Pack two floats within range into one float

Question

In HLSL, how would I go about packing two floats within the range of 0-1 into one float with an optimal precision. This would be incredibly useful to compress my GBuffer further.

Answer 1

//Packing
float a = 0.45;
float b = 0.55;
uint aScaled = a * 0xFFFF;
uint bScaled = b * 0xFFFF;
uint abPacked = (aScaled << 16) | (bScaled & 0xFFFF);
float finalFloat = asfloat(abPacked);

//Unpacking
float inputFloat = finalFloat;
uint uintInput = asuint(inputFloat);
float aUnpacked = (uintInput >> 16) / 65535.0f;
float bUnpacked = (uintInput & 0xFFFF) / 65535.0f;

Answer 2

Converting floating point numbers to fixed point integers is an error prone idea, due to floats covering much larger magnitudes. Say unpacking sRGB will give you pow(255,2.2) values, which are larger than 0xffff, and you will need several times than amount for robust HDR. Generally fixed point code is very fragile, obfuscated and a nightmare to debug. People invented floats for a good reason.

There are several 16-bit float formats. IEEE 16-bit float one is optimized for numbers between -1.0 to 1.0, but also support numbers up to 0x10000, just in case you need HDR, still so you will need to normalize your larger floats for it, Then there is bfloat16, which behaves like normal 32-bit float, just with less precision. IEEE 16-bit floats are widely supported by modern CPUs and GPUs, and can also be converted quickly even in software. bfloat16 is just gaining popularity, so you will have to research if it is suitable for your needs. Finally you can introduce your own 16-bit float format, using integer log function, which is provided by most CPUs as a single instruction.