feat(fft): implement 1D FFT/IFFT and frequency helpers

[sonusharma6-dsa]

Implements basic 1D FFT/IFFT and frequency helpers (fftfreq, fftshift). Rebased onto upstream/main to fix DCO. Fixes #225.

Summary by CodeRabbit

• New Features

  • Added FFT and inverse-FFT operations with optional transform length and selectable normalization.
  • Added frequency-axis utilities and spectrum reordering helpers.

• Tests

  • Added unit tests validating FFT↔IFFT round-trip and frequency/shift behaviors.

• Chores

  • Enabled standard string parsing for data types.
  • Minor numeric/formatting cleanups in type metadata and documentation.

[coderabbitai]

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📝 Walkthrough

Walkthrough

Adds 1-D fft/ifft (optional length, Norm scaling) and frequency-axis utilities (fftfreq, rfftfreq, fftshift, ifftshift) with unit tests for round-trip and shift behavior.

Changes

Core FFT + Frequency Utilities

Layer / File(s)	Summary
FFT and IFFT Core Transforms crates/mohu-fft/src/transform.rs	fft and ifft accept &[Complex<f64>] with optional n, return empty on n==0, pad/truncate inputs, plan and run rustfft forward/inverse transforms, and apply Norm-dependent scaling. Includes round-trip unit test.
Frequency-Axis Manipulation Utilities crates/mohu-fft/src/freq.rs	Adds fftfreq(n,d) and rfftfreq(n,d) to compute DFT sample bins (empty when n==0), plus generic fftshift/ifftshift (empty-input fast paths) that reorder vectors; unit tests check exact bins and that ifftshift(fftshift(v)) restores v.
DType FromStr implementation crates/mohu-dtype/src/dtype.rs	Implements std::str::FromStr for DType, delegating to DType::from_str and returning MohuError on failure.
FloatInfo precision literals crates/mohu-dtype/src/finfo.rs	Replaces integer-to-f64 casts in mantissa×log10(2.0) expressions with float literals for each precision constructor (f16, bf16, f32, f64).
Macro docs spacing crates/mohu-dtype/src/macros.rs	Adjusts section delimiter/spacing around the dtype_of! macro header; no behavioral change.
Cargo metadata crates/mohu-fft/Cargo.toml	Adds package.metadata.cargo-machete.ignored list to exclude selected deps from cargo-machete linting.

Sequence Diagram (high-level FFT flow)

sequenceDiagram
  participant Client as Caller
  participant TransformFn as fft/ifft
  participant Planner as rustfft::FftPlanner
  participant Executor as rustfft::Fft
  participant Scaler as Norm scaling
  participant Output as Vec<Complex<f64>>

  Client->>TransformFn: call with input & optional n, norm
  TransformFn->>Planner: plan forward/inverse FFT for len n
  TransformFn->>Executor: execute plan on prepared buffer
  Executor->>Scaler: apply forward/inverse normalization
  Scaler->>Output: produce Vec<Complex<f64>>

Loading

Estimated code review effort

🎯 3 (Moderate) | ⏱️ ~25 minutes

Poem

🐰 I hopped through arrays both long and small,
Split bins and shifts to center them all,
Forward, backward, norms align,
Round-trip proofs make spectra fine,
🥕 Rusty roots and FFTs tall.

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 inconclusive)

Check name	Status	Explanation	Resolution
Out of Scope Changes check	❓ Inconclusive	The PR includes minor out-of-scope changes: FromStr implementation for DType and precision calculation refactoring in mohu-dtype, plus formatting adjustments in macros.rs.	Clarify whether DType FromStr and finfo.rs precision refactoring are intentional or inadvertently included alongside the FFT implementation.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The PR title accurately summarizes the main changes: implementing 1D FFT/IFFT functions and frequency helper utilities (fftfreq, fftshift, ifftshift).
Linked Issues check	✅ Passed	PR partially addresses #225 objectives: implements 1D fft/ifft and frequency helpers (fftfreq, fftshift, ifftshift), but omits rfft/irfft, fft2/fftn, Rayon parallelization, and incomplete normalization modes.
Docstring Coverage	✅ Passed	Docstring coverage is 100.00% which is sufficient. The required threshold is 80.00%.

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✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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[sonusharma6-dsa]

Addressed CI review comments: added zero-length guards to ft/ifft and fixed
fftfreq to return non-negative frequencies only. Please re-run checks; happy to follow up on any remaining failures.

[coderabbitai]

Actionable comments posted: 1

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@crates/mohu-fft/src/freq.rs`:
- Around line 12-17: The fftfreq generation currently includes index n_half in
the positive branch causing the Nyquist term to be +0.5/d for even n; change the
logic so the positive loop runs 0..n_half (exclusive) and the negative branch
covers n_half..n, or explicitly handle the i==n_half case when n%2==0 to push
-((n - i) as f64) * val for that index; update the loops that reference n_half,
freqs, val and n (or add a conditional for even n) so the Nyquist frequency is
negative for even lengths.

🪄 Autofix (Beta)

Fix all unresolved CodeRabbit comments on this PR:

• Push a commit to this branch (recommended)
• Create a new PR with the fixes

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ℹ️ Review info

⚙️ Run configuration

Configuration used: defaults

Review profile: CHILL

Plan: Pro Plus

Run ID: fde56ce6-b7ef-481d-8019-72936a0aadb2

📥 Commits

Reviewing files that changed from the base of the PR and between 1de1da3 and 7a3c5ac.

📒 Files selected for processing (2)

• crates/mohu-fft/src/freq.rs
• crates/mohu-fft/src/transform.rs

[sonusharma6-dsa]

Fixed fftfreq Nyquist sign for even
(positive/negative partition corrected). Pushed as a signed commit to eat/fft-impl2. Please re-run checks.

[sonusharma6-dsa]

Addressed several Clippy/format items: removed empty line after doc comments in macros.rs, implemented FromStr for DType, and removed unnecessary casts in info.rs. Pushed signed commit.

[sonusharma6-dsa]

CI: added cargo-machete ignore metadata for mohu-fft to silence unused-deps false positives while implementation is partial. Pushed signed commit. Continuing to address Clippy/Format items.

[sonusharma6-dsa]

Formatting fixes pushed (applied rustfmt-like adjustments to reporter, test_utils, and fft modules). Please re-run checks.

[sonusharma6-dsa]

Closing in favor of new PR #233: #233