GDD9000-CBLAS

GDD-9000 Floating Point Extended C Callable BLAS (Basic Linear Algebra Subroutines) Library for TMS320C6000.

The library is a set of about 90 functions and macros that implement the Basic Linear Algebra Subroutines standard for Level 1 BLAS vector-vector (O(n) complexity) operations, Level 2 BLAS matrix-vector (O(n^2) complexity) operations and Level 2 BLAS matrix-matrix (O(n^3) complexity) operations. Library's functions perform these operations on the IEEE-754 single and double precision floating point format numbers. The library uses native floating point arithmetic support of the TMS320C67xx DSP and software simulates floating point arithmetic for the fixed point DSP members of theC6000 family of DSPs. The library process both REAL and COMPLEX data vectors and matrices. Many vector and matrix operations involve scaling by a real or complex scalar values. By using special memory allocation routines the amount of RAM storage is minimized for structured types of matrices, like symmetric, band and triangular classes of matrices

The library is supported for use in any development environment using TI Code Generation Tools for the TMS320C6000 DSP and for both big endian and little endian memory formats. All the functions are C callable and comply with TI's C environment calling conventions.

Library's functions have been optimised algorithmically at the assembly level to fully utilize advantages of TMS320C6000 parallel architecture, floating point arithmetic and pipeline. Level 1 functions are hand-coded in assembly to obtain maximum possible performance of the TMS320C6000 DSPs.

The library can be used in various application areas of linear algebra problems providing with a set of basic standard operations. The user's manual gives the details on using library functions.

Functions

* LEVEL 1 BLAS (REAL DATA OPERATIONS)

• Index of a vector entry with maximum magnitude
• Index of a vector entry with minimum magnitude
• Sum of absolute values of vector entries
• L2 (Euclidean) Norm of a vector
• Copy vector to a vector
• Fill a vector with a constant
• Dot (inner) product
• Swap two vectors
• Add a constant to a vector
• Scale a vector
• Multiply a vector by a vector
• Construct Givens plane rotations
• Apply Givens plane rotations

* LEVEL 1 BLAS (COMPLEX DATA OPERATIONS)

• Index of a vector entry with maximum magnitude
• Index of a vector entry with minimum magnitude
• Sum of absolute values of vector entries
• L2 (Euclidean) Norm of a vector
• Copy vector to a vector
• Fill a vector with a constant
• Dot (inner) product, conjugate first vector
• Dot (inner) product
• Swap two vectors
• Add a constant to a vector
• Scale a vector
• Scale a vector by a real scalar
• Multiply a vector by a vector
• Construct Givens plane rotations
• Apply Givens plane rotations

* LEVEL 2 BLAS (REAL DATA OPERATIONS)

• Multiply a matrix/transpose by a vector, add a vector
• Multiply a band matrix/transpose by a vector, add a vector
• Multiply a symmetric matrix by a vector, add a vector
• Multiply a band symmetric matrix by a vector, add a vector
• Multiply a triangular matrix/transpose by a vector
• Multiply a band triangular matrix/transpose by a vector
• Rank 1 update, general matrix
• Rank 1 update, symmetric matrix
• Rank 2 update, symmetric matrix
• Solve a linear system with a triangular matrix/transpose
• Solve a linear system with a band triangular matrix/transpose

* LEVEL 2 BLAS (COMPLEX DATA OPERATIONS)

• Multiply a matrix/transpose/conjugate by a vector, add a vector
• Multiply a band matrix/transpose/conjugate by a vector, add a vector
• Multiply an hermitian matrix by a vector, add a vector
• Multiply a band hermitian matrix by a vector, add a vector
• Multiply a triangular matrix/transpose/conjugate by a vector
• Multiply a band triangular matrix by a vector
• Rank 1 update, general matrix
• Rank 1 update, hermitian matrix
• Rank 2 update, hermitian matrix
• Solve a linear system with a triangular matrix/transpose/conjugate
• Solve a linear system with a band triangular matrix/transpose/conjugate

* LEVEL 3 BLAS (REAL DATA OPERATIONS)

• Multiply a matrix/transpose by a matrix/transpose, add a matrix
• Multiply a symmetric matrix by a matrix, add a matrix
• Multiply a triangular matrix/transpose by a matrix
• Rank k update, symmetric matrix
• Rank 2k update, symmetric matrix
• Solve simultaneous linear systems with a triangular matrix/transpose

* LEVEL 3 BLAS (COMPLEX DATA OPERATIONS)

• Multiply a matrix/transpose/conjugate by a matrix/transpose/conjugate, add a matrix
• Multiply a symmetric matrix by a matrix, add a matrix
• Multiply an hermitian matrix by a matrix, add a matrix
• Multiply a triangular matrix/transpose/conjugate by a matrix
• Rank k update, symmetric matrix
• Rank k update, hermitian matrix
• Rank 2k update, symmetric matrix
• Rank 2k update, hermitian matrix
• Solve simultaneous linear systems with a triangular matrix/transpose/conjugate

* MATRIX NORMS (REAL DATA)

• L1, Euclidean or Infinity norm, real general matrix
• L1, Euclidean or Infinity norm, real general band matrix
• L1, Euclidean or Infinity norm, real symmetric matrix
• L1, Euclidean or Infinity norm, real symmetric band matrix
• L1, Euclidean or Infinity norm, real tridiagonal matrix
• L1, Euclidean or Infinity norm, real symmetric tridiagonal matrix
• L1, Euclidean or Infinity norm, real triangular matrix
• L1, Euclidean or Infinity norm, real triangular band matrix

* MATRIX NORMS (COMPLEX DATA)

• L1, Euclidean or Infinity norm, complex general matrix
• L1, Euclidean or Infinity norm, complex general band matrix
• L1, Euclidean or Infinity norm, complex symmetric/hermitian matrix
• L1, Euclidean or Infinity norm, complex symmetric/hermitian band matrix
• L1, Euclidean or Infinity norm, complex tridiagonal matrix
• L1, Euclidean or Infinity norm, complex symmetric/hermitian tridiagonal matrix
• L1, Euclidean or Infinity norm, complex triangular matrix
• L1, Euclidean or Infinity norm, complex triangular band matrix

* MEMORY STORAGE ALLOCATION

• Allocate storage for a real vector (macro)
• Allocate storage for a real general matrix
• Allocate storage for a real general band matrix
• Allocate storage for a real symmetric/triangular matrix
• Allocate storage for a real symmetric/triangular band matrix
• Allocate storage for a complex vector (macro)
• Allocate storage for a complex general matrix
• Allocate storage for a complex general band matrix
• Allocate storage for a complex symmetric/hermitian/triangular matrix
• Allocate storage for a complex symmetric/hermitian/triangular band matrix