[shibaacharya]

CPU ReduceSum for integer types accumulated in double, so int64/uint64 inputs above 2^53 lost precision before summation started. Kahan compensation can't recover bits already dropped in the conversion.

This PR:

Adds ExactIntSum, a two-word (128-bit, two's complement) accumulator in reduction_ops.h.
Uses it in ReduceAggregatorSum for the scalar update/get_value path and aggall. The same accumulator is used in the fast RK, KRK and RKR paths.
Saturates only the final result to T::max()/T::lowest(), so overflow behaviour is unchanged. Intermediate partial sums outside the range of T no longer affect the result.
Moves the existing double/Kahan accumulation into ReduceAggregatorMean, so ReduceMean behaves as before.
Adds ReduceSum_int64_ExactAbove2Pow53 with these cases:
[2^53+1, -2^53] → 1
[2^53, 1] → 2^53+1
the RK fast path
cancellation after the partial sum exceeds int64
Motivation and Context
Fixes #33579. Before this change, ReduceSum on [2^53+1, -2^53] returned 0 instead of 1, even though the inputs and the result all fit in int64.

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🟡 Changes recommended

The new tests have a compilation error, include incompatible CUDA expectations, and do not exercise the modified fast reduction paths.

3 open issues

• Use unordered_set for OpTester exclusions · New
• Exclude CUDA from exact-integer regression tests · New
• Add tests that exercise all integer fast paths · New

What changed in this PR

Addresses #33579 by making CPU integer ReduceSum exact above 2^53, while preserving final-result saturation and existing ReduceMean behavior.

Changes:

• Adds a two-word integer accumulator for scalar and fast reduction paths.
• Keeps double/Kahan accumulation in ReduceMean.
• Adds int64 regressions for precision loss and cancellation after intermediate overflow.

File	Description
onnxruntime/​test/​providers/​cpu/​reduction/​reduction_ops_test.cc	Adds integer exactness and cancellation regression cases.
onnxruntime/​core/​providers/​cpu/​reduction/​reduction_ops.h	Implements exact integer sums while preserving mean accumulation.

_{Review effort: Balanced}

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[shibaacharya]

Hi, I've updated the PR to address the review comments and pushed the changes. I tried running the Azure Pipelines using /azp run, but the bot reported that I don't have sufficient privileges for this PR. Could a maintainer please trigger the required pipelines? Thanks!