modules/shapes: introduce an approximate atan2f()

Taken from this excellent post:
https://mazzo.li/posts/vectorized-atan2.html

While I haven't gone full vectorized, just getting rid of the
regular atan2f() call will be a big improvement.

This just adds the functionality, nothing is calling it yet.

1 files changed, 39 insertions, 0 deletions

diff --git a/src/modules/shapes/shapes.c b/src/modules/shapes/shapes.c
index 6de14ee..236861c 100644
--- a/src/modules/shapes/shapes.c
+++ b/src/modules/shapes/shapes.c
@@ -113,6 +113,45 @@ static void shapes_prepare_frame(til_module_context_t *context, til_stream_t *st
 }
 
 
+/* simple approximation taken from https://mazzo.li/posts/vectorized-atan2.html */
+static inline float atan_scalar_approximation(float x) {
+	/* TODO: this is probably more terms/precision than needed, but when I try just dropping some,
+	 * the circle+slight pinches gets artifacts.  So leaving for now, probably needs slightly different
+	 * values for fewer terms.
+	 */
+	float	a1  =  0.99997726f;
+	float	a3  = -0.33262347f;
+	float	a5  =  0.19354346f;
+	float	a7  = -0.11643287f;
+	float	a9  =  0.05265332f;
+	float	a11 = -0.01172120f;
+	float	x_sq = x*x;
+
+	return x * (a1 + x_sq * (a3 + x_sq * (a5 + x_sq * (a7 + x_sq * (a9 + x_sq * a11)))));
+}
+
+
+static float atan2_approx(float y, float x) {
+	// Ensure input is in [-1, +1]
+	int swap = fabs(x) < fabs(y);
+	float atan_input = (swap ? x : y) / (swap ? y : x);
+
+	// Approximate atan
+	float res = atan_scalar_approximation(atan_input);
+
+	// If swapped, adjust atan output
+	res = swap ? (atan_input >= 0.0f ? M_PI_2 : -M_PI_2) - res : res;
+
+	// Adjust quadrants
+	if (x <  0.0f && y >= 0.0f)
+		res =  M_PI + res; // 2nd quadrant
+	else if (x <  0.0f && y <  0.0f)
+		 res = -M_PI + res; // 3rd quadrant
+
+	return res;
+}
+
+
 static void shapes_render_fragment(til_module_context_t *context, til_stream_t *stream, unsigned ticks, unsigned cpu, til_fb_fragment_t **fragment_ptr)
 {
 	shapes_context_t	*ctxt = (shapes_context_t *)context;