gemm: tiled F32 forward + transpose + backward (dA/dB)

Hand-written tiled GEMM (csrc/ops/gemm.cu, TILE_SIZE=32, FP32 accumulate,
boundary-masked) plus an out-of-place transpose kernel. Wire both through
xtrain-cuda FFI (no_cuda-gated) and expose at the tensor level:
Tensor::matmul, transpose_2d, and matmul_backward computing
dA = dC·Bᵀ and dB = Aᵀ·dC by materializing transposes and reusing the
forward. Also declare cuBLAS sgemm FFI + link cublas, used only as a
correctness reference in tests.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

crates/xtrain-cuda/build.rs

@@ -22,6 +22,8 @@ fn main() {
     println!("cargo:rustc-link-search=native={cuda_path}/lib64");
     println!("cargo:rustc-link-lib=dylib=cudart");
     println!("cargo:rustc-link-lib=dylib=cuda");
+    // cuBLAS is used only as a correctness reference for the hand-written GEMM.
+    println!("cargo:rustc-link-lib=dylib=cublas");
 
     cc::Build::new()
         .cuda(true)
@@ -29,6 +31,7 @@ fn main() {
         .flag("-gencode=arch=compute_120,code=sm_120")
         .file("../../csrc/test/vecadd.cu")
         .file("../../csrc/ops/elementwise.cu")
+        .file("../../csrc/ops/gemm.cu")
         .compile("xtrain_cuda_kernels");
 }
 

crates/xtrain-cuda/src/ffi.rs

@@ -39,4 +39,56 @@ unsafe extern "C" {
         n: i32,
         stream: CudaStream,
     );
+
+    // Tiled GEMM: C = A @ B, row-major F32. A:[M,K] B:[K,N] C:[M,N]
+    // (csrc/ops/gemm.cu).
+    pub fn launch_gemm_tiled_f32(
+        a: *const f32,
+        b: *const f32,
+        c: *mut f32,
+        m: i32,
+        n: i32,
+        k: i32,
+        stream: CudaStream,
+    );
+
+    // Out-of-place 2D transpose: out[j,i] = in[i,j]. in:[rows,cols] row-major,
+    // out:[cols,rows] row-major (csrc/ops/gemm.cu).
+    pub fn launch_transpose_f32(
+        input: *const f32,
+        out: *mut f32,
+        rows: i32,
+        cols: i32,
+        stream: CudaStream,
+    );
 }
+
+// cuBLAS — used ONLY as a correctness reference for the hand-written GEMM in
+// tests. Declared (and linked, see build.rs) only when CUDA is compiled in.
+#[cfg(not(no_cuda))]
+pub type CublasHandle = *mut c_void;
+
+#[cfg(not(no_cuda))]
+unsafe extern "C" {
+    pub fn cublasCreate_v2(handle: *mut CublasHandle) -> i32;
+    pub fn cublasDestroy_v2(handle: CublasHandle) -> i32;
+    pub fn cublasSgemm_v2(
+        handle: CublasHandle,
+        transa: i32,
+        transb: i32,
+        m: i32,
+        n: i32,
+        k: i32,
+        alpha: *const f32,
+        a: *const f32,
+        lda: i32,
+        b: *const f32,
+        ldb: i32,
+        beta: *const f32,
+        c: *mut f32,
+        ldc: i32,
+    ) -> i32;
+}
+
+#[cfg(not(no_cuda))]
+pub const CUBLAS_OP_N: i32 = 0;