CUDA Index Width in PyTorch

Use this skill when a CUDA kernel overflows int indexing, fails near 2^31 elements, or needs a review of int vs int64_t index math.

Start with the overflow site

Do not blindly convert all index variables to int64_t. Find the expression that can exceed 32 bits and classify where it runs:

• One-time setup per CTA or per output element group: prefer one local 64-bit cast at the first multiply.
• Hot per-element linear indexing: template the kernel on index_t and dispatch int vs int64_t.
• Unsupported algorithm with 32-bit-only assumptions: add a clear TORCH_CHECK(canUse32BitIndexMath(...)) instead of silently overflowing.
• Grid dimension overflow: changing arithmetic type is not enough; add tiling/striding over that dimension.

Canonical utilities

Include/use the existing PyTorch utilities instead of ad hoc checks:

#include <ATen/native/CanUse32BitIndexMath.h>
#include <ATen/cuda/detail/KernelUtils.h>

• at::native::canUse32BitIndexMath(tensor, INT_MAX) checks both numel and maximum storage offset.
• For CUDA files that already include cuda detail wrappers, at::cuda::detail::canUse32BitIndexMath may be available as an alias.
• AT_DISPATCH_INDEX_TYPES(cond ? ScalarType::Int : ScalarType::Long, "name", [&] { ... }); provides index_t.
• CUDA_KERNEL_LOOP_TYPE(index, nthreads, index_t) keeps grid-stride loops correct for either width.

Check every tensor whose offsets are computed with the selected index type, not just the output tensor.

Fix patterns

1. Localized base-offset overflow

If only a base pointer offset can overflow and it is computed outside the hot loop, keep the kernel otherwise unchanged:

int64_t plane = blockIdx.x;
input = input + plane * strideD;
output = output + plane * osizeH * osizeW;

This avoids doubling kernel instantiations and keeps inner-loop arithmetic 32-bit. Use this when dimensions inside the tile still fit in int.

2. Grid-stride linear kernels

If the loop index, modulo/division decomposition, or final data[index] access can exceed 32 bits, template the kernel:

template <typename scalar_t, typename index_t>
__global__ void kernel(index_t n, const scalar_t* in, scalar_t* out) {
  CUDA_KERNEL_LOOP_TYPE(index, n, index_t) {
    out[index] = in[index];
  }
}

AT_DISPATCH_INDEX_TYPES(
    canUse32BitIndexMath(out, INT_MAX) && canUse32BitIndexMath(in, INT_MAX)
        ? ScalarType::Int
        : ScalarType::Long,
    "kernel_index_type",
    [&] {
      kernel<scalar_t, index_t><<<blocks, threads, 0, stream>>>(n, in, out);
      C10_CUDA_KERNEL_LAUNCH_CHECK();
    });

Prefer this over unconditionally changing the loop index to int64_t, because 64-bit division/modulo in a hot CUDA loop can be measurable.

3. TensorInfo/accessor or strided kernels

When offsets are computed from sizes/strides, dispatch on an index type only if all participating tensors pass canUse32BitIndexMath for that type. Remember that a small numel() tensor can still need 64-bit offsets if it is a large strided view.

4. 32-bit-only kernels

If supporting 64-bit indexing would require a larger algorithm rewrite or would exceed CUDA launch limits, fail early:

TORCH_CHECK(
    canUse32BitIndexMath(input) && canUse32BitIndexMath(output),
    "op_name: tensors must fit into 32-bit index math");

Only use this when the operator already has a documented or accepted size limitation; do not turn a reported correctness bug into an unnecessary limitation.

Binary-size and performance tradeoffs

Templating on index_t duplicates each affected kernel for every scalar dtype and memory-format specialization. Before adding index dispatch to several kernels, ask whether the overflow is in a hot path or only in one setup expression.

A/B candidate fixes when the choice is not obvious:

1. Build each candidate from a clean diff using the same build environment.
2. Record changed CUDA object and library sizes:

   stat -c '%s %n' build/aten/src/ATen/CMakeFiles/torch_cuda.dir/native/cuda/<file>.cu.o torch/lib/libtorch_cuda.so
   

3. Check symbol multiplication for the kernel name:

   nm -S --size-sort -C torch/lib/libtorch_cuda.so | rg '<kernel_name>|index_t|long|int'
   

4. If hot-loop arithmetic changed, benchmark representative small and large tensors; do not report performance from sanitizer runs.

Default decision:

• One or two 64-bit setup multiplies: prefer the local cast.
• Per-element indexing may exceed 32 bits: prefer index_t dispatch.
• Existing kernel family already dispatches index_t: extend the existing pattern.
• Changing many scalar-specialized kernels: consider binary size before templating all of them.

Tests for large-index fixes

Add a regression that crosses the exact boundary that failed:

• Use the smallest dtype and output size that still exercises the overflow.
• Assert tensor.numel() > torch.iinfo(torch.int32).max or assert the specific offset boundary.
• Sample values from both below and above the boundary; avoid full-tensor CPU comparisons for huge tensors.
• Run the original repro under compute-sanitizer for memory bugs:

  CUDA_LAUNCH_BLOCKING=1 PYTORCH_NO_CUDA_MEMORY_CACHING=1 compute-sanitizer --tool memcheck --error-exitcode=99 <python> repro.py
  

For PyTorch tests, prefer adding the regression near related pooling/indexing tests and guard expensive cases with @largeTensorTest and the relevant device decorator.

Review checklist

• The exact overflowing expression is identified.
• 64-bit math is limited to the expressions that need it, or the kernel is templated when the hot index needs it.
• canUse32BitIndexMath considers every tensor whose offsets use the selected type.
• CUDA launch dimensions still fit hardware limits.
• The test fails before the fix and passes after it, or the report explains why pre-fix failure was not rerun.
• Binary-size/performance impact is mentioned if new index_t dispatch duplicates kernels.