From 5e29f2c1b7844492c5ccaf194f524fe810947c3f Mon Sep 17 00:00:00 2001
From: Damian Schneider <daedae@gmx.ch>
Date: Tue, 15 Oct 2024 20:11:33 +0200
Subject: [PATCH] fixed atan2_t

approximation was incorrect, now doing it right.
also removed hypotf() from octopus, saving a little flash.
---
 wled00/FX.cpp        |  6 ++++--
 wled00/wled_math.cpp | 39 +++++++++++++++++----------------------
 2 files changed, 21 insertions(+), 24 deletions(-)

diff --git a/wled00/FX.cpp b/wled00/FX.cpp
index 338dd2df9..5b4513dc7 100644
--- a/wled00/FX.cpp
+++ b/wled00/FX.cpp
@@ -7749,8 +7749,10 @@ uint16_t mode_2Doctopus() {
     const int C_Y = (rows / 2) + ((SEGMENT.custom2 - 128)*rows)/255;
     for (int x = 0; x < cols; x++) {
       for (int y = 0; y < rows; y++) {
-        rMap[XY(x, y)].angle  = 40.7436f * atan2_t((y - C_Y), (x - C_X));  // avoid 128*atan2()/PI
-        rMap[XY(x, y)].radius = hypotf((x - C_X), (y - C_Y)) * mapp;      //thanks Sutaburosu
+        rMap[XY(x, y)].angle  = int(40.7436f * atan2_t((y - C_Y), (x - C_X)));  // avoid 128*atan2()/PI
+        int dx = (x - C_X);
+        int dy = (y - C_Y);
+        rMap[XY(x, y)].radius = sqrtf(dx * dx + dy * dy) * mapp; //thanks Sutaburosu
       }
     }
   }
diff --git a/wled00/wled_math.cpp b/wled00/wled_math.cpp
index 080cc9425..1825ab198 100644
--- a/wled00/wled_math.cpp
+++ b/wled00/wled_math.cpp
@@ -88,8 +88,8 @@ uint8_t cos8_t(uint8_t theta) {
 float sin_approx(float theta)
 {
   theta = modd(theta, TWO_PI); // modulo: bring to -2pi to 2pi range
-  if(theta < 0) theta += M_TWOPI; // 0-2pi range
-  uint16_t scaled_theta = (uint16_t)(theta * (0xFFFF / M_TWOPI));
+  if(theta < 0) theta += TWO_PI; // 0-2pi range
+  uint16_t scaled_theta = (uint16_t)(theta * (0xFFFF / TWO_PI));
   int32_t result = sin16_t(scaled_theta);
   float sin = float(result) / 0x7FFF;
   return sin;
@@ -110,28 +110,23 @@ float tan_approx(float x) {
 #define ATAN2_CONST_A 0.1963f
 #define ATAN2_CONST_B 0.9817f
 
-// fast atan2() approximation source: public domain
+// atan2_t approximation, with the idea from https://gist.github.com/volkansalma/2972237?permalink_comment_id=3872525#gistcomment-3872525
 float atan2_t(float y, float x) {
-  if (x == 0.0f) return (y > 0.0f) ? M_PI_2 : (y < 0.0f) ? -M_PI_2 : 0.0f;
-
-  float abs_y = (y < 0.0f) ? -y : y + 1e-10f;  // make sure y is not zero to prevent division by 0
-  float z = abs_y / x;
-  float atan_approx;
-
-  if (z < 1.0f) {
-    atan_approx = z / (1.0f + ATAN2_CONST_A * z * z);
-    if (x < 0.0f) {
-      return (y >= 0.0f) ? atan_approx + PI : atan_approx - PI;
-    }
+	float abs_y = fabs(y);
+  float abs_x = fabs(x);
+  float r = (abs_x - abs_y) / (abs_y + abs_x + 1e-10f); // avoid division by zero by adding a small nubmer
+  float angle;
+  if(x < 0) {
+    r = -r;
+    angle = M_PI/2.0f + M_PI/4.f;
   }
-  else {
-    z = x / abs_y;
-    atan_approx = M_PI_2 - z / (1.0f + ATAN2_CONST_A * z * z);
-    if (y < 0.0f) {
-      return -atan_approx;
-    }
-  }
-  return atan_approx;
+  else
+    angle = M_PI/2.0f - M_PI/4.f;
+
+  float add = (ATAN2_CONST_A * (r * r) - ATAN2_CONST_B) * r;
+	angle += add;
+  angle = y < 0 ? -angle : angle;
+	return angle;
 }
 
 //https://stackoverflow.com/questions/3380628