Fast log2 approximation

gistfile1.txt

	static NX_FORCEINLINE float FastLog2_P2(float a)
	{
		// Based on code by Norbert Juffa
		// r = log2(1 + m) for m in [sqrt(0.5) - 1, sqrt(2.0) - 1] range

		const int	e = (FloatAsUInt(a) - 0x3f3504f3) & 0xff800000;
		const float	m = UIntAsFloat(FloatAsUInt(a) - e) - 1.0f;
		const float	i = (float)e * 1.19209290e-7f;
		float		r = -6.8969686599880982e-1f;

		r = r * m +  1.4839160720006022f;
		r = r * m + -1.2646480695796084e-3f;

		return r + i;
	}

	static NX_FORCEINLINE float FastLog2_P3(float a)
	{
		// Based on code by Norbert Juffa
		// r = log2(1 + m) for m in [sqrt(0.5) - 1, sqrt(2.0) - 1] range

		const int	e = (FloatAsUInt(a) - 0x3f3504f3) & 0xff800000;
		const float	m = UIntAsFloat(FloatAsUInt(a) - e) - 1.0f;
		const float	i = (float)e * 1.19209290e-7f;
		float		r = 4.4759492291223656e-1f;

		r = r * m + -7.6096527469413136e-1f;
		r = r * m +  1.4456437789495665f;
		r = r * m +  5.8326606506381397e-4f;

		return r + i;
	}

	static NX_FORCEINLINE float FastLog2_P4(float a)
	{
		// Based on code by Norbert Juffa
		// r = log2(1 + m) for m in [sqrt(0.5) - 1, sqrt(2.0) - 1] range

		const int	e = (FloatAsUInt(a) - 0x3f3504f3) & 0xff800000;
		const float	m = UIntAsFloat(FloatAsUInt(a) - e) - 1.0f;
		const float	i = (float)e * 1.19209290e-7f;
		float		r = -3.2646323399139144e-1f;

		r = r * m +  5.1888522452341036e-1f;
		r = r * m + -7.2591518470029981e-1f;
		r = r * m +  1.4416386189833927f;
		r = r * m +  4.7638297248616513e-5f;

		return r + i;
	}


	static NX_FORCEINLINE float FastLog2_P5(float a)
	{
		// Based on code by Norbert Juffa
		// r = log2(1 + m) for m in [sqrt(0.5) - 1, sqrt(2.0) - 1] range

		const int	e = (FloatAsUInt(a) - 0x3f3504f3) & 0xff800000;
		const float	m = UIntAsFloat(FloatAsUInt(a) - e) - 1.0f;
		const float	i = (float)e * 1.19209290e-7f;
		float		r = 2.5384347251568954e-1f;
	    
		r = r * m + -3.9703738348466398e-1f;
		r = r * m +  4.8700114843625382e-1f;
		r = r * m + -7.1992337841478827e-1f;
		r = r * m +  1.4425493859924388f;
		r = r * m + -9.2658550204675742e-6f;

		return r + i;
	}