Replace O(N) recursive sequence_map_inverse with O(1) pack expansion

[tenpercent]

Summary

Replace the O(N) recursive sequence_map_inverse implementation with O(1) template depth using pack expansion to reduce compile time (#3575).

Approach

• Use constexpr loop in find_source_index to locate permutation inverse indices
• Expand via pack expansion for O(1) template instantiation depth

Why It Works

Template recursion requires N template instantiations for N iterations, each with its own overhead. Constexpr loops execute within a single template instantiation, avoiding per-instantiation overhead.

Build Performance Impact

Template Instantiation Reduction (measured on device_grouped_conv3d_fwd_bias_bnorm_clamp_instance target, 248 files):

• Baseline: 7,748,880 total instantiations
• PR Replace O(N) recursive sequence_map_inverse with O(1) pack expansion #3596: 7,621,984 total instantiations
• Improvement: -126,896 instantiations (1.6% reduction)

This confirms the optimization successfully reduces template instantiation overhead by eliminating recursive template patterns in favor of pack expansion.

Test Plan

• Existing SequenceMapInverse.InverseMap and SequenceMapInverse.InverseIdentityMap tests validate correctness
• CI

Notes

• sequence_merge optimization removed from this PR (handled in Optimize sequence_gen and uniform_sequence_gen to reduce template instantiation depth #3585)
• Callers validate input via is_valid_sequence_map before calling sequence_map_inverse

[Copilot]

Pull request overview

This PR optimizes sequence_map_inverse by replacing O(N) recursive template instantiation with O(1) template depth using pack expansion and constexpr loops, reducing compilation overhead.

Changes:

• Replaced recursive sequence_map_inverse_impl with ConstexprArray and constexpr loop-based find_inverse
• Added detailed comments explaining the compilation performance benefits
• Achieved 1.6% reduction in template instantiations (126,896 fewer instantiations)

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[shumway]

I think we want to remove the O(N^2) loop and probably add memoization, too.

[shumway]

Can we make this a compile-time error, just to catch anything that is really broken?

The two patterns I know are to use a static_assert or to call a consteval function that throws an error. We don't want to have this logic silently fail.

[cgmillette]

Does this handle repeated indices?

[ammallya]

Imported to ROCm/rocm-libraries