Store latitude in 3.5 bytes

Question

I know that title sounds little bit weird but it's extremely important to compact our message into 16 bytes. However, whole data is 17. The only possible solution that I can think of is to try to save one byte putting coordinates into 7 bytes instead of 8.

Requirement for coordinates is to store value with 5 decimal places as the very minimum, e.g., 0.00001.

Say we have 3.5 bytes (28 bits). One bit will be used for sign, another 4 for scale, 2 for exponent and 21 bits for decimal points which are 2097152 of unique values which is enough to store 6 decimal places even.

My question is how can I convert 4 byte float to 3.5 byte float in C/Java? Can you refer me to existing solutions for "fine-tuning" floats like this where I can define all the components of float number? Thanks.

Answer 1

My first choice in this case wouldn't be a strange 3.5 byte "float" but to pack it into an integer. Assuming your latitude range is -90 to 90 and longitude from -180 to 180 it would look something like this (Cish code, untested):

 float latitude = 45.12345
 float longitude = 110.12345

 unsigned int packedLatitude  = (latitude + 90) * 100000     //25 bits
 unsigned int packedLongitude = (longitude + 180) * 100000   //26 bits

 float unpackedLatitude  = packedLatitude / 100000.0f - 90.0f
 float unpackedLongitude = packedLongitude / 100000.0f - 180.0f 

This gives you your coordinate in 6.4 bytes. All that is left is to pack these 6.4 bytes into your 16-18 byte structure which I assume you already know how to do (it depends on what you're packing it into and where).

Note there are a few gotchas with this method you need to be aware of. The lower limits (-90 and -180) are hard limits and if exceeded your unpacked coordinates won't be correct. Your upper limits have a little give: latitude can go to 245, longitude to 491 but you probably should make sure they are normalized to -90-90/-180-180. If it matters you should also be aware of how you are rounding or truncating extra digits below 0.00001 (I believe this method truncates them).