optimized bellcurve function (including desmos) [0.0....1.0] input, [0.0....1.0] output

gistfile1.txt

// optimized bellcurve function
// https://www.desmos.com/calculator/xxwdiqa4sk
  
STATIC_INLINE_PURE float const __vectorcall bellcurve(float x) // 0..1 input to 0..1 output
{
	// mu is 0.0 (centered) sigma is 0.5
	constexpr float const c(XM_PI / -1.25331414f);  // optimized magic value - bellcurve perfect match (to six digits of precision)
							// removes sqrt
							// https://www.desmos.com/calculator/xxwdiqa4sk
							
	x = 2.0f * (x * 2.0f - 1.0f);  // converts input range
		
	return(SFM::__exp(x * x * c));
}
	
// vector intrinsic support
STATIC_INLINE_PURE XMVECTOR const __vectorcall bellcurve(XMVECTOR x) // 0..1 input to 0..1 output
{
	// mu is 0.0 (centered) sigma is 0.5
	constexpr float const c(XM_PI / -1.25331414f);  // optimized magic value - bellcurve perfect match (to six digits of precision)
							// removes sqrt
							// https://www.desmos.com/calculator/xxwdiqa4sk
	XMVECTOR const xmTwo(XMVectorReplicate(2.0f));

	x = XMVectorMultiply(SFM::__fms(x, xmTwo, XMVectorReplicate(1.0f)), xmTwo);  // converts input range

	return(SFM::__exp(XMVectorMultiply(XMVectorMultiply(x, x), XMVectorReplicate(c))));
}