1 files changed, 3 insertions, 30 deletions
diff --git a/TODO.md b/TODO.md
index 3943a61..0184f0a 100644
--- a/TODO.md
+++ b/TODO.md
@@ -16,37 +16,10 @@ Procedural spectrogram tool: 50-100× compression (5 KB .spec → ~100 bytes C++
 
 **Status:** 38/38 tests passing
 
-### Fix FFT twiddle factor accumulation bug (`src/audio/fft.cc`)
+### ✅ Fix FFT twiddle factor accumulation bug (`src/audio/fft.cc`) — DONE
 
-**Root cause:** `fft_radix2` updates twiddle factors iteratively over 256 iterations
-in the final stage (N=512). Accumulated floating-point drift causes sign flips on
-specific DCT coefficients. Round-trip (DCT+IDCT) still works because both sides
-make the same errors symmetrically, masking the bug.
-
-**Fix:** Replace iterative twiddle update with direct `cosf/sinf` per k:
-```cpp
-// fft_radix2, inner loop — replace:
-wr = wr_old * wr_delta - wi * wi_delta;
-wi = wr_old * wi_delta + wi * wr_delta;
-// with:
-wr = cosf(angle * (float)k);
-wi = sinf(angle * (float)k);
-```
-
-**Test plan (`src/tests/audio/test_fft.cc`):** add one test per component, in order:
-
-- [ ] **A: `bit_reverse_permute`** — for N=8 verify exact index mapping:
-      0→0, 1→4, 2→1, 3→6, 4→2, 5→7, 6→3, 7→5 (must be exact)
-- [ ] **B: `fft_radix2` small N** — DFT of `[1,0,0,0]` (N=4) via FFT vs direct sum;
-      all 4 unit impulses. Expect machine epsilon.
-- [ ] **C: twiddle accumulation** — compare iterative vs `cosf/sinf` twiddle factors
-      at k=128..255, stage size=512. **This test must fail before the fix.**
-- [ ] **D: `dct_fft` small N** — all 8 unit impulses for N=8 vs reference.
-      Expect machine epsilon (exact for small N).
-- [ ] **E: `dct_fft` large N** — all original test cases (N=512): impulse[0],
-      impulse[N/2], sinusoidal, complex. Expect < 1e-5 after fix.
-
-Revert threshold in `arrays_match` back to `5e-3` (or tighter) once fixed.
+`fft_radix2` now computes `wr = cosf(angle*k); wi = sinf(angle*k);` directly per k.
+Tests A–E added to `test_fft.cc`. `arrays_match` default tolerance reverted to 5e-3.
 
 ## Priority 4: Audio System Enhancements [LOW PRIORITY]