diff --git a/rts/Sim/Units/Scripts/UnitScript.cpp b/rts/Sim/Units/Scripts/UnitScript.cpp
index 7a018a601e..9ebe6d85a0 100644
--- a/rts/Sim/Units/Scripts/UnitScript.cpp
+++ b/rts/Sim/Units/Scripts/UnitScript.cpp
@@ -372,7 +372,7 @@ void CUnitScript::StopSpin(int piece, int axis, float decel)
 
 void CUnitScript::Turn(int piece, int axis, float speed, float destination)
 {
-	AddAnim(ATurn, piece, axis, std::max(speed, -speed), destination, 0);
+	AddAnim(ATurn, piece, axis, std::max(speed, -speed), ClampRad(destination), 0);
 }
 
 
@@ -406,7 +406,7 @@ void CUnitScript::TurnNow(int piece, int axis, float destination)
 		ShowUnitScriptError("[US::TurnNow] invalid script piece index");
 		return;
 	}
-	destination = math::fmod(destination, math::TWOPI);
+	destination = ClampRad(destination);
 
 	LocalModelPiece* p = pieces[piece];
 
diff --git a/rts/Sim/Units/Scripts/UnitScript.h b/rts/Sim/Units/Scripts/UnitScript.h
index 257bcc0af0..c0cec58d0b 100644
--- a/rts/Sim/Units/Scripts/UnitScript.h
+++ b/rts/Sim/Units/Scripts/UnitScript.h
@@ -109,8 +109,8 @@ class CUnitScript
 	bool Tick(int tickRate);
 	// note: must copy-and-set here (LMP dirty flag, etc)
 	bool TickMoveAnim(int tickRate, LocalModelPiece& lmp, AnimInfo& ai) { float3 pos = lmp.GetPosition(); const bool ret = MoveToward(pos[ai.axis], ai.dest, ai.speed / tickRate); lmp.SetPosition(pos); return ret; }
-	bool TickTurnAnim(int tickRate, LocalModelPiece& lmp, AnimInfo& ai) { float3 rot = lmp.GetRotation(); rot[ai.axis] = math::fmod(rot[ai.axis], math::TWOPI); const bool ret = TurnToward(rot[ai.axis], ai.dest, ai.speed / tickRate         ); lmp.SetRotation(rot); return ret; }
-	bool TickSpinAnim(int tickRate, LocalModelPiece& lmp, AnimInfo& ai) { float3 rot = lmp.GetRotation(); rot[ai.axis] = math::fmod(rot[ai.axis], math::TWOPI); const bool ret =     DoSpin(rot[ai.axis], ai.dest, ai.speed, ai.accel, tickRate); lmp.SetRotation(rot); return ret; }
+	bool TickTurnAnim(int tickRate, LocalModelPiece& lmp, AnimInfo& ai) { float3 rot = lmp.GetRotation(); rot[ai.axis] = ClampRad(rot[ai.axis]); const bool ret = TurnToward(rot[ai.axis], ai.dest, ai.speed / tickRate         ); lmp.SetRotation(rot); return ret; }
+	bool TickSpinAnim(int tickRate, LocalModelPiece& lmp, AnimInfo& ai) { float3 rot = lmp.GetRotation(); rot[ai.axis] = ClampRad(rot[ai.axis]); const bool ret =     DoSpin(rot[ai.axis], ai.dest, ai.speed, ai.accel, tickRate); lmp.SetRotation(rot); return ret; }
 	void TickAnims(int tickRate, const TickAnimFunc& tickAnimFunc, AnimContainerType& liveAnims, AnimContainerType& doneAnims);
 
 	// animation, used by CCobThread
diff --git a/rts/System/FastMath.h b/rts/System/FastMath.h
index 6377f87591..fafabab818 100644
--- a/rts/System/FastMath.h
+++ b/rts/System/FastMath.h
@@ -36,7 +36,7 @@ namespace fastmath {
 	float apxsqrt2(float x) _const;
 	float sin(float x) _const;
 	float cos(float x) _const;
-	template<typename T> float floor(const T& f) _const;
+	template<typename T> T floor(T f) _const;
 
 	/****************** Square root functions ******************/
 
@@ -198,13 +198,21 @@ namespace fastmath {
 	/**
 	* @brief fast version of std::floor
 	*
-	* Like 2-3x faster than glibc ones.
-	* Note: The results differ at the end of the 32bit precision range.
+	* About 2x faster than glibc ones.
+	*
+	* Unlike std::floor, this one returns the different (positive)
+	* result for negative float zero input (0.0f).
 	*/
 	template<typename T>
-	inline float floor(const T& f)
+	inline T floor(T f)
 	{
-		return (f >= 0) ? int(f) : int(f+0.000001f)-1;
+		//return (f >= 0) ? int(f) : int(f+0.000001f)-1;
+		// it's about the same performance as the former code above,
+		// but without arbitratry number shenanigans
+		// Perf comparison:
+		// https://quick-bench.com/q/rwmaN33UJ4cTEViBGqQYuVgyyOc
+		T truncX = static_cast<T>(static_cast<int>(f));
+		return truncX - static_cast<T>(truncX > f);
 	}
 }
 
diff --git a/rts/System/SpringMath.inl b/rts/System/SpringMath.inl
index f9813e2136..1dc7387716 100644
--- a/rts/System/SpringMath.inl
+++ b/rts/System/SpringMath.inl
@@ -144,8 +144,17 @@ inline int2 IdxToCoord(unsigned x, unsigned array_width)
 
 inline float ClampRad(float f)
 {
+	// handle a special case of f==-0.0f, it can be elliminated by adding 0.0f
+	f += 0.0f;
+	// fmod is not good here because it calculates the remainder, but we need the arithmetic modulus
+	/*
 	f  = math::fmod(f, math::TWOPI);
 	f += (math::TWOPI * (f < 0.0f));
+	*/
+	f = f - math::TWOPI * math::floor(f / math::TWOPI);
+
+	// there should be no negative zeros (-0.0f) or negatives in general
+	assert(!std::signbit(f));
 	return f;
 }
 
@@ -172,7 +181,7 @@ inline float3 GetRadAngleToward(float3 v1, float3 v2) {
 
 inline bool RadsAreEqual(const float f1, const float f2)
 {
-	return (math::fmod(f1 - f2, math::TWOPI) == 0.0f);
+	return ClampRad(f1 - f2) == 0.0f;
 }
 
 inline float GetRadFromXY(const float dx, const float dy)