Fast pow-2 approximation

gistfile1.txt

	static NX_FORCEINLINE float FastPow2_P2(float p)
	{
		// 2^x = 2^xi * 2^xf
		// pow2f - polynomial approximation of e(x) on <0, 1) range

		const float	pi	= floorf(p);
		const float	pf	= p - pi;
		const float	pow2i	= UIntAsFloat((1 << 23) * ((int)pi + 127));
		float		pow2f	= 3.4400110689651967e-1f;

		pow2f = pow2f * pf + 6.5104678030290902e-1f;
		pow2f = pow2f * pf + 1.0024760564002857f;

		return pow2i * pow2f;
	}

	static NX_FORCEINLINE float FastPow2_P3(float p)
	{
		// 2^x = 2^xi * 2^xf
		// pow2f - polynomial approximation of e(x) on <0, 1) range

		const float	pi	= floorf(p);
		const float	pf	= p - pi;
		const float	pow2i	= UIntAsFloat((1 << 23) * ((int)pi + 127));
		float		pow2f	= 7.9204240219773237e-2f;

		pow2f = pow2f * pf + 2.2433836478672357e-1f;
		pow2f = pow2f * pf + 6.9645739499350319e-1f;
		pow2f = pow2f * pf + 9.9989296565051542e-1f;

		return pow2i * pow2f;
	}

	static NX_FORCEINLINE float FastPow2_P4(float p)
	{
		// 2^x = 2^xi * 2^xf
		// pow2f - polynomial approximation of e(x) on <0, 1) range

		const float	pi	= floorf(p);
		const float	pf	= p - pi;
		const float	pow2i	= UIntAsFloat((1 << 23) * ((int)pi + 127));
		float		pow2f	= 1.3697664475809267e-2f;

		pow2f = pow2f * pf + 5.1690358205939469e-2f;
		pow2f = pow2f * pf + 2.4163844572498163e-1f;
		pow2f = pow2f * pf + 6.9296612266139567e-1f;
		pow2f = pow2f * pf + 1.000003704465937f;

		return pow2i * pow2f;
	}

	static NX_FORCEINLINE float FastPow2_P5(float p)
	{
		// 2^x = 2^xi * 2^xf
		// pow2f - polynomial approximation of e(x) on <0, 1) range

		const float	pi	= floorf(p);
		const float	pf	= p - pi;
		const float	pow2i	= UIntAsFloat((1 << 23) * ((int)pi + 127));
		float		pow2f	= 1.8964611454333148e-3f;

		pow2f = pow2f * pf + 8.9428289841091295e-3f;
		pow2f = pow2f * pf + 5.5866246304520701e-2f;
		pow2f = pow2f * pf + 2.4013971109076949e-1f;
		pow2f = pow2f * pf + 6.9315475247516736e-1f;
		pow2f = pow2f * pf + 9.9999989311082668e-1f;

		return pow2i * pow2f;
	}