Introduction

In a traditional source code, most of the lines of source files of a program are code, scripts, Makefiles, and only a few lines are comments explaining parts of the code that are non-trivial to understand. The documentation of the prorgam is usually written in a separate directory, and is often outdated compared to the code.

Literate programming is a different approach to programming, where the program is considered as a publishable-quality document. Most of the lines of the source files are text, mathematical formulas, tables, figures, etc, and the lines of code are just the translation in a computer language of the ideas and algorithms expressed in the text. More importantly, the "document" is structured like a text document with sections, subsections, a bibliography, a table of contents etc, and the place where pieces of code appear are the places where they should belong for the reader to understand the logic of the program, not the places where the compiler expects to find them. Both the publishable-quality document and the binary executable are produced from the same source files.

Literate programming is particularly well adapted in this context, as the central part of this project is the documentation of an API. The implementation of the algorithms is just an expression of the algorithms in a language that can be compiled, so that the correctness of the algorithms can be tested.

We have chosen to write the source files in org-mode format, as any text editor can be used to edit org-mode files. To produce the documentation, there exists multiple possibilities to convert org-mode files into different formats such as HTML or PDF. The source code is easily extracted from the org-mode files invoking the Emacs text editor from the command-line in the Makefile, and then the produced files are compiled. Moreover, within the Emacs text editor the source code blocks can be executed interactively, in the same spirit as Jupyter notebooks.

For a tutorial on literate programming with org-mode, follow this link.

Any text editor can be used to edit org-mode files. For a better user experience Emacs is recommended. For users hating Emacs, it is good to know that Emacs can behave like Vim when switched into ``Evil'' mode.

In the tools/init.el file, we provide a minimal Emacs configuration file for vim users. This file should be copied into .emacs.d/init.el.

For users with a preference for Jupyter notebooks, we also provide the tools/nb_to_org.sh script can convert jupyter notebooks into org-mode files.

Note that pandoc can be used to convert multiple markdown formats into org-mode.

Most of the codes of the TREX CoE are written in Fortran with some scripts in Bash and Python. Outside of the CoE, Fortran is also important (Casino, Amolqc), and other important languages used by the community are C and C++ (QMCPack, QWalk), and Julia is gaining in popularity. The library we design should be compatible with all of these languages. The QMCkl API has to be compatible with the C language since libraries with a C-compatible API can be used in every other language.

High-performance versions of the QMCkl, with the same API, will be rewritten by the experts in HPC. These optimized libraries will be tuned for specific architectures, among which we can cite x86 based processors, and GPU accelerators. Nowadays, the most efficient software tools to take advantage of low-level features of the processor (intrinsics) and of GPUs are for C++ developers. It is highly probable that the optimized implementations will be written in C++, and this is agreement with our choice to make the API C-compatible.

Fortran is one of the most common languages used by the community, and is simple enough to make the algorithms readable both by experts in QMC, and experts in HPC. Hence we propose in this pedagogical implementation of QMCkl to use Fortran to express the QMC algorithms. As the main languages of the library is C, this implies that the exposed C functions call the Fortran routine. However, for internal functions related to system programming, the C language is more natural than Fortran.

The Fortran source files should provide a C interface using the iso_c_binding module. The name of the Fortran source files should end with _f.f90 to be properly handled by the Makefile. The names of the functions defined in Fortran should be the same as those exposed in the API suffixed by _f.

For more guidelines on using Fortran to generate a C interface, see this link.

The authors should follow the recommendations of the C99 SEI+CERT C Coding Standard.

Compliance can be checked with cppcheck as:

cppcheck --addon=cert --enable=all *.c &> cppcheck.out

The proposed API should allow the library to: deal with memory transfers between CPU and accelerators, and to use different levels of floating-point precision. We chose a multi-layered design with low-level and high-level functions (see below).

To avoid namespace collisions, we use qmckl_ as a prefix for all exported functions and variables. All exported header files should have a file name prefixed with qmckl_.

If the name of the org-mode file is xxx.org, the name of the produced C files should be xxx.c and xxx.h and the name of the produced Fortran file should be xxx.f90.

Arrays are in uppercase and scalars are in lowercase.

In the names of the variables and functions, only the singular form is allowed.

In the C language, the number of bits used by the integer types can change from one architecture to another one. To circumvent this problem, we choose to use the integer types defined in <stdint.h> where the number of bits used for the integers are fixed.

To ensure that the library will be easily usable in any other language than C, we restrict the data types in the interfaces to the following:

• 32-bit and 64-bit integers, scalars and and arrays (int32_t and int64_t)
• 32-bit and 64-bit floats, scalars and and arrays (float and double)
• Pointers are always casted into 64-bit integers, even on legacy 32-bit architectures
• ASCII strings are represented as a pointers to character arrays and terminated by a '\0' character (C convention).
• Complex numbers can be represented by an array of 2 floats.
• Boolean variables are stored as integers, 1 for true and 0 for false
• Floating point variables should be by default double unless explicitly mentioned
• integers used for counting should always be int64_t

To facilitate the use in other languages than C, we will provide some bindings in other languages in other repositories.

Global variables should be avoided in the library, because it is possible that one single program needs to use multiple instances of the library. To solve this problem we propose to use a pointer to a context variable, built by the library with the qmckl_context_create function. The =context= contains the global state of the library, and is used as the first argument of many QMCkl functions.

The internal structure of the context is not specified, to give a maximum of freedom to the different implementations. Modifying the state is done by setters and getters, prefixed by qmckl_set_ an qmckl_get_.

A single qmckl.h header to be distributed by the library is built by concatenating some of the produced header files. To facilitate building the qmckl.h file, we separate types from function declarations in headers. Types should be defined in header files suffixed by _type.h, and functions in files suffixed by _func.h. As these files will be concatenated in a single file, they should not be guarded by #ifndef *_H, and they should not include other produced headers.

Some particular types that are not exported need to be known by the context, and there are some functions to update instances of these types contained inside the context. For example, a qmckl_numprec_struct is present in the context, and the function qmckl_set_numprec_range takes a context as a parameter, and set a value in the qmckl_numprec_struct contained in the context. Because of these intricate dependencies, a private header is created, containing the qmckl_numprec_struct. This header is included in the private header file which defines the type of the context. Header files for private types are suffixed by _private_type.h and header files for private functions are suffixed by _private_func.h. Fortran interfaces should also be written in the *fh_func.f90 file, and the types definitions should be written in the *fh_type.f90 file.

Low-level functions are very simple functions which are leaves of the function call tree (they don't call any other QMCkl function).

These functions are pure, and unaware of the QMCkl context. They are not allowed to allocate/deallocate memory, and if they need temporary memory it should be provided in input.

High-level functions are at the top of the function call tree. They are able to choose which lower-level function to call depending on the required precision, and do the corresponding type conversions. These functions are also responsible for allocating temporary storage, to simplify the use of accelerators.

The high-level functions should be pure, unless the introduction of non-purity is justified. All the side effects should be made in the context variable.

The number of bits of precision required for a function should be given as an input of low-level computational functions. This input will be used to define the values of the different thresholds that might be used to avoid computing unnecessary noise. High-level functions will use the precision specified in the context variable.

In order to automatize numerical accuracy tests, QMCkl uses Verificarlo and its CI functionality. You can read Verificarlo CI's documentation at the following link. Reading it is advised to understand the remainder of this section.

To enable support for Verificarlo CI tests when building the library, use the following configure command :

QMCKL_DEVEL=1 ./configure --prefix=$PWD/_install --enable-silent-rules --enable-maintainer-mode CC=verificarlo-f FC=verificarlo-f --host=x86_64 --enable-vfc_ci

Note that this does require an install of Verificarlo with Fortran support. Enabling the support for CI will define the VFC_CI preprocessor variable which use will be explained now.

As explained in the documentation, Verificarlo CI uses a probes system to export variables from test programs to the tools itself. To make tests easier to use, QMCkl has its own interface to the probes system. To make the system very easy to use, these functions are always defined, but will behave differently depending on the VFC_CI preprocessor variable. There are 3 functions at your disposal. When the CI is enabled, they will place a vfc_ci probe as if calling vfc_probes directly. Otherwise, they will either do nothing or perform a check on the tested value and return its result as a boolean that you are free to use or ignore. Here are these 3 functions :

• qmckl_probe : place a normal probe witout any check. Won't do anything when vfc_ci is disabled (false is returned).
• qmckl_probe_check : place a probe with an absolute check. If vfc_ci is disabled, this will return the result of an absolute check (|val - ref| < accuracy target ?). If the check fails, true is returned (false otherwise).
• qmckl_probe_check_relative : place a probe with a relative check. If vfc_ci is disabled, this will return the result of a relative check (|val - ref| / ref < accuracy target?). If the check fails, true is returned (false otherwise).

If you need more details on these functions or their Fortran interfaces, have a look at the tools/qmckl_probes files.

Finally, if you need to add a QMCkl kernel to the CI tests or modify an existing one, you should pay attention to the following points :

• you should add the new kernel to the vfc_tests_config.json file, which controls the backends and repetitions for each executable. More details can be found in the vfc_ci documentation.
• in order to call the qmckl_probes functions from Fortran, import the qmckl_probes_f module.
• if your tests include some asserts that rely on accurate FP values, you should probably wrap them inside a #ifndef VFC_CI statement, as the asserts would otherwise risk to fail when executed with the different Verificarlo backends.

Reducing the scaling of an algorithm usually implies also reducing its arithmetic complexity (number of flops per byte). Therefore, for small sizes \(\mathcal{O}(N^3)\) and \(\mathcal{O}(N^2)\) algorithms are better adapted than linear scaling algorithms. As QMCkl is a general purpose library, multiple algorithms should be implemented adapted to different problem sizes.