docs: Add Task #67 for DCT/FFT performance benchmarking

Adds low-priority task to measure and compare DCT/IDCT performance:

**Goal:** Quantify performance differences between implementations
- Reference O(N²) naive DCT/IDCT
- Current FFT-based O(N log N) implementation
- Future SIMD-optimized versions (when written)

**Location:** test_dct.cc or test_fft.cc

**Measurements:**
- Average time per transform (microseconds)
- Throughput (transforms per second)
- Speedup factor vs reference
- Multiple test sizes (128, 256, 512, 1024) for scaling analysis

**Implementation:**
- std::chrono::high_resolution_clock for timing
- 1000+ iterations to reduce noise
- Min/avg/max statistics
- Guarded with !STRIP_ALL for zero production impact

**Benefits:**
- Validate FFT speedup claims (O(N log N) vs O(N²))
- Quantify SIMD optimization gains when implemented
- Detect performance regressions in CI

**Priority:** Very Low (informational, not blocking any features)

This will be useful when optimizing audio performance in Phase 2.

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

1 files changed, 20 insertions, 0 deletions

diff --git a/TODO.md b/TODO.md
index 5fcad5d..76a2ba0 100644
--- a/TODO.md
+++ b/TODO.md
@@ -307,6 +307,26 @@ This file tracks prioritized tasks with detailed attack plans.
   - **Benefits**: Non-programmers can edit tempo, easier iteration, version control friendly
   - **Priority**: Low (current hardcoded approach works, but less flexible)
 
+- [ ] **Task #67: DCT/FFT Performance Benchmarking**: Add timing measurements to audio tests
+  - **Goal**: Compare performance of different DCT/IDCT implementations
+  - **Location**: Add timing code to `test_dct.cc` or `test_fft.cc`
+  - **Measurements**:
+    - Reference IDCT/FDCT (naive O(N²) implementation)
+    - FFT-based DCT/IDCT (current O(N log N) implementation)
+    - Future x86_64 SIMD-optimized versions (when implemented)
+  - **Output Format**:
+    - Average time per transform (microseconds)
+    - Throughput (transforms per second)
+    - Speedup factor vs reference implementation
+  - **Test Sizes**: DCT_SIZE=512 (production), plus 128, 256, 1024 for scaling analysis
+  - **Implementation**:
+    - Use `std::chrono::high_resolution_clock` for timing
+    - Run each test 1000+ iterations to reduce noise
+    - Report min/avg/max times
+    - Guard with `#if !defined(STRIP_ALL)` to avoid production overhead
+  - **Benefits**: Quantify FFT speedup, validate SIMD optimizations, identify regressions
+  - **Priority**: Very Low (nice-to-have for future optimization work)
+
 ### Developer Tools
 - [ ] **Task #66: External Asset Loading for Debugging**: mmap() asset files instead of embedded data
   - **Current**: All assets embedded in `assets_data.cc` (regenerate on every asset change)