From c5a1b3f4d8d0cacdfe93edce2a897270debfc0cc Mon Sep 17 00:00:00 2001
From: HEIHUAa <112499486+HEIHUAa@users.noreply.github.com>
Date: Sun, 25 Jan 2026 16:42:59 +0800
Subject: [PATCH 1/3] FlxMath::fastSinCos (#18)

---
 flixel/math/FlxMath.hx | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/flixel/math/FlxMath.hx b/flixel/math/FlxMath.hx
index b0c579e4d9..6243a4bdad 100644
--- a/flixel/math/FlxMath.hx
+++ b/flixel/math/FlxMath.hx
@@ -548,6 +548,26 @@ class FlxMath
 		return fastSin(n + 1.570796327); // sin and cos are the same, offset by pi/2
 	}
 
+	/**
+	 * ~1.3x faster than calling fastSin() + fastCos() separately.
+	 */
+	public static inline function fastSinCos(angle:Float):{sin:Float, cos:Float}
+	{
+		var n = angle * 0.3183098862;
+
+		if (n > 1.0 || n < -1.0)
+		{
+			n -= Math.ffloor(n * 0.5 + 0.5) * 2.0;
+		}
+
+		final n2 = n * n;
+
+		final sin = n * (3.1 + n2 * (0.5 + n2 * (-7.2 + n2 * 3.6)));
+		final cos = 1.0 - 0.5 * n2 + 0.0417 * n2 * n2 - 0.00139 * n2 * n2 * n2;
+
+		return {sin: sin, cos: cos};
+	}
+
 	/**
 	 * Hyperbolic sine.
 	 */

From 5e1d3c35f2c48faa75a820e7db79c27271457a5b Mon Sep 17 00:00:00 2001
From: HEIHUAa <112499486+HEIHUAa@users.noreply.github.com>
Date: Tue, 10 Feb 2026 08:53:55 +0800
Subject: [PATCH 2/3] Update FlxMath.hx (#19)

---
 flixel/math/FlxMath.hx | 27 ++++++++++++++++++++++-----
 1 file changed, 22 insertions(+), 5 deletions(-)

diff --git a/flixel/math/FlxMath.hx b/flixel/math/FlxMath.hx
index 6243a4bdad..5ed9cf553d 100644
--- a/flixel/math/FlxMath.hx
+++ b/flixel/math/FlxMath.hx
@@ -555,15 +555,32 @@ class FlxMath
 	{
 		var n = angle * 0.3183098862;
 
-		if (n > 1.0 || n < -1.0)
+		if (n > 1)
+		{
+			n -= (Math.ceil(n) >> 1) << 1;
+		}
+		else if (n < -1)
 		{
-			n -= Math.ffloor(n * 0.5 + 0.5) * 2.0;
+			n += (Math.ceil(-n) >> 1) << 1;
 		}
 
-		final n2 = n * n;
+		var sin:Float;
+		if (n > 0)
+		{
+			sin = n * (3.1 + n * (0.5 + n * (-7.2 + n * 3.6)));
+		}
+		else
+		{
+			sin = n * (3.1 - n * (0.5 + n * (7.2 + n * 3.6)));
+		}
 
-		final sin = n * (3.1 + n2 * (0.5 + n2 * (-7.2 + n2 * 3.6)));
-		final cos = 1.0 - 0.5 * n2 + 0.0417 * n2 * n2 - 0.00139 * n2 * n2 * n2;
+		var cos = Math.sqrt(1 - sin * sin);
+
+		var originalN = n * Math.PI;
+		if (originalN < -Math.PI * 0.5 || originalN > Math.PI * 0.5)
+		{
+			cos = -cos;
+		}
 
 		return {sin: sin, cos: cos};
 	}

From ed899429f0a84fbb1736bcc93642a80e3eda2d04 Mon Sep 17 00:00:00 2001
From: HEIHUAa <112499486+HEIHUAa@users.noreply.github.com>
Date: Wed, 11 Feb 2026 10:36:45 +0800
Subject: [PATCH 3/3] Animation improvement

---
 flixel/animation/FlxAnimation.hx | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/flixel/animation/FlxAnimation.hx b/flixel/animation/FlxAnimation.hx
index a49c91f94c..006234d78f 100644
--- a/flixel/animation/FlxAnimation.hx
+++ b/flixel/animation/FlxAnimation.hx
@@ -177,7 +177,7 @@ class FlxAnimation extends FlxBaseAnimation
 
 		reversed = Reversed;
 		paused = false;
-		_frameTimer = 0;
+		_frameTimer = -FlxG.elapsed / 2;
 		finished = frameDuration == 0;
 
 		var maxFrameIndex:Int = numFrames - 1;