oscillators article

articles/oscillators/page.mmd

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+Title:  Programmatic Oscillators
+Brief:  Sine, cosine, saw and square oscillators with minimal binary footprint.
+Date:   1684748529
+Tags:   Programming, Music, C
+CSS:    /style.css
+
+Wanted to have some beep bops for my [4mb-jam](https://itch.io/jam/4mb-jam-2023) entry, so
+I ended up with implementations of three oscillators that would require minimal amount of calculations.
+
+Idea is to precalculate initial state offline and only have short frame generation procedure in final binary.
+Thinking about using it in tracker format of sorts that would have runtime generated samples.
+
+Inspirations are taken from [musicdsp](https://www.musicdsp.org/).
+
+### Sine/Cosine ###
+
+```c
+/* Intended to be executed offline with values then embedded in the binary.
+ * By having usage of glibc sin and cos functions strictly offline it's easier to have it freestanding
+ */
+struct sinewave {
+  float f, s, c;
+} init_sinewave(float frequency, float phase, float amplitude) {
+  struct sinewave r;
+  r.f = 2.f * sinf((float)M_PI * frequency / AUDIO_FRAME_RATE);
+  r.s = amplitude * sinf(phase);
+  r.c = amplitude * cosf(phase);
+  return r;
+}
+
+/* Use `s` for sine value and `c` for cosine on caller side */
+void pump_sinewave(struct sinewave *wave) {
+  wave->s -= wave->f * wave->c;
+  wave->c += wave->f * wave->s;
+}
+
+```
+
+### Square ###
+
+```c
+/* Implemented over sinewave */
+struct sqrtwave {
+  struct sinewave w;
+  union {
+    float f;
+    uint32_t u;
+  } v;
+} init_sqrtwave(float frequency, float phase, float amplitude) {
+  struct sqrtwave r;
+  r.w = init_sinewave(frequency, phase, 1.f);
+  r.v.f = amplitude;
+  return r;
+}
+
+/* Use floating point bit representation to infer sign, all other bits are set to amplitude */
+void pump_sqrtwave(struct sqrtwave *wave) {
+  union {
+    float f;
+    uint32_t u;
+  } v;
+  pump_sinewave(&wave->w);
+  v.f = wave->w.s;
+  wave->v.u = (wave->v.u & 0x7fffffff) | (v.u & 0x80000000);
+}
+
+```
+
+### Saw ###
+
+```c
+struct sawtwave {
+  float v, a, i;
+} init_sawtwave(float frequency, float phase, float amplitude) {
+  struct sawtwave r;
+  r.v = sinf(phase) * amplitude;
+  r.a = amplitude;
+  r.i = frequency / AUDIO_FRAME_RATE * amplitude;
+  return r;
+}
+
+/* Simple amplitude overflow check with truncation */
+void pump_sawtwave(struct sawtwave *wave) {
+  wave->v += wave->i;
+  if (wave->v > wave->a)
+    wave->v -= wave->a;
+}
+
+```