# Chapter 10: Case Study — Building Custom GLM Kernels (ex_glmbayes)

#### Kjell Nygren

#### 2026-07-15

## Overview

Chapters 03-10 describe the infrastructure of `nmathopencl`: the shim layer, the `nmath` library, the kernel format, and the runner API. This chapter shows how to put all of it together by walking through a concrete downstream use-case: the `ex_glmbayes` example built into the package.

`ex_glmbayes` implements GPU-accelerated evaluation of the log-posterior and gradient (`f2`/`f3`) for Bayesian GLMs (Gaussian, Gamma, binomial with logit/probit/cloglog links, and Poisson). It is the type of component a package author would build on top of `nmathopencl` to accelerate their own likelihood computations. The name `ex_glmbayes` signals that this is an example, not a core part of the library; it lives entirely in `ex_glmbayes_*`-prefixed files and within the `ex_glmbayes` C++ namespace.

## Step 1 — Identify the nmath functions your kernel needs

For each GLM family, determine which nmath functions the GPU kernel must call:

Kernel | nmath function(s) called | Link function
--- | --- | ---
`f2_f3_binomial_logit.cl` | `dbinom_raw` | logit
`f2_f3_binomial_probit.cl` | `dbinom_raw`, `pnorm5`, `dnorm4` | probit
`f2_f3_binomial_cloglog.cl` | `dbinom_raw` | cloglog
`f2_f3_gamma.cl` | `dgamma` | log
`f2_f3_gaussian.cl` | `dnorm4` | identity/log
`f2_f3_poisson.cl` | `lgamma` (OpenCL built-in) | log

For `f2_f3_poisson`, `lgamma` is an OpenCL built-in (part of the OpenCL 1.1 math specification) so no nmath files are needed at all. For the others, consult the `@all_depends_nmath` tag of each kernel file to get the full transitive dependency list.

## Step 2 — Extract the minimal nmath subset

The `@all_depends_nmath` tag in each kernel file gives the complete transitive closure. Taking the union across the five non-Poisson kernels yields 20 files (17 nmath functions + `Rmath`, `nmath`, `refactored` as infrastructure):

    Rmath, nmath, refactored,
    chebyshev, cospi, fmax2, gammalims, lgammacor,
    gamma, lgamma,
    stirlerr_cycle_free, pgamma_utils, stirlerr_cycle_dependent, stirlerr, bd0,
    dpois, dgamma, dnorm, pnorm, dbinom

These files are stored in `inst/cl/ex_glmbayes_nmath/`. Rather than copying them manually, use `extract_library_subset()` to derive this directory automatically from the kernel annotations:

    nmath_dir <- system.file("cl", "nmath",           package = "nmathopencl")
    src_dir   <- system.file("cl", "ex_glmbayes_src", package = "nmathopencl")

    # Load the pre-built dependency index (read once, reuse across calls)
    idx <- readRDS(file.path(nmath_dir, "kernel_dependency_index.rds"))

    result <- extract_library_subset(
        kernel_paths = list.files(src_dir, pattern = "\\.cl$", full.names = TRUE),
        library_dir  = nmath_dir,
        dest_dir     = "inst/cl/ex_glmbayes_nmath",
        depends_tag  = "depends_nmath",
        index        = idx
    )

`extract_library_subset()` copies the 20 `.cl` files plus both index files (`kernel_dependency_index.rds` and `kernel_dependency_index.tsv`) into the destination directory. The index files are required for the indexed loading described in Step 5.

A package developer would create an analogous subdirectory for their own kernel set using the same function.

## Step 3 — Write the kernel files

Each kernel file in `inst/cl/ex_glmbayes_src/` starts with the dependency metadata block followed by the kernel body:

    // @library_deps: nmath
    // @calls_nmath: dbinom_raw
    // @depends_nmath: dbinom
    // @all_depends_nmath_count: 17
    // @all_depends_nmath: Rmath, nmath, refactored, chebyshev, cospi, fmax2,
    //   gammalims, lgammacor, gamma, lgamma, stirlerr_cycle_free, pgamma_utils,
    //   stirlerr_cycle_dependent, stirlerr, bd0, dbinom
    // @calls_opencl_builtin: (none)

    #pragma OPENCL EXTENSION cl_khr_fp64 : enable
    #pragma OPENCL EXTENSION cl_khr_printf : enable

    #define MAX_L2 64   // upper bound on l2

    __kernel void f2_f3_binomial_logit(
        __global const double* X,      // design matrix,  size = l1 x l2, col-major
        __global const double* B,      // grid,            size = m1 x l2
        __global const double* mu,     // prior mean,      length = l2
        __global const double* P,      // prior precision, size = l2 x l2
        __global const double* alpha,  // offset,          length = l1
        __global const double* y,      // response,        length = l1
        __global const double* wt,     // weights,         length = l1
        __global double*       qf,     // out: neg log-posterior, length = m1
        __global double*       grad,   // out: gradient,   size = m1 x l2
        const int l1,
        const int l2,
        const int m1
    ) {
        int j = get_global_id(0);
        if (j >= m1) return;

        // prior quadratic form: 0.5 * (B_j - mu)' P (B_j - mu)
        double tmp[MAX_L2];
        for (int k = 0; k < l2; ++k) {
            double acc = 0.0;
            for (int l = 0; l < l2; ++l)
                acc += P[k*l2 + l] * (B[j*l2 + l] - mu[l]);
            tmp[k] = acc;
        }
        double res_acc = 0.0;
        for (int k = 0; k < l2; ++k)
            res_acc += 0.5 * (B[j*l2 + k] - mu[k]) * tmp[k];

        // gradient: prior part
        double g_loc[MAX_L2];
        for (int k = 0; k < l2; ++k) g_loc[k] = tmp[k];

        // data likelihood: logistic link + dbinom_raw
        for (int i = 0; i < l1; ++i) {
            double dot = -alpha[i];
            for (int k = 0; k < l2; ++k)
                dot -= X[k*l1 + i] * B[j*l2 + k];
            double e = exp(dot <= 0 ? dot : -dot);
            double p = dot <= 0 ? 1.0/(1.0+e) : e/(1.0+e);
            double q = 1.0 - p;
            res_acc += -dbinom_raw(y[i], wt[i], p, q, 1);
            double resid = p < 0.5 ? p*wt[i] - y[i]*wt[i]
                                    : (1-y[i])*wt[i] - q*wt[i];
            for (int k = 0; k < l2; ++k)
                g_loc[k] += X[k*l1 + i] * resid;
        }

        qf[j] = res_acc;
        for (int k = 0; k < l2; ++k)
            grad[k * m1 + j] = g_loc[k];
    }

Key design choices:

- `MAX_L2 64` — a compile-time upper bound on the number of predictors, used to size local arrays (OpenCL C does not support variable-length arrays in all implementations).
- Column-major layout for `X` (matches R’s memory layout for matrices passed from R to C without transposition).
- A single work-item per grid point `j`; all `l1` observations are processed sequentially within that work-item. This is appropriate when `m1` (number of grid points) is much larger than `l1` (number of observations), as is typical for envelope sampling.

## Step 4 — Write the kernel runner (C++)

The kernel runner is the low-level C++ function that manages the OpenCL lifecycle for this specific kernel. It lives in `ex_glmbayes_kernel_runners.cpp` inside the `ex_glmbayes::opencl` namespace:

    // ex_glmbayes_kernel_runners.cpp (abbreviated)
    namespace ex_glmbayes {
    namespace opencl {

    void f2_f3_kernel_runner(
        const std::string& kernel_source,
        const char*        kernel_name,
        int l1, int l2, int m1,
        const std::vector<double>& X_flat,
        const std::vector<double>& B_flat,
        const std::vector<double>& mu_flat,
        const std::vector<double>& P_flat,
        const std::vector<double>& alpha_flat,
        const std::vector<double>& y_flat,
        const std::vector<double>& wt_flat,
        std::vector<double>& qf_flat,
        std::vector<double>& grad_flat
    ) {
        // Select platform and device
        // Create context, command queue, program, kernel
        // Create input buffers (CL_MEM_READ_ONLY) and output buffers (CL_MEM_WRITE_ONLY)
        // Set kernel arguments
        // Enqueue kernel with global_size = m1
        // Read back qf_flat and grad_flat
        // Release all resources
    }

    }} // namespace ex_glmbayes::opencl

The runner uses the error-handling utilities from `openclPort.h` (`opencl_make_context_error`, `opencl_status_name`) to produce informative exceptions on failure.

## Step 5 — Write the kernel wrapper (C++)

The kernel wrapper is the R-facing `[[Rcpp::export]]` function. It validates and converts R inputs, selects the kernel name based on family/link, assembles the program string using the dependency index, calls the runner, and returns results as R objects. It lives in `ex_glmbayes_kernel_wrappers.cpp`:

    // ex_glmbayes_kernel_wrappers.cpp (abbreviated)
    namespace ex_glmbayes {
    namespace opencl {

    // [[Rcpp::export]]
    Rcpp::List f2_f3_opencl(
        std::string family, std::string link,
        Rcpp::NumericMatrix b,  Rcpp::NumericVector y,
        Rcpp::NumericMatrix x,  Rcpp::NumericMatrix mu,
        Rcpp::NumericMatrix P,  Rcpp::NumericVector alpha,
        Rcpp::NumericVector wt, int progbar)
    {
        int l1 = x.nrow(), l2 = x.ncol(), m1 = b.ncol();

        // 1. Flatten R matrices into contiguous vectors
        auto X_flat  = openclPort::flattenMatrix(x);
        auto B_flat  = openclPort::flattenMatrix(b);
        // ... (all inputs)

        // 2. Dispatch: set kernel_name and kernel_file based on family/link
        std::string kernel_name, kernel_file;
        if (family == "binomial" && link == "logit") {
            kernel_name = "f2_f3_binomial_logit";
            kernel_file = "ex_glmbayes_src/f2_f3_binomial_logit.cl";
        } // ... (all families)

        // 3. Assemble program source using the pre-built dependency index.
        //    load_library_for_kernel() reads @depends_nmath from the kernel file,
        //    looks up the transitive closure in kernel_dependency_index.tsv, and
        //    loads only the required subset in the correct order --- no sort at runtime.
        std::string nmath_src = openclPort::load_library_for_kernel(
            kernel_file,          // kernel .cl path (relative to inst/cl/)
            "ex_glmbayes_nmath",  // library subdir containing index + .cl files
            "nmathopencl",        // package
            "depends_nmath"       // annotation tag listing direct nmath entry points
        );
        std::string kernel_src = openclPort::load_kernel_source(
            kernel_file, "nmathopencl");
        std::string program_source = nmath_src + "\n" + kernel_src;

        // 4. Allocate output buffers
        std::vector<double> qf_flat(m1);
        std::vector<double> grad_flat(static_cast<size_t>(m1) * l2);

        // 5. Run the kernel
        f2_f3_kernel_runner(program_source, kernel_name.c_str(),
                            l1, l2, m1,
                            X_flat, B_flat, mu_flat, P_flat,
                            alpha_flat, y_flat, wt_flat,
                            qf_flat, grad_flat);

        // 6. Wrap outputs as R objects and return
        Rcpp::NumericVector qf(qf_flat.begin(), qf_flat.end());
        // ... (reshape grad_flat into a matrix)
        return Rcpp::List::create(Rcpp::Named("qf") = qf, ...);
    }

    }} // namespace ex_glmbayes::opencl

### Why `load_library_for_kernel()` rather than `load_kernel_library()`?

`load_kernel_library()` sorts and concatenates every file in the subdirectory on every call. For a 137-file library like `nmath` this requires reading all files sequentially. `load_library_for_kernel()` reads the pre-built `kernel_dependency_index.tsv` once, then reads only the small subset of files that the specific kernel actually needs — 3 files for `f2_f3_gaussian`, 17 for `f2_f3_binomial_logit`, and so on. The savings are significant for large libraries and become important when the kernel wrapper is called repeatedly.

The old full-library approach is still available for cases where the exact dependency set is unknown or all files are genuinely needed:

    // Old approach --- loads all files in the subdirectory (kept for reference)
    // std::string nmath_src = openclPort::load_kernel_library(
    //     "ex_glmbayes_nmath", "nmathopencl", false);

## Step 6 — Write the Rcpp export wrappers (C++ and R)

The `[[Rcpp::export]]` annotation on `f2_f3_opencl` causes `Rcpp::compileAttributes()` to generate:

- A `.Call` entry in `RcppExports.cpp`
- An R wrapper in `RcppExports.R`

The R-side convenience function in `ex_glmbayes.R` adds a `nmathopencl_has_opencl()` guard and CPU fallback:

    f2_f3_opencl_R <- function(family, link, b, y, x, mu, P, alpha, wt,
                                 use_opencl = TRUE) {
      if (use_opencl && nmathopencl_has_opencl()) {
        f2_f3_opencl(family, link, b, y, x, mu, P, alpha, wt, progbar = 0L)
      } else {
        f2_f3_non_opencl(family, link, b, y, x, mu, P, alpha, wt)
      }
    }

## Step 7 — Implement the CPU fallback

The CPU fallback uses the same mathematical logic as the kernel but executes in C++ using standard R math calls. The relevant code lives in:

- `ex_glmbayes_famfuncs_binomial.cpp` — binomial family functions
- `ex_glmbayes_famfuncs_poisson.cpp` — Poisson family
- `ex_glmbayes_famfuncs_Gamma.cpp` — Gamma family
- `ex_glmbayes_famfuncs_gaussian.cpp` — Gaussian family
- `ex_glmbayes_EnvelopeEval.cpp` — orchestrates the CPU path
- `ex_glmbayes_EnvelopeSize.cpp` — memory allocation for the envelope

These files are grouped under the `ex_glmbayes::fam` and `ex_glmbayes::env` sub-namespaces. They use R’s standard `<Rmath.h>` functions (the same mathematical functions as the GPU kernels, but via the C runtime rather than OpenCL).

## File inventory

The complete set of files contributing to the `ex_glmbayes` example:

### OpenCL source (`inst/cl/`)

Directory | Files
--- | ---
`ex_glmbayes_nmath/` | 20 files: the minimal nmath subset
`ex_glmbayes_src/` | 6 files: one `f2_f3_*.cl` kernel per GLM family
`ex_glmbayes_draft_src/` | Draft versions (work in progress)

### C++ source (`src/`)

File | Namespace | Role
--- | --- | ---
`ex_glmbayes_kernel_runners.cpp` | `ex_glmbayes::opencl` | Low-level OpenCL runner for the `f2_f3` kernels
`ex_glmbayes_kernel_wrappers.cpp` | `ex_glmbayes::opencl` | R-facing wrapper: input validation, program assembly, runner dispatch
`ex_glmbayes_export_wrappers.cpp` | (Rcpp export) | `[[Rcpp::export]]` entry points for `EnvelopeSize`, `EnvelopeEval`, `glmb_Standardize_Model`
`ex_glmbayes_famfuncs_binomial.cpp` | `ex_glmbayes::fam` | CPU binomial likelihood
`ex_glmbayes_famfuncs_poisson.cpp` | `ex_glmbayes::fam` | CPU Poisson likelihood
`ex_glmbayes_famfuncs_Gamma.cpp` | `ex_glmbayes::fam` | CPU Gamma likelihood
`ex_glmbayes_famfuncs_gaussian.cpp` | `ex_glmbayes::fam` | CPU Gaussian likelihood
`ex_glmbayes_EnvelopeEval.cpp` | `ex_glmbayes::env` | CPU envelope evaluation (f2/f3 orchestrator)
`ex_glmbayes_EnvelopeSize.cpp` | `ex_glmbayes::env` | Envelope memory sizing
`ex_glmbayes_glmb_Standardize_Model.cpp` | `ex_glmbayes::sim` | Design matrix standardization

### C++ headers (`src/`)

File | Namespace declared
--- | ---
`ex_glmbayes_opencl.h` | `ex_glmbayes::opencl`
`ex_glmbayes_famfuncs.h` | `ex_glmbayes::fam`
`ex_glmbayes_Envelopefuncs.h` | `ex_glmbayes::env`
`ex_glmbayes_simfuncs.h` | `ex_glmbayes::sim`

### R source (`R/`)

File | Role
--- | ---
`ex_glmbayes.R` | R-facing API: `f2_f3_opencl_R`, `f2_f3_non_opencl`
`ex_glmbayes_rcpp_wrappers.R` | Thin Rcpp wrappers for the three exported C++ export functions

## Adapting this pattern for a new package

To build a similar component in your own package:

1. Identify your nmath dependencies — write the `@depends_nmath` annotation in each of your kernel files (listing the direct nmath entry points your kernel calls). Then call `extract_library_subset()` to copy the exact transitive closure of files, plus the companion index files, into your package’s `inst/cl/<yourpkg_nmath>/`:

       nmath_dir <- system.file("cl", "nmath", package = "nmathopencl")
       idx <- readRDS(file.path(nmath_dir, "kernel_dependency_index.rds"))

       extract_library_subset(
           kernel_paths = list.files("inst/cl/mypkg_src", "\\.cl$", full.names = TRUE),
           library_dir  = nmath_dir,
           dest_dir     = "inst/cl/mypkg_nmath",  # must exist
           depends_tag  = "depends_nmath",
           index        = idx
       )

2. Write your kernel(s) — add `@library_deps`, `@calls_nmath`, and `@all_depends_nmath` tags at the top of each `.cl` file. Store them in `inst/cl/<yourpkg_src>/`.

3. Write a kernel runner — use `openclPort::opencl_dbl_scalar_kernel_runner` directly if your kernel fits the double-scalar layout, or write a custom runner following the same OpenCL lifecycle pattern as `f2_f3_kernel_runner`. Use `openclPort::opencl_make_context_error` and `opencl_status_name` for error handling.

4. Write a kernel wrapper — flatten your R inputs with `openclPort::flattenMatrix` / `openclPort::copyVector`, assemble the program string with `openclPort::load_library_for_kernel()` + `openclPort::load_kernel_source()`, call the runner, and return an R-friendly result. The `@depends_nmath` annotation in your kernel file drives the subset selection automatically.

5. Write a CPU fallback — implement the same computation using standard R math (`<Rmath.h>`) or base-R functions. Guard the GPU path with `nmathopencl_has_opencl()`.

6. Add `LinkingTo: nmathopencl` to your `DESCRIPTION` file so that `openclPort.h` is found at compile time.

7. Add configure scripts for CRAN safety — this is the step most commonly overlooked.

   A package that references `-lOpenCL` or `CL/cl.h` in a static `src/Makevars` will fail to compile on CRAN’s build machines (which have no GPU SDK), and no binary will be produced. The solution is a pair of configure scripts (`configure` for Linux/macOS, `configure.win` for Windows) that generate `src/Makevars` dynamically at install time: if the SDK is found they write `-DUSE_OPENCL` and the link flags; if not they write a CPU-only Makevars. The package always compiles cleanly.

   Copy the generic templates into your package root with:

       use_opencl_configure()

   This writes `configure` and `configure.win` to the current directory, sets `configure` as executable (on Linux/macOS), and prints a checklist. The templates honor `OPENCL_HOME` / `OPENCL_SDK` environment variables so developers with non-standard SDK locations can point to them without modifying system paths.

   The three-entity relationship that the scripts establish:

       configure / configure.win
         -> detects CL/cl.h + libOpenCL at install time
         -> writes -DUSE_OPENCL into Makevars   (or omits it for CPU-only)

       #ifdef USE_OPENCL  (in your C++ source)
         -> guards all GPU code; compiles cleanly either way

       nmathopencl_has_opencl()  (in your R code)
         -> calls a compiled-in bool that mirrors the compile-time decision
         -> TRUE only if -DUSE_OPENCL was set when the package was built

   On Linux the `configure` script also runs a runtime probe (`clGetPlatformIDs`) before setting `USE_OPENCL`. This extra check catches the common case where the ICD loader (`libOpenCL.so`) is installed but no vendor platform has been registered in `/etc/OpenCL/vendors/`. `configure.win` (Windows) detects the header only; the ICD loader (`OpenCL.dll`) is installed with the GPU driver and does not require a separate probe.

   Add the generated files to `.gitignore` — they are build artifacts, not source files:

       src/Makevars
       src/Makevars.win

   For more detail, including the migration plan for when these templates move to `opencltools`, see `system.file("configure-templates", "README.md", package = "nmathopencl")`.

The `ex_glmbayes` files are the authoritative reference implementation for steps 1–6; step 7 applies universally to any downstream package that exposes GPU acceleration.