README

Overview

This repo contains a tested version of CBLAS with BLAS, both entirely written in C. Having all soure code in C allows to easily convert the library to WASM.

CLAPACK is also included but no tests were run.

For install instructions, please refer to INSTALL.

This repository contains the following directories

bash . ├── CBLAS/ ├── CLAPACK-3.2.1/ ├── f2c_BLAS-3.8.0/ ├── libf2c/ └── patches/

• CLAPACK contains the CLAPACK source code with redundancies (e.g. BLAS) removed.
• CBLAS contains the original source code of CBLAS
• f2c_BLAS-3.8.0 contains the source code of BLAS-3.8.0 converted to C using the f2c program. For more information about this conversion, please this section.
• libf2c contains functions and structure definition required by f2c converted programs to run.

The dependencies look as follows:

mermaid graph TD BLAS --> libf2c CBLAS --> BLAS CLAPACK --> libf2c CLAPACK --> CBLAS

To avoid breaking the license of CBLAS, CLAPACK or BLAS, the source code of these libraries is distributed as found in the original packages. However, to successfully compile and use these libraries, these source files have to be slightly modified. These modifications are stored as patches under the directory patches. The patches are automatically applied before compiling the different components.

The changes applied by each patch are described in files named changelog.txt located under CBLAS, CLAPACK-3.2.1, f2c_BLAS-3.8.0 and libf2c.

For a summary of what changed in these components, please read below.

Automatic FORTRAN 77 to C translation

f2c

f2c is a tool that converts FORTRAN to C code. To account for the fact that FORTRAN real type is equivalent to C float type, the -R flags has been systematically used.

The version of the program, which is not provided as it is not necessary is 20191129.

libf2c

Any code translated using the program f2c needs to be link against the libf2c.alibrary. This library can be created using the files in the directory libf2c/, which is provided in this repo.

Note that the header file f2c.h in libf2c has been modified to account for the fact that ints in modern C compilers are 4 bytes long. In short, the following command has been run:

bash sed -i 's/long int /int /g' f2c.h

For the complete list of changes made to libf2c, please refer to ./libf2c/changelog.txt.

Automated translation of BLAS from FORTRAN to C

BLAS, which is originally written in FORTRAN, has been tranlated to C using the program f2c using the command

bash mkdir f2c_BLAS-3.8.0 f2c -d f2c_BLAS-3.8.0 -aR *.c

in the BLAS (version 3.8.0) directory.

This produces C files in the directory f2c_BLAS-3.8.0/. Note that the files xerbla.f and xerbla_array.f cannot be translated to C with f2c as they contain non FORTRAN 77 instructions. For these two files, the C source code has been taken from CLAPACK-3.2.1.

All other changes (mostly function signature changes) are listed in f2c_BLAS-3.8.0/changelog.txt.

CBLAS

CBLAS changes

The original source code of CBLAS contains the following BLAS wrappers written in FORTRAN:

bash cdotcsub.f cdotusub.f dasumsub.f ddotsub.f dnrm2sub.f dsdotsub.f dzasumsub.f dznrm2sub.f icamaxsub.f idamaxsub.f isamaxsub.f izamaxsub.f sasumsub.f scasumsub.f scnrm2sub.f sdotsub.f sdsdotsub.f snrm2sub.f zdotcsub.f zdotusub.f

As these were simple wrappers, their usage in the C code has been replaced by direct calls to the BLAS subroutines (provided by the BLAS library). The modifications had to make the following assumptions:

• BLAS to C type equivalence
  • REAL -> float
  • DOUBLEREAL -> double
  • INTEGER -> int
  • VOID -> void
• f2c converted function interface
  • The subroutines cdotc, cdotu, zdotc, and zdotu return no value but store the result in a pointer given as a subroutine parameter
• Complex types
  • The then missing C types complex and doublecomplex have been defined in include/cblas_f77.h

With these modifications, the FORTRAN free code of CBLAS passes all the (unmodified) tests in the testing directory.

For the complete list of changes, please refer to CBLAS/changelog.txt

CBLAS test suite

To allow automated testing of the generated CBLAS library in wasm, the test suites has also been converted to c using f2c. To ensure that the converted tests are correct, the following procedure has been followed:

1. Convert BLAS to C and CBLAS to C without modifying the test source code
2. Once CBLAS passes all the original tests, convert the test source code without modifying the CBLAS or BLAS C code.
3. Check that all the tests (now written in C) pass with the BLAS and CBLAS code (written in C too)

CLAPACK

Usage of the following functions had to be changed: * xerbla_ (return value type) * lsame_ (return value and argument list) * s_copy (return value type) * s_cat (return value type)

For the complete list of changes, please refer to CLAPACK/changelog.txt

For more information about CLAPACK and LAPACK, please refer to

Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A. & Sorensen, D. LAPACK Users' Guide Society for Industrial and Applied Mathematics, 1999

Linking against CLAPACK

To use the various libraries, assuming that the variable CLAPACKROOT contains the path to the root of this directory, link as follows:

$(CLAPACKROOT)/CLAPACK-3.2.1/lapack.a $(CLAPACKROOT)/CLAPACK-3.2.1/libcblaswr.a \ $(CLAPACKROOT)/CBLAS/lib/cblas.a \ $(CLAPACKROOT)/f2c_BLAS-3.8.0/blas.a $(CLAPACKROOT)/libf2c/libf2c.a