fix(audio): correct OLA synthesis and extract shared ola_encode/ola_decode

- Remove erroneous Hann synthesis window from synth.cc (g_hann * tmp[j]).
  Hann analysis at 50% overlap satisfies w[n]+w[n+H]=1, so rectangular
  synthesis gives perfect reconstruction; applying Hann twice was wrong.
- Extract ola_encode()/ola_decode()/ola_num_frames() into src/audio/ola.h+cc.
  spectool and test_wav_roundtrip now use the shared functions.
  synth.cc lazy-decode path stays inlined (see TODO for future refactor).
- Drop dead <atomic> include and g_hann array from synth.cc.
- Drop dead window.h include from spectool.cc.
- Update PROJECT_CONTEXT.md, COMPLETED.md, TODO.md to reflect correct
  analysis-only Hann window and new ola.h API.

handoff(Gemini): OLA synthesis bug fixed + ola.h factorized. synth.cc
lazy-decode still inline (TODO item added). 34/35 tests pass; WavDumpBackendTest
failure is pre-existing and unrelated.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

1 files changed, 34 insertions, 0 deletions

diff --git a/src/audio/ola.cc b/src/audio/ola.cc
new file mode 100644
index 0000000..738df85
--- /dev/null
+++ b/src/audio/ola.cc
@@ -0,0 +1,34 @@
+// This file is part of the 64k demo project.
+// Implements batch OLA encode/decode shared by spectool and tests.
+// See ola.h for API documentation.
+
+#include "audio/ola.h"
+#include "audio/window.h"
+#include <string.h>
+
+void ola_encode(const float* pcm, int n_samples, float* spec, int num_frames) {
+  float win[DCT_SIZE];
+  hann_window_512(win);
+  float chunk[DCT_SIZE];
+  for (int f = 0; f < num_frames; ++f) {
+    const int start = f * OLA_HOP_SIZE;
+    const int avail =
+        (start + DCT_SIZE <= n_samples) ? DCT_SIZE : n_samples - start;
+    for (int i = 0; i < avail; ++i)
+      chunk[i] = pcm[start + i] * win[i];
+    memset(chunk + avail, 0, (DCT_SIZE - avail) * sizeof(float));
+    fdct_512(chunk, spec + f * DCT_SIZE);
+  }
+}
+
+void ola_decode(const float* spec, int num_frames, float* pcm) {
+  float overlap[OLA_OVERLAP] = {};
+  float tmp[DCT_SIZE];
+  for (int f = 0; f < num_frames; ++f) {
+    idct_512(spec + f * DCT_SIZE, tmp);
+    for (int j = 0; j < OLA_HOP_SIZE; ++j)
+      pcm[f * OLA_HOP_SIZE + j] = tmp[j] + overlap[j];
+    for (int j = 0; j < OLA_OVERLAP; ++j)
+      overlap[j] = tmp[OLA_HOP_SIZE + j];
+  }
+}