From 1a8aaa3b26feba106259b6842ad9f8998fb3233d Mon Sep 17 00:00:00 2001
From: Damian Schneider <daedae@gmx.ch>
Date: Tue, 26 Nov 2024 20:32:39 +0100
Subject: [PATCH] Speed improvements, commented legacy _t trig functions

- speed improvement: by default M_TWOPI is treated as a double float
- directly calling sin16_t in cos_approx() saves a lot of overhead
---
 wled00/wled_math.cpp | 23 ++++++++++++++---------
 1 file changed, 14 insertions(+), 9 deletions(-)

diff --git a/wled00/wled_math.cpp b/wled00/wled_math.cpp
index a191968e1..583381d66 100644
--- a/wled00/wled_math.cpp
+++ b/wled00/wled_math.cpp
@@ -10,14 +10,17 @@
 
 //#define WLED_DEBUG_MATH
 
-#define modd(x, y) ((x) - (int)((x) / (y)) * (y))
-
-// Note: cos_t, sin_t and tan_t are very accurate but may be slow
+// Note: cos_t, sin_t and tan_t are very accurate but slow
 // the math.h functions use several kB of flash and are to be avoided if possible
 // sin16_t / cos16_t are faster and much more accurate than the fastled variants
 // sin_approx and cos_approx are float wrappers for sin16_t/cos16_t and have an accuracy better than +/-0.0015 compared to sinf()
 // sin8_t / cos8_t are fastled replacements and use sin16_t / cos16_t. Slightly slower than fastled version but very accurate
 
+
+// Taylor series approximations, replaced with Bhaskara I's approximation
+/*
+#define modd(x, y) ((x) - (int)((x) / (y)) * (y))
+
 float cos_t(float phi)
 {
   float x = modd(phi, M_TWOPI);
@@ -54,6 +57,7 @@ float tan_t(float x) {
   #endif
   return res;
 }
+*/
 
 // 16-bit, integer based Bhaskara I's sine approximation: 16*x*(pi - x) / (5*pi^2 - 4*x*(pi - x))
 // input is 16bit unsigned (0-65535), output is 16bit signed (-32767 to +32767)
@@ -85,17 +89,18 @@ uint8_t cos8_t(uint8_t theta) {
   return sin8_t(theta + 64); //cos(x) = sin(x+pi/2)
 }
 
-float sin_approx(float theta)
-{
-  uint16_t scaled_theta = (int)(theta * (0xFFFF / M_TWOPI)); // note: do not cast negative float to uint! cast to int first (undefined on C3)
+float sin_approx(float theta) {
+  uint16_t scaled_theta = (int)(theta * (float)(0xFFFF / M_TWOPI)); // note: do not cast negative float to uint! cast to int first (undefined on C3)
   int32_t result = sin16_t(scaled_theta);
   float sin = float(result) / 0x7FFF;
   return sin;
 }
 
-float cos_approx(float theta)
-{
-  return sin_approx(theta + M_PI_2);
+float cos_approx(float theta) {
+  uint16_t scaled_theta = (int)(theta * (float)(0xFFFF / M_TWOPI)); // note: do not cast negative float to uint! cast to int first (undefined on C3)
+  int32_t result = sin16_t(scaled_theta + 16384);
+  float cos = float(result) / 0x7FFF;
+  return cos;
 }
 
 float tan_approx(float x) {