms

          CXML provides four random number generator subprograms:

          o  Produce a vector of uniform [0,1], long-period random numbers us-
             ing the L’Ecuyer multiplicative method. Two auxiliary input rou-
             tines are provided to allow this subprogram to be called from within
             a parallel section of a program.

          o  Produce a vector of N(0,1), normally-distributed random numbers.
             Two auxiliary input routines are provided to allow this subprogram
             to be called from within a parallel section of a program.

                                           23

 



          HP Fortran for OpenVMS


          o  Produce single precision random numbers using a linear multiplica-
             tive algorithm

          o  Produce single precision random numbers using a Lehmer multiplica-
             tive generator

          Signal Processing Subprograms

          The CXML Signal Processing library contains a set of subprograms in
          four basic areas of signal processing:

          o  Fast Fourier Transforms (FFT)

          o  Fast Cosine and Fast Sine Transforms (FCT and FST)

          o  Convolution and correlation

          o  Digital filters

          Fast Fourier Transforms and Cosine and Sine Transforms

          CXML provides one-dimensional, two-dimensional, three-dimensional, and
          group FFT routines and one-dimensional FCT/FST routines. Each routine
          is supplied in two forms:

          o  The first form computes the transform in one unit operation. This
             is convenient for programs requiring speed on only one or a few op-
             erations.

          o  The second form is provided for programs requiring speed on repeated
             operations. With this form, each routine is subdivided into three
             routines. One routine builds the rotation factors, a second rou-
             tine applies them to perform the transform, and a third routine deal-
             locates any virtual memory allocated in the first routine. Thus,
             for repeated operations, the rotation factors need to be built only
             once.





                                           24

 



          HP Fortran for OpenVMS


          Convolution and Correlation

          CXML provides routines for computing one-dimensional discrete convo-
          lutions and correlations. These routines can process both periodic and
          nonperiodic data.

          Digital Filters

          CXML provides support for one-dimensional, nonrecursive digital fil-
          tering. Based on the Kaisers Sinh-Bessel algorithm, these routines al-
          low programming of bandpass, bandstop, low-pass, and high-pass fil-
          ters.

          Cray SciLib Portability Support

          SCIPORT is an HP implementation of v7 of the Cray Research scientific
          numerical library, SciLib. SCIPORT provides 64 bit single-precision
          and 64-bit integer interfaces to underlying CXML routines for Cray users
          porting programs to Alpha systems running OpenVMS. SCIPORT also pro-
          vides equivalent versions of almost all Cray Math Library and CF77 (Cray
          Fortran 77) Math intrinsic routines.

          In order to be completely source code compatible with SciLib, the SCI-
          PORT library calling sequence supports 64-bit integers passed by ref-
          erence. However, internally, SCIPORT uses 32 bit integers. Consequently,
          some run-time uses of SciLib are not supported by SCIPORT.

          SCIPORT provides the following:

          o  64-bit versions of all Cray SciLib single-precision BLAS Level 1,
             Level 2, and Level 3 routines

          o  All Cray SciLib LAPACK routines

          o  All Cray SciLib Special Linear System Solver routines

          o  All Cray SciLib Signal Processing routines

          o  All Cray SciLib Sorting and Searching routines


                                           25

 



          HP Fortran for OpenVMS


          These routines are completely interchangeable with their Cray SciLib
          counterparts up to the runtime limit on integer size, and with the ex-
          ception of the ORDERS routine, require no program changes to function
          correctly. Owing to endian differences of machine architecture, spe-
          cial considerations must be given when the ORDERS routine is used to
          sort multibyte character strings.


          RUN-TIME LIBRARY REDISTRIBUTION

          The HP Fortran kit may include updated Run-Time Library shareable im-
          ages. HP grants the user a nonexclusive royalty-free worldwide right
          to reproduce and distribute the executable version of the Run-Time Li-
          brary (the “RTLs”), provided that the user does all of the following:

          o  Distributes the RTLs only in conjunction with and as a part of the
             user’s software application product that is designed to operate in
             the OpenVMS environment.

          o  Does not use the name, logo, or trademarks of HP to market the user’s
             software application product.

          o  Includes the copyright notice of HP Fortran on the user’s product
             disk label and/or on the title page of the documentation for soft-
             ware application product.

          o  Agrees to indemnify, hold harmless, and defend HP from and against
             any claims or lawsuits, including attorney’s fees, that arise or
             result from the use or distribution of the software application prod-
             uct.

          Except as expressly provided herein, HP grants no implied or express
          license under any of its patents, copyrights, trade secrets, trade-
          marks, or any license or other proprietary interests and rights.

          The RTL image is designated as DEC$FORRTL.EXE. HP Fortran may include
          a separate installation kit for the purpose of installing the HP For-
          tran Run-Time Library. This kit, installable with the POLYCENTER[R]
          Software Installation Utility (a component of OpenVMS), must be used
          to install the RTL image on other systems.

                                           26

 



          HP Fortran for OpenVMS


          HARDWARE REQUIREMENTS

          Processors Supported:

          Any Alpha system that is capable of running OpenVMS Alpha Version 7.3-
          2 or later.

          OpenVMS I64 Version 8.2-1 supports all Integrity Servers.

          Refer to the OpenVMS Operating System's Software Product Description
          (SPD 82.35.xx) for details.

          ___________________________________________________________________

          Table 2:  Disk Space Requirements on OpenVMS Alpha (Block Cluster
          __________Size_=_1)________________________________________________

          TASK____________SIZE_______________________________________________

          Compiler In-    50,000 blocks (25.0 MB)
          stallation:

          Compiler        40,200 blocks (20.1 MB)
          Permanent:

          CXML Instal-    150,000 blocks (75.0 MB)
          lation:

          CXML Perma-     150,000 blocks (75.0 MB)
          nent:______________________________________________________________

          ___________________________________________________________________

          Table 2:  Disk Space Requirements on OpenVMS I64 (Block Cluster
          __________Size_=_1)________________________________________________

          TASK____________SIZE_______________________________________________

          Compiler In-    62,000 blocks (31 MB)
          stallation:

          Compiler        60,000 blocks (30 MB)
          Permanent:_________________________________________________________

                                           27

 



          HP Fortran for OpenVMS


          These counts refer to the disk space required on the system disk. The
          sizes are approximate; actual sizes may vary depending on the user’s
          system environment, configuration, and software options.


          CLUSTER ENVIRONMENT

          This layered product is fully supported when installed on any valid
          and licensed VMScluster* configuration without restrictions. The HARD-
          WARE REQUIREMENTS sections of this product’s Software Product Descrip-
          tion and System Support Addendum detail any special hardware required
          by this product.

          *  VMScluster configurations are fully described in the VMScluster Soft-
             ware Product Description (SPD 42.18.xx) and include CI, Ethernet,
             DSSI, FDDI, SCSI and Mixed Interconnect configurations.

          SOFTWARE REQUIREMENTS

          For All Systems Using Terminals DECwindows Interface:

          o  OpenVMS Alpha Operating System V7.3-2 & higher

          o  OpenVMS I64 Operating System V8.2-1 & higher

          For All Workstations Running DECwindows:

          o  OpenVMS Alpha Operating System V7.3-2 & higher

          OpenVMS Optional Components

          The OpenVMS operating system can be configured to include or omit cer-
          tain components. HP Fortran requires the following components to be
          included:

          o  Programming Support

          o  Utilities

          The default for OpenVMS Alpha installation is to include all compo-
          nents.

                                           28

 



          HP Fortran for OpenVMS


          SOFTWARE LICENSING INFORMATION

          A software license is required in order to use HP Fortran software.
          For VAX and Alpha platforms, HP Fortran is offered with Concurrent Use,
          Personal Use and Traditional 'capacity' licenses. For I64, it is of-
          fered with Concurrent Use licenses. Version update licenses are not
          available for the I64 platform. Rights to use future revisions of HP
          Fortran are available only through a Support Agreement or through a
          new license purchase. For more information about OpenVMS license terms
          and policies, contact your local HP sales office, or reference the Soft-
          ware Licensing site at: <http://licensing.hp.com/swl/view.slm?page=index>

          LICENSE MANAGEMENT FACILITY SUPPORT

          HP Fortran supports the License Management Facility of HP.

          License units for HP Fortran on Alpha is allocated on an Unlimited Sys-
          tem Use plus Concurrent Use basis. For HP Fortran on I64 is allocated
          on Concurrent Use basis.

          Each Concurrent Use license allows any one individual at a time to use
          the layered product.

          OPTIONAL SOFTWARE

          o  DECset V11.1-V12.7 for OpenVMS Alpha

          o  CDD/Repository V5.3 for OpenVMS Alpha

          o  DECset V12.7 for OpenVMS I64

          GROWTH CONSIDERATIONS

          The minimum hardware/software requirements for any future version of
          this product may be different from the requirements for the current
          version.





                                           29

 



          HP Fortran for OpenVMS


          DISTRIBUTION MEDIA

          This product is available on the HP CD-ROM Software Library for Open-
          VMS Alpha (QA-03XAA-H8). Documentation in printed format can be or-
          dered separately (see the HP Fortran “read first” cover letter or the
          online release notes).

          HP Fortran OpenVMS I64 ONLY:

          HP Fortran for OpenVMS I64 is available on the OpenVMS Layered Prod-
          uct Library. The library package includes media and documentaion on
          CD-ROM.

          SOFTWARE WARRANTY

          This software is provided by HP with a 90 day conformance warranty in
          accordance with the HP warranty terms applicable to the license pur-
          chase.

          The above information is valid at time of release. Please contact your
          local HP office for the most up-to-date information.

          ORDERING INFORMATION

          When purchasing HP Fortran both a license and media must be ordered.
          The license deliverable provides the LMF PAK required to run the HP
          Fortran software. The VMS Operating System or Operating Environment
          (license and media) is a prerequisite to running HP Fortran.

          Software Licenses:

             Unlimited System Use: QL-MV1A*-AA
             Concurrent Use: QL-100AA-3B
             Concurrent 5 Pack: QL-100AA-3C
             Concurrent 10 Pack: QL-100AA-3D

          Software Documentation:

             HP Fortran 95/90 Documentation: QA-MV1AA-GZ


                                           30

 



          HP Fortran for OpenVMS


             HP Fortran 77 Documentation: QA-MV1AB-GZ

          HP Fortran for OpenVMS I64 ONLY:

          Software Licenses:
             Concurrent Use: BA368AC
          Software Media:
             Foundation Operating Media, BA322AA or
             Enterprise Operating Media, BA323AA or
             Mission Critical Media, BA324AA
          Software Documentation (Hard Copy): BA368MN

          An example of a new order for HP Fortran:

          Concurrent Use License - BA368AC
          Binaries: Operating Environment Media - BA32*A
          Hardcopy Documentation Kit (Optional) BA368MN

          For more information on the Operating Environments, please see the HP
          Operating Environments for OpenVMS I64 SPD: 82.34.**

          *  Denotes variant fields. For additional information on available li-
             censes, services, and media, refer to the appropriate price book.

          The above information is valid at time of release. Please contact your
          local HP office for the most up-to-date information.

          SOFTWARE PRODUCT SERVICES

          A variety of service options are available from HP. For more infor-
          mation, contact your local HP account representative or distributor.
          Information is also available on www.hp.com/hps/software.

          TRADEMARK INFORMATION

          © 2007 Hewlett-Packard Development Company, L.P.





                                           31

 



          HP Fortran for OpenVMS


          Confidential computer software. Valid license from HP and/or its sub-
          sidiaries required for possession, use, or copying. Consistent with
          FAR 12.211 and 12.212, Commercial Computer Software, Computer Soft-
          ware Documentation, and Technical Data for Commercial use.

          The information contained herein is subject to change without notice.
          The only warranties for HP products and services are set forth in the
          express warranty statements accompanying such products and services.
          Nothing here in should be construed as constituting an additional war-
          ranty. HP shall not be liable for technical or editorial errors or omis-
          sions contained herein.






























                                           32

 



          HP Fortran for OpenVMS











































                                           33